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Journal of Financial Economics 102 (2011) 1–27
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Behavioral biases of mutual fund investors$ Warren Bailey a,n, Alok Kumar b, David Ng c,d a
Cornell University, Johnson Graduate School of Management, USA University of Miami, School of Business Administration, USA c Cornell University, USA d University of Pennsylvania, Wharton School, USA b
a r t i c l e i n f o
abstract
Article history: Received 19 October 2009 Received in revised form 6 July 2010 Accepted 9 July 2010 Available online 27 May 2011
We examine the effect of behavioral biases on the mutual fund choices of a large sample of US discount brokerage investors using new measures of attention to news, tax awareness, and fund-level familiarity bias, in addition to behavioral and demographic characteristics of earlier studies. Behaviorally biased investors typically make poor decisions about fund style and expenses, trading frequency, and timing, resulting in poor performance. Furthermore, trend chasing appears related to behavioral biases, rather than to rationally inferring managerial skill from past performance. Factor analysis suggests that biased investors often conform to stereotypes that can be characterized as Gambler, Smart, Overconfident, Narrow Framer, and Mature. & 2011 Elsevier B.V. All rights reserved.
JEL classification: G11 D03 D14 Keywords: Individual investors Mutual funds Trend chasing Behavioral biases Factor analysis
1. Introduction
$ We thank an anonymous referee, Malcolm Baker (American Finance Association discussant), Nick Barberis, Robert Battalio, Zahi Ben-David, Garrick Blalock, Charles Chang, Susan Christoffersen, Josh Coval, Andrew Karolyi, George Korniotis, Lisa Kramer, Charles Lee, Ulrike Malmendier (AFA session chair), J. Spencer Martin, Jay Ritter, Rene´ Stulz, Jeremy Tobacman, Jeff Wurgler, and seminar participants at BSI Gamma Foundation conference (Frankfurt), Cornell University, Federal Reserve Bank of Boston, Ohio State’s Alumni Summer conference, Northern Finance Association meetings, McGill University, and 2009 AFA meetings (San Francisco) for comments and helpful discussions. We also thank Zoran Ivkovic´ and Lu Zheng for providing data for identifying the mutual funds in our sample. We are grateful to the BSI Gamma Foundation for financial support. Taehoon Lim provided excellent research assistance. All remaining errors and omissions are our own. Early presentations of this paper were entitled ‘‘Why Do Individual Investors Hold Stocks and High-Expense Funds Instead of Index Funds?’’ n Corresponding author. E-mail address:
[email protected] (W. Bailey).
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.05.002
Previous studies of behavioral biases in the investment decisions of individual investors focus on the selection of individual stocks. Odean (1998, 1999), Barber and Odean (2001), and other empirical studies show that the stockpicking decisions of individual investors exhibit a variety of behavioral biases. However, little work has been done to link the decision-making biases of individuals to their mutual fund investments. Understanding the role of behavioral biases in individual mutual fund decisions is important for several reasons. First, individual investors increasingly use mutual funds to invest in the equity market instead of trading individual stocks. French (2008, p. 1539) reports: ‘‘Individuals hold 47.9% of the market in 1980 and only 21.5% in 2007. This decline is matched by an increase in the holdings of open-end mutual funds, from 4.6% in 1980 to 32.4% in 2007.’’ Hence, it is increasingly important to
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understand how individual investors hold and trade mutual funds. Second, even though direct stock trading by individuals has declined, their mutual fund investment decisions can affect stock returns indirectly. Coval and Stafford (2007) argue that large flows force some mutual funds to trade heavily, causing price pressure for securities held across many funds. Previous papers show that mutual fund flows affect individual stock returns. Gruber (1996) and Zheng (1999) find that fund flows are followed by positive short-term fund returns, perhaps due to a momentum effect. Frazzini and Lamont (2008) show that mutual fund flows appear to be ‘‘dumb money’’: Fund inflows are associated with low future returns, while outflows are associated with high future returns. Third, the manner in which individuals employ mutual funds cuts right to the heart of basic principles of financial management. Traditional portfolio choice models imply a simple investment strategy based on well-diversified, low expense mutual funds and minimal portfolio rebalancing. Index funds, and other equity funds with low fees and low turnover, are cheap, convenient vehicles for individual investors to implement such a strategy. The extent to which individuals adhere to these principles in their use of mutual funds is an important measure of the rationality and effectiveness with which investors approach capital markets. The purpose of our paper is to test whether behavioral biases explain why the use of mutual funds varies substantially across individual investors and often departs from the simple strategies suggested by classic theories. The growing literature on behavioral finance has uncovered a variety of decision-making biases in how investors use individual common stocks. These behavioral forces should also have an impact on whether a particular investor uses mutual funds and whether she uses them effectively. The mutual fund literature has already revealed two specific anomalies. First, individual investors buy funds with high fees. Gruber (1996) and Barber, Odean and Zheng (2005) show that many individual investors hold significant positions in high expense mutual funds. Even more puzzling is the finding of Elton, Gruber and Busse (2004) that substantial amounts have gone into index funds charging high fees (over 2% per year) for passive holdings of broad indexes such as the Standard & Poor’s (S&P) 500. Second, individual investors chase returns. Sirri and Tufano (1998), Bergstresser and Poterba (2002), and Sapp and Tiwari (2004) find that fund flows tend to chase funds with high past returns. This could be fostered by Morningstar’s practice of rating funds based on past returns (Del Guercio and Tkac, 2008). Several explanations have been offered for these two anomalies. Carlin (2008) explains participation in high fee index funds using a model with search costs. Choi, Laibson and Madrian (2010) interpret their experiments on Wharton School master of business administration students and participation in high fee funds as consistent with behavioral biases. Return-chasing has been ascribed to an agency problem that induces fund managers to alter the riskiness of the fund to maximize investment flows
instead of risk-adjusted expected returns (Chevalier and Ellison, 1997). It could also reflect inferring managerial skill from past returns (Sirri and Tufano, 1998; Gruber, 1996; Berk and Green, 2004). However, with the exception of the experimental data used by Choi, Laibson and Madrian (2010), these authors study aggregate fund flows, not individual investor behavior. In contrast to previous studies, we link the decisionmaking biases of particular individual investors to their individual history of mutual fund investing using a database of tens of thousands of brokerage records of US individual investors. The key to our experiment is the use of individual investor records of stock holdings and trading to estimate the behavioral bias proxies that previous authors have used to explain how investors trade individual stocks. These individual behavioral bias proxies are, in turn, related to the mutual fund holdings and trading of those individuals in a variety of empirical specifications that reveal different facets of mutual fund investor behavior. We can easily imagine behavioral biases affecting mutual fund selection. For example, the disposition effect (selling winners too quickly and holding losers too long) could lead some investors to overestimate expected holding periods and mistakenly select high front-end load funds. Investors with narrow framing bias (buying and selling individual assets without considering total portfolio effects), overconfidence (frequent trading plus poor performance), or a preference for speculative stocks could select funds that facilitate aggressive switching across asset classes without considering higher fees. Local bias (preference for stocks of companies geographically close to home) could induce the selection of locally managed mutual funds without regard to cost or expected performance. Investors who view their portfolios in terms of layers that serve different purposes (Shefrin and Statman, 2000) could demonstrate different behavior in their use of individual stocks versus mutual funds. For example, if mutual funds are viewed as substantially safer than selecting individual stocks on their own, investors could let their guard down and spend less time assessing fund performance and costs. Regardless of the type of behavioral bias, poor decisions about timing, holding periods, and choice of funds can combine with the substantial variety in mutual fund fee structures to yield poor performance. To examine the interactions and consequences of mutual fund choices and behavioral biases, we adopt two empirical viewpoints. First, we present tests across individual investors. Estimates of several dimensions of behavioral bias for each individual in our sample are used to explain individual investor choices across index funds, other types of mutual funds, and individual stocks. We also test whether behavioral biases influence associations between trading decisions and recent fund performance because those biases could cause some investors to misuse performance information. Second, we present tests across different types of funds. We summarize individual investor holding periods and returns across mutual funds classified by fee structure and by the extent of several behavioral biases of each
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fund’s investors. Behaviorally biased investors could cluster in particular types of funds and demonstrate poor performance or very frequent trading. Furthermore, the fund industry’s offerings could include some funds designed to attract and perhaps even exploit such investors. A large and growing number of mutual funds offer a variety of themes and fee structures to US individual investors. Even across relatively generic index funds, many competing products offer a wide range of fee structures and resultant performance (Elton, Gruber and Busse (2004); Hortacsu and Syverson, 2004). It is plausible that different types of funds attract different clienteles (Nanda, Wang, and Zheng, 2009), and some funds could have been designed specifically with behaviorally biased clienteles in mind.1 A handful of previous papers have examined specific dimensions of the mutual fund choices of individual investors. Barber, Odean and Zheng (2005) find that investors are more sensitive to salient fees such as front-end loads, but not as sensitive to hidden management fees. Christoffersen, Evans and Musto (2006) consider how fund managers respond to the preferences of their investors. Malloy and Zhu (2004) show that investors who reside in less affluent and less educated neighborhoods tend to select high expense funds. Zhu (2005) shows that busy investors are more likely to invest in funds instead of individual stocks. Huang, Wei and Yan (2007) characterize the effect of the information environment on the associations between fund flows and past performance. Bergstresser, Chalmers and Tufano (2009) study whether mutual fund brokers help educate investors and attenuate their behavioral biases, but they conclude that brokers do not deliver tangible benefits for the fees they earn. Ivkovic´ and Weisbenner (2009) examine aggregate individual investor fund flows for tax effects. Our paper offers several substantial contributions. First, unlike earlier studies, we examine a combination of behavioral factors, plus controls for other likely influences on portfolio selection, to reveal the interactions between investor decisions, the characteristics of the mutual funds they select, and the consequences for portfolio performance. Second, because we employ proxies for a number of dimensions of investor behavior in our tests, we are also able to study the associations between different investor characteristics. In particular, applying factor analysis to the correlation structure of our investor characteristics reveals interesting overlaps among biases and other characteristics, and it permits us to identify and profile five investor stereotypes that we label Gambler, Smart, Overconfident, Narrow Framer, and
Mature. Third, our tests take the viewpoints of both the investor, who could ignore or misuse mutual funds, and the mutual fund industry, which could design some of its products to exploit the poor decision-making skills of some investors. Last, we extend the empirical behavioral literature beyond the choice of individual stocks to decisions about professionally managed portfolios. A summary of our results is as follows. We find that sophisticated investors (better informed, higher income, older, and more experienced) investors make good use of mutual funds, holding a high proportion of funds for long periods, avoiding high expense funds, and experiencing relatively good performance. However, investors with strong behavioral biases or lack of attention to firmspecific or macro-economic news are less likely to hold mutual funds or select mutual funds for the wrong reasons. When they do buy mutual funds, they trade them frequently, tend to time their buys and sells badly, and prefer high expense funds and active funds rather than index funds. We also find that biased investors are more likely to chase fund performance, casting doubt on the idea that trend chasing reflects rational fund selection decisions. Evidently, these decisions are suboptimal because they are associated with lower overall returns. For instance, top-quintile narrow-framing investors have average mutual fund returns that are 2.16% lower than those in the bottom quintile, and top-quintile disposition effect investors have average returns that are 0.89% lower than those in the bottom quintile. In contrast, behavioral biases do not appear to affect the performance of index fund holdings. Thus, our behavioral bias and news inattentiveness proxies, though crude, demonstrate that behavioral effects are at work in the mutual fund decisions of many investors and take a toll on performance. Furthermore, the bias and inattention to news proxies are themselves correlated in interesting ways that allow us to identify and study stereotypical investors. The five factors identified using factor analysis can explain over 75% of the variance of the behavioral factors and other investor characteristics. The intuitive combinations of investor characteristics that comprise these five factors relate to mutual fund trading habits and performance in an interesting and consistent manner. The rest of the paper is organized as follows. Section 2 describes our explanatory variables and test specifications. Section 3 describes the individual investor database and other data sources. We present our empirical results in Sections 4 and 5, and we conclude in Section 6 with a brief discussion.
1 Some evidence exists that skilled capital market participants outsmart individual mutual fund investors. Money market funds appear to raise fees to exploit investors who are insensitive to fees and performance (Christoffersen and Musto, 2002). Weak associations between equity fund fees and performance could also reflect such behavior (Gil-Bazo and Ruiz-Verdu, 2009). Corporations are aware of patterns in mutual fund inflows and outflows and attempt to exploit them in timing equity issues (Frazzini and Lamont, 2008). Mutual fund inflows are attracted to seemingly high performance assessed against benchmarks that funds specify but which do not match fund styles (Sensoy, 2009).
2. Measuring investor characteristics Our main objective is to relate mutual fund use and performance to behavioral factors that vary across our sample of investors. We begin by using each sample investor’s record of common stock holdings and trading to estimate a set of variables that proxy for the behaviors evident in each investor’s common stock portfolio. Recognizing that behavioral factors are unlikely to be the only
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determinant of mutual fund choices, we also construct controls for other drivers of mutual fund decisions suggested by the mutual fund and behavioral finance literatures. We use these variables in a variety of tests across individual investors and then across types of mutual funds. Detailed descriptions of behavioral factors, other investor characteristics, and references to supporting papers can be found in Appendix A. 2.1. Behavioral bias proxies We begin by estimating Disposition Effect and Narrow Framing, two mental accounting biases that have been explored extensively in the behavioral finance literature. The Disposition Effect is the propensity of an investor to sell winners too early and hold losers too long. As detailed in Appendix A, we measure each investor’s peer groupadjusted disposition effect by comparing each investor’s actual propensity to realize gains versus losses with a peer group’s propensity to realize gains and losses. A positive value of our disposition effect proxy indicates that the investor sells a greater proportion of winners and a relatively smaller proportion of losers. Disposition Effect could be related to tax incentives. For example, selling winners but retaining losers is particularly costly for high-income US individuals. In contrast, realizing losses in December instead of other months could represent a sophisticated tax minimization strategy. To distinguish disposition effect from tax loss selling, we construct a disposition effect times high income interaction variable (DEnHigh Income) and a disposition effect times no December tax loss selling interaction variable (DEnNo December Tax Loss Selling). Selling winners too soon and holding losers too long is particularly costly for higher-income investors because they face higher marginal tax rates. Similarly, a cleaner measure of disposition effect could be isolated by identifying individuals who appear entirely unaware of the tax consequences of their trades. Therefore, both of these interaction terms are intended to isolate cleaner and severe facets of the disposition effect. Our second bias proxy, Narrow Framing, is the propensity of an investor to select investments individually, instead of considering the broad impact on her portfolio. Intuitively, the time interval between two consecutive decisions reflects the decision frame, with temporally separated decisions more likely to be framed narrowly than simultaneous decisions. Hence, investors who execute less-clustered trades are more likely to be using narrower decision frames. The appendix describes how each investor’s trade clustering measure is peer-group adjusted for portfolio size, number of stocks, and trading frequency. A low trade clustering measure indicates an investor who is more likely to use a narrow viewpoint in making investment choices.2 2 Odean (1998) computes Disposition Effect as the proportion of losses realized minus the proportion of gains realized and notes that this measure is sensitive to portfolio size and trading frequency. For example, proportions are likely to be smaller for investors who hold larger portfolios and trade frequently because those portfolios contain a
Another important concept from the empirical behavioral finance literature is overconfidence, an investor’s propensity to trade frequently but unsuccessfully. Our Overconfidence Dummy variable is set to one for investors in the highest portfolio turnover quintile and lowest performance quintile for their individual common stock trading.3 Because male investors typically exhibit overconfidence, we use a male dummy as an additional proxy for overconfidence. Next, we compute a proxy for familiarity, as articulated by Merton (1987) and Huberman (2001).4 Specifically, the Local Bias of an investor’s common stock portfolio equals the mean distance between her home zip code and the headquarters’ zip codes of companies in her portfolio minus the mean distance to the companies’ headquarters in the market portfolio. Fund Level Local Bias equals the mean distance between the investor’s home zip code and the headquarters of the mutual funds in her portfolio, minus the same measure aggregated across all funds held by all investors in the sample. We measure each investor’s preference for gambling and speculation. Following Kumar (2009), Lottery Stocks Preference is the investor’s mean portfolio weight (relative to the weight in the market portfolio) assigned to stocks that have low prices, high idiosyncratic volatility, and high idiosyncratic skewness. Last, we construct two indicators of whether a particular investor appears to ignore potentially relevant economic news. One variable captures inattention to earnings news, and the other captures inattention to macroeconomic news. Both measures are computed using each individual’s record of individual stock trades using the formula 1 (number of investor trades around the event)/(total number of investor trades), where ‘‘around’’ the event is defined as days t 1, t, and t þ1, where t is the earnings announcement date. To compute Inattention to Earnings News, earnings announcements for each stock held by the individual are collected from the Institutional Brokers’ Estimate System, I/B/E/S. To compute Inattention
(footnote continued) larger number of stocks with capital gains and capital losses. Thus, use of the original measure of the Disposition Effect in cross-sectional analysis is likely to induce mechanical associations with variables that are correlated with portfolio size and trading frequency. Similar issues apply to the Narrow Framing measure because the trade clustering measure used to proxy for narrow framing is correlated with portfolio size, number of stocks, and trading frequency. Further, there might be a mechanically induced relation between proxies for Narrow Framing and Disposition Effect. To minimize the potential influences of portfolio size, number of stocks, and trading frequency, we compute peer group-adjusted proxies of both Disposition Effect and Narrow Framing biases. Our stock-level and fund-level local bias measures are adjusted with the means for the market. This does not affect estimation because the same constant is applied to all investors, but this allows us to think about an investor’s portfolio characteristics relative to a typical investor. 3 We measure the performance and turnover from the stock holdings of the investors for the entire period. We also construct an alternative measure for performance and turnover using the first year of investors’ record. The results are very similar. 4 A related concept is home bias, the tendency for some investors to under-diversify their portfolios internationally. See Bailey, Kumar and Ng (2008) for evidence that home bias could have its origins in behavioral biases.
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to Macroeconomic News, we collect dates of federal funds target rate (www.federalreserve.gov/releases/h15/update/) changes, Non-Farm Payroll Reports (www.bls.gov/bls/archi ved_sched.htm), and producer price index releases (www. bls.gov/ppi/ppirel.pdf).5 The measures we construct are only proxies for behavioral biases. They do not correspond exactly to the definitions of decision-making biases in the psychology literature. Nonetheless, at the very least, these measures are indicators of suboptimal stock investment decisions. They reflect portfolio management mistakes and allow us to measure associations between an individual’s propensity to make such mistakes, his use of mutual funds, and the consequences for portfolio performance. Furthermore, there are other ways to think about the behavioral bias proxies and our results. What we call ‘‘behavioral bias proxies’’ could simply represent each investor’s ‘‘financial literacy.’’ Put another way, it is costly to continually acquire the skills and information needed to make successful investment decisions. While basic notions of portfolio management suggest that a simple buy-and-hold use of index funds is a sensible way to avoid incurring such costs, ‘‘bounded rationality’’ could lead some investors to other decisions. For example, an investor could display narrow framing bias if he elects not to incur the cost of thinking more carefully about investment decisions. Aside from recognizing that each investor could rationally strike a different balance between the costs and benefits of becoming a better investor, we must also consider preferences. While a preference for lottery-type stocks sounds suboptimal and is associated with underperformance, it could simply represent skewness preference in the investor’s objective function. Finally, some behavioral bias proxies could represent frictions in the investment process. For example, our overconfidence proxy identifies investors whose individual stock portfolio is high on turnover and low on return. While this could represent investors who are irrationally aggressive, it could also reflect a combination of small portfolio size, commission costs, and other frictions. With a portfolio of only a few stocks, rebalancing by trading just one stock yields high turnover, and even overconfidence if performance is poor. If such small investors recognize that mutual funds are particularly advantageous, this could even induce a correlation between overconfidence and the propensity to use mutual funds. Our inclusion of portfolio size as a control variable in our regressions might not completely correct for such effects. 2.2. Control variables Though we focus on the behavioral forces for which Section 2.1 describes proxies, we also control for other factors that are likely to influence mutual fund choices. Specifically, we consider a set of demographic characteristics, which 5 Subsequent results shed light on whether inattention is a bias or part of a sensible passive strategy. For example, Barber and Odean (2008) find no evidence that trading based on other measures of news arrival is beneficial.
5
includes Age, Marital Status (a dummy set to one for married investors), Family Size (number of family members in the household), Professional Dummy (a dummy set to zero for the investor in a blue collar profession, one otherwise), and Retired Dummy (a dummy set to one if the investor is retired). These factors could proxy for forces, such as the availability of time to study investments (Zhu, 2005) that can affect portfolio selection. Other control variables are more directly related to each individual’s investment activities. Stock portfolio diversification is measured as the negative of Normalized Portfolio Variance (that is, the variance of the portfolio of individual domestic securities divided by the average variance of the individual common stocks in the portfolio). Investors who demonstrate awareness of the value of diversification in their portfolio of individual stocks are likely to extend that insight into their choice of mutual funds. Income (the total annual household income) and Portfolio Size (the sample-period natural log of the average market capitalization of the investor’s common stock portfolio) identify investors who are more likely to understand the basic precepts of portfolio management and, therefore, tend to select index funds or other low expense funds and hold them for relatively long periods. Investment Experience (years since the brokerage account was open) and a dummy for residence in a Financial Center could indicate more experienced investors with easier access to information and opinions about investments (Christoffersen and Sarkissian, 2009). The Options Dummy equals one if the investor executes at least one option trade during the sample period. The Short Sale Dummy equals one if the investor executes at least one short trade during the sample period.6 Stock Portfolio Performance (the intercept from the market model time series regression with the monthly common stock portfolio return as dependent variable) could identify particularly skillful, successful investors. Success could originate from a variety of strategies, ranging from selecting individual stocks to timing the market.7 No December Tax Loss Selling equals one minus the ratio of realized losses in December to both realized and paper losses in December. Holds Tax-Deferred Account is a dummy variable equal to one if the investor holds an Individual Retirement Account (IRA) or Keogh account at the brokerage. Stock Portfolio Beta, Size, Value, and Momentum Factor loadings are computed with market or four-factor regressions using monthly returns. 3. Data and summary statistics Having outlined the behavioral proxies and control variables that support our study of multiple dimensions of investors’ mutual fund decisions, we now describe the data sets needed for the empirical tests. 6 Options and short sale dummies could proxy for skill and experience, or they could reflect a tendency to speculate. See Campbell (2006) on the correlation between investor sophistication and investment mistakes. 7 For example, an informed investor could optimally focus on only a few stocks (Goetzmann and Kumar, 2008; Ivkovic´, Sialm, and Weisbenner, 2008; Van Nieuwerburgh and Veldkamp, 2010).
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Table 1 Summary statistics on mutual fund investments of individual investors. This table summarizes the stock and mutual fund investment activities of our sample individual investors. The individual investor data are from a large US discount brokerage house for the 1991–1996 period. The median numbers are indicated in parentheses. We identify a total of 136 index funds that were available to our sample of investors during this time period. The Center for Research in Securities Prices (CRSP) universe of individual stocks available during this time period is about 12,000. Statistic
Equity funds
Index funds
Stocks
Number of assets
1,492
33
10,877
Sample-period trades Number of investors with trades Number of buys Number of sells Mean (median) number of trades Mean buy trade quantity Mean buy trade size Mean sell trade quantity Mean sell trade size
32,122 405,376 (67.03%) 199,365 (32.97%) 19 (6) 2,787 $9,929 4,226 $15,744
5,594 15,354 (73.66%) 5,491 (26.34%) 4 (2) 470 $6,879 964 $13,244
62,387 1,015,735 (54.76%) 839,041 (45.24%) 30 (11) 634 $11,251 694 $13,684
End-of-month positions Number of investors with positions Mean (median) portfolio size Mean (median) number of assets
29,381 $39,986 ($12,827) 3.51 (2)
4,432 $13,659 ($5,200) 1.37 (1)
59,387 $35,629 ($13,869) 3.89 (3)
3.1. Data sources
3.2. Summary statistics
Our primary database is a 6-year (January 1991– November 1996) panel of trades and monthly portfolio positions of individual investors with accounts at a major US discount broker.8 The database has been used by a number of other authors including Odean (1998) and Barber and Odean (2000). The database indicates the end-of-month portfolios of all investors, records all trades by these investors, and supplies demographic information (measured as of June 1997 and supplied to the brokerage house by Infobase) such as age, occupation, income, selfreported net worth, gender, marital status, and zip code.9 We obtain the zip codes of the headquarters of a subset of mutual fund families from Professors Josh Coval and Zoran Ivkovic´. We supplement this data set with additional information from the Lionshare database, 1996 Nelson’s Directory of Investment Managers, and Google searches. We also obtain data from several standard sources. For each common stock and mutual fund in our sample, we obtain monthly returns data from the Center for Research in Security Prices (CRSP). We also use the CRSP mutual fund database to obtain information on fund characteristics such as the expense ratio and front-end load. Finally, we obtain the monthly time series of the three FamaFrench factors and the momentum factor from Professor Kenneth French’s data library.10
Table 1 provides summary statistics on individual investor trading and holding of mutual funds and, for comparison, individual stocks. Sample investors traded or held 1,492 different equity mutual funds (of which 33 are index funds) and close to 11,000 stocks. A total of 32,122 investors have executed at least one mutual fund trade and 29,381 have held equity mutual funds at least once. Among these, only 5,594 have executed at least one index fund trade and 4,432 have held index funds at least once. The balance of buys and sells suggests that, in contrast to individual stocks, mutual fund investors tend to buy and hold funds, rather than buying and selling more actively as with individual stocks. Trade sizes and quantities are typically modest. The mean (median) number of equity funds in a typical mutual fund portfolio is 3.51 (2.0) and number of trades executed is 19 (6.0). The mean (median) number of index funds held is 1.37 (1.0) and number of trades executed is 4 (2.0). In contrast, a typical investor holds 3.89 individual stocks (median is three) and executes 30 (median is 11) stock trades. Beyond what is reported in the table, the proportion of mutual funds in a typical equity portfolio that includes mutual funds is 23.78%.11 This proportion increases slightly with equity portfolio size to about 26% in the highest size decile portfolios. The proportion of index funds in the aggregate mutual fund portfolio is low, varying between 5.30% and 8.39%, with a mean of only 6.54%. Nevertheless, among the investors who hold index funds, the proportion of index funds in the mutual fund portfolio is about 38%. Furthermore, there is much
8 The brokerage firm has not made more recent data available. The time period covered largely excludes such phenomena as exchange-traded funds (ETFs) and high-frequency online day trading by individuals. 9 Each demographic variable is available for only a subset of the investors in the sample. For instance, both age and income are available for only 31,260 investors. Consequently, the number of observations in each cross-sectional regression depends upon the subset of demographic variables included. 10 The data library is available at http://mba.tuck.dartmouth.edu/ pages/faculty/ken.french/.
11 If we include all investors, not just those who hold mutual funds, this proportion is only 13.49%. Consistent with the common industry trend, it has grown steadily from 7.63% in January 1991 to 16.58% in November 1996. About 10% of all investors hold only mutual funds in their equity portfolios while about 17% hold more than three-fourths in equity mutual funds.
0.010 0.012 0.444 1.000 0.004 0.002 1.000 0.444 0.013 1.000 0.002 0.012 1.000 0.013 0.004 0.010 0.003 0.043 0.008 0.009 0.005 0.001 0.028 0.023 0.013 0.002 0.037 0.031 0.024 0.002 0.007 0.009 0.009 0.004 0.006 0.016 0.011 0.005 0.200 0.121 0.006 0.004 0.922 0.481
0.007 0.012 0.001 0.006
0.009 0.008 0.043 0.003 1.000 0.060 0.008 0.021 0.002 0.010 0.011
0.010
0.481 0.121 0.006 0.016 0.009 0.031 0.023 0.922 0.200 0.001 0.006 0.007 0.037 0.028 0.004 0.005 0.012 0.004 0.002 0.002 0.001 0.006 0.011 0.007 0.009 0.024 0.013 0.005 0.011 0.010 0.010 0.002 0.008 0.021 0.060 0.038 0.082 0.015 0.004 0.011 0.065 1.000 0.044 0.081 0.062 0.006 0.041 1.000 0.065 0.006 0.007 0.039 0.010 1.000 0.041 0.011 0.008 0.012 0.019 1.000 0.010 0.006 0.004 0.230 1.000 0.080 0.012 0.007 0.081 0.082 1.000 0.230 0.013 0.008 0.006 0.044 0.038
0.013 0.080 1.000 0.019 0.039 0.062 0.015
DEnNo December DEn High Selling Income Fund-Level Inattention Fund-Level Local Bias Inattention to Macroeconomic News Inattention toEarnings News Lottery Stocks Preference Local Bias
Disposition Effect Narrow Framing Overconfidence Dummy Male Dummy Local Bias Lottery Stocks Preference Inattention to Earnings News Inattention to Macroeconomic News Fund-Level Local Bias Fund-Level Inattention DEnNo December Selling DEnHigh Income
12 Ivkovic´ et al. (2005) find the distribution of stock holding periods is very similar across our sample and the general population reflected in tax returns. Zhu (2005), Goetzmann and Kumar (2008), and Ivkovic´, Sialm and Weisbenner (2008) confirm that our sample closely resembles the general US individual investor population. Bailey, Kumar and Ng (2008) show similarities with the Census Bureau’s 1995 Survey of Income and Program Participation and the Federal Reserve Board’s Survey of Consumer Finances of 1992 and 1995. 13 These statistics are computed prior to 1% winsorizing which is employed throughout the balance of the paper.
Male Dummy
The recent behavioral finance literature has proposed a number of behavioral factors. However, previous papers typically focus on only one behavioral factor. One of our contributions is to examine different behavioral factors jointly and to measure how they relate to each other and to other investor characteristics. Table 2 presents correlations among the behavioral biases that we measure. A number of statistically significant associations are evident. Disposition Effect, Narrow Framing, Lottery Stocks Preference, and Inattention to Earnings News often appear in the same individuals. These individuals time their trades poorly, make decisions in isolation, buy speculative stocks, and ignore firm-specific
Overconfidence Dummy
4.1. Associations between investor characteristics
Narrow Framing
We begin by examining our behavioral bias and news inattention proxies in more detail and, in particular, look for intuition from the associations among these proxies and with other investor characteristics. Next, we study mutual fund participation and fund selection decisions across our sample investors. We then arrange information about these decisions by type of fund, not by individuals. In these tests, we examine the fees and expenses of funds chosen by the investors in our sample and whether there are associations with turnover, performance, and behavioral biases. We also investigate whether investors’ trend-chasing behavior is influenced by their behavioral biases. Further tests summarize the impact of individual investors’ mutual fund investment decisions on portfolio performance. Last, we report the results of various robustness checks.
Disposition Effect
4. Empirical results
7
Measure
evidence that our sample of brokerage records represents typical US individual investors.12 In addition to detailed descriptions of each investor characteristic variable, the appendix includes univariate summary statistics on those variables.13 Features of the data are noteworthy. For example, some of the behavioral bias proxies are skewed to the left (Disposition Effect, Narrow Framing) and others are skewed right with large positive outliers (Lottery Stock Preference). The median age of our sample investors is about 50 years, median income is $87,500 per year, and median family size is two. Almost 90% of the accounts are held by males. The average (median) market risk-adjusted return on an investor’s portfolio of individual stocks is an unflattering 0.378% ( 0.278%) per month and ranges from a minimum of 11.474% to a maximum of 6.437%. The median individual stock portfolio beta is a surprisingly high 1.157.
Table 2 Cross-correlations of the behavioral measures. Computations are based on 21,542 individuals who have traded individual stocks during the sample period. Any correlation coefficient with t-statistic greater than or equal to 2.576 is presented in bold type to indicate strong statistical significance. All series are winsorized at the 1% level, and results throughout the paper are very similar for winsorizing at the 5% level.
W. Bailey et al. / Journal of Financial Economics 102 (2011) 1–27
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information. Although uncorrelated with Disposition Effect, Overconfidence Dummy is significantly positively correlated with Narrow Framing, Male Dummy, and Lottery Stocks Preference, suggesting a class of particularly aggressive investors prone to speculation. Some correlations for Local Bias suggest a cautious investor type (negative correlation with Overconfidence Dummy and Lottery Stocks Preference). Inattention to Macroeconomic News is negatively correlated with Inattention to Earnings News, suggesting that some individuals invest on a top down basis and look at broad news, while ignoring firm-specific news. To save space, we do not report correlations among the other investor characteristics or between the behavioral biases and the other characteristics (they are available upon request). We summarize these correlations as follows. Many of the other investor characteristics are related in sensible ways. For example, Age is positively correlated with Marital Status, Retired Dummy, Investment Experience, and Stock Portfolio Size. Income is positively correlated with Family Size, Professional Dummy, and Financial Center Dummy. The use of options or short sales is correlated with Investment Experience and Financial Center Dummy. Financial sophistication is evident in correlations among Investment Experience, Options Dummy, Short Sale Dummy, Stock Portfolio Diversification, and tax minimization. A number of correlations are unexpected, such as no association between Investment Experience and Stock Portfolio Performance and negative association between Stock Portfolio Diversification and Stock Portfolio Performance. High loadings of individual stock portfolios on market, size, value, and momentum factors are associated with poor performance. The (unreported) correlations between the behavioral bias variables and the other investor characteristics begin to suggest links between investment decision-making biases and more fundamental individual characteristics. For example, it is sensible that maturity and intelligence (represented by Age, Income, Professional Dummy, and Retired Dummy) are typically uncorrelated or even negatively correlated with biases. Narrow Framing is more likely for young, relatively low-income investors, which is consistent with the findings of Kumar and Lim (2008). Lottery stock preference is associated with growth and value stocks [as proxied by SMB (small minus big) and HML (high minus low) factor exposures] and poor performance. Among the biases, only Local Bias is positively correlated with Stock Portfolio Performance, suggesting that familiarity bias is not necessarily detrimental. As we would predict given its definition, Narrow Framing tends to be negatively correlated with Stock Portfolio Diversification. While it is difficult to comprehensively grasp hundreds of individual cross correlations, some hint at effective investing, some suggest cautious behavior, and many imply that poor decision making leads to inferior stock portfolio performance. To highlight these associations in a more formal and dramatic manner, Table 3 presents the results of factor analysis applied to the observed characteristics of the 21,542 investors in the database who traded individual stocks during the sample period. The first factor explains 21.8% of the variance of the investor characteristics. This factor has substantial
positive loadings on Disposition Effect, Narrow Framing, and, especially, Lottery Stocks Preference. This suggests that this factor reflects investors with substantial behavioral biases, particularly a taste for risky stocks. We label this factor Gambler. Negative loadings on Age, Income, Professional Dummy, Retired Dummy, Investment Experience, and Portfolio Size suggest that Gambler is relatively young, poor, unsophisticated, and inexperienced. The negative loading on Stock Portfolio Diversification indicates a tendency to plunge rather than spread risk. This is consistent with models (Mitton and Vorkink, 2007; Barberis and Huang, 2008) in which some investors take undiversified positions in skewed securities that appeal to their preferences. The loadings on risk factors indicate an appetite for high beta stocks, small stocks, value stocks, and trading against momentum. The negative loading on Stock Portfolio Performance suggests that Gambler typically suffers poor performance. This is consistent with the empirical finding in Kumar (2009) that investors with high Lottery Stocks Preference often select small value stocks that do not perform well. The second factor explains 18.1% of the variation of the investor characteristics. In contrast to Gambler, this factor represents investors who seem to do everything right and earn good returns from individual stocks as a consequence. We label this factor Smart. Smart displays negative loadings on several behavioral biases and has high income, professional status, and long investment experience. Smart’s large, diverse individual stock portfolio has relatively modest loadings on market, size, value, and momentum risks and reflects the value of December tax loss selling. Among the first five factors, Smart is the most likely to maintain a tax-deferred brokerage account. This combination of good characteristics yields relatively high individual stock portfolio performance. Smart is likely to use short-selling, implying sophistication in investment tactics. The third factor explains 15.3% of the investor characteristics and puts cumulative variance explained above 55%. We label this factor Overconfident given the large positive loading on Overconfidence Dummy (which, by construction, is consistent with the large negative loading on Stock Portfolio Performance). Overconfident is typically male, inclined to Lottery Stocks Preference, single, not retired, and inexperienced with investments. An association between male gender and overconfident investing mirrors the findings of Barber and Odean (2001). Overconfident’s individual stock portfolio is poorly diversified and has a large loading on market risk. The use of options is associated with this ineffective decision maker, unlike the use of short sales which is associated with the successful Smart investor. The fourth factor explains 12.3% of the investor characteristics. We label it Narrow Framer given its particularly large loading on that bias. With significant positive loadings on three biases, youth, and low income, poor Stock Portfolio Diversification, and weak Stock Portfolio Performance, Narrow Framer is reminiscent of the Gambler and Overconfident stereotypes. Similar to the findings in Kumar and Lim (2008), Narrow Framer exhibits stronger disposition effect and hold less diversified portfolios. Narrow Framer does seem aware of tax issues, given the negative loading on No December Tax Loss Selling, perhaps
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Table 3 Factor analysis for the behavioral measures and other investor characteristics. Computations are based on 21,542 individuals who have traded individual stocks during the sample period. The ‘‘varimax’’ method is run for ten factors but only the first five are reported given variance explained. Factor Variable Factor Characteristics Eigenvalue Variance explained Cumulative variance explained Factor Loadings Disposition Effect Narrow Framing Overconfidence Dummy Male Dummy Local Bias Lottery Stocks Preference Inattention to Earnings News Inattention to Macroeconomic News Fund-Level Local Bias Fund-Level Inattention DEnNo December Tax Loss Selling DEnHigh Income Age Income High Income Marital Status Family Size Professional Dummy Retired Dummy Investment Experience Financial Center Dummy Options Dummy Short Sale Dummy Stock Portfolio Diversification. Stock Portfolio Size Stock Portfolio Performance No December Tax Loss Selling Holds Tax-Deferred Account Market Factor Exposure SMB Factor Exposure HML Factor Exposure UMD Factor Exposure
Gambler
Smart
Overconfident
Narrow Framer
2.288 0.218 0.218
1.894 0.181 0.399
1.607 0.153 0.552
1.286 0.123 0.675
0.189 0.216 0.055 0.021 0.044 0.563 0.058 0.029 0.020 0.005 0.023 0.028 0.335 0.404 0.027 0.032 0.008 0.155 0.342 0.333 0.045 0.066 0.014 0.323 0.202 0.454 0.006 0.004 0.471 0.806 0.594 0.555
0.213 0.101 0.058 0.004 0.206 0.202 0.011 0.007 0.033 0.017 0.028 0.027 0.067 0.020 0.196 0.033 0.04 0.332 0.055 0.509 0.005 0.094 0.332 0.723 0.407 0.354 0.498 0.202 0.091 0.125 0.121 0.087
0.055 0.095 0.472 0.202 0.02 0.143 0.090 0.052 0.000 0.001 0.028 0.037 0.026 0.005 0.010 0.255 0.023 0.002 0.331 0.221 0.032 0.301 0.014 0.333 0.080 0.828 0.088 0.027 0.556 0.150 0.213 0.045
0.253 0.588 0.090 0.001 0.005 0.011 0.196 0.011 0.032 0.004 0.015 0.022 0.202 0.167 0.004 0.001 0.001 0.000 0.008 0.015 0.007 0.010 0.012 0.41 0.303 0.236 0.398 0.005 0.220 0.023 0.110 0.072
because he or she carefully accounts for each stock, though separately. The fifth factor explains 10.2% of variance and, given that it is the last factor with eigenvalue above one and puts cumulative variance explained above 75%, it is the final factor for which we offer detailed interpretation.14 Given that this factor has a high loading on Age, Retired Dummy, and Investment Experience, a negative loading on behavioral biases, a large, well-diversified portfolio, and an understanding of tax-timing, we label it Mature. Unlike Smart, Mature’s individual stock portfolio performance is not extraordinary, but it successfully avoids the cost of obvious biases and mistakes. Caution is also reflected in Mature’s relatively modest loadings on market, size, value, and momentum risks. Mature is less likely to hold a tax-deferred account, perhaps because such accounts must be drawn
Mature
1.071 0.102 0.777 0.302 0.221 0.232 0.013 0.020 0.243 0.013 0.008 0.016 0.010 0.015 0.019 0.458 0.126 0.085 0.054 0.104 0.589 0.890 0.292 0.059 0.029 0.011 0.403 0.552 0.020 0.311 0.311 0.046 0.044 0.059 0.010
down upon approaching retirement or are less valuable to relatively low income investors. Many of the characteristics of Mature parallel what Korniotis and Kumar (2011) report for older investors. To reconcile generally unbiased decision making with mediocre performance, they suggest that aging is associated with deterioration in cognitive skills We recognize that the labels we have placed on the first five factors are at best speculative. Nonetheless, the clusters of characteristics they identify across tens of thousands of individual US investors are intuitive. They validate the behavioral biases and other investor characteristics that the empirical behavioral finance literature has developed. We employ these biases, and the factors we have extracted, in subsequent tests to understand how behavioral biases affect the use of equity mutual funds. 4.2. Participation in open end mutual funds: logit regression estimates
14 Given that we use factor analysis instead of principal components, a cutoff of one for the eigenvalue is conservative. Information on the sixth through tenth factors is unreported but available on request.
Our next set of tests examines investors’ mutual fund participation decisions. We estimate logit regressions in
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W. Bailey et al. / Journal of Financial Economics 102 (2011) 1–27
decision to participate in mutual funds generally. The evidence on behavioral biases and index funds in Specifications 3 and 4 largely echoes what we find for mutual funds generally in Specifications 1 and 2. Investors who score high on Disposition Effect, Narrow Framing, Inattention to Earnings News, and Disposition Effect interacted with No December Tax Loss Selling are more likely to avoid index funds. Once again, the importance of the propensity to trade risky individual stocks is evident: The strong aversion to mutual funds for those with Lottery Stocks Preference is heightened for index funds. The association between overconfidence and mutual fund investment disappears, perhaps indicating that overconfident investors confine themselves to actively managed funds. Again, these findings are robust to the inclusion of the control variables. The estimates of the coefficients on the control variables also suggest that older investors, higher income investors, those with smaller stock portfolios, those who appear to value diversification, those who are cognizant of tax issues, those who do not live near a financial center, and those who avoid individual stocks with high loadings on market and size risks are more likely to value index funds. Thus, the clientele of index funds differs somewhat from the clientele of other mutual funds. However, behavioral biases appear to have a significant influence on the use of equity mutual funds regardless of type. In the following sections, we conduct additional tests to refine and extend these findings.
which the dependent variable is the fund participation dummy, which equals one for an investor who invests in mutual funds at least once during the sample period. The main independent variables of interest are the behavioral bias proxies, inattention measures, and tax-related interactives. The logit regression estimates are presented in the first four specifications of Table 4. The independent variables are standardized so that coefficient estimates can be easily compared within and across specifications.15 In specifications 1 and 2 of Table 4, we explain the mutual fund participation dummy with behavioral bias proxies. Specification 2 also includes the control variables previously described. Consistent with the presence of behavioral biases, negative slopes on Disposition Effect, Narrow Framing, Lottery Stocks Preference, and Inattention to Earnings News indicate that investors who score high on these characteristics are less likely to invest in equity mutual funds. The negative slope on the interactive term for Disposition Effect and No December Tax Loss Selling indicates that investors prone to both the Disposition Effect and no attention to tax issues are even less likely to invest in equity mutual funds. Somewhat surprisingly, we find that overconfident investors (that is, those who trade stocks more frequently, yet earn lower returns) are more likely to invest in mutual funds. This could reflect overconfidence in their ability to identify good funds.16 In economic terms, the logit regression estimates indicate that the propensity to invest in mutual funds declines by 3.15% (0.126 25), 3.90%, 4.67%, and 0.95% when the level of disposition effect, narrow framing, lottery preference, or inattention to earnings news increases by one standard deviation, respectively.17 The absolute size of slope coefficients is the largest for Lottery Stocks Preference, suggesting that the propensity to pick individual stocks is most likely to divert investment away from sensible strategies involving mutual funds. The finding for Lottery Stocks Preference is particularly significant as, unlike some of our other factors as discussed in Section 2.1, it is hard to characterize this factor as anything other than behavioral or, at best, skewness preference. These findings are robust to the inclusion of the control variables. Moreover, the estimated slopes on the control variables are intuitive. We find that investors who earn higher income, work as a professional, do not live near a financial center, are sufficiently sophisticated to use options, or who appear to value diversification in their stock portfolios are also more likely to invest in mutual funds. Those who ignore tax loss selling of their individual stocks or load high on market, size, or value risks are less likely to hold equity mutual funds. Specifications 3 and 4 repeat the tests described previously but for the index fund participation dummy, which is set to one only for those investors who invest in index funds at least once during the sample period. The decision to participate in index funds could be different from the
In our third set of tests, we estimate cross-sectional regressions with portfolio weights in mutual funds as dependent variables. Similar to the participation regressions, the independent variables are the behavioral factors that we focus on, plus control variables. One concern in such regressions is that the cross-correlation of individuals in decision making could inflate the statistical significance of our regressions. For instance, some segment of investors could select very similar portfolios of funds and have correlated preferences for active, small cap, and industry funds. As a result, their fund choices could be correlated. We take the following steps to address such concerns for each of our cross-sectional regressions. First, clustered standard errors are intended to correct for correlation of residuals within each cluster (Petersen, 2009), though this method assumes independence across groups.18 We do not know the exact nature of any crosssectional dependence of returns residuals. Therefore, we try two different forms of clustered standard errors, by zip code (treating each investor within a zip code as one observation) and by peer group (same quintile of portfolio size, trading frequency, and number of stocks).19
15 To alleviate concerns about multi-collinearity, we check the variance inflation factor (VIF) for each explanatory variable. 16 Subsequent tests address this potentially puzzling finding. 17 Following Wooldridge (2003), we use a factor of 25% to interpret the logit regression results.
18 Kumar (2009) uses a similar method to account for potential cross-sectional dependence in performance across investors. 19 The results with peer group-clustered standard errors are very similar. For brevity, we report the results with zip code-clustered standard errors only.
4.3. Extent of fund investment: cross-sectional regression estimates
Table 4 Investor characteristics and mutual fund participation decisions and stock versus funds allocation The first four specifications in the table are logit regressions. In Specifications 1 and 2, the dependent variable is one for investors who hold or trade mutual funds at least once during the sample period. In Specifications 3 and 4, the dependent variable in the logit regression is one for investors who hold or trade index funds at least once during the sample period. Specifications 5 and 6 are cross-sectional regression estimates in which the proportion of mutual funds in the equity portfolio is the dependent variable. In Specification 5, the dependent variable is the mean weight of mutual funds in the total equity (stocks and mutual funds) portfolio. In Specification 6, the dependent variable is the mean weight of index funds only. The dependent variable is multiplied by one hundred. Independent variables are defined in Appendix A, and a constant term is included. They are standardized so coefficients can be compared within or across specifications. There is one observation per investor. An intercept is included but not reported. Robust zip code clustered standard errors are used to obtain the t-statistics. The statistically significant coefficient estimates are indicated in bold font. The individual investor data are from a large US discount brokerage house for the 1991–1996 period. Mutual fund participation dummy (LOGIT) All mutual funds (1)
Behavioral Bias Proxies Disposition Effect Narrow Framing Overconfidence Dummy Male Dummy Local Bias Lottery Stocks Preference Inattention to Earnings News Inattention to Macroeconomic News DEnHigh Income DEnNo December Tax Loss Selling
(2)
(3)
Mutual fund weight
Index fund weight
(5)
(6)
(4)
Coefficient
z-value
Coefficient
z-value
Coefficient
z-value
Coefficient
z-value
Coefficient
t-statistic
Coefficient
t-statistic
0.126 0.156 0.057 0.017 0.014 0.187 0.038 0.019 0.021 0.091
3.37 5.91 2.19 1.04 1.16 8.91 2.17 1.18 1.73 2.98
0.092 0.106 0.060 0.017 0.014 0.170 0.044 0.013 0.018 0.081
2.78 4.39 3.30 0.52 1.31 6.29 2.11 1.09 1.68 2.11
0.106 0.104 0.005 0.032 0.013 0.239 0.047 0.014 0.014 0.074
3.12 4.54 0.63 1.38 0.41 10.14 2.49 1.14 1.42 3.14
0.096 0.092 0.004 0.016 0.014 0.230 0.057 0.013 0.013 0.069
2.67 3.67 0.62 1.11 0.33 9.10 2.11 1.03 1.21 2.84
1.081 1.936 0.790 0.288 0.242 1.319 0.580 0.452 0.401 0.327
3.11 7.95 3.67 1.35 1.01 5.35 2.30 1.78 1.60 3.10
0.569 1.122 0.800 0.311 0.172 0.911 0.690 0.206 0.388 0.430
1.77 3.36 2.22 0.74 1.13 3.04 2.55 1.42 1.66 2.74
0.022 0.035 0.050 0.006 0.024 0.032 0.009 0.029 0.084 0.066 0.033 0.158 0.022 0.035 0.047 0.135 0.041 0.168 0.038 0.017
1.19 2.26 2.90 1.44 0.70 1.99 0.22 1.51 3.98 3.01 1.17 6.80 0.98 1.70 2.52 9.08 2.60 5.91 2.27 1.68
0.186 0.046 0.084 0.021 0.003 0.030 0.028 0.028 0.067 0.016 0.025 0.273 0.160 0.020 0.036 0.105 0.031 0.055 0.009 0.010
4.01 1.77 3.01 1.30 0.31 1.20 1.55 1.40 2.11 1.11 1.55 7.16 2.11 1.40 1.95 7.11 3.01 4.53 1.20 2.09
0.488 0.767 0.588 0.727 0.208 0.454 0.071 0.122 1.034 0.101 0.717 0.940 1.399 0.105 1.013 2.452 0.980 0.937 0.392 0.462
1.60 2.60 2.11 2.01 0.70 1.86 0.41 0.40 3.44 1.53 2.01 3.11 10.02 0.36 2.06 7.46 2.93 3.72 2.93 2.09
1.355 0.838 0.438 0.101 0.055 0.200 1.011 0.533 0.960 0.188 0.142 0.767 0.594 0.409 1.322 0.650 0.148 0.242 0.375 0.400
3.25 2.18 2.18 0.43 0.22 1.11 2.91 3.01 3.11 0.76 0.61 3.30 2.55 2.21 3.44 2.29 1.70 1.77 2.19 2.13
Control Variables Age Income High Income Dummy Marital Status Family Size Professional Dummy Retired Dummy Investment Experience Financial Center Dummy Options Dummy Short Sale Dummy Stock Portfolio Diversification Stock Portfolio Size Stock Portfolio Performance No Dec Tax Loss Selling Holds Tax-Deferred Account Market Factor Exposure SMB Factor Exposure HML Factor Exposure UMD Factor Exposure Pseudo R2 Number of Observations
Index funds only
0.038 22,984
0.092 21,542
0.027 22,984
0.074 21,542
0.104 21,542
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Independent Variable
Mutual fund portfolio weight
0.126 21,542 11
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Second, we construct risk-adjusted returns to remove the market-wide movement in returns that is common to all investors. Specifications 5 and 6 of Table 4 present the regression estimates. In Specification 5, the dependent variable is the mean weight assigned to mutual funds in an investor’s equity portfolio. The results parallel the findings from the participation regressions reported in Table 3. Individuals who score high on Disposition Effect, Narrow Framing, Lottery Stocks Preference, Inattention to Earnings News, or interaction between Disposition Effect and No December Tax Loss Selling typically put a smaller fraction of their portfolio in mutual funds, while overconfident investors typically allocate a larger proportion of their equity portfolio to mutual funds. In economic terms, a one standard deviation increase in narrow framing propensity is associated with a 1.94% lower allocation to mutual funds. The estimates of other statistically significant behavioral bias proxies are also economically significant. The estimates for the coefficients on the control variables show that investors who have higher income, are married, do not live near a financial center, understand short selling and diversification, have relatively small stock portfolios, understand tax issues, and have relatively low loadings on risk factors in their stock portfolios typically hold a higher proportion in mutual funds. Thus, similar forces drive the decision to participate in mutual funds and the extent of that participation. In Specification 6, the dependent variable is the mean weight assigned to index funds. The cross-sectional regression results with index fund weight reinforce the findings from the index fund participation regressions. Investors with stronger behavioral biases typically allocate a smaller proportion of their equity portfolio to index funds, although the effect of overconfidence flips between Specifications 5 and 6. Even though overconfident investors allocate a slightly larger weight to mutual funds, they allocate a smaller proportion of their equity portfolio to index funds. Thus, such investors focus more on actively managed funds. The extent to which index funds are held goes up as individual stock portfolio performance goes down. 4.4. Behavioral biases and preference for certain types of mutual funds To better understand investor preferences for different types of funds, we examine three additional characteristics of investors’ mutual fund portfolios. Table 5, Panel A presents the cross-sectional estimates. In Specifications 1–3, the dependent variable is the mean expense ratio, the mean front-end load, and the mean fund turnover, respectively, for each individual’s mutual fund portfolio. Specification 1 shows that investors with stronger Disposition Effect, Narrow Framing, Overconfidence Dummy, Lottery Stocks Preference, Inattention to Earnings News, and interaction between Disposition Effect and No December Tax Loss Selling tend to select mutual funds with higher expense ratios. Specification 2 examines front-end loads and confirms that the same set of biases that drive investors to higher expense funds is also associated with
choosing mutual funds with higher front end loads. Specification 3 shows that individuals who are overconfident, male, have lottery stocks preference, display inattention to earnings news, and have positive loading on measures of particularly severe disposition effect (Disposition EffectnHigh Income and Disposition EffectnNo December Tax Loss Selling) tend to invest in funds with higher turnover. If we assume that funds with higher expense ratios, higher front-end loads, and high levels of turnover are poor choices, our evidence indicates that investors who demonstrate poor decision making with individual stocks also appear to make poor decisions about mutual funds. The slope coefficients on behavioral factors in Specification 2 are particularly large, suggesting that behavioral biases are important in driving investors into high front end load funds. The slope coefficients on the control variables indicate that younger, poorer, less experienced, and less tax-savvy investors are more likely to elect these apparently poor choices. 4.5. A closer look at fund-level local bias and inattention Why do some investors go against common wisdom and hold high front-end load funds? One possibility is that they are unaware of the load.20 Alternatively, some investors could be more willing to pay a high load for funds they are familiar with. In particular, they could have more awareness of funds headquartered in their geographic area, perhaps due to localized marketing efforts.21 As a result, they are willing to pay high fees for such funds. To investigate this thesis, we test whether investors with high Fund-Level Local Bias are more likely to hold funds with high fees and expenses. Having employed proxies for local bias and inattention to news based on trading of individual stocks, we also investigate whether some investors concentrate their equity mutual fund trades around news. In Table 5, Panel B we introduce our Fund-Level Local Bias measure into the cross-sectional regression specification. This variable is distinct from individual equity local bias in that it measures the geographical proximity between an investor’s home and the headquarters of mutual funds held by the investor, not the proximity of the headquarters of an individual listed company. We also introduce Fund-Level Inattention to the cross sectional regressions. This variable measures each individual’s propensity to trade mutual funds around macroeconomic news events as 1 (number of mutual fund trades around the event)/(total number of mutual fund trades). The estimates in Specifications 1–3 show that investors with stronger Fund-Level Local Bias tend to select mutual funds with higher expense ratios, front end loads, and turnover, even after controlling for other behavioral 20 See Capon, Fitzsimons and Prince (1996) for survey evidence that about 39% of mutual fund investors were unaware of the load charged by the funds they held. 21 Starks and Yates (2008) investigate a related familiarity-based hypothesis and find that individuals often cluster their choice of funds within the same family of funds.
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13
Table 5 Characteristics of investors and the funds they select. This table reports cross-sectional regression estimates in which three different mutual fund portfolio characteristics are employed as dependent variables. In Panel A, Specifications 1–3, the mean expense ratio, the mean front-end load, and the mean turnover of the funds in the mutual fund portfolio is the dependent variable, respectively. In all specifications, the dependent variable is multiplied by one hundred. There is one observation per investor. Independent variables are defined in Appendix A, and an intercept term is included but not reported. In Panel B, we consider two additional independent variables. Zip code clustered standard errors are used to obtain the t-statistics. The statistically significant coefficient estimates are indicated in bold font. There is one observation per individual. (1) Expense ratio Independent Variable
Coefficient
Panel A: Mutual fund portfolio characteristic regression estimates Behavioral Bias Proxies Disposition Effect 0.012 Narrow Framing 0.019 Overconfidence Dummy 0.020 Male Dummy 0.005 Local Bias 0.003 Lottery Stocks Preference 0.024 Inattention to Earnings News 0.013 Inattention to Macroeconomic News 0.005 DEnHigh Income 0.007 DEnNo December Tax Loss Selling 0.024 Control Variables Age Income High Income Dummy Marital Status Family Size Professional Dummy Retired Dummy Investment Experience Financial Center Dummy Options Dummy Short Sale Dummy Stock Portfolio Diversification Stock Portfolio Size Stock Portfolio Performance No December Tax Loss Selling Holds Tax-Deferred Account Market Factor Exposure SMB Factor Exposure HML Factor Exposure UMD Factor Exposure
0.014 0.007 0.003 0.005 0.004 0.007 0.015 0.014 0.008 0.002 0.003 0.001 0.001 0.006 0.015 0.022 0.010 0.018 0.003 0.019
Adjusted R2 Number of Observations
(2) Front-end load
(3) Fund turnover
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
3.02 3.55 3.11 1.05 0.18 3.95 2.33 1.13 1.60 3.60
0.033 0.041 0.029 0.012 0.021 0.033 0.022 0.017 0.011 0.026
3.11 2.42 2.50 1.22 1.70 2.29 2.65 1.54 1.69 2.44
0.004 0.004 0.022 0.018 0.009 0.017 0.019 0.003 0.021 0.025
0.55 1.01 2.67 2.19 1.40 2.66 2.08 0.34 2.80 3.51
2.30 1.51 0.90 1.70 0.80 1.11 2.30 2.59 1.41 0.35 1.13 0.11 0.17 1.54 2.52 4.81 2.56 3.17 0.93 3.72
0.030 0.011 0.015 0.008 0.012 0.024 0.012 0.025 0.004 0.012 0.014 0.003 0.008 0.004 0.031 0.013 0.016 0.012 0.012 0.024
1.65 1.00 0.69 0.50 1.01 1.22 0.56 2.51 1.22 1.33 0.99 0.90 0.45 0.26 2.89 3.53 2.65 2.26 2.39 3.34
0.037 0.023 0.034 0.005 0.015 0.021 0.017 0.033 0.027 0.019 0.013 0.013 0.005 0.009 0.034 0.020 0.022 0.024 0.001 0.031
2.98 1.71 2.30 0.55 0.70 2.05 1.81 3.00 2.67 2.75 1.99 1.09 0.60 0.91 2.99 3.86 2.97 3.39 0.23 3.52
0.071 21,542
0.054 21,542
0.066 21,542
Panel B: Regression estimates with the fund-level local bias and inattentiveness measures Behavioral Bias Proxies Disposition Effect 0.013 2.99 0.032 Narrow Framing 0.016 3.44 0.045 Overconfidence Dummy 0.018 3.24 0.025 Male Dummy 0.004 0.87 0.012 Local Bias 0.004 0.29 0.020 Lottery Stocks Preference 0.022 4.12 0.028 Inattention to Earnings News 0.011 2.19 0.022 Inattention to Macroeconomic News 0.008 1.85 0.019 DEnHigh Income 0.007 1.63 0.016 DEnNo December Tax Loss Selling 0.022 3.49 0.022
3.07 2.44 2.32 1.21 1.68 2.49 2.49 2.68 2.03 2.36
0.002 0.003 0.022 0.016 0.011 0.017 0.015 0.002 0.017 0.023
0.21 0.50 2.43 2.31 1.52 2.74 2.58 0.22 2.29 3.44
Fund-level bias proxies Fund-Level Local Bias Fund-Level Inattention to Macro News Control Variables Age Income High Income Dummy Marital Status Family Size Professional Dummy Retired Dummy
0.024 0.018
5.43 2.37
0.050 0.017
3.59 2.11
0.036 0.002
4.65 0.54
0.016 0.007 0.003 0.006 0.005 0.005 0.014
2.42 1.23 0.50 1.70 1.02 1.06 1.93
0.028 0.011 0.015 0.007 0.018 0.017 0.011
1.33 1.05 0.65 0.70 1.03 0.98 0.55
0.034 0.021 0.030 0.005 0.014 0.025 0.018
2.03 1.60 2.13 0.51 0.74 2.05 1.83
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Table 5 (continued ) (1) Expense ratio Independent Variable Investment Experience Financial Center Dummy Options Dummy Short Sale Dummy Stock Portfolio Diversification Stock Portfolio Size Stock Portfolio Performance No December Tax Loss Selling Holds Tax-Deferred Account Market Factor Exposure SMB Factor Exposure HML Factor Exposure UMD Factor Exposure
(2) Front-end load
(3) Fund turnover
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
0.015 0.004 0.002 0.008 0.004 0.002 0.008 0.013 0.020 0.011 0.018 0.003 0.021
2.61 1.06 0.30 1.53 0.76 0.38 1.51 2.33 4.71 2.55 3.11 0.90 3.70
0.016 0.005 0.011 0.018 0.004 0.011 0.007 0.030 0.012 0.015 0.012 0.013 0.026
2.12 1.35 1.35 1.39 0.91 1.01 0.30 2.80 3.33 2.78 2.21 2.43 3.54
0.025 0.024 0.021 0.013 0.011 0.007 0.008 0.029 0.021 0.023 0.023 0.001 0.030
2.62 2.63 3.22 2.02 1.06 0.60 0.74 2.71 3.67 2.73 3.32 0.21 3.50
Adjusted R2 Number of Observations
0.072 21,542
biases. Indeed, Fund-Level Local Bias emerges as the variable with the largest economic and statistical significance compared with all other behavioral biases. Intriguingly, further correlation analysis (unreported but available upon request) shows that Fund-Level Local Bias is negatively correlated with age and positively correlated with Retired Dummy and Stock Portfolio Size. This again suggests localized marketing efforts: Older investors are typically cleverer and avoid Fund-Level Local Bias, but retired investors with large portfolios could be subjected to recommendations or marketing efforts from brokers, bankers, and social peers. Thus, investors who exhibit a stronger preference to hold local funds, which could be thought of as a familiarity effect, are more likely to buy funds with high fees, expenses, and turnover. Furthermore, Fund-Level Inattention is positive and significant in two of the three specifications, those for expense ratios and front end loads. Investors who pay less attention to news seem to select funds that impose higher expenses and loads on themselves. These findings suggest that behavioral biases can combine with ignorance to yield costly suboptimal mutual fund investment decisions. 4.6. Behavioral biases and trend chasing behavior Our next set of tests examines whether behavioral biases also play an important role in explaining individual investors’ trend-chasing behavior. Many explanations have previously been proposed for this robust pattern observed in mutual fund flow data. Chevalier and Ellison (1997) show that agency problems induce fund managers to alter the riskiness of the fund to maximize investment flows instead of risk-adjusted expected returns. Sirri and Tufano (1998) and Gruber (1996) propose that investors infer managerial skill from past returns. Berk and Green (2004) feature investors who infer managerial skill from past returns and, therefore, chase returns. However, fund managers facing decreasing returns to scale in their active portfolios no longer outperform the index when more funds flow in, and, as a consequence, past performance
0.056 21,542
0.069 21,542
does not predict future returns. Instead of analyzing aggregate flows, our data allow us to study the relation between behavioral tendencies and trend-chasing behavior at the individual investor level. Table 6 examines trend chasing in individual mutual fund portfolios. For each mutual fund purchase, we compute the return prior to the purchase, which is then averaged for each individual. Specification 1 uses 1-year past returns as dependent variable, and Specification 2 uses the 2-year past returns. The results from both specifications show that investors with certain behavioral biases, or inattention to macro news, tend to buy funds with more positive recent returns. Although the disposition effect does not seem to be associated with trend chasing, the coefficients on the Disposition EffectnHigh Income and Disposition EffectnNo December Tax Loss Selling are strongly significantly positive. Among the coefficients on the control variables, some evidence shows that sophisticated investors (those who are professionals, live near a financial center, trade options, or have welldiversified, well-performing individual stock portfolios) are less likely to engage in trend chasing. As was found previously (Table 5) for the propensity to select high-cost mutual funds, the size of slope coefficients suggest that Overconfidence Dummy and Lottery Stocks Preference are among the strongest predictors of whether a particular investor will trend-chase with mutual funds. This evidence suggests that trend chasing is not a rational strategy. This interpretation is supported by the empirical results of previous authors concerning mutual fund flows and subsequent returns on individual stocks held by the funds. Frazzini and Lamont (2008) find relatively poor monthly returns on portfolios of individual stocks held disproportionately heavily by mutual funds that experience high inflows over the previous 6 months to 3 years. We find that it is more behaviorally biased individuals who are responsible for trend-chasing inflows. Thus, some of what they describe as the ‘‘dumb money’’ effect must be ascribed to a subset of investors who we have also identified as making poor decisions with their individual stock portfolios.
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Table 6 Returns chasing and fund selection. This table reports cross-sectional regression estimates with two different mutual fund portfolio performance measures as dependent variables, the 12-month past return and the 24-month past return. There is one observation per investor. The independent variables include behavioral bias proxies, control variables, and an intercept term that is included but unreported. Independent variables are defined in Appendix A. Investors with fewer than 12 months of data are excluded. Zip code clustered standard errors are used to obtain the t-statistics. The statistically significant coefficient estimates are indicated in bold font. The individual investor data are from a large US discount brokerage house for the 1991–1996 period. (1) 12-Month past return Independent Variable
(2) 24-Month past return
Coefficient
t-statistic
Coefficient
t-statistic
Behavioral Bias Proxies Disposition Effect Narrow Framing Overconfidence Dummy Male Dummy Local Bias Lottery Stocks Preference Inattention to Earnings News Inattention to Macroeconomic News DEnHigh Income DEnNo December Tax Loss Selling
0.022 0.644 1.370 0.062 0.154 0.978 0.199 0.581 0.353 0.480
0.25 4.35 5.04 0.46 1.09 6.39 1.62 2.18 2.05 2.16
0.087 0.764 1.604 0.258 0.034 1.196 0.291 0.492 0.508 0.390
0.34 3.45 6.87 2.51 0.33 5.75 1.85 2.84 2.57 2.06
Control Variables Age Income High Income Dummy Marital Status Family Size Professional Dummy Retired Dummy Investment Experience Financial Center Dummy Options Dummy Short Sale Dummy Stock Portfolio Diversification Stock Portfolio Size Stock Portfolio Performance No December Tax Loss Selling Holds Tax-Deferred Account Market Factor Exposure SMB Factor Exposure HML Factor Exposure UMD Factor Exposure
0.329 0.427 0.061 0.077 0.149 0.629 0.487 0.057 0.404 0.347 0.024 0.093 0.139 0.558 0.380 0.062 0.862 0.393 0.068 0.228
1.66 1.83 0.58 0.81 1.22 2.32 2.91 0.30 2.13 2.71 0.12 0.46 0.68 3.46 1.92 0.61 3.87 2.64 0.67 2.40
0.886 0.542 0.196 0.443 0.609 1.052 0.152 0.468 0.510 0.492 0.070 0.492 0.103 0.768 0.407 0.168 0.565 0.485 0.151 0.264
2.11 1.62 1.49 1.52 1.76 2.92 1.92 1.98 1.63 2.63 0.46 2.02 0.71 2.13 2.93 2.38 3.54 3.82 2.15 2.51
Adjusted R2 Number of Observations
The disposition effect result merits further discussion. In the classic form of this bias, investors sell wellperforming individual stocks too quickly and hold poorperforming stocks too long. Trend chasing by individuals who invest in mutual funds is broadly contradictory to a disposition effect in individual stocks: Trend-chasers seek and then hold good performers, instead of selling them quickly. Our disposition effect interactive terms isolate investors who display a disposition effect that is likely to be particularly severe, and both terms earn a strongly significantly positive slope coefficient in the regressions of Table 6. Thus, individuals who display particularly damaging forms of the disposition effect in their individual stock portfolios tend to contradict themselves by displaying trend chasing in their mutual fund choices. This implies that behavioral biases do not just vary across individuals but also across the components within a particular investor’s portfolio, with professionally managed assets handled in a radically different manner than individual stocks. This could be consistent with the idea
0.091 21,542
0.076 21,542
that investors decompose their portfolios into layers that serve different purposes (Shefrin and Statman, 2000). Overall, our cross-sectional regression estimates reported in Tables 4–6 confirm that investors who are more behaviorally biased on any of several dimensions or do not pay attention to salient news are more likely to display poor mutual fund investment decisions. They typically have a greater proportion of their equity investment in individual stocks, not mutual funds, suggesting that they do not value diversification. When they buy funds, they prefer actively managed funds to index funds, tend to buy funds with high fees and loads, and chase funds with high recent returns. The strength of one of our simplest behavioral bias measures, Lottery Stocks Preference, is particularly compelling. The missing link in our evidence and interpretations to this point is more explicit evidence on performance. While it appears that behavioral biases and ignoring news lead to poor choices, we must also show the consequences for performance. For example, individual investors
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typically avoid high front-end load funds (Barber, Odean and Zheng, 2005), but some investors could be able to discriminate between good and bad quality front-end load funds and enjoy superior portfolio performance from those high load funds that they do elect to hold. Thus, our next task is to examine the performance of investors’ mutual fund portfolios. 4.7. Performance of mutual fund portfolios We again estimate cross-sectional regressions with the same behavioral proxies and controls as explanatory variables. Table 7, Panel A studies mutual fund performance for each investor’s actual holdings. The dependent variables are four measures of the sample period performance of each investor’s mutual fund portfolio, the raw performance measure (mean monthly portfolio return), the net-of-expenses performance measure (the net monthly return), the Sharpe ratio, and the market model alpha. We again use zip code clustered standard errors to compute the t-statistics because performance estimates are unlikely to be independent.22 Specification 1 explains the mean monthly return. Disposition Effect, Narrow Framing, Overconfidence Dummy, Lottery Stock Preference, and both measures of inattention to news are associated with lower performance. For example, mean monthly return is lower by 0.041 per month for each standard deviation of increase in narrow framing. Because the highest and lowest quintiles of narrow framing differ by 4.3 standard deviations, this implies a 2.12% per year lower return for highest quintile narrow framing investors compared with those in the lowest quintile. Similarly, highest quintile disposition effect investors have returns 1.34% lower than those in the lowest quintile.23 Thus, our behavioral proxies detect poor decision-making skills that reduce portfolio performance. Among the control variables, investment experience is significant, and the positive slope makes sense. The use of options or short sales is associated with better mutual fund performance, which is consistent with those variables reflecting skill or financial sophistication. Specification (2) examines net monthly returns and shows similar associations between behavioral biases and performance. Specification 3 examines the Sharpe ratio. We again find broadly similar associations with the behavioral bias proxies, inattention measures, and control variables. Narrow Framing, Overconfidence Dummy, and, to a lesser extent, Disposition Effect are associated with lower performance. Results are similar when we account for potential cross-sectional dependence in performance induced by market-wide factors and consider a risk-adjusted performance measure as the dependent variable (Specification 4). Collectively, the evidence in Table 7, Panel A shows that behavioral biases measured from individual stock selection are also associated with lower raw and 22 As before, other forms of standard error clustering yield very similar results. 23 Given that the highest and lowest quintiles of disposition effect differ by 4.13 standard deviations, their yearly performance difference is 1.34% ( 0.027% times 12 times 4.13).
risk-adjusted returns from mutual funds. Thus, poor decision making in one domain appears to spill over into the performance experienced with other classes of investments. While Table 7, Panel A describes the actual realized returns of individual investors based on their total holdings at the end of each month, Panel B studies performance based on investor trades under both actual and hypothetical holding periods computed using daily fund returns data from Morningstar.24 Specifications 1 and 2 study actual holding period returns from trades. They confirm that investors with higher values on most of our behavioral bias proxies and inattention to news measures have significantly lower holding period returns and shorter holding period, in contrast to the buy-and-hold strategies prescribed by standard portfolio theory. Local Bias is associated with longer holding periods. Correlation analysis (unreported but available upon request) indicates that Local Bias is associated with poor diversification and mediocre performance in the individual stock portfolio, but Specification 2 shows us that it could also yield sensible low turnover of mutual fund holdings. Specifications 3 and 4 adopt the alternative viewpoint of returns based on actual trades but standardized hypothetical holding periods. Following Odean (1999) and Kumar and Lee (2006), we calculate the subsequent k-month returns following each buy trade averaged over the trading history of an individual and subtract the subsequent k-month returns following each sell trade averaged over the trading history. The summary statistics on 1- and 12-month post-trade buy–sell return differentials show that investors who score high on most of our behavioral and inattention proxies have lower post-trade buy–sell returns differentials. In other words, investors with strong behavioral biases tend to time their buys and sells poorly, and they experience inferior performance relative to less-biased investors. The results are especially significant for 12-month returns differentials. Table 8 features interactions between investor portfolio characteristics and fund characteristics to explain performance. Individual household mutual fund performance is regressed on the behavioral biases and inattention measures previously employed, characteristics of the individual’s mutual fund portfolio (the weight of the portfolio held in mutual funds, and the averages of the expense ratio, 12-B-1 fee, and front-end load on the funds held), interactive terms that combine behavioral and portfolio characteristics, and (unreported) control variables. The results confirm the negative impact of disposition effect, narrow framing, overconfidence, lottery stocks preference, and inattention to news on performance as documented previously. Among the mutual fund portfolio characteristics, investors with higher weight on mutual funds tend to enjoy superior fund performance, which is consistent with classic notions of portfolio management.
24 Partial sales are excluded from our calculations. Unlike Panel A, these calculations exclude any funds that were held prior to the start of our sample period.
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17
Table 7 Investor characteristics and performance of mutual fund investments. This table reports cross-sectional regression estimates to explain two measures of mutual fund portfolio performance, position-based performance measures in Panel A and trade-based performance measures in Panel B. In Panel A, the dependent variables are (1) the mean monthly percent return (in percentage terms), (2) the net monthly return which equals the mean monthly return minus expenses (but not loads), (3) the Sharpe ratio of net returns multiplied by one hundred, and (4) the monthly market model alpha. In Panel B, the dependent variables in Specifications 1 to 4 are the mean annualized holding period return, the mean holding period, the one-month post trade buy–sell return differential, and the 12-month post trade buy–sell return differential (PTBSD), respectively. Independent variables are defined in appendix. A constant term is included. Investors with fewer than 12 months of data are excluded. Zip code clustered standard errors are used to obtain the t-statistics. The statistically significant coefficient estimates are indicated in bold font. The individual investor data are from a large US discount brokerage house from 1991 to 1996. Panel A: Position-Based Mutual Fund Portfolio Performance Regression Estimates (1) Mean monthly returns (2) Net monthly returns Independent Variable
(3) Net Sharpe ratio 100
(4) Market model alpha
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Behavioral Bias Proxies Disposition Effect Narrow Framing Overconfidence Dummy Male Dummy Local Bias Lottery Stocks Preference Inattention to Earnings News Inattention to Macroeconomic News DEnHigh Income DEnNo December Tax Loss Selling
0.027 0.041 0.025 0.009 0.010 0.026 0.014 0.022 0.009 0.016
2.14 2.94 2.17 1.05 1.20 2.99 2.18 2.22 1.26 1.66
0.028 0.047 0.031 0.012 0.010 0.024 0.015 0.024 0.012 0.016
2.16 2.75 2.60 1.42 1.30 2.78 2.48 2.45 1.26 1.62
0.554 1.550 1.502 1.503 0.113 1.249 1.041 1.010 0.143 0.155
1.94 3.83 2.39 1.90 0.42 1.97 2.13 2.03 0.19 0.51
0.027 0.050 0.033 0.039 0.006 0.059 0.026 0.019 0.006 0.028
1.96 2.65 2.06 2.29 0.88 3.26 2.82 1.92 0.80 2.58
Control Variables Age Income High Income Dummy Marital Status Family Size Professional Dummy Retired Dummy Investment Experience Financial Center Dummy Options Dummy Short Sale Dummy Stock Portfolio Diversification Stock Portfolio Size Stock Portfolio Performance No December Tax Loss Selling Holds Tax-Deferred Account Market Factor Exposure SMB Factor Exposure HML Factor Exposure UMD Factor Exposure
0.007 0.002 0.026 0.004 0.004 0.002 0.003 0.028 0.001 0.034 0.051 0.028 0.023 0.032 0.003 0.003 0.021 0.012 0.007 0.031
1.59 0.22 1.63 0.34 0.34 0.12 0.21 3.15 0.08 2.51 2.36 1.83 1.39 1.29 0.29 0.59 2.78 1.38 1.35 3.35
0.008 0.003 0.030 0.009 0.004 0.017 0.003 0.026 0.011 0.043 0.021 0.024 0.023 0.033 0.002 0.003 0.019 0.004 0.006 0.024
1.45 0.18 1.89 0.59 0.40 0.87 0.18 2.89 0.88 1.79 1.55 1.57 1.43 2.07 0.18 0.58 2.43 0.66 1.22 2.98
0.448 0.581 0.200 0.218 0.679 0.308 0.046 1.991 0.510 1.517 0.978 0.105 1.288 0.672 0.614 0.168 0.595 0.670 0.025 0.449
0.65 0.88 1.04 0.36 0.97 0.40 0.08 2.72 0.85 2.62 1.64 0.18 2.03 1.17 1.66 1.02 3.08 3.51 0.14 2.75
0.003 0.011 0.026 0.003 0.039 0.002 0.034 0.051 0.014 0.062 0.035 0.013 0.011 0.001 0.018 0.017 0.009 0.038 0.014 0.016
0.72 0.31 0.48 0.08 1.91 0.43 1.54 2.35 1.42 3.12 1.33 0.94 0.28 0.31 1.47 1.62 0.51 2.71 1.39 1.68
Adjusted R2 Number of Observations
0.042 21,542
Panel B: Trade-Based Mutual Fund Portfolio Performance (1) Holding period return Independent Variable
0.043 21,542
(2) Holding period
0.037 21,542
(3) One-month PTBSD
0.029 20,142
(4) 12-month PTBSD
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
0.418
12.57
444.20
17.85
0.042
0.97
2.526
14.34
Behavioral Bias Proxies Disposition Effect Narrow Framing Overconfidence Dummy Male Dummy Local Bias Lottery Stocks Preference Inattention to Earnings News Inattention to Macroeconomic News DEnHigh Income DEnNo December Tax Loss Selling
0.059 0.054 0.066 0.018 0.005 0.037 0.010 0.048 0.065 0.037
2.46 3.40 3.06 0.53 0.14 2.27 1.26 2.29 3.17 1.99
25.15 15.16 42.61 3.36 10.02 24.17 4.02 11.71 19.66 15.69
4.26 2.97 7.75 0.56 2.67 2.36 1.62 2.85 2.67 2.89
0.070 0.096 0.090 0.018 0.013 0.058 0.033 0.029 0.061 0.002
2.48 3.48 2.17 1.09 0.69 2.27 2.66 2.60 2.55 0.36
0.295 0.462 0.569 0.114 0.356 0.551 0.474 0.526 0.485 0.079
2.26 3.26 2.99 1.63 2.27 2.34 2.36 2.69 2.07 1.39
Control Variables Age Income High Income Dummy
0.049 0.015 0.014
2.46 0.22 0.94
18.65 2.27 4.58
1.99 0.25 1.39
0.054 0.005 0.024
2.06 0.15 1.63
0.417 0.084 0.257
2.23 0.72 1.26
Intercept
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Table 7 (continued ) Panel B: Trade-Based Mutual Fund Portfolio Performance (1) Holding period return Independent Variable Marital Status Family Size Professional Dummy Retired Dummy Investment Experience Financial Center Dummy Options Dummy Short Sale Dummy Stock Portfolio Diversification Stock Portfolio Size Stock Portfolio Performance No December Tax Loss Selling Holds Tax-Deferred Account Market Factor Exposure SMB Factor Exposure HML Factor Exposure UMD Factor Exposure Adjusted R2 Number of Observations
(2) Holding period
(3) One-month PTBSD
(4) 12-month PTBSD
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
Coefficient
t-statistic
0.025 0.016 0.010 0.038 0.038 0.006 0.040 0.034 0.013 0.026 0.042 0.015 0.023 0.004 0.035 0.015 0.024
1.09 1.82 0.18 1.68 2.21 0.31 1.97 1.82 0.73 1.70 2.50 1.32 1.95 0.16 1.98 1.21 1.11
5.02 2.65 4.49 27.61 8.67 16.56 33.55 12.02 41.47 3.33 25.00 45.25 7.11 26.14 23.73 2.36 16.83
0.59 0.27 0.42 3.33 1.58 2.03 5.56 2.01 3.88 0.55 4.92 3.35 1.53 3.53 3.86 0.51 2.99
0.008 0.007 0.013 0.037 0.089 0.020 0.050 0.041 0.016 0.022 0.017 0.074 0.013 0.047 0.013 0.025 0.017
0.46 0.17 0.88 2.17 3.50 1.31 2.14 1.86 1.01 1.55 1.05 2.77 0.38 2.09 0.95 1.65 0.88
0.183 0.061 0.191 0.197 0.587 0.051 0.302 0.181 0.091 0.071 0.409 0.223 0.035 0.261 0.457 0.234 0.095
1.61 0.20 1.27 2.19 3.14 0.31 2.71 1.98 1.33 0.95 2.65 1.85 0.25 1.78 3.13 1.68 0.76
0.045 15,210
Investors with higher weight on expenses, 12-B-1 marketing fees, and front-end load funds typically experience inferior fund performance. Among the interactive terms, we see particularly poor performance for high disposition effect investors who select funds with high 12-B-1 marketing fees or high front-end loads. This also appears to be the case for investors with strong framing effects or overconfidence. The coefficients for interactives for high inattention and fees are uniformly significantly negative. Thus, investors with particularly high behavioral biases who choose to remain poorly informed could make particularly poor choices, stumbling into mutual funds with high expense ratios, high 12-B-1 marketing fees, or front-end loads. This echoes the finding in Table 5 that behavioral biases are particularly powerful in pulling investors into high front end load funds. This is also consistent with the possibility that the mutual fund industry positions certain products to exploit particularly biased individuals. In unreported results, we examine the performance differences among investors who use index funds. We do not find significant associations between the performance of individual index fund portfolios and individual behavioral biases. We consider different types of tests, including univariate sorts and multivariate regressions with and without controls or interaction terms. All our results consistently show that behavioral biases do not affect the performance of investors’ index fund portfolios. This evidence indicates that investors can protect themselves from their own worst impulses by holding index funds and reinforces the classic intuition that most individual investors perform better if they stick to well-diversified index funds. Our findings also echo Korniotis and Kumar (forthcoming) who show that the performance difference between smart and dumb investors is insignificant when both hold well-diversified stock portfolios, but it is highly
0.093 15,210
0.040 18,002
0.064 18,002
significant for those that choose concentrated portfolios, with smart investors outperforming by a wide margin.25
4.8. Aggregating the behavioral bias proxies and other characteristics Next, we measure the combined effects of investor characteristics using both the factors constructed from the behavioral bias proxies and other investor characteristics and an equally weighted index that combines the behavioral bias proxies. Panel A of Table 9 summarizes regressions similar to those of Tables 4–7 but replaces the individual investor characteristics with the first five factors resulting from factor analysis described in Section 4.1. The first two columns study the first factor, which we previously labeled Gambler. The evidence in the table confirms this characterization. Gambler represents individuals who are less likely to use mutual funds, tend to select high expense funds, are more likely to trend-chase, and suffer significantly inferior mutual fund portfolio performance as a consequence. Put another way, Gambler employs mutual funds less than he probably should, but, when he does, he makes poor use of them. We previously identified the second factor as Smart, given that the individual stock portfolio of this stereotype avoids biases and displays relatively good performance. The evidence in Panel A of Table 9 suggests that Smart’s beneficial behavior extends to his use of mutual funds. The signs and significance of regression coefficients indicate that the Smart stereotype is more likely to use 25 This supports the notion that individual investors should be encouraged to make good decisions, as with retirement savings plan (Benartzi and Thaler, 2007).
W. Bailey et al. / Journal of Financial Economics 102 (2011) 1–27
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Table 8 Behavioral biases, mutual fund portfolio characteristics, and portfolio performance. This table reports cross-sectional regression estimates with two different mutual fund portfolio performance measures as dependent variables: (1) the mean net monthly percent return and (2) the Sharpe ratio computed using net returns multiplied by 100. There is one observation per investor. The independent variables are behavioral bias proxies and inattention measures, mutual fund characteristics, bias-load interaction terms, and control variables. Independent variables are defined in Appendix A. Mutual fund characteristics include the initial weight assigned to mutual funds in the equity (stocks and mutual funds) portfolio and three expense measures of the mutual fund portfolio: the sample period mean expense ratio, the sample period mean 12-B-1 fee, and the sample period mean front-end load. Bias-load interaction terms equal the multiplication between each of three behavioral bias measures and each of three mutual fund expense ratio measures. The three behavioral bias measures are high disposition effect, strong framing effects, and overconfidence. The inattention measure is the equally weighted average of the two stock-level inattention measures. The three expense ratio measures are high expense ratios, high 12-B-1 fees, and high front-end loads. The mutual fund portfolio weight is measured at the time an investor enters the sample or invests in mutual funds for the first time. High and low dummy variables are defined using the highest and the lowest quintile of the respective variable. Investors with fewer than 12 months of data are excluded. Zip code clustered standard errors are used to obtain the t-statistics. The statistically significant coefficient estimates are indicated in bold font. The individual investor data are from a large US discount brokerage house for the 1991–1996 period. (1) Net monthly return Independent Variable Intercept
(2) Net Sharpe ratio 100
Coefficient
t-statistic
Coefficient
t-statistic
1.320
13.14
40.156
21.80
Behavioral Bias Proxies Disposition Effect Narrow Framing Overconfidence Dummy Male Dummy Local Bias Lottery Stocks Preference Inattention to Earnings News Inattention to Macroeconomic News DEnHigh Income DEnNo December Tax Loss Selling
0.025 0.043 0.021 0.010 0.009 0.033 0.015 0.025 0.011 0.015
2.01 2.90 2.00 1.12 0.56 3.11 2.11 2.34 1.55 1.52
0.556 1.565 1.446 1.498 0.100 1.301 1.114 0.989 0.101 0.151
1.98 3.67 2.24 1.81 0.22 1.99 2.34 2.00 0.16 0.59
Mutual Fund Portfolio Characteristics Initial Weight in Mutual Funds Mutual Fund Portfolio Expense Ratio Mutual Fund Portfolio 12-B-1 Fee Mutual Fund Portfolio Front-End Load
0.044 0.010 0.051 0.048
3.71 0.74 3.55 3.97
1.721 0.730 2.234 2.142
3.65 3.44 4.36 5.02
Bias-load interaction terms High Disposition EffectnHigh Expense Ratio High Disposition EffectnHigh 12-B-1 Fee High Disposition EffectnHigh Front-End Load Strong Framing EffectsnHigh Expesne Ratio Strong Framing EffectsnHigh 12-B-1 Fee Strong Framing EffectsnHigh Front-End Load OverconfidentnHigh Expense Ratio OverconfidentnHigh 12-B-1 Fee OverconfidentnHigh Front-End Load High InattentionnHigh Expense Ratio High InattentionnHigh 12-B-1 Fee High InattentionnHigh Front-End Load
0.004 0.025 0.054 0.008 0.015 0.055 0.006 0.024 0.052 0.017 0.022 0.063
0.40 2.99 5.09 0.86 1.91 7.09 0.71 3.88 6.86 3.88 2.46 4.97
0.487 2.356 2.381 0.268 2.298 2.464 0.544 2.433 2.312 1.119 2.106 0.927
1.49 7.15 8.58 0.79 6.93 8.71 1.66 7.39 8.35 2.83 4.73 2.21
Control Variables Coefficient estimates have been suppressed. Adjusted R2 Number of Observations
mutual funds, more likely to use funds with low expense ratios or loads, less likely to trend-chase, and enjoys significantly positive mutual fund performance based on all eight of the performance measures we examine. We previously labeled the third factor Overconfident based on trading of individual equities and other characteristics. The evidence on Overconfident’s mutual fund portfolio confirms our impression that this stereotype is a poor decision-maker. Overconfident avoids participation in mutual funds and trend-chases to an even greater degree than Gambler, and he also tends to select high expense, high load, and high turnover funds. Whether Overconfident’s mutual fund performance is
0.055 21,542
0.051 21,542
even worse than Gambler’s varies across our eight performance measures. We labeled the fourth factor Narrow Framer. Narrow Framer’s mutual fund participation is about as bad as Gambler’s, though not as bad as Overconfident’s. Small holdings of mutual funds, selection of high expense funds, trend chasing, and consequent poor performance are also evident, though milder than for Gambler and Overconfident. Finally, the mutual fund use and performance represented by the fifth factor, Mature, mirrors what we reported earlier for Mature’s individual stock portfolio. To Mature’s credit, he participates and holds mutual funds
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W. Bailey et al. / Journal of Financial Economics 102 (2011) 1–27
to a greater extent than our other stereotypes and avoids high-expense funds and trend chasing to an even greater extent than Smart. However, other elements of Mature’s decision making about mutual funds yield significant negatives on four of our eight performance measures. This finding is consistent with the evidence in Korniotis and Kumar (2011), who show that older investors are more likely to follow common investing rules but employ them less effectively and subsequently experience worse portfolio performance. One interesting observation from Panel A of Table 9 concerns the use of index funds. Unsurprisingly, Gambler, Overconfident, and Narrow Framer score negatively on both index fund participation and holdings. Their lack of interest in these useful and prudent funds is consistent with a pattern of bad decision making in their use of other funds and individual stocks. Mature seems to participate in index funds as frequently as Smart and holds an even greater proportion of such funds than Smart. However, this is not enough to overcome Mature’s other decisionmaking problems and yield positive performance. As an alternative to the five named factors from factor analysis, Panel B of Table 9 presents similar results based on an equally weighted behavioral index.26 Specifically, we normalize each behavioral factor to have a mean of zero and a standard deviation of one, then average these normalized behavioral proxies for each individual in the sample. The table shows that in all cases the bias index is statistically significant and, more important, economically significant. In the discussion that follows, we infer the decisions of investors in the lowest and the highest bias quintiles. The average behavioral bias index values of investors in the extreme bias quintiles are 0.709 and 0.627. The standard deviation of the behavioral bias measure is 0.491, which indicates that the low and high behavioral bias quintiles are 2.721 standard deviations away from each other. In the participation regressions, the bias index estimates indicate that an investor who moves from the lowest to highest bias quintile reduces the probability of investing in mutual funds by 0.439 2.721 ¼1.189%, while the propensity to invest in index funds drops by 1.933%. In the holdings regressions, we find that moving across the extreme bias quintiles reduces the weight assigned to mutual funds by 2.038%. This effect is even stronger (5.254%) for index funds. The other regressions summarized in Panel B of Table 9 paint a similar picture. Behavioral biases are associated with selecting higher expense funds, trend chasing with funds, and significant under-performance from fund holdings. In economic terms, the combined effects of all behavioral biases are moderately to strongly significant. 5. Additional diagnostics In this section, we discuss additional tests that augment our main results by examining their robustness, 26 This includes the five basic biases and the two inattention measures but excludes the two tax interactives.
considering alternative explanations for our findings, and offering additional evidence on the most biased investors. 5.1. ‘‘Play money’’ accounts? In our first set of additional considerations, we test whether our results are driven primarily by a ‘‘play money’’ effect. We compute the average portfolio size-to-annual income ratio for each investor, excluding investors in the lowest quintile. Unreported results indicate that our findings remain qualitatively similar even when we exclude investors who hold portfolios that are small relative to their annual income. For example, the coefficient estimate of the bias index in Table 4, Column 1 is 0.749 (t-statistic¼ 5.49) for the full sample and 0.755 (t-statistic ¼ 5.88) for the subsample that excludes potential play money. This evidence indicates that our results are unlikely to be induced by a subset of investors who maintain a small portfolio and trade it for irrational or frivolous reasons. 5.2. Mutual fund decisions for retirement accounts Many investors in our sample hold personal retirement accounts. About 42% of the accounts in our sample are retirement accounts (IRA or Keogh).27 Thus, we examine whether investors’ mutual fund choices vary between retirement and non retirement accounts.28 It is plausible that the adverse effects of behavioral biases on mutual fund decisions are mainly concentrated in non retirement accounts. We could view a retirement account as the opposite of a play money account and predict that it is managed in a more conservative manner. We define a ‘‘taxable account only’’ dummy, which is set to zero for investors who hold only retirement accounts in their equity portfolios and one otherwise. We include this dummy variable as an additional independent variable in our regression specifications.29 We find that investors do not exhibit a greater propensity to hold mutual funds in their retirement accounts. The taxable account only dummy has an insignificant coefficient estimate ( 0.003 with z-statistic of 0.25). No evidence exists of a stronger propensity to hold index funds for investors who hold retirement accounts. The taxable account only dummy has a coefficient estimate of 0.011 and z-statistic of 1.19. Even among investors who choose to hold mutual funds, no evidence shows that they allocate a larger proportion of their equity portfolio 27 Among 158,031 accounts in our sample there are 64,416 IRA and 1,299 Keogh accounts. A typical household holds multiple accounts. Out of 77,995 households in the sample, 43,706 hold at least one retirement account. 28 See Sialm and Starks (forthcoming) for evidence that funds directed at taxable investors appear more tax-efficient than funds directed at retirement accounts. This approach is distinct from our use of the holds tax deferred account dummy in earlier regressions, which identifies all accounts, regular or tax-deferred, held by someone who holds at least one tax-deferred account. 29 All results are qualitatively similar when reestimated over two subsamples: investors who hold only retirement accounts and investors who hold retirement and non-retirement accounts.
Table 9 Associations between aggregated behavioral biases and other characteristics, fund decisions, and consequences. Panel A reports the combined effect of multiple bias proxies on mutual fund decisions using the five most important factors from factor analysis of the behavioral bias proxies and other investor characteristics. Panel B reports the combined effect of multiple bias proxies on mutual fund decisions using an equally weighted index of the behavioral bias proxies. The behavioral factors are defined in Appendix A and the factor analysis is detailed in Table 3. This table summarizes estimates of the regressions of Tables 4–7 in which the behavioral proxies and other investor characteristics are replaced with the five most important factors from factor analysis. For brevity, only the coefficient estimates for the variable of interest are reported. PTBSD equals the post-trade buy–sell return differential. Panel A: Estimates when the dependent variable is a factor of the behavioral bias proxies and other investor characteristics Gambler factor Smart factor Overconfident factor Regression Type
Holdings (Table 4) Weight in all mutual funds: column 5 Weight in index funds only: column 6 Portfolio characteristics (Table 5) Expense ratio: column 1 Front-end load: column 2 Fund turnover: column 3 Trend chasing (Table 6) 12-Month lagged fund performance: column 1 24-Month lagged fund performance: column 2 Portfolio performance (Table 7) Mean monthly returns: Panel A, column 1 Net monthly returns: Panel A, Column 2 Net Sharpe ratio: Panel A, column 3 Four-factor alpha: Panel A, Column 4 Holding period returns: Panel B, column 1 Holding period: Panel B, column 2 One-month PTBSD: Panel B, column 3 One-year PTBSD: Panel B, column 4
Mature factor
Adjusted R2
Number of Observations
Coefficient
t- or zstatistic
Coefficient
t- or zstatistic
Coefficient
t- or zstatistic
Coefficient
t- or zstatistic
Coefficient
t- or zstatistic
0.339 0.229
3.77 2.93
0.125 0.171
2.24 2.59
0.722 0.402
3.75 2.68
0.350 0.311
2.73 2.60
0.258 0.174
3.11 2.81
0.059 0.051
21,542 21,542
2.827 1.901
3.02 2.71
1.764 1.166
1.42 1.81
3.193 2.792
3.75 3.18
1.981 1.591
2.73 2.76
2.541 2.407
3.55 2.76
0.049 0.055
21,542 21,542
0.209 0.132 0.114
5.15 2.72 3.71
0.014 0.017 0.029
2.88 2.15 2.31
0.079 0.082 0.145
4.46 2.21 3.59
0.027 0.063 0.033
2.13 1.91 1.22
0.111 0.085 0.148
5.42 3.11 4.68
0.038 0.031 0.043
21,542 21,542 21,542
1.180
2.93
0.096
1.23
1.729
3.02
0.863
1.97
1.367
2.65
0.071
21,542
1.156
2.61
0.532
2.33
1.941
2.98
1.167
2.57
2.079
3.14
0.050
21,542
0.109
2.65
0.085
2.33
0.111
2.82
0.066
1.92
0.025
1.82
0.028
21,542
0.122 2.568 0.164 0.095
2.60 3.20 2.84 3.08
0.076 2.853 0.123 0.059
2.51 3.12 2.34 2.42
0.189 1.110 0.092 0.074
3.77 2.04 2.78 2.90
0.058 2.109 0.058 0.078
1.98 3.08 2.88 2.94
0.019 0.664 0.026 0.055
1.31 1.12 1.26 2.40
0.026 0.024 0.021 0.033
21,542 21,542 21,542 15,210
27.904 0.152 0.916
3.07 3.49 3.37
18.514 0.125 0.936
2.38 3.48 3.70
15.504 0.093 0.691
2.27 3.36 3.28
8.211 0.051 0.544
2.58 2.77 2.82
21.675 0.076 0.722
2.99 3.21 2.87
0.065 0.025 0.050
15,210 15,210 15,210
Panel B: Estimates when dependent variable is equally weighted index of behavioral bias proxies Regression Type Coefficient
t- or z-statistic
Adjusted R2
Number of Observations
0.439 0.719
7.11 7.41
0.033 0.065
21,542 21,542
Holdings (Table 4) Weight in all mutual funds: column 5 Weight in index funds only: column 6
0.744 1.933
5.44 4.72
0.068 0.142
21,542 21,542
0.032
4.13
0.055
21,542
Portfolio characteristics (Table 5) Expense ratio: column 1
21
Participation (Table 4) All mutual funds: column 2 Index funds only: column 4
W. Bailey et al. / Journal of Financial Economics 102 (2011) 1–27
Participation (Table 4) All mutual funds: column 2 Index funds only: column 4
Narrow Framer factor
21,542 21,542 21,542 20,142 15,210 15,210 15,210 15,210 0.038 0.042 0.031 0.028 0.033 0.080 0.029 0.048 Portfolio performance (Table 7) Mean monthly returns: Panel A, column 1 Net monthly returns: Panel A, column 2 Net Sharpe ratio: Panel A, column 3 Four-factor alpha: Panel A, Column 4 Holding period returns: Panel B, Column 1 Holding period: Panel B, Column 2 One-month PTBSD: Panel B, column 3 One-year PTBSD: Panel B, column 4
0.052 0.062 2.499 0.055 0.063 21.175 0.381 0.622
3.71 3.47 3.85 3.39 5.16 4.44 4.12 4.23
21,542 21,542 0.083 0.065 1.441 1.276 Trend chasing (Table 6) 12 month lagged fund performance: column 1 24 month lagged fund performance: column 2
4.90 3.55
21,542 21,542 0.044 0.053 3.55 2.01 0.033 0.016 Front-end load: column 2 Fund turnover: column 3
Panel B: Estimates when dependent variable is equally weighted index of behavioral bias proxies Regression Type Coefficient
Table 9 (continued )
t- or z-statistic
Number of Observations
W. Bailey et al. / Journal of Financial Economics 102 (2011) 1–27
Adjusted R2
22
to mutual funds. The taxable account only dummy has statistically insignificant estimates in all specifications. Examining the characteristics of funds in the portfolios of investors who hold only retirement accounts, we find that they do not have lower expense ratios, lower front end loads, or lower turnover. Moreover, there is a greater tendency to engage in trend chasing among these investors. When we reestimate the trend chasing regressions of Table 6 with the taxable account only dummy variable, it has a significantly positive coefficient estimate (coefficient estimate¼0.029, t-statistic ¼2.99). To examine whether ‘‘retirement accounts only’’ investors exhibit better performance, we reestimate all the performance regressions with the taxable account dummy as an additional independent variable. In all specifications, this dummy variable has an insignificant coefficient estimate. Overall, we do not find evidence of superior mutual fund decisions when investors hold retirement accounts. The adverse effects of behavioral biases on mutual fund decisions are similar across both retirement and non retirement accounts. Thus, behaviorally biased investors do not manage retirement funds any more carefully than their regular accounts.
5.3. How do the most severely biased investors use mutual funds? Next, we consider whether the most severely behaviorally biased investors tend to concentrate in particular types of funds, how often they trade those funds, and what consequences for performance result. We summarize unreported (but available on request) evidence on holdings, holding periods, and returns for the mutual funds owned by quintiles of investors who score highest on disposition effect, narrow framing, overconfidence, local bias, preference for lottery stocks, and inattention to news. Our primary prediction is that severely biased investors are more likely to select higher expense funds and avoid index funds. We also expect the strongest Disposition Effect and Overconfidence Dummy investors to turn their mutual fund holdings over relatively frequently. There is much evidence to support such conjectures. For example, front-load funds are 27.15% of the mutual fund holdings of typical investors, but we observe statistically significantly greater front-load fund holdings for the highest Disposition Effect (31.05%), Narrow Framing (26.69%), and Overconfidence Dummy (30.81%) cohorts. The mutual fund holdings of the highest Local Bias and Inattention Bias investors have, on average, about 2% less front load funds than typical investors. Holding periods for front end load funds are, on average, significantly low for highest Disposition Effect (215 days) and Overconfidence Dummy (233 days) investors and are significantly high for highest Narrow Framing (306 days), Local Bias (323 days), and Inattention Bias (327 day) investors. Somewhat similar, but weaker, results are observed for holdings of back-end load funds and in comparing holdings of index funds and other funds.
W. Bailey et al. / Journal of Financial Economics 102 (2011) 1–27
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Table A1 Brief description of behavioral proxies and other investor characteristics. Variable
Description
References
Calculation
Disposition Effect
Investor’s propensity to sell winners too early and hold losers too long. Measured by the proportion of gains realized minus proportion of losses realized, adjusted for the peer group’s disposition effect.
Shefrin and Statman (1985), Odean (1998), and Kumar and Lim (2008).
Narrow Framing
Investor’s propensity to select investments individually instead of considering the broad impact on her portfolio. Measured by the degree of trade clustering, adjusted for the peer group’s framing propensity. Investor’s propensity to trade frequently but unsuccessfully. Measured with a dummy variable.
Kahneman and Lovallo (1993), Kahneman (2003), and Kumar and Lim (2008).
Proportion of gains realized (PGR) ¼realized gains/(realized gains þpaper gains). Proportion of losses realized (PLR) ¼realized losses/ (realized losses þ paper losses). A peer group of an investor is defined as those in the same quintile of portfolio size, trading frequency and number of stocks. Adjusted PGR ¼PGR of an investor – mean PGR of peer group. Adjusted PLR ¼PLR of an investor – mean PLR in her peer group. Adjusted disposition effect ¼adjusted PGR – adjusted PLR. Trade clustering ¼ 1 – (number of trades/number of trading days). A peer group of an investor is defined as those in the same quintile of portfolio size, trading frequency, and number of stocks. Adjusted trade clustering ¼ trade clustering – mean trade clustering of the peer group.
Overconfidence
Odean (1999) and Barber and Odean (2001).
Huberman (2001), Coval and Moskowitz (1999), Grinblatt and Keloharju (2001), Zhu (2003), and Ivkovic´ and Weisbenner (2005). Barberis and Huang (2008), and Kumar (2009).
Local Bias
Investor’s propensity to select stocks with headquarters close to his geographical location.
Lottery Stock Preference
Investor’s propensity to select stocks with lottery-like features (low price, volatile returns, and skewed returns).
Inattention to Earnings News
Degree to which investor does not trade a particular individual stock around earnings news.
New in this paper.
Inattention to Macroeconomic News
Degree to which investor does not trade any individual stocks around macroeconomic news events.
New in this paper.
Fund-Level Local Bias
Investor’s propensity to select funds with headquarters close to his geographical location.
New in this paper.
Fund Level Inattention
New in this paper.
Age Income High Income Dummy
Individual’s propensity to trade mutual funds around macroeconomic news events. Extent of Disposition Effect for investor who ignores tax loss selling. Extent of Disposition Effect for investor with high income. Age of the investor. Income of the investor. Affluence of the household
Marital Status
Marital status of the investor.
Family Size Professional Dummy
Family size.
DEnNo December Tax Loss Selling DEnHigh Income
New in this paper.
New in this paper. Self-reported. Self-reported. Graham and Kumar (2006). Self-reported. Self-reported. Self-reported.
Dummy variable equal to one for investors in the highest portfolio turnover quintile and lowest performance quintile for their individual common stock trading and zero otherwise. Also captured by a gender dummy variable equal to one if the investor is male. Local bias of an investor’s common stock portfolio ¼ mean distance between her home zip code and the headquarters’ zip codes of companies in her portfolio – mean distance between home zip code and the headquarters’ zip codes of companies in the market portfolio. Investor’s mean portfolio weight (relative to the weight in the market portfolio) assigned to stocks that have bottom quintile prices, top quintile idiosyncratic volatility, and top quintile idiosyncratic skewness. 1 – (number of investor trades around the event)/(total number of investor trades) on days t–1, t, and t þ1 where t is the date of quarterly earnings announcement from the Institutional Brokers’ Estimate System (I/B/E/S). Only trades around each firm’s own earnings news are considered. 1 – (number of investor trades around the event)/(total number of investor trades) on days t–1, t, and t þ1 where t is the date of federal funds target rate changes, Non-Farm Payroll reports, and producer price index announcements. Equals mean distance between the investor’s home zip code and the headquarters of the mutual funds in his portfolio – the same mean distance averaged across all investors in the sample. Equals 1 - (number of mutual fund trades around the event)/(total number of mutual fund trades). Disposition Effect times dummy variable equal to one for investor with no December tax loss selling. Disposition Effect times High Income Dummy. Age of the investor. Annual income of investor. Equals one if the investor’s average income exceeds $125,000 and zero otherwise. Equals one if the investor is married and zero otherwise. Number of family members in the household.
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W. Bailey et al. / Journal of Financial Economics 102 (2011) 1–27
Table A1 (continued ) Variable
Retired Dummy Investment Experience
Description A indicator whether an investor is a white collar or blue collar worker. Retirement status of investor.
References
Equals zero for investor in a blue collar profession and one otherwise. Self-reported.
Investment experience of investor. An indicator whether an investor lives near a financial center.
Self-reported.
An indicator for whether the investor has ever traded an option in the investment account. An indicator for whether the investor has ever shorted a stock in the investment account. The extent to which the stock portfolio of the investor is diversified.
Based on investment record.
The size of the investor’s portfolio. Risk-adjusted excess returns of the investor’s stock portfolios.
Based on investment record. Based on investment record.
An indicator if the investor fails to realized losses of his stock trade in December An indicator for whether the investor holds a tax deferred account in the brokerage. The beta of the investor’s stock portfolio.
Based on investment record.
Stock Portfolio SMB Factor (Size) Exposure
The loading of the stock portfolio on the small-minus-big factor (SMB) in a four-factor model regression.
Based on investment record.
Stock Portfolio HML Factor (Value) Exposure
The loading of the stock portfolio on the high-minus-low book-tomarket factor (HML) in a fourfactor model regression.
Based on investment record.
Stock Portfolio UMD Factor (Momentum) Exposure
The loading of the stock portfolio on the up-minus-down factor (UMD) in a four-factor model regression.
Based on investment record.
Financial Center Dummy
Options Dummy
Short Sale Dummy
Stock Portfolio Diversification
Stock Portfolio Size Stock Portfolio Performance
No December Tax Loss Selling Holds Tax-Deferred Account Stock Portfolio Market Factor (Beta) Exposure
Calculation
Based on self reported address.
Based on investment record. Based on investment record.
Based on investment record. Based on investment record.
6. Summary and conclusions Using thousands of brokerage accounts of US individual investors, we show that behavioral factors influence the decisions of individual investors to hold individual stocks as opposed to mutual funds, including passive index funds. As might be expected, investors with higher income, relatively higher educational level, and greater investment experience are more likely to use mutual funds and benefit from their choices. However, investors
Equals one if the investor is retired and zero otherwise. Years since the brokerage account was open. Equals one if the zip code of the investor’s address is close to a metropolitan area and zero otherwise. Equals one if the investor executes at least one option trade during the sample period and zero otherwise. Equals one if the investor executes at least one short trade during the sample period and zero otherwise. Negative of Normalized Portfolio Variance, that is, the variance of the portfolio of individual domestic securities divided by the average variance of the individual common stocks in the portfolio. Sample-period average market capitalization of the investor’s common stock portfolio. The intercept, alpha, from the Capital Asset Pricing Model regression with the monthly common stock portfolio return as dependent variable. 1– proportion of realized losses in December¼1 – (realized losses in December/number of paper losses) Equals one if the investor holds an Individual Retirement Account (IRA) or Keogh account in the brokerage. The loading of the stock portfolio on the market factor in a four-factor regression model with market, size, value, and momentum factors. All four factors come from Ken French’s website, (mba.tuck.dartmouth.edu/pages/faculty/ ken.french/). The loading of the stock portfolio on the size (SMB) factor in a four-factor regression model with market, size, value, and momentum factors. All four factors come from Ken French’s website. The loading of the stock portfolio on the value (HML) factor in a four-factor regression model with market, size, value, and momentum factors. All four factors come from Ken French’s website. The loading of the stock portfolio on the momentum (UMD) factor in a four-factor regression model with market, size, value, and momentum factors. All four factors come from Ken French’s website.
with strong behavioral biases tend to gravitate toward individual stocks and avoid low expense index funds. When they do invest in mutual funds, they tend to select high expense funds, trade funds frequently, avoid index funds, and time their buys and sells poorly, thereby damaging their portfolio’s performance. They also exhibit stronger trend-chasing behavior, suggesting that trend chasing by mutual fund investors is not the result of rationally inferring managerial skill from past performance.
W. Bailey et al. / Journal of Financial Economics 102 (2011) 1–27
25
Table A2 Univariate summary statistics on investor characteristics (21,542 observations). Variable
Mean
Standard deviation
Minimum
10th percentile
25th percentile
Median
75th percentile
90th percentile
Maximum
Disposition Effect Narrow Framing Overconfidence Dummy Male Dummy Local Bias Lottery Stocks Preference Inattention to Earnings News Inattention to Macroeconomic News Fund Level Local Bias Fund Level Inattention Age Income High Income Dummy Marital Status Family Size Professional Dummy Retired Dummy Investment Experience Financial Center Dummy Options Dummy Short Sale Dummy Stock Portfolio Diversification Stock Portfolio Size Ln(Stock Portfolio Size) Stock Portfolio Performance No December Tax Loss Selling Holds Tax-Deferred Account Market Factor Exposure SMB Factor Exposure HML Factor Exposure UMD Factor Exposure
3.719 0.010 0.090 0.898 0.273 12.025 0.057 0.301
112.197 0.155 0.287 0.282 0.395 17.206 0.061 0.143
100.00 0.683 0.000 0.000 1.323 0.000 0.000 0.000
100.00 0.207 0.000 0.899 0.204 0.000 0.000 0.133
11.111 0.081 0.000 1.000 0.058 0.000 0.000 0.214
12.609 0.038 0.000 1.000 0.272 4.265 0.048 0.292
66.667 0.131 0.000 1.000 0.542 18.510 0.087 0.375
100.000 0.181 0.000 1.000 0.773 33.644 0.133 0.476
100.000 0.440 1.000 1.000 0.996 100.000 0.500 1.000
0.000 0.303 50.429 89.358 0.241 0.736 2.814 0.610 0.166 9.809 0.327 0.124 0.138 0.422 36.410 2.797 0.378 0.818 0.490 1.196 0.853 0.182 0.331
0.703 0.107 11.537 60.381 0.427 0.386 1.417 0.336 0.256 3.190 0.469 0.330 0.345 0.135 98.119 1.159 1.460 0.386 0.500 0.557 1.028 0.838 0.667
1.249 0.000 18.000 7.500 0.000 0.000 1.000 0.000 0.000 5.255 0.000 0.000 0.000 0.966 0.001 7.082 11.474 0.000 0.000 1.911 2.163 3.258 3.898
0.854 0.250 36.000 35.000 0.000 0.000 1.000 0.000 0.000 5.880 0.000 0.000 0.000 0.598 4.255 1.448 2.111 0.000 0.000 0.555 0.268 0.797 1.182
0.468 0.304 42.000 62.500 0.000 0.736 2.000 0.610 0.000 6.915 0.000 0.000 0.000 0.514 7.824 2.057 1.116 1.000 0.000 0.850 0.098 0.359 0.704
0.97 0.304 52.000 87.500 0.000 1.000 3.000 1.000 0.000 9.630 0.000 0.000 0.000 0.422 15.326 2.729 0.278 1.000 0.000 1.157 0.675 0.119 0.267
0.394 0.304 56.000 112.500 0.000 1.000 4.000 1.000 0.166 12.019 1.000 0.000 0.000 0.323 32.277 3.474 0.468 1.000 1.000 1.521 1.410 0.647 0.089
1.015 0.333 68.000 250.000 1.000 1.000 5.000 1.000 0.166 13.964 1.000 1.000 1.000 0.245 71.899 4.275 1.253 1.000 1.000 1.895 2.257 1.269 0.410
4.171 1.000 94.000 250.000 1.000 1.000 10.000 1.000 1.000 22.373 1.000 1.000 1.000 0.000 4079.582 8.314 6.437 1.000 1.000 3.901 7.810 5.279 2.986
When we use factor analysis to characterize associations among investor characteristics, we find interesting and intuitive patterns along multiple dimensions of bias and other characteristics that often crop up in the same individual. There is consistency across the behavioral biases, other characteristics, use of individual stocks, use of mutual funds, and resultant performance that our Gambler, Smart, Overconfident, Narrow Framer, and Mature stereotypes display. Our evidence on behavioral biases and mutual fund clienteles provides a new perspective on puzzles in mutual fund investment presented by previous authors. Several authors trace the mutual fund decisions of individual investors to such factors as excess focus on frontend loads, advertising, search costs, and complexity of fund features intended to exploit consumers.30 Our evidence shows that investors who score high on behavioral biases tend to invest in funds with higher expense ratios and loads. They experience poor investment performance as a result. In his American Finance Association presidential address, Martin Gruber (1996) notes several puzzling
30 See Barber, Odean and Zheng (2005), Hortacsu and Syverson (2004), and Carlin (2008).
aspects of individual portfolio allocation decisions. He speaks of ‘‘sophisticated’’ investors who make decisions based on performance and ‘‘disadvantaged’’ investors who are susceptible to sales pressure or constrained by tax or institutional issues. In his presidential address, John Campbell (2006) suggests that naı¨ve investors could subsidize sophisticated investors in financial products such as mortgages. Our results echo the spirit of these ideas. A complex set of factors, some rational and some behavioral, appear to drive investors’ stocks versus funds decisions and their mutual fund choices after they decide to invest in mutual funds. Some types of investors appear to make effective choices that enhance portfolio performance, while others do not. Given the misuse of equity mutual funds, a public campaign to increase awareness of basic investment principles and the benefits and pitfalls of equity mutual funds is likely to help many types of individual investors make better decisions. Furthermore, the lack of attention to low cost or index funds suggests more explicit disclosure of fund expenses and turnover, perhaps even as prominent as the health warnings now displayed on packets of cigarettes. Finally, the reliance of mutual fund investors on broker-supplied information at the time a fund is selected and on delegated investment decisions afterward suggests that even more explicit disclosure of
26
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fund characteristics be imposed on brokerage firms and fund managers.
Appendix A Descriptions of behavioral proxies and other investor characteristics can be found in Tables A1. Summary statistics on investor characteristics can be found in Tables A2.
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Journal of Financial Economics 102 (2011) 28–44
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Payday lenders: Heroes or villains?$ Adair Morse Booth School of Business, University of Chicago, United States
a r t i c l e in f o
abstract
Article history: Received 23 September 2009 Received in revised form 19 August 2010 Accepted 7 September 2010 Available online 30 March 2011
Does access to high-interest credit (payday loans) exacerbate or mitigate individual financial distress. Using natural disasters as an exogenous shock, I apply a propensity score-matched, triple-difference specification to identify a causal relation between welfare and access to credit. California foreclosures increase by 4.5 units per 1,000 homes after a natural disaster. The existence of payday lenders mitigates 1.0–1.3 of them, with the caveat that not all payday loans are for emergency distress. Payday lenders also mitigate larcenies (but not burglaries or vehicle thefts). In a placebo test of disasters covered by homeowner insurance, payday lending has no mitigation effect. & 2011 Elsevier B.V. All rights reserved.
JEL classification: D14 G21 Keywords: Payday lending Access to credit Natural disasters Foreclosures Welfare
There is little debate that access to finance enhances value for firms.1 A similar consensus does not exist, however, as to whether access to consumer credit necessarily provides a benefit to households. If individuals have financial literacy shortcomings (Johnson, Kotlikoff, and Samuelson, 2001;
$ I greatly benefited from comments and suggestions during seminars at Berkeley, Columbia, Duke, the European University Institute, the FDIC, the Federal Reserve Bank of Cleveland, the Federal Reserve Bank of New York, Harvard Business School, MIT, New York University, Northwestern University, Ohio State University, UCLA, University of Chicago, University of Illinois, University of Maryland, University of Michigan, University of Southern California, Wharton, Yale, the WFA, and the European Summer Symposium in Financial Markets (Gerzensee). In addition, I would like to thank my committee E. Han Kim, Michael Barr, Fred Feinberg, Tyler Shumway, and Luigi Zingales as well as David Brophy, Alexander Dyck, Amiyatosh Purnanandam, and Amit Seru for their helpful comments. Tel.: þ1 773 834 1615. E-mail address:
[email protected] 1 See Jayaratne and Strahan (1996), Rajan and Zingales (1998), Levine and Demirguc-Kunt (2001), Dahiya, John, Puri, and Ramirez (2003), Guiso, Sapienza, and Zingales (2004), Cetorelli and Strahan (2006), and Paravisini (2008).
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.03.022
Stango and Zinman, 2011; Lusardi and Tufano, 2008) or engage in utility-destroying temptation consumption (O’Donoghue and Rabin, 2007), financial institutions might cater to these biases (Campbell, 2006), and access to finance could make borrowers worse off. In this paper, I study the personal welfare effects of access to distress finance for credit constrained individuals. The primary providers of distress finance for constrained households are payday lenders, who offer small, short-term advances intended to sustain individuals till the next payday. The fees charged in payday lending annualize to implied rates well over 400%. I examine whether these 400 þ% loans mitigate or exacerbate the effect of financial distress on individuals’ welfare as measured by foreclosures and small property crimes. How can small shocks lead to such drastic outcomes? Individuals frequently experience some sort of personal emergency (e.g., an out-of-pocket medical expense or car breakdown) leaving them without cash for their shortterm obligations. Without access to credit, these smallscale personal emergencies can lead to bounced checks, late fees, utility suspensions, repossessions, and, in some
A. Morse / Journal of Financial Economics 102 (2011) 28–44
cases, foreclosures, evictions, and bankruptcies. The United States works very much on a fee-based system for delinquencies, such that once low-margin individuals get into distress, they often end up in a cycle of debt. With up to 20% of U.S. residents financially constrained, the importance of knowing the welfare implications of payday lending is likely to be both timely and large. Fifteen percent of U.S. residents have borrowed from payday lenders in a market that now provides over $50 billion in loans each year.2 Despite (or because of) the growing demand, state and federal authorities are working toward regulating and curbing the supply of payday lending. Thus far, fifteen states prohibit payday lending. From one perspective, payday lenders should help distressed individuals bridge financial shortfalls by enabling them to smooth liquidity shocks, a welfareenhancing proposition. An opposite perspective is that payday lending destroys welfare. The availability of cash from payday loans might tempt individuals to overconsume. An individual who is likely to succumb to temptation might prefer the discipline of limited access to cash before temptation arises (Gul and Pesendorfer, 2001, 2004; O’Donoghue and Rabin, 2007; Fudenberg and Levine, 2006). A related argument is that because individuals might be naive about time-inconsistent preferences, they could spend with a bias toward the present moment (e.g., Jones, 1960; Thaler, 1990; Attanasio and Browning, 1995; Stephens, 2006) or be unable to save adequately (e.g., Thaler and Shefrin, 1981; Laibson, 1997; Laibson, Repetto, and Tobacman, 1998; Choi, Laibson, and Madrian, forthcoming). Cash (or access to cash) from payday lending might encourage either present-biased consumption or a lack of saving. In these views, payday lending can be welfare destroying.3 To determine whether payday lending exacerbates or mitigates the welfare effect of distress, I use natural disasters as a community-level natural experiment. I perform the analysis at the zip-code level for the State of California for the period 1996–2002. The difficulty in measuring how payday lending affects welfare over time lies in disentangling a causal payday lender effect from endogenous location decisions of lenders and from correlated community economic circumstances that cause welfare outcomes. To overcome the endogeneities, I set up a matched triple-difference framework. The matching aligns communities on the propensity of residents to be financially constrained prior to the natural experiment. I generate these propensities at the zip-code level by estimating the probability that an individual in the U.S. Federal Reserve’s Survey of Consumer Finances (SCF) is financially constrained as a function of socioeconomic characteristics. I then project the relation onto zip codes by applying the SCF coefficients to socioeconomic variables observed at the community level in the U.S. Census.
2 For a market overview, see Caskey (1994, 2005), Fannie Mae (2002), Barr (2004), and Bair (2005). 3 For temptation consumption, the argument of welfare destruction takes an ex ante lifetime consumption view, not a revealed preference one.
29
Matching alone does not solve the endogeneities of the lender location decision, but it does facilitate a counterfactual framework using a triple-difference (difference-indifference-in-differences) specification. The key exogeneity assumption is that the non-disaster communities provide an unbiased benchmark of how lender and nonlender communities would have differed in welfare growth had they not been hit by a disaster. Thus, by subtracting this benchmark from the observed lender minus non-lender welfare growth for disaster communities, I can difference away endogeneities associated with the observed existence of a lender in a location. The results indicate that payday lenders offer a positive service to individuals facing financial distress. Natural disasters increase foreclosures by 4.5 units per 1,000 homes in the year following the event, but payday lenders mitigate 1.0 to 1.3 units of this increase. In rate terms, natural disasters increase the rate of foreclosures per home from 0.972% to 1.5% in my sample of zip codes. (As a comparison, the 2009 foreclosure rate for California was 1.88% following the financial crisis.) Lenders mitigate 0.10–0.12% of the disaster-induced increase, after controlling for a number of different disaster resiliency stories. In a placebo test for natural disasters covered by homeowner insurance, I find no payday lending mitigation effect. The results also indicate that payday lenders alleviate individuals’ need to resort to small property crimes in times of financial distress. I find significant results, however, only for larceny (shoplifting), the crime that carries the lightest sentencing of all property crimes. My experimental design necessitates a caveat in how the results can be interpreted. Individuals can use payday loans in situations not caused by financial distress. In a survey of payday borrowers, Elliehausen and Lawrence (2001) report that 33% of loans are not for emergency needs. Some borrowers might habitually overconsume and use payday loans regularly to fill cash shortfalls. Skiba and Tobacman (2005) provide evidence consistent with the use of payday lending in such settings. The habitual overconsumers are those most likely to have negative welfare effects from temptation consumption. Because I do not identify the net benefit of payday lending across the distribution of borrowers, my results should be interpreted as payday lenders providing a valuable service to individuals facing unexpected financial distress (any type of unexpected financial distress) but do not speak to the effect on those habitually falling to temptation. In this sense, payday lenders can be both heroes and villains. A set of concurrent papers also addresses the welfare implications of payday borrowing. On the surface, the results are conflicting, with Morgan and Strain (2007) showing a welfare-improving role for lenders and Skiba and Tobacman (2007) and Melzer (forthcoming) showing a welfare-destroying role for lenders. However, I believe that these results suggest the pressing importance of understanding the heterogeneity of borrowers and the circumstances they might face (Bertrand and Morse, 2009), as well as the mistakes they might make (Brito and Hartley, 1995; Bernheim and Rangel, 2006; Skiba and Tobacman, 2009; Bertrand and Morse, forthcoming).
30
A. Morse / Journal of Financial Economics 102 (2011) 28–44
The remainder of the paper proceeds as follows. Section 1 offers an overview of the market for payday loans. Section 2 outlines the triple-differencing empirical methodology. Section 3 presents the intermediate propensity-score matching results. Section 4 describes the data sources and summary statistics. Section 5 presents the empirical results for foreclosures and crimes, and Section 6 concludes. 1. Payday lending market To take out a payday loan, an individual visits a payday lender with his or her most recent paycheck stub and bank statement. (The unbanked and unemployed do not qualify.) A typical loan is $350 with a fee of $50. For a $350 loan, the borrower writes a check (or authorizes a bank draw) for $400, post-dating it to the next payday, usually 10–14 days hence. The fee is posted on the wall as a dollar fee per $100 in loan. The implied annual interest rate is usually over 400%, which is disclosed at the closing of the transaction in the loan paperwork. The payday lender verifies the borrower’s employment and bank information, but does not run a formal credit check. On payday, if the individual is not able to cover the check, which happens more often than not, he or she returns to the payday store and refinances the loan, incurring another $50 fee, which is paid in cash. To put payday borrowing in context, one has to consider why borrowers do not seek cheaper forms of finance. Research covering the last three decades finds that up to 20% of U.S. residents are credit constrained (Hall and Mishkin, 1982; Hubbard and Judd, 1986; Zeldes, 1989; Jappelli, 1990; Gross and Souleles, 2002). When expense or income shocks arrive, banks and credit cards usually do not provide these constrained borrowers with distress loans. Default risk and transaction costs make these loans infeasible without lenders coming into conflict with usury laws or the threat of greater regulation. Individuals restricted in access to credit resort to borrowing from high-interest lenders. These fringe financial institutions are only sparsely studied in the finance literature (see Caskey, 1994, 2005), despite the fact that payday lenders issue an estimated $50 billion in loans per year (Los Angeles Times, December 24, 2008). Loans collateralized by car titles (title loans) and household assets (pawnshop loans) offer cheaper alternatives, but because these loans require clear ownership of valuable assets, the markets are much smaller. The main alternatives to payday lending for individuals in distress are bank overdraft loans and bounced checks. Bouncing checks (or overextending on debit cards) to buy a few days of float is still a very common way to borrow funds. Although the implied interest rate depends on the duration and the number of checks bounced, the cost of bouncing checks is usually close to that of taking out a payday loan. Bouncing checks also adds an implicit cost via a negative entry on one’s credit history, which does not happen with payday borrowing. Bank overdraft loans differ from bounced checks in that banks pre-agree to clear the overdraft check(s) for a fee. Overdraft loans are cheaper for the borrower than
bouncing checks since the borrower gains more time to repay the debt. Nevertheless, the overdraft fees can be quite high in annual percentage rate (APR) terms, especially if the checks overdrawn were for small face values. My sample largely predates the widespread availability of overdraft loans, especially for individuals with poor credit history and/or no direct deposit, to whom the bank is unlikely to offer overdraft loans. The upshot of this quick description of the market is that, for the majority of people in my sample, no obvious alterative to a payday loan exists. 2. Empirical methodology The goal of the analysis is to test the extent to which the existence of a lender mitigates or exacerbates the effect of financial distress on individual welfare. Although I later aggregate to (and estimate at) a community level, the story is one of individuals in distress. Thus, I start with a fairly general depiction of individual distress and welfare. Eq. (1) is an individual fixed-effects model of welfare in which financial distress (f, an indicator) linearly affects the change welfare, and the existence of a high-interest lender (L) can mitigate or exacerbate the situation:
Dt wizt ¼ giz þ a1 Lzt þ a2 fizt þ a3 Lzt fizt þ tt þ eizt
ð1Þ
where Dt wizt denotes the change in welfare for individual i in zip code z at time t, and Dt refers to a first differencing from t 1 to t. I refer to the change over time as welfare growth. The giz are the welfare growth fixed effects of individuals. Time dummy variables (tt ) remove any economy-wide fluctuations in welfare growth. Indicator variable Lzt is equal to one if the individual has access to a distress lender, where access is defined geographically at the community (zip code) level z.4 If Eq. (1) could be estimated, the estimates of primary interest, a^ 2 and a^ 3 , would capture the extent to which distress affects welfare growth and the extent to which access to a payday lender mitigates or exacerbates the distress effect, respectively. Three substantial problems exist with estimating Eq. (1). First, the variables necessary to measure welfare and financial distress are not available at the individual level. Second, the location of lenders is endogenous, potentially causing an ordinary least squares (OLS) estimate of a3 to be biased. Third, financial distress and welfare growth are simultaneously caused by the economic conditions of the community, also implying that OLS estimates of a2 and a3 are likely to be biased. Another problem is that the residuals can be serially correlated, but this problem can be handled with relatively more ease. In what follows, I do a couple of transformations on (1) and set up a counterfactual framework to difference away these concerns. I first break financial distress (fizt) into two types: pers personal-emergency distress (f izt ) and natural-disaster 4 Elliehausen and Lawrence’s (2001) survey evidence finds that individuals do not travel far to go to a lender. For densely populated areas, the next community might only be a short distance away; thus, in estimation, I drop densely populated areas.
A. Morse / Journal of Financial Economics 102 (2011) 28–44 dis
distress (f izt ). For example, a personal emergency occurs when the transmission in one’s car gives out, and one depends on the car to get to work but does not have the cash or credit to repair it. A natural-disaster distress example is when one’s car floods, leaving a large repair bill. Since it is possible for both types of distress to occur at the same time, the appropriate indicator-variable breakpers dis pers dis down is: fizt ¼f izt þf izt f izt f izt . A benefit from this dis decomposition is that f izt is unrelated to the location decision of the lender. One might be speculate that lenders chase disasters or prefer disaster-prone areas, but this is not empirically supported: the correlation between the occurrence of a disaster and the existence of a lender is 0.005. Lenders depend on the profits created by borrowers with personal-emergency needs, not those whose needs for finance only occur after extreme events. I next aggregate the model to the community (zip code) level and average over the community population nzt. The average number of personal-emergency distresses among community members is equivalent to the propensity of any individual in the community to be financially constrained due to personal emergencies, which I denote P zt pers by rzt , where rzt ð1=nzt Þ ni ¼ 1 fizt . Since natural disasters hit areas as opposed to individuals and since zip codes are fairly small areas, I treat the natural-disaster variable as a zip-code level observation dis (f zt ) rather than an individual-level variable. If zip codes are much larger in area than disasters, the cost of this aggregation is in biasing my tests toward finding no effects from the disasters. The benefit from the aggredis gation is that measures rzt and f zt are either estimatable dis (rzt ) or observable (f zt ) with a little work described in later sections. I am left with a potential estimating equation for which all data are available:
Dt Wzt ¼ gz þ a1 Lzt þ a2 ðrzt þfztdis rzt fztdis Þ þ a3 Lzt ðrzt þ fztdis rzt fztdis Þ þ tt þ ezt , ð2Þ Pnzt Pnzt where Dt Wzt i ¼ 1 Dt wizt =nzt and ezt i ¼ 1 eizt =nzt . The fixed effect gz is now the mean community welfare growth absent lenders and distress. In the empirical section, I refer to ðrzt þfztdis rzt fztdis Þ as the variable Distresszt, and thus Eq. (2) can be written:
Dt Wzt ¼ gz þ a1 Lzt þ a2 Distresszt þ a3 Lzt Distresszt þ tt þ ezt : ð2aÞ 2.1. Counterfactual framework The distress decomposition and aggregation to the community level do not solve the problems of lender location endogeneity and omitted-variable bias inherent in Eq. (1). However, Eq. (2) does facilitate a counterfactual framework to solve these problems using a matching and differencing approach. A counterfactual framework, originating in the statistics and program evaluation studies of Neyman (1923) and Rubin (1974), is an experimental treatment design in which the treatment effect is assessed against an estimation of the counterfactual had the individual not been subject to the treatment. Framed this
31
way, the basic idea of my identification strategy is that I can use the difference in welfare growth for lender communities compared to non-lender communities in areas not hit by a disaster as a matched benchmark for what the lender-versus-non-lender welfare differential in a disaster area would have been had no disaster occurred. To illustrate how the counterfactual setup works, I first need some labels. I denote by treat (for treated) the communities that have been or will be hit by a natural disaster, and by cntrl (for control) those not ever affected by a natural disaster. I mark communities that have access to a lender with a subscript L, and those with no access with N. For each control community with access to a lender, imagine choosing another control community with no lender, with the pair matched in time and on the propensity of the residents to be in personal-emergency distress. Focusing on one particular pair of communities with no natural disaster, suppose rcntrl ¼ rcntrl Lt Nt rt . Differencing the matched pair using Eq. (2) gives a difference-in-differences (DID) estimator of the difference in welfare growth for lender versus non-lender areas for these control communities: cntrl cntrl cntrl ½Dt WLt Dt WNt jrt ¼ gcntrl gcntrl þ a1 þ a3 rt þ ecntrl L N Lt eNt :
ð3Þ The left-hand side is the difference in welfare growth from t 1 to t between the community with a lender and the community with no lender, with communities matched on rt and in time. The equation says that this difference is equal to gcntrl gcntrl (the difference in the L N community fixed effects) plus a1 (the parameter measuring the welfare increase or decrease associated with being in a community with a lender) plus a3 rt (the welfare growth increase or decrease associated with the existence of a lender for those facing personal distress) plus the difference in error terms. An important feature to note in Eq. (3) is that the parameters remain associative in nature. The difference in welfare growth of communities with lenders as compared to those without could well be due to endogenous location decisions of lenders and other economic trends correlated with the existence of lenders in a community. The same matching exercise for a set of treatment communities yields a DID estimator: treat treat treat ½Dt WLt Dt WNt jrt ¼ gtreat gtreat þ a1 þ a3 þ etreat L N Lt eNt :
ð4Þ As in the control case, I cannot interpret this DID estimator causally. Welfare growth could differ in locations with payday lenders compared to locations without lenders, for reasons unrelated to any financial distress caused by disasters. This does not rule out the possibility that the welfare reaction to disaster distress could be causally affected by access to a lender, but the DID estimate in Eq. (4) would capture both the endogenous and the causal effect of having a lender in the community. The key identification insight is, however, that the control group in Eq. (3) is the counterfactual for how the lender and non-lender communities would have differed in welfare
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A. Morse / Journal of Financial Economics 102 (2011) 28–44
growth had there been no natural disaster. A final differencing subtracts the DID estimate of Eq. (3) from the DID estimate of Eq. (4). After averaging m¼1,y,M matches of four communities at a point in time, the resulting triple difference of welfare growth DDD is
DDD
M 1 X treat treat cntrl cntrl ½ðDt WmL Dt WmN ÞðDt WmL Dt WmN Þjrm Mm¼1
¼ a3 ð1r Þ,
ð5Þ PM
where r ¼ ð1=MÞ i ¼ 1 rm is the average propensity to be credit constrained across all sets of matches M, and P PM treat treat cntrl cntrl ð1=MÞ M i ¼ 1 em ¼ ð1=MÞ i ¼ 1 ½ðemL emN ÞðemL emN Þ C 0, which I defend in the next section. The community fixed cntrl effects ðgtreat gtreat gcntrl L N ÞðgL N Þ will cancel out if disasters hit randomly and as long as the sample is sufficiently large. Also, as long as I choose a disaster and non-disaster match at the same time, the time dummies drop out. I include time dummies in my estimation in case there are any residual concerns about time effects. The essence of the counterfactual framework is that although the lender locations are probably endogenous with respect to welfare growth, these endogeneities exist in the same way for matched disaster and non-disaster communities and can be differenced out during estimation. All that is left after the triple differencing is the impact of lenders mitigating or exacerbating distress following a disaster, a3 , multiplied by the proportion of individuals not already in distress on average across the M sets of matched communities, ð1r Þ. 2.2. Regression framework How is DDD ¼ a3 ð1r Þ estimated? An estimating equation similar to Eq. (2) provides the answer:
Dt Wzt ¼ a0 þ a1 Lzt þ a2 Distresszt þ a3 Lzt Distresszt þ ezt :
ð6Þ
The only things new are that the community fixed effects are omitted, because I estimate a collapsed equation with only one observation of Dt Wzt per zip code in the time dimension and the data are limited to the matched sets of communities. I collapse each zip code to one observation, to handle the serial correlation discussed in Bertrand, Duflo, and Mullainathan (2004) by taking the average of the welfare variable in the four quarters after the event and subtracting out the average of four quarters before the event. We can now consider the properties of the OLS estimator. The vector of right-hand side variables xz (including the constant) for observation z is [1, Lzt, Distresszt, Lzt Distresszt]. For simplicity, consider a matched, four-observation dataset, all with the same r. The first two observations are from the control group and the latter two are from the treated group. Observations 2 and 4 have a lender in the community. The four observations imply a Y vector and an X matrix of 2 3 2 0 3 2 3 xcntrl,N,t Dt WNcntrl 1 0 r 0 6 7 6 x0 7 6 cntrl 6 Dt WL 7 6 cntrl,L,t 7 6 1 1 r r 7 7 7 6 7 Y ¼6 7: 6 Dt W treat 7, X ¼ 6 x0treat,N,t 7 ¼ 6 4 5 4 5 41 0 1 05 N 0 treat xtreat,L,t Dt WL 1 1 1 1
The OLS vector of estimates is a^ ¼ ðX 0 XÞ1 X 0 Y. Solving for a^ 3 using the matrices above leads to a^ 3 ¼ ð1=ð1rÞÞ ½ðDt WLtreat Dt WNtreat ÞðDt WLcntrl Dt WNcntrl Þ. Rearranging and averaging over all M sets of four community matches brings us back to DDD ¼ a^ 3 ð1r Þ. This demonstrates that an OLS estimate of Eq. (6) gives the triple-differencing solution. It is now easy to show what is required for the estimate to be unbiased, i.e., for EðejXÞ ¼ 0. Using the X matrix above, a3 will be an unbiased estimator if ð1=ð1rÞÞ½ðetreat etreat Þðecntrl L N L ecntrl Þ ¼ 0, or in terms of all possible matches N M 1 X 1 cntrl cntrl ½ðetreat etreat N,m ÞðeL,m eN,m Þ ¼ 0: M m ¼ 1 1rm L,m
ð7Þ
What this relies on is that any endogeneities between the lender location and the error term are same for disaster PM PM treat and non-disaster areas, or ðetreat m ¼ 1P m¼1 L,m eN,m Þ ¼ M cntrl cntrl cntrl cntrl ðeL,m eN,m Þ, which holds even if m ¼ 1 ðeL,m eN,m Þa0 PM cntrl cntrl and even if m ¼ 1 ðeL,m eN,m Þ correlates with the existence of a lender, Lz. If so, the estimates a^2 and a^3 causally measure the effect of distress on welfare and the extent to which financial distress is mitigated or exacerbated by the existence of a lender. The properties in a standard difference-in-differences setup for this to be true are now fairly innocuous: there must be a sufficiently large sample of zip codes, and natural disasters must hit randomly. 2.3. Possible disaster omitted variables and other robustness The matched triple-difference framework leaves one possible dimension in which an omitted variable might remain. An argument might be made that reactions to a disaster differ across communities only in the case of a natural disaster in a way that could be correlated with the existence of a lender. For this to be a problem, it must be that this reaction is specific to disasters as opposed to personal emergencies. Three potential stories help to illustrate this argument, which I call disaster resiliency. The first story is that lenders locate in communities with more (or less) adhesive community or family ties that provide support during disasters. This support during disasters would have to be different from the support during personal financial distresses, such as helping family or neighbors cope with health expenses or job losses. This story seems unlikely. The other two stories emerge from the possibility that lenders locate in communities in which the commercial activity is up-and-coming rather than declining, and this characteristic of the community only differentiates a community during a natural disaster relative to its personal-emergency-matched community. Both stories build on the intuition that since payday lenders’ largest expense is default and since default occurs more frequently in areas where people become unemployed, payday lenders prefer up-and-coming areas, all else equal. The first of these stories concerns the effect of the disaster on property damage directly. Suppose that in upand-coming communities, land quickly becomes valuable.
A. Morse / Journal of Financial Economics 102 (2011) 28–44
While people investing in existing properties upgrade the structures over time, this does not happen as rapidly as land price increases in desirable locations. This would imply that disasters affect the up-and-coming areas less, all else equal, because disasters presumably affect structures more than they affect land value.5 The other up-and-coming story concerns the type of economy that the community is. Suppose two communities have the same propensity to be financially constrained, but a lender chooses to locate in the one with a vibrant service sector rather than the one with a declining manufacturing sector. When a natural disaster strikes, the service sector might retrench quickly, whereas a manufacturing sector in decline might just face an accelerated demise. To take the omitted-variable concern of these stories seriously, I implement two further steps in my specification. First, I construct multiple controls for the damage caused by the disaster, controlling both for the property damage of each disaster and for the damage to commercial activity in the communities. Second, I allow for a differential effect of disasters on lagged building permit values (to address story two) and the extent of the service orientation of the community (to address story three). I discuss these variables in more detail in the results section. In addition to the concern about resiliency, the formulation requires that the predicted welfare impact from a natural disaster is higher for communities with lower initial levels of personal emergencies. To see this, image that I estimate a coefficient a^2 . The predicted impact of a disaster for a non-lender community with a low propensity to be credit constrained, a^2 ð1rLOW Þ, will be higher than that for one with a high propensity, a^2 ð1rHIGH Þ, because more people in high personal-emergency areas were already in distress. Realistically, we would expect people in poorer areas to be more vulnerable to naturaldisaster distress, not less. However, this is not going to be much of a concern for interpreting my results since the vast majority of the variation in Distress comes from whether or not a disaster occurs (the standard deviation around r is much smaller than around fdis), implying that the differential in effect between areas with high and low r is very small. Nevertheless, I show the robustness of my results to a standard difference-in-differences estimation around the natural disaster itself rather than around the Distress variable, i.e.,
Dt Wzt ¼ gz þ b1 Lzt þ b2 fztdis þ b3 Lzt fztdis þ tt þ ezt :
ð8Þ
3. Matching The methodology section called for a matching of zip codes on r, the propensity of individuals in a community to be financially constrained. Databases such as the Survey of Consumer Finances contain a number of 5
I thank an anonymous referee for this suggestion.
33
measures that identify individuals who are constrained financially. However, even if geographic identifiers were available for the SCF, the observation counts are insufficient to be representative of individual communities. Thus, I estimate the relation between individuals’ socioeconomic attributes and their probability of being financially constrained using the SCF and then project the relation onto the same socioeconomic information available at the zip-code level from the U.S. Census. This section describes the procedure and estimation. I use three measures of financial constraints for the 4,300 individuals in the 1998 SCF. I use the 1998 SCF because it is the center of my 1996–2002 time period. AtLimit is an indicator variable equal to one if the individual’s outstanding credit-card balance is within $1,000 of the card limit, if the individual has credit-card debt. Approximately 9% of respondents are within $1,000 of their credit limits, with a standard deviation of 0.287. HiDebt is equal to one if the individual’s credit-card debt is equal to more than 10% of yearly income. Twenty-eight percent of the sample have high debt, with a standard deviation of 0.451. The final measure, BehindPayments, is equal to one if the individual responds affirmatively to a question about being behind on any payments. Twelve percent of individuals are behind, with a standard deviation of 0.334. To project the relation between these measures and individual socioeconomic characteristics onto zip codes, I follow Jappelli (1990) and Calem and Mester (1995), employing the set of their explanatory variables also available in the U.S. Census files—wealth, income, age, education, marital status, race, sex, family size, home and car ownership, and shelter costs. Table 1 presents the logistic estimation of the probability of being financially constrained on these socioeconomic variables. The logistic estimates predict correctly whether an individual is financially constrained 89% of the time. I only briefly highlight some of the coefficients and refer interested readers to Jappelli (1990) and Calem and Mester (1995). The coefficients in Table 1 should be interpreted as ‘‘compared to a wealthy, well educated, single male senior.’’ For all three dependent variables, the probability of being financially constrained is highest in the $15,000– 45,000 range. Survey data in Elliehausen and Lawrence (2001) finds that individuals in the $25,000–$50,000 income range account for more than half of payday borrowers, suggesting that I am identifying a relevant profile of individuals. Constraints generally decline with age, after peaking somewhere between 18 and 34. Non-white persons and those with vehicles face more constraints. The other results vary by which dependent-variable measure of financial constraints is used. Of these, education is particularly interesting. Education has very little explanatory power once income is included except in the BehindPayments specification, in which those reaching but not finishing high school are most constrained. I take the coefficients and project the linear relation onto U.S. Census data for 1,762 California zip codes by multiplying each coefficient by the percentage of residents having that characteristic in a zip code and
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A. Morse / Journal of Financial Economics 102 (2011) 28–44
Table 1 Survey of consumer finance estimations of financial constraints. The first column presents the average across zip codes of the proportion of population (or households) in each category. For example, the first line shows that 21.5% percent of residents have an income of less than $15,000. The last three columns present the logistic estimation results for the dependent variables at credit card limit, high debt/income, and behind on payments. Standard errors are not presented in the interest of space. nnn, nn, and n denote significance at the 1%, 5%, and 10% levels.
$0 r Household incomeo $15,000 $15,000 r Household income o $30,000 $30,000 r Household income o $45,000 $45,000 r Household income o $60,000 $60,000 r Household income o $75,000 $75,000 r Household income o $100,000 $100,000 r Household income o $125,000 $125,000 r Household incomeo $150,000 $150,000 r Household income Unemployed Persons 12 r Persons’ Age r 17 18 r Persons’ Age r 24 25 r Persons’ Age r 34 35 r Persons’ Age r 44 45 r Persons’ Age r 54 55 r Persons’ Age r 64 65 r Persons’ Age r 74 75 r Persons’ Age Educated 0–8 years Educated 9–12 years, no degree High School Graduate Attended Some College Associate Degree Bachelors Degree Graduate Degree Homeowning Households $0 r Shelter Costs o $300 $300r Shelter Costso $500 $500r Shelter Costso $750 $750 r Shelter Costso $1,000 $1,000 r Shelter Costs Owns 1þ Vehicles Female Persons Non-white Persons Person per Household ¼ 1 Person per Household ¼ 2 3 r Person per Household r 5 Person per Household Z 6 Married Persons Observations in SCF Pseudo R-Square
Census: Proportion in Zip Code
SCF Logit: At Credit Card Limit
SCF Logit: High Debt/Income
SCF Logit: Behind on Payments
0.215 0.162 0.274 0.132 0.082 0.066 0.031 0.013 0.026 0.082 0.093 0.122 0.218 0.195 0.127 0.101 0.089 0.056 0.110 0.134 0.236 0.225 0.075 0.142 0.077 0.204 0.279 0.173 0.185 0.129 0.234 0.922 0.470 0.158 0.234 0.318 0.390 0.058 0.220
2.183nnn 2.454nnn 2.472nnn 2.240nnn 2.111nnn 1.778nnn 1.805nnn 0.982 – 0.094 – 2.025nnn 1.869nnn 1.498nnn 1.588nnn 1.257nnn 0.801n – 0.199 0.205 0.304 0.326 0.083 0.128 – 0.080 0.053 0.262 0.273 0.207 – 0.354n 0.182 0.379nnn – 0.122 0.135 0.417 0.130 4,305 0.104
1.507nnn 1.978nnn 1.948nnn 2.059nnn 2.047nnn 1.594nnn 1.782nnn 0.922nnn – 0.197 – 1.703nnn 1.791nnn 1.705nnn 1.647nnn 1.280nnn 0.805nnn – 0.218 0.015 0.282nn 0.542nnn 0.583nnn 0.187 – 0.218nn 0.533nnn 0.094 0.210 0.125 – 0.828nnn 0.341nnn 0.112 – 0.016 0.087 0.005 0.334nnn 4,305 0.150
1.158nnn 1.267nnn 1.263nnn 0.782nnn 0.730nnn 0.527n 0.879nnn 0.616 – 0.048 – 1.080nnn 1.627nnn 1.646nnn 1.666nnn 1.309nnn 0.406 – 0.182 0.418nn 0.035 0.240 0.169 0.037 – 0.313nn 0.308n 0.450nn 0.555nnn 0.461nn – 0.244 0.108 0.229n – 0.056 0.291nn 0.072 0.104 4,305 0.096
summing. I do this for each of the three measures of financially constraint and for each of the U.S. Census data years 1990, 1997 (an update containing most socioeconomic variables), and 2000. I interpolate the in-between years to avoid jumps in my projections over time. Each of the three measures might capture an important part of being constrained. In the end, I would like a single measure that captures features of each. For simplicity and because I do not want to impose subjective assumptions, I rescale the predicted variables to have equal means, which I fix to be equal to 0.10 for ease of exposition. I then take an average of the three measures for each zip code. As a check that I am not losing too much information by creating this index, I examine the principal components of the three variables. The first principal component captures 80% of the variability of the three
measures (with an eigenvalue of 2.4). The factor loading weights are almost equal across the three measures, and the factor score is correlated over 0.95 with my equalweighted index. With propensity scores in hand, I am ready to take the nearest neighbor match. Because my foreclosure and crime data are not equivalent in the coverage of zip codes and years (only a subset of counties report for each), I do a different matching for crime and foreclosures. Although my methodology section suggests that I should do a four-way match (disaster/not and lender/not) all at once, I have to deal with the fact that my pool of disasters is small relative to the pool of non-disaster communities. Thus, for communities that are hit by disasters I choose a matched-propensity community from the pool of non-disaster communities, on the basis of access to a lender or not within a common support. When a
A. Morse / Journal of Financial Economics 102 (2011) 28–44
control-group observation is chosen multiple times, I weight the observation accordingly. I run a chi-square test to see if the mean propensities of residents to be credit constrained are equal for all four sets of communities. The Bonferroniadjusted p-value of 0.438 cannot reject that the propensities are all the same. 4. Data and summary statistics I limit the analysis to the State of California to make use of panel micro-data available for payday lenders and welfare variables and to isolate the analysis in a single regulatory environment. I drop the big-city counties to focus on areas where crossing zip-code lines is not done as a course of everyday business and areas where my crime data are more precise (as described below). In particular, I throw out 11 large-city counties (out of a total of 58) with a population of over 800,000 people. I choose this threshold to drop all counties with populations equal to or greater than that of San Francisco County.6 The time period of the analysis is 1996–2002. 4.1. Natural-disaster data Natural-disaster data come from the University of South Carolina’s SHELDUS (Spatial Hazard and Loss Database for the United States), which provides the location (by county), type (flood, wildfire, etc.), and magnitude (property damage) of natural disasters. Although disaster observations are at a county level, the comment field in SHELDUS contains more detailed location information, most often in the form of city names or NOAA (National Oceanic and Atmospheric Administration) codes that identify the specific local area hit by the disaster. For each line item, I manually attribute the disaster to the smallest area provided and then use a GIS (geographic information system) program to overlay the disasters to zipcode affiliations. The Hazard database contains all natural disasters that cause more than $50,000 in property damage. Table 2, Panel A, shows statistics for the 1,568 disasters in the sample period 1997–2002 for which I have all data and am able to successfully match. The average zip code incurs $12.6 million in property damage, with the median being only $391,000. (Note that if a disaster affects more than one zip code, the property damage is divided according to population.) I include a breakdown of the disaster statistics according to the insurance coverage available and utilized in California.7 The category of earthquakes, floods, and landslides represents the largest number of communities affected (787) and the most damage ($24 million per disaster on average). These types of disasters are almost never covered by insurance, especially for the profile of 6 The dropped counties are Los Angeles, San Diego, Orange, Riverside, San Bernardino, Santa Clara, Alameda, Sacramento, Contra Costa, Fresno, Ventura, and San Francisco. 7 The breakdown of disasters that are effectively covered in California comes from a series of interviews with insurers from the Insurance Information Network of California, Milliman Agency, and walletpop.com/blog/category/insurance-home, all referenced as of 2/ 2010.
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individuals borrowing from payday lenders. Storms, wildfires, and coastal damage are often included in homeowner insurance, but the coverage is usually insufficient. Finally, my sample includes 350 communities hit by hail, lightning, tornadoes, or wind; these are smaller-impact natural-disaster categories that are covered by standard homeowner insurance. I expect that any disaster effects should be lower for this final category. 4.2. Payday lender data The State of California Senate Bill 1959 legalized payday lending in 1996 and placed its licensing and regulation under the authority of the California Department of Corporations. The Department has license information for each payday store, with an original license date and date of suspension, if applicable, for each active and non-active lender. The categories containing the payday licenses during this time (California Finance Lenders and Consumer Finance Lenders) also contain other types of lenders, such as insurance companies, auto loan companies, and realty lenders, which I am able to filter out. What I am unable to fully remove are check cashiers with a license to lend who make only title loans or non-payday small consumer loans. However, my data tabulate to 2,160 payday stores in 2002, representing one lender for every 16,000 people in the state. This figure is almost exactly in line with the California figure cited in Stegman and Faris (2003) and the data obtained from the attorney general by Graves and Peterson (2005). Table 2 presents the community-level summary statistics for payday lenders. The first row in Panel B shows that mean (median) number of payday lenders per zip code is 2.00 (1.00). The empirical design is based on the yes/no question of whether payday lenders exist in the zip code, which is equivalent to being above or below median. Fig. 1 depicts the mapping of payday locations to the zip codes for 2002, together with the propensities of communities to be credit constrained. The larger the dots on the zip code, the greater is the density of lenders. The minimum-size dot indicates that no lenders are in the zip code. The zip-code shadings reflect the credit-constrained propensities; the higher the propensity to be credit constrained, the darker is the color. Because zip codes have varying sizes and densities of commercial activity, I use a second set of measures of payday loans for robustness. I construct the number of lenders within a radius of 10 or 20 miles from the center of the zip code using the GIS plotting of payday stores. As Table 2 presents, these are much larger numbers, with a mean (median) number of lenders of 72.6 (37.5) within 10 miles and 215.9 (101.5) within 20 miles. In the estimation, I use the log of these variables to offer a (non-skewed) continuous measure of payday density. 4.3. Welfare data For foreclosures to be a measure of welfare, individuals’ utilities must decline when their homes are foreclosed. Admittedly, having one’s house foreclosed can be efficient in some circumstances, even taking into account the large transaction costs involved. A general rule is that a foreclosure
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A. Morse / Journal of Financial Economics 102 (2011) 28–44
Table 2 Disaster, payday and welfare summary statistics. Panel A: Natural Disaster Property Damage Statistics (in $1,000s)
Earthquakes, Floods, Landslides (No Insurance Usually) Storms, Wildfires, Coastal Damage (Insufficient Insurance on Average) Hail, Lightning, Tornados, Wind (Insured Usually in Homeowners’ Policy) All Disasters in Sample
Mean
St. Dev.
Minimum
Median
Maximum
Count
24,227
86,721
50
1,600
719,300
787
1,303
3,863
50
215
66,900
431
169
138
50
164
550
350
12,556
62,600
50
391
719,300
1,568
Mean
St. Dev.
Minimum
Median
Maximum
Count
2.00 72.60 215.9 3.10 4.30 10.52 2.43 0.65 60.8 1.93 11.14 0.75 20.4 0.77
3.92 87.22 251.8 1.93 1.86 15.52 5.59 1.71 172.9 44.7 31.7 9.18 50.9 17.8
0 0 0 0 0 0 0 5.72 0 340.2 0 63.4 0 125.3
1.00 37.5 101.5 3.65 4.63 5.00 1.38 0.49 16.6 0.01 2.42 0 6.90 0.05
44 364 914 5.90 6.82 243 171.6 3.71 1857 312.7 360.8 61.9 489.3 128.2
2,306 2,278 2,278 2,278 2,278 2,306 2,306 2,306 767 767 767 767 767 767
Panel B: Lender and Welfare Variable Statistics
Payday Lenders in Zip Code Payday Lenders within 10 Miles Payday Lenders within 20 Miles (Log) Lender 10 Miles (Log) Lender 20 Miles Foreclosures (Quarterly) Foreclosure Rate (/1,000 Owned Homes) Change in Foreclosure Rate (Pre-to-Post) Larcenies per Household (Yearly) Change in Larcenies per Household Vehicle Thefts per Household (Yearly) Change in Vehicle Thefts per Household Burglaries per Household (Yearly) Change in Burglaries per Household
Notes: 1. All variables are at the zip code level for 1996–2002. 2. Natural disasters data are from the University of South Carolina’s SHELDUS Hazard database, which identifies the location, type, and magnitude of natural disasters. 3. Yearly data on payday lending are from the State of California Department of Corporations. Payday Lenders is an indicator variable. Payday Lenders within 10 (20) Miles is the count of lenders within this distance from the center of the zip code. Log Lender 10 (20) miles is the log of this count þ 1. 4. Foreclosure counts are from the California Association of Realtors. 5. Yearly crime data are from the State of California Criminal Justice Statistics Center. 6. Population and number of owned housing units (to normalize crime and foreclosures, respectively) are from the U.S. Bureau of the Census for the 1990 or 2000 Census or the 1997 Update, depending on the year in question.
is inefficient if the present value of the homeowner’s income is sufficient to cover the present value of consumption, including housing consumption, but the homeowner lacks access to credit to smooth consumption using future income as collateral. In my empirical design, the matched triple differences subtract out the general pattern of foreclosures for similar communities (with the non-disaster areas) and the effect of disasters on foreclosures (with the disaster, nonlender communities), thus isolating only financial-distressforcing foreclosures. I use quarterly residential foreclosures in a zip code recorded by the California Association of Realtors, available at RAND Statistics, for each quarter over the period 1996–2002. Per my methodology, the dependent variable is changes in foreclosure rates. To get to rates, I divide foreclosures by the total number of owner-occupied dwellings in a zip-code community available from the U.S. Census. Table 2, panel B, reports that, in the matched sample used in the estimations, foreclosures range from zero to 243 per quarter per zip code, with a mean (median) of 10.5 (5). This translates to a mean rate of
2.43 foreclosures per thousand owner-occupied housing units. To get changes in these rates, I subtract the average of the four quarters prior to the natural disaster from the average of quarters 4 to 7 after the disaster. I leave three quarters to allow for the average processing time of a foreclosure in the State of California. I winsorize the changes in foreclosure rates to the middle 95 percentile density. I do this because the estimated coefficients are anticonservative with respect to the outliers. All significance and signs remain the same. The mean changes in foreclosures is negative, suggesting that foreclosures were declining in California at a rate of half a foreclosure for every 1,000 homes over a two-year period. The second measure of welfare is small property crimes, following Garmaise and Moskowitz (2006). California crime data are from the State of California Criminal Justice Statistics Center made available through RAND Statistics for the period 1996–2002 for each police jurisdiction. Since a police jurisdiction might be a county, city, town, or local authority (e.g., a university or railroad police force), I need to allocate crime to zip codes in a
A. Morse / Journal of Financial Economics 102 (2011) 28–44
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Fig. 1. California payday lending locations and propensities to be credit constrained by zip code. The dots indicate the density of payday lenders in each zip code for 2002; larger dots indicate a higher quartile of payday lender counts. The minimum size dot indicates that no lenders are in the zip code. The blocks shown are the 2001 zip code delineation from the postal service. The darker the shading on the zip code, the higher is the propensity to be credit constrained according to the matching methodology projections. The few zip codes with entirely white shading are those altered by the post office during the sample or those of natural parks. These are not included in the analysis.
meaningful way. I manually identify all zip codes covered by the police jurisdiction and allocate crimes by population weight within the covered zip codes. I then aggregate the crimes committed in a zip code across all police forces. This method is admittedly not perfect. The biggest bias would be in Los Angeles, because I allocate all crimes caught by the Los Angeles county and city police forces to the zip codes within Los Angeles based on population. I throw out these big-city counties. The problem is least severe for small towns, where the local police force is well defined within a zip code. Among possible crime measures, I focus on small property crimes—larcenies (non-forceful theft, e.g., shoplifting), vehicle thefts, and burglaries because they are non-violent, and the link between relieving financial distress and criminal action is most direct. Since the intensity of the crime is, according to sentencing standards, monotonically increasing from larceny to vehicle theft to burglary, I can study the degree to which individuals use crime to relieve financial distress. Table 2 reports that the mean larcenies, vehicle thefts, and burglaries per household are 60.8, 11.14 and 20.4, respectively, in the matched sample. The summary statistics are winsorized, removing only 0.5% of the sample on each end, outliers which act anticonservatively in estimation.
5. Results 5.1. Baseline foreclosure results Table 3 reports the baseline foreclosure results. The dependent variable is the change in the quarterly rate of foreclosures by zip code, where change is defined to be the average foreclosure rate in quarters 4–7 after the disaster (aligned for the matched group) minus the average foreclosure rate in the 4 months prior to the disaster. I use a single collapsed observation for a zip code to eliminate the serial correlation concerns in differencing specifications highlighted by Bertrand, Duflo, and Mullainathan (2004). In the first column of Table 3, Distress, defined as ðrzt þ fztdis rzt fztdis Þ, is positive and significant; distress causes 1.228 more foreclosures per 1,000 homes. DistressLender is strongly significant with a coefficient of 0.503. Column 2 shows that the coefficients on Disaster and DisasterLender are equivalent (up to the transformation) to those on Distress; I present the rest of the results using the Disaster variable because of the greater ease in interpreting the natural-disaster effect, and because using Disaster rather than Distress does not have the odd implication that disaster increases distress more in wealthy communities than in poor ones. In
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A. Morse / Journal of Financial Economics 102 (2011) 28–44
Table 3 Baseline lender effect on foreclosures after disasters.
Lender Distress LendernDistress
1
2
0.164 [0.156] 1.228nnn [0.155] 0.503nnn [0.186]
0.110 [0.139]
1.104nnn [0.138] 0.450nnn [0.166]
Disaster LendernDisaster Lenders 10 Miles
3
4
1.315nnn [0.239]
1.302nnn [0.324]
0.067 [0.049] 0.135nn [0.056]
Lenders 10 MilesnDisaster Lenders 20 Miles Lenders 20 MilesnDisaster Constant Observations R-squared
1.612nnn [0.152] 2,306 0.097
1.481nnn [0.143] 2,306 0.098
1.691nnn [0.239] 2,278 0.099
0.041 [0.052] 0.099 [0.061] 1.631nnn [0.303] 2,278 0.097
Notes: 1. The dependent variable is the change in quarterly foreclosures per owner-occupied home around the natural disaster or its match in time, where the pre-period is the four quarters before the event and the post period is quarters 4–7 after the disaster. 2. The analysis is quarterly at the zip-code level, with only one observation per disaster zip code (and its match). 3. Distress is equal to ðr þ f dis rf dis Þ, where r is the propensity of the community to be financially constrained and f dis indicates a natural disaster. Disaster¼ f dis. 4. The independent variable Lender is an indicator for a lender in the community. The dependent variables Lender10 Miles and Lender20 Miles are the log of the count of payday lenders within 10 or 20 miles from the center of the zip code. 5. Year dummy variables are included but not shown. nnn, nn, and n denote significance at the 1%, 5%, and 10% levels. Robust standard errors are reported in brackets.
Column 2, a natural disaster causes 1.1 more foreclosures per quarter (up from a baseline of 2.43) or 4.4 more foreclosures per year. How does this disaster effect compare to the literature on disasters? Murdoch, Singh, and Thayer (1993) and Bin and Polasky (2004) study housing values following the Loma Prieta earthquake and Hurricane Floyd, finding that the natural disaster reduced home values by 10% and 5.8%, respectively. More directly, Anderson and Weinrobe (1986) find that the 1971 San Fernando earthquake caused 31 more defaults from 372 afflicted houses than would have been predicted without an earthquake. This is a huge effect; 9% of afflicted homes defaulted. In zip-code terms, if there were an average of 4,328 owner-occupied homes per zip code; Anderson and Weinrobe’s coefficient would be 7.16 more foreclosures per 1,000 homes. My natural-disaster effect looks somewhat small (4.4 versus 7.16) in comparison, but my natural disasters are much smaller on average than the San Fernando earthquake, which inflicted $553 million in property damage according to the authors. Returning to the question of disaster mitigation, Column 2 suggests that communities with lenders experience an overall increase in foreclosures after disasters but much less so (only 1.1 0.45¼0.65 more foreclosures) compared to matched communities experiencing disasters without access to a lender. In Column 3, the continuous variable (log of) Lenders 10 Miles also has
explanatory power, mitigating the effect of disasters. The mitigation effect is equally strong economically: 0.131 times the Lenders 10 Mile standard deviation of 1.93 is similar to 0.450 times the standard deviation of Lenders of 0.50. However, as one might expect, the results erode at the 20-mile radius in Column 4. Before jumping to interpretation of these effects, I first need to address resiliency. 5.2. Resiliency variables One could make an argument that disaster resiliency is driving the disaster mitigation effect of payday lenders found in Table 3. Both of the up-and-coming stories presented earlier have a hypothesis consistent with the results. To address this concern, I first control for the disaster economic effect directly using the property damage caused by the storm (from SHELDUS), the change in quarterly housing prices (from the California Association of Realtors), the change in yearly number of establishments per population (from the Bureau of Labor Statistics (BLS)), and the change in yearly payroll per population (from BLS). I include these variables alone and interacted with Disaster to remove the level effect and capture the economic damage of the disaster. The summary statistics and correlations of these variables are included in Table 4.
A. Morse / Journal of Financial Economics 102 (2011) 28–44
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Table 4 Disaster resiliency variables summary statistics. Panel A: Summary Statistics
House Price D House Price Payroll Paid per Population D Payroll Paid Establishments per Population D Establishments Residential Building Permit Value (lagged) McDonald’s
Mean
St. Dev.
Minimum
Median
Maximum
Count
Yearly $mill. 2007
0.172 0.028 15.65 0.002 2.38 0.05 0.202 0.98
0.166 0.113 85.03 0.014 2.03 0.14 0.242 1.17
2.25 1.90 0.00 0.044 0.011 1.70 0.0 0.0
0.144 0.013 5.38 0.001 1.87 0.02 0.142 1.00
3.54 3.39 1883.3 0.462 12.91 0.93 2.20 6.00
2292 2292 2279 2292 2279 2292 779 2292
House Price
Change in House Price
Payroll Paid
Change in Payroll Paid
Establishments
Change in Establishments
Building Permit Value
1 0.412n 0.028 0.024 0.314n 0.016 0.096n 0.091n
1 0.009 0.008 0.112n 0.115n 0.015 0.020
1 0.838n 0.180n 0.021 0.548n 0.033
1 0.145n 0.038 0.147n 0.024
1 0.302n 0.227n 0.495n
1 0.036 0.281n
1 0.052
Quarterly $mill. Yearly $1,000s Yearly 1,000s
Panel B: Correlations
House Price D House Price Payroll Paid D Payroll Establishments D Establishments Building Permit Value McDonald’s
Notes: 1. Variables are all defined in the data section of the paper. 2. All variable summaries represent statistics from the sample used, not the population in California. 3. In Panel B, n indicates that the correlation is significant at the 5% level.
Second, to directly address the structure-to-land value story (that disasters affect structures more and up-andcoming communities have relatively more land value), I collect the time series of zip-code level residential building value per permit issued from RAND. I use the lag of the average number of residential building permits by zip code in the matched sample to capture, all else equal, how much construction cost goes into a community. Presumably, up-and-coming areas have more money being invested in the community. (Because the sample is a matched one, I can include the level of house price in this estimation and the results remain the same.) Panel B of Table 4 shows that building permits are capturing something more than just house values. The correlation of building permit values with house prices is significant but small (0.096). Building permits is instead more positively correlated with payroll (0.548), changes in payroll (0.147) and the number of establishments (0.227). These correlations are at least consistent with building permits capturing some degrees of the up-andcoming nature of communities. To address the service economy orientation of the zip code (that service communities retrench quickly), I proxy service orientation with McDonald’s locations from the GIS website (http://www.poi-factory.com).8 The
8 The data are static as of 2007, but any lookback growth effect should be small in that most of McDonald’s domestic growth pre-dates my sample.
justification for using McDonald’s stores as a proxy comes from the fact that McDonald’s targets locations in hightraffic corridors (stated in their policy) combined with the intuition that all else equal, high traffic corridors are likely to contain services, especially given that I have already controlled for other measures of commercial activity.9 Table 4, Panel B, shows that McDonald’s locations are very, but not completely, correlated with number of establishments (0.495) and the growth in the number of establishments (0.281). The number of McDonald’s locations is somewhat correlated with house prices but is not related to residential construction, probably because the commercial and residential aspects of a community are related in conflicting ways. The number of McDonald’s stores is not related to payroll in either direction, which suggests that it is not capturing an income dimension. 5.3. Main results controlling for resiliency Turning to the estimations, Column 1 of Table 5 examines the relation between foreclosures and the resiliency controls by themselves. As expected, foreclosures increase with the extent of property damage caused by the disaster. The property damage variable is in hundreds of millions; thus, to induce one more foreclosure per zip code per year (the mean number foreclosures per zip code is 10.52 quarterly or 42 yearly), the damage 9
I thank an anonymous referee for this suggestion.
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A. Morse / Journal of Financial Economics 102 (2011) 28–44
Table 5 Main foreclosure results, with resiliency controls and tests. 1 Disaster
2 nnn
0.873 [0.097]
Lender LendernDisaster
3 nnn
1.088 [0.143] 0.136 [0.139] 0.458nnn [0.166]
Lenders 10 Miles
4 nnn
1.383 [0.250]
5 nnn
0.771 [0.160]
6 nnn
1.108 [0.234] 0.006 [0.170] 0.677nnn [0.223]
0.075 [0.049] 0.143nn [0.056]
Lenders 10 MilesnDisaster
0.455nn [0.192] 0.901nnn [0.345]
Building Permit Value Building PermitnDisaster
0.360nn [0.183] 0.384 [0.315]
7 nnn
1.117 [0.337]
D House PricenDisaster D Payroll Paid D Payroll PaidnDisaster D Establishments D EstablishmentsnDisaster Observations R-squared
0.184nnn [0.065] 0.406 [0.546] 0.321 [0.816] 10.28nnn [2.372] 16.07nn [6.689] 0.373 [0.442] 1.143nn [0.512] 2292 0.105
0.179nnn [0.061] 0.388 [0.545] 0.283 [0.802] 10.58nnn [2.404] 17.81nn [7.048] 0.313 [0.441] 0.879n [0.508] 2292 0.110
0.175nnn [0.063] 1.223 [1.352] 1.011 [1.477] 10.39nnn [2.372] 19.06nnn [6.834] 0.606 [0.503] 1.348nn [0.564] 2278 0.113
773 0.067
0.128nn [0.050] 0.579 [0.570] 0.476 [0.738] 38.84nnn [13.39] 26.80n [16.19] 0.834n [0.502] 0.610 [0.587] 773 0.110
1.134 [0.145] 0.154 [0.146] 0.320n [0.174]
0.123nn [0.053] 0.668 [0.579] 0.773 [0.753] 31.81nn [13.87] 20.75 [16.32] 0.877 [0.557] 1.068n [0.611] 773 0.090
1.456nnn [0.255]
0.079 [0.048] 0.125nn [0.055]
0.012 [0.063] 0.248nnn [0.072]
McDonald’snDisaster
D House Price
1.087 [0.112]
9 nnn
0.063 [0.075] 0.151n [0.089] 0.208 [0.220] 0.268 [0.367]
McDonald’s
Property Damage
8 nnn
2306 0.106
0.029 [0.072] 0.194nn [0.082] 0.189nnn [0.049] 0.389 [0.543] 0.130 [0.807] 10.65nnn [2.433] 17.64nn [7.766] 0.360 [0.466] 0.242 [0.542] 2292 0.120
0.037 [0.066] 0.196nnn [0.076] 0.186nnn [0.049] 1.216 [1.346] 0.871 [1.473] 10.44nnn [2.398] 18.68nn [7.708] 0.675 [0.531] 0.609 [0.599] 2278 0.124
Notes: 1. The dependent variable is the change in quarterly foreclosures per owner-occupied home around the natural disaster or its match in time, where the pre-period is the four quarters before the event and the post period is quarters 4–7 after the disaster. The analysis is quarterly at the zip-code level, with only one observation per disaster zip code (and its match). 2. The matching is redone in Columns 4–6 due to a smaller sample of zip codes covered in the building permit dataset. 3. The independent variable Lender is an indicator for a lender; Lender10 Miles is the log of the number of payday lenders within 10 miles of the center of the zip code area. 4. Year dummy variables are included but not shown. The other independent variables are defined in the robust variables section. 5. nnn, nn, and n denote significance at the 1%, 5%, and 10% levels. Robust standard errors are reported in brackets.
must be $31 million more than the mean, or half a standard deviation from Table 2. In the presence of the property damage variable, the average house price in a zip code has no explanatory power. The more payroll that is paid in a zip code implies fewer foreclosures, but a disaster negates this negative relation. Finally, a disaster induces fewer foreclosures if there is concurrent growth in the number of establishments (or fewer establishment closings), but this effect is small in magnitude. Columns 2 and 3 of Table 5 show that the inclusion of disaster resiliency controls does not reduce the magnitude or economic significance of payday lenders mitigating the disaster effect on foreclosures. The remaining columns explore whether the mitigation effect of payday lending can hold up when allowing the up-and-coming effect of communities to load on building permit values or McDonald’s locations. Columns 4 and 7 show baseline disaster results with building permit values (Column 4) or McDonald’s locations (Column 7) interacted with disaster.
I find strong support for both stories. All else equal, matched communities with higher building-permit values or more McDonald’s stores experience lower growth in foreclosures after a disaster. The up-and-coming nature of a community seems to matter. Columns 5–6 and 8–9 show that the mitigating effect of payday lenders remains, albeit diminished in both significance and magnitude in one specification. Because Columns 8 and 9 are the most conservative columns, I use them to interpret the economic magnitudes of the payday lender effect. Column 8 of Table 5 shows that disasters induce 4.5 ( ¼1.134 per quarter 4 quarters) more foreclosures per 1,000 owner-occupied homes in a zip code in the year following the disaster. The existence of access to credit via a payday lender mitigates 1.3 ( ¼ 0.32 4) of them. Column 9’s economic significance addresses the density of lenders, rather than the existence of a lender. A 20% higher number of payday lenders in a ten-mile radius of the zip code (about one standard deviation) mitigates one
A. Morse / Journal of Financial Economics 102 (2011) 28–44
foreclosure per 1,000 homes ( ¼0.125 2 4 quarters) in the year following the disaster. We can easily translate these to rates for comparison to current events. The sample mean annual foreclosure rate is 0.972% (¼0.243% 4 quarters) of homes. After a disaster, Column 9 implies that the rate increases to 1.55% of homes, and Column 8 implies that the rate increase to 1.43%. As a comparison, the 2009 foreclosure rate in California (from RealtyTrac) was 1.88%, larger than but quite comparable with a disaster effect. In my most conservative estimations, payday lenders mitigate from 0.10 percentage points to 0.13 percentage points of the foreclosure rate (1.0–1.3 foreclosures per 1,000 people) following a disaster. At the risk of overqualifying, I want to emphasize how these numbers apply and do not apply to non-naturaldisaster situations. My design uses disasters as a natural experiment for financial shocks inducing distress. I do not claim that payday lenders lower the foreclosure rate in general. Rather, among those individuals going to payday lenders following a financial shock (a personal emergency or natural disaster), lenders have a large mitigating effect in helping these individuals catch up with their obligations before facing foreclosure. Some individuals use payday lending as a very expensive form of ordinary medium-term finance for non-distress situations. My results do not apply to them. 5.4. Placebo test and instrumental variables robustness As a robustness check, I first use the fact that I can categorize disasters into those that insurance is unlikely to cover (earthquakes, floods, landslides, storms, wildfires and coastal damage) and those that are often included in homeowners policies (hail, lightning, tornadoes and wind). I can use the insured disasters as a placebo; I should not find an effect of lenders. Table 6, Columns 2 and 3, shows exactly this: the payday lending variables interacted with Disaster are insignificant. Columns 3 and 4 are the subsample of insufficiently insured disasters for which the payday mitigation effect is apparent. As a final test of robustness using the foreclosure dependent variable, I find an instrument for Lenders 10 Miles. I relegate this instrumental variables approach to robustness for two reasons. First, following the methodology section, I believe that my matched triple differencing approach with resiliency controls removes concerns about my results being driven by endogeneities. Second, it is hard to prove the validity of any instrument. My instrument is the count of intersections per area of surface (non-residential) roads in a zip code in the year 2006, in quadratic form. A valid instrument must satisfy the usual two properties—being relevant in the first stage and meeting the exclusion restriction in the second stage. The relevance criterion is easily met. Payday lenders, like gas stations, locate at intersections according to survey results from the U.S. Department of Treasury (2000). This result is intuitive: lenders locate where people can easily access the service during regular commuting. For the exclusion restriction to hold, it must be that intersections are unrelated to the unexplained portion of changes in foreclosures. Working in a matched set of
41
communities with a time first-differenced dependent variable alleviates many concerns about violations of the exclusion restriction. For a violation to occur, a static measure of intersections in levels must predict residual changes to foreclosures. Nevertheless, one might worry about the relation between intersections and population density. The post office adjusts the size of zip codes from time to time to realign zip codes with population targets. As a result, more densely populated zip codes have smaller land areas. It is not obvious on a set of matched communities with the same population whether bigger or smaller land mass areas would have more intersections. A second argument questioning the exclusion restriction is that the existence of more intersections relates to growth in commercial activity. Because my measure of intersections follows (in 2006) the analysis period, more intersections could have resulted from commercial growth in the zip code during the sample period. This is unlikely, but not impossible. The processes of roads changing from residential to commercial and of new surface roads being built are both very slow-moving. In addition, roads do not generally close down or lose commercial zoning when commercial activity declines. Following Wooldridge (2001), I use a control function approach to instrumental variables in which the residuals from the first stage are included in the second stage. I do this because the need to interact the instrument with disasters in the second stage creates nonlinearities in the way the instrument enters the second stage. I correct the second-stage residuals for the generated regressor by bootstrapping the first stage following Petrin and Train (2002). In the first-stage regression, the number of intersections is significant at the 1% level in predicting whether a payday lender exists in a location. The firststage F-statistic of 19.8 passes the threshold for instrument relevance. I take the predicted probability from this regression as the instrument for Lender10 Miles. Column 5 reports the instrumental variables results. The key result is that the coefficient on the instrument interacted with Disaster is negative and significant, consistent with the prior results. As a final test (not shown), I consider the popular view that payday lenders target military bases (see, e.g., Carrell and Zinman, 2008). (The federal government made lending to military personnel illegal in 2006.) Because there are many military bases in California and because military personnel might not follow a regular pattern of foreclosures, it could be that I am picking up a military effect. In order for this to explain my results, it must be the case that lender communities with military bases are prevalent in areas hit by disasters and lender communities without military bases are prevalent in areas not hit by disasters (or vice versa). Nevertheless, to the extent that this is true, I re-run my tests throwing out all military communities. I measure a military community by whether there exists a military bank or its ATM in the zip code. Locations for military banks and ATMs are from the Army Bank, Navy Bank, Air Force Bank, and Bank of America Military Bank web pages. I find no change in my foreclosure results.
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A. Morse / Journal of Financial Economics 102 (2011) 28–44
Table 6 Robustness of payday lender effect: placebo test of insurance coverage.
Lender Disaster LendernDisaster
Usually Insured
Usually Insured
1
2
0.079 [0.220] 0.901nnn [0.207] 0.195 [0.276]
Lenders 10 Miles Lenders 10 MilesnDisaster Constant Observations R-squared
1.502nnn [0.199] 743 0.075
1.014nnn [0.377]
0.076 [0.071] 0.037 [0.088] 1.773nnn [0.334] 741 0.078
Insufficient Insurance 3
Insufficient Insurance 4
IV-Insufficient Insurance 5
0.047 [0.169] 1.101nnn [0.167] 0.463nn [0.197]
1.417nnn [0.288]
1.351nnn [0.292]
0.065 [0.061] 0.181nnn [0.068] 1.666nnn [0.292] 1829 0.102
0.088 [0.068] 0.163nn [0.076] 1.689nnn [0.316] 1829 0.120
1.446nnn [0.233] 1843 0.099
Notes: 1. The dependent variable is the change in quarterly foreclosures per owner-occupied home around the natural disaster or its match in time, where the pre-period is the four quarters before the event and the post period is quarters 4–7 after the disaster. 2. The analysis is quarterly at the zip-code level, with only one observation per disaster zip code (and its match). 3. The independent variable Lender is an indicator for a lender in the community; Lender 10 Miles is the log of the number of payday lenders within 10 miles of the center of the zip code area. 4. Disasters included in ‘‘Usually Insured’’ are earthquakes, floods, landslides, storms, wildfires, and coastal damage. Disasters in ‘‘Insufficient Insurance’’ are hail, lightning, tornadoes, and wind. 5. The intersections per area and its square are the instrument for the log of payday lenders within 10 miles in Column 5. The F-statistic in the first stage is 19.8. 6. Year dummy variables are included but not shown. nnn, nn, and n denote significance at the 1%, 5%, and 10% levels. Robust standard errors are reported in brackets.
5.5. Small property crime results As an additional test, I turn now to the small property crime dependent variables, following Garmaise and Moskowitz (2006). Table 7 reports the results for the three small property crime variables—larceny, vehicle theft, and burglary. The dependent variable is the change in annual crimes per household, where change is defined to be the average crimes in the year of the disaster (aligned for the match group) minus the average foreclosure rate in the year prior to the disaster. I include the same resiliency covariates – establishments and community payroll per capita – but instead of house prices, I include violent crimes as a natural covariate. Columns 1 and 2 in Table 7 show that natural disasters increase larcenies by about 12 crimes per 1,000 households per year, compared to a mean of 60 crimes per 1,000 households per year. The negative significant coefficient on LendernDisaster implies that the disaster-driven increase in larcenies is mitigated when a lender is accessible. I qualify this result that the significance is weaker, but nevertheless, the larceny result supports the main foreclosure results. Payday lending seems to offer those in distress an option to weather financial distress. Turning to the other small property crimes, the remaining columns report that payday lenders play no role in people’s decisions to engage in vehicle thefts or burglaries. The only independent variables that explain any of the variation in the changes in these crimes are the change in violent crimes (very strongly) and payroll (weakly). Perhaps it is intuitive that in times of financial
distress, the benefit from access to credit matters only for the smallest of the small property crimes, e.g., shoplifting, where the connection between the need for cash and criminal action is arguably the most direct. 6. Conclusions Taking advantage of the exogenous shock of natural disasters in a matched-triple-difference framework, I find that the existence of payday lending increases welfare for households that might face foreclosures or be driven into small property crime in times of financial distress. Specifically, the main result is that foreclosures increase dramatically (4.5 more foreclosures per 1,000 homes) in the year following a natural disaster; however, 1.0–1.3 of the 4.5 increase is mitigated by access to a lender. The implication is that access to finance can be welfare improving, even at a 400% APR. Payday lending also discourages shoplifting but does not factor into decisions of more serious crimes such as vehicle thefts and burglaries. A qualification is that welfare improvement comes from the mitigating role of payday lenders following shock-driven distress. I do not capture the welfare impact of payday lenders on those borrowing as a regular process of balancing their budgets or as a means to fund temptation consumption. For this subset of the population, there could likely be negative implications to spending facilitated by payday loans (Skiba and Tobacman, 2005, 2007; Melzer, forthcoming). However, my results should apply to the common occurrence of people facing personal
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Table 7 Effect of payday lending on crime after a disaster.
Lender Disaster LendernDisaster
D Violent Crime D Violent CrimenDisaster
Larceny 1
Larceny 2
Vehicle Thefts 3
Vehicle Thefts 4
Burglaries 5
Burglaries 6
8.792 [5.431] 11.64n [5.962] 11.69n [6.473] 0.127nnn [0.023] 1.678nnn [0.612]
9.662n [5.151] 12.28n [6.335] 12.35nn [6.239] 0.126nnn [0.023] 1.686nnn [0.624] 2.303n [1.360] 2.963 [2.452] 11.56 [14.14] 10.84 [19.87] 11.86 [8.393] 767 0.349
1.434n [0.857] 0.545 [0.940] 0.698 [1.039] 0.0214nnn [0.003] 0.502nnn [0.082]
1.400n [0.832] 0.733 [0.988] 0.595 [1.025] 0.021nnn [0.003] 0.505nnn [0.081] 0.397n [0.215] 0.760n [0.399] 0.272 [2.437] 0.310 [3.730] 2.895nn [1.369] 767 0.495
0.554 [1.398] 0.009 [1.624] 0.191 [1.840] 0.046nnn [0.007] 0.999nnn [0.139]
0.849 [1.264] 0.111 [1.678] 0.307 [1.792] 0.045nnn [0.007] 1.004nnn [0.140] 0.097 [0.335] 0.622 [0.753] 3.573 [4.540] 2.637 [6.133] 0.846 [1.426] 767 0.538
D Payroll per Population D PayrollnDisaster D Establishments D EstablishmentsnDisaster Constant Observations R-squared
11.18 [8.075] 767 0.347
2.752nn [1.335] 767 0.492
0.759 [1.404] 767 0.537
Notes: 1. The analysis is yearly at the zip-code level, with only one observation per disaster zip code (and its match). 2. The dependent variables are the change in annual crimes per zip code household. Change is calculated as the crimes in the year of the disaster (aligned for the match group) minus crime in the year prior to the disaster. 3. The resiliency covariates – establishments and community payroll per capita – are as in Table 5. Instead of house prices, I include violent crimes. 4. The independent variable Lender is an indicator for a lender. 5. Year dummy variables are included but not shown. nnn, nn, and n denote significance at the 1%, 5%, and 10% levels. Robust standard errors are reported in brackets.
emergencies, which, Elliehausen and Lawrence (2001) accounts for two-thirds of the self-reported reason for payday borrowing. My results speak more generally to the benefits of local finance for individuals. Prior research documents the benefits of access to finance for aggregate growth (e.g., Jayaratne and Strahan, 1996; Rajan and Zingales, 1998; Levine and Demirguc-Kunt, 2001), firm entrant growth (Guiso, Sapienza, and Zingales, 2004; Cetorelli and Strahan, 2006; Paravisini, 2008) and corporate bankruptcy recovery (e.g., Dahiya, John, Puri, and Ramirez, 2003), but little work has been done to gauge the benefit of access to finance in individuals-specific measures. (An exception similar in spirit to this work is Garmaise and Moskowitz, 2006.) In addition, my work speaks to the community-level importance of resiliency. I find that financial institutions aid the resiliency of communities to financial downturns, a important topic not just for natural-disaster recovery but also for planning for economic downturns and structural job shifts. The results have important policy implications for payday lending. Fifteen states have recently banned payday lending, and legislation is pending in many of the others. If the existence of payday lending is valuable for those facing personal disaster, then regulators should strive to make access to finance easier and more affordable for those facing distress. This does not mean that payday lending is the best product conceivable, but it
does suggest that efforts should be focused on opening up the market for product innovation in (cheaper) high-risk and short-term personal finance to help those in need. References Anderson, D., Weinrobe, M., 1986. Mortgage default risks and the 1971 San Fernando earthquake. American Real Estate and Urban Economics Association Journal 14, 110–135. Attanasio, O., Browning, M., 1995. Consumption over the life cycle and over the business cycle. American Economic Review 85, 1118–1137. Bair, S., 2005. Low-cost payday loans: opportunities and obstacles. A Report by the Isenberg School of Management University of Massachusetts at Amherst Prepared for The Annie E. Casey Foundation. Barr, M., 2004. Banking the poor. Yale Journal on Regulation 121, 121–237. Bernheim, B., Rangel, A., 2006. Behavioral public economics: welfare and policy analysis with non-standard decision-makers. In: Diamond, P., Vartiainen, H. (Eds.), Economic Institutions and Behavioral Economics. Princeton University Press, Princeton. Bertrand, M., Duflo, E., Mullainathan, S., 2004. How much should we trust differences-in-differences estimates? Quarterly Journal of Economics 119, 249–275. Bertrand, M., Morse, A., 2009. What do high-interest borrowers do with their tax rebates? American Economic Review 99, 418–423. Bertrand, M., Morse, A. Information disclosure, cognitive biases and payday borrowers. Journal of Finance, forthcoming. Bin, O., Polasky, S., 2004. Effects of flood hazards on property values: evidence before and after Hurricane Floyd. Land Economics 80, 490–500. Brito, D., Hartley, P., 1995. Consumer rationality and credit cards. Journal of Political Economy 103, 400–433. Calem, P., Mester, L., 1995. Consumer behavior and the stickiness of credit card interest rates. American Economic Review 85, 1327–1336.
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Campbell, J., 2006. Household finance. Journal of Finance 61, 1553–1604. Carrell, S., Zinman, J., 2008. In harm’s way? Payday loan access and military personnel performance. Working Paper. Caskey, J., 1994. Fringe Banking: Check-cashing Outlets, Pawnshops, and the Poor. Russell Sage Foundation, New York. Caskey, J., 2005. Fringe banking and the rise of payday lending. In: Bolton, P., Rosenthal, H. (Eds.), Credit Markets for the Poor. Russel Sage Foundation, New York. Cetorelli, N., Strahan, P., 2006. Finance as a barrier to entry: bank competition and industry structure in local U.S. markets. Journal of Finance 61, 437–461. Choi, J., Laibson, D., Madrian, B. $100 bills on the sidewalk: suboptimal savings in 401(k) plans. Review of Economics and Statistics, forthcoming. doi:10.1162/REST_a_00102. Dahiya, S., John, K., Puri, M., Ramirez, G., 2003. Debtor-in-possession financing and bankruptcy resolution: empirical evidence. Journal of Financial Economics 69, 259–280. Elliehausen, G., Lawrence, E., 2001. Payday advance credit in America: An analysis of customer demand. Georgetown University Credit Research Center Monograph No. 35. Fannie Mae, 2002. Analysis of alternative financial service providers. The Fannie Mae Foundation and Urban Institute, Washington, DC. Fudenberg, D., Levine, D., 2006. A dual self model of impulse control. American Economic Review 96, 1449–1476. Garmaise, M., Moskowitz, T., 2006. Bank mergers and crime: the real and social effects of credit market competition. Journal of Finance 61, 495–538. Graves, S., Peterson, C., 2005. Predatory lending and the military: the law and geography of ‘payday’ loans in military towns. Ohio State Law Review 66, 653–832. Gross, D., Souleles, N., 2002. Do liquidity constraints and interest rates matter for consumer behavior? Evidence from credit card data. Quarterly Journal of Economics 117, 149–185. Guiso, L., Sapienza, P., Zingales, L., 2004. Does local financial development matter? Quarterly Journal of Economics 119, 929–969. Gul, F., Pesendorfer, W., 2001. Temptation and self-control. Econometrica 69, 1403–1435. Gul, F., Pesendorfer, W., 2004. Self-control and the theory of consumption. Econometrica 72, 119–158. Hall, R., Mishkin, F., 1982. The sensitivity of consumption to transitory income: estimates from panel data on households. Econometrica 50, 461–481. Hubbard, R., Judd, K., 1986. Liquidity constraints, fiscal policy, and consumption. Brooking Papers of Economic Activity 1986, 1–60. Jappelli, T., 1990. Who is credit constrained in the U.S. economy? Quarterly Journal of Economics 105, 219–234. Jayaratne, J., Strahan, P., 1996. The finance-growth nexus: evidence from bank branch deregulation. Quarterly Journal of Economics 111, 639–670. Johnson, S., Kotlikoff, L., Samuelson, W., 2001. Can people compute? An experimental test of the life cycle consumption model. In: Kotlikoff, L. (Ed.), Essays on Saving, Bequests, Altruism, and Life-Cycle Planning. MIT Press, Boston. Jones, R., 1960. Transitory income and expenditures on consumption categories. American Economic Review 50, 584–592. Laibson, D., 1997. Golden eggs and hyperbolic discounting. Quarterly Journal of Economics 112, 443–477.
Laibson, D., Repetto, A., Tobacman, J., 1998. Self-control and saving for retirement. Brookings Papers on Economic Activity 91–196. Levine, R., Demirguc-Kunt, A., 2001. Financial Structure and Economic Growth: A Cross-country Comparison of Banks, Markets, and Development. MIT Press, Cambridge, MA. Lusardi, A., Tufano, P., 2008. Debt literacy, financial experience, and overindebtedness. Working Paper. Melzer, B. The real costs of credit access: evidence from the payday lending market. Quarterly Journal of Economics, forthcoming, 126. Morgan, D., Strain, M., 2007. Payday holiday: How households fare when states ban payday loans. Federal Reserve Bank of New York Working Paper. Murdoch, J., Singh, H., Thayer, M., 1993. The impact of natural hazards on housing values: the Loma Prieta Earthquake. Journal of the American Real Estate and Urban Economic Association 21, 167–184. Neyman, J., 1923. On the application of probability theory to agricultural experiments. Essay on principles. Statistical Science 5, 465–472. O’Donoghue, T., Rabin, M., 2007. Incentives and self-control. In: Blundell, R., Newey, W., Persson, T. (Eds.), Advances in Economics and Econometrics: Volume 2: Theory and Applications. Cambridge University Press, Cambridge, pp. 215–245. Paravisini, D., 2008. Local bank financial constraints and firm access to external finance. Journal of Finance 63, 2161–2193. Petrin, A., Train, K., 2002. Omitted product attributes in discrete choice models. University of California at Berkeley, Working Paper. Rajan, R., Zingales, L., 1998. Financial dependence and growth. American Economic Review 88, 559–586. Rubin, D., 1974. Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of Educational Psychology 66, 688–701. Skiba, P., Tobacman, J., 2005. Payday loans, consumption shocks, and discounting. Working Paper. Skiba, P., Tobacman, J., 2007. Do payday loans cause bankruptcy? Working Paper. Skiba, P., Tobacman, J., 2009. The profitability of payday loans. Working Paper. Stango, V., Zinman, J., 2011. Fuzzy math, disclosure regulation, and credit market outcomes. Review of Financial Studies 24, 506–534. Stegman, M., Faris, R., 2003. Payday lending: a business model that encourages chronic borrowing. Economic Development Quarterly 17, 8–32. Stephens Jr., M., 2006. Job loss expectations, realizations, and household consumption behavior. Review of Economic and Statistics 86, 253–269. Thaler, R., 1990. Anomalies: saving, fungibility, and mental accounts. Journal of Economic Perspectives 4, 193–205. Thaler, R., Shefrin, H., 1981. An economic theory of self-control. Journal of Political Economy 89, 392–406. U.S. Department of Treasury, 2000. Survey of non-bank financial institutions. U.S. Department of Treasure Report with Dove Consulting. Washington, DC. Wooldridge, J., 2001. Econometric Analysis of Cross Section and Panel Data. MIT Press, Boston. Zeldes, S., 1989. Consumption and liquidity constraints: an empirical investigation. Journal of Political Economy 97, 305–346.
Journal of Financial Economics 102 (2011) 45–61
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Long-run risk in durable consumption$ Wei Yang William E. Simon Graduate School of Business Administration, University of Rochester, Rochester, NY 14627, United States
a r t i c l e i n f o
abstract
Article history: Received 1 June 2009 Received in revised form 25 August 2010 Accepted 23 November 2010 Available online 31 March 2011
Durable consumption growth is persistent and predicted by the price–dividend ratio. This provides strong and direct evidence for the existence of a highly persistent expected component. Durable consumption growth is left-skewed and exhibits timevarying volatility. I model durable consumption growth as containing a persistent expected component and driven by counter-cyclical volatility, nondurable consumption as a random walk, and dividend growth as exposed to the expected component of durable consumption growth. Together with nonseparable Epstein-Zin preferences, the model demonstrates that long-run risk in durable consumption can explain major asset market phenomena. The model also generates an upward-sloping real term structure. & 2011 Elsevier B.V. All rights reserved.
JEL classification: E21 G12 Keywords: Durable consumption Long-run risk Skewness Equity premium Term structure of real interest rates
1. Introduction Consumers possess large stocks of durable goods, and service flows from durables constitute a substantial fraction of aggregate consumption.1 The consumption-based asset pricing literature has largely focused on nondurable consumption. This traditional focus rests on the assumption of separability between different consumption goods
$ I am grateful for detailed feedback from Rene´ Stulz (the editor) and an anonymous referee, and helpful comments from Ravi Bansal, Geert Bekaert, Stijn Van Nieuwerburgh, Jerry Warner, Yangru Wu, Amir Yaron, and participants at the 20th Conference on Financial Economics and Accounting and the American Finance Association 2010 Annual Meeting. Special thanks to Toni Whited for many valuable suggestions. E-mail address:
[email protected] 1 According to the Bureau of Economic Analysis, in 2007, U.S. consumers spent about $23,000 per person in nondurable goods and services, and held a net stock of durable goods of about $15,000 per person at the year end. Both are in year 2000 dollars. Major subcategories of durable goods are motor vehicles and parts, furnishings and durable household equipment, recreational goods and vehicles, and others.
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.03.023
in the utility function. A number of studies, however, document considerable evidence for nonseparability.2 In an influential study, Bansal and Yaron (2004) demonstrate that persistent predictable components and time-varying volatility in nondurable consumption and dividend growth, in conjunction with Epstein and Zin (1989) preferences, can explain major asset market phenomena. The growing literature on long-run consumption risk spawned by this study has also focused on nondurable consumption.3 In this paper, I document strong and direct evidence for the existence of a highly persistent expected component in durable consumption growth, and present a model to show that nonseparability in Epstein-Zin preferences allows long-run durable consumption risk to explain key features of the asset market data. The empirical evidence
2 See, among others, Dunn and Singleton (1986), Eichenbaum and Hansen (1990), Ogaki and Reinhart (1998), Yogo (2006), and Gomes, Kogan, and Yogo (2009). 3 See Bansal (2008) for a survey of the long-run consumption risk literature.
46
W. Yang / Journal of Financial Economics 102 (2011) 45–61
in this paper is complementary to that reported in Bansal and Yaron (2004), Bansal, Kiku, and Yaron (2007), and Hansen, Heaton, and Li (2008) for nondurable consumption. To maintain parsimony and highlight the role of durable consumption, I model nondurable consumption growth as random walk shocks. In addition, consumption shares are constant in my model and dividend growth is exposed to the expected durable consumption growth. Taken together, this study puts the focus, and consequently the burden, almost entirely on durable consumption in explaining asset market phenomena. My empirical analysis focuses on the annual data of 1952–2007. Durable consumption growth exhibits highly significant first- and second-order autocorrelations of 0.65 and 0.42, respectively. More importantly, durable consumption growth is predicted by the price-dividend ratio with strongly positive coefficients. These results provide strong and direct evidence for the existence of a highly persistent predictable component. I also report that durable consumption growth is left-skewed, with a strongly negative estimate of 0.51. Durable consumption growth also exhibits persistent time-varying volatility. For the realized volatility of the innovations to durable consumption growth, the variance ratio increases substantially with the horizon, indicating a positive serial correlation. Additionally, the realized volatility is predicted by and predicts the price–dividend ratio, both with negative slopes. These empirical findings motivate a parsimonious model of durable consumption growth containing a highly persistent expected component and driven by shocks with conditional volatility that varies negatively with the expected component. In the model, the expected component — that is, the long-run risk component — exhibits a left-skewed unconditional distribution. It spends more time above zero, but there is also an important fat left tail. Following the convention in the literature, I calibrate the parameters of the model for durable consumption, nondurable consumption, and dividend growth at the monthly frequency so that the model-implied annual growth rates replicate the salient features of the observed annual data. In particular, given the high persistence of durable consumption growth and the predictability by the price–dividend ratio, I set the persistence parameter of the expected component at 0.99. The exposure of dividend growth to the expected component is 0.8. The growth rate dynamics are set into nonseparable Epstein–Zin preferences. In each period the representative agent values durable and nondurable consumption with a Cobb-Douglas utility, which implies that the elasticity of substitution between the two goods is 1. The Cobb-Douglas utility also implies constant consumption shares, and I set the share of durable consumption at 0.5. I then embed the intra-period utility in Epstein-Zin preferences, which differentiate risk aversion and elasticity of intertemporal substitution. As in Bansal and Yaron (2004), the results of this paper are based on a risk aversion of 10, and an elasticity of intertemporal substitution of 1.5 is needed to generate small and smooth risk-free rates. Since the elasticities between goods and across time are different, the resulting utility is nonseparable between the two goods. This allows
the durable consumption growth dynamics to generate important asset pricing implications. I present approximate analytical solutions to demonstrate the model intuition, and rely on numerical solutions and simulations to assess the model’s quantitative implications. In the model, the high persistence of the expected component in durable consumption growth and Epstein-Zin preferences with early resolution of uncertainty give rise to a large market price of the long-run risk. This market price resembles that in Bansal and Yaron (2004), except that in my model, since the long-run risk arises from durable consumption, its market price also depends on the durable consumption share. The high persistence further results in a large exposure of the stock return to the long-run risk. Together, the large market price of long-run durable consumption risk and the large exposure of the stock return to this risk generate a large equity premium and a high stock return volatility. Moreover, because durable consumption growth and, in particular, the long-run risk component exhibit countercyclical volatility, the large market price of the long-run risk and the large exposure to this risk also give rise to large counter-cyclical variations in the equity premium and the stock return volatility. The results show that the model is able to justify a broad set of asset pricing phenomena, including procyclical price–dividend ratios, large and counter-cyclical equity premiums and stock return volatilities, low and smooth risk-free rates, and the stock return predictability. The model is also capable of generating the volatility feedback effect. In addition, it generates positive, countercyclical real bond risk premiums, and an upward-sloping real term structure. Lastly, the model is capable of matching the empirically documented predictabilities of durable consumption growth and its realized volatility by the price–dividend ratio. This paper expands the scope of the long-run risk literature and suggests long-run durable consumption risk as a plausible channel to explain key asset market phenomena. Bakshi and Chabi-Yo (2010) suggest that the leftskewed long-run risk in this paper could lead to an improved fit to the variance bounds proposed in their study. This paper is also related to several recent studies that incorporate multiple consumption goods in the representative agent’s utility. In my model, the CobbDouglas utility implies that the shares of durable and nondurable consumption are constant. The implications of a time-varying composition are emphasized in Piazzesi, Schneider, and Tuzel (2007), in which the utility is nonseparable between nondurable consumption and housing. Also, my paper highlights the asset market implications of long-run durable consumption risk in a calibrated model economy. The objective and the approach of my study are complementary to the empirical studies of Yogo (2006) and Pakos (2005) that focus on GMM estimation. In the rest of the paper, I first discuss the data in Section 2. Section 3 focuses on the empirical properties of the durable consumption growth data. These properties motivate the model of durable consumption growth, which is presented in Section 4, followed by the calibration of the parameters. Section 5 specifies the pricing
W. Yang / Journal of Financial Economics 102 (2011) 45–61
kernel, calibrates the preference parameters, and discusses the model intuition using approximate analytical solutions. In Section 6, I present the numerical solutions and the simulations to discuss the model’s quantitative implications. The concluding section addresses the limitations of the paper, and the appendices collect additional details of the model.
47
levels by the quarterly data. The relevant results from the quarterly series will be reported mostly in footnotes. The stock market returns are value-weighted annual returns for the NYSE, and the risk-free rates are 3-month T-bill rates, both adjusted for inflation. All data series are obtained from the CRSP. Year-end price–dividend ratios and annual real dividend growth rates are computed from the value-weighted annual returns for the NYSE with and without distributions, and adjusted for inflation.
2. Data 3. Empirical properties of growth rates Fig. 1 plots annual durable and nondurable consumption growth, with shaded regions marking the NBERdated economic contractions. On average, durable consumption grows at about 4% per year. This rate is about two times that of nondurable consumption. As a result, the ratio of durable consumption to nondurable consumption tends to rise over time. As pointed out in Ogaki and Reinhart (1998) and Yogo (2006), this trend is consistent with the downward trend in the relative purchase price of durables with respect to nondurables. Durable consumption growth is also more volatile. Its volatility of about 2% is about two times that of nondurable consumption growth. In time series, both growth rates tend to be low (high) during recessions (expansions). Durable consumption growth also tends to decrease consecutively during recessions, and increase consecutively during expansions. This suggests that durable consumption growth is persistent.
0.08
Durable
0.06 0.04 0.02 0 −0.02
1960
1970
1980
1990
2000
1990
2000
Year 0.08 0.06
Nondurable
The consumption data are from the Bureau of Economic Analysis (BEA). Consumption is the service flow delivered by goods and services within a period (e.g., one year). Following the convention in the literature, nondurable goods and services are assumed to be entirely consumed in the period of purchase. Hence, nondurable consumption is measured as the sum of real personal consumption expenditures on nondurable goods and services. In contrast, durable goods, once purchased, provide service flows for more than one period. Hence, consumption expenditures on durable goods, which record the purchase of new durable goods in a period, do not measure service flows. The BEA also estimates the depreciation of consumer durable goods, which is not a measure of service flows either. Following the convention in the literature, I assume that the service flow of durable goods is proportional to the net stock, and thus measure durable consumption by the year-end real net stock of consumer durable goods.4 Both durable and nondurable consumption series are divided by the population to obtain per capita values. Although annual data are available from late 1920s, I use the sample period of 1952–2007. The Great Depression era experienced unusually negative consumption growth rates. The period after World War II but before 1952 is associated with unusually high growth in the stock of durables.5 Following Ogaki and Reinhart (1998) and Yogo (2006), I exclude these unusual periods to ensure that the key data characteristics are stable, and in particular, not driven by outliers. Quarterly data are also available for the period after WWII. However, they may involve seasonalities that confound the inference. In addition, the stock of durable goods is reported only at year-ends, and thus the quarterly series of the stock must be constructed from the annual series using quarterly real expenditures on durable goods and imputed depreciation rates (Yogo, 2006). In this study, I focus on the annual data following the convention in the literature. I also construct the quarterly series of the stock of durables for the same period of 1952–2007, and find that the results obtained from the annual data are confirmed with even higher significance
0.04 0.02 0
4
See Herman (2000) for the methodology used by the BEA to determine the depreciation and the net stock of consumer durables. 5 Ogaki and Reinhart (1998) find that when their sample period begins in 1947, the cointegrating relation, with which they estimate the elasticity of substitution between durables and nondurables, is strongly rejected. Consequently, they exclude the unusual period of the restocking of durables immediately following WWII.
−0.02
1960
1970
1980
Year Fig. 1. Annual durable and nondurable consumption growth of 1952–2007. The shaded regions mark the NBER-dated recessions.
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W. Yang / Journal of Financial Economics 102 (2011) 45–61
Table 1 Panel A presents the first- to third-order autocorrelations, AC(1) to AC(3), of durable consumption growth in the empirical data. Panel B compares the empirical results of the predictive regressions with those from the model-implied, simulated data. The cumulative durable consumption growth from year t to year t þ J is regressed on the log price–dividend ratio of year t. Here, J is the horizon. The empirical data are annual for the period 1952–2007. The empirical estimates are obtained with GMM, and the standard errors are Newey and West (1987) corrected with ten lags. The model-implied results are the averages over 10,000 samples simulated from the numerical solution of the model. Each simulated sample is 56 12-month long, and is then time-aggregated to the annual frequency.
AC(1)
Std Err
AC(2)
Panel A: Autocorrelations Std Err
AC(3)
Std Err
0.65
(0.08)
0.42
(0.11)
0.07
(0.14)
Panel B: Durable consumption growth predicted by log price–dividend ratio Data
Horizon (year) 1 3 5
Slope
Std Err
R2
Slope
R2
0.017 0.052 0.092
(0.005) (0.015) (0.032)
0.10 0.13 0.20
0.040 0.096 0.131
0.16 0.22 0.25
Table 2 Skewness of durable consumption growth in the empirical data for the period 1952–2007. Bootstrap confidence percentiles are computed by resampling the original data for 10,000 times. Skewness
0.51
Model
Bootstrap confidence percentiles 5%
10%
90%
95%
98%
0.86
0.78
0.20
0.12
0.03
3.1. Durable consumption growth Panel A of Table 1 reports that the first-order autocorrelation of durable consumption growth is 0.65, which is highly significant. Moreover, the second-order autocorrelation is also significant at 0.42.6 These estimates provide strong evidence that durable consumption growth is persistent.7 More strikingly, as reported in Panel B of Table 1, durable consumption growth is predicted by the price– dividend ratio. Here, the cumulative durable consumption growth from year t to year t þJ is regressed on the log price–dividend ratio of year t. The results indicate highly significant, positive slope coefficients, and both the slope and R2 increase with the horizon. With first- and secondorder autocorrelations of 0.91 and 0.81, the price–dividend ratio is highly persistent. In addition, the potential biases in the slope coefficients for these predictive regressions (Stambaugh, 1986) are small.8 Hence, these results provide strong and direct evidence that durable
6 For the data on quarterly durable consumption growth, the fourthand eighth-order autocorrelations (standard errors) are 0.57 (0.08) and 0.34 (0.12), respectively. 7 I also conduct robustness checks. For the subsample periods of 1952–1979 and 1980–2007, the first-order autocorrelations of annual durable consumption growth are 0.51 and 0.79, respectively. For the long sample period 1929–2007, the first-order autocorrelation is 0.76. For 1932–2007, it is 0.73. 8 For example, for the one-year-ahead predictive regression, the bias computed following Stambaugh (1986) and Lewellen (2004) is about 0.0009, much smaller than the slope coefficient of 0.017.
consumption growth contains a highly persistent predictable component, or a long-run risk component. Table 2 reports that durable consumption growth exhibits a negative skewness of 0.51. To assess the statistical significance of the point estimate, I use the bootstrap method to find the confidence intervals. More specifically, I generate 10,000 bootstrap samples, measure skewness for each sample, and report the percentiles of these estimates.9 Since the 98th percentile is still negative, I conclude that the point estimate of skewness is significantly negative at the 2% level. Furthermore, in the quarterly data for durable consumption growth, the skewness is 0.46, significantly negative at a confidence level much better than 1%. Taken together, negative skewness appears to be a robust property of the empirical durable consumption growth data.10 Finally, I investigate time-varying volatility in durable consumption growth. As in Bansal and Yaron (2004), I perform the variance ratio test on the realized volatility of innovations. I first obtain residuals, eDd,t , from an AR(5) regression of durable consumption growth. Using five lags is more than adequate to account for the autocorrelation. Then I compute the variance ratios for the absolute value of the residuals P var½ J1 je j j ¼ 0 Dd,t þ j VRJ ¼ , ð1Þ J var½jeDd,t j where J is the horizon in years. For statistical inference, I generate 10,000 bootstrap samples and compute variance ratios for each sample. Here, the resampling treats each data point in the time series as independent. Hence, the bootstrap samples and the percentiles are obtained under the null hypothesis of 9 In other words, here the resampling and the confidence intervals are obtained under the null hypothesis that skewness is equal to the empirical estimate (which is not zero). 10 I also conduct robustness checks. For the subsample periods of 1952–1979 and 1980–2007, the skewness estimates of annual durable consumption growth are 0.53 and 0.47, respectively. For the period 1929–2007, the skewness is 0.49. For 1932–2007, it is 0.53.
W. Yang / Journal of Financial Economics 102 (2011) 45–61
49
Table 3 Realized volatility of durable consumption growth, jeDd j, is the absolute value of the residuals from an AR(5) regression of durable consumption growth Dd. Panel A presents the variance ratios, VR, of the realized volatility of durable consumption growth in the empirical data. Bootstrap percentiles are computed under the null hypothesis of no serial correlation by resampling the realized volatility series for 10,000 times. ‘‘VR Adj’’ is VR divided by the bootstrap mean to adjust for the small-sample bias. Panels B and C compare the empirical results of the predictive regressions with those from the model-implied, simulated data. In Panel B, the realized volatility of durable consumption growth of year t þ J is regressed on the log price–dividend ratio of year t. In Panel C, the log price–dividend ratio of t þ J is regressed on the realized volatility of t. Here, J is the horizon. The empirical estimates are obtained with GMM, and the standard errors are Newey and West (1987) corrected with ten lags. The model-implied results are the averages over 10,000 samples simulated from the numerical solution of the model. Each simulated sample is 56 12-month long, and is then time-aggregated to the annual frequency. The empirical data are annual for the period 1952–2007. Panel A: Variance ratios of jeDd j Horizon VR
VR Adj
Bootstrap percentiles
(year) 2 4 5 8 10
1.09 1.31 1.48 1.51 1.62
1.11 1.39 1.61 1.77 2.01
Horizon (year)
Mean
5%
10%
90%
95%
0.98 0.94 0.92 0.85 0.81
0.76 0.57 0.50 0.36 0.30
0.80 0.63 0.57 0.43 0.36
1.16 1.28 1.31 1.37 1.38
1.22 1.40 1.46 1.59 1.63
Data Slope
Std Err
Model 2
Slope
R2
R
Panel B: jeDd j predicted by log price–dividend ratio 1 0.0065 3 0.0050 5 0.0048
(0.0026) (0.0034) (0.0034)
0.104 0.059 0.055
0.0034 0.0029 0.0026
0.044 0.031 0.025
Panel C: Log price–dividend ratio predicted by jeDd j 1 14.0 3 18.5 5 17.2
(9.7) (8.6) (8.5)
0.079 0.131 0.108
18.2 11.9 7.3
0.043 0.031 0.026
serial independence. This allows me to test the null by comparing the empirical estimates with the bootstrap percentiles under the null. To examine the dependence of the variance ratio on the horizon, I follow Poterba and Summers (1988) and adjust for the small-sample bias by dividing the empirical estimates by the averages of the bootstrap results. Without time-varying volatility, the adjusted variance ratios would be flat with respect to the horizon, and stay close to 1. Panel A of Table 3 shows the opposite: The adjusted variance ratios are all above 1, and increase substantially with the horizon. Moreover, for all horizons beyond four years, the null of no serial correlation is rejected at the 10% level. At the five-year horizon, the null is also rejected at the 5% level. These results suggest positive serial correlation in the realized volatility.11 To provide additional evidence for time-varying volatility, Panels B and C of Table 3 explore the predictive relations between the realized volatility and the price– dividend ratio. The results indicate that realized volatilities in the future are predicted by the log price–dividend ratio with negative slopes. Conversely, log price–dividend
11 For the quarterly data of durable consumption growth, I verify that the residuals from an AR(4) regression are not serially correlated. Variance ratio tests on the absolute value of the residuals indicate that the null of no serial correlation is rejected at the 5% level beyond horizons of 8 quarters, and at the 2% level beyond horizons of 12 quarters.
ratios in the future are also predicted by the realized volatility with negative slopes. These results are similar to those reported in Bansal, Khatchatrian, and Yaron (2004) for nondurable consumption growth.
3.2. Nondurable consumption and dividend growth Table 4 presents the empirical properties of nondurable consumption growth for the period of 1952–2007. Panel A reports a significant first-order autocorrelation of 0.36, while the second-order autocorrelation is insignificant. These estimates are close to those reported in Bansal and Yaron (2004) for the period 1929–1998.12 Panel B indicates that nondurable consumption growth exhibits a small negative skewness, which is not significantly different from zero at the 10% level. Panel C shows that for innovations to nondurable consumption growth, the variance ratio for the realized volatility increases slowly with respect to the horizon, and are all bracketed within the 10% confidence intervals. The adjusted variance ratios are close to 1. Hence, the null of no serial correlation cannot be rejected. Overall, these results are consistent with the evidence in previous studies (Bansal and Yaron, 2004; Bansal, Kiku, and 12 As emphasized in Bansal and Yaron (2004), in finite samples, it is difficult to distinguish between a pure i.i.d. process and a process with small persistence (Shephard and Harvey, 1990).
50
W. Yang / Journal of Financial Economics 102 (2011) 45–61
Table 4 Empirical properties of nondurable consumption growth. The empirical data are annual for the period 1952–2007. Panel A presents the first- to third-order autocorrelations, AC(1) to AC(3), of nondurable consumption growth. The empirical estimates are obtained with GMM, and the standard errors are Newey and West (1987) corrected with ten lags. Panel B presents skewness. Bootstrap confidence percentiles are computed by resampling the original data for 10,000 times. Panel C presents the variance ratios, VR, for the realized volatility, or the absolute value of the residuals from an AR(5) regression of nondurable consumption growth. Bootstrap percentiles are computed under the null hypothesis of no serial correlation by resampling the realized volatility series for 10,000 times. ‘‘VR Adj’’ is VR divided by the bootstrap mean to adjust for the small-sample bias. Panel A: Autocorrelations AC(1)
Std Err
AC(2)
Std Err
AC(3)
Std Err
0.36
(0.11)
0.03
(0.17)
0.05
(0.15)
Panel B: Skewness Skewness
Bootstrap confidence percentiles
0.18
5%
10%
90%
95%
0.49
0.42
0.09
0.16
Panel C: Variance ratios of realized volatility Horizon VR VR Adj (year) 2 5 10
0.86 0.87 0.86
0.88 0.94 1.06
Bootstrap percentiles Mean
5%
10%
90%
95%
0.98 0.92 0.81
0.76 0.50 0.29
0.81 0.57 0.35
1.16 1.33 1.39
1.22 1.48 1.66
Yaron, 2007; Hansen, Heaton, and Li, 2008).13 To sharpen the focus of this paper and highlight the implications of the empirical properties of durable consumption, I subsequently model nondurable consumption as a pure random walk. Lastly, for dividends, the average growth rate is about the same as that of nondurable consumption, while the volatility is high. The first-order autocorrelation is about 0.29. The correlation between dividend growth and durable consumption growth is 0.11.14 As presented subsequently, dividend growth is modeled as exposed to the expected component in durable consumption growth. The small correlation suggests that the exposure parameter is small. These empirical properties of dividend growth are presented in Table 6, in which they will be compared with the simulation results implied by the calibrated model.
Table 6 compares the salient properties of the empirical data with those implied by the growth rate models, which are obtained from 10,000 simulated samples. Each simulated sample is 56 12-month long, and is then time-aggregated to the annual frequency. 4.1. Durable consumption growth The model for durable consumption growth is motivated by the robust empirical properties reported earlier. Specifically, durable consumption growth has a mean of md and contains two components as specified in
Ddt þ 1 ¼ log
Dt þ 1 ¼ md þxt þ sd ot ed,t þ 1 , Dt
xt þ 1 ¼ fxt þ sx ot ex,t þ 1 , 4. Models of growth rates
ot ¼ In this section I present the models for durable, nondurable, and dividend growth rates, and then calibrate the parameters. Following the convention in the literature,15 the models are calibrated at the monthly interval so that simulated monthly series, after time aggregation to the annual frequency, replicate the salient features of the empirical data. The calibrated parameters are listed in Table 5. 13 I also conduct robustness checks for longer sample periods. For the period 1929–2007, annual nondurable consumption growth exhibits a first-order autocorrelation of 0.44 and a skewness of 1.61. In 1932– 2007, the autocorrelation is 0.13 and the skewness is essentially zero. 14 As a robustness check, in the period 1929–2007, the correlation between durable consumption and dividend growth is about 0.12. 15 See Kandel and Stambaugh (1991), Campbell and Cochrane (1999), and Bansal and Yaron (2004), among others.
pffiffiffiffiffiffiffiffiffiffiffiffiffi 1zxt ,
ex,t þ 1 , ed,t þ 1 i:i:d: Nð0,1Þ:
ð2Þ ð3Þ ð4Þ ð5Þ
The expected component xt is an AR(1) process of the persistence parameter 0 o f o1, driven by shocks of time-varying volatility sx ot . The other component is random walk shocks with time-varying volatility sd ot . The time-varying ot is a function that varies negatively with xt, with a sensitivity parameter of z. The square root functional form ultimately contributes a term linear in xt to the expected excess returns. The volatility approaches zero when xt -1=z, and in the continuous time limit, xt never exceeds 1=z. In this specification, durable consumption growth contains two types of risks. The ‘‘short-run’’ risk comes from the random walk shocks, while the ‘‘long-run’’ risk
W. Yang / Journal of Financial Economics 102 (2011) 45–61
51
Table 5 The calibrated parameters for the dynamics of durable consumption growth [Eqs. (2)– (5)], nondurable consumption growth [Eq. (6)], dividend growth [Eq. (7)], and the preferences [Eq. (16)] at the monthly interval. Durable
md
sd
f
sx
z
0.00325
0.0026
0.99
0.000242
278
Nondurable
Dividend
mc
sc
my
sy
l
0.00173
0.004
0.00162
0.0378
0.8
Preferences
a
d
g
c
0.5
0.998
10
1.5
Table 6 This table compares the properties of the annual empirical growth rate data with the model-implied, simulated data. Here, AC(1) to AC(3) are the first- to third-order autocorrelations. Realized volatility jeDd j is the absolute value of the residuals from an AR(5) regression of durable consumption growth Dd, and VR(5) and VR(10) are the variance ratios of five- and ten-year horizons. The empirical data are annual for the period 1952–2007. Except skewness and variance ratios, the empirical estimates are obtained with GMM, and standard errors are Newey and West (1987) corrected with ten lags. The model-implied results are the means and percentiles from 10,000 samples simulated from the models of the growth rates. Each simulated sample is 56 12-month long, and is then time-aggregated to the annual frequency. Data Estimate
Model Std Err
Mean
Panel A: Durable consumption growth ðDdÞ Mean (%) 3.93 (0.33) 3.92 Std Dev (%) 1.88 (0.18) 1.88 AC(1) 0.65 (0.08) 0.63 AC(2) 0.42 (0.11) 0.49 AC(3) 0.07 (0.14) 0.38 Skewness 0.51 0.51 jeDd j-VRð5Þ 1.48 1.19 jeDd j-VRð10Þ 1.62 1.26
5%
95%
2.08 1.20 0.38 0.20 0.06 1.19 0.61 0.40
5.37 2.83 0.83 0.75 0.67 0.07 1.97 2.70
Panel B: Nondurable consumption growth ðDcÞ Mean (%) Std Dev (%)
2.08 1.12
(0.17) (0.09)
2.08 1.12
1.78 0.94
2.38 1.31
(0.8) (1.0) (0.11) (0.10) (0.08)
1.93 10.7 0.23 0.02 0.10
1.27 8.9 0.02 0.24 0.16
5.12 12.5 0.42 0.21 0.36
Panel C: Dividend growth ðDyÞ Mean (%) Std Dev (%) AC(1) AC(2) corrðDy, DdÞ
1.93 10.7 0.29 0.02 0.11
consumption is expected to grow slowly, and volatilities are high. As shown earlier, durable consumption growth is predicted by the price–dividend ratio. With first- and second-order autocorrelations of 0.91 and 0.81, the price–dividend ratio is highly persistent. This provides direct evidence for the highly persistent x component in the model. Consequently, I set the persistence parameter f to 0.99.16 The two volatility parameters sx and sd are calibrated to match the autocorrelations and the standard deviation of the annual data. The mean md is chosen to match the average annual growth rate. The counter-cyclical volatility following ot is motivated by, and allows the model to generate, both negative skewness and time-varying volatility documented above. In particular, negative skewness arises because the shocks have a high (low) volatility when the expected growth is low (high). I set the parameter z to match the skewness of the annual data, which leads to a value of 278. The resulting average skewness of the simulated quarterly series is about 0.52, broadly consistent with the empirical estimate of 0.46 for the quarterly data. Hence, this mechanism is able to replicate the skewness at both annual and quarterly frequencies. The variance ratios for the realized volatility of durable consumption growth are not included as targets of matching in the calibration. Still, Panel A of Table 6 shows that the variance ratios of the simulated data are largely consistent with the empirical estimates. The top panel in Fig. 2 plots the counter-cyclical volatility function oðxÞ with respect to x scaled by qffiffiffiffiffiffiffiffiffiffiffiffiffi sx = 1f2 , which would be the unconditional volatility of x without the counter-cyclical o. By construction, o ¼ 1 at x ¼0. With the calibrated z ¼ 278, the volatility
comes from the shocks to the expected component. The persistence of xt implies that its shocks will have a longlasting effect. The conditional volatility for the shocks varies counter-cyclically with respect to the long-run risk component. When xt is high, durable consumption is expected to grow fast, and volatilities are low for both short-run and long-run shocks. When xt is low, durable
qffiffiffiffiffiffiffiffiffiffiffiffiffi 2 becomes zero at x ¼ 2:097sx = 1f . This is also the maximum of x. For negative x, o rises slowly and reaches
16 This is consistent with 0.911/12 ¼ 0.9922. Also, Bansal and Yaron (2004) calibrate a persistence of 0.979 for expected nondurable consumption growth, and 0.987 for the volatility state variable.
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W. Yang / Journal of Financial Economics 102 (2011) 45–61
2
ω
1.5
1
0.5
0 −4
−3
−2
−1
0
1
2
3
−3
−2
−1
0
1
2
3
0.5
Density
0.4 0.3 0.2 0.1 0 −4
pffiffiffiffiffiffiffiffiffiffiffiffi Fig. 2. The top panel plots oðxÞ ¼ 1zx, the function underlying the volatility of durable consumption growth, with the calibrated sensitivity parameter z ¼ 278. The bottom panel plots the left-skewed, unconditional distribution of x. The vertical, dotted line marks the maximal value of x. Here, x is the expected component of durable consumption growth, sx is the standard deviation of the shocks to x, and f is the persistence of x.
qffiffiffiffiffiffiffiffiffiffiffiffiffi 2 about 1.6 when x=ðsx = 1f Þ ¼ 4. The bottom panel of Fig. 2 plots the model-implied unconditional density of x. The distribution, due to the conditional volatility, is negatively skewed. Hence, x is more often positive, but there are also important, although less frequent, realizations in the fat left tail. Additional simulation results suggest that the countercyclical volatility mechanism is critical for the model to match the empirically observed skewness. Consider, for example, an alternative in which negative skewness is unrelated to conditional volatility, but arises solely because long-run and/or short-run shocks follow skewed distributions. Simulation results indicate that this alternative mechanism is too weak — monthly i.i.d. shocks with a very negative skewness of 1.5 generate only a skewness of about 0.1 in the time-aggregated annual series. Furthermore, it is important that volatility varies with the expected component xt of durable consumption growth. Should ot depend on some additional state variable unrelated to xt, the resulting growth rate series would exhibit zero skewness. In addition, it is also
important that volatility is counter-cyclical not just for the short-run shocks, but also for the long-run shocks. With counter-cyclical volatility, both types of shocks can generate negative skewness, but with opposite behaviors with respect to time aggregation. Simulation results indicate that, with counter-cyclical volatility only in the long-run shocks, skewness becomes much more negative when quarterly series are aggregated to the annual frequency. In contrast, if counter-cyclical volatility appears only for the short-run shocks, annual series are much less negatively skewed than quarterly series. As reported earlier, the empirical skewness is 0.46 in the quarterly data and 0.51 in the annual data. This slightly increasing pattern suggests that both long-run and shortrun components are at play. For parsimony, I specify the same counter-cyclical function ot for both components. As shown above, the model replicates the skewness estimates at both annual and quarterly frequencies.17 Finally, in my model, the time-varying volatility is modeled together with negative skewness by specifying the conditional volatility following ot . The simulation results in Table 6 suggest that this parsimonious mechanism appears to be largely adequate in matching the empirical variance ratios of the realized volatility of durable consumption growth. However, the resulting perfect negative correlation between the conditional volatility and xt is a strong restriction. For example, it implies that all asset pricing results vary with one single state variable xt. In the cross section, this implies that all asset returns line up perfectly with their exposure to the long-run risk. These implications are doomed to be oversimplifying vis-a -vis the empirical asset market data. A potential extension of this specification is to introduce a separate state variable to represent a component of time-varying volatility unrelated to xt, in the spirit of Bansal and Yaron (2004). This introduces an additional source of risk, and will raise the equity premium and generate additional time-varying implications. It also enhances the flexibility of the model to match the empirical data. For example, Bansal, Kiku, and Yaron (2007) show that, while the long-run risk in nondurable consumption growth is the leading factor to explain the cross section of stock returns, the short-run risk and the volatility risk are also required. To sharpen the focus of the current paper, this interesting extension is left for future research. 4.2. Nondurable consumption and dividend growth To highlight the implications of the durable consumption growth dynamics, I specify nondurable consumption growth as pure random walk shocks,
Dct þ 1 ¼ log
Ct þ 1 ¼ mc þ sc ec,t þ 1 , Ct
ec,t þ 1 i:i:d: Nð0,1Þ: ð6Þ
Here, mc is the mean and sc is the volatility of the i.i.d. shocks. These parameters are calibrated to match the 17 An anonymous referee points out that, in a regime-switching framework with x as the filtered growth rate, both positive and negative correlations between volatility and x may arise.
W. Yang / Journal of Financial Economics 102 (2011) 45–61
average and the standard deviation of the empirical nondurable consumption growth data, as confirmed in Panel B of Table 6. Lastly, I specify dividend growth as
Dyt þ 1 ¼ log
Yt þ 1 ¼ my þ lxt þ sy ey,t þ 1 , Yt
ey,t þ 1 i:i:d: Nð0,1Þ: ð7Þ
Here, my is the mean, l is the parameter characterizing the exposure of dividend growth to the expected component of durable consumption growth. The random walk shocks of dividend growth have a volatility of sy . The correlation between dividend and durable consumption growth, reported in Panel C of Table 6, suggests a small exposure parameter l, which is set to 0.8.18 The mean parameter is set to match the average dividend growth, and a large sy is needed to replicate the empirical volatility. Panel C of Table 6 confirms the match, and in particular, shows that the model replicates the first-order autocorrelation of dividend growth as well as the correlation between durable consumption growth and dividend growth. With a small l and a large sy , dividend growth is close to a process of i.i.d. shocks. However, as shown subsequently, the high persistence of the expected durable consumption growth implies that even a small l for dividend growth is able to generate a large exposure of the stock return to the long-run risk. For parsimony, all shocks — ex,t þ 1 , ed,t þ 1 , ec,t þ 1 , and ey,t þ 1 — are mutually independent. This leaves the burden of the model performance entirely on the expected durable consumption growth xt. The model could be enriched by allowing for correlations between the shocks. For example, in the empirical data, the correlation between annual durable and nondurable consumption growth rates is about 0.18. This can be replicated by correlated ed,t þ 1 and ec,t þ 1 shocks. The correlation between annual dividend and nondurable consumption growth is about 0.35. This can be replicated by correlated ey,t þ 1 and ec,t þ 1 shocks. These enrichments result in only minor qualitative and quantitative changes in the model’s asset pricing implications, because the prices of risk are small for ed,t þ 1 and ec,t þ 1 shocks.19 Lastly, as modeled in my paper, both log durable consumption d and log nondurable consumption c are difference stationary, and so d c is difference stationary with a drift. Ogaki and Reinhart (1998) make the same assumptions and confirm the empirical validity of these assumptions in their paper. Fig. 1 also suggests that these assumptions are empirically plausible. 18 To provide further support to the calibration of l, I regress dividend growth on a proxy of xt, computed as the trailing K-year moving average of past durable consumption growth. The slope coefficient (standard error) is 0.42(0.59) for K¼ 1, and decreases to 0.22(0.57) for K¼ 3. These slope estimates are low and the standard errors are large, potentially because of the measurement errors in the proxies for xt. Still, the results are consistent with a calibration of l below 1. 19 Bansal and Yaron (2004) focus on the long-run risk in nondurable consumption growth. The correlation between dividend and nondurable consumption growth, replicated by modeling dividend growth as a levered claim on the expected component in nondurable consumption growth, yields major asset pricing results in their paper.
53
5. Asset pricing This section presents the details of the model for a representative agent with nonseparable utility over both durable and nondurable consumption embedded in Epstein-Zin preferences. This is followed by the calibration of the model parameters and the discussions of the model intuition using approximate analytical solutions. 5.1. Utility In each period, the representative agent consumes Ct units of nondurable goods, and derives the service flow proportional to the stock, Dt, of durable goods. The agent has an intra-period Cobb-Douglas utility function Vt ¼ Ct1a Dat ,
ð8Þ
where 0 o a o1 is a constant. The numeraire is nondurable goods. Since durable goods last for more than one period, the price of the one-period service flow is not the purchase price. Rather, it is the user cost, which is implied by the utility function, Qt ¼
@Vt =@Dt a Ct ¼ : @Vt =@Ct 1a Dt
ð9Þ
Hence, measured in terms of nondurables, durable consumption or the service flow of durables during period t is Qt Dt .20 The empirical evidence presented earlier indicates that the dynamics of durable and nondurable consumption growth are very different. For example, durable consumption grows much faster than nondurable consumption, and thus the ratio D/C has risen considerably over time. However, the Cobb-Douglas utility implies that Qt is proportional to Ct/Dt. Hence, variations in Dt relative to Ct are accompanied with exactly opposite variations in Qt. In particular, as Dt/Ct increases over time, Qt decreases and its decrease exactly cancels the increase in Dt/Ct. As a result, Qt D t ¼
a 1a
Ct :
ð10Þ
That is, when measured in terms of the nondurable numeraire, durable consumption is proportional to Ct. The total consumption is then Gt ¼ Ct þ Qt Dt ¼
1 Ct , 1a
ð11Þ
which is also proportional to nondurable consumption. In addition, the consumption shares are constant regardless of the variations in Dt/Ct, since Ct ¼ 1a, C t þ Qt D t 20
Qt D t ¼ a: Ct þ Qt Dt
ð12Þ
The stock of durable goods evolves following: Dt þ 1 ¼ ð1dD ÞDt þ ED,t þ 1 ,
where dD is the depreciation rate, and ED,t þ 1 is the expenditure. Let PD,t denote the purchase price of durable goods in terms of nondurables, then PD,t ED,t is the expenditure on new durable goods.
54
W. Yang / Journal of Financial Economics 102 (2011) 45–61
This provides an interpretation of a as the share of durable consumption. The Cobb-Douglas utility is the special case of r ¼ 1 for the constant elasticity of substitution utility function 11=r
ðð1aÞCt
11=r 1=ð11=rÞ
þ aDt
Þ
:
ð13Þ
There are two motivations for the choice of r ¼ 1 in this paper. First, empirical estimates of r are not very different from 1. For example, Ogaki and Reinhart (1998) find r to be about 1.2,21 and Yogo (2006) estimates it at about 0.8. Secondly, under a general r, the durable consumption share is
aðDt =Ct Þ11=r 1a þ aðDt =Ct Þ11=r
:
ð14Þ
Hence, ra1 introduces another state variable Dt/Ct to the model, and the share of durable consumption varies with time. This induces composition risk, similar to that in Piazzesi, Schneider, and Tuzel (2007). In the data, the ratio of D/C tends to rise over time. This implies an increasing (decreasing) share of durable consumption if r 41ð o1Þ, while r ¼ 1 implies a constant share of durable consumption.22 It turns out that when r is not very different from 1, this generates only small temporal variations in the quantities of interest. Overall, setting r ¼ 1 maintains parsimony, sharpens the focus of the paper, and the implications — consumption shares are constant, and total consumption grows at the same rate as that of nondurable consumption — appear to be economically reasonable. The intra-period utility is embedded in Epstein-Zin preferences 11=c
Ut ¼ ðð1dÞVt
1g
þ dðEt ½Ut þ 1 Þð11=cÞ=ð1gÞ Þ1=ð11=cÞ :
ð15Þ
Here, 0 o d o 1 is the time discount factor, g is the risk aversion parameter, and c is the elasticity of intertemporal substitution. Following Bansal, Tallarini, and Yaron (2008) and Yogo (2006), the pricing kernel is y=c Dt þ 1 =Ct þ 1 ayð11=cÞ y1 y Ct þ 1 Mt þ 1 ¼ d Rg,t þ 1 , ð16Þ Ct Dt =Ct where y ¼ ð1gÞ=ð11=cÞ: Here, Rg,t þ 1 ¼
Wt þ 1 Wt Gt
ð17Þ
21 Specifically, Ogaki and Reinhart (1998) assume c and d are difference stationary, and then show that the log price of durables in terms of nondurables, p, is also difference stationary, and ½p,cd is cointegrated with a cointegrating vector ð1,1=rÞ. They confirm the empirical validity of these stationarity assumptions, and utilizing the cointegration relation, they estimate r to be about 1.2. With r ¼ 1, my model implicitly assumes that ½p,cd is cointegrated with a vector (1, 1). However, this relation is not imposed or utilized in my model in any explicit way. 22 For a general r, the user cost is
Qt ¼
@Vt =@Dt a Dt 1=r ¼ : @Vt =@Ct 1a Ct
Hence, the user cost decreases when D/C increases as long as r 4 0. When r 4 1ð o 1Þ, the decrease in the user cost under-compensates (over-compensates) the rise in D/C, resulting in an increasing (decreasing) share of durable consumption.
is the wealth return (or total consumption return), and the wealth Wt is the claim to the entire future stream of total consumption. The parameters in the preferences, as presented in Table 5, are chosen to take into account the empirical evidence and economic considerations. The empirical estimates of a are about 0.8 in Yogo (2006), and about 0.6 in Gomes, Kogan, and Yogo (2009). I calibrate a ¼ 0:5, giving equal weights to the service flows of durables and nondurables in the total consumption. The parameters of Epstein-Zin preferences follow Bansal and Yaron (2004). The time discount factor d o1, the risk aversion parameter g ¼ 10, and the elasticity parameter c ¼ 1:5. As in Bansal and Yaron (2004), the model in this study relies on c 4 1 to generate small and stable risk-free rates.23 With c ¼ 1:5 and thus car ¼ 1, the utility is nonseparable between durable and nondurable consumption. This is a critical ingredient of the model that allows durable consumption growth, in particular, its long-run risk component, to generate important asset pricing implications.24 5.2. Pricing kernel The model has only one state variable xt, which fully characterizes the solutions. As shown in Appendix A, the approximate analytic solution for the log price–total consumption ratio is 1c1 a Pg,t log ¼ zg,t Ag0 þAg1 xt , Ag1 ¼ : ð18Þ Gt 1kg1 f Here, Pg,t is the ex-dividend price of the claim to the entire future stream of total consumption, kg1 is a constant very close to 1, Ag0 and Ag1 are constants, and Ag1 40 when c 4 1. Therefore, a rise in the expected durable consumption growth increases the price of the total consumption claim. A higher persistence parameter f amplifies the response to a much greater extent. Since durable consumption makes up a fraction a of total consumption, the magnitude of Ag1 is proportional to a. Following the price–total consumption ratio, the innovation to the pricing kernel is mt þ 1 Et ½mt þ 1 ¼ gsc ec,t þ 1 ðg1Þaðsd ot ed,t þ 1 sc ec,t þ 1 Þ kg1 a 1 soe ð19Þ g c 1kg1 f x t x,t þ 1
23 Bansal and Yaron (2004) present more detailed discussions regarding the debate whether c is above or below 1. 24 For general r, define
Ft ¼ FðDt =Ct Þ ¼ Vt =Ct ¼ ð1a þ aðDt =Ct Þ11=r Þ1=ð11=rÞ : The pricing kernel is y
Mt þ 1 ¼ d
Ct þ 1 y=c Ft þ 1 yð1=r1=cÞ y1 Rg,t þ 1 : Ct Ft
If rac, then durable and nondurable consumption are nonseparable. When r ¼ ca1, Ft þ 1 =Ft drops out of the pricing kernel, but Dt =Ct drives time-varying consumption shares and appears in Rg,t þ 1 , and thus the utility function is still nonseparable. Finally, if r ¼ c ¼ 1, consumption shares are constant, and durable consumption completely drops out of the pricing kernel.
W. Yang / Journal of Financial Economics 102 (2011) 45–61
¼ pc sc ec,t þ 1 pdc ðsd ot ed,t þ 1 sc ec,t þ 1 Þ px sx ot ex,t þ 1 : ð20Þ The first term is familiar from the studies based on power utility: The risk is the shocks to nondurable consumption growth, and its market price of risk is risk aversion g. In the second term, the risk is the random walk (or shortrun) shocks to durable and nondurable consumption growth, and the market price of risk is positive if g 4 1.25 The small volatilities of nondurable and durable consumption growth imply that, in order for these two terms to generate the observed equity premium, an extraordinarily high risk aversion is required. The third term is for the long-run risk in durable consumption growth, or the shocks to the expected durable consumption growth. The market price of risk is positive if g 4 1=c (i.e., Epstein-Zin preferences with early resolution of uncertainty), and can be very large with high persistence f. In addition, the market price of risk contains a and inherits the time-varying conditional volatility following ot . 5.3. Real bond yields Following the pricing kernel, the approximate analytical solution for the log risk-free rate can also be computed. The details are in Appendix B. The risk-free rate is measured in terms of the numeraire nondurable good, and 1 1 y1 rf ,t logd þ mc 1 aðmd þ xt mc Þ E ½r r : c c y t g,t þ 1 f ,t ð21Þ The equation highlights several determinants of the riskfree rate. In particular, the first three terms above are a special case of r ¼ 1 for the general result of logd þ
1 1 ð1aÞmc þ aðmd þxt Þ aðmd þxt mc Þ:
c
r
Here, the first term is the discount effect. If d is small, or future consumption is heavily discounted, the agent wants to borrow to increase consumption today, driving up the riskfree rate. The second term reflects the effect of intertemporal substitution. If c is small, the agent prefers to smooth over time. Hence, when both durable and nondurable consumption growth are high, the agent will want to borrow, driving up the risk-free rate. Lastly, the third term represents the effect of substitution between goods. If r is small, the agent wants to smooth between durable and nondurable consumption. Consequently, when the expected durable consumption growth is higher than that for nondurable consumption, the agent will want to save so as to increase nondurable consumption in the future, driving down the risk-free rate. The variations of the risk-free rate are practically determined by its dependence on xt in 1 1 a xt
c
r
from the preceding equation. In the calibration of this paper, c ¼ 1:5 4 r ¼ 1, and thus the effect of goods 25
Under a general r, this is actually g 4 1=r.
55
smoothing dominates that of intertemporal smoothing. As a result, the risk-free rate varies counter-cyclically with xt and is high when xt is low (and the conditional pffiffiffiffiffiffiffiffiffiffiffiffiffi volatility, proportional to ot ¼ 1zxt , is high). The counter-cyclicality becomes stronger if c is larger, r is smaller, or a is higher. Because the volatility of xt is small, the risk-free rate is smooth. Appendix B also computes the log price for an n-period real zero-coupon bond n 1 1f bn,t Bn,0 þBn,1 xt , Bn,1 ¼ 1 a : ð22Þ c 1f With c 41, Bn,1 4 0, and thus real bond yields, bn,t =n, vary counter-cyclically. Again, because the effect of goods smoothing dominates that of intertemporal smoothing, the agent wants to save when xt is high. This drives up the bond prices and drives down the bond yields (including the risk-free rate discussed above). Real bonds, therefore, contain positive exposure to xt, and the exposure increases with the bond maturity, since Bn,1 rises with n. For the holding period return, hpr n,t þ 1 ¼ bn1,t þ 1 bn,t ,
ð23Þ
hpr n,t þ 1 Et ½hpr n,t þ 1 Bn1,1 sx ot ex,t þ 1 :
ð24Þ
The positive loading implies a positive, counter-cyclical bond risk premium Et ½hpr n,t þ 1 rf ,t þ 12vart ½hpr n,t þ 1 covt ½mt þ 1 ,hpr n,t þ 1 ð25Þ ¼ Bn1,1 px s2x o2t ¼ Bn1,1 px s2x ð1zxt Þ:
ð26Þ
As shown in Appendix B, this positive bond risk premium implies an upward-sloping yield curve. The slope also varies counter-cyclically. The slope becomes steeper and its counter-cyclicality becomes stronger if c is larger, r is smaller, or a is higher. 5.4. Stock returns The approximate analytical solution for the log price– dividend ratio is l þ 1c1 a Pt log ¼ zt A0 þA1 xt , A1 ¼ : ð27Þ Yt 1k1 f Here, Pt is the ex-dividend price of the dividend claim, Yt is the dividend, k1 is a constant very close to 1, and A0 and A1 are constants. Since A1 4 0, a positive shock to xt is also magnified to a rise in the log price–dividend ratio. The magnification factor increases with the persistence parameter f. The return innovation is rt þ 1 Et ½rt þ 1 k1 A1 sx ot ex,t þ 1 þ sy ey,t þ 1
ð28Þ
¼ bx sx ot ex,t þ 1 þ sy ey,t þ 1 :
ð29Þ
Since all shocks are assumed to be mutually independent, the stock return is only exposed to the long-run risk in durable consumption growth. Consequently, 1 Et ½rt þ 1 rf ,t þ vart ½rt þ 1 covt ½mt þ 1 ,rt þ 1 2
ð30Þ
56
¼ bx px s2x o2t ¼ bx px s2x ð1zxt Þ:
W. Yang / Journal of Financial Economics 102 (2011) 45–61
ð31Þ
Hence, the expected excess return varies negatively with xt. These results suggest that the model generates a large equity premium and a high stock return volatility because the market price of the long-run risk is high, and the exposure of the stock return to this risk is also large. At the same time, because the long-run risk exhibits counter-cyclical volatility following ot , this mechanism also gives rise to large counter-cyclical variations in the equity premium and the stock return volatility. Further, since A1 4Ag1 , the stock return has a larger exposure to the long-run risk than the wealth return. This implies that both the risk premium and the volatility are higher for the stock return than for the wealth return.26 Similar to Bansal and Yaron (2004), the model in this paper is also able to generate the volatility feedback effect, or the negative correlation between the return innovation and the conditional volatility innovation (Campbell and Hentschel, 1992; Glosten, Jaganathan, and Runkle, 1993). As shown in Appendix C,
3 covt rt þ 1 Et ½rt þ 1 ,vart þ 1 rt þ 2 Et vart þ 1 ½rt þ 2 ¼ bx s4x zo2t :
ð32Þ The negative correlation results from the counter-cyclical volatility following ot . Altogether, these results show that with nonseparability, interesting asset market implications can be generated almost solely based on the empirically motivated dynamics of durable consumption growth, even though nondurable consumption growth is modeled as random walk shocks, and there is no variation in consumption shares. With these results and the strong empirical evidence shown earlier, long-run durable consumption risk appears to be a plausible channel to explain asset market phenomena. 6. Model implications I solve the model numerically using the projection method in Judd (1998) with cubic splines. Expectations are evaluated using Gaussian quadrature. As demonstrated in the figures presented subsequently, the numerical solutions confirm the intuition illustrated in the approximate analytical solutions. The numerical solutions are obtained for the monthly frequency. Then I simulate monthly series, time-aggregate to the annual frequency, and compare with the observed annual data. 6.1. Numerical solution Fig. 3 plots the valuation ratios. Both the log price– total consumption ratio and the log price–dividend ratio are pro-cyclical functions of x, consistent with the approximate analytical solutions. The risk-free rate, as plotted in Fig. 4, is countercyclical. As indicated earlier, this is primarily the result of the effect of goods smoothing dominating that of 26 These implications are consistent with the study of Lustig, Van Nieuwerburgh, and Verdelhan (2008).
7.5 log (P/G)
7 6.5 6
log (P/Y) 5.5 5 4.5 −4
−3
−2
−1
0
1
2
3
Fig. 3. Log price–total consumption ratio, logðP=GÞ, and the log price– dividend ratio, logðP=YÞ, as functions of x. The vertical, dotted line marks the maximal value of x. Here, x is the expected component of durable consumption growth, sx is the standard deviation of the shocks to x, and f is the persistence of x.
intertemporal smoothing. When xt is high, the expected durable consumption growth is high. The tendency to smooth consumption over time will drive the agent to borrow from the future. However, the tendency to smooth between durable and nondurable goods will drive the agent to save so as to increase nondurable consumption in the future. With c ¼ 1:54 r ¼ 1, the latter dominates the former, resulting in a low risk-free rate.27 At x¼ 0, the annualized risk-free rate is 1.73%. The graph also suggests that the volatility of the risk-free rate is small. Fig. 4 also plots the five-year real bond yield, indicating a counter-cyclical dependence on x. The curve is above the risk-free rate, suggesting a term structure with a small positive slope. In addition, both the level and the slope of the term structure decrease when x increases. Fig. 4 shows that the risk premiums for both wealth and stock returns are counter-cyclical. As discussed earlier, this ultimately results from the counter-cyclical volatility in the expected durable consumption growth. In the model, total consumption growth is equal to nondurable consumption growth, which is a process of i.i.d. shocks and the exposure to the long-run risk component xt is zero. In contrast, the exposure of dividend growth to xt is l ¼ 0:8. At the annualized level, the total consumption risk premium is about 1.60% at x ¼0, while the annualized equity risk premium is 5.31% at x ¼0. 27 I regress the risk-free rate of year t þ 1 on the price–dividend ratio of year t using the empirical data and find a slope coefficient of 0.012, with a standard error of 0.011, and an R2 ¼ 0.036. This result, while not significant at conventional confidence levels, is consistent with countercyclicality. Running the same regression using the model-implied, simulated data, I obtain an average slope coefficient of 0.0007 and an average R2 ¼ 0.38. These model-implied results are broadly consistent with the empirical results. The small empirical R2 is most likely due to the high volatility of the empirical risk-free rate as a result of containing unexpected inflation.
W. Yang / Journal of Financial Economics 102 (2011) 45–61
57
0.2
10
E [r − r f ]× 12
0.15
Volatility
Rate and return (%)
8
6
0.1 0.05
4
2
0 −4
E [r g − r f ]× 12 r f (5y) r f × 12
−2
−1
0
1
2
3
−3
−2
−1
0
1
2
3
1.2 1
−3
−2
−1
0
1
2
3
Fig. 4. This figure plots the risk-free rate, rf 12, the five-year real bond yield, rf ð5yÞ, the expected excess return to the total consumption claim, E½rg rf 12, and the expected excess return to the dividend claim, E½rrf 12. All are annualized and plotted as functions of x. The vertical, dotted line marks the maximal value of x. Here, x is the expected component of durable consumption growth, sx is the standard deviation of the shocks to x, and f is the persistence of x.
Variations in the equity risk premium are also more sensitive to x, as indicated by its steeper slope than that for the total consumption risk premium. While l o 1 for dividend growth, the exposure of durable consumption growth on xt, by construction, is 1. Hence, the dividend claim earns a lower return than a claim that pays durable consumption. The model solution indicates an annualized risk premium of 7.27% at x ¼0 for the durable consumption claim. This is broadly consistent with the evidence in Gomes, Kogan, and Yogo (2009) that the average return to a portfolio of the stocks of durablegood producers is higher than that of the aggregate stock market. As emphasized earlier, the relative price of durables varies with the ratio of nondurable to durable consumption, and as a result, total consumption is proportional to nondurable consumption. Hence, the risk premium is high for the durable consumption claim, but low for the total consumption claim. Fig. 5 plots the conditional volatilities and the Sharpe ratios, both annualized. The total consumption return has a much lower volatility than the stock return, while its Sharpe ratio is much higher. For example, at x¼0, the conditional volatility of the total consumption return is about 0.027, in contrast to a level of 0.163 for the stock return. The conditional Sharpe ratio of the total consumption return is 0.59 at x ¼0, while that for the stock return is 0.33. The maximal Sharpe ratio, which is also the volatility of the log pricing kernel, is 0.663 at x¼0. The total consumption return is close to achieving the maximal Sharpe ratio, but the stock return is far below.
Sharpe ratio
0 −4
−3
0.8 0.6 0.4 0.2 0 −4
Fig. 5. The top panel plots p the ffiffiffiffiffiffi conditional volatility of the total consumption return, s½rg 12, and that of the stock return, pffiffiffiffiffiffi s½r 12. The bottom panel plots the conditional Sharpe ratio of the pffiffiffiffiffiffi total consumption return, pffiffiffiffiffiffi E½rg rf =s½rg 12, and that of the stock return, E½rrf =s½r 12. All are annualized and plotted as functions of x. The vertical, dotted line marks the maximal value of x. Here, x is the expected component of durable consumption growth, sx is the standard deviation of the shocks to x, and f is the persistence of x.
As shown in Eq. (19), all three shocks — nondurable consumption growth shocks, random walk shocks to durable consumption growth, and shocks to the expected durable consumption growth — contribute to the variance of the pricing kernel. Variance decomposition based on the numerical solution indicates that the long-run durable consumption risk contributes more than 98% of the variations of the pricing kernel. The two short-run risks combined contribute the remaining 1.5% of the variance of the pricing kernel. 6.2. Simulation results I turn to simulations to gauge the model’s quantitative performance in matching the key aspects of the observed asset market data. I simulate 10,000 samples, each of 56 12 months, and then time-aggregate to the annual frequency. Table 7 reports the mean and 5th and 95th percentiles of key moments across the simulated samples, and compares them with those obtained from the empirical data. The model produces an average equity premium of 5.07%, only slightly below the observed value. Note that
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W. Yang / Journal of Financial Economics 102 (2011) 45–61
Table 7 This table compares the properties of the annual empirical asset market data with the model-implied, simulated data. Here, r is the stock return, rf is the risk-free rate, P=Y is the price–dividend ratio, py is the log price–dividend ratio, AC(1) and AC(2) are the first- and second-order autocorrelations, E½ denotes the mean, and s½ denotes the volatility. The empirical data are annual for the period 1952–2007. The empirical estimates are obtained with GMM, and standard errors are Newey and West (1987) corrected with ten lags. The model-implied results are the means and percentiles from 10,000 samples simulated from the numerical solution of the model. Each simulated sample is 56 12-month long, and is then time-aggregated to the annual frequency. Data
E½rrf s½r E½rf s½rf E½P=Y s½py ACð1Þ½py ACð2Þ½py
Table 8 Predictability of excess stock returns by the log price–dividend ratio. This table compares the empirical results of the predictive regressions with those from the model-implied, simulated data. The cumulative excess stock return from year t to year t þ J is regressed on the log price– dividend ratio of year t. Here, J is the horizon. The empirical data are annual for the period 1952–2007. The empirical estimates are obtained with GMM, and the standard errors are Newey and West (1987) corrected with ten lags. The model-implied results are the averages over 10,000 samples simulated from the numerical solution of the model. Each simulated sample is 56 12-month long, and is then time-aggregated to the annual frequency. Horizon
Model
Data
Model
Estimate
Std Err
Mean
5%
95%
(year)
Slope
Std Err
R2
Slope
R2
5.46% 0.154 1.68% 2.23% 32.2 0.354 0.91 0.81
(1.79%) (0.015) (0.50%) (0.21%) (4.4) (0.034) (0.04) (0.06)
5.07% 0.160 1.72% 0.02% 21.7 0.195 0.86 0.75
1.93% 0.134 1.70% 0.01% 18.0 0.133 0.68 0.47
8.16% 0.187 1.75% 0.06% 25.2 0.280 0.95 0.87
1 3 5
0.096 0.188 0.264
(0.046) (0.096) (0.124)
0.047 0.081 0.097
0.140 0.260 0.363
0.036 0.089 0.129
the only source of equity premium in the model is the long-run durable consumption risk. Hence, the model performance in terms of generating sizable excess returns is impressive. The average return volatility of 0.160 is slightly higher than the observed level. The mean risk-free rate is 1.72%, also matching the empirical estimate. The volatility of 0.02% is very low. This, however, is not a serious concern, since the volatility of the ex ante real risk-free rate is most likely much lower than the realized 2.23% for the ex post real rate, which contains unexpected inflation.28 For the price–dividend ratio, the modelimplied moments are somewhat smaller than their empirical counterparts, but are largely consistent. Overall, Table 7 suggests that the model in this paper is capable of reproducing the key aspects of the asset market data. Additional sensitivity analyses suggest that the equity premium can be further increased by increasing risk aversion in the model. Because the market price of longrun durable consumption risk is proportional to the durable consumption share, both the equity premium and the stock return volatility decrease when the share is lower. In particular, the equity premium decreases about linearly with decreasing share of durables. Finally, decreasing the elasticity of intertemporal substitution results in a higher risk-free rate. 6.3. Predictive regressions In the empirical stock market data, future excess returns are predictable by the price–dividend ratio (Campbell and Shiller, 1988). In the model of this paper, the equity premium varies counter-cyclically with xt, the log price– dividend ratio is a pro-cyclical function of xt, and xt is a persistent process. Hence, excess returns are predictable by 28 Indeed, Campbell and Cochrane (1999) construct their model to generate a constant risk-free rate.
the price–dividend ratio with negative slopes in the model. Table 8 compares the results for the predictive regressions in the observed data with those from the model-implied, simulated data. In the regressions, the cumulative excess stock returns of horizons of one, three, and five years are regressed on the log price–dividend ratio. In both the empirical and simulated data, the slope coefficient and R2 increase with the horizon.29 The model-implied slopes are somewhat higher than the empirical values, while the model-implied R2 values match the empirical estimates well. Overall, the model is capable of capturing the salient features of the observed excess return predictability. As presented in Section 3, this study also documents a number of empirical predictive relations. An important empirical fact that motivates the model in this paper is that durable consumption growth rates are predicted by the price–dividend ratio with positive slopes. In the model solution, the price–dividend ratio is a pro-cyclical function of the persistent component in durable consumption growth. Hence, the model also implies a positive predictive relation. Panel B of Table 1 confirms that the model-implied results are consistent with the empirical results. Finally, in the model, the conditional volatility of durable consumption growth varies counter-cyclically while the price–dividend ratio is pro-cyclical. Hence, the model is able to replicate the empirically observed negative predictive relations between the realized volatility of durable consumption growth and the price–dividend ratio. Panels B and C of Table 3 confirm that the modelimplied results are broadly consistent with the empirical results. 29 The slopes and R2 in Table 8 for the empirical data over the period 1952–2007 are low in magnitude in comparison to, for example, those in Bansal and Yaron (2004) for the period 1929–1998. To provide assurance, I run the same predictive regressions for the sample of 1929–2007 and find that, for horizons of one, three, and five years, the slopes are 0.11, 0.30, and 0.46, while the R2 values are 0.04, 0.14, and 0.25. These results are larger in magnitudes and comparable to those in Bansal and Yaron (2004). Consequently, I conclude that the small magnitudes reported in my paper are specific to the sample period 1952–2007.
W. Yang / Journal of Financial Economics 102 (2011) 45–61
7. Concluding remarks
59
Also
In this paper I show that the empirical data properties suggest a model for durable consumption growth as containing a long-run risk component with counter-cyclical volatility. I model dividend growth as exposed to the long-run risk component, and show that nonseparable Epstein-Zin preferences allow the long-run risk dynamics of durable consumption growth to generate interesting asset pricing implications, even though nondurable consumption growth is modeled as pure i.i.d. shocks, and the consumption shares are constant. In concluding the paper, I point out some limitations and thus possible extensions of this study. A simplifying assumption in this paper is to set the elasticity of substitution between durable and nondurable consumption to be 1. This yields constant consumption shares and saves an extra state variable. If the elasticity is different from 1, it implies a time-varying share of durable consumption and introduces composition risk, similar to that in Piazzesi, Schneider, and Tuzel (2007). Although the effects of this variation on the equity premium and the stock return volatility are small as long as the elasticity is not very different from 1, it would be interesting to explore the implications further. A conclusion of this paper is that with nonseparability, durable consumption is able to generate interesting asset pricing implications even if nondurable consumption, when modeled as a random walk, does not deliver comparable results. The list of goods can be further extended, and nonseparability suggests that interesting dynamics along these additional dimensions will become reflected in asset prices. These interesting extensions are beyond the scope of the current paper and thus left for future research. Lastly, following the convention in the consumptionbased asset pricing literature, this study takes the empirical properties of the durable consumption growth data as given in order to focus on the asset market implications. A general equilibrium model incorporating both consumption and production decisions is worth exploring. This merits a separate study, and is also left for future research.
Ddt þ 1 Dct þ 1 ¼ md þ xt þ sd ot ed,t þ 1 mc sc ec,t þ 1 , Dgt þ 1 ¼ Dct þ 1 : Assume the price–total consumption ratio is log
Pg,t ¼ zg,t Ag0 þ Ag1 xt : Gt
ð33Þ
Using the Taylor expansion, rg,t þ 1 ¼ logð1þ ezg,t þ 1 Þ þ Dgt þ 1 zg,t kg0 þ kg1 zg,t þ 1 þ Dgt þ 1 zg,t ¼ kg0 þ kg1 Ag0 þ kg1 Ag1 xt þ 1 þ Dct þ 1 zg,t ¼ kg0 þ kg1 Ag0 þ kg1 Ag1 fxt þ kg1 Ag1 sx ot ex,t þ 1 þ mc þ sc ec,t þ 1 Ag0 Ag1 xt , where kg1 o 1, but very close to 1. The pricing equation 1 ¼ Et ½emt þ 1 þ rg,t þ 1 implies 0 Et ½mt þ 1 þrg,t þ 1 þ 12vart ½mt þ 1 þrg,t þ 1 :
Collect terms linear in xt and ignore quantitatively small contributions from the variance term, then 1c1 a 1 axt þ yðkg1 Ag1 fxt Ag1 xt Þ, Ag1 ¼ : 0 ¼ y 1 c 1kg1 f The return innovation is rg,t þ 1 Et ½rg,t þ 1 ¼ kg1 Ag1 sx ot ex,t þ 1 þ sc ec,t þ 1 : The pricing kernel innovation is mt þ 1 Et ½mt þ 1 ¼
y 1 se þ y 1 aðsd ot ed,t þ 1 c c c c,t þ 1
sc ec,t þ 1 Þ þðy1Þðkg1 Ag1 sx ot ex,t þ 1 þ sc ec,t þ 1 Þ ¼ gsc ec,t þ 1 ðg1Þaðsd ot ed,t þ 1 sc ec,t þ 1 Þ þðy1Þkg1 Ag1 sx ot ex,t þ 1 ¼ gsc ec,t þ 1 ðg1Þaðsd ot ed,t þ 1 sc ec,t þ 1 Þ kg1 a 1 g soe : c 1kg1 f x t x,t þ 1 In addition, Et ½rg,t þ 1 ¼ kg0 þ kg1 Ag0 þ kg1 Ag1 fxt þ mc Ag0 Ag1 xt 1 ¼ kg0 þ kg1 Ag0 þ mc Ag0 1 axt ,
c
Appendices
and
The approximate analytical solutions of the model are based on log-linearization and thus require keeping track of linear terms of xt. For tractability, I ignore quantitatively small contributions from the variance terms in the pricing equations. More discussions of this point are provided in Appendix D.
y 1 m þ y 1 aðmd þ xt mc Þþ ðy1ÞEt ½rg,t þ 1 c c c 1 1 ¼ const þ y 1 axt ðy1Þ 1 axt c c 1 ¼ const þ 1 axt :
Et ½mt þ 1 ¼ ylogd
c
Appendix A. Log price–total consumption ratio Appendix B. Real bond yields The pricing kernel is mt þ 1 ¼ ylogd
ð34Þ
y 1 aðDdt þ 1 Dct þ 1 Þ þðy1Þrg,t þ 1 : Dc þ y 1 c c tþ1
The pricing equation 1 ¼ Et ½emt þ 1 þ rf ,t
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W. Yang / Journal of Financial Economics 102 (2011) 45–61
Finally, in
implies rf ,t
Et ½mt þ 1 12vart ½mt þ 1 :
0 Et ½mt þ 1 þ rt þ 1 þ 12vart ½mt þ 1 þrt þ 1 ,
Ignoring the quantitatively small variance term, this implies y 1 rf ,t ylogd þ mc y 1 aðmd þ xt mc Þðy1ÞEt ½rg,t þ 1 : c c Add ðy1Þrf ,t to both sides, and divide by y (assume ya0), 1 1 y1 rf ,t logd þ mc 1 aðmd þ xt mc Þ E ½r r : c c y t g,t þ 1 f ,t Variations in rf ,t are practically driven by the xt term in the above. Assume the log price of an n-period real zero-coupon bond is
ð36Þ
collect terms linear in xt and ignore quantitatively small contributions from the variance term, l þ 1c1 a 1 axt þ k1 A1 fxt þ lxt A1 xt , A1 ¼ : 0 ¼ 1 c 1k1 f Hence, the log return innovation is rt þ 1 Et ½rt þ 1 ¼ k1 A1 sx ot ex,t þ 1 þ sy ey,t þ 1 ¼ bx sx ot ex,t þ 1 þ sy ey,t þ 1 : The conditional variance is 2
vart ½rt þ 1 ¼ bx s2x o2t þ s2y : Hence, the innovation to the conditional variance is
bn,t ¼ Bn,0 þ Bn,1 xt :
2
Then the log holding period return is
vart þ 1 ½rt þ 2 Et ½vart þ 1 ½rt þ 2 ¼ bx s2x zsx ot ex,t þ 1 :
hpr n,t þ 1 ¼ bn1,t þ 1 bn,t :
The covariance between the return innovation and the conditional variance innovation is
In
3
covt ½rt þ 1 Et ½rt þ 1 ,vart þ 1 ½rt þ 2 Et ½vart þ 1 ½rt þ 2 ¼ bx s4x zo2t :
0 Et ½mt þ 1 þ hpr n,t þ 1 þ 12vart ½mt þ 1 þhpr n,t þ 1 , collect terms linear in xt and ignore quantitatively small contributions from the variance term, then 1 0 ¼ 1 axt þ Bn1,1 fxt Bn,1 xt :
c
With the initial condition B0,1 ¼ 0, it yields n 1 1f a : Bn,1 ¼ 1 c 1f Hence, the log return innovation is hpr n,t þ 1 Et ½hpr n,t þ 1 ¼ Bn1,1 sx ot ex,t þ 1 : Using zero yields rf ,n,t ¼ bn,t =n, the excess return can be rewritten as hpr n,t þ 1 rf ,t ¼ nr f ,n,t ðn1Þrf ,n1,t þ 1 rf ,t : Hence, Et ½hpr n,t þ 1 rf ,t ¼ nr f ,n,t Et ½ðn1Þrf ,n1,t þ 1 rf ,t : The left-hand side is the one-period bond risk premium, while the right-hand side is the one-period term premium. Appendix C. Log price–dividend ratio Log dividend growth is
Dyt þ 1 ¼ lxt þ sy ey,t þ 1 : Assume log
Pt ¼ zt A0 þ A1 xt : Yt
As presented above, the log-linear approximate analytical solutions involve keeping track of linear xt terms in the pricing equations. In doing so, I have ignored the variance terms. As demonstrated in Bansal and Yaron (2004), variance terms can be critical for deriving approximate analytical solutions. In particular, in their model, volatility is a separate state variable. In order to track this state variable, it is essential to include the variance terms. My model has only one state variable xt. Underlying the pffiffiffiffiffiffiffiffiffiffiffiffiffi conditional volatility is ot ¼ 1zxt , an exact function of xt. In other words, volatility or ot is not a separate state variable. Rather, conditional volatility generates time-varying implications in my model solely through xt terms. For example, as long as the valuation ratios depend on xt, then the pricing kernel innovation and the return innovation contain x shocks and exhibit time-varying volatilities. Consequently, both the expected excess returns and the return volatilities vary with time. Hence, for log-linear approximations, it is important to track the linear xt terms properly. The variance terms in the pricing equations also generate linear xt terms. For example, the variance term in the pricing equation for the total consumption claim [Eq. (34) in Appendix A] is 1 2 2 2 2 2 vart ½mt þ 1 þ rg,t þ 1 ¼ const þ y 1 a sd ot
c
ð35Þ
Using the Taylor expansion, zt þ 1
Appendix D. Variance terms
rt þ 1 ¼ logð1 þ e Þ þ Dyt þ 1 zt k0 þ k1 zt þ 1 þ Dyt þ 1 zt ¼ k0 þ k1 A0 þ k1 A1 xt þ 1 þ Dyt þ 1 zt ¼ k0 þ k1 A0 þ k1 A1 fxt þ k1 A1 sx ot ex,t þ 1 þ lxt þ sy ey,t þ 1 A0 A1 xt :
2
þ y k2g1 A2g1 s2x o2t , and the variance term in the pricing equation for the dividend claim [Eq. (36) in Appendix C] is 1 2 2 2 2 2 vart ½mt þ 1 þ rt þ 1 ¼ const þ y 1 a s d ot
c
þ ððy1Þkg1 Ag1 þ k1 A1 Þ2 s2x o2t :
W. Yang / Journal of Financial Economics 102 (2011) 45–61
These variance terms contribute linear xt terms because o2t ¼ 1zxt . I have ignored these contributions for two reasons. First, they tend to be small, as a result of small variances s2d and s2x . Second, including these terms results in much less tractable for the unknowns Ag1 and A1 , and the solutions will be difficult to interpret. In the paper, I confirm that the approximate analytical solutions are qualitatively consistent with the more accurate numerical solutions, which are plotted in the figures. Hence, ignoring the variance terms does not appear to alter the qualitative nature of the approximate analytical solutions. On the other hand, the numerical solutions also indicate nontrivial nonlinearities. The model’s quantitative performance is ultimately assessed with the numerical solutions and the simulations based on them. References Bakshi, G., Chabi-Yo, F., 2010. Implications of variance bounds on the permanent and transitory components of stochastic discount factors for asset pricing models. Unpublished working paper, University of Maryland and Ohio State University. Bansal, R., 2008. Long-run risks and risk compensation in equity markets. In: Mehra, R. (Ed.), Handbook of the Equity Risk Premium. Elsevier, Amsterdam, pp. 167–193. Bansal, R., Khatchatrian, V., Yaron, A., 2004. Interpretable asset markets? European Economic Review 49, 531–560. Bansal, R., Kiku, D., Yaron, A., 2007. Long run risks: Estimation and inference. Unpublished working paper, Duke University and University of Pennsylvania. Bansal, R., Tallarini, T.D., Yaron, A., 2008. The return to wealth, asset pricing, and the intertemporal elasticity of substitution. Unpublished working paper, Duke University, Board of Governors of the Federal Reserve System, and University of Pennsylvania. Bansal, R., Yaron, A., 2004. Risks for the long run: a potential resolution of asset pricing puzzles. Journal of Finance 59, 1481–1509. Campbell, J.Y., Cochrane, J.H., 1999. By force of habit: a consumptionbased explanation of aggregate stock market behavior. Journal of Political Economy 107, 205–251. Campbell, J.Y., Hentschel, L., 1992. No news is good news: an asymmetric model of changing volatility in stock returns. Journal of Financial Economics 31, 281–318.
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Campbell, J.Y., Shiller, R.J., 1988. The dividend–price ratio and expectations of future dividends and discount factors. Review of Financial Studies 1, 195–227. Dunn, K.B., Singleton, K.J., 1986. Modeling the term structure of interest rates under non-separable utility and durability of goods. Journal of Financial Economics 17, 27–55. Eichenbaum, M., Hansen, L.P., 1990. Estimating models with intertemporal substitution using aggregate time series data. Journal of Business and Economic Statistics 8, 53–69. Epstein, L.G., Zin, S.E., 1989. Substitution, risk aversion and the temporal behavior of consumption and asset returns: a theoretical framework. Econometrica 57, 937–969. Glosten, L., Jaganathan, R., Runkle, D.E., 1993. On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance 48, 1779–1801. Gomes, J.F., Kogan, L., Yogo, M., 2009. Durability of output and expected stock returns. Journal of Political Economy 117, 941–986. Hansen, L.P., Heaton, J.C., Li, N., 2008. Consumption strikes back? Measuring long-run risk. Journal of Political Economy 116, 260–302. Herman, S.W., 2000. Fixed assets and consumer durable goods for 1925–99. Survey of Current Business, September issue, 19–30. Judd, K., 1998. Numerical Methods in Economics. MIT Press, Cambridge, MA. Kandel, S., Stambaugh, R.F., 1991. Asset returns and intertemporal preferences. Journal of Monetary Economics 27, 39–71. Lewellen, J.W., 2004. Predicting returns with financial ratios. Journal of Financial Economics 74, 209–235. Lustig, H.N., VanNieuwerburgh, S., Verdelhan, A., 2008. The wealthconsumption ratio. Unpublished working paper, University of California at Los Angeles, New York University, and Massachusetts Institute of Technology. Newey, W.K., West, K.D., 1987. A simple, positive semi-definite, heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708. Ogaki, M., Reinhart, C.M., 1998. Measuring intertemporal substitution: the role of durable goods. Journal of Political Economy 106, 1078–1098. Pakos, M., 2005. Asset pricing with durable goods and non-homothetic preferences. Unpublished working paper, Carnegie Mellon University. Piazzesi, M., Schneider, M., Tuzel, S., 2007. Housing, consumption, and asset pricing. Journal of Financial Economics 83, 531–569. Poterba, J.M., Summers, L.H., 1988. Mean reversion in stock prices: evidence and implications. Journal of Financial Economics 22, 27–59. Shephard, N.G., Harvey, A.C., 1990. On the probability of estimating a deterministic component in the local level model. Journal of Time Series Analysis 11, 339–347. Stambaugh, R.F., 1986. Bias in regressions with lagged stochastic regressors. Unpublished manuscript, University of Chicago. Yogo, M., 2006. A consumption-based explanation of expected stock returns. Journal of Finance 61, 539–580.
Journal of Financial Economics 102 (2011) 62–80
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Institutional investors and the limits of arbitrage$ Jonathan Lewellen Tuck School of Business, Dartmouth College, Hanover, NH 03755, USA
a r t i c l e in f o
abstract
Article history: Received 21 February 2008 Received in revised form 28 February 2009 Accepted 2 March 2009 Available online 1 June 2011
The returns and stock holdings of institutional investors from 1980 to 2007 provide little evidence of stock-picking skill. Institutions as a whole closely mimic the market portfolio, with pre-cost returns that have nearly perfect correlation with the valueweighted index and an insignificant CAPM alpha of 0.08% quarterly. Institutions also show little tendency to bet on any of the main characteristics known to predict stock returns, such as book-to-market, momentum, or accruals. While particular groups of institutions have modest stock-picking skill relative to the CAPM, their performance is almost entirely explained by the book-to-market and momentum effects in returns. Further, no group holds a portfolio that deviates efficiently from the market portfolio. & 2011 Elsevier B.V. All rights reserved.
JEL classification: G11 G23 Keywords: Institutional investors Arbitrage Trading strategies
1. Introduction Institutional investors play a growing role in the US stock market. From 1980 to 2007, the share of US common equity held by mutual funds, hedge funds, pensions, bank trust departments, and other institutions increased from 32% to 68% of total market value, according to quarterly 13F filings compiled by Thomson Financial. The growth of institutional investors coincides with a large literature on institutions’ performance and trading strategies. Recent studies that use stock-holdings data suggest that institutions in general, and mutual funds in particular, have stock-picking skill even though their returns after costs and fees seem to be poor. For example, Daniel, Grinblatt, Titman, and Wermers (1997) show that stocks held by mutual funds outperform a variety of benchmarks, building on the results of Grinblatt and
$ I am grateful to Ken French, Stefan Nagel, Jeff Pontiff, Bill Schwert, Jay Shanken, Jeremy Stein, Jerry Warner, two anonymous referees, and workshop participants at numerous universities for helpful comments and suggestions. E-mail address:
[email protected]
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.05.012
Titman (1989, 1993) and Grinblatt, Titman, and Wermers (1995). More broadly, Gompers and Metrick (2001) show that institutional ownership (the fraction of a firm’s shares held by all institutions) predicts returns cross sectionally after controlling for other firm characteristics, and Cohen, Gompers, and Vuolteenaho (2002) show that institutions, as a group, exploit price momentum at the expense of individuals.1 This paper offers new results on the performance of institutional investors. I provide an updated and comprehensive analysis of institutions’ returns, both in aggregate and for different groups of institutions, and test whether their investment decisions are constrained by the socalled ‘‘limits of arbitrage’’ discussed by Shleifer and Vishny (1997). The evidence, as a whole, provides a more negative assessment of institutions’ stock-picking skill than have other recent studies.
1 Other studies that explore institutions’ returns and holdings include Nofsinger and Sias (1999), Wermers (1999, 2000), Chen, Jegadeesh, and Wermers (2000), Chen, Hong, and Stein (2002), Bennett, Sias, and Starks (2003), Kovtunenko and Sosner (2004), and Brunnermeier and Nagel (2004).
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
My initial tests focus on institutions’ aggregate performance. While prior studies consider a variety of return benchmarks and weighting schemes (equal weights versus value weights versus cross-sectional regressions), I argue that the best way to evaluate institutions’ overall stock-picking skill is just to sum their holdings and study their aggregate returns. This approach leads to a surprisingly simple view of performance: Institutions as a whole essentially hold the market portfolio. From 1980 to 2007, the aggregate portfolio held by institutions has a return correlation of 99.8% with the value-weighted market index and a beta of 1.01 (see also Cohen, Gompers, and Vuolteenaho, 2002). Given those facts, it should come as little surprise that institutions, overall, have little stockpicking still even before costs and fees, with a CAPM alpha of 0.08% per quarter and a Carhart (1997) four-factor alpha of 0.05% per quarter (both insignificant). My tests find weaker performance than prior studies in part because of my longer sample—institutions’ returns have been poor since 2000—but, more importantly, because I focus directly on institutions’ returns rather than the predictive power of institutional ownership (IO). In fact, I confirm that IO predicts returns cross-sectionally during my sample. But I also show that institutions’ stockpicking ability is reliable only for smaller stocks, which make up a tiny fraction of their holdings. For example, institutions’ investment in micro-cap stocks (below the NYSE 20th percentile) outperforms a value-weighted index of those stocks by a significant 0.57% quarterly but represents just 1% of their total holdings. Institutions’ investment in large-cap stocks (above the NYSE 80th percentile) outperforms a value-weighted index of those stocks by 0.01% quarterly and represents nearly 80% of their holdings. The near-perfect correlation between institutions’ returns and market returns is surprising, in some ways, because institutions have been found to tilt toward certain types of stocks, deviating significantly from the market portfolio. For example, Gompers and Metrick (2001) regress IO on firm characteristics and find that institutions prefer larger, older stocks with higher prices, book-to-market (B/M) ratios, volatility, and turnover, and, controlling for those characteristics, lower past returns (see also Grinblatt, Titman, and Wermers, 1995; Del Guercio, 1996; Falkenstein, 1996; Bennett, Sias, and Starks, 2003). Institutions’ aggregate holdings, however, convey a much different picture. Specifically, I sort stocks into quintiles based on a variety of characteristics and compare how much institutions invest in each quintile with the quintile’s weight in the market portfolio. Viewed from this perspective, institutions show little tendency to bet on any of the most common characteristics considered in the asset pricing literature. Institutions tilt a bit toward large stocks (77% of the institutional portfolio versus 73% of market cap) and away from low-turnover (7% institutional versus 12% market) and low-beta (14% institutional versus 16% market) stocks. But for sorts based on eight other characteristics—B/M, momentum, long-term returns, volatility, stock issuance, accruals, asset growth, and profitability—not a single quintile has a weight in the institutional portfolio that differs from its value weight by
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more than 2 percentage points, and most differ by less than 1. In short, institutions do not bet, to a significant degree, on any of the main characteristics found to predict stock returns. These results have several implications. Most directly, they show that institutions in aggregate do little more than hold the market portfolio, presumably generating significant costs and fees in the process. Active trading by one institution largely offsets active trading by other institutions, implying that institutions mostly profit from (or lose to) each other, not individuals. In addition, to the extent that institutions do trade together (e.g., Sias, 2004), such ‘‘herding’’ seems to have little impact on performance, in the sense that an investor who actively mimics institutions’ trades or passively holds the market portfolio would earn almost identical pre-cost returns. Further, the results suggest that institutions do not invest like Shleifer and Vishny’s (1997) rational but constrained arbitrageurs, as I discuss further below. My tests also explore the stock-picking ability of different types of institutions, motivated by a number of issues that have been studied previously in the mutual fund literature, such as: Do money managers benefit from economies of scale? Does performance persist? Does money flow to the best institutions? Does active trading help or hurt performance? Sorting institutions first by business type, I find that the equity holdings of banks, insurance companies, and all other institutions have return correlations of 99.3%, 99.7%, and 99.7%, respectively, with the market index (the ‘‘other’’ category includes mutual funds, hedge funds, pensions, investment advisors, endowments, etc.). Banks have the best performance with a CAPM alpha of 0.19% and a four-factor alpha of 0.12% quarterly (t-statistics of 2.02 and 1.31, respectively), compared with alphas of 0.01–0.07% quarterly for insurance companies and other institutions. Ranked by equity under management, the largest institutions (top quartile) have the highest correlation with the market (99.8%) and the smallest alphas (0.04–0.07% quarterly for the different factor models). Small and medium-sized institutions have somewhat better returns yet still hold portfolios with greater than 99% correlation with the market. The middle two quartiles have the highest CAPM alphas of 0.21% and 0.24% quarterly (t-statistics of 2.61 and 2.89), while the smallest quartile has the highest four-factor alpha of 0.26% quarterly (t-statistic of 2.68). Ranked by past annual returns and growth, the bestperforming and fastest-growing institutions have the highest CAPM alphas, largely a consequence of momentum in stock returns (consistent with Carhart’s (1997), results for mutual funds). The top performers hold, in aggregate, a portfolio with a CAPM alpha of 0.40% quarterly (t-statistic of 2.19) and a four-factor alpha of 0.12% quarterly (t-statistic of 0.71). The fastest-growing institutions hold a portfolio with a CAPM alpha of 0.16% quarterly (t-statistic of 1.52) and a four-factor alpha of 0.04% quarterly (t-statistic of 0.38). Ranked by annual turnover, institutions that trade the least seem to do the best, even without accounting for
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J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
trading costs. Low-turnover institutions have a return correlation of 99.3% with the market, a CAPM alpha of 0.24% quarterly (t-statistic of 2.66), and a four-factor alpha of 0.17% quarterly (t-statistic of 1.99). High-turnover institutions have a correlation of 98.5% with the market, a CAPM alpha of 0.06% (t-statistic of 0.38), and a four-factor alpha of 0.14% (t-statistic of 0.99). Last, grouping institutions by the types of stocks they hold, I find that institutions that tilt the most toward small, high-B/M, or high-momentum stocks have the highest CAPM alphas, with quarterly estimates of 0.17%, 0.58%, and 0.32%, respectively (only the second of these is significant, with a t-statistic of 2.21). Again, no group has a significant four-factor alpha; the largest point estimate is 0.12% quarterly for these three groups and 0.16% quarterly across all 12 size-, B/M-, and momentum-tilt quartiles. In sum, several groups of institutions appear to have some stock-picking ability relative to the CAPM but the only groups that have a statistically significant four-factor alpha—taking their t-statistics in isolation, but not accounting for the fact that we searched across 31 groups—are the smallest and lowest-turnover institutions, with point estimates of 0.26% and 0.17% quarterly. My final tests explore whether any of the groups deviate efficiently from the market portfolio: Does any group generate a CAPM alpha that is high relative to the amount of idiosyncratic risk it takes on (as opposed to just a positive alpha)? One motivation for the tests is to explore the limits-of-arbitrage view of Shleifer and Vishny (SV, 1997). SV argue that institutions (i.e., professional traders) may be reluctant to bet heavily on anomalies because mispricing could widen unexpectedly in the short run, leading to poor returns and, consequently, client withdrawals. Their arguments suggest that institutions might forgo investments with high alphas, and might choose not to hold the tangency portfolio, if it means deviating too much from the market portfolio and taking on too much idiosyncratic risk. However, even if an institution is not willing to bet heavily on mispricing, it would still want to move toward the tangency portfolio by holding a portfolio with a high alpha per unit of idiosyncratic risk. Thus, my final tests ask whether institutions deviate efficiently from the market portfolio, not whether they deviate a lot. Statistically, the test takes a simple form: I just use the institutional portfolio as an asset pricing factor in timeseries regressions, i.e., I test whether alphas are zero when B/M and momentum portfolios are regressed on the market return and either institutions’ aggregate return or the return of a particular type of institution. The logic of the test follows from Gibbons, Ross, and Shanken’s (1989) general analysis of mean-variance tests: If an institution maximizes alpha per unit of idiosyncratic risk, given the opportunities presented by B/M and momentum portfolios, the institutional and market portfolios will together span the tangency portfolio and drive B/M and momentum alphas to zero. This is true even if the institution holds a portfolio that is very close to the market index in mean-variance space. The results from the test are clearly negative for institutions taken as a whole or grouped by business type,
turnover, growth, or the size and momentum of stocks they hold. For each of these classifications, adding the institutions’ return as a second factor in CAPM regressions has little impact on B/M and momentum alphas. The implication is that none of these groups, or institutions overall, tilts toward the tangency portfolio in the way suggested by SV’s limits-of-arbitrage view. The same conclusion holds when institutions are grouped by size, past returns, or ownership of value stocks, but the results are more nuanced. Portfolios held by most groups within these classifications explain neither the B/M nor momentum effects. The exceptions are that portfolios held by medium-sized and valueoriented institutions partially explain the B/M effect, and the portfolio held by top-performing institutions partially explains momentum. (No group exploits both B/M and momentum.) The strongest results are for institutions that hold value stocks: Adding their return as a factor in CAPM regressions pushes up the alpha of low-B/M stocks from 0.36% to 0.06% quarterly and pushes down the alpha of high-B/M stocks from 1.44% to 0.71% quarterly. The t-statistic for the difference between the high- and low-B/M alphas drops from 2.97 to 1.93. Put differently, we cannot reject that value-oriented institutions tilt optimally toward the tangency portfolio achievable from B/M quintiles. The paper is organized as follows: Section 2 describes the data; Section 3 studies institutions’ aggregate performance; Section 4 studies the performance of different types of institutions; Section 5 presents the efficiency tests and relates them to SV’s (1997) limits-of-arbitrage arguments; Section 6 concludes. 2. Data My tests use data from four sources. Stock returns, market values, trading volume, and T-bill rates come from the Center for Research in Security Prices (CRSP) monthly files. Returns on the Fama-French size, B/M, and momentum factors (SMB, HML, and UMD) come from Kenneth French’s website at Dartmouth College.2 Accounting data, including the book value of assets, common equity, operating accruals, and earnings, come from the Compustat annual file, supplemented with Davis, Fama, and French’s (2000) hand-collected book equity data from Moody’s (available on French’s website). Finally, institutional stock holdings come from the CDA/Spectrum files maintained by Thomson Financial. The CDA/Spectrum database is compiled from institutions’ 13F filings with the Securities and Exchange Commission (SEC). The SEC requires large institutional investors—those that ‘‘exercise investment discretion over $100 million or more’’ in so-called 13(f) securities, including institutions such as hedge funds or foreignbased funds that do not have to be registered investment advisors—to report their quarter-end holdings of US stocks and other exchange-traded securities within 45 days after the end of the calendar quarter. The only 2
http://mba.tuck.dartmouth.edu/pages/faculty/ken.french.
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
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Fig. 1. Institutional ownership, 1980–2007. The left panel shows the number of institutions in the 13F files (from Thomson Financial) and the average number of institutions holding a given stock, value-weighting across common stocks on CRSP. The right panel shows the fraction of stocks with positive institutional ownership (IO) and the share of the overall market held, in aggregate, by institutions.
exceptions are for small holdings (below ten thousand shares and $200,000) or in special circumstances in which the SEC grants a confidentiality waiver. Securities are listed by CUSIP number, allowing an easy merge with CRSP and Compustat. Institutions in the 13F database can be tracked through time, and Thomson identifies each as being one of five types: (1) banks, (2) insurance companies, (3) investment companies, (4) investment advisors, and (5) other. The last three types include mutual funds, pensions, brokerage firms, hedge funds, endowments, and all remaining institutions. Unfortunately, the breakdown into the last three categories is somewhat arbitrary and Thomson mistakenly re-classified many institutions as ‘‘other’’ beginning in the fourth quarter of 1998, a change that seems to affect categories (3), (4), and (5) the most, though not exclusively [see the Wharton Research Data Services (WRDS) User Guide for details].3 For simplicity, then, I merge those three categories into a single group for any test that uses Thomson’s classification. I also use Thomson’s code at the end of 1997 for any institution that is in the database at that time instead of updating it if the classification changes. An additional problem with the 13F database concerns late filers who miss the SEC’s 45-day deadline. The WRDS User Guide explains that share holdings for late filers are (or might be?) adjusted for stock splits that occur after the quarter. Fortunately, less than 0.02% of the records in the 13F database seem to be affected after WRDS deletes duplicate entries, i.e., the record’s filing and report dates are different, signaling a late filer, and a stock split was recorded on CRSP between the two dates. In these cases, I reverse Thomson’s split adjustment using CRSP’s shareprice adjustment factors. Fig. 1 illustrates a few features of the data. The sample extends from 1980Q1 to 2007Q4. At the beginning of the sample, just under five hundred institutions owned shares in 3,329 common stocks for which I could find returns and
3 The WRDS User Guide is available online at http://wrds.wharton. upenn.edu.
market values on CRSP (stocks that represent 72% of firms and 99% of the total market value of common stocks on CRSP). As group, institutions in the 13F database held 32% of total market cap on March 31, 1980. The number of institutions in the database steadily increases to 2,681 by the end of 2007, at which time they hold 68% of the stock market. Nearly all stocks on CRSP, representing close to 100% of market cap, are held by at least one institution at the end of the sample. The number of institutions holding shares of an average firm (including firms with no institutional ownership) rises from 164 to 649 on a value-weighted basis and from 17 to 110 on an equalweighted basis during the sample. As a data check, I flag observations for which institutions, in aggregate, hold more than 100% of the shares outstanding on CRSP. These observations represent less than 1% of firms and less than 0.5% of market cap in an average quarter. In about half of those cases, the number of shares held by institutions exceeds shares outstanding by less than 5%, a scenario that is plausibly attributable to short selling, not data error (shares owned and lent out are included in an institution’s holdings, but shares borrowed and sold short are not). The issue, overall, appears to be minor, and my solution is just to set the maximum ownership of institutions at 100%. 3. Institutions’ aggregate performance My initial tests focus on the aggregate portfolio held collectively by all institutions. This portfolio simply sums their holdings, treating institutions as one big investor, and provides the best measure of their overall stockpicking skill before costs and fees. Returns on the portfolio are the same as institutions’ size-weighted average returns (size, here, being equity under management). I also consider the aggregate portfolio held by everyone else, referred to simply, if not quite accurately, as ‘‘individuals.’’ Table 1 reports quarterly excess returns over T-bills for institutions, individuals, the CRSP value-weighted index (MKT), and the Fama-French size, B/M, and momentum factors. (Quarterly returns are compounded from monthly
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J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
Table 1 Institutions’ quarterly returns and alphas, 1980–2007. Panel A reports average quarterly excess returns (Avg), standard deviations (Std), and t-statistics (t-stat) for the aggregate portfolios held by institutions and individuals and for the CRSP value-weighted index (MKT) and the Fama-French size, B/M, and momentum factors (SMB, HML, and UMD). Panel B reports CAPM, three-factor, and four-factor regressions for institutions and individuals: R¼ aþ b MKTþ s SMBþ h HMLþm UMD þ e. se(a) is the standard error of a, t(a) is the t-statistic for a, and GRS F is the Gibbons, Ross, and Shanken (1989) F-statistic testing whether intercepts for institutions and individuals are jointly significant (p-value in parentheses). Columns labeled MKT, SMB, HML, and UMD report the slope on each factor. Returns come from CRSP, institutional ownership comes from Thomson Financial, and SMB, HML, and UMD come from Kenneth French’s website at Dartmouth College. Panel A: Excess returns (percent) Portfolio
Avg
Std
t-Stat
Institutions Individuals MKT SMB HML UMD
2.18 2.02 2.09 0.47 1.15 2.44
8.33 8.20 8.25 5.21 6.35 7.14
2.76 2.60 2.66 0.94 1.91 3.60
a
se(a)
t(a)
MKT
Institutions Individuals
0.08 0.05
0.05 0.05
1.56 1.10
1.01 0.99
Institutions Individuals
0.08 0.02
0.06 0.05
1.36 0.48
1.01 0.99
0.02 0.00
0.00 0.01
Institutions Individuals
0.05 0.00
0.06 0.05
0.87 0.05
1.02 0.99
0.02 0.00
0.00 0.02
Panel B: Regressions Portfolio
data; I compound each side of the strategy and then difference for long-short portfolios.) The table also reports CAPM, Fama-French (1993) three-factor, and Carhart (1997) four-factor regressions for institutions and individuals. The main message from Table 1 is that institutions as a group have returns that are only slightly higher than and almost perfectly correlated with the value-weighted index. From 1980 to 2007, institutions’ returns have a correlation of 99.8% with the market index and a CAPM beta of 1.008. Institutions outperform the market by a modest 0.10% per quarter and individuals by 0.16% per quarter. Adjusting for risk, institutions have a slightly positive CAPM alpha of 0.08% quarterly and a four-factor alpha of 0.05% quarterly. Institutions’ returns load a bit negatively on SMB and a bit positively on UMD, but only the three-factor slope on SMB is borderline significant (t-statistic of 1.97). Statistically, Table 1 provides little evidence of institutional stock-picking skill. The t-statistics for alpha are insignificant (the highest is 1.56 for the CAPM) and we cannot reject that institutions and individuals perform the same or that alphas for the two groups are both zero (neither the GRS F-statistics in the table nor t-statistics testing for a difference between the groups’ alphas are significant). And the small standard errors imply that the range of statistically likely true alphas is quite narrow, extending from below zero to a best-case scenario around 0.20% for all three factor models.4 4 The tests in Table 1 use only common stocks to be consistent with most asset pricing studies. Institutions’ performance looks incrementally better if the tests are expanded to all securities on CRSP: Alphas increase by 0.02% quarterly for all three models and the CAPM alpha, while still
SMB
HML
UMD
0.01 0.01
R2
GRS F
1.00 1.00
1.24 (0.29)
1.00 1.00
1.55 (0.22)
1.00 1.00
1.05 (0.35)
More importantly, institutions’ alphas are economically small and would be wiped out by tiny trading costs, not to mention management fees. We can get a rough, almost certainly conservative, sense of institutions’ trading costs from their quarterly holdings, estimating each institution’s turnover based on its split-adjusted change in holdings during the quarter (multiplied by quarter-end share prices). Institutions buy new shares equal to 12.4% of their aggregate portfolio in an average quarter and sell shares equal to 10.5% of their aggregate portfolio, for average round-trip turnover of 11.4%. Therefore, one-way trading costs of 0.25% would cut institutions’ alphas by 0.06% (0.114 2 0.0025), to 0.00–0.03% quarterly, while one-way costs of 0.50% would push all of the estimates below zero. Fig. 2 shows that institutions’ performance is fairly stable during the sample but declines after 2000. Ten-year rolling estimates of alpha vary from roughly 0.00% to 0.20% for all factor three models. Alphas drop during the late 1990s, spike up in 2000, and decline again from 2001 to 2007. The CAPM alpha reaches a low of 0.02% quarterly at the end of 2007 (estimated from 1997Q4 to 2007Q3), while the four-factor alpha reaches a low of 0.06% quarterly at the end of the 2006 (estimated from 1997Q1 to 2006Q4). To be fair, the alphas in Table 1 do not imply that institutions have no stock-picking skill. Like Gompers and
(footnote continued) economically small, becomes statistically significant (t-statistic of 2.04). On a separate note, institutions’ characteristic-adjusted average return, using the approach of Daniel, Grinblatt, Titman, and Wermers (1997), is very similar to the four-factor alpha in Table 1 (0.05% quarterly with a t-statistic of 1.47).
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
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Fig. 2. The figure shows ten-year rolling estimates of institutions’ quarterly CAPM, Fama-French (FF) three-factor, and Carhart four-factor alphas (in percent) from 1980 to 2007. Dates on the x-axis give the ending quarter for each ten-year sample. Returns come from CRSP, institutional ownership comes from Thomson Financial, and the Fama-French factors come from Kenneth French’s website at Dartmouth College.
Table 2 Institutional performance and firm size, 1980–2007. The table reports quarterly average excess returns and alphas (in percent) for institutions’ holdings of small, medium, and large stocks compared with a value-weighted index of each group. Firm-size quintiles are based on NYSE breakpoints. IW is a quintile’s institutional-weighted return (weighting by the institutional holdings of each stock); VW is the quintile’s value-weighted return (weighting by market value); IW–VW is the difference between IW and VW. aCAPM, aFF, and a4Fac are CAPM, Fama-French (FF) three-factor, and Carhart four-factor alphas for IW–VW, with t-statistics denoted by t( ). Returns come from CRSP, institutional ownership comes from Thomson Financial, and the Fama-French factors come from Kenneth French’s website at Dartmouth College. Size quintile
Q1 (small) Q2 Q3 Q4 Q5 (big)
IW
2.81 2.87 2.68 2.65 2.10
VW
2.15 2.45 2.40 2.44 2.05
IW–VW
0.66 0.42 0.28 0.21 0.05
Alphas for IW–VW aCAPM
t(aCAPM)
aFF
t(aFF)
a4Fac
t(a4Fac)
0.57 0.34 0.25 0.18 0.01
2.89 2.37 2.15 2.18 0.17
0.29 0.14 0.12 0.13 0.01
1.48 0.96 1.07 1.52 0.25
0.67 0.34 0.18 0.17 0.05
3.35 2.26 1.39 1.76 0.94
Metrick (2001), my Appendix shows that institutional ownership (the fraction of a firm’s shares held by institutions) has some cross-sectional predictive power for returns, most reliably in tests that include smaller stocks. But the evidence in Table 1 does imply that any skill washes out on an aggregate basis, which is the right metric for evaluating institutions’ overall performance. Table 2 explores the connection between firm size and institutions’ stock-picking skill in more detail. I sort stocks into size quintiles (using NYSE breakpoints) and test how well institutions’ holdings within each group perform relative to a value-weighted index of the stocks. Institutions’ holdings of the smallest stocks (Quintile 1) beat a value-weighted index of those stocks by an impressive 0.66% quarterly, but performance drops steadily as stocks get bigger, to a low of 0.05% for Quintile 5. Adjusting for risk, the institutional portfolio significantly beats the value-weighted index in Quintiles 1–4 using the CAPM (alphas of 0.18–0.57% with t-statistics of 2.15–2.89) and in Quintiles 1 and 2 using the four-factor model (alphas of 0.67% and 0.34% with t-statistics of 3.35 and 2.26). The strong performance among smaller stocks has a modest aggregate effect, however, because Quintiles 1 and 2 together represent just 4% of institutions’ overall holdings. Nearly 80% of institutions’ holdings are in the top size
quintile, for which there is no evidence they can beat the market. (The holdings of institutions are discussed further below.) It is useful to note that the near-perfect correlation between institutions’ aggregate returns and the market index suggests that any risk model that includes MKT would give similar results. The impact on alpha of adding a new factor to a CAPM regression can be shown to equal the Sharpe ratio of the portion of the factor that is uncorrelated with the market (an ‘‘orthogonalized’’ factor) multiplied by the standard deviation of the portion of returns explained by the orthogonalized factor. The second term is bounded above by the residual standard deviation of returns missed by the market, 0.54% quarterly for institutions. Thus, if we add an orthogonalized factor with, say, the same Sharpe ratio as the market, 0.25, institutions’ alpha could go up or down by at most 0.13% quarterly (0.25 0.54). The actual impact would be much smaller unless the factor is highly correlated with institutions’ residual returns. The near-perfect correlation with MKT also suggests that institutions’ aggregate holdings must not deviate too much from a value-weighted portfolio (and, to the extent that institutions’ holdings do deviate from value weights, they must bet primarily on idiosyncratic returns). This implication
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J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
and the table reports the time-series averages from 1980 to 2007. The 11 characteristics are:
is somewhat surprising because prior research has found that institutions tilt significantly toward or away from particular types of stocks (e.g., Grinblatt, Titman, and Wermers, 1995; Del Guercio, 1996; Falkenstein, 1996; Gompers and Metrick, 2001; Bennett, Sias, and Starks, 2003). However, the literature emphasizes cross-sectional regressions of institutional ownership on firm characteristics, which have only indirect and hard-to-assess implications for aggregate portfolio weights. As an alternative, Table 3 looks directly at the aggregate portfolio held by institutions. I sort stocks into quintiles based on a variety of firm characteristics and compare the fraction of the institutional portfolio invested in each (relative to institutions’ investment in all five quintiles) with the quintile’s weight in the market portfolio (the quintile’s market cap relative to the market cap of all five quintiles). The weights are found each quarter, using all stocks with data for the characteristic,
(1) size—market cap of the stock at the beginning of the quarter, (2) B/M—book value of common equity for the prior fiscal year (with a four-month delay) divided by size, (3) momentum—returns for months 12 to 2 relative to the sort date, (4) reversals—returns for months 36 to 13 relative to the sort date, (5) volatility—daily return volatility from month 12 to 1 relative to the sort date, (6) beta—market beta estimated from at least 24 months and up to 60 months of past monthly returns, (7) turnover—trading volume divided by shares outstanding over the past 12 months,
Table 3 Institutional portfolio versus market portfolio, 1980–2007. The table compares the weight invested by institutions in each group of stocks with its weight in the market portfolio (weights are relative to the total investment in, or market cap of, stocks included in the five portfolios in each row). The weights are found quarterly, and the table reports their timeseries averages. Stock portfolios are based on NYSE quintile breakpoints for each of the 11 variables listed in the table and described more thoroughly in the text. Market values come from CRSP, accounting data come from Compustat (supplemented with Davis, Fama, and French’s, 2000, equity data), and institutional holdings come from Thomson Financial. Characteristic
Weight
Stock quintile Low
2
3
4
High
Size (market cap)
Institutions Market Difference
0.01 0.03 0.02
0.03 0.04 0.01
0.06 0.07 0.01
0.14 0.13 0.00
0.77 0.73 0.04
B/M (book-to-market equity)
Institutions Market Difference
0.43 0.41 0.02
0.23 0.22 0.00
0.16 0.17 0.01
0.12 0.13 0.01
0.06 0.07 0.01
Momentum (returns for months 12 to 2)
Institutions Market Difference
0.11 0.12 0.01
0.18 0.19 0.00
0.21 0.21 0.00
0.25 0.24 0.00
0.26 0.25 0.01
Reversal (returns for months 36 to 13)
Institutions Market Difference
0.11 0.11 0.01
0.17 0.17 0.00
0.20 0.20 0.00
0.24 0.24 0.00
0.28 0.27 0.00
Volatility (daily, past 12 months)
Institutions Market Difference
0.21 0.23 0.02
0.31 0.30 0.02
0.23 0.22 0.01
0.15 0.14 0.00
0.10 0.11 0.02
Beta (past 24- to 60-month estimate)
Institutions Market Difference
0.14 0.16 0.02
0.24 0.24 0.00
0.22 0.21 0.01
0.21 0.20 0.01
0.19 0.19 0.01
Turnover (past 12 months)
Institutions Market Difference
0.07 0.12 0.05
0.22 0.24 0.02
0.25 0.23 0.02
0.23 0.20 0.03
0.23 0.21 0.03
Share issuance (past 12 months)
Institutions Market Difference
0.25 0.24 0.01
0.19 0.20 0.01
0.18 0.18 0.00
0.19 0.18 0.01
0.19 0.20 0.01
Accruals (as per Sloan, 1996)
Institutions Market Difference
0.17 0.18 0.00
0.24 0.24 0.00
0.22 0.21 0.00
0.20 0.20 0.00
0.17 0.17 0.00
Asset growth (prior year)
Institutions Market Difference
0.10 0.11 0.00
0.19 0.19 0.00
0.23 0.23 0.00
0.25 0.24 0.01
0.23 0.23 0.00
ROA (prior year)
Institutions Market Difference
0.11 0.11 0.00
0.18 0.18 0.00
0.16 0.17 0.01
0.22 0.22 0.00
0.34 0.33 0.02
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
(8) share issuance—percent change in split-adjusted shares outstanding over the past 12 months, (9) accruals—operating accruals, as per Sloan (1996), (10) asset growth—percent change in the book value of total assets during the last fiscal year, and (11) ROA—return on assets, equal to income before extraordinary items divided by lagged assets (per share).
These characteristics have been used by prior studies to predict the cross section of expected returns, for the most part successfully. My focus is not on their predictive power per se but, rather, on whether institutions underor overweight the various quintiles relative to the market portfolio. That is, do institutions tilt their holdings toward or away from particular types of stocks? The answer, in Table 3, is almost uniformly negative: Institutions’ average holdings from 1980 to 2007 line up very closely with value weights. Institutions tilt somewhat toward large stocks (the top size quintile is 77% of the institutional portfolio compared with 73% of the market) and away from low-turnover and low-beta stocks (institutional weights of 7% and 14% for the first quintiles of those variables, compared with value weights of 12% and 16%, respectively). But for the other eight characteristics, not a single quintile has an institutional weight that differs from its value weight by more than 2 percentage points and most differ by less than 1 (looking closely, institutions take tiny bets on growth, momentum, and profitability, and against share issuers). These results suggest that, viewed from the perspective of portfolio weights, the institutional preferences found in crosssectional regressions by Del Guercio (1996), Gompers and Metrick (2001), and Bennett, Sias, and Starks (2003) have little aggregate effect. (For comparison, the Appendix reports cross-sectional evidence that is similar to those studies.)5 The patterns in Table 3 are quite stable during the sample. The key exception is that institutions’ bias toward large stocks declines over time. Institutions overweight the largest quintile by 10 percentage points in the early 1980s, but this bias drops steadily to zero by the end of the sample. (Part of this effect could be due to reporting requirements because the minimum holding that must be disclosed—ten thousand shares or $200,000—has not changed over time, likely increasing the reported holdings of smaller stocks.) Fig. 3 plots average institutional and market weights for select characteristic portfolios in each of the 1980s, 1990s, and 2000s. In sum, institutions as a group seem to do little more than hold the market portfolio. They do not bet to a significant degree on any of the most important 5 I do not report statistical tests in Table 3 because it is unclear what the right notion of statistical randomness would be, since the results are essentially population values for institutions’ portfolio holdings. In return tests, randomness comes from returns themselves—we are interested in expected returns but the tests use realized returns—and there is no corresponding notion of such randomness here. In any case, the differences are economically small regardless of whether they are statistically significant or not.
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characteristics known to predict stock returns, and their aggregate returns are almost perfectly correlated with the market index. The close correspondence with market returns and the small, precisely estimated alphas provide strong evidence that institutions do not earn significant abnormal returns, even before costs and fees. 4. The cross section of institutional performance A natural and important follow-up question is whether particular types of institutions have stock-picking ability, even if institutions overall do not. The groups I consider are motivated by issues that have been studied in the mutual fund literature: Do organizational or regulatory constraints affect performance? Do institutions benefit from economies of scale? Does performance persist? Does money flow to the best institutions? Does active trading help performance? Specifically, Table 4 reports the performance of institutions sorted by (1) business type (banks; insurance companies; all others), (2) size (equity under management at the beginning of the quarter), (3) past annual returns of their equity portfolios, (4) past annual growth in equity under management, (5) past annual turnover (inferred from quarterly changes in their holdings), and (6) the type of stocks in an institution’s portfolio (the holding-weighted averages of the log market cap, log B/M ratio, and 12-month momentum of the stocks). All classifications other than business type sort institutions into quartiles. As before, I focus on the aggregate holdings of each group, treating institutions within the group as one big investor. The last column in the table reports the fraction of total equity under management held by each group. The basic conclusion from Table 4 is that some groups have a modest amount of stock-picking ability relative to the CAPM and the Fama-French three-factor model, but there is little evidence any group does so as measured by the four-factor model. The majority of groups hold portfolios that, in aggregate, closely mimic the market index: twenty out of 31 have return correlations with the market index of 99% or higher, including 15 of the 19 groups sorted by business type, size, past returns, past growth, and turnover (the other categories sort by the type of stocks held by the institution, so it is not surprising that they have lower correlations). In Panel A, the portfolios held by banks, insurance companies, and other institutions have return correlations with the market index of 99.3%, 99.7%, and 99.7%, respectively. Banks appear, weakly, to have the best performance, with a CAPM alpha of 0.19% quarterly (t-statistic of 2.02) and a four-factor alpha of 0.12% quarterly (t-statistic of 1.31). Insurance companies and other institutions have small alphas relative to any of the factor models, with estimates of 0.01–0.07% quarterly. None of the alphas for insurance companies or other institutions is individually significant, nor are any of the GRS F-statistics testing whether alphas for the three groups are jointly significant. In Panel B, the portfolio held by large institutions (top quartile) has the strongest correlation with the market (99.8%) and the smallest alphas (0.04–0.07% quarterly, with t-statistics of 0.69–1.21). Small and medium-sized institutions earn somewhat better returns yet also hold
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J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
Fig. 3. Institutional and market weights during the 1980s, 1990s, and 2000s for stock quintiles (Q1–Q5) sorted by size, B/M, momentum (returns from month 12 to 2), volatility (daily for past 12 months), accruals (per Sloan, 1996), and ROA (earnings per share before extraordinary items divided by lagged assets per share). The weights are found quarterly, and the figure shows the time-series average each decade. Market values come from CRSP, accounting data come from Compustat, and institutional holdings come from Thomson Financial.
portfolios with greater than 99% correlation with the market. The middle two quartiles have the best CAPM and three-factor performance, with statistically significant alphas of 0.16–0.24% quarterly. Small institutions (Quartile 1) have insignificant CAPM and three-factor alphas but, interestingly, the highest four-factor alpha of 0.26% (t-statistic of 2.68). The GRS F-statistic, testing the joint significance of the groups’ alphas, has a p-value just greater than 0.05 for both the CAPM and four-factor model. Loadings on the Fama-French factors suggest that the bottom three quartiles all tilt a bit toward small, value stocks.6
6 Sorting institutions based on the number of stocks they hold—closely related to institutional size—gives similar results. Institutions in the middle two quartiles have the best performance, with quarterly CAPM alphas of 0.29% and 0.19% (t-statistics of 3.79 and 2.58) and four-factor alphas of 0.21% and 0.16% (t-statistics of 2.30 and 1.86).
In Panels C and D, institutions with the best past annual returns and growth have the highest CAPM and three-factor alphas, largely a consequence of momentum in stock returns. The spread between the best- and worstperforming institutions is greatest using three-factor alphas: Institutions with the highest past returns have a big positive alpha of 0.64% quarterly (t-statistic of 3.37), while institutions with the lowest past returns have a big negative alpha of 0.50% quarterly (t-statistic of 2.30). Likewise, the fastest-growing institutions have a threefactor alpha of 0.31% quarterly (t-statistic of 2.97), while the slowest-growing institutions have a three-factor
(footnote continued) Those groups account for roughly 20% of total equity under management.
Table 4 The cross section of institutional performance, 1980–2007. The table reports quarterly CAPM, three-factor, and four-factor regressions for institutional investors grouped by business type, size (equity under management), past annual returns, past annual growth, past turnover, and by the average market cap, B/M ratio, or momentum of stocks in an institution’s portfolio (the last three are based on the holding-weighted average of the log market cap, log B/M ratio, and return from month 12 to 2 of stocks held by the institution). Groups are quartiles except those for business type; the last rows in Panels B–H show results for the top quartile minus the bottom quartile. The regression is: R ¼a þb MKTþ s SMBþ h HMLþm UMD þe, where R is a group’s excess return, MKT is the excess return on the CRSP value-weighted index, and SMB, HML, and UMD are the Fama-French size, B/M, and momentum factors from Kenneth French’s website at Dartmouth College. t(a) is the t-statistic for a and F is the Gibbons, Ross, and Shanken (1989) F-statistic testing whether alphas for the groups are jointly significant (with p-value below). %Assets is the fraction of total institutional assets held by each group. Bold indicates estimates of s, h, or m that are greater than 1.96 standard errors from zero. Returns come from CRSP, accounting data come from Compustat, and institutional holdings come from Thomson Financial. CAPM
Three factor
Four factor
F
a
t(a)
b
s
h
0.94 1.00 1.04
0.99 0.99 0.99
1.65 0.18
0.09 0.02 0.07
1.19 0.36 1.06
0.98 1.01 1.03
0.11 0.04 0.02
1.61 2.61 2.89 1.21 1.03
1.03 1.02 1.01 1.01 0.02
0.98 0.99 0.99 1.00 0.02
2.44 0.05
0.10 0.16 0.17 0.07 0.04
1.10 2.18 2.16 1.16 0.50
1.01 1.00 1.01 1.02 0.01
Panel C: Grouped by past returns Low 0.22 1.07 2 0.07 0.64 3 0.20 2.94 High 0.40 2.19 H–L 0.63 1.70
1.03 0.99 0.98 1.03 0.01
0.94 0.98 0.99 0.95 0.01
2.61 0.04
0.50 0.11 0.14 0.64 1.14
2.30 1.08 1.96 3.37 3.00
Panel D: Grouped by past growth Low 0.01 0.08 2 0.07 0.73 3 0.12 1.95 High 0.16 1.52 H–L 0.15 0.60
1.02 0.99 1.00 1.04 0.03
0.96 0.99 0.99 0.99 0.00
1.22 0.31
0.24 0.06 0.09 0.31 0.55
Panel E: Grouped by turnover Low 0.24 2.66 2 0.09 1.27 3 0.03 0.36 High 0.06 0.38 H–L 0.18 0.79
0.94 0.99 1.07 1.15 0.21
0.99 0.99 0.99 0.97 0.36
6.07 0.00
Panel F: Grouped by market cap of holdings Small 0.17 0.67 1.14 2 0.15 1.35 1.04 3 0.06 0.97 1.00 Large 0.10 0.85 0.94 L–S 0.07 0.21 0.20
0.93 0.98 0.99 0.98 0.17
1.16 0.33
a
t(a)
Panel A: Grouped by business type Banks 0.19 2.02 Insurance 0.04 0.58 All others 0.04 0.71 Panel B: Grouped by size Small 0.17 2 0.21 3 0.24 Large 0.07 L–S 0.11
b
R
%Assets
2
F
a
t(a)
b
s
h
m
0.04 0.00 0.01
0.99 0.99 0.99
0.73 0.54
0.12 0.03 0.01
1.31 0.44 0.18
0.98 1.01 1.03
0.11 0.04 0.02
0.04 0.00 0.00
0.13 0.09 0.07 0.03 0.16
0.04 0.03 0.04 0.00 0.04
0.99 0.99 0.99 1.00 0.58
1.68 0.16
0.26 0.14 0.14 0.04 0.22
2.68 1.68 1.55 0.69 3.11
1.00 1.01 1.01 1.02 0.01
0.12 0.09 0.07 0.03 0.15
1.08 1.03 1.01 0.98 0.11
0.00 0.03 0.04 0.05 0.05
0.13 0.08 0.03 0.11 0.24
0.95 0.99 0.99 0.96 0.08
2.84 0.03
0.03 0.03 0.02 0.12 0.09
0.13 0.30 0.24 0.71 0.28
1.05 1.02 1.01 1.00 0.05
1.38 0.69 1.46 2.97 2.26
1.06 1.02 1.02 1.00 0.06
0.01 0.03 0.05 0.03 0.02
0.12 0.06 0.01 0.07 0.19
0.96 0.99 1.00 0.99 0.14
2.19 0.08
0.14 0.06 0.03 0.04 0.10
0.86 0.60 0.49 0.38 0.49
0.09 0.03 0.11 0.41 0.31
1.17 0.47 1.41 2.93 1.75
0.99 1.02 1.04 1.05 0.06
0.10 0.03 0.03 0.16 0.26
0.06 0.05 0.06 0.15 0.21
0.99 0.99 0.99 0.98 0.66
6.52 0.00
0.17 0.04 0.00 0.14 0.03
0.10 0.03 0.07 0.17 0.07
0.64 0.27 1.27 1.88 0.39
1.04 1.04 1.01 0.98 0.07
0.47 0.11 0.06 0.18 0.65
0.07 0.07 0.01 0.04 0.11
0.98 0.99 1.00 0.99 0.80
1.26 0.29
0.04 0.01 0.05 0.13 0.10
R
2
F
0.01 0.00 0.02
0.99 0.99 0.99
0.62 0.61
0.27 0.09 0.63
0.02 0.03 0.04 0.00 0.02
0.05 0.01 0.01 0.01 0.05
0.99 0.99 0.99 1.00 0.68
2.45 0.05
0.01 0.03 0.09 0.86
0.05 0.04 0.03 0.10 0.15
0.06 0.06 0.04 0.04 0.11
0.16 0.04 0.04 0.16 0.32
0.96 0.99 0.99 0.97 0.42
0.35 0.84
0.14 0.34 0.36 0.17
1.04 1.01 1.02 1.02 0.02
0.03 0.04 0.04 0.06 0.08
0.07 0.04 0.02 0.04 0.11
0.12 0.04 0.02 0.09 0.20
0.97 0.99 1.00 0.99 0.44
0.34 0.85
0.12 0.28 0.38 0.22
1.99 0.50 0.01 0.99 0.19
0.99 1.02 1.05 1.06 0.07
0.11 0.03 0.04 0.18 0.29
0.05 0.05 0.05 0.12 0.17
0.02 0.02 0.03 0.08 0.11
0.99 0.99 0.99 0.99 0.72
3.47 0.01
0.32 0.31 0.25 0.11
0.22 0.11 0.75 1.36 0.47
1.04 1.04 1.01 0.98 0.07
0.48 0.11 0.05 0.18 0.66
0.07 0.07 0.01 0.04 0.11
0.02 0.00 0.01 0.01 0.01
0.98 0.99 1.00 0.99 0.80
0.53 0.71
0.07 0.20 0.49 0.24
R
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
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0.94 0.45 0.95 0.99 0.99 0.98 0.75 0.22 0.05 0.02 0.19 0.41 0.18 0.11 0.01 0.14 0.32 0.02 0.07 0.05 0.13 0.15 1.03 1.01 1.01 1.04 0.02 0.70 0.12 0.81 0.86 0.08 0.14 0.01 0.07 0.12 0.02 5.29 0.00 0.92 0.98 0.99 0.97 0.40 0.28 0.13 0.00 0.22 0.50 0.04 0.06 0.06 0.08 0.04 1.06 1.02 1.01 1.01 0.05 2.53 1.41 1.75 4.23 3.71 0.61 0.15 0.13 0.78 1.39
0.94 0.99 0.98 0.89 0.11
0.89 0.98 0.99 0.95 0.08
Panel G: Grouped by B/M ratio of holdings Low 0.12 0.55 1.13 2 0.03 0.35 1.00 3 0.27 2.46 0.96 High 0.58 2.21 0.92 H–L 0.70 1.55 0.20
Panel H: Grouped by momentum of holdings Low 0.05 0.17 0.96 2 0.12 0.99 0.95 3 0.14 1.87 0.99 High 0.32 1.51 1.13 H–L 0.36 0.83 0.17
1.82 0.13
0.17 0.34 0.33 0.15 1.94 0.11 0.99 0.99 0.99 0.97 0.83 0.13 0.01 0.04 0.07 0.20 0.27 0.03 0.10 0.36 0.64 0.01 0.08 0.02 0.13 0.15 1.02 1.01 1.00 1.03 0.01 0.74 0.69 1.60 0.20 0.28 0.10 0.06 0.16 0.03 0.07 3.97 0.00 0.98 0.99 0.99 0.96 0.76 0.33 0.03 0.12 0.39 0.72 0.05 0.08 0.01 0.15 0.20 1.00 1.01 1.01 1.05 0.05 3.64 1.05 0.27 1.24 2.96 0.55 0.08 0.03 0.20 0.75
R h s b t(a) a F
R b
2.70 0.03
F F
a
t(a)
b
s
h
m
R
2
Four factor
2
Three factor
2
a
t(a)
CAPM Table 4 (continued )
0.13 0.31 0.38 0.18
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
%Assets
72
alpha of 0.24% quarterly (t-statistic of 1.38). Abnormal performance all but vanishes, however, once we control for momentum using the four-factor model: alphas of the two top quartiles shrink to 0.12% and 0.04%, alphas of the two bottom quartiles jump to 0.03% and 0.14%, and none of the estimates (or GRS F-statistics) remains statistically significant. In Panel E, institutions that trade the least seem to have the best performance, a result that would undoubtedly be strengthened by trading costs. Low-turnover institutions trade just 4.7% of their holdings in an average quarter and tilt toward large, value stocks. They are the only group with significant CAPM and four-factor alphas, of 0.24% and 0.17%, respectively (t-statistics of 2.66 and 1.99). In contrast, high-turnover institutions tend to invest in small, low-B/M, high-momentum stocks and trade 28.8% of their holdings in an average quarter. They have small CAPM and four-factor alphas but a significant Fama-French alpha of 0.41% quarterly (t-statistic of 2.93). Finally, in Panels F, G, and H, institutions grouped by the characteristics of stocks they hold (small-cap versus large-cap; growth versus value; losers versus winners) also show evidence of stock-picking ability relative to the CAPM and the three-factor model but not relative to the four-factor model. As one might expect, institutions that tilt the most toward small, value, or winner stocks have the highest CAPM alphas within each panel, with quarterly estimates of 0.17%, 0.58%, and 0.32%, respectively (only the middle number is significant, with a t-statistic of 2.21). Those compare with insignificant CAPM alphas of 0.10%, 0.12%, and 0.05% for institutions that hold the opposite types of stocks. Again, alphas essentially vanish using the four-factor model. The point estimates all become slightly positive and insignificant, ranging from 0.01% to 0.16% quarterly for the 12 groups in Panels F, G, and H. Loadings on the Fama-French factors exhibit the expected patterns as institutions invest in progressively smaller, higher-B/M, or higher-momentum stocks. None of the four-factor GRS F-statistics is statistically significant. Overall, a number of institutional groups appear to have stock-picking ability relative to the CAPM, but their abnormal performance is almost fully explained by the groups’ modest tilts toward small, value, and highmomentum stocks. Across all 31 groups in Table 4, only two (small and low-turnover institutions) have fourfactor alphas greater than 0.17% quarterly with t-statistics that are individually significant (not accounting for the implicit data-mining we do by searching across groups). Returns earned by most groups closely mimic market returns.
5. Limits of arbitrage The tests above ask whether institutions have stockpicking ability, i.e., do their equity holdings have positive alphas? Evidence that some groups do when performance is measured by the CAPM implies that those groups’ portfolios, when combined appropriately with the market index, would achieve a higher Sharpe ratio than provided by the market portfolio alone.
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
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Table 5 B/M and momentum portfolios, 1980–2007. The table reports quarterly excess returns and CAPM regressions (in percent) for B/M and momentum quintiles. Avg, Std, and t(Avg) are the average, standard deviation, and t-statistic of excess returns, respectively. aCAPM is the CAPM alpha with t-statistic t(aCAPM); Beta is the slope on the market portfolio; R2 is the regression adjusted R2; GRS F is the Gibbons, Ross, and Shanken (1989) F-statistic (with p-value immediately below) testing whether intercepts for the five quintiles are jointly significant. The portfolios are value-weighted with breakpoints determined by NYSE percentiles. B/M quintiles are formed in June each year based on B/M as of the prior December. Momentum quintiles are formed monthly based on returns from months 12 to 2 relative to the sort date. Returns and market values come from CRSP; book values come from Compustat and Kenneth French’s website at Dartmouth College. Variable
Portfolio
Avg
Std
t(Avg)
aCAPM
t(aCAPM)
Beta
R2
GRS F
B/M
Low (G) 2 3 4 High (V) V-G
1.95 2.28 2.31 2.51 3.02 1.07
9.47 8.31 7.66 7.61 7.59 6.80
2.17 2.89 3.17 3.48 4.19 1.65
0.36 0.27 0.51 0.82 1.44 1.80
1.48 1.12 1.80 2.29 3.38 2.97
1.11 0.97 0.86 0.81 0.76 0.35
0.93 0.92 0.85 0.77 0.67 0.17
2.50 0.04
Momentum
Low (L) 2 3 4 High (W) W-L
0.68 1.85 1.45 2.33 3.20 2.52
11.30 8.08 7.25 7.41 9.66 8.55
0.63 2.42 2.11 3.32 3.49 3.11
1.75 0.05 0.26 0.57 0.91 2.67
3.00 0.13 1.04 2.33 2.72 3.18
1.17 0.87 0.82 0.85 1.10 0.07
0.72 0.78 0.87 0.89 0.87 0.00
4.87 0.00
My final tests ask a stronger question: Does any group deviate efficiently from the market portfolio, i.e., does any group have a CAPM alpha that is high relative to the amount of idiosyncratic risk it takes on, given the investment opportunities available in the market? This question is obviously strongly than asking whether institutions have a positive alpha, and, as I explain below, the test provides a measure of how effectively the groups exploit anomalies in returns. One motivation for the test comes from the limits-ofarbitrage view of Shleifer and Vishny (SV, 1997). SV argue that institutions may be reluctant to bet heavily on anomalies, even those thought to reflect mispricing, out of fear that mispricing might widen in the short run, leading to short-term losses and client withdrawals (this reluctance provides one reason that mispricing may not get fully arbitraged away in equilibrium). SV’s arguments suggest that institutions might limit investments in stocks with high alphas, and might elect not to hold the tangency portfolio, if it would require the institution to deviate too much from the market portfolio and take on too much idiosyncratic risk. However, even if institutions do act in this way, a smart institution would still want to move toward the tangency portfolio by holding a portfolio with a high alpha per unit of idiosyncratic risk (though it might take only a modest bet on this portfolio). In other words, the limits-of-arbitrage view suggests that we should test whether institutions deviate efficiently from the market portfolio, not whether they deviate a lot.7 7 My discussion here assumes that institutions care about marketadjusted returns, but the tests are valid even if absolute performance is important. In that case, an arbitrageur would want to hold the tangency portfolio, which is just a special case of a portfolio with a high alpha per unit of idiosyncratic risk—indeed, all portfolios that maximize alpha per unit of idiosyncratic risk represent different combinations of the market and tangency portfolios. Also, I use the phrase ‘‘limits of arbitrage’’ to refer exclusively to the problems highlighted by SV caused by delegated portfolio management. The literature sometimes uses the phrase more generally to refer to any trading friction (e.g., Pontiff, 1996). My tests do
Statistically, the test takes a simple form: I just use the institutional portfolio as an asset pricing factor in timeseries regressions, i.e., I test whether alphas are zero when B/M and momentum portfolios are regressed on the market return and either institutions’ aggregate return or the return of a particular group of institutions. The logic here follows from Gibbons, Ross, and Shanken’s (1989) general analysis of mean-variance tests: If institutions maximize alpha per unit of idiosyncratic risk, given the opportunities presented by B/M and momentum portfolios, then some unspecified combination of the institutional and market portfolios should produce the tangency portfolio and explain expected returns on the B/M and momentum portfolios. Thus, testing whether the institutional return shrinks B/M and momentum alphas toward zero (when added to the CAPM) provides a way to assess whether institutions tilt optimally toward the tangency portfolio and, in particular, take advantage of the mean-variance opportunities provided by B/M and momentum portfolios. (I focus on B/M and momentum effects because they are well known and significant during my sample, but the tests could be expanded to other portfolios.) Table 5 reports descriptive statistics for the B/M and momentum portfolios. Both sets of portfolios are valueweighted, with breakpoints determined by NYSE quintiles. Following Fama and French (1993), the B/M quintiles are re-formed in June each year using stocks with positive B/M ratios as of the prior December (to allow for a lag in reporting). The momentum quintiles are formed monthly based on returns from months 12 to 2 relative to the sort date. The table shows that the B/M and momentum effects are strong from 1980 to 2007. Focusing on alphas for the extreme quintiles, high-B/M stocks outperform low-B/M
(footnote continued) not address whether institutions forgo positive-alpha investments because of other frictions.
74
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
stocks by 1.80% per quarter (t-statistic of 2.97) and highmomentum stocks outperform low-momentum stocks by 2.67% per quarter (t-statistic of 3.18). The GRS F-statistic, testing whether the portfolios’ alphas are jointly significant, is marginal for the B/M portfolios, with a p-value of 0.04, but strong for the momentum portfolios, with a p-value of 0.00. The CAPM alphas provide a benchmark for the tests, in Table 6, that add institutions’ returns as a second factor. A portion of the CAPM results are reproduced in Panel A of Table 6 for ease of reference. The remaining panels show regressions that add either the aggregate institutional return (Panel B) or the return of a particular group of institutions (Panels C–J) as a second factor: Ri ¼ ai þ bi MKTþ gi INST þei ,
ð1Þ
where Ri is the excess return on a B/M or momentum portfolio and INST is the excess return on the institutional portfolio. Again, testing whether the B/M and momentum portfolios’ alphas are zero in this regression is equivalent to asking whether institutions maximize their CAPM alpha per unit of idiosyncratic risk. For brevity, I report only estimates of ai and gi for the long-short B/M and momentum strategies (Quintile 5 minus Quintile 1), along with the GRS F-statistics for all five B/M and momentum portfolios. Rows that are in bold indicate institutional groups that have statistically significant stock-picking ability relative to the CAPM (see Tables 1 and 4). The overall conclusion from Table 6 is that no group of institutions tilts optimally toward the tangency portfolio achievable from B/M and momentum portfolios. The portfolios held by a few groups help explain either the B/M or momentum effects—never both—but the improvements are generally modest, with a couple of exceptions. Panel B shows that institutions’ aggregate return explains almost none of the B/M and momentum effects, as measured by alphas for long-short B/M and momentum strategies (V-G and W-L, respectively). The B/M effect increases slightly, from 1.80% to 1.85% quarterly, and the momentum effect decreases slightly, from 2.67% to 2.56% quarterly, when the aggregate institutional portfolio is added as a factor. Both alphas remain significant, and we cannot reject that institutions’ aggregate return has no explanatory power. These results are consistent with my finding that institutions add little beyond the market index. Similarly, portfolios held by most subgroups of institutions explain only a small portion of the B/M and momentum effects. For classifications based on business type (Panel C), turnover (Panel G), and the market cap of an institution’s holdings (Panel H), no group of institutions has a meaningful effect on the alphas of V-G and W-L when the group’s portfolio is added to the regression. Among those groups, the largest effect is for institutions that hold moderately small stocks (group 2 in Panel H). Adding their portfolio to the regressions decreases the B/M effect from 1.80% to 1.45% quarterly but increases the momentum effect from 2.67% to 2.92% quarterly. Both alphas remain significant. Institutions grouped by size (Panel D), past growth (Panel F), or the momentum of their stock holdings (Panel J) have a somewhat larger impact on alphas, but still no
group within those classifications explains either the B/M or momentum effect. Among these groups, the portfolio held by medium-sized institutions (Quartile 3 in Panel D) has the biggest impact on the value effect, reducing V-G’s alpha to 1.27% quarterly and its t-statistic to 2.10. The fastest-growing and most winner-oriented institutions have the biggest impact on momentum, each reducing W-L’s alpha from 2.67% to 1.83% quarterly, but the t-statistics remain greater than 2.50. Thus, even institutions that invest most strongly in winners do not tilt optimally toward the tangency portfolio that is achievable from momentum portfolios (let alone from B/M portfolios). It is useful to note, too, that short-sale constraints do not seem to explain this result: When the winner-oriented group’s return is added as a factor, both the long and short sides of the W-L portfolio continue to have significant alphas (not shown in the table). Quintile 1 has an alpha of 1.31% quarterly with a t-statistic of 2.56, and Quintile 5 has an alpha of 0.51% quarterly with a t-statistic of 2.45. The groups that best take advantage of the B/M or momentum effects (no group exploits both) are the bestperforming institutions (in Panel E) and institutions that invest most in value stocks (in Panel I). In particular, the portfolio held by the most value-oriented institutions, when used as a factor, accentuates the momentum effect but reduces V-G’s alpha to 0.76% quarterly (t-statistic of 1.93), down from a CAPM alpha of 1.80%. Conversely, the portfolio held by the top-performing institutions accentuates the B/M effect but reduces W-L’s alpha to 1.39% quarterly (t-statistic of 2.03), down from a CAPM alpha of 2.67%. Thus, on a statistical basis, we cannot reject that value-oriented institutions fully exploit the opportunities presented by B/M portfolios and we can only marginally reject that top-performing institutions exploit the opportunities presented by momentum portfolios. Overall, the results provide little support for the limitsof-arbitrage view that (1) the B/M and momentum effects reflect exploitable mispricing and (2) the anomalies persist because professional traders are reluctant to bet too heavily on them. In practice, institutions overall or grouped by type often do not exploit the anomalies at all and certainly not in a way that maximizes alpha (per unit of idiosyncratic risk). Remarkably, no group in Table 6 simultaneously takes advantage of both the B/M and momentum effects: When I use the groups’ portfolios as factors, not once do the alphas of V-G and W-L both decrease.8 The results suggest that the anomalies persist either because institutions do not take advantage of them for reasons other than SV’s (1997) limits-of-arbitrage arguments or because institutions themselves have the same biases that create the anomalies in the first place.
8 The point estimates for V-G and W-L simultaneously drop in a single case, when the portfolio held by above-average performing institutions (Group 3 in Panel E) is used as a factor, but the decline in V-G’s alpha is not statistically significant. The drop is not obvious in the table because the time period used for Panels E, F, and G differs from the other panels, beginning in 1981 instead of 1980, a result of requiring one year of past data for the sorts in those panels. The quarterly CAPM alphas of V-G and W-L are 1.90% and 2.52%, respectively, for the matching time period.
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
75
Table 6 Testing the efficiency of institutional portfolios, 1980–2007. The table reports quarterly CAPM and two-factor regressions for B/M and momentum quintiles. Intercepts are in percent. V-G is B/M Quintile 5 minus B/M Quintile 1. W-L is momentum Quintile 5 minus momentum Quintile 1. Panel A reports CAPM regressions: R ¼a þb MKT þe, where R is the excess return for either V-G or W-L and MKT is the excess return on the CRSP value-weighted index. Panels B–J report regressions that add the return for the specified group of institutions (INST) as a second factor: R¼ aþ b MKTþg INST þe. MKT is included in the regressions but its slope is not reported. t(a) is the t-statistic for a; the column labeled INST shows the slope on INST, with t-statistic t(INST); R2 is the regression adjusted R2; GRS F is the Gibbons, Ross, and Shanken (1989) F-statistic testing whether intercepts for all five B/M or momentum quintiles (not just V-G and W-L) are jointly significant and F pval is its p-value. The B/M and momentum quintiles are value-weighted with breakpoints determined by NYSE stocks. B/M is measured as of the prior December, with a six-month delay; momentum is based on returns from months 12 to 2 relative to the sort date. Returns and market values come from CRSP, book values come from Compustat and Ken French’s website at Dartmouth College, and institutional ownership comes from Thomson Financial. Bold rows indicate institutional groups that have statistically significant CAPM alphas in Tables 1 or 4. Portfolio
R2
GRS F
F pval
0.17 0.00
2.50 4.87
0.04 0.00
0.58 0.72
0.17 0.17
2.24 2.30
0.06 0.05
1.25 0.40
0.82 0.23
0.01 0.01
4.29 4.56
0.00 0.00
2.97 3.00 2.98
0.22 0.73 0.44
0.35 0.80 0.46
0.17 0.17 0.17
2.05 2.41 2.40
0.08 0.04 0.04
2.63 2.66 2.61
3.07 3.15 3.10
0.17 0.27 1.41
0.20 0.21 1.07
0.01 0.01 0.00
4.26 4.76 4.76
0.00 0.00 0.00
1.48 1.35 1.27 1.87
2.54 2.25 2.10 3.08
1.81 2.08 2.22 1.15
3.54 3.04 3.31 1.09
0.25 0.23 0.24 0.17
1.96 1.56 1.47 2.34
0.09 0.18 0.20 0.05
3.31 3.07 3.01 2.54
4.43 3.60 3.48 3.02
3.72 1.91 1.44 1.84
5.67 1.96 1.49 1.27
0.22 0.02 0.01 0.00
6.47 4.48 4.21 4.48
0.00 0.00 0.00 0.00
2.07 1.80 1.82 2.23
3.48 3.06 2.87 3.69
0.72 1.61 0.43 0.81
2.63 2.93 0.50 2.58
0.21 0.22 0.16 0.21
3.94 2.81 2.21 3.72
0.00 0.02 0.06 0.00
1.98 2.74 1.64 1.39
2.91 3.50 1.99 2.03
2.43 3.20 4.30 2.83
7.79 4.36 3.88 7.96
0.36 0.14 0.11 0.37
4.22 4.51 2.69 3.46
0.00 0.00 0.03 0.01
1.89 1.82 2.00 2.13
3.23 3.03 3.24 3.56
1.02 1.23 0.83 1.41
3.01 1.95 0.86 2.55
0.23 0.19 0.16 0.21
3.20 2.60 2.46 3.44
0.01 0.03 0.04 0.01
2.56 2.74 2.13 1.83
3.61 3.43 2.54 2.53
2.77 3.19 3.32 4.39
6.73 3.79 2.52 6.60
0.29 0.11 0.04 0.28
4.99 4.63 3.61 3.97
0.00 0.00 0.00 0.00
1.74 1.70 1.84 1.96
2.77 2.87 3.16 3.30
0.69 2.33 2.25 0.88
1.07 2.88 3.20 2.49
0.17 0.22 0.23 0.21
1.79 2.28 2.72 3.17
0.12 0.05 0.02 0.01
2.83 2.82 2.61 2.42
3.26 3.43 3.21 3.00
1.28 3.29 3.03 1.60
1.43 2.93 3.09 3.36
0.01 0.06 0.07 0.09
4.32 4.47 4.73 4.43
0.00 0.00 0.00 0.00
a
t(a)
Panel A: CAPM benchmark V-G W-L
1.80 2.67
2.97 3.18
Panel B: All institutions and individuals V-G All institutions Individuals
1.85 1.75
3.01 2.87
0.64 0.92
2.56 2.69
3.02 3.17
1.84 1.82 1.82
W-L
Institutional group used as a factor
All institutions Individuals
Panel C: Institutions grouped by business type V-G Banks Insurance All others W-L
Banks Insurance All others
Panel D: Institutions grouped by size V-G Smallest 2 3 Largest W-L
Smallest 2 3 Largest
Panel E: Institutions grouped by past returns V-G Low returns 2 3 High returns W-L
Low returns 2 3 High returns
Panel F: Institutions grouped by past growth V-G Low growth 2 3 High growth W-L
Low growth 2 3 High growth
Panel G: Institutions grouped by turnover V-G Low turnover 2 3 High turnover W-L
Low turnover 2 3 High turnover
INST
t(INST)
76
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
Table 6 (continued ) Portfolio
Institutional group used as a factor
Panel H: Institutions grouped by market cap of holdings V-G Small stocks 2 3 Large stocks W-L
Small stocks 2 3 Large stocks
Panel I: Institutions grouped by B/M ratio of holdings V-G Low B/M stocks 2 3 High B/M stocks W-L
Low B/M stocks 2 3 High B/M stocks
Panel J: Institutions grouped by momentum of holdings V-G Low ret stocks 2 3 High ret stocks W-L
Low ret stocks 2 3 High ret stocks
a
t(a)
INST
t(INST)
R2
GRS F
F pval
1.65 1.45 1.92 2.00
2.90 2.61 3.22 3.58
0.82 2.26 2.11 2.03
3.91 4.83 2.24 4.55
0.27 0.31 0.20 0.30
2.39 2.10 2.48 2.91
0.04 0.07 0.04 0.02
2.80 2.92 2.51 2.47
3.41 3.53 3.02 3.04
0.76 1.70 2.71 1.96
2.52 2.44 2.07 3.02
0.04 0.04 0.02 0.07
5.01 4.75 4.60 4.69
0.00 0.00 0.00 0.00
1.55 1.87 1.08 0.76
3.89 3.25 1.97 1.93
2.07 2.57 2.70 1.78
12.07 3.66 5.69 12.62
0.64 0.26 0.36 0.66
4.00 2.56 1.29 1.76
0.00 0.03 0.27 0.13
2.93 2.60 3.50 3.57
4.28 3.16 4.42 4.74
2.21 2.45 3.15 1.55
7.49 2.45 4.60 5.80
0.33 0.04 0.15 0.23
6.02 5.17 6.15 6.27
0.00 0.00 0.00 0.00
1.85 1.56 1.97 2.21
3.51 2.78 3.23 4.01
1.14 2.01 1.25 1.29
6.00 4.48 1.64 5.21
0.37 0.30 0.19 0.33
4.80 2.62 2.44 4.66
0.00 0.03 0.04 0.00
2.56 2.98 2.27 1.83
4.25 3.81 2.74 2.87
2.20 2.69 2.78 2.66
10.13 4.30 2.68 9.24
0.48 0.13 0.05 0.43
5.55 5.11 4.03 4.39
0.00 0.00 0.00 0.00
Table A1 Quarterly stock returns regressed on IO and other characteristics, 1980–2007. The table reports Fama-MacBeth cross-sectional regressions (slope estimates are followed by t-statistics) of quarterly stock returns (in percent) on institutional ownership (IO) and other firm characteristics. The left-hand columns use all firms, while the right-hand columns use only firms with market cap above the NYSE median. Regressors are measured at the end of the prior quarter and winsorized at the 1st and 99th percentiles. IO is the fraction of a firm’s shares held by institutions; LogSize is log market cap; LogB/M is log book equity for the most recent fiscal of year (with a four-month delay) minus LogSize; Returns 12 to 2 are returns from month 12 to 2; Returns 36 to 13 are returns from month 36 to 13; Volatility 12 to 1 is the daily standard deviation of returns during the prior 12 months; Beta is the market beta estimated from at least 24 and up to 60 months of past monthly returns; Turnover 12 to 1 equals shared traded divided by shares outstanding for the prior 12 months; Issuance 12 to 1 is the log growth in splitadjusted shares outstanding during the prior 12 months; Accruals 1 are operating accruals, as per Sloan (1996); Asset growth 1 is the log growth in the book value of total assets during the prior fiscal year; and ROA 1 is earnings per share before extraordinary items divided by lagged assets per share. N is the average number of firms in the sample. All regressions require firms to have data for LogSize, LogB/M, Returns 12 to 2, and IO. Returns, market cap, shares outstanding, and turnover come from CRSP, accounting data come from Compustat, and institutional holdings come from Thomson Financial. All stocks LogSize LogB/M Returns 12
to 2
0.24 1.25 1.57 5.29 3.19 5.79
IO Returns 36
Large stocks
0.27 0.21
0.37 2.11 1.50 5.11 3.19 5.71 1.82 2.58
4,661
4,661
to 13
Volatility 12
to 1
Beta Turnover 12 Issuance 12
to 1
to 1
Accruals 1 Asset growth 1 ROA 1 N
4,661
0.35 3.52 0.67 3.10 2.80 7.28 1.95 3.24 0.13 0.53 1.61 0.42 0.56 1.58 9.84 3.66 2.84 5.20 2.68 3.04 2.77 8.14 3.48 3.20 3,633
0.11 0.71 0.68 2.09 2.70 3.87
1,090
0.93 1.40
0.18 1.09 0.68 2.11 2.71 3.88 1.20 1.77
1,090
1,090
0.24 1.82 0.52 2.04 2.73 4.78 0.62 1.05 0.09 0.29 11.71 1.77 0.20 0.42 1.68 0.64 2.54 3.66 2.47 1.92 1.36 3.24 4.53 2.74 906
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
6. Conclusions The performance of institutional investors has been the subject of much research. Prior studies suggest that institutions have some stock-picking skill even though they deliver mediocre returns, at best, to their clients. That view has important effects on how we think about institutions’ role in capital markets, the economics of the
Table A2 IO-sorted portfolios, 1980–2007. The table reports average quarterly excess returns (in percent) for institutional-ownership (IO) portfolios. Stocks are sorted into quintiles (using NYSE breakpoints) based on the fraction of a firm’s shares held by institutions at the beginning of the quarter. The top row shows the average value-weighted IO of each portfolio. Returns-VW and ReturnsIW are the portfolios’ value-weighted and institutional-weighted excess returns, respectively (institutional weights are determined by institutions’ holdings of each stock). Weight-MKT is the fraction of the market portfolio invested in each portfolio and Weight-INST is the fraction of institutions’ total holdings invested in each portfolio. All numbers are time-series averages from 1980 to 2007. Returns and market values come from CRSP and institutional holdings come from Thomson Financial. IO portfolio Low
2
3
4
High
IO
0.07
0.27
0.43
0.57
0.72
Returns-VW Returns-IW
1.41 2.09
2.11 2.14
2.19 2.20
2.16 2.17
2.25 2.24
Weight-MKT Weight-INST
0.08 0.01
0.14 0.09
0.29 0.26
0.28 0.32
0.22 0.33
77
money management industry, and market efficiency more generally. For example, it supports Berk and Green’s (2004) contention that many stylized facts about mutual fund performance and flows are consistent with a rational, competitive mutual fund industry. My results provide a more pessimistic view of the value added by institutional investors. Quite simply, institutions as a whole seem to do little more than hold the market portfolio, at least from the standpoint of their pre-cost and pre-fee returns. Institutions’ aggregate returns almost perfectly mimic the value-weighted index, with an economically small CAPM alpha of 0.08% quarterly, and institutions take essentially no aggregate bet on any of the most important firm characteristics known to predict stock returns. The implication is that, to the extent that institutions deviate from the market portfolio, they seem to bet primarily on idiosyncratic returns—bets that do not deliver much value. The same conclusions apply, for the most part, to different types of institutions. I find modest stock-picking ability relative to the CAPM for banks, medium-sized and low-turnover institutions, institutions with strong past performance, and institutions that invest in high-B/M or high-momentum stocks, but their performance is almost entirely explained by the B/M and momentum effects in returns. Only two groups out of 31 total have a four-factor alpha that is greater than 0.17% quarterly. And even groups that have some stock-picking ability relative to the CAPM do not take advantage of the risk-return opportunities presented by B/M and momentum portfolios. Put differently, the B/M and momentum effects can explain the groups’ returns, but the groups’ returns cannot, in turn, explain the B/M and momentum effects.
Table A3 IO and firm characteristics, 1980–2007. The table reports the correlation between institutional ownership (IO) and firm characteristics and slopes from Fama-MacBeth regressions of IO on all of the characteristics taken together. The correlations and regression slopes are estimated quarterly; the table reports the average (Avg), standard deviation (Std), and fraction that are positive (Pos) of the quarterly estimates. The left-hand columns use all firms while the right-hand columns use only firms with market cap above the NYSE median. All variables other than IO are winsorized at the 1st and 99th percentiles. IO is the fraction of a firm’s shares held by institutions; LogSize is log market cap; LogB/M is log book equity for the most recent fiscal of year (with a 4-month delay) minus LogSize; Returns 12 to 2 are returns from month 12 to 2; Returns 36 to 13 are returns from month 36 to 13; Volatility 12 to 1 is the daily standard deviation of returns during the prior 12 months; Beta is the market beta estimated from at least 24 and up to 60 months of past monthly returns; Turnover 12 to 1 equals shared traded divided by shares outstanding for the prior 12 months; Issuance 12 to 1 is the log growth in split-adjusted shares outstanding during the prior 12 months; Accruals 1 are operating accruals, as per Sloan (1996); Asset growth 1 is the log growth in the book value of total assets during the prior fiscal year; and ROA 1 is earnings per share before extraordinary items divided by lagged assets per share. All of the estimates require firms to have data for LogSize, LogB/M, Returns 12 to 2, and IO. Returns, stock prices, shares outstanding, and turnover come from CRSP, accounting data come from Compustat, and institutional holdings come from Thomson Financial. Characteristic
All stocks Correlation
LogSize LogB/M Returns 12 to 2 Returns 36 to 13 Volatility 12 to 1 Beta Turnover 12 to 1 Issuance 12 to 1 Accruals 1 Asset growth 1 ROA 1
Large stocks Regression slope
Correlation
Regression slope
Avg
Std
Pos
Avg
Std
Pos
Avg
Std
Pos
Avg
Std
Pos
0.68 0.10 0.09 0.20 0.42 0.10 0.27 0.09 0.02 0.07 0.28
0.03 0.08 0.09 0.11 0.07 0.11 0.12 0.05 0.03 0.05 0.04
1.00 0.05 0.79 0.93 0.00 0.77 0.99 0.08 0.72 1.00 1.00
0.07 0.02 0.02 0.02 0.46 0.02 0.71 0.08 0.06 0.03 0.11
0.01 0.02 0.02 0.02 0.34 0.02 0.30 0.04 0.07 0.02 0.04
1.00 0.86 0.19 0.14 0.00 0.89 1.00 0.02 0.20 0.07 0.99
0.11 0.06 0.03 0.03 0.05 0.18 0.29 0.05 0.01 0.00 0.06
0.14 0.07 0.09 0.08 0.11 0.13 0.11 0.06 0.04 0.06 0.05
0.82 0.23 0.63 0.67 0.76 0.96 0.96 0.26 0.64 0.50 0.90
0.02 0.02 0.01 0.02 1.49 0.08 1.14 0.13 0.02 0.04 0.10
0.02 0.02 0.05 0.04 0.67 0.08 0.60 0.10 0.13 0.06 0.16
0.85 0.26 0.45 0.26 0.00 0.79 1.00 0.08 0.45 0.26 0.69
78
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
Appendix A Section 3 shows that institutions, taken in aggregate, have little stock-picking skill and place almost no bet on the main characteristics known to predict returns. For comparison with prior studies, this Appendix explores the same issues
via cross-sectional regressions, i.e., I test whether institutional ownership (IO), equal to the fraction of a firm’s shares owned by institutions, is correlated with a firm’s future returns and the firm characteristics considered in Section 3. Table A1 reports Fama-MacBeth regressions of quarterly stock returns on IO and other characteristics
Fig. A1. Institutional ownership for characteristic-sorted portfolios, 1980–2007. The figure shows equal-weighted (EW) and value-weighted (VW) institutional ownership for stock quintiles (Q1–Q5) sorted by size (market value), B/M (book equity for the most recent fiscal of year divided by size), momentum (returns from month 12 to 2), reversals (returns from month 36 to 13), volatility (daily standard deviation during the prior 12 months), beta (estimated from at least 24 and up to 60 months of past monthly returns), turnover (shared traded divided by shares outstanding for the prior 12 months), issuance (growth in split-adjusted shares outstanding during the prior 12 months), accruals (as per Sloan, 1996), asset growth (growth in the book value of total assets during the prior fiscal year), and ROA (earnings per share before extraordinary items divided by lagged assets per share). Returns, market cap, shares outstanding, and turnover come from CRSP, accounting data come from Compustat, and institutional holdings come from Thomson Financial.
J. Lewellen / Journal of Financial Economics 102 (2011) 62–80
(t-statistics are reported below the slopes). The regressors, defined in the table, are measured at the end of the prior quarter and winsorized at the 1st and 99th percentiles. Results in the left-hand columns use all stocks, while results in the right-hand columns use only stocks larger than the NYSE median value. IO has little direct correlation with future returns (used alone, IO has a t-statistic of 0.21 for all stocks and 1.40 for large stocks) but becomes statistically significant after controlling for size, B/M, and momentum (a t-statistic of 2.58 for all stocks and 1.77 for large stocks). A 25 percentage point increase in IO (roughly one standard deviation) predicts an increase in next quarter’s return of 0.46% in regressions with all stocks and 0.30% in regressions with large stocks, assuming no change in size, B/M, or momentum. The slope on IO remains significant when other characteristics are added to the all-stock regression but the t-statistic drops to 1.05 in the large-stock regression. In short, IO seems to have reliable predictive power for returns in the full sample but relatively weak predictive power for larger stocks. The weaker effect among large stocks helps explain why institutions’ aggregate returns only slightly beat the market index. Additional evidence is provided in Table A2, which reports summary statistics for IO-sorted portfolios (quintiles based on NYSE breakpoints). Like the regressions in Table A1, the portfolios suggest that IO is positively related to expected returns: high-IO stocks outperform low-IO stocks by a significant 0.84% quarterly (value-weighted excess returns, with a t-statistic of 2.08). But the table also shows that the effect is largely concentrated in portfolio 1—the spread between portfolios 1 and 2 is 0.70% quarterly, while the spread between portfolios 2 and 5 is 0.14% quarterly—which makes up a small fraction of both the market portfolio (8%) and the aggregate institutional portfolio (1%). Thus, while institutions seem to have some stock-picking skill, the impact on their aggregate returns is small. Table A2 also shows that, to the extent institutions do invest in low-IO stocks, they tend to hold better ones: the institutional-weighted average return for low-IO stocks is significantly higher than the value-weighted average return, 2.09% versus 1.41% quarterly (t-statistic of 2.42). But, again, the impact on institutions’ aggregate returns is tiny because low-IO stocks represent just 1% of their holdings. Table A3 and Fig. A1 explore the correlation between IO and firm characteristics. Statistical inference in these tests is complicated by the fact that IO is very persistent (see also footnote 5 in the text). For this reason, Gompers and Metrick (2001) and Bennett, Sias, and Starks (2003) simply emphasize how frequently their quarterly estimates are positive versus negative. I follow that approach here. In particular, Table A3 shows that, in the full sample of stocks, IO is positively correlated with firm size, momentum, long-term past returns, beta, turnover, asset growth, and ROA in more than 75% of the quarters and negatively correlated with B/M, volatility, and share issuance in more than 90% of the quarters. The results are similar, but weaker, among large stocks (only the correlation with volatility changes sign). The results are also similar in multiple regressions that include all
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variables, with three notable differences: (1) The relation between IO and B/M becomes positive in the full sample of stocks, while the simple correlation is negative (the slope and correlation are both negative among large stocks); (2) the slopes on momentum, long-term past returns, and asset growth all become negative, compared with simple correlations that are all positive; and (3) the slope on volatility is strongly negative for both samples of stocks, whereas the simple correlation is negative for all stocks but positive for large stocks. These results are generally consistent with the findings of Gompers and Metrick and Bennett, Sias, and Starks (to the extent our variables overlap). The strength of the correlations is easiest to see in Fig. 1A, which shows how IO varies across characteristicsorted portfolios. Focusing on the value-weighted results, IO varies substantially across size, volatility, beta, and turnover portfolios and has some correlation with all of the other variables (except perhaps with accruals). The patterns are typically more pronounced for equal-weighted IO. The bottom line is that institutions clearly display a preference for certain types of stocks—preferences that show up significantly when IO is regressed on firm characteristics—but, as emphasized in Section 3, the impact on institutions’ aggregate portfolio weights is quite small.
References Bennett, J., Sias, R., Starks, L., 2003. Greener pastures and the impact of dynamic institutional preferences. Review of Financial Studies 16, 1203–1238. Berk, J., Green, R., 2004. Mutual fund flows and performance in rational markets. Journal of Political Economy 112, 1269–1295. Brunnermeier, M., Nagel, S., 2004. Hedge funds and the technology bubble. Journal of Finance 59, 2013–2040. Carhart, M., 1997. On persistence in mutual fund performance. Journal of Finance 52, 57–82. Chen, H.-L., Jegadeesh, N., Wermers, R., 2000. The value of active fund management: an examination of the stockholdings and trades of fund managers. Journal of Financial and Quantitative Analysis 35, 343–368. Chen, J., Hong, H., Stein, J., 2002. Breadth of ownership and stock returns. Journal of Financial Economics 66, 171–205. Cohen, R., Gompers, P., Vuolteenaho, T., 2002. Who underreacts to cashflow news? Evidence from trading between individuals and institutions. Journal of Financial Economics 66, 409–462. Daniel, K., Grinblatt, M., Titman, S., Wermers, R., 1997. Measuring mutual fund performance with characteristic-based benchmarks. Journal of Finance 52, 1035–1058. Davis, J., Fama, E., French, K., 2000. Characteristics, covariances, and average returns: 1929–1997. Journal of Finance 55, 389–406. Del Guercio, D., 1996. The distorting effect of the prudent-man laws on institutional equity investment. Journal of Financial Economics 40, 31–62. Falkenstein, E., 1996. Preferences for stock characteristics as revealed by mutual fund portfolio holdings. Journal of Finance 51, 111–135. Fama, E., French, K., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3–56. Gibbons, M., Ross, S., Shanken, J., 1989. A test of the efficiency of a given portfolio. Econometrica 57, 1121–1152. Gompers, P., Metrick, A., 2001. Institutional investors and equity prices. Quarterly Journal of Economics 116, 229–260. Grinblatt, M., Titman, S., 1989. Mutual fund performance: an analysis of quarterly portfolio holdings. Journal of Business 62, 393–416. Grinblatt, M., Titman, S., 1993. Performance measurement without benchmarks: an examination of mutual fund returns. Journal of Business 66, 47–68. Grinblatt, M., Titman, S., Wermers, R., 1995. Momentum investment strategies, portfolio performance, and herding: a study of mutual fund behavior. American Economic Review 85, 1088–1105.
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Kovtunenko, B., Sosner, N., 2004. Avoidance of Small Stocks and Institutional Performance. Unpublished Working Paper. Harvard University, Cambridge, MA. Nofsinger, J., Sias, R., 1999. Herding and feedback trading by institutional and individual investors. Journal of Finance 54, 2263–2295. Pontiff, J., 1996. Costly arbitrage: evidence from closed-end funds. Quarterly Journal of Economics 111, 1135–1151. Shleifer, A., Vishny, R., 1997. The limits of arbitrage. Journal of Finance 52, 35–55.
Sias, R., 2004. Institutional herding. Review of Financial Studies 17, 165–206. Sloan, R., 1996. Do stock prices fully reflect information in accruals and cash flows about future earnings. Accounting Review 71, 289–315. Wermers, R., 1999. Mutual fund herding and the impact on stock prices. Journal of Finance 54, 581–622. Wermers, R., 2000. Mutual fund performance: an empirical decomposition into stock-picking talent, style, transaction costs, and expenses. Journal of Finance 55, 1655–1695.
Journal of Financial Economics 102 (2011) 81–101
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Short-term termination without deterring long-term investment: A theory of debt and buyouts$ Alex Edmans a,b, a b
Wharton School, University of Pennsylvania, Philadelphia, PA 19104, United States National Bureau of Economic Research, Cambridge, MA 02138, United States
a r t i c l e i n f o
abstract
Article history: Received 25 May 2010 Received in revised form 22 October 2010 Accepted 7 February 2011 Available online 28 June 2011
The option to terminate a manager early minimizes investor losses if he is unskilled. However, it also deters a skilled manager from undertaking efficient long-term projects that risk low short-term earnings. This paper demonstrates how risky debt can overcome this tension. Leverage concentrates equityholders’ stakes, inducing them to learn the cause of low earnings. If they result from investment (poor management), the firm is continued (liquidated). Therefore, unskilled managers are terminated and skilled managers invest without fear of termination. Unlike models of managerial discipline based on total payout, dividends are not a substitute for debt—they allow for termination upon non-payment, but at the expense of investment since they do not concentrate ownership and induce monitoring. Debt is dynamically consistent as the manager benefits from monitoring. In traditional theories, monitoring constrains the manager; here, it frees him to invest. & 2011 Elsevier B.V. All rights reserved.
JEL classification: D82 G32 G33 Keywords: Termination Liquidation Managerial myopia Leverage Private equity
1. Introduction
$ I am indebted to the referee, Patrick Bolton, for excellent comments and insights that substantially improved this paper. I also thank Raj Aggarwal, Franklin Allen, Philip Bond, Mathias Dewatripont, Xavier Gabaix, Itay Goldstein, Zhiguo He, Steve Kaplan, Anastasia Kartasheva, Gustavo Manso, Stew Myers, Greg Nini, Antti Petajisto, Uday Rajan, Berk Sensoy, (especially) Gustav Sigurdsson, Leonid Spesivtsev, Jeremy Stein, and seminar participants at Australian National University, Baruch, MIT, Ohio State, Singapore Management University, University of New South Wales, Wharton, the EFA, Michigan Mitsui Conference, and Minnesota Corporate Finance Conference for helpful suggestions, and Chong Huang, Edmund Lee, and Qi Liu for very good research assistance. I gratefully acknowledge funding from the MIT Sloan Stone Fund, the Wharton Dean’s Research Fund, and the Goldman Sachs Fellowship from the Rodney L. White Center for Financial Research. Correspondence address: Wharton School, University of Pennsylvania, 3620 Locust Walk, Philadelphia, PA 19104, United States. E-mail address:
[email protected]
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2010.11.005
This paper studies the tension between two first-order problems faced by the modern firm. The first is how to terminate unskilled managers early. The financial crisis demonstrates the substantial losses that can occur if misguided decisions are left unchecked. A quite separate challenge is how to incentivize skilled managers to invest for the long-term. Nowadays, competitive success increasingly hinges upon intangible assets such as human capital (Zingales, 2000). Since intangibles only pay off in the long-run, managers may underinvest in them (Stein, 1988). These two challenges fundamentally conflict. Investors can mitigate the value destroyed by an unskilled manager by forcing him to reveal short-term earnings, thus giving themselves the option to terminate him if profits are low. However, the same termination threat may deter a skilled
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manager from undertaking efficient long-term projects that risk low short-term earnings. This paper demonstrates how risky debt can alleviate this tension, by playing two distinct roles which address the two separate challenges. The disciplinary effect of debt addresses termination by forcing the manager to make an interim payment. The failure to do so reveals that earnings are weak, the manager is likely unskilled, and thus termination is desirable. Indeed, Jensen (1989) argues that this disciplinary effect explains why buyouts are levered: debt is ‘‘a mechanism to force managers to disgorge cash rather than spend it on empire-building projects’’. However, such a justification leaves many questions unanswered. First, dividends can also impose discipline: as Jensen also notes, ‘‘debt is a substitute for dividends’’. Second, buyouts typically feature a concentrated shareholder, but if the only effect of debt is discipline, equityholders are irrelevant and dispersed ownership would be equally effective. Third, it is the manager who controls leverage going forward, and he can raise equity to repay the debt and free himself from its discipline. Fourth, the disciplinary effect may deter investment. This is where the second effect of debt comes in: the concentration effect, which addresses investment. The core model contains a single firm, single large investor, and a continuum of atomistic investors. If atomistic investors provide debt, the large investor’s limited funds comprise a greater proportion of the total equity. Thus, a non-paying manager is not automatically fired; instead, the large investor’s concentrated stake gives her an incentive to gather costly information on the underlying cause of weak earnings. If the cause is low managerial skill, the firm is liquidated; if the cause is investment, it is continued. Knowing that investors will make an informed liquidation decision ex post, the manager pursues longrun growth ex ante. A skilled manager invests without fear of termination; an unskilled manager is efficiently terminated. The concentration effect distinguishes this paper from theories of the disciplinary role of debt: it has different implications for the substitutability of dividends for debt, the effect of debt on investment, the optimal level of debt, and the concurrence of risky debt with concentrated equity. In Jensen (1986), Stulz (1990), and Zwiebel (1996), debt also forces the manager to pay out cash. Dividends would have the same disciplinary effect, since missing a dividend also reveals low earnings, and are thus a perfect substitute—these models are theories of total payout (debt plus dividends) rather than debt in particular. Here, the financing structure must not only allow termination, but also induce investment. The latter requires the concentration effect, which only debt has. Turning to the effect of debt, in Jensen (1986) and Stulz (1990), debt reduces investment by lowering free cash; here, it can have the opposite effect by inducing monitoring. Moving to the optimal level of debt, it is borderline nonrepayable in disciplinary models. Since the only role of debt is to impose discipline, it should be just high enough that a bad type cannot pay it. In Lambrecht and Myers (2008), strictly nonrepayable debt induces excessive divestment; here, it is efficient as it increases concentration. Finally, the model
predicts that leverage should coincide with concentrated equity investors who actively monitor, as shown empirically by Cotter and Peck (2001). The above predictions are primarily generated by the concentration effect. Moreover, by analyzing two distinct and conflicting agency problems (liquidation and investment), the model studies the interaction between the concentration and disciplinary effects together, which generates additional implications. These relate to the joint determinants of capital structure and dividend policy as a function of the relative severity of a firm’s agency issues. While standard empirical studies analyze the determinants of leverage (e.g., Rajan and Zingales, 1995), this paper emphasizes that leverage is the product of two factors: the level of total payout and its division between debt and dividends. The importance of short-term termination determines the need for the disciplinary effect and thus the level of total payout. If termination is unlikely to be optimal (e.g., the firm is a start-up with low liquidation value), total payout should be low; indeed, such firms are typically unlevered and pay no dividends. The importance of long-term investment determines the need for the concentration effect and thus the composition of total payout. If growth opportunities are attractive, any payout should be in the form of debt. While Rajan and Zingales find that leverage is negatively correlated with growth opportunities, the model predicts a positive correlation once total payout is controlled for. Their negative correlation suggests that a growing firm prefers to be unlevered, but if termination is important, being unlevered is not an option. The appropriate comparison is debt versus other forms of payout that would achieve termination; debt is less detrimental to growth than dividends. One application of the model is to leveraged buyouts (LBOs), which are often undertaken to discipline managers to scrap inefficient projects, but monitoring helps ensure that efficient investment is not also cut. Indeed, ¨ Kaplan and Stromberg (2009) show that, from the 1990s, buyouts have predominantly been in middle-aged firms in growing industries such as IT/media/telecoms, financial ¨ services, and healthcare. Lerner, Sorensen, and Stromberg (2011) find that LBOs lead to no decrease in innovation activity and an increase in the quality of innovation. The above single-firm model is analyzed in Section 2. Section 3 extends the model to multiple large investors and heterogeneous managers, where good managers have a higher probability of having growth opportunities than bad types. A separating equilibrium is sustainable where bad managers run unlevered firms financed exclusively by small shareholders, and good managers run levered firms and are financed by both large and atomistic investors. The two roles of debt, which lead to firm viability in a single-manager setting, also achieve separation in a multimanager setting. The disciplinary effect of debt renders it a credible signal of managerial quality: bad managers avoid leverage as they are likely to default. However, in models where only credibility of the signal matters, borderline nonrepayable debt is optimal—debt is just high enough that a bad type defaults; additional debt would augment signaling costs. In addition, dividends are equally credible as they also have a disciplinary effect: Bhattacharya (1979)
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shows that Ross’s (1977) idea of signaling with debt can also be achieved with dividends. However, credibility is not the only issue. The signal must be a desirable one that good managers wish to emit. In standard models, a good manager automatically wishes to reveal his quality, as his pay is exogenously assumed to depend on short-run value (Ross, 1977; Bhattacharya, 1979) or signaling quality is necessary to raise financing (Myers and Majluf, 1984; Fulghieri and Lukin, 2001). Here, pay is not tied to short-run value and even bad managers can raise financing, so the traditional motives to signal do not exist. This is where the concentration effect comes in: it provides a motive to signal. This motive is not to obtain a greater level of funds, but to attract a different type of funds. Signaling quality attracts large investors. A large investor provides no more funds than several small investors, but is critically different as she has the incentive to monitor, thus allowing the long-term project to be taken. Since good managers have a greater probability of having growth opportunities, this advantage is more important to them and separation is achieved. The different motives for signaling lead to different results on the dynamic consistency of debt and the effect of signaling on total surplus. In this and other models, debt hurts the manager owing to the disciplinary effect, but he willingly bears these costs to signal quality. If the goal of signaling is to raise funds, it is already achieved in the first period. Hence, once funds have been raised, the manager has incentives to delever and free himself from discipline. This concern applies not only to signaling theories, but also to single-firm models in which investors initially impose debt on the manager to solve free cash flow problems (e.g., Jensen, 1986; Stulz, 1990). As noted by Zwiebel (1996), it is the manager who controls leverage going forward, and he may subsequently reduce it to increase free cash. Here, debt is dynamically consistent since its advantages are not confined to the first period, and so the manager has an incentive to retain it. Debt benefits the manager by inducing monitoring: this requires not only attracting a large investor through initially signaling quality, but also persuading her to monitor in the future by maintaining leverage. In short, the disciplinary effect renders debt a credible signal in the first period. The concentration effect renders it a desirable signal that the firm wishes to maintain in future periods. This persistence of leverage is consistent with the findings of Lemmon, Roberts, and Zender (2008). The manager’s desire for monitoring in turn results from the analysis of a different agency problem to prior debt theories. In Jensen (1986), Stulz (1990), and Zwiebel (1996), there is a fundamental effort conflict where firm value maximization requires the manager to exert effort or forgo private benefits. Investors’ role is to be an ‘‘adversary’’ of the manager, preventing shirking or private benefits. Monitoring hurts the manager, and so he wishes to delever to reduce investors’ incentives to do so. Here, there is no effort conflict with respect to project selection: the long-term project maximizes both firm value and private benefits. A monitor’s role is to be an ‘‘ally’’ of the manager, allowing him to choose the project
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that he wishes to anyway in the absence of termination concerns. Since the monitor helps the manager, the latter has an incentive to retain the former through maintaining leverage.1 Indeed, Cornelli and Karakas (2010) find that LBOs lead to increases in operating performance, but also a reduction in CEO turnover, suggesting that buyouts allow the manager to have a longer-term horizon. Turning to welfare effects, signaling reduces fundamental value in traditional models. In Ross (1977), it leads to bankruptcy risk; in Stein (1989) and Miller and Rock (1985), it reduces investment. There are no offsetting real benefits as separation merely changes outsiders’ perceptions of short-run value. In Myers and Majluf (1984) and Fulghieri and Lukin (2001), signaling does have real benefits, because it allows a firm to raise financing and thus invest. Here, the real benefits arise through a quite different mechanism. Signaling has no effect on the level of funds raised: firms receive the same as in a pooling equilibrium. Instead, the benefit comes in the different type of funds. Signaling allocates scarce large investors to good managers, who benefit most from monitoring as they are most likely to have growth opportunities. Some features of this paper have been individually examined in prior models. By bringing together effects studied in previously disparate literatures, this paper analyzes unexplored interactions (e.g., the trade-off between termination and investment,2 and the concentration effect alleviating a side-effect of the disciplinary effect) and thus generates new insights unattainable from piecing together the individual results of prior research. In Boot and Thakor (1993), as in this paper, leverage concentrates shareholders’ fixed dollar wealth and induces monitoring.3 In their model, monitoring has no real effects. While one could combine their result with the literature on the disciplinary effect of blockholders (e.g., Burkart, Gromb, and Panunzi, 1997) and conclude that the concentration effect can alleviate agency issues, such logic implies that the manager will unlever; here, he wishes to retain leverage. The concentration effect echoes Jensen and Meckling (1976) and Innes (1990), where debt magnifies a manager’s equity holding, directly inducing effort. Here, there is no fundamental effort conflict, yet debt is still effective. Leverage incentivizes effort by investors rather than the manager, indirectly improving the manager’s actions. The model contains two layers of agency problems: investor monitoring and managerial investment; solving the former addresses the latter. In a 1 Zwiebel (1996) also achieves dynamic consistency, through the different mechanism of an ever-present raider (an adversary). 2 Acharya, Mehran, and Thakor (2010) also show how capital structure is driven by a trade-off between its effects on investment and managerial rent extraction (the analogy of inefficient continuation). However, in that paper, the goal is to deter rather than encourage risky investments. 3 In Boot and Thakor and the present paper, debt is valuable as it makes equity informationally sensitive and induces shareholders to monitor. By contrast, in Gorton and Pennacchi (1990), the desirability of debt arises because it is informationally insensitive and its owners have low incentives to monitor. Thus, uninformed investors wish to trade debt. Mahrt-Smith (2005) studies how institutional factors jointly affect capital structure and ownership structure, rather than how the former affects the latter.
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model of investment alone, growth could be induced by simply giving the manager a long-term contract and so there is no role for debt. This paper adds a termination problem to endogenize giving the manager short-term concerns (via the threat of firing) as optimal. Other papers contain a link between leverage and monitoring that does not arise through concentration. In Townsend (1979), debt ensures that verification only occurs in bankruptcy; his is a pure exchange economy with no real effects. In Harris and Raviv (1990), debt leads to monitoring because they exogenously assume that an audit occurs if and only if the firm is bankrupt. In reality, investigations can occur at all times; this paper endo¨ genizes the monitoring decision.4 In Gumbel and White (2007), debt induces monitoring by shifting control to a ‘‘tough’’ investor, rather than by the concentration effect.5 The manager makes an effort decision and the monitor is an adversary; here, she is an ally, giving the manager a reason to retain her. Von Thadden (1995) and Edmans (2009) also analyze how ex post monitoring can induce ex ante investment. Von Thadden assumes that monitoring is contractible; this paper shows how debt can induce non-verifiable monitoring. He also studies how debt can exert discipline; dividends would have the same effect. As in this paper, Edmans studies how ownership concentration can induce monitoring, but assumes that the monitor’s dollar investment can always be increased if required and so capital structure is irrelevant. Here, her funds are limited and concentration is instead achieved using debt. This method of achieving concentration has an important advantage as it is directly under the manager’s control. Another difference is that this paper endogenizes the manager’s shortterm concerns via a termination problem. Monitoring in Diamond (1984) is similarly induced by increasing the monitor’s dollar investment rather than by capital structure. In addition, the monitor in Diamond is a creditor and motivated by downside protection. Here, the gains from monitoring are the upside potential from growth opportunities, which are only enjoyed if the monitor is a shareholder. Diamond (1991, 1993) also considers the costs and benefits of short-term debt. As in this paper, short-term debt can lead to inefficient liquidation, although not distortions in investment as there is no such decision. The benefit of short-term debt is that a high-quality borrower expects that positive information will freely appear, reducing refinancing costs. In this paper, information is costly and debt has the different objective of inducing its production. In Aghion and Bolton (1992) and Dewatripont and Tirole
4 Debt has a second informational role in Harris and Raviv: nonpayment reveals that cash flows are low. This role is also featured here and is not unique to debt—non-payment of dividends has the same effect. 5 Specifically, debt shifts control to the creditor, who is biased towards shut-down owing to his concave claim. Since the equityholder has a convex claim, she has incentives to gather information to allow the firm to continue. Here, debt has no control-shift effect compared to dividends: equityholders in a firm that has missed its dividend are already tough and wish to liquidate the firm—the essence of the investment issue.
Fig. 1. Timeline of the model.
(1994), an interim termination/continuation decision also depends on the realization of a public signal. In those models, the signal automatically appears; here, it must be generated at a cost and so the financial structure must elicit monitoring. Cohn and Rajan (2010) also feature a concentrated outside investor whose governance role is to generate a public signal, rather than engage in direct intervention like an ‘‘adversary’’. None of the above papers consider dividends as an alternative to debt. The modeling setup draws from Stein (2005), who also analyzes the tension between liquidation and long-term decisions, within the context of financial arbitrageurs contemplating long-run convergence trades. This paper builds on Stein by adding leverage and a monitoring technology, to allow both issues to be solved simultaneously. 2. The model A manager (M) seeks financing of I, dollars for a project. A single large investor (L) has funds of x, and a pool of atomistic investors has one dollar each, where 1 o x oI. In reality, L corresponds to an institutional investor such as a private equity fund or mutual fund, and the atomistic investors represent households.6 There are four periods, summarized in Fig. 1. At t ¼0, M raises x of funds from L and I x of funds from the atomistic investors. (It will become clear that any structure in which L invests less than x is weakly dominated, as her monitoring incentives are weaker.) M is restricted to issue the standard securities of debt and equity (in any combination); as I will show, this restriction is without loss of generality. As in an IPO, all equityholders pay the same price for their shares and all creditors pay the same price for their debt. The face value of debt raised is denoted F; debt matures at t ¼2 and its market value D is determined to ensure all creditors break even. M, can also promise a 6 x is the maximum that L can invest after taking on as much personal leverage as she is able to. The assumption of limited funds, even in the presence of personal leverage, is standard in the literature (see, e.g., Boot and Thakor, 1993; and Fulghieri and Lukin, 2001) and necessary in models of ownership structure. If x was unlimited, a single investor could own the entire firm, which would cure most agency problems.
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dividend at t¼2. Let P denote the total payment required at t ¼2, which is the sum of the debt repayment F and the promised dividend. I will sometimes use the term ‘‘financing structure’’ to refer to M’s joint decisions of capital structure and dividend policy. At t ¼1, with probability p the manager is ‘‘inspired’’, i.e., obtains an investment idea. Whether he is inspired is private information. An inspired manager can invest in either a Risky (R) or Safe (S) project; the project choice is non-contractible. (I will sometimes refer to choosing R rather than S as ‘‘investing’’.) An uninspired manager has no project ideas and loses money over time. At t ¼2, the firm generates unobservable cash E (also referred to as ‘‘earnings’’). If the firm is liquidated at t ¼2 it is worth V2 Z E; if it is continued until t ¼3 it is worth V3 (also referred to as ‘‘fundamental value’’). V2 is verifiable at t ¼2 if the firm is liquidated, and V3 is verifiable at t ¼3 if the firm is still in existence. The manager is assumed to be essential for the firm’s continuation, so termination of the manager is equivalent to liquidation of the firm. As in Stein (2005), equityholders capture the full surplus, so creditors break even and M’s objective function consists of private benefits, such as reputational concerns or utility from incumbency, which are increasing in both firm value and his tenure. He earns b2 if the firm is terminated and b3 in total if the firm is continued, and his outside option is zero. Appendix B shows that the model’s results also hold if M instead receives a fraction of the firm’s assets that increases in his tenure. The payoffs are given in Table 1. The parameters in Table 1 satisfy the following conditions: V U oK U oI, U
U
M
ð1Þ L
K V 4 b b ,
ð2Þ
V R 4 V S 4K S 4 I,
ð3Þ
bM 4 bL 4 0,
ð4Þ
bH 4 bM :
ð5Þ
Eq. (1) means that terminating an uninspired manager at t ¼2 increases investor returns; Eq. (2) means it also increases total surplus. Eq. (3) demonstrates that R leads to a higher V3 than S. The disadvantage of R is that it has a probability g of leading to the same low earnings as an uninspired manager at t ¼2. I will sometimes refer to a manager who chooses R but delivers E ¼ V U as ‘‘unlucky’’ Table 1 Payoffs to investment strategies. This table details earnings E, firm value V, and private benefits b under an uninspired manager, an inspired manager who chooses the safe project S, and an inspired manager who chooses the risky project R. Variable Uninspired Inspired, S Inspired, R E V2 V3 b2 b3
VU KU VU bL bM
KS KS VS bL bM
VU with probability g, KS w.p. 1g KU if E ¼ V U , KS if E ¼ K S VR bL bH
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or suffering ‘‘interim losses’’. The ‘‘investment problem’’ refers to the challenge of inducing an inspired manager to efficiently choose R, since he may prefer S to avoid being viewed as uninspired. Eq. (4) denotes that M prefers not to be terminated. The ‘‘termination problem’’ refers to the challenge of efficiently firing an uninspired manager, since he will not depart voluntarily. Eq. (5) means that M’s incentives are aligned with investors if the firm is allowed to continue until t ¼3: the same project that maximizes firm value (R) also maximizes M’s private benefits. This distinguishes the paper from models of the effort conflict, where actions that benefit investors are intrinsically costly to managers. While E is unobservable directly, the above conditions mean that promising P 4 V U reveals E to investors: only firms for which E ¼ K S will be able to make the full repayment. A required payment of P 4 V U thus has a disciplinary effect.7 At t ¼2, events proceed as follows. First, the level of E determines which claimholders are in control and have the right to choose whether to continue or liquidate the firm. Creditors have control if E o F, else shareholders. Second, to guide the liquidation decision, any investor may choose to engage in monitoring at t ¼2; the decision to monitor is unobservable. Monitoring costs the investor c and has a probability f o 1 of success; as in Diamond (1984), I assume no gains from duplicate monitoring.8 If monitoring succeeds, it generates a publicly observable, unverifiable signal that is fully informative of V3.9 Formally, the public signal is N 2 fV R ,V S ,V U ,+g, where N stands for ‘‘news’’. The signal Vi indicates that V3 ¼ V i ; + is the null signal that appears if no monitoring occurs,
7 Since the maximum possible E is KS, we restrict the analysis to P r K S and so for brevity do not include the condition P r K S in the rest of the paper. 8 We assume that the cost is non-pecuniary (e.g., effort expenditure). The model can easily be extended to allow c to be a financial cost, as in Boot and Thakor (1993) and Fulghieri and Lukin (2001). In addition, investors cannot coordinate to share the monitoring costs. This assumption is standard in any model with multiple shareholders, else shareholder structure would be irrelevant. The results continue to hold if shareholders can coordinate but at a cost. The model can be extended to allow for the possibility of duplicate monitoring; it would merely involve additional conditions to show that households will choose not to monitor. 9 The nonverifiability of the signal rules out contracts that directly reward L for producing a signal. The assumption that signals are observable but non-contractible is standard in the incomplete contracts literature (e.g., Aghion and Bolton, 1992; Dewatripont and Tirole, 1994). It is likely difficult to write into a contract what constitutes a good or bad signal, even though this will be evident ex post, since the number of possible such signals is likely to be very large. Once the signal is discovered, its nature (good or bad) is unambiguous; for example, monitoring could involve undertaking an independent analysis of a drug in progress or the quality of an existing product. Even if we allow the signal to be falsified, the monitor has no incentives to do so since, given the signal, all parties agree on the termination decision. The model can be extended to signals that are only privately observable to the monitor. To ensure the monitor does not shirk and simply claim to have found a positive signal, she could write credit protection to credibly communicate a positive signal, communicate it via trading shares (see, e.g., Edmans, 2009), or there could be a cost of communicating the signal so that she will only do so if the signal is truly positive. The analysis assumes observable signals since our focus is information acquisition incentives; the credible communication of acquired information has been studied elsewhere.
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or monitoring occurs and is unsuccessful (w.p. 1f). Third, the party in control takes the continuation/liquidation decision based on the signal N and the level of earnings E, if the latter has been revealed via P 4V U . Formally, she chooses action A : N E-fT,Cg where T (C) refers to termination (continuation). If a signal is generated, all investors agree on the optimal decision—firm value is maximized by liquidation upon N ¼ V U and continuation upon N 2 fV R ,V S g; since both debt and equity are non-decreasing in firm value, the optimal termination decision is taken regardless of who has control. When N ¼ + and so firm value is uncertain, I will show that, under the optimal financing structure, the party in control will always take the first-best decision. Thus, the identity of the party in control does not matter. This deliberately distinguishes the model from Dewatripont and Tirole ¨ (1994), Grinstein (2006), and Gumbel and White (2007) where the signal is not fully informative and so creditors may take the conservative action T even when it is inefficient, because they have a concave claim in the firm. Here, the driver of capital structure is monitoring incentives rather than control rights. In sum, if a signal is generated, it is sufficient to determine A and earnings do not matter; earnings only affect A if there is no signal. Thus, the action function is either A(N) or Að+,EÞ. The timing of events is similar to Aghion and Bolton (1992) and Dewatripont and Tirole (1994) except that in those papers, the public signal automatically appears; here, it must be generated at a cost.10 The first-best solution involves an uninspired manager always being terminated at t¼2, and an inspired manager always choosing R at t ¼1 and being continued at t ¼2. To make the financing problem interesting, I need to impose two sets of parametric restrictions. The first ensures that an investment problem exists (i.e., a manager forced to make a high interim payment will choose S) but can be cured by monitoring. It is clearer to introduce these assumptions later during the actual analysis, as the reader can more easily see their effect. These will be conditions (10), (11), and (15). The second ensures that the termination and investment problems are sufficiently severe that, if unsolved, the firm is negative-NPV—i.e., the firm is only viable if it achieves sufficiently close to first-best. These assumptions are
pV S þð1pÞK U o I,
ð6Þ
pV R þ ð1pÞV U o I:
ð7Þ
Condition (6) states that, if an inspired manager always chooses S, the firm is unprofitable, even if investors obtain the maximum liquidation value of KU if M is uninspired. Condition (7) states that, if an uninspired manager is never terminated, the firm is unprofitable, even if investors obtain the maximum terminal value of 10 Also as in these papers, we assume no bankruptcy costs in a reorganization (i.e., when creditors have control and continue the firm); if bankruptcy costs exist, they reduce the desirability of debt. Since the negative effect of bankruptcy costs on leverage has been well explored in the literature, we exclude them here.
VR if M is inspired. While conditions (10), (11), and (15) are imposed throughout the paper, (6) and (7) are relaxed in Section 2.4. The full optimization problem involves M choosing the amount of debt and equity to issue to both L and atomistic investors, the amount of dividends to promise and the level of monitoring by each investor, to maximize his private benefits subject to the participation constraint that all investors at least break even, and the incentive constraint that each investor’s monitoring decision is incentive compatible. To highlight the importance of monitoring, and the role of debt in inducing non-contractible monitoring, I commence in Section 2.1 by analyzing a variant of the model in which monitoring is impossible and derive conditions under which the firm is unviable. I assume contractible monitoring in Section 2.2 and show that the firm is viable when monitoring occurs. In Section 2.1, the optimization problem does not involve M choosing each investor’s level of monitoring nor monitoring incentive compatibility constraints; in Section 2.2, M chooses the monitoring level but there are no incentive constraints. Section 2.3 considers the core model with non-contractible monitoring and thus all constraints, and analyzes how to induce monitoring via the choice of financing structure. Section 2.4 compares total surplus under different financing structures. I use the Perfect Bayesian Equilibrium (PBE) solution concept throughout: all players take the optimal actions given their beliefs about other players’ actions, these beliefs are correct in equilibrium, and updated according to Bayes’ rule.
2.1. No monitoring If there is no monitoring technology, the action A cannot depend on the signal N, but can depend on earnings E if they are revealed through a disciplinary payment of P 4V U . Since there is no monitoring constraint in Sections 2.1 and 2.2, there is no role for debt and so I can assume that the payment P is entirely in the form of dividends without loss of generality. I first consider the case where P rV U so all firms can make the payment. Since investors never learn E, M need not worry about it and can simply choose R if inspired. I assume that
pV R þ ð1pÞV U 4 pðgK U þ ð1gÞK S Þ þ ð1pÞK U ,
ð8Þ
and so firm value is maximized under continuation at t ¼2. Since equity value equals firm value, shareholders always take the efficient termination decision that maximizes firm value (in this case, continuation at t ¼2), and so the action is renegotiation-proof.11 Since the firm is always continued, it is worth V R if M is inspired and VU otherwise. Lemma 1 (No monitoring, no discipline). Assume that no monitoring occurs. In the subgame following the announcement 11 A renegotiation-proof termination decision is one that maximizes firm value, rather than total surplus (the sum of firm value and private benefits). This is because private benefits are inalienable and so the manager cannot offer them in a renegotiation.
A. Edmans / Journal of Financial Economics 102 (2011) 81–101
of a non-disciplinary payment P r V U , the unique PBE is the following: (i) If the firm is financed, the manager chooses R if inspired. (ii) If the firm is financed, it is never liquidated at t ¼2. (iii) The firm is not financed and all payoffs are zero. Proof. Part (i) follows automatically from (5). For part (ii), investors’ beliefs are pð1gÞ that the manager has chosen R and E ¼ V U , pg that the manager has chosen R and E ¼ K S , and 1p that the manager is uninspired. From (8), the firm is continued. For part (iii), the expected gross return to investors is
pV R þ ð1pÞV U :
ð9Þ
From (7), investors make a loss, and therefore will not finance the firm to begin with. & The problem with the above structure is that an uninspired manager is never terminated, since he is not forced to reveal his low earnings at t ¼2. A possible solution is for M to promise a disciplinary payment of P 4 V U . Since an uninspired manager cannot make such a payment, his low quality is revealed even without a monitoring technology, allowing efficient liquidation. However, the disadvantage is that the high payment requirement may deter an inspired manager from choosing R since it risks yielding E ¼ V U , in which case he cannot make the payment and may be viewed as uninspired. This leads to the following lemma. Lemma 2 (No monitoring, discipline). Assume that no monitoring occurs and that the following two conditions hold: 1p pg VU þ V R oK U , 1p þ pg 1p þ pg
ð10Þ
ð1gÞbH þ gbL obM :
ð11Þ
In the subgame following the announcement of a disciplinary payment P 4 V U , the unique PBE is the following: (i) If the firm is financed, the manager chooses S if inspired. (ii) If the firm is financed, it is liquidated at t¼2 if the payment is not met, otherwise it is continued. (iii) The firm is not financed and all payoffs are zero. Proof. Let an inspired manager pursue a mixed strategy of R w.p. a and S w.p. ð1aÞ. The posterior probability that a non-paying manager is inspired is pag=ð1p þ pagÞ. Investors will terminate the firm if ½ð1pÞ=ð1p þ pagÞ V U þ½pag=ð1p þ pagÞV R oK U , which holds from (10). This proves part (ii). Given this, part (i) follows from (11). For part (iii), the expected gross return to investors is
pV S þ ð1pÞK U :
ð12Þ
From (6), investors make a loss, and therefore will not finance the firm to begin with. & The intuition is as follows. The maximum posterior probability that a non-paying manager is inspired is pg= ð1p þ pgÞ. This probability is reached if an inspired manager always chooses R, otherwise the posterior is
87
lower. Eq. (10) means that investors prefer to terminate a non-paying manager: even if the posterior probability that M is inspired is the highest possible, it is still insufficient to outweigh the gains from early liquidation if M is uninspired. Eq. (11) shows that an inspired manager myopically chooses S to avoid the risk of nonpayment, and so the firm is not viable from (6). For the remainder of the paper, I assume that (10) and (11) hold, else there is no investment problem: an inspired manager nonchalantly chooses R. Combining the results of Lemmas 1 and 2 yields the following corollary: Corollary 1. (Firm unviable without monitoring.) In the absence of a monitoring technology, the firm cannot be financed. Proof. Directly from Lemmas 1 and 2.
&
The firm cannot be financed without monitoring. If a low payment is promised, an inspired manager chooses R but an uninspired manager is never terminated. If a high payment is promised, an uninspired manager is terminated but an inspired manager chooses S. This is the tension between termination and investment, which is the focus of the paper. The model has a close parallel to the case in which E is publicly observable and so there is no need for a disciplinary payment. The high-payment case of Lemma 2 corresponds to giving M a short-term contract which allows him to be fired at t¼2. This enables investors to terminate an uninspired manager, but deters an inspired manager from choosing R. The low-payment case of Lemma 1 corresponds to giving M a long-term contract which guarantees his employment until t ¼3. This induces investment, but prevents termination if E ¼ V U . Indeed, in standard myopia models (e.g., Stein, 1988), the manager is exogenously assumed to place weight on interim earnings but the investment issue would be solved by a long-term contract. Here, such a solution is unworkable as there is also a termination issue. 2.2. Contractible monitoring I now introduce a contractible monitoring technology. While I assume that monitoring is verifiable, I continue to assume that investors cannot observe whether M is inspired or which project he selects. This highlights the fact that eliciting monitoring is sufficient both to induce optimal project selection by an inspired manager and to overcome an uninspired manager’s desire to continue— i.e., solving investors’ moral hazard problem is sufficient to solve M’s moral hazard problem. If M’s project choice and inspiration were observable, monitoring would be unnecessary as investors could just terminate a manager they know to be uninspired and instruct an inspired manager to choose R. That the key unobservable action is at the investor level distinguishes the model from Jensen and Meckling (1976), where debt is used to directly solve agency problems at the manager level. Since L has the greatest stake in the firm, she has the strongest incentive to monitor (which becomes important
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in Section 2.3 when monitoring is non-contractible), so the analysis focuses on her being the monitor. If monitoring is successful, the efficient action is given by AðV U Þ ¼ T and AðV R Þ ¼ AðV S Þ ¼ C. If monitoring is unsuccessful, there are four possible termination policies. The first is Að+Þ ¼ C, i.e., there is no disciplinary payment and the firm is continued in the absence of a signal. Since the termination decision does not depend on E, an inspired manager need not be concerned with E and so chooses R. If he is uninspired, with probability f monitoring succeeds and investors terminate the firm for KU, else the firm is continued and investors recover VU. The returns to all investors and the manager are given by
pV R þ ð1pÞðfK U þð1fÞV U Þc,
ð13Þ
pbH þ ð1pÞðfbL þ ð1fÞbM Þ:
ð14Þ U
A second option is Að+,V Þ ¼ T, i.e., at t¼ 0, M has promised a disciplinary payment of P 4V U and so, if there is no signal to guide the liquidation decision, liquidation occurs if and only if the payment is not met. Note that L does not need to monitor if the payment has been made as this reveals E ¼ K S and thus A ¼C is optimal. If the payment is missed (which reveals E ¼ V U ), monitoring occurs and the firm is terminated if N 2 fV U ,+g. Since the termination decision now depends on E, an inspired manager who chooses R risks termination if he is unlucky (w.p. g) and monitoring fails (w.p. 1f). Nevertheless, he still chooses R if ð1gð1fÞÞbH þ gð1fÞbL 4 bM ,
ð15Þ
i.e., the gain in private benefits from pursuing R outweighs the risk of termination. The key difference with (11), M’s incentive constraint without monitoring, is that he is only terminated with probability gð1fÞ rather than g—even if he is unlucky, he is continued if monitoring is successful. Put differently, monitoring means that (w.p. f) investors make the liquidation decision according to fundamental value rather than earnings. Therefore, the manager chooses the project which maximizes fundamental value rather than earnings, i.e., R. I assume that (15) holds throughout the paper, otherwise monitoring becomes irrelevant as it cannot cure myopia. In sum, assumptions (10), (11), and (15) jointly mean that M acts myopically if and only if there is no monitoring. The returns to all investors and the manager are given by ðppgð1fÞÞV R þð1p þ pgð1fÞÞK U ð1p þ pgÞc,
ð16Þ
ðppgð1fÞÞbH þ ð1p þ pgð1fÞÞbL :
ð17Þ
A third possibility is Að+Þ ¼ T. As with Að+Þ ¼ C, E is irrelevant for the termination decision so an inspired manager chooses R. However, from (8), it is never efficient to terminate a manager in the absence of a signal or earnings realization. A final possibility is Að+,V U Þ ¼ C (i.e., monitor if and only if a disciplinary payment is not met, and continue the firm if monitoring is unsuccessful), but from (10) it is never efficient to continue a lossmaking manager in the absence of a signal. Thus, neither of these termination policies are renegotiation-proof.
In sum, both Að+Þ ¼ C or Að+,V U Þ ¼ T involve renegotiation-proof termination decisions. I will call these the ‘‘non-disciplinary policy’’ and the ‘‘disciplinary policy,’’ respectively. Comparing investor payoffs under the two policies ((13) and (16)), the difference is that if monitoring fails, the disciplinary policy leads to the ‘‘Type I error’’ of inefficient termination of an inspired but unlucky manager, and the non-disciplinary policy leads to the ‘‘Type II error’’ of inefficient continuation of an uninspired manager. Note that (10) implies that (16) 4 (13), i.e., investor returns are higher under the disciplinary policy. This is intuitive: (10) means it is optimal to shut down a loss-making manager in the absence of a signal, and so Type II errors are more important than Type I errors. Thus, the disciplinary policy maximizes investor returns as it minimizes Type II errors. However, since M’s payoff is higher under the non-disciplinary policy (i.e., (14) 4(17)), either may be the first-best policy that maximizes total surplus (the sum of firm value and private benefits).12 Since monitoring is contractible, there are no incentive constraints and only participation constraints. Let wðÞ be the payoff received by L for a given firm value; I later show how to implement the payoff function wðÞ by the choice of capital structure. The following lemmas summarize the two potential first-best termination policies. Lemma 3 (Monitoring, no discipline). Assume that L always monitors. In the subgame following the announcement of a non-disciplinary payment P r V U , the unique PBE is the following: (i) If the firm is financed, the manager chooses R if inspired. (ii) If the firm is financed, it is liquidated at t¼2 if N ¼ V U , otherwise it is continued. (iii) If the firm is financed, the expected gross returns to L and all households are, respectively:
pwðV R Þ þð1pÞðfwðK U Þ þ ð1fÞwðV U ÞÞc,
ð18Þ
pðV R wðV R ÞÞ þ ð1pÞðfðK U wðK U ÞÞ þ ð1fÞðV U wðV U ÞÞÞ: ð19Þ If (18) Zx and (19) Z Ix, the firm is financed and the manager’s payoff is
pbH þ ð1pÞðfbL þ ð1fÞbM Þ,
ð20Þ
else the firm is not financed and all payoffs are zero. Proof. Part (i) is as in Lemma 1. For part (ii), the optimal A is automatic for Na+. For N ¼ +, A¼C from (8). Part (iii) follows from simple calculations. & 12 The ‘‘efficient termination decision’’ and the ‘‘first-best termination policy’’ are two separate concepts. The former is a t¼ 2 concept: after any payment, if promised, has been made or not made, and any signal has been realized, is it optimal to terminate or continue the firm? The latter is a t¼ 0 concept that also studies whether it is optimal to demand a payment in the first place (and thus make the termination decision depend on it), i.e., compares returns across the cases where a payment is promised and a payment is not promised. An additional difference is the first-best termination policy maximizes total surplus, whereas the efficient termination decision maximizes investor returns alone since it is concerned with renegotiation-proofness (see also footnote 11).
A. Edmans / Journal of Financial Economics 102 (2011) 81–101
Lemma 4 (Monitoring, discipline). Consider the subgame following the announcement of a disciplinary payment P 4 V U and assume that L monitors if the payment is not met. The unique PBE is the following: (i) If the firm is financed, the manager chooses R if inspired. (ii) If the firm is financed, it is liquidated at t ¼2 if both the payment is not met and N 2 fV U ,+g, otherwise it is continued. (iii) If the firm is financed, the expected gross returns to L and all households are, respectively: ðppgð1fÞÞwðV R Þ þ ð1p þ pgð1fÞÞwðK U Þð1p þ pgÞc, ð21Þ ðppgð1fÞÞðV R wðV R ÞÞ þð1p þ pgð1fÞÞðK U wðK U ÞÞ: ð22Þ If (21) Z x and (22) Z Ix, the firm is financed and the manager’s payoff is ðppgð1fÞÞbH þð1p þ pgð1fÞÞbL ,
ð23Þ
else the firm is not financed and all payoffs are zero. Proof. Part (i) is as in Lemma 2. For part (ii), the optimal A is automatic for Na+. For N ¼ +, A¼T from (10). Part (iii) follows from simple calculations. & 2.3. Non-contractible monitoring I now move to the core case of non-contractible monitoring, which requires us to impose the monitoring constraints. The previous two subsections have shown that the firm is viable only if monitoring occurs, so I focus on how to induce voluntary monitoring by L. I consider the two potential first-best termination policies in turn. The non-disciplinary policy Að+Þ ¼ C corresponds to P r V U , in which case L’s incentive constraint is
fð1pÞðwðK U ÞwðV U ÞÞ Z c:
ð24Þ
Since the default decision is continuation, a signal is only valuable if it leads to termination, i.e., delivers N ¼ V U . This occurs if the manager is uninspired (w.p. ð1pÞ) and monitoring is successful (w.p. f). Efficient termination augments L’s payoff by wðK U ÞwðV U Þ. The disciplinary policy Að+,V U Þ ¼ T corresponds to P 4 V U , in which case L monitors at t ¼2 if and only if the payment is missed. The incentive constraint is now
f
pg 1p þ pg
ðwðV R ÞwðK U ÞÞ Zc:
ð25Þ
The posterior probability that a non-paying manager is inspired is pg=ð1p þ pgÞ, in which case successful monitoring leads to efficient continuation and so L’s payoff rises by wðV R ÞwðK U Þ. In either case, L’s payoff wðÞ must be sufficiently sensitive for monitoring to be incentive compatible. Regardless of which termination policy we wish to implement, wðÞ can only take on two values and so it is sufficient to consider linear schemes that satisfy limited liability. Such a scheme has the general form wðzÞ ¼ maxðgz þ h,0Þ. Since a positive h increases wðK U Þ, wðV U Þ,
89
and wðV R Þ equally, it has no effect on monitoring incentives and so I can consider only non-positive h. The payoff function wðzÞ ¼ maxðgz þh,0Þ for hr 0 can be implemented by issuing debt with face value h=g and giving L equity. Without loss of generality, I can thus restrict the analysis to M issuing only the standard securities of debt and equity, and L holding equity. L thus has an equity stake of x=ðIDÞ. In the presence of multiple claims (debt and equity), it is not automatic that the party in control will take the efficient termination decision when N ¼ +, so I must verify that the action is efficient (so that there is no scope for renegotiation) in addition to L’s monitoring constraint being satisfied. The non-disciplinary policy Að+Þ ¼ C involves P rV U and thus can be implemented with debt of F r V U ; since the payment is non-disciplinary, there is no role for dividends. The disciplinary policy Að+,V U Þ ¼ T can be implemented either with risky debt of F 4 K U or a combination of debt and dividends that yields a total required payment P 4V U . This latter includes the case of V U o F r K U : while debt of F 4V U is risky to the manager since he cannot repay it if he delivers E ¼ V U , it is not risky to creditors if F rK U , since they can recover KU in a liquidation. I thus use the terms ‘‘riskless’’ and ‘‘risky’’ debt to denote the cases of F r K U and F 4 K U , and ‘‘repayable’’ and ‘‘nonrepayable’’ debt to denote the cases of F r V U and F 4 V U . I first consider risky debt of F 4K U to implement the disciplinary policy. I then study repayable debt of F r V U to implement the non-disciplinary policy. Finally, I analyze riskless debt and dividends where P 4 V U and F r K U to implement the disciplinary policy.
2.3.1. Risky debt With F 4K U , creditors have control if E ¼ V U . If N ¼ +, they liquidate the firm if 1p pg VU þ F o KU: 1p þ pg 1p þ pg
ð26Þ
This holds as a direct consequence of (10); (10) also means that liquidation is efficient.13 I now consider whether L will gather information. With risky debt and L owning equity, wðV R Þ ¼ ½x=ðIDÞ ðV R FÞ and wðK U Þ ¼ 0. Indeed, from the incentive constraint (25), L’s monitoring incentives are maximized when wðK U Þ is at its lowest possible value of zero; this is achieved by having risky debt of at least KU. Then, the incentive constraint (25) becomes
f
pg x ðV R FÞ Z c: 1p þ pg ID
ð27Þ
13 Eq. (10) also means that, even if we introduce new players into the model (potential new investors at t¼ 2), the manager cannot continue by raising external funds—since the firm is now negativeNPV, no investor will finance it. An outside investor also has no incentive to pay c to decide whether to invest, because the signal is public and so a non-investor can never profit from monitoring. With private signals, the results of the model still go through as debt allows new investors to acquire concentrated stakes if they receive a good signal, increasing their profits and thus monitoring incentives.
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The left-hand side (LHS) of (27) contains the term x=ðIDÞ. I denote the positive effect of F on x=ðIDÞ and thus monitoring incentives as the concentration effect. (I will shortly derive conditions on F to ensure that (27) is satisfied.) With incentive-compatible monitoring and efficient termination under a disciplinary payment, the equilibrium is similar to Lemma 4 and given as follows: Lemma 5 (Risky debt, no dividends). Assume that L’s monitoring constraint (27) holds. In the subgame in which there is risky debt of F 4K U and no dividends, the following is a PBE: (i) If the firm is financed, the manager chooses R if inspired. (ii) If the firm is financed and the payment is met, L does not monitor at t ¼2. If the payment is not met, L monitors. If N 2 fV R ,V S g, the firm is continued, otherwise it is liquidated. If the payment is not met and L does not monitor, the firm is liquidated. (iii) The expected gross returns to L and all other shareholders are, respectively: x ½ðppgð1fÞÞðV R FÞð1p þ pgÞc, ID
ð28Þ
IDx ½ðppgð1fÞÞðV R FÞ: ID
ð29Þ
If (28) Z x, the firm is financed and the manager’s payoff is ðppgð1fÞÞbH þð1p þ pgð1fÞÞbL ,
ð30Þ
else the firm is not financed and all payoffs are zero. (iv) If the firm is financed, the market value of debt is given by ð31Þ D ¼ ðppgð1fÞÞF þ ð1p þ pgð1fÞÞK U :
Proof. Parts (i) and (ii) are as in Lemma 4. Parts (iii) and (iv) follow from simple calculations. Since (28) Zx (L’s participation constraint being satisfied) implies (29) 4 IDx (households’ participation constraint being satisfied), (28) Zx is sufficient for all shareholders’ participation constraints to be satisfied and so for the firm to be financed. & The lower bound to F is the minimum debt level that allows L’s monitoring constraint (27) to be satisfied. Substituting the market value of debt (31) into (27) defines the lower bound as F¼
cð1p þ pgÞðIð1p þ pgð1fÞÞK U ÞfpgxV R : cð1p þ pgÞðppgð1fÞÞfpgx
ð32Þ
The upper bound to F is given by substituting (31) into D ¼ Ix, i.e., F¼
Ixð1p þ pgð1fÞÞK U : ppgð1fÞ
ð33Þ
Therefore, if
f
pg 1p þ pg
ðV R F Þ Zc,
ð34Þ
then monitoring can be induced under risky debt. If (34) is violated, the monitoring technology is sufficiently ineffective
that, even if L holds the firm’s entire equity, she still does not monitor. The power of risky debt comes from two effects. The disciplinary effect forces the firm to pay out cash. Since uninspired managers cannot make the payment, they are efficiently terminated. However, the disciplinary effect has the potential disadvantage of deterring inspired managers from choosing R. This is where the second role of risky debt comes in: the concentration effect. Leverage increases L’s equity stake x=ðIDÞ and thus her monitoring incentives in (27). Note that there is a countervailing effect: creditors gain FK U from the efficient continuation of an unlucky manager. Thus, if debt is riskier, they profit more and so shareholders’ gains V R F are reduced—an example of debt overhang (Myers, 1977). Combining the two effects, a rise in F reduces the total gains to all shareholders from efficient continuation, but gives L a greater proportion of these equity gains. The overall effect of increasing F on L’s incentives is given by differentiating the left-hand side of her monitoring constraint (27) to yield
f
pg 1p þ pg
x
ðV R FÞðppgð1fÞÞðIDÞ ðIDÞ2
:
ð35Þ
If the firm is viable, we have (29) 4 IDx (households’ participation constraint is satisfied) which implies (35) 4 0, i.e., the concentration effect of debt outweighs the debt overhang effect. The firm is viable under risky debt only if the net benefits of debt are positive, as is intuitive. 2.3.2. Repayable debt and no dividends With repayable debt of D ¼ F r V U , shareholders always have control. Since repayable debt simply reduces their payoff in all cases by F, it has no effect on their termination decision and the efficient action is always taken. I first assume no dividends, so P ¼ F r V U and all firms can make the payment. This implements the nondisciplinary policy Að+Þ ¼ C. We have wðK U Þ ¼ ðx=ðIFÞÞ ðK U FÞ and wðV U Þ ¼ ðx=ðIFÞÞðV U FÞ, so the monitoring constraint (24) becomes
fð1pÞ
x ðK U V U Þ Z c: IF
ð36Þ
If (36) is satisfied, then L monitors and the firm is liquidated if and only if N ¼ V U . Hence, repayable debt achieves both (occasional) liquidation and investment. The equilibrium is the following analog of Lemma 3: Lemma 6 (Repayable debt, no dividends). Assume that L’s monitoring constraint (36) holds. In the subgame in which there is repayable debt of F rV U and no dividends, the unique PBE is the following: (i) If the firm is financed, the manager chooses R if inspired. (ii) If the firm is financed, L monitors at t ¼2. If N ¼ V U , the firm is liquidated, otherwise it is continued. If L does not monitor, the firm is continued. (iii) If the firm is financed, the expected gross returns to L and all other shareholders are, respectively: x ½pV R þ ð1pÞðfK U þð1fÞV U ÞFc, IF
ð37Þ
A. Edmans / Journal of Financial Economics 102 (2011) 81–101
IFx ½pV R þð1pÞðfK U þ ð1fÞV U ÞF, IF
ð38Þ
else the firm is not financed and all payoffs are zero. If (37) Z x, the firm is financed and the manager’s payoff is
pbH þ ð1pÞðfbL þð1fÞbM Þ:
ð39Þ
Proof. Parts (i) and (ii) are as in Lemma 3. Part (iii) follows from simple calculations. Since (37) Zx (L’s participation constraint being satisfied) implies (38) 4 IDx (households’ participation constraint being satisfied), (37) Zx is sufficient for all shareholders’ participation constraints to be satisfied and so for the firm to be financed. & It may not be possible to satisfy L’s monitoring constraint (36) with repayable debt. L’s monitoring incentives are maximized when F is at its highest possible repayable value of VU. Indeed, from the general incentive constraint (24), L’s monitoring incentives are maximized when wðV U Þ is at its lowest possible value of zero; since L holds equity, this is achieved by having debt of VU. Thus, if
fð1pÞ
x ðK U V U Þ o c, IV U
addresses the two above drawbacks. If F r V U (i.e., the discipline comes from dividends), shareholders have control if E ¼ V U and always take the efficient termination decision as in Section 2.3.2. If F 4 V U , creditors have control if E ¼ K S and liquidate if (26) holds, which is efficient as in Section 2.3.1. We have wðV R Þ ¼ ðx=ðIFÞÞ ðV R FÞ and wðK U Þ ¼ ðx=ðIFÞÞðK U FÞ. L’s incentive constraint (25) becomes
f
2.3.3. Riskless debt and dividends The two weaknesses of repayable debt can be addressed by increasing P above VU in one of two ways: either increasing F to between V U and KU so that it becomes nonrepayable (but stays riskless), or combining it with a dividend promise exceeding V U F, so that P 4 V U . Either change leads to a disciplinary effect and
pg x ðV R K U Þ Zc: 1p þ pg IF
ð41Þ
Lemma 7 (Riskless debt, dividends). Assume that L’s monitoring constraint (41) is satisfied. In the subgame in which there is riskless debt of F r K U and dividends so that P 4K U , the strategy profile in Lemma 5 is a PBE. If L’s monitoring constraint (41) is satisfied, riskless debt and dividends have the same effect as risky debt. However, it may not be possible to satisfy (41) with riskless debt. L’s monitoring incentives are maximized when F is at its highest possible riskless value of KU. Thus, if
ð40Þ
then L will not monitor under repayable debt. The equilibrium is as in the no-monitoring, low-payment case (Lemma 1); the firm is unviable since an uninspired manager is never terminated. Eq. (40) is likely to be satisfied when I is large compared to x (L’s funds fall significantly short of the total needed to finance the firm) and VU is small (repayable debt capacity is low). Repayable debt has a concentration effect, but no disciplinary effect and thus suffers two drawbacks. First, in the absence of discipline, the default decision is to continue the firm, and so the gains from monitoring are the savings from efficient liquidation, K U V U . In contrast, the disciplinary effect of risky debt changes the default decision to liquidation. Therefore, the incentive to monitor depends on the gains from continuation, V R F. This may be significantly larger than K U V U , particularly in growth firms where VR is high. Thus, L’s incentive constraint (36) may be violated. Second, even if the incentive constraint can be satisfied (i.e., (40) does not hold), L monitors excessively. Monitoring is only worthwhile if E ¼ V U , because if E ¼ K S , L automatically knows that M is inspired. Since all firms can repay the debt, L is unable to learn E and must pay the monitoring cost in all states. Thus, L’s participation constraint (37) Zx may be violated. The disciplinary effect of risky debt reveals E without cost: if the firm meets its debt repayment, L knows that E ¼ K S and so does not need to monitor. This echoes Townsend (1979), where verification only occurs in bankruptcy.
91
f
pg x ðV R K U Þ oc, 1p þ pg IK U
ð42Þ
then insufficient concentration is achieved under riskless debt. The equilibrium is as in the no-monitoring, highpayment case (Lemma 2), and the firm is unviable since an inspired manager chooses S. Using the results of Lemmas 5–7 leads to Proposition 1. Proposition 1. Assume that (34), (40), and (42) hold (monitoring is induced under risky debt, but not repayable debt nor riskless debt and dividends), and that (28) 4 x (L’s participation constraint is satisfied under risky debt). The firm cannot be financed with pure equity or riskless debt, but can be financed by risky debt. Proof. See Lemmas 5–7. Appendix A proves that the set of parameters that satisfies these conditions is nonempty. & If the conditions in Proposition 1 are satisfied, both effects of risky debt are necessary for the firm to be viable. Like debt, dividends also impose discipline: indeed, in a number of theories of debt (e.g., Jensen, 1986; Stulz, 1990; Zwiebel, 1996), the only purpose of debt is to force payout of cash and so dividends are a substitute. Similarly, in the dividend model of Myers (2000), the manager must pay out dividends to prevent diversion and is terminated if he misses a payment; debt would have the same effect. Here, allowing liquidation is not the only objective. Dividends are not a satisfactory substitute for risky debt because they do not achieve sufficient concentration, and thus have the side-effect of deterring investment. ¨ Gumbel and White (2007) were the first to note that debt increases shareholders’ incentives to monitor because it shifts control to creditors and thus changes the default decision to liquidation. In their setting, there is no concentration effect because a shareholder has unlimited funds, and only the disciplinary effect matters. Therefore, the optimal level of debt is borderline nonrepayable: F is
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Table 2 Implementation of equilibria. This table illustrates how the four equilibria defined in Lemmas 1–4 can be implemented via the choice of capital structure and dividend policy. Equilibrium
Implementation
No monitoring, no discipline (Lemma 1) No monitoring, discipline (Lemma 2) Monitoring, no discipline (Lemma 3) Monitoring, discipline (Lemma 4)
No dividends, no debt Dividend exceeding VU, no debt Repayable debt F r V U , no dividends Risky debt F 4 K U , no dividends
just above VU, i.e., just sufficient to shift control to creditors. Here, the concentration effect is also important, and so the optimal debt level is strictly nonrepayable.
2.4. Comparison of financing structures Thus far, I have assumed that both the termination and investment problems need to be simultaneously solved for the firm to be viable (assumptions (6) and (7)), and so monitoring is crucial. Combined with the conditions in Proposition 1, only risky debt achieves sufficient concentration to induce monitoring. However, in other settings, one of the agency problems may be relatively unimportant, and so it may be possible to finance the firm even if it is not solved. In such a case, other financing structures become feasible and may dominate the levered firm. This subsection relaxes assumptions (6) and (7), so that the non-monitoring equilibria of Lemmas 1 and 2 may become viable, and condition (40) so that monitoring may be feasible under repayable debt, allowing the equilibrium of Lemma 3 to hold.14 The four equilibria in Lemmas 1–4 can be implemented by the capital structures given in Table 2. From Lemmas 1–4, total surplus under each structure is given by15 Unlevered, No dividend ðNODIVÞ: pðV R þ bH Þ þ ð1pÞðV U þ bM Þ,
ð43Þ Unlevered, Dividend ðDIVÞ: pðV S þ bM Þ þ ð1pÞðK U þ bL Þ, ð44Þ Repayable debt ðREPAYABLEÞ: pðV R þ bH Þ þð1pÞðfðK U þbL Þ þ ð1fÞðV U þ bM ÞÞc,
ð45Þ
Risky debt ðRISKYÞ: ðppgð1fÞÞðV R þ bH Þ þð1p þ pgð1fÞÞðK U þ bL Þð1p þ pgÞc:
ð46Þ
14 I do not separately consider the case of riskless debt plus a dividend because, if monitoring is incentive compatible, it leads to the same outcome as risky debt. 15 I compare total surplus since either investor returns or private benefits may be relevant for determining which structure is observed empirically. If only one structure generates sufficient investor returns to allow investors to break even, that structure will be chosen; if more than one structure achieves break-even, the manager will choose the structure that maximizes his private benefits.
The relative surplus depends on a number of terms. The term ðK U V U Þ reflects the magnitude of the termination issue: if it is high, there are significant savings from terminating an uninspired manager. It will be high if the firm has tangible assets that can be eroded by inefficient continuation, for example, free cash that could be wasted, or non-core assets which would decline in value if not sold. If the firm has predominantly intangible assets, liquidation value is low even with early termination, and so there are few gains from efficient liquidation. The term ðV R V S Þ reflects the magnitude of the investment issue: if it is high (e.g., the firm has significant growth opportunities), there is significant value creation from inducing an inspired manager to take the risky project. The variable p reflects the manager’s quality. If it is low, the manager is likely uninspired and so termination becomes important. The ratio of f to c reflects the effectiveness of monitoring. The term ðbM bL Þ reflects the private benefits lost from early termination, and ðbH bM Þ measures the manager’s intrinsic incentives to choose R over S. As previously established, if both termination and investment are important (ðK U V U Þ and ðV R V S Þ are high), RISKY maximizes investor returns and may indeed be the only viable financing structure. This is likely the case in middle-aged firms. Such firms have both growth opportunities and tangible assets. The model can thus justify risky debt in public middle-aged firms, and also in LBOs. Concerning the latter, Jensen (1989) highlights that one advantage of leverage is that it forces ‘‘managers to disgorge cash rather than spend it on empire-building projects’’. However, if only the disciplinary effect is important, then dividends would be equally effective, borderline nonrepayable debt would be optimal, and there would be no role for shareholder monitoring so ownership concentration would be unimportant. Here, the concentration effect is also important and thus debt is not a substitute for dividends, strictly nonrepayable debt is efficient, and large shareholders actively monitor. If high leverage coincides with dispersed ownership, there is no monitoring and so the requirement to repay debt will induce myopia.16 Indeed, Cotter and Peck (2001) find that concentrated private equity investors engage in active monitoring, and LBOs perform more strongly if
16 The prediction that high leverage coincides with concentrated ¨ ownership is also generated by Gumbel and White (2007), although for reasons unrelated to myopia.
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ownership is concentrated. Denis (1994) compares the recapitalization of Kroger with the LBO of Safeway. In both cases, the debt-to-value ratio jumped to over 90%, but ownership remained dispersed at the former whereas Kohlberg Kravis Roberts obtained a concentrated stake in the latter. Both firms generated cash due to the disciplinary effect of debt, but Kroger achieved this primarily by cutting capital expenditures whereas Safeway sold noncore assets. Denis does not study the quality of investment (which is typically hard to measure); if some of the projects scrapped at Kroger were positive-NPV, this result is consistent with the model’s predictions that debt plus shareholder monitoring imposes discipline without inducing myopia. While LBOs in the 1980s were in mature firms in oldeconomy industries and predominantly undertaken to ¨ curb inefficient investment, Kaplan and Stromberg (2009) show that, from the 1990s, buyouts have predominantly been in middle-aged firms in growing industries such as IT/media/telecoms, financial services, and healthcare. Such LBOs aim to preserve growth opportunities in addition to scrapping bad projects. Indeed, if reducing waste is the only goal, it may be more effectively achieved by asking the manager to pay high dividends, which would save on the transaction costs of an LBO. However, the former might deter efficient investment. Kaplan (1989) finds that investment in general declines after an LBO but value increases, which suggests that it is inefficient projects that are being cut. Lerner, Sorensen, and ¨ Stromberg (2011) find that innovation as measured by patenting activity does not fall and patent quality as measured by citations rises, which implies that efficient investment is not harmed. Cornelli and Karakas (2010) find that LBOs both improve performance and reduce CEO turnover, suggesting that they allow the manager to take a longer-term perspective. Investment, but not termination, is an important issue in two main types of firms. First, a start-up has high growth opportunities ðV R V S Þ, but the savings from efficient termination ðK U V U Þ are low because it has little cash for an uninspired manager to waste, and few tangible assets that can be recovered even if liquidation comes early. Second, if the manager is talented (p is high), it is unlikely that termination is optimal. From (43)–(46), NODIV and REPAYABLE lead to the greatest investor returns. When investment is important, it is critical to achieve V R with the highest probability. These structures achieve this because they never terminate an inspired manager that pursues R, even if he becomes unlucky (i.e., they minimize Type I errors). The disadvantage is that they do not terminate an uninspired manager with certainty, but Type II errors are unimportant if the termination issue is minor. Indeed, start-ups are typically unlevered and pay few dividends. I now compare NODIV and REPAYABLE. Comparing investor returns under both structures ((43) and (45)), investor returns are higher under REPAYABLE if c o ð1pÞfðK U V U þ bL bM Þ:
ð47Þ
For REPAYABLE to be feasible, L’s monitoring constraint (36) must be satisfied. Since F o Ix, (36) implies
93
c o ð1pÞfðK U V U Þ. Therefore, if the monitoring technology is sufficiently effective for repayable debt to be feasible, it always increases investor returns. However, M’s payoff is lower under REPAYABLE as he is sometimes terminated, so either financing structure may maximize total surplus. In contrast, if (36) is violated, there is no monitoring under repayable debt, so it leads to the same outcome as the unlevered firm with no dividends. Indeed, NODIV is a special case of REPAYABLE where F ¼0. The final case is where termination is important, but investment is less so. This is likely the case in a mature firm with few growth opportunities and significant free cash flow, or if managerial quality is low. In such a firm, DIV and RISKY achieve the highest investor payoffs, because they terminate an uninspired manager with certainty. Comparing investor returns under both structures ((44) and (46)), they are higher under dividends than debt if ð1p þ pgÞc 4 pðV R V S þ bH bM Þ pgð1fÞðV R K U þ bH bL Þ:
ð48Þ
For the risky structure to be feasible, L’s monitoring constraint (27) must be satisfied. This condition is consistent with ð1p þ pgÞc 4 pðV R V S Þpgð1fÞðV R K U Þ, i.e., investor returns being higher under DIV. Thus, even though M’s payoff is lower (from (15)), total surplus may be higher. Previously I showed that, if REPAYABLE is feasible (i.e., (36) is satisfied), investor returns are always higher than under NODIV. Here, even if RISKY is feasible (i.e., L’s monitoring constraint (27) is satisfied), investor returns can still be inferior to DIV. The intuition is as follows. If g is sufficiently high, investors would like to dissuade M from pursuing R if inspired, because it runs the risk of liquidation if monitoring is unsuccessful. If VR is low (investment is unimportant), this disadvantage is not outweighed by the upside of R. L can dissuade M from pursuing R by committing not to monitor if earnings are low. However, the decision to monitor only takes place once low earnings have been realized, and so does not depend on g (see the monitoring constraint (27)): g only affects the possibility that low earnings are realized in the first place. Thus, even if g is high (so that, ex ante at t ¼1, L wishes an inspired manager to choose S), she may still monitor ex post at t¼2 once losses have occurred. Since M expects to be monitored, he selects R. If the disciplinary payout at t ¼2 is via dividends rather than debt, the concentration effect is avoided and L can commit not to monitor.
2.5. Discussion and empirical implications The NODIV and REPAYABLE structures considered above involve little payout, DIV involves a high payout in the form of dividends, and RISKY involves a high payout in the form of debt. Thus, while most existing research focuses on the factors affecting total debt, the above analysis suggests that total debt should be decomposed into two components: the level of total payout P (debt plus dividends) and the composition of a given level of
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total payout between debt and dividends, F=P. We have Debt Debt ¼ Total payout , |ffl{zffl} |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} Total payout |fflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflffl} F P F=P
where Total payout ¼ Debt þ Dividends: In turn, the two components of debt depend on the importance of the disciplinary and concentration effects, and thus the two agency problems. The severity of the termination issue determines the importance of the disciplinary effect, and thus the optimal level of total payout. For firms in which early termination is unlikely to be optimal (e.g., start-ups), there is no need to discipline the manager—requiring a payment would merely induce myopia. Therefore, both debt and dividends should be low, as is the case empirically. The severity of the investment issue determines the importance of the concentration effect, and thus the optimal composition of a given level of total payout. If the termination issue is important and an interim payout is required, it should be in the form of debt rather than dividends if long-run investment is critical. This has both cross-sectional and time-series implications. With regards to the cross-section, firms with more growth opportunities should feature debt rather than dividends. The positive association between growth opportunities and debt appears to contradict existing theory (Myers, 1977) and evidence (Rajan and Zingales, 1995). Those papers argue that debt is detrimental to growth, and so a growing firm would prefer to be unlevered rather than levered. However, if the termination issue is important, then being unlevered is not an option. The appropriate comparison is debt versus other forms of payout that would achieve termination; debt is less detrimental to growth than these other solutions. While Rajan and Zingales show that growth firms use less debt, the model predicts that this relationship is overturned once total payout P is controlled for, or equivalently when studying F=P instead of F. The time-series implication is that changes in the relative severity of the two agency problems within a firm should drive changes in capital structure and dividend policy. For a start-up, inefficient continuation is a minor issue and so total payout should be zero. As it matures, payout is necessary to address the termination issue; the model predicts that firms should start issuing debt before they commence paying dividends. In addition to the determinants of debt, the model also makes predictions on its effects. Compared to the counterfactual of paying out the equivalent amount of dividends, debt increases the level of investment, by changing it from short-term to long-term projects. This contrasts the standard intuition that debt reduces investment—as explained above, if the termination issue is important, debt should be compared to dividends rather than the case of no debt. I finally discuss whether other securities can play the role of debt in the model. Preferred equity also has a disciplinary effect since preferred shareholders are promised a dividend, and a concentration effect since it does
not dilute ordinary shareholders. Thus, the model can also be applied as a theory of preferred equity. Heinkel and Zechner (1990) is the only other theory of preferred equity of which I am aware,17 which is based on the flexibility afforded by the ability to defer preferred dividends, rather than the concentration and disciplinary effects. In contrast, repurchases are not a substitute for debt. The manager could promise to repurchase at least VU dollars of shares at t ¼2, leading to a disciplinary effect. However, repurchases do not generate the concentration effect when it is needed. The manager is able to repurchase shares if E ¼ K S , which concentrates L’s stake, but this is of little use since monitoring is unnecessary in this state. In contrast, if E ¼ V U , the manager cannot execute the full repurchase. Thus, full concentration is not achieved, precisely when monitoring is necessary.
3. Heterogeneous managers 3.1. Analysis This section extends the model to a setting of heterogeneous managers and multiple large investors. There now exist two manager types. There are n good managers (type G) who have a probability pG of becoming inspired, and a continuum of bad managers (type B) who have a probability pB of becoming inspired, where pB o p o pG . The manager’s type is private information. In addition, there are n large investors.18 I now allow bankruptcy to be costly to the manager. In the core model, a manager who is unable to pay debt is just as likely to be fired as one who misses a dividend. In reality, firing is likelier in a bankruptcy because the ‘‘default’’ decision is liquidation; if a dividend is missed, the firm remains solvent and it requires an active decision by shareholders to close the firm. For example, Zwiebel (1996) assumes that managers are efficiently replaced in bankruptcy with certainty, but shareholders face a cost of firing a manager in solvency due to entrenchment. Myers (2000) assumes that shareholders face costs of collective action in liquidating a solvent firm. I model such costs by specifying that, if creditors have control and liquidation is optimal for them, it occurs with certainty, but if shareholders have control and liquidation is optimal for them, it occurs only with probability l o1. Section 2 assumed that l ¼ 1, i.e., the disciplinary effect of dividends and debt are the same; with l o 1, the results of Section 2
17 Other debt theories based on tax advantages or contingent control cannot be applied to preferred equity, since it does not have these features. 18 This assumption simplifies the analysis as it means that each G can be financed by one L, but it is not critical. If the number of large investors is nL o nG , some good managers can only obtain financing from atomistic investors, which leads to a very similar separating equilibrium as what follows but with nG effectively being nL. If nG 4 nL , some managers will be held by multiple large investors, which has no effect as a single large investor will monitor them anyway (given pG 4 p and (27)). The analysis is thus the same as if nG ¼ nL .
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would be stronger—risky debt would be even more preferred as it has a greater disciplinary effect.19,20 I continue to relax (6) and (7) and instead make the following assumptions:
N 2 fV R ,V S g, the firm is continued, otherwise it is liquidated. If L does not monitor, the firm is liquidated. The gross returns to investors and the manager are given by
pB V S þð1pB ÞðlK U þð1lÞV U Þ ¼ I,
ð49Þ
ðpG pG gð1fÞÞV R þ ð1pG þ pG gð1fÞÞK U
pB V R þ ð1pB ÞV U oI,
ð50Þ
1pG pG g VU þ V R o KU: 1pG þ pG g 1pG þ pG g
ð51Þ
ð1pG þ pG gÞc,
Assumption (49) states that a firm run by a bad manager breaks even, if M pursues S if inspired and is fired with probability l if uninspired. Thus, an unlevered firm which requires dividends of VU is borderline viable. If the lefthand side was less than I, managers known to be bad would never be funded and so a separating equilibrium cannot exist. In reality, the pricing of physical capital will adjust so that bad managers will generate zero NPV; for example, if bad managers were unable to raise financing, demand for physical capital would drop, causing its price I to fall. Assumption (50) means that, if a bad manager runs an unlevered firm and is never fired, the firm is unviable. By (51), even if a good manager can signal his quality and all good managers who become inspired choose R, investors prefer to terminate a loss-making manager if N ¼ +.21 If (51) does not hold, signaling high quality would automatically solve myopia: a good manager is not fired if E ¼ V U , and so he can choose R if he becomes inspired. Proposition 2 gives conditions under which a separating equilibrium is feasible. Proposition 2. Assume that the following conditions hold: ðpG pG gð1fÞÞbH þ ð1pG þ pG gð1fÞÞbL 4 pG bM þ ð1pG ÞðlbL þ ð1lÞbM Þ,
ð52Þ
ðpB pB gð1fÞÞbH þ ð1pB þ pB gð1fÞÞbL o pB bM þð1pB ÞðlbL þ ð1lÞbM Þ:
ð53Þ
A separating equilibrium is sustainable in which:
(i) Good managers are financed with D of risky debt, x of equity from L, and IDx of equity from atomistic investors. If the manager becomes inspired, he chooses R. If the payment is not met, L monitors at t ¼2. If 19 Dewatripont and Tirole (1994) identify a similar reason why debt imposes greater discipline than dividends. Under certain parameter values, equityholders will not fire the manager if he fails to pay dividends as they have a convex claim; therefore, it is necessary to shift control to the creditor. Here, as in Myers (2000), equityholders do wish to fire the manager upon non-payment, which is the essence of the myopia issue. 20 All of the results in this section continue to hold with l ¼ 1 if we instead assume that M suffers an additional reputational loss of y from his firm being bankrupt. We only require that M wishes to avoid bankruptcy, either because firing is more common (l o 1) or more painful (y 4 0). 21 If creditors have control, they will terminate if ðð1pG Þ= ð1pG þ pG gÞÞV U þ ðpG g=ð1pG þ pG gÞÞF o K U , which holds from F r V R and (51).
H
ð54Þ L
ðpG pG gð1fÞÞb þ ð1pG þ pG gð1fÞÞb :
ð55Þ
(ii) Bad managers are financed with equity from atomistic investors and promise a dividend exceeding VU. If the manager becomes inspired, he chooses S. No monitoring occurs at t ¼2. If the dividend payment is met, the firm is continued, otherwise it is liquidated with probability l. The net returns to each atomistic investor are zero and M’s payoff is given by
pB bM þ ð1pB ÞðlbL þð1lÞbM Þ:
ð56Þ
(iii) Investors have the off-equilibrium path belief that a manager who establishes any other structure is bad.
Since pG 4 pB , conditions (52) and (53) can simultaneously be satisfied. The first (second) condition ensures that G ðBÞ does not deviate. L will monitor at t ¼2 if
f
pG g x ðV R FÞ Zc, 1pG þ pG g ID
ð57Þ
which determines the lower bound on F. From pG 4 p and (34) (which guarantees that L monitors under risky debt in the single-firm model), (57) can always be satisfied. In the analysis of Section 2, the disciplinary and concentration effects allowed the firm to be viable under risky debt. Here, the same two effects allow a separating equilibrium to be viable: the disciplinary effect means that debt is a credible signal of managerial quality, and the concentration effect renders it a desirable signal which good managers are willing to emit. First, l o1 means that an uninspired manager is only occasionally fired from an unlevered firm but is always fired from a levered firm. Debt therefore imposes stronger discipline than dividends. As in Ross (1977), this renders it particularly costly to bad managers, as they are more likely to be uninspired, and so taking on leverage can credibly signal managerial quality. Second, good managers desire to signal as they benefit from revealing their quality, but the gains from signaling are quite different from standard signaling theories. In traditional models, the manager immediately benefits from revealing his quality: in Ross (1977) and Bhattacharya (1979), the signal leads to a higher stock price, to which his compensation is tied; in Myers and Majluf (1984) and Fulghieri and Lukin (2001), signaling high quality is necessary to raise funds. Here, managers are not paid according to the firm’s market value and do not benefit from receiving a greater level of funds, since all managers are financed and receive I. Even if a manager is revealed bad, he can still raise funds as the pricing of funds adjusts to reflect his low quality; such pricing does not affect his payoff as he receives only private benefits. I deliberately assume a constant investment scale of I and
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that the manager only receives private benefits so that the traditional motives to signal do not apply. Despite this, good managers do have an incentive to signal due to the concentration effect. Here, the benefit of signaling manifests solely in the type of funds. By revealing his quality, a good manager attracts scarce large investors. One large investor provides no more funds than multiple small investors, but is critically different as she has the incentive to monitor. Monitoring is beneficial because it allows inspired managers to pursue risky projects; this benefit is particularly large for good managers, since they are most likely to become inspired. In sum, the benefits of leverage are highest for type G and the costs are highest for type B, so separation is achieved. The difference in the incentives to signal leads to dynamic consistency of leverage. Zwiebel (1996) notes that some theories of debt are ‘‘setup models,’’ where high debt is only possible when the firm is initially set up. The manager dislikes the disciplinary effect of debt; thus, in Jensen (1986) and Stulz (1990), the manager does not adopt debt voluntarily but investors must force it upon him in the initial period. However, such leverage is unsustainable since it is the manager who controls the debt level going forward, and he may issue equity to buy back debt, thus freeing him from discipline. Even in models in which the manager voluntarily chooses high leverage to signal quality in the initial period in order to raise funds, he may wish to reverse leverage later once funds have been raised.22 Dynamic consistency issues occur in such models because debt’s only role is to act as either a signal (which is only valuable in the first period) or disciplining device (imposed by shareholders who only control leverage in the first period). Zwiebel (1996) was the first to present a dynamically consistent model of debt; he solves this issue by introducing a raider who is present in every period, and so it is individually rational for the manager to retain debt in every period.23 Dividends would be equally effective; the theory is a dynamically consistent model of total payout. This paper presents a dynamically consistent model of debt in particular, which arises from its two roles. The disciplinary effect credibly signals high quality, but this signal is only relevant at t¼0, when funds are raised. If raising funds was the only goal, then immediately after funds were raised at t ¼0, the manager would undo the signal and delever. The concentration effect gives the manager an ongoing incentive to maintain leverage. Unlike in traditional models where the benefits of signaling are obtained only at t ¼0 when funds are raised, here the benefits are earned at t ¼2 in the form of monitoring. Delevering would reduce L’s incentives to acquire information, thus preventing M from taking R if he becomes inspired. Dynamic consistency can be shown by giving the manager of a
22 If outsiders expect such deleveraging, debt will be unable to signal quality in the first place. 23 The key ingenuity in Zwiebel’s model is that, even though the raider is always present, his presence is not sufficient to deter overinvestment, because investment is sunk and cannot be overturned by the raider. Thus, debt is needed to deter overinvestment.
levered firm the option to issue equity to repurchase debt and promise a dividend just after t ¼0, once funds have already been raised. A repurchase of debt at t¼ 0 must be accompanied by a dividend promise, because any structure that does not involve risky debt reveals the manager as bad from part (iii) of Proposition 2.24 From (49) and (50), investors will immediately terminate a bad manager at t ¼0 unless he promises a dividend. By promising a dividend, a manager who delevers avoids being fired since the firm remains viable (from (49)) and so the threat of firing which leads to dynamic consistency in Zwiebel (1996) does not apply here. Instead, a good manager retains debt even absent an external threat—he does so because of the desire to pursue internal growth opportunities. Delevering loses the concentration effect of debt, preventing him from choosing R if inspired. From (52), this disadvantage outweighs the fact that delevering reduces the firing probability if he turns out to be uninspired. As in Section 2, the importance of the concentration effect means that strictly nonrepayable debt is optimal. If credibility is the only requirement for signaling, only the disciplinary effect is important (since a bad manager wishes to avoid discipline) and so borderline nonrepayable debt is optimal to minimize signaling costs. However, for signaling to be desirable for good managers, debt must also lead to concentration. Also as in Section 2, the importance of the concentration effect means that dividends are not a substitute for debt. A final difference with standard signaling models is that signaling can increase economy-wide fundamental value. In a pooling equilibrium where all firms are unlevered and financed with dividends, a firm run by a good manager is worth
pG V S þð1pG ÞðlK U þ ð1lÞV U Þ, compared to (54) in a separating equilibrium. If ðV R V S Þ and ðK U V U Þ are sufficiently high, i.e., the termination and investment issues are sufficiently important, the returns generated by a good manager are higher in a separating equilibrium. This is because the separating equilibrium allows good managers to be monitored, which encourages them to take R and also leads to them being terminated with certainty (rather than probability l) if they become uninspired. The bad manager yields the same returns in both a pooling and separating equilibrium. This result contrasts with a number of classical signaling models (e.g., Ross, 1977; Bhattacharya, 1979; Miller and Rock, 1985; Stein, 1989) where signaling only increases outsiders’ perceptions of firm value in the short-term; actual fundamental value falls because signaling is costly.25 In Myers and Majluf (1984) and Fulghieri and Lukin (2001), signaling can increase real value by allowing a firm to raise funds and invest. Here, 24 This off-equilibrium path belief is ‘‘reasonable’’ in the sense of Cho and Kreps (1987), since bad types would like to avoid leverage to reduce the probability of being terminated. 25 Moreover, since the increased perceived value of good firms is accompanied by a reduced perceived value of bad firms, even the shortrun effect is a redistribution rather than an aggregate increase.
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signaling has no effect on the level of funds raised, since all managers raise I in both equilibria. Instead, signaling affects the type of funds: scarce large investors are allocated to good managers, who benefit most from monitoring. Note that the allocation of blockholders is different from that implied by disciplinary theories (e.g., Burkart, Gromb, and Panunzi, 1997; Maug, 1998; Kahn and Winton, 1998; Bolton and von Thadden, 1998) which would predict that monitors should acquire stakes in bad firms to correct agency problems. Here, the monitor is an ‘‘ally’’ of good managers rather than an ‘‘adversary’’ of bad managers, and so should be allocated to the former. 3.2. Applications and empirical implications While Section 2.5 considered implications of the single-firm model, this section discusses further implications generated by the extended model and applications of the separating equilibrium. The extended model generates the broad implication that managers should willingly seek and retain leverage. This has both cross-sectional and time-series implications. First, the model is consistent with the widespread prevalence of debt in reality: if leverage were not dynamically consistent, only firms that have just raised funds would be levered, and so the vast majority of firms at a given time would have no debt. Second, in a given firm, leverage should be persistent over time, as found by Lemmon, Roberts, and Zender (2008). The core model predicts that debt is positively correlated with investment when total payout is controlled for, since it induces monitoring. The extended model provides another reason for this association—debt wards off unskilled managers who are unable to innovate. Considering a single agent, Manso (forthcoming) shows that tolerance of failure encourages innovation. This model shows an important counteracting effect in the presence of heterogeneous agents: intolerance of failure through disciplinary debt may screen out low-quality agents who are unable to innovate. I now turn to real-life applications of the separating equilibrium. Good managers take on risky debt and bad managers are unlevered; one interpretation is that the former corresponds to an LBO firm and the latter to a public corporation with low leverage.26 Unlike in some signaling theories, here the motive for signaling is not to obtain more funds. This is consistent with the fact that private firms are typically smaller than public firms. In addition, while traditional signaling models suggest that borderline nonrepayable debt is optimal, in LBOs the debt is risky. The model also predicts that LBOs should outperform regular corporations because they attract high-quality managers and allow them to invest optimally: investor returns are strictly positive. Such outperformance is shown
26 Axelson, Stromberg, and Weisbach (2009) justify leverage in buyouts based on agency problems between fund managers and fund investors, rather than between fund managers and operating company managers.
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by Ljungqvist and Richardson (2003) and Kaplan and Schoar (2005).27 Second, the model can be applied to analyze the capital structure of investment companies, the focus of Stein (2005). The two fund types analyzed by Stein have natural analogs in this model. The closed-end fund is similar to the unlevered firm with no dividends, which allows investment but not liquidation. The open-end mutual fund is analogous to the unlevered firm with dividends: openending allows liquidation through permitting investor withdrawals, but at the expense of deterring long-term arbitrage trades. The levered structure is not considered by Stein. The analogy is hedge funds: leverage allows hedge funds to undertake risky arbitrage trades, but also deters bad managers from establishing such funds as they will likely be terminated. Indeed, Ackermann, McEnally, and Ravenscraft (1999) find that the average hedge fund consistently outperforms mutual funds, even after risk and fees. 4. Conclusion This paper addresses a fundamental dilemma in corporate governance: how can investors ensure that bad managers are terminated, without inducing good managers to take myopic actions to avoid termination? Equity financing without dividends allows investment but prevents optimal shut-down; promising dividends achieves termination but at the expense of myopia. I show that debt can alleviate this tension by concentrating equityholders’ stakes and thus inducing monitoring. Monitoring is desirable even absent an effort conflict as it allows investment. As a result, debt is superior to other disciplinary mechanisms that achieve termination, such as dividends, as it does not suffer the side-effect of inducing myopia. In addition, strictly nonrepayable debt is optimal because it increases concentration. The monitoring induced by leverage allows a separating equilibrium to be sustainable: good managers are willing to signal quality by assuming debt. Even though signaling does not lead to more initial funds, and the manager is not aligned to the firm’s market value, a good manager has an incentive to signal to attract a different type of funds: active monitors, who allow him to undertake long-term projects. Once the signal has been given and financing has been raised, the manager has continued incentives to maintain leverage and thus a concentrated monitor. While existing empirical studies investigate the determinants of total leverage, this paper suggests new avenues for future empirical work: breaking down leverage into total payout (which depends on the magnitude of the termination issue), and the division of total payout 27 While buyouts usually do not retain their high leverage permanently, leverage typically remains significantly above the pre-buyout level (Kaplan, 1991). In addition, delevering is achieved through selling assets, rather than raising equity and diluting ownership. As assets are sold, the issue of inefficient continuation in non-core businesses is reduced; this reduces the optimal level of total payout and is consistent with the fall in debt.
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between debt and dividends (which depends on the magnitude of the investment issue). The conventional wisdom that debt is detrimental to growth may be overturned when levered companies are compared not to unlevered peers, but peers that pay out the same amount of cash in the form of dividends to overcome a termination problem. This prediction is consistent with the recent wave of LBOs, which are concentrated in middle-aged firms in industries with growth opportunities, and so the goal is to curb wasteful projects without deterring efficient investment. Appendix A. Proofs
Proof of Proposition 1. It is sufficient to show that the conditions in Proposition 1 can be satisfied when x ¼ ID. Then, by continuity, there exists an open set of parameters satisfying all of the conditions. Setting ID ¼ x, the condition (28) 4 x becomes ½ðppgð1fÞÞðV R FÞð1p þ pgÞc 4x:
ð58Þ
Note that F rF ¼
Ið1p þ pgð1fÞÞK U : ppgð1fÞ
Fix the values of all of the parameters except c=f, and then choose a value for c=f such that (34) is satisfied at the upper bound of F given above. Then (40), (42), and (58) can be satisfied as long as c and x are small (so f and I D are also small). Thus, the set of parameters satisfying all of the conditions is non-empty. Appendix B. Incentive pay This section shows that the model’s results are robust to replacing the manager’s private benefits with incentive pay. So that the manager’s pay is unaffected by the firm’s leverage, I compensate him with a fraction of the firm’s assets (rather than equity alone) and assume that his pay is senior to creditors. If pay depended on equity or was junior to creditors, pay would be reduced by increasing leverage and so the capital structure decision would be distorted by the desire to increase or decrease the manager’s pay. Sundaram and Yermack (2007) and Wei and Yermack (in press) show that managers are compensated with debt as well as equity, and Calcagno and Renneboog (2007) cite bankruptcy regulations in certain countries (e.g., US, UK, and Germany) that management can use to ensure that salaries are senior to creditors in a bankruptcy, and give a number of examples where this occurred. For each period after t¼1 that the manager is employed by the firm, he receives a fraction b of the final firm value. Thus, he receives bV2 if it is liquidated at t ¼2, and 2bV3 if it is continued until t¼3. It is necessary for the fraction of assets received by the manager to increase with tenure (from b to 2b) to create a termination issue, i.e., give him an incentive to continue the firm even if he is uninspired. Otherwise, an uninspired manager would
voluntarily liquidate the firm. In reality, managers are given additional equity compensation for each extra year they work; Gibbons and Murphy (1992) and Cremers and Palia (2010) find that a manager’s equity alignment is increasing in his tenure, and Sundaram and Yermack (2007) find the same for a manager’s debt stakes. Note that I do not consider giving the manager an optimal incentive contract. This is standard in models with a termination issue (e.g., Stulz, 1990; Diamond, 1991, 1993; Zwiebel, 1996), where the manager receives private benefits that increase with his tenure or an investment issue (e.g., Stein, 1988), where the manager is exogenously aligned with short-term earnings; if it were possible to write an optimal contract that aligned the manager perfectly with firm value, all agency problems would disappear and there would be no need for external monitoring. Agency problems exist in reality since they may be too large to address with a contract, for example, myopic actions and entrenchment were severe in the recent financial crisis despite managers having substantial incentive pay (see, e.g., Fahlenbrach and Stulz, 2011). The problem of solving agency issues through contracting rather than monitoring is a separate question studied by a different literature. In particular, I show that it is not necessary to write an optimal contract to solve the manager’s agency problem—inducing investor monitoring (i.e., solving the investor’s agency problem) is sufficient. With the manager receiving a fraction of the firm’s assets that increases in his tenure, the payoffs in Table 1 now become (using b now to denote the manager’s pay): Variable Uninspired Inspired, S E V2
VU ð1bÞK U
KS ð1bÞK S
V3 b2 b3
ð12bÞV U bK U 2bV U
ð12bÞV S bK S 2bV S
Inspired, R
VU with probability g, KS w.p. 1g ð1bÞK U if E ¼ V U , ð1bÞK S if E ¼ KS ð12bÞV R bK U if E ¼ V U , bK S if E ¼ K S 2bV R
The analysis is very similar to the main paper. I first start by assuming no monitoring technology, as in Section 2.1. In the absence of a disciplinary payment, the condition for all shareholders to wish the firm to continue at t ¼2 (Eq. (8)) becomes ð12bÞðpV R þ ð1pÞV U Þ 4ð1bÞðpðgK U þ ð1gÞK S Þ þ ð1pÞK U Þ,
and the payoff to investors (Eq. (9)) is ð12bÞðpV R þ ð1pÞV U Þ: As before, investors make a loss (from (7)) and so will not finance the firm to begin with.28 Thus, Lemma 1 continues to hold. With a disciplinary payment, the conditions for Lemma 2 (Eqs. (10) and (11)) become 1p pg ð12bÞ VU þ V R o ð1bÞK U , ð59Þ 1p þ pg 1p þ pg
28 Indeed, in the presence of incentive compensation, (7) can be weakened to ð12bÞðpV R þ ð1pÞV U Þ o I, although this is not necessary.
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2ð1gÞV R þ gK U o 2V S ,
ð60Þ
and the payoff to investors (Eq. (12)) is
As before, investors make a loss (from (6)) and so will not finance the firm to begin with.29 Thus, Lemma 2 continues to hold. With contractible monitoring and no disciplinary payment, Lemma 3 continues to hold and the expected gross returns to L, all households, and the manager are given by U
The market value of debt (31) and its upper and lower bounds for debt, ((32) and (33)), are D ¼ ðppgð1fÞÞF þ ð1bÞð1p þ pgð1fÞÞK U ,
pð12bÞV S þð1pÞð1bÞK U :
R
U
pwðV Þ þ ð1pÞðfwðK Þ þ ð1fÞwðV ÞÞc,
F¼
cð1p þ pgÞ½Ið1bÞð1p þ pgð1fÞÞK U fpgxð12bÞV R , cð1p þ pgÞðppgð1fÞÞfpgx
F¼
Ixð1bÞð1p þ pgð1fÞÞK U , ppgð1fÞ
and so the condition for risky debt to induce monitoring, (34), is
f
pðð12bÞV R wðV R ÞÞþ ð1pÞðfðð1bÞK U wðK U ÞÞ
2bpV R þ bð1pÞðfK U þ2ð1fÞV U Þ:
f
If a disciplinary payment is required, an inspired manager will choose R if the following analog of (15) is satisfied: U
S
2ð1gð1fÞÞV þ gð1fÞK 42V : As in the core model, this inequality is fully consistent with (60): in the presence of a disciplinary payment, monitoring is necessary and sufficient to encourage M to choose R. Lemma 4 continues to hold and the payoffs are given by ðppgð1fÞÞwðV R Þ þ ð1p þ pgð1fÞÞwðK U Þð1p þ pgÞc, ðppgð1fÞÞðð12bÞV R wðV R ÞÞ þ ð1p þ pgð1fÞÞðð1bÞK U wðK U ÞÞ,
ðð12bÞV R F Þ Zc:
ð62Þ
x
ðð12bÞV R FÞðppgð1fÞÞðIDÞ ðIDÞ2
,
which is positive if (61) 4x, i.e., the firm is viable. Turning to repayable debt (Section 2.3.2), the condition for L to monitor, (36), becomes
fð1pÞ
x ðð1bÞK U ð12bÞV U Þ Zc: IF
Lemma 6 continues to hold and the payoffs are given by x ðpð12bÞV R þ ð1pÞðfðð1bÞK U Þ þ ð1fÞð12bÞV U ÞFÞc, IF IFx ðpð12bÞV R þ ð1pÞðfðð1bÞK U Þ þ ð1fÞð12bÞV U ÞFÞ, IF
ð63Þ
However, L will not monitor under repayable debt if the following analog of (40) holds:
With non-contractible monitoring and risky debt (Section 2.3.1), creditors liquidate (the equivalent of (26)) if 1p pg VU þ F o ð1bÞK U , ð12bÞ 1p þ pg 1p þ pg which holds from (59). The condition for L to monitor, (27), becomes
fð1pÞ
x ðð1bÞK U ð12bÞV U Þ o c: IV U
ð64Þ
With riskless debt plus a dividend, the condition for L to monitor, (41), becomes
f
pg x ðð12bÞV R ð1bÞK U Þ, 1p þ pg IF
and monitoring is impossible if the following analog of (42) holds:
pg x ðð12bÞV R FÞ Zc: 1p þ pg ID
Again, the x=ðIDÞ term demonstrates the concentration effect. Lemma 5 continues to hold and the payoffs are given by x ðppgð1fÞÞðð12bÞV R FÞð1p þ pgÞc, ID IDx ðppgð1fÞÞðð12bÞV R FÞ, ID 2bðppgð1fÞÞV R þ bð1p þ pgð1fÞÞK U :
pg 1p þ pg
2bpV R þ bð1fÞðfK U þ2ð1fÞV U Þ:
2bðppgð1fÞÞV R þ bð1p þ pgð1fÞÞK U :
f
pg 1p þ pg
The marginal effect of increasing F on L’s incentive to monitor, (35), is
þ ð1fÞðð12bÞV U wðV U ÞÞÞ,
R
99
ð61Þ
As in the core model, (61) 4 x is consistent with (6) and (7), so the firm may be viable. 29 Indeed, in the presence of incentive compensation, (6) can be weakened to pð12bÞV S þ ð1pÞð1bÞK U o I.
f
pg x ðð12bÞV R ð1bÞK U Þ oc: 1p þ pg IK U
ð65Þ
Thus, if (62), (64), and (65) hold, and (61) 4x, then risky debt is the only viable financing structure (the analog of Proposition 1). To prove that the set of parameters satisfying these conditions is non-empty, as in the proof of Proposition 1, I only need to consider the case x ¼ ID. Then (61) 4 x becomes ðppgð1fÞÞðð12bÞV R FÞð1p þ pgÞc 4x:
ð66Þ
I first take x¼0. The LHS of (64) and (65) are zero, so for any positive c, (64) and (65) trivially hold. Now I only need to set c=f 2 ð0,ðpg=ð1p þ pgÞÞðð12bÞV R F ÞÞ to make (62) hold. When c is sufficiently small (so that f is also small but c=f is fixed), (66) holds. Since all inequalities are strict and all functions are continuous,
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^ there exists x^ 2 ð0,1Þ such that for all x 2 ð0, xÞ, all conditions hold. Finally, for the extension to heterogeneous managers, Section 3, conditions (49)–(51) become
pB ð12bÞVS þð1pB Þðlð1bÞK U þ ð1lÞð12bÞV U Þ ¼ I, ð12bÞðpB V R þð1pB ÞV U Þ oI, ð12bÞ
1pG pG g VU þ V R oð1bÞK U : 1pG þ pG g 1pG þ pG g
The sufficient conditions for a separating equilibrium, (52) and (53), are now 2ðpG pG gð1fÞÞV R þð1pG þ pG gð1fÞÞV U 42pG V S þ ð1pG ÞðlV U þ2ð1lÞV S Þ, 2ðpB pB gð1fÞÞV R þð1pB þ pB gð1fÞÞV U 42pB V S þ ð1pB ÞðlV U þ2ð1lÞV S Þ: The returns to investors in a levered firm, a good manager, and a bad manager ((54)–(56)) are, respectively, given by ðpG pG gð1fÞÞð12bÞV R þ ð1pG þ pG gð1fÞÞð1bÞK U ð1pG þ pG gÞc, 2ðpG pG gð1fÞÞbV R þ ð1pG þ pG gð1fÞÞbK U , 2pB bV S þ ð1pB ÞðlbV U þ 2ð1lÞbV S Þ: L will monitor at t ¼2 if
f
pG g x ðð12bÞV R FÞ Zc, 1pG þ pG g ID
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Journal of Financial Economics 102 (2011) 102–126
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Hedge fund leverage$ Andrew Ang a, Sergiy Gorovyy b,, Gregory B. van Inwegen c a
Columbia University and NBER, United States Columbia University, United States c Citi Private Bank, United States b
a r t i c l e in f o
abstract
Article history: Received 8 September 2010 Received in revised form 26 January 2011 Accepted 6 February 2011 Available online 25 June 2011
We investigate the leverage of hedge funds in the time series and cross-section. Hedge fund leverage is counter-cyclical to the leverage of listed financial intermediaries and decreases prior to the start of the financial crisis in mid-2007. Hedge fund leverage is lowest in early 2009 when the market leverage of investment banks is highest. Changes in hedge fund leverage tend to be more predictable by economy-wide factors than by fund-specific characteristics. In particular, decreases in funding costs and increases in market values both forecast increases in hedge fund leverage. Decreases in fund return volatilities predict future increases in leverage. & 2011 Elsevier B.V. All rights reserved.
JEL classification: G11 G18 G23 G32 Keywords: Capital structure Long–short positions Alternative investments Exposure Hedging Systemic risk
1. Introduction The events of the financial crisis over 2007–2009 have made clear the importance of leverage of financial intermediaries to both asset prices and the overall economy. The observed ‘‘deleveraging’’ of many listed financial
$ We thank Viral Acharya, Tobias Adrian, Zhiguo He, Arvind Krishnamurthy, Stefan Nagel (the referee), Tano Santos, Roberto Savona, Suresh Sundaresan, and seminar participants at Columbia University, Risk USA 2010, and 3rd Annual Conference on Hedge Funds for helpful comments. Corresponding author. E-mail addresses:
[email protected] (A. Ang),
[email protected] (S. Gorovyy),
[email protected] (G.B. van Inwegen). URL: http://www.columbia.edu/~aa610 (S. Gorovyy). 1 See, for example, Adrian and Shin (2009), Brunnermeier (2009), Brunnermeier and Pedersen (2009), and He, Khang, and Krishnamurthy (2010), among many others.
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.02.020
institutions during this period has been the focus of many regulators and the subject of much research.1 The role of hedge funds has played a prominent role in these debates for several reasons. First, although in the recent financial turbulence no single hedge fund has caused a crisis, the issue of systemic risks inherent in hedge funds has been lurking since the failure of the hedge fund Long-Term Capital Management L.P. (LTCM) in 1998.2 Second, within the asset management industry, the hedge fund sector makes the most use of leverage. In fact, the relatively high
1 See, for example, Adrian and Shin (2009), Brunnermeier (2009), Brunnermeier and Pedersen (2009), and He, Khang, and Krishnamurthy (2010), among many others. 2 Systemic risks of hedge funds are discussed by the President’s Working Group on Financial Markets (1999), Chan, Getmansky, Haas, and Lo (2007), Kambhu, Schuermann, and Stiroh (2007), Financial Stability Forum (2007), and Banque de France (2007).
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
and sophisticated use of leverage is a defining characteristic of the hedge fund industry. Third, hedge funds are large counterparties to the institutions directly overseen by regulatory authorities, especially commercial banks, investment banks, and other financial institutions which have received large infusions of capital from governments. However, while we observe the leverage of listed financial intermediaries through periodic accounting statements and reports to regulatory authorities, little is known about hedge fund leverage despite the proposed regulations of hedge funds in the U.S. and Europe. This is because hedge funds are by their nature secretive, opaque, and have little regulatory oversight. Leverage plays a central role in hedge fund management. Many hedge funds rely on leverage to enhance returns on assets which on an unlevered basis would not be sufficiently high to attract funding. Leverage amplifies or dampens market risk and allows funds to obtain notional exposure at levels greater than their capital base. Leverage is often employed by hedge funds to target a level of return volatility desired by investors. Hedge funds use leverage to take advantage of mispricing opportunities by simultaneously buying assets which are perceived to be underpriced and shorting assets which are perceived to be overpriced. Hedge funds also dynamically manipulate leverage to respond to changing investment opportunity sets. We are the first paper, to our knowledge, to formally investigate hedge fund leverage using actual leverage ratios with a unique data set from a fund-of-hedge-funds. We track hedge fund leverage in time series from December 2004 to October 2009, a period which includes the worst periods of the financial crisis from 2008 to early 2009. We characterize the cross-section of leverage: we examine the dispersion of leverage across funds and investigate the macro and fund-specific determinants of future leverage changes. We compare the leverage and exposure of hedge funds with the leverage and total assets of listed financial companies. As well as characterizing leverage at the aggregate level, we investigate the leverage of hedge fund sectors. The prior works on hedge fund leverage are only estimates (see, e.g., Banque de France, 2007; Lo, 2008) or rely only on static leverage ratios reported by hedge funds to the main databases. For example, leverage at a point in time is used by Schneeweis, Martin, Kazemi, and Karavas (2004) to investigate the relation between hedge fund leverage and returns. Indirect estimates of hedge fund leverage are computed by McGuire and Tsatsaronis (2008) using factor regressions with time-varying betas. Even without considering the sampling error in computing time-varying factor loadings, this approach requires that the complete set of factors be correctly specified, otherwise the implied leverage estimates suffer from omitted variable bias. Regressions can also not adequately capture abrupt changes in leverage. Other work by Brunnermeier and Pedersen (2009), Gorton and Metrick (2009), Adrian and Shin (2010), and others, cites margin requirements, or haircuts, as supporting evidence of timevarying leverage taken by proprietary trading desks at investment banks and hedge funds. These margin requirements give maximum implied leverage, not the actual
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leverage that traders are using. In contrast, we analyze actual leverage ratios of hedge funds. Our work is related to several large literatures, some of which have risen to new prominence with the financial crisis. First, our work is related to optimal leverage management by hedge funds. Duffie, Wang, and Wang (2008) and Dai and Sundaresan (2010) derive theoretical models of optimal leverage in the presence of management fees, insolvency losses, and funding costs and restrictions at the fund level. At the finance sector level, Acharya and Viswanathan (2011) study optimal leverage in the presence of moral hazard and liquidity effects showing that due to deleveraging, bad shocks that happen in good times are more severe. A number of authors have built equilibrium models where leverage affects the entire economy. In Fostel and Geanakoplos (2008), economywide equilibrium leverage rises in times of low volatility and falls in periods where uncertainty is high and agents have very disperse beliefs. Leverage amplifies liquidity losses and leads to overvalued assets during normal times. Stein (2009) shows that leverage can be chosen optimally by individual hedge funds, but this can create a fire-sale externality causing systemic risk by hedge funds simultaneously unwinding positions and reducing leverage. There are also many models where the funding available to financial intermediaries, and hence leverage, affects asset prices. In many of these models, deleveraging cycles are a key part of the propagating mechanism of shocks.3 Finally, a large literature in corporate finance examines how companies determine optimal leverage. Recently, Welch (2004) studies the determinants of firm debt ratios and finds that approximately two-thirds of variation in corporate leverage ratios is due to net issuing activity. The remainder of the paper is organized as follows. We begin in Section 2 by defining and describing several features of hedge fund leverage. Section 3 describes our data. Section 4 outlines the estimation methodology which allows us to take account of missing values. Section 5 presents the empirical results. Finally, Section 6 concludes. 2. The mechanics of hedge fund leverage 2.1. Gross, net, and long-only leverage A hedge fund holds risky assets in long and short positions together with cash. Leverage measures the extent of the relative size of the long and short positions in risky assets relative to the size of the portfolio. Cash can be held in both a long position or a short position, where the former represents short-term lending and the latter represents short-term borrowing. The assets under management (AUM) of the fund is cash plus the difference between the fund’s long and short positions and is the value of the claim all investors have on the fund. The net asset value (NAV) per share is the value of the fund per 3 See, for example, Gromb and Vayanos (2002), He and Krishnamurthy (2009), Brunnermeier and Pedersen (2009), and Adrian and Shin (2010).
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share and is equal to AUM divided by the number of shares. We use the following three definitions of leverage, which are also widely used in industry: Gross leverage is the sum of long and short exposure per share divided by NAV. This definition implicitly treats both the long and short positions as separate sources of profits in their own right, as would be the case for many long–short equity funds. This leverage measure overstates risk if the short position is used for hedging and does not constitute a separate active bet. If the risk of the short position by itself is small, or the short position is usually taken together with a long position, a more appropriate definition of leverage can be: Net leverage is the difference between long and short exposure per share expressed as a proportion of NAV. The net leverage measure captures only the long positions representing active positions which are not perfectly offset by short hedges, assuming the short positions represent little risk by themselves. Finally, we consider, Long-only leverage or long leverage is defined as the long positions per share divided by NAV. Naturally, by ignoring the short positions, long-only leverage could result in a large underestimate of leverage, but we examine this conservative measure because the reporting requirements of hedge fund positions by the U.S. Securities and Exchange Commission (SEC) involve only long positions.4 We also investigate if long leverage behaves differently from gross or net leverage, or put another way, if hedge funds actively manage their long and short leverage positions differently. Only a fund 100% invested in cash has a leverage of zero for all three leverage definitions. Furthermore, for a fund employing only levered long positions, all three leverage measure coincide. Thus, active short positions induce differences between gross, net, and long-only leverage. Appendix A illustrates these definitions of leverage for various hedge fund portfolios.
2.2. How do hedge funds obtain leverage? Hedge funds obtain leverage through a variety of means, which depend on the type of securities traded by the hedge fund, the creditworthiness of the fund, and the exchange, if any, on which the securities are traded. Often leverage is provided by a hedge fund’s prime broker, but not all hedge funds use prime brokers.5 By far the vast majority of leverage is obtained through short-term funding as there are very few hedge funds able to directly issue long-term debt or secure long-term borrowing. In the U.S., regulations govern the maximum leverage permitted in many exchange-traded markets. The Federal 4 Regulation 13-F filings are required by any institutional investor managing more than $100 million. Using these filings, Brunnermeier and Nagel (2004) examine long-only hedge fund positions in technology stocks during the late 1990s bull market. 5 In addition to providing financing for leverage, prime brokers provide hedge fund clients with risk management services, execution, custody, daily account statements, and short-sale inventory for stock borrowing. In some cases, prime brokers provide office space, computing and trading infrastructure, and can even contribute capital.
Table 1 Margin requirements by security type. The table lists the margin requirements and their implied level of leverage in various security markets. The data are obtained by collating information from prime brokers and derivatives exchanges as of March 2010.
Treasuries Investment grade corp bonds High yield bonds Convertible bonds Equities Commodity futures Financial futures Foreign exchange futures Options (equity) Interest rate swaps Foreign exchange swaps Total return swaps
Margin (haircut)
Implied leverage
0.1–3% 5–10% 10–15% 15–20% 5–50% 10% 3% 2% 75% 1% 1% 10%
33–100 10–20 6.6–10 5–6.6 2–20 10 33 50 1.3 100 100 10
Reserve Board’s Regulation T (Reg T) allows investors to borrow up to a maximum 50% of a position on margin (which leads to a maximum level of exposure equal to 1/0.5¼2). For a short position, Reg T requires that short-sale accounts hold collateral of 50% of the value of the short implying a maximum short exposure of two. By establishing offshore investment vehicles, hedge funds can obtain ‘‘enhanced leverage’’ higher than levels allowable by Reg T. Prime brokers have established facilities overseas in less restrictive jurisdictions to provide this service. Another way to obtain higher leverage than allowed by Reg T is ‘‘portfolio margining’’ which is another service provided by prime brokers. Portfolio margining was approved by the SEC in 2005 and allows margins to be calculated on a portfolio basis, rather than on a security-by-security basis.6 Table 1 reports typical margin requirements (‘‘haircuts’’) required by prime brokers or other counterparties. The last column of the Table 1 lists the typical levels of leverage able to be obtained in each security market, that are the inverse of the margin requirements. These are obtained at March 2010 by collating information from prime brokers and derivatives exchanges.7 Note that some financial instruments, such as derivatives and options, have embedded leverage in addition to the leverage available from external financing. The highest leverage is available in Treasury, foreign exchange, and derivatives security markets such as interest rate and foreign exchange swaps. These swap transactions are over the counter and permit much higher levels of leverage than Reg T. These securities enable investors to have large notional exposure with little or no initial investment or collateral. Similarly, implied leverage is high in futures
6 Portfolio margining only applies to ‘‘hardwired’’ relations, such as calls and puts on a stock, and the underlying stock itself, rather than to any statistical correlations between different assets. 7 Brunnermeier and Pedersen (2009) and Gorton and Metrick (2009) show that margin requirements changed substantially over the financial crisis.
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markets because the margin requirements there are much lower than in the equity markets. Based on the dissimilar margin requirements of different securities reported in Table 1, it is not surprising that hedge fund leverage is heterogeneous and depends on the type of investment strategy employed by the fund. Our results below show that funds engaged in relative value strategies, which trade primarily fixed income, swaps, and other derivatives, have the highest average gross leverage of 4.8 through the sample. Some relative value funds in our sample have gross leverage greater than 30. Credit funds which primarily hold investment grade and high yield corporate bonds and credit derivatives have an average gross leverage of 2.4 in our sample. Hedge funds in the equity and event-driven strategies mainly invest in equity and distressed corporate debt and hence have lower leverage. In particular, equity and event-driven funds have average gross leverage of 1.6 and 1.3, respectively, over our sample. The cost of leverage to hedge funds depends on the method used to obtain leverage. Prime brokers typically charge a spread over London Interbank Offered Rate (LIBOR) to hedge fund clients who are borrowing to fund their long positions and brokers pay a spread below LIBOR for cash deposited by clients as collateral for short positions. These spreads are higher for less creditworthy funds and are also higher when securities being financed have high credit risk or are more volatile. The cost of leverage through prime brokers reflects the costs of margin in traded derivatives markets. We include instruments capturing funding costs like LIBOR and interest rate spreads in our analysis. In many cases, there are maximum leverage constraints imposed by the providers of leverage on hedge funds. Hedge fund managers make a decision on optimal leverage as a function of the type of the investment strategy, the perceived risk-return trade-off of the underlying trades, and the cost of obtaining leverage, all subject to exogenously imposed leverage limits. Financing risk is another consideration as funding provided by prime brokers can be subject to sudden change. In contrast, leverage obtained through derivatives generally has lower exposure to funding risk. Prime brokers have the ability to pull financing in many circumstances, for example, when performance or NAV triggers are breached. Dai and Sundaresan (2010) show that this structure effectively leaves the hedge funds short an option vis-a -vis their prime broker. Adding further risk to this arrangement is the fact that the hedge fund is also short an option vis-a vis another significant financing source, their client base, which also has the ability to pull financing following terms stipulated by the offering memorandum.8 We do not consider the implicit leverage in these funding options in our analysis as we are unable to obtain data on hedge fund prime broker agreements or the full set of investment memoranda of hedge fund clients; our analysis applies
8 In many cases, hedge funds have the ability to restrict outflows by invoking gates even after lockup periods have expired (see, for example, Ang and Bollen, 2010).
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only to the leverage reported by hedge funds in their active strategies.9 2.3. Reported hedge fund leverage An important issue with hedge fund leverage is which securities are included in the firm-wide leverage calculation and how the contribution of each security to portfolio leverage is calculated. The most primitive form of leverage calculation is unadjusted balance sheet leverage, which is simply the value of investment assets, not including notional exposure in derivatives, divided by equity capital. Since derivative exposure for hedge funds can be large, this understates, in many cases dramatically, economic risk exposure. To remedy this shortcoming, leverage is often adjusted for derivative exposure by taking delta-adjusted notional values of derivative contracts.10 For example, to account for the different volatility and beta exposures of underlying investments, hedge funds often beta-adjust the exposures of (cash) equities by upward adjusting leverage for high-beta stock holdings. Likewise, (cash) bond exposures are often adjusted to account for the different exposures to interest rate factors. In particular, the contribution of bond investments to the leverage calculation is often scaled up or down by calculating a 10-year equivalent bond position. Thus, an investment of $100 in a bond with twice the duration of a 10-year bond would have a position of $200 in the leverage calculation. The issues of accounting for leverage for swaps and futures affect fixed income hedge funds the most and long–short equity hedge funds the least. For this reason, we break down leverage statistics by hedge fund sectors. Funds investing primarily in futures, especially commodities, report a margin-to-equity ratio, which is the amount of cash used to fund margin divided by the nominal trading level of the fund. This measure is proportional to the percentage of available capital dedicated to funding margin requirements. It is frequently used by commodity trading advisors as a gauge of their market exposure. Other funds investing heavily in other zero-cost derivative positions like swaps also employ similar measures based on ratios of nominal, or adjusted nominal, exposure to collateral cash values to compute leverage. Thus, an important caveat with our analysis is that leverage is not measured in a consistent fashion across hedge funds and the hedge funds in our sample use different definitions of leverage. Our data are also self-reported by 9 Dudley and Nimalendran (2009) estimate funding costs and funding risks for hedge funds, which are not directly observable, using historical data on margins from futures exchanges and Chicago Board Options Exchange Market Volatility Index (VIX). They do not consider hedge fund leverage. 10 Many hedge funds account for the embedded leverage in derivatives positions through internal reporting systems or external, thirdparty risk management systems like RiskMetrics. These risk system providers compute risk statistics like deltas, left-hand tail measures of risk like Value-at-Risk (VAR), and implied leverage at both the security level and the aggregate portfolio level. RiskMetrics allows hedge funds to ‘‘pass through’’ their risk statistics to investors who can aggregate positions across several funds.
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hedge funds. These effects are partially captured in our analysis through fund-fixed effects. Our analysis focuses on the common behavior of leverage across hedge funds rather than explaining the movements in leverage of a specific hedge fund.
3. Data 3.1. Macro data We capture the predictable components of hedge fund leverage by various aggregate market price variables, which we summarize in Appendix B. We graph two of these variables in Fig. 1. We plot the average cost of protection from a default of major ‘‘investment banks’’ (Bear Stearns, Citibank, Credit Suisse, Goldman Sachs, HSBC, JP Morgan, Lehman Brothers, Merrill Lynch, and Morgan Stanley) computed using credit default swap (CDS) contracts in the solid line with the scale on the left-hand axis. This is the market-weighted cost of protection per year against default of each firm. Our selected firms are representative of broker/dealers and investment banking activity and we refer to them as investment banks even though many of them are commercial banks and some became commercial banks during the sample period. In Fig. 1 we also plot the VIX volatility index in the dotted line with the scale on the right-hand axis. The correlation between VIX and investment bank CDS protection is 0.89. Both of these series are low at the beginning of the sample and then start to increase in mid-2007, which coincides with the initial losses in subprime mortgages and other certain securitized markets. In late 2008, CDS spreads and VIX increase dramatically after the bankruptcy of Lehman Brothers, with VIX reaching a peak of 60% at the end of October 2008 and the CDS spread reaching 3.55% per annum in September 2008. 0.6
0.04
0.5
0.03
0.4
0.02
0.3
0.01
0.2
VIX
CDS
0.05
0 2005
2006
2007
2008
2009
0.1 2010
Fig. 1. VIX and CDS protection. The market-value-weighted credit default swap (CDS) cost of protection for the investment banks (Bear Stearns, Citibank, Credit Suisse, Goldman Sachs, HSBC, JP Morgan, Lehman Brothers, Merrill Lynch, and Morgan Stanley) is shown in the solid line with the axis on the left-hand scale. We plot the VIX volatility index in the dotted line with the axis on the right-hand scale. The data sample is from December 2004 to October 2009 at a monthly frequency.
In 2009, both CDS and VIX decline after the global financial sector is stabilized. Our other macro series are monthly returns on investment banks, monthly returns on the S&P 500, the threemonth LIBOR rate, and the three-month Treasury over Eurodollar (TED) spread. The LIBOR and TED spreads are good proxies for the aggregate cost of short-term borrowing for large financial institutions. Prime brokers pass on at least the LIBOR and TED spread costs to their hedge fund clients plus a spread. Finally, we also include the term spread, which is the difference between the 10-year Treasury bond yield and the yield on three-month T-bills. This captures the slope of the yield curve, which under the Expectations Hypothesis is a forward-looking measure of future short-term interest rates and thus provides a simple way of estimating future short-term borrowing costs. 3.2. Hedge fund data Our hedge fund data are obtained from a large fund-ofhedge-funds (which we refer to as the ‘‘Fund’’). The original data set from the Fund contains over 45,000 observations of 758 funds from February 1977 to December 2009. In addition to hedge fund leverage, our data include information on the strategy employed by the hedge funds, monthly returns, NAVs, and AUMs. The hedge funds are broadly representative of the industry and contain funds managed in a variety of different styles including global macro funds, fundamental stock-picking funds, credit funds, quantitative funds, and funds investing using technical indicators. The hedge funds invest both in specific asset classes, for example, fixed income or equities, and also across global asset classes. Our data include both U.S. and international hedge funds, but all returns, NAVs, and AUMs are in U.S. dollars. An important issue is whether the hedge funds in the database exhibit a selection bias. In particular, do the hedge funds selected by the Fund have better performance and leverage management than a typical hedge fund? The Fund selects managers using both a ‘‘top down’’ and a ‘‘bottom up’’ approach. The former involves selecting funds in various sector allocation bands for the Fund’s different fund-of-funds portfolios. The latter involves searching for funds, or reallocating money across existing funds, using a primarily qualitative, proprietary approach. Leverage is a consideration in choosing funds, but it is only one of many factors among the usual suspects—Sharpe (1992) ratios and other performance criteria, due diligence considerations, network, manager quality, transparency, gates and restrictions, sector composition, investment style, etc. The Fund did not add leverage to its products and only very rarely asked hedge funds to provide a customized volatility target or to provide leverage which differed from the hedge funds’ existing product offerings. There is no reason to believe that the Fund’s selection procedure results in funds with leverage management practices that are significantly different to the typical hedge fund. Our Fund database includes funds that are present in TASS, CISDM, Barclay Hedge, or other databases commonly
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
12−Month rolling volatility
0.04 0.03 0.02
2010
2009.5
2009
2008.5
2008
2007.5
2007
2006.5
2005
2005.5
0
2006
0.01
Fig. 2. Rolling 12-month hedge fund volatilities. This figure compares volatilities of returns of different hedge fund strategies over the sample period. The monthly volatility for each strategy is constructed as an average value of sample volatilities of returns over the past 12 months for the hedge funds that belong to the strategy. The strategies are relative value (RV), equity (EQ), event-driven (ED), credit (CR), and the whole hedge fund sample is denoted HF. The data sample is from December 2004 to October 2009.
0.09 0.08
25th percentile of volatility in HFR Median volatility in HFR 75th percentile of volatility in HFR Average volatility in the data sample
0.07 0.06 0.05 0.04 0.03
2010
2009.5
2009
2008.5
2008
2007.5
2007
0.01
2006.5
0.02
2006
3.2.2. Hedge fund returns, volatilities, and flows We have monthly returns on all the hedge funds. These returns are actual realized returns, rather than returns reported to the publicly available databases. In addition to examining the relation between past returns and leverage, we construct volatilities from the returns. We construct monthly hedge fund volatility using the sample standard deviation of returns over the past 12 months. Fig. 2 plots the volatilities of all hedge funds and different hedge fund strategies over the sample. The volatilities follow the same broad trend and are approximately the same. This is consistent with hedge funds using leverage to scale returns to similar volatility levels. Fig. 2 shows that at the beginning of the sample, hedge fund volatilities were around 3% per month and reach a low of around 2% per month in 2006. As subprime mortgages start to deteriorate in mid-2007, hedge fund return volatility starts to increase and reaches 4–5% per month by 2009. Volatility stays at this high level until the end of the sample in October 2009. This is because we use rolling 12-month sample volatilities which include the very volatile, worst periods of the financial crisis 12 months prior to October 2009. Fig. 3 compares the rolling 12-month volatilities of hedge fund returns in the data sample with the rolling 12month volatilities of hedge fund returns in the Hedge Fund Research, Inc. (HFR) database for the December 2004–October 2009 time period. We observe that the
HF RV EQ ED CR
0.05
2005.5
3.2.1. Hedge fund leverage Leverage is reported by different hedge funds at various frequencies and formats, which are standardized by the Fund. Appendix C discusses some of these formats. Most reporting is at the monthly frequency, but some leverage numbers are reported quarterly or even less frequently. For those funds reporting leverage at the quarterly or at lower frequencies, the Fund is often able to obtain leverage numbers directly from the hedge fund managers at other dates through a combination of analyst site visits and calls to hedge fund managers. The data are of high quality because the funds undergo thorough due diligence by the Fund. In addition, the performance and risk reports are audited, and the Fund conducts regular, intensive monitoring of the investments made in the individual hedge funds.
0.06
2005
used in research and also includes other funds which do not report to the public hedge fund databases. This mitigates the reporting bias of the TASS database (see Malkiel and Saha, 2005; Ang, RhodesKropf, and Zhao, 2008; Agarwal, Fos, and Jiang, 2010). However, the composition by sector is similar to the overall sector weighting of the industry as reported by TASS and Barclay Hedge. Survival biases are mitigated by the fact that often hedge funds enter the database not when they receive funds from the Fund, but several months prior to the Fund’s investment and they often exit the database several months after disinvestment. Our database also includes hedge funds which terminate due to poor performance. The aggregate performance of the Fund is similar to the performance of the main hedge fund indexes.
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Fig. 3. Hedge fund volatilities vs. HFR volatilities. We plot 25th, 50th, and 75th percentile values of 12-month rolling volatilities of returns of funds in the HFR database and the average 12-month rolling volatility of returns of funds in the Fund’s database. The data sample is from December 2004 to October 2009.
average volatilities of hedge funds in the data closely track the median hedge fund volatility in the HFR database. Thus, the Fund’s hedge funds have very similar return behavior as the typical hedge fund reported on the publicly available databases. Since hedge funds often use leverage to target particular levels of volatility, this partially alleviates concerns that the Fund’s hedge funds have atypical leverage policies.
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A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
Table 2 Summary statistics of data. Panel A lists the number of observations and number of hedge funds broken down by strategy. Panel B reports summary statistics for the hedge fund variables across all funds. We report means, standard deviation, and autocorrelation of the monthly frequency variables. The means and standard deviation are computed using the full observed data while the autocorrelations are computed only using observations with adjacent months for each fund. We compute the variables for each fund and then report the average across funds for each variable. Hedge fund flows are computed using assets under management (AUM) and fund returns over the past three months following Eq. (1). The last column reports the percentage of observations that are observed in the data set. The data sample is from December 2004 to October 2009. Panel A: Number of observations Strategy
Observations
Funds
Relative value (RV) Credit (CR) Event-driven (ED) Equity (EQ)
1414 875 1408 4439
36 21 37 114
Total hedge funds
8136
208
Mean
Standard deviation
2.130 0.587 1.360 0.003 0.026 0.022 8.528
0.616 0.278 0.382 0.031 0.010 0.226 0.143
Panel B: Fund-specific variables
Observed gross leverage Observed net leverage Observed long-only leverage Past 1-month returns Past 12-month volatility Past 3-month flows Log AUM
In addition to hedge fund volatility, we also use hedge fund flows as a control variable. We construct hedge fundlevel flows over the past three months using the return and AUM information from the following formula: Flowt ¼
AUMt ð1 þ Rt2 Þð1þ Rt1 Þð1 þ Rt Þ, AUMt3
ð1Þ
where Flowt is the past three-month flow in the hedge fund, AUMt is assets under management at time t, and Rt is the hedge fund return from t1 to t. The flow formula in Eq. (1) is used by Chevalier and Ellison (1997), Sirri and Tufano (1998), and Agarwal, Daniel, and Naik (2009), among others. We compute three-month flows, as the flows over the past month tend to be very volatile. We also compute past three-month hedge fund flows for the aggregate hedge fund industry as measured by the Barclay Hedge database using Eq. (1).
3.3. Summary statistics We clean the raw data from the Fund and impose two filters. First, often investments are made by the Fund in several classes of shares of a given hedge fund. All of these share classes have almost identical returns and leverage ratios. We use the share class with the longest history or the share class representing the largest AUM. Our second filter is that we require funds to have at least two years of leverage observations. The final sample spans December 2004 to October 2009 and thus, our sample includes the poor returns of quantitative funds during Summer 2007 (see Khandani and Lo, 2007) and the financial crisis of 2008 and early 2009. There are at least 63 funds in our sample at any one time. The maximum number of funds at any given month is 163 over the sample period.
Autocorrelation 0.680 0.595 0.690 0.241 0.828 0.620 0.883
% Observed 82.0% 82.0% 82.1% 100.0% 69.6% 77.4% 85.0%
Panel A of Table 2 lists the number of observations and number of hedge funds broken down by strategy. The strategies are defined by the Fund and do not exactly correspond to the sector definitions employed by TASS, Barclay Hedge, CISDM, or other hedge fund databases (which themselves employ arbitrary sector definitions). The TASS categories of fixed income arbitrage and convertible arbitrage fall under the Fund’s relative value sector. In the relative value sector, hedge funds invest in both developed and emerging markets and can also invest in a variety of different asset classes. Most of the Fund’s investments have been in long–short equity funds in the equity category and this is also by far the largest hedge fund sector in TASS, as reported, for example, by Chan, Getmansky, Haas, and Lo (2007). At the last month of our sample, October 2009, the proportion of equity funds reported in Barclay Hedge, not including multi-strategy, other, and sector-specific categories, is also over 40%. After our data filters, there are a total of 208 unique hedge funds in our sample with 8,136 monthly observations. Over half (114) of the funds in our sample run long– short equity strategies. The number of funds in the areas of credit and relative value are 21 and 36, respectively. The remaining 37 funds are in the event-driven strategy, which are mainly merger arbitrage and distressed debt. The number of funds reported in Panel A of Table 2 is large enough for reliable inference when averaged across strategies and across all hedge funds.11 In Panel B of Table 2, we report summary statistics of all the hedge fund variables observed in the sample. These
11 The sample also includes commodity trading funds and global macro funds, but we do not break out separate performance of these sectors as there are too few funds for reliable inference.
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
statistics should be carefully interpreted because they do not sample all hedge funds at the same frequency and there are missing observations in the raw data. Panel B reports that the average gross leverage across all hedge funds is 2.13 with a volatility of 0.62. This volatility is computed using only observed data and the true volatility of leverage, after estimating the unobserved values, will be lower, as we show below. Nevertheless, it is clear that hedge fund leverage changes over time. Even without taking into account missing observations, this volatility is much lower than the volatility of leverage reported in the estimations of McGuire and Tsatsaronis (2008) using factor regressions. This discrepancy could possibly result from the large error in their procedure of inferring leverage from estimated factor coefficients in regressions on short samples. Individual gross hedge fund leverage is also persistent, with an average autocorrelation of 0.68 across all the hedge funds. Again because of unobserved leverage ratios, this persistence is biased downwards and we report more accurate measures of autocorrelation taking into account other predictive variables below. Panel B of Table 2 also reports the summary statistics for the other two leverage measures. The average net leverage of hedge funds is 0.59 and average long-only leverage is 1.36. The raw volatilities of net leverage and long-only leverage are 0.28 and 0.38, respectively, which are significantly lower than the volatility of gross leverage. Thus, in our analysis, we break out gross, net, and long-only leverage separately. The other variables reported in Panel B of Table 2 are control variables used in our analysis. The average hedge fund return is 29 basis points per month. These returns are autocorrelated, with an average autocorrelation of 0.24 across funds, which indicates that out- or underperforming manager returns are persistent, as noted by Getmansky, Lo, and Makarov (2004) and Jagannathan, Malakhov, and Novikov (2010). The returns are lower than those reported by previous literature because our sample includes the financial crisis during which many hedge funds did poorly.12 The average 12-month rolling volatility across hedge funds is 2.65% per month. The volatility is computed only when all fund returns in the previous 12 months are observed. This explains why only approximately 70% of fund volatilities are observed. Nevertheless, our volatility estimates are close to those reported in the literature by Ackermann, McEnally, and Ravenscraft (1999) and Chan, Getmansky, Haas, and Lo (2007), among others. The last two fund-specific variables we include are past three-month hedge fund flows and log AUMs. Flows are on average positive, at 2.2% per month and exhibit a large average autocorrelation of 0.62. The average fund size over our sample is $962 million. The median fund size is $430 million. The difference between mean and median of fund size is explained by the presence of some large funds, with the largest funds having AUMs well over $10
12 See, among many others, Fung and Hsieh (1997, 2001), Brown, Goetzmann, and Ibbotson (1999), and more recently, Bollen and Whaley (2009).
109
billion in just one share class. Our sample is slightly biased upwards in terms of size compared to recent estimates such as those by Chan, Getmansky, Haas, and Lo (2007) and the Banque de France (2007). This is due to the application of filters which tend to remove smaller funds which are effectively different share classes of larger funds. Our filters also remove funds which are in their infancy. These funds are likely to have lower levels of leverage, with more onerous financing conditions, than more established funds, making the levels of our leverage ratios conservatively biased upwards. The last column in Panel B, Table 2 lists the proportion of months across all funds where the variables are observed. While we always observe returns, the leverage variables are observed approximately 80% of the time. We do not restrict our analysis to a special subset of data where all variables are observed. Instead, our algorithm permits us to use all the available data and to infer the leverage ratios when they are missing. We now discuss our estimation methodology. 4. Methodology 4.1. Predictive model We specify that leverage over at month t þ1 for fund i, Li,t þ 1 , is predictable at time t by both economy-wide variables, xt, and fund-specific variables, which we collect in the vector yi,t , in the linear regression model:13
DLi,t þ 1 ¼ ci þ g xt þ r yi,t þ ei,t þ 1 ,
ð2Þ
where DLi,t þ 1 ¼ Li,t þ 1 Li,t is the change in fund i leverage from t to t þ 1, g is the vector of predictive coefficients on economy-wide variables, r is the vector of coefficients on fund-specific variables, and the idiosyncratic error ei,t þ 1 Nð0, s2 Þ is independent and identically distributed (i.i.d.) across funds and time. The set of firm-specific characteristics, yi,t , includes lagged leverage, Li,t , which allows us to estimate the degree of mean reversion of the leverage employed by funds. We capture fund-fixed effects in the constants ci which differ across each fund. We estimate the parameters y ¼ ðci grs2 Þ using a Bayesian algorithm which also permits estimates of non-observed leverage and other fund-specific variables. Appendix Appendix D contains details of this estimation. Briefly, the estimation method treats the non-reported variables as additional parameters to be inferred along with y. As an important byproduct, the estimation supplies posterior means of leverage ratios where these are unobserved in the data. We use these estimates, combined with the observed leverage ratios, to obtain time-series estimates of aggregate hedge fund leverage and leverage for each sector. Since we use uninformative priors, the special case where both the regressors and regressands in Eq. (2) are all observed in the data is equivalent to running standard ordinary least squares (OLS) regression. 13 We also investigate the forecastability of proportional leverage changes, DLi,t þ 1 =ð1 þ Li,t Þ, in the same regression specification of Eq. (2). The results are very similar to the results for leverage changes.
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
4.2. Contemporaneous model The model in Eq. (2) is a predictive model where leverage over the next period is forecastable by macro and fund-specific variables at the beginning of the period. We consider an alternative model where leverage is determined contemporaneously with instruments: ð3Þ
where we use the same set of macro variables in xt as in the predictive model (2), but we now assume that the fund-specific variables, yi,t , do not include lagged leverage. In Eq. (3), the potential observable determinants of leverage like VIX, interest rate spreads, hedge fund flows, etc. in xt and yi,t are persistent. The unobserved determinants, which are in the error term ei,t , are also likely to be persistent so we specify that the errors are serially correlated and follow
5.1. Time series of leverage 5.1.1. Gross leverage We begin our analysis by presenting the time series of gross leverage of hedge funds. This is obtained using the model in Eq. (2) with all macro and fund-specific variables and fund-fixed effects. We graph gross hedge fund leverage for all hedge funds and the hedge fund sectors in Fig. 4. We report the posterior mean of gross leverage across all hedge funds in the solid line. Gross leverage is stable at approximately 2.3 until mid-2007 where it starts to decrease from 2.6 in June 2007 to a minimum of 1.4 in March 2009. At the end of our sample, October 2009, we estimate gross leverage across hedge funds to be 1.5. Over the whole sample, average gross leverage is 2.1. As expected from the fairly smooth transitions in Fig. 4, gross leverage is very persistent with an autocorrelation of 0.97. The patterns of gross leverage for all hedge funds are broadly reflected in the dynamics of the leverage for hedge fund sectors, which are also highly persistent with correlations well above 0.95. Leverage for event-driven and equity funds is lower, on average, at 1.3 and 1.6, respectively, than for all hedge funds, which have an average gross leverage of 2.1 over the sample. Both the event-driven and equity sectors reach their highest peaks of gross leverage in mid-2007 and gradually decrease 7
HF RV EQ ED CR
ð4Þ 6 5 4 3 2
2009.5
2009
2008.5
2008
2007.5
2007
0
2006.5
1
2006
where vt i.i.d. Nð0, s2 Þ. It can be shown that accounting for the persistence in the regressands in Eq. (3) through VAR or autoregressive specifications produces a reducedform model of the same form as Eq. (2), except without a lagged leverage term. The relation between Eq. (2) and (3) involves the persistence of the regressands and the strength of the serial correlation, fe , of the error terms. Appendix Appendix D describes the estimation of the contemporaneous system and compares it with the predictive model. The contemporaneous model (3) can be used to test various theories on the determinants of hedge fund leverage. It is important to note, however, that Eq. (3) is not a structural model. Many of the fund-specific variables, and perhaps some of the macro variables, are jointly endogenously determined with hedge fund leverage. Put another way, while Eq. (3) can shed light on contemporaneous correlations between hedge fund leverage and various instruments, it is silent on causation. We can expect that some variables that are contemporaneously associated with hedge fund leverage in Eq. (3) can have the opposite sign when used as a predictor of hedge fund leverage in Eq. (2). Some of this can be due to the effect of the serially correlated errors in the contemporaneous specification or that the contemporaneous vs.
2005.5
et ¼ fe et1 þ vt ,
5. Empirical results
2005
Li,t ¼ ci þ g xt þ r yi,t þ ei,t ,
predictive relations between certain variables and leverage are indeed different.
2010
An advantage of our procedure is that we are able to use all observations after imposing the data filters. Using OLS would result in very few funds and observations because both the complete set of regressors and the regressand must be observed. Taking only observed leverage produces a severely biased sample as different types of funds report at quarterly or lower frequencies versus the monthly frequency. Sudden stops in leverage reporting correlate with unexpected bad performance. Linearly interpolating unobserved leverage produces estimates that are too smooth because it relies on filling in points based on the mean reversion properties of leverage alone. We show below that other variables significantly predict leverage, both in the time series and cross-section.
Leverage
110
Fig. 4. Hedge fund gross leverage. The figure plots hedge fund gross leverage for all hedge funds (HF) and hedge fund sectors. The sectors are relative value (RV), equity (EQ), event-driven (ED), and credit (CR). The leverage aggregates all observed hedge fund leverage and estimated hedge fund leverage when these are unobserved following the estimation method outlined in Appendix D. These estimates are obtained using the model in Eq. (2) using all macro and fund-specific variables and fund-fixed effects. The data sample is from December 2004 to October 2009.
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
their leverage over the financial crisis. Event-driven leverage falls below one and reaches a low of 0.8 in December 2008 before rebounding. Credit funds steadily increase their gross leverage from 1.5 at the beginning of 2005 to reach a peak of 3.9 at June 2007. This decreases to 1.1 at the end of the sample. Fig. 4 shows that the most pronounced fall in leverage is seen in the relative value sector: relative value gross leverage reaches an early peak of 6.8 in April 2006 and starts to cut back in early 2006. This is well before the beginning of the deterioration in subprime mortgages in 2007. In December 2007, gross leverage in relative value funds falls to 4.5 and decreases slightly until a sharp increase over April to June 2008 to reach a local high of 5.8 in June 2008. These periods coincide with increasing turbulence in financial markets after the purchase of Bear Stearns by JP Morgan Chase in March 2008 and the illiquidity of many securitized asset markets.14 The increasing leverage in early 2008 in relative value is not due to any one fund; several large funds in the database exhibit this behavior and, in general, the leverage of all relative value funds over the financial crisis is volatile. From June 2008 gross leverage of the relative value sector decreases from 5.8 to 2.3 at October 2009. Over the whole sample, relative value gross leverage is 4.8.
5.1.2. Dispersion of gross leverage While Fig. 4 shows the average hedge fund leverage, an open question is how the cross-section of leverage changes over time. We address this in Fig. 5 which plots the median and the cross-sectional interquartile range (25th and 75th percentiles) of gross leverage. The crosssectional distribution of all leverage measures does change, but is fairly stable across the sample. Since there are some funds with very large leverage in our sample, the median falls closer to the 25th percentile than to the 75th percentile for all the leverage ratios. During 2005 to early 2007, the interquartile range for gross hedge fund leverage stays in the range 1.0–1.3. During mid-2007, the interquartile cross-sectional dispersion increases to 1.6 in May 2007 and then falls together with the overall decrease in leverage during this period. Interestingly, the largest decline in leverage in 2008 during the financial crisis is not associated with any significant change in the cross-section of hedge fund leverage. In summary, although hedge fund leverage is heterogeneous, the cross-sectional pattern of hedge fund leverage is fairly stable and in particular, does not significantly change in 2008 when the overall level of leverage is declining. 14 Relative value strategies (e.g., capital structure arbitrage and convertible bond arbitrage) tend to be more sensitive to the relative relation between securities and asset classes than credit, equity, and event-driven strategies, which tend to be based more on single-security fundamentals. When markets showed signs of normalizing after the Bear Stearns takeover in March 2008, many relative value strategies were quick to reapply leverage to take advantage of the stabilized and converging valuations. This period of improved market conditions was brief as new financial sector shocks occurred during the Summer of 2008, at which time relative value managers quickly brought leverage down.
111
3
2.5
2
1.5
1
0.5 2005
2006
2007
2008
2009
2010
Fig. 5. Cross-sectional dispersion of gross hedge fund leverage. The figure plots the median (solid line) together with the 25th and 75th cross-sectional percentiles (dashed and dashed-dot lines, respectively) of gross hedge fund leverage across all funds. The hedge fund leverage ratios consist of all observed hedge fund leverage and estimated hedge fund leverage when these are unobserved following Eq. (2) and the estimation method outlined in Appendix D using all macro and fundspecific variables and fund-fixed effects. The data sample is from December 2004 to October 2009.
5.1.3. Gross vs. net and long-only leverage In Fig. 6 we plot gross, net, and long-only leverage across all hedge funds (top panel) and for hedge fund sectors (bottom four panels). The lines for gross leverage are the same as Fig. 4 and are drawn so we can compare net and long-only leverage. Fig. 6 shows that the three leverage measures, for all hedge funds and within the hedge fund sectors, are highly correlated and have the same broad trends. Table 3 reports correlations of the gross, net, and long-only leverage and they are all high. In particular, gross, net, and long-only leverage all have pairwise correlations above 0.92 in Panel A. Panel B of Table 3 reports the correlations of gross, net, and long leverage for the hedge fund sectors. If there are no independent active short bets, then the correlations of all leverage measures should be one. Thus, we can infer the extent of the separate management of long and short positions by examining the correlations between gross and net leverage. The correlation of net and gross leverage is lowest for equity hedge funds, at 0.49, and above 0.80 for the other hedge fund sectors. This is consistent with funds in the equity sector most actively separately managing their long and short bets. In contrast, the highest correlation between net and gross leverage is 0.88 for relative value funds, which indicates these funds are most likely to take positions as long–short pairs. One difference between the leverage measures in Fig. 6 is that the net and long-only leverage ratios are smoother than gross leverage. For all hedge funds the standard deviation of gross leverage is 0.36, whereas the standard deviations for net and long leverage are 0.14 and 0.25, respectively. Thus, hedge funds manage the leverage associated with active long and short positions in
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A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
All hedge funds
3
Gross Net Long−only
2.5 2 1.5 1 0.5 0 2005
2006
2007
Relative value
8
2008
2009
2010
Equity
2.5 2
6
1.5 4
1
2 0 2005
0.5 2006
2007
2008
2009
2010
Event−driven
2
0 2005
3
1
2
0.5
1
2006
2007
2008
2009
2010
2007
2008
2009
2010
2009
2010
Credit
4
1.5
0 2005
2006
0 2005
2006
2007
2008
Fig. 6. Gross, net, and long-only hedge fund leverage. The figure shows the dynamics of the posterior means of gross leverage (solid line), net leverage (dashed-dot line), and long-only leverage (dashed line) for all hedge funds and for hedge fund sectors at the monthly frequency. The hedge fund leverage ratios consist of all observed hedge fund leverage and estimated hedge fund leverage when these are unobserved following Eq. (2) and the estimation method outlined in Appendix D using all macro and fund-specific variables and fund-fixed effects. The data sample is from December 2004 to October 2009.
different ways. This pattern is also repeated in each of the hedge fund sectors. The largest difference in the volatility of gross leverage compared to net leverage is for relative value, where gross and net leverage standard deviations are 1.22 and 0.20, respectively. The mean of net leverage for relative value is also much lower, at 0.82, than the average level of gross leverage at 4.84. The low volatility of net leverage for relative value funds is consistent with these funds maintaining balanced long–short positions where a large number of their active bets consist of taking advantage of relative pricing differentials between assets. The stable and low net leverage for relative value funds could also imply that focusing on gross leverage overstates the market risk of this hedge fund sector. An interesting episode for equity hedge funds is the temporary ban on shorting financial stocks which was imposed in September 2008 and repealed one month later (see Boehmer, Jones, and Zhang, 2009, for details). Equity
hedge fund leverage was already trending downwards prior to this period beginning in mid-2007 and there is no noticeable additional effect in September or October 2008 for gross leverage or long-only leverage. However, Fig. 6 shows there is a small downward dip in net leverage during these months with net leverage being 0.48, 0.44, and 0.50 during the months of July, September, and October 2008, respectively. Thus, this event seems to affect the short leverage positions of equity funds, but the overall effect is small. This could be because the ban affected only the financial sector or because these hedge funds were able to take offsetting trades in derivatives markets or other non-financial firms to maintain their short positions. Finally, we observe a high level of covariation for net and long-only leverage in Fig. 6 across all hedge funds and within sectors. This is similar to the high degree of comovement of gross leverage across sectors in Fig. 4.
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
Table 3 Correlations of gross, net, and long-only leverage. The table reports correlations of the posterior means of gross, net, and long-only leverage for all hedge funds and for hedge fund sectors at a monthly frequency. Gross leverage is a sum of long and short exposures as a portion of assets under management (AUM). Net leverage is a difference of long and short exposures as a portion of AUM. Long-only leverage is the long exposure as a portion of AUM. The hedge fund leverage ratios consist of all observed hedge fund leverage and estimated hedge fund leverage when these are unobserved following Eq. (2) and the estimation method outlined in Appendix D using all macro and fund-specific variables and fund-fixed effects. The data sample contains 8136 monthly observations that cover 208 hedge funds during a period from December 2004 to October 2009. Gross
Net
Long-only
Gross
Net
Long-only
113
Table 4 Cross-correlations of hedge fund leverage within sectors. The table reports correlations of the posterior means of leverage of hedge funds (HF) and average leverage of their specific strategies (RV, EQ, ED, CR) for each of the definitions of hedge fund leverage: Gross leverage (Panel A), Net leverage (Panel B), and Long-only leverage (Panel C) separately at a monthly frequency. Gross leverage is a sum of long and short exposures as a portion of assets under management (AUM). Net leverage is a difference of long and short exposures as a portion of AUM. Long-only leverage is the long exposure as a portion of AUM. The hedge fund leverage ratios consist of all observed hedge fund leverage and estimated hedge fund leverage when these are unobserved following Eq. (2) and the estimation method outlined in Appendix D using all macro and fund-specific variables and fund-fixed effects. The data sample contains 8136 monthly observations that cover 208 hedge funds during a period from December 2004 to October 2009.
Panel A: All hedge funds Gross Net Long-only
1.000 0.927 0.994
1.000 0.962
Hedge fund strategies
1.000
Relative value
Equity
Gross Net Long-only
1.000 0.490 0.955
1.000 0.910
1.000
Event-driven Gross Net Long-only
1.000 0.835 0.974
1.000 0.725
1.000
Credit 1.000 0.938
RV
EQ
ED
CR
1.000 0.930 0.761 0.846 0.836
1.000 0.557 0.650 0.738
1.000 0.899 0.853
1.000 0.786
1.000
1.000 0.780 0.932 0.963 0.921
1.000 0.695 0.657 0.578
1.000 0.857 0.854
1.000 0.879
1.000
1.000 0.683 0.736 0.751
1.000 0.920 0.917
1.000 0.857
1.000
Panel A: Gross leverage
Panel B: Hedge fund sectors
1.000 0.876 0.997
All hedge funds (HF)
1.000
1.000 0.805 0.981
All hedge funds (HF) Relative value (RV) Equity (EQ) Event-driven (ED) Credit (CR) Panel B: Net leverage
1.000 0.904
1.000
We report correlations for all hedge funds and across sectors for each leverage measure in Table 4. These cross correlations are high indicating that each leverage measure generally rises and falls in tandem for each hedge fund sector. In particular, Panel A shows that although the relative value sector contains the smallest number of funds, the correlation of gross leverage of relative value with all hedge funds is 0.93. The lowest correlation is between relative value and event-driven, at 0.65. Put another way, looking at gross leverage across all hedge funds is a good summary measure for what is happening to gross leverage in the various hedge fund sectors. Panels B and C also show that this is true for net and long-only leverage. Thus, sector-level variation in hedge fund leverage is similar to the aggregate-level behavior of leverage across all hedge funds. 5.2. Macro predictors of hedge fund leverage In this section, we discuss the ability of various macro and fund-specific variables to predict hedge fund leverage. We first report estimates of the predictive model in Eq. (2) taking only economy-wide variables and report the results in Table 5. We consider gross leverage in Panel A, net leverage in Panel B, and long-only leverage in Panel C. In all regressions we include lagged leverage as an independent variable. Regressions (1)–(8) add each macro variable one at a time together with lagged leverage, while all variables jointly enter regression (9). We use fund-level fixed effects in all regressions. In each panel, the coefficients on lagged leverage are negative with very high posterior t-statistics. The lagged leverage coefficients
All hedge funds (HF) Relative value (RV) Equity (EQ) Event-driven (ED) Credit (CR)
Panel C: Long-only leverage All hedge funds (HF) Relative value (RV) Equity (EQ) Event-driven (ED) Credit (CR)
1.000 0.923 0.866 0.915 0.877
range from 0.20 to 0.31 indicating that hedge fund leverage is strongly mean-reverting. Panel A, which reports results for gross leverage, shows that all the macro variables, with the exception of aggregate hedge fund flows, significantly predict changes in hedge fund leverage when used in conjunction with past leverage. The largest coefficient in magnitude is on investment bank CDS protection, where for a 1% increase in CDS spreads, next-month hedge fund leverage shrinks by 11.5%, on average. As investment banks perform well (regression (2)) or the S&P 500 posts higher returns (regression (3)), hedge fund leverage tends to increase next month. We observe that when volatility increases, as measured by VIX (regression (4)), or assets become riskier, as measured by the TED spread (regression (6)), hedge fund leverage tends to decrease over the next month. This is consistent with hedge funds targeting a specific risk profile of their returns, where an increase in the riskiness of the assets leads to a reduction in their exposure. In particular, a 1% movement in VIX predicts that gross leverage declines by 0.9% over the next month and a 1% increase in the TED spread predicts gross leverage will fall over the next month by 15.2%.
114
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
0.2446 [ 32.0] 11.49 [ 12.4]
0.2228 [ 28.8]
0.2250 [ 30.7]
0.2423 [ 31.8]
0.2378 [ 30.0]
0.2288 [ 29.5]
0.2401 [ 31.5]
0.2347 [ 30.9]
0.2447 [ 32.0] 9.3278 [ 3.54] 0.0436 [ 0.26] 0.6750 [2.09] 0.1010 [ 0.51] 6.6629 [ 2.35] 7.5973 [1.90] 10.32 [ 2.80] 0.0934 [0.38] 0.131
Panel A: Gross leverage Past gross lev IB CDS IB ret
0.5968 [6.11]
S&P 500 ret
1.3684 [7.68]
VIX
0.9238 [ 11.9]
LIBOR
4.3489 [7.66]
TED spread
15.19 [ 8.64]
Term spread
6.8214 [ 9.54]
Agg HF flows Adjusted R
2
0.130
0.118
0.121
0.129
0.120
0.122
0.123
7.7129 [1.15] 0.120
0.3114 [ 3.48] 3.3967 [ 3.69]
0.2931 [ 3.75]
0.3003 [ 3.31]
0.3013 [ 4.22]
0.3053 [ 3.61]
0.2965 [ 3.49]
0.3036 [ 3.90]
0.2959 [ 3.86]
Panel B: Net leverage Past net lev IB CDS IB ret S&P 500 ret VIX
0.2644 [5.88] 0.5101 [5.92] 0.2854 [ 4.83]
0.3052 [ 3.82] 1.1898 [ 1.04] 0.1340 [1.83] 0.0784 [0.57] 0.1051 [ 1.22]
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
Table 5 Macro predictors of hedge fund leverage. The table reports regression coefficients of Eq. (2) to predict changes in gross leverage (Panel A), net leverage (Panel B), and long-only leverage (Panel C) over the next month. Gross leverage is a sum of long and short exposures as a portion of assets under management (AUM). Net leverage is a difference of long and short exposures as a portion of AUM. Long-only leverage is the long exposure as a portion of AUM. The first row in each panel reports the coefficient on the lagged leverage variable and the other right-hand side variables are all macro variables. Each column reports a different regression. ‘‘IB CDS’’ is the equity market-value weighted cost of CDS protection on defaults on 10-year senior bonds of major investment banks (IB), ‘‘IB ret’’ is the return on the market-value weighted portfolio of IB common stocks, ‘‘S&P 500 ret’’ is the monthly total return on the S&P500 index, ‘‘Agg HF flows’’ is the past three-month flow on the aggregate hedge fund industry as reported by Barclay Hedge. All variables are described in detail in Appendix B. The table reports posterior means of coefficients and posterior means of t-statistics in square brackets below each coefficient. All estimations have fund-fixed effects. Appendix D contains details of the estimation, including the implementation of fixed effects and the calculation of the adjusted R2. The data sample contains 8136 monthly observations that cover 208 hedge funds during a period from December 2004 to October 2009.
LIBOR
1.4241 [2.75]
TED spread
4.5400 [ 4.26]
Term spread
2.0531 [ 3.16]
Agg HF flows 0.155
0.150
0.151
0.155
0.151
0.149
0.153
0.3295 [3.29] 0.149
0.2376 [ 31.2] 6.9342 [ 12.6]
0.2157 [ 27.0]
0.2177 [ 29.1]
0.2351 [ 31.3]
0.2301 [ 28.4]
0.2219 [ 29.9]
0.2324 [ 29.4]
0.2273 [ 30.1]
Adjusted R2
0.9969 [0.85] 0.7010 [ 0.43] 0.5129 [0.34] 0.0668 [ 0.61] 0.156
Panel C: Long-only leverage Past long lev IB CDS
0.4228 [6.77]
S&P 500 ret
0.9124 [8.52]
VIX
0.5741 [ 12.7]
LIBOR
2.5667 [7.59]
TED spread
9.4262 [ 8.51]
Term spread
4.0850 [ 9.48]
Agg HF flows Adjusted R2
0.126
0.116
0.118
0.126
0.116
0.118
0.119
0.6891 [7.81] 0.117
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
IB ret
0.2373 [ 29.9] 4.9876 [ 3.39] 0.0433 [0.40] 0.3891 [1.92] 0.0918 [ 0.79] 2.8146 [ 1.58] 3.2221 [1.31] 4.6731 [ 2.00] 0.0152 [0.10] 0.127
115
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In regression (5), the sign on LIBOR is unexpectedly positive. We might expect increases in funding rates, of which LIBOR should be a large component, to decrease future leverage. Instead, the coefficient on LIBOR is positive at 4.35. This is surprising given that Fig. 4 shows that hedge fund leverage decreases before and during the financial crisis. However, in the joint regression (9), the coefficient on LIBOR flips sign and is now negative at 6.66. Thus, controlling for other variables, which are significantly correlated especially over the 2007–2009 period, produces the expected negative relation between LIBOR and future leverage changes. In fact, LIBOR, the TED spread, CDS spreads, and VIX are very highly correlated, all around 90%, and capture common effects associated with the financial crisis over the sample period. Thus, it is not surprising that the coefficient on VIX also becomes insignificant in the joint regression (9). In contrast, the term spread coefficients are consistently negative as expected, which implies that higher expected funding costs reduce leverage next period. In regression (9), where we take all macro variables together, the predictors of hedge fund leverage which have posterior t-statistics greater than two in absolute value are investment bank CDS spreads, the lagged S&P 500 return, LIBOR, and the term spread. Increases in current funding costs, as measured by CDS spreads and LIBOR predict decreases in leverage, as do increases in future expected funding costs, as measured by the term spread. In Panels B and C of Table 5, we report estimates of the same regressions for net and long-only leverage. In Panel B, all the coefficients on the macro variables are significant in the bivariate regressions (1)–(8), with the same signs as Panel A for gross leverage but with smaller magnitudes. However, there are no significant macro predictors of net leverage in the joint regression (9). Thus, overall net leverage is mostly determined only by its lagged value. Said differently, the only significant distinguishing feature of net leverage predictability is that it is highly mean-reverting. In Panel C, long-only leverage is significantly predicted by each individual macro variable in regressions (1)–(8) with the same signs as gross leverage in Panel A. The last column in Panel C for regression (9) reports that increases in the cost of investment bank CDS protection and the term spread significantly lower future long leverage. This indicates that most of the predictability in gross leverage by macro determinants in Panel A is coming from the predictability of longonly leverage by macro variables. 5.3. Fund-specific predictors of hedge fund leverage In Table 6 we examine the ability of fund-specific variables to predict hedge fund leverage. All the regressions in Table 6 include the macro predictors used in Table 5 which are not reported as they have the same signs, same significance levels, and approximately the same magnitudes, as the coefficients reported in the macro-only regressions of Table 5. The main surprising result of Table 6 is that, with one exception, all of the fund-specific variables have insignificant
coefficients. This is for both the case of the bivariate regressions (1)–(4), where the fund-specific variables are used together with past leverage, and in the case of the joint regression (5). This occurs for all three measures of leverage in Panels A–C. Moreover, the adjusted R2s of the macro-only specifications in Table 5 are almost identical to their counterparts in the fund-specific variable specifications in Table 6. This finding suggests that hedge funds exhibit a high degree of similarity in their leverage exposures that depends largely only on the aggregate state of the economy. Said differently, predictable changes in hedge fund leverage are mostly systematic and there are few fund-level idiosyncratic effects.15 The only fund-specific variable that has a posterior t-statistic larger than two is hedge fund return volatility. In Panel A for gross leverage, this variable has a coefficient of 1.41 in the joint regression (5) with a posterior t-statistic of 2.11. The bivariate regression (2) also has a similar coefficient on fund-specific volatility of 1.34 with a posterior t-statistic of 1.93. In the deleveraging cycles of Brunnermeier and Pedersen (2009) and others, fund return volatility affects margins and since margins correspond to limits in leverage, increases in fund return volatility should lead to lower leverage levels of hedge funds. Thus, our findings confirm the prediction of Brunnemeier and Pedersen of a significantly negative coefficient on return volatility. This is essentially the only significant fund-specific effect and it occurs only for gross leverage. 5.4. Contemporaneous relations with hedge fund leverage We now investigate the contemporaneous relations of gross leverage in the model in Eq. (3) with macro and fund-specific variables. Table 7 reports the regression coefficients of the contemporaneous model (3) and compares them with the predictive model (2), which are identical to regression (9) of Table 5 for the macro-only predictors and regression (5) of Table 6 for the fundspecific predictors. The contemporaneous model has significantly lower adjusted R2s than the predictive model, at 0.08 vs. 0.13 for the macro-only system and 0.09 vs. 0.13 for the fundspecific variable system. Thus, the fit of the contemporaneous model without lagged leverage is worse than the predictive system with lagged leverage. Hence, the lagged leverage coefficient is an extremely important predictor. The contemporaneous model does have significantly autocorrelated error terms, with estimates of fe of 0.25 and 0.55 for the macro-only and fund-specific variable cases, respectively. As a specification check, we compute the autocorrelation of error terms in the predictive specification. This turns out to be 0.03. Thus, absorbing 15 Our filters remove young hedge funds which tend to be smaller and tend to have higher funding costs. Thus, our data filters could account for the lack of a relation between AUM and hedge fund leverage. The lack of a relation between past flows and leverage can be due to notice period, lockups, and gates restrictions (see, for example, Ang and Bollen, 2010), which give managers advance notice of flows before they actually occur.
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
117
Table 6 Fund-specific predictors of hedge fund leverage. The table reports regression coefficients of Eq. (2) to predict changes in gross leverage (Panel A), net leverage (Panel B), and long-only leverage (Panel C) over the next month. Gross leverage is a sum of long and short exposures as a portion of assets under management (AUM). Net leverage is a difference of long and short exposures as a portion of AUM. Long-only leverage is the long exposure as a portion of AUM. The first row in each panel reports the coefficient on the lagged leverage variable and the other right-hand side variables are fund-specific and macro variables. Each column reports a different regression. ‘‘Past ret’’ is the fund’s return in the past month, ‘‘12-Month vol’’ is the volatility of the hedge fund’s returns computed using monthly data over the past 12 months, ‘‘3-Month flows’’ is the hedge fund flow over the past three months computed using Eq. (1), and ‘‘Log AUM’’ is the logarithm of each hedge fund’s AUM. All the regression specifications also control for the macro predictors used in Table 5: the cost of CDS protection on major investment banks, the return on the market-value weighted portfolio of investment banks, the S&P 500 return, option VIX volatility, LIBOR, the TED spread, the term spread, and aggregate hedge fund flows. All variables are described in detail in Appendix B. The table reports posterior means of coefficients and posterior means of t-statistics in square brackets below each coefficient. All estimations have fund-fixed effects. Appendix D contains details of the estimation, including the implementation of fixed effects and the calculation of the adjusted R2. The data sample contains 8136 monthly observations that cover 208 hedge funds during a period from December 2004 to October 2009. (1)
(2)
(3)
(4)
(5)
0.2443 [ 30.3] 0.1288 [ 0.49]
0.2452 [ 30.5]
0.2445 [ 30.5]
0.2451 [ 30.1]
0.2455 [ 31.1] 0.2151 [ 0.82] 1.4139 [ 2.11] 0.0024 [ 0.10] 0.0414 [ 1.43] 0.131
Panel A: Gross leverage Past gross lev Past ret 12-Month vol
1.337 [ 1.93]
3-Month flows
0.0053 [ 0.21]
Log AUM Adjusted R2
0.130
0.131
0.131
0.0325 [ 1.13] 0.131
0.3107 [ 3.69] 0.2357 [ 1.93]
0.3066 [ 3.99]
0.3106 [ 3.59]
0.3089 [ 3.71]
Panel B: Net leverage Past net lev Past ret 12-Month vol
0.1615 [0.51]
3-Month flows
0.0142 [1.35]
Log AUM Adjusted R2
0.157
0.156
0.156
0.0183 [ 1.41] 0.157
0.2371 [ 30.4] 0.1923 [ 1.20]
0.2372 [ 32.1]
0.2373 [ 31.1]
0.2381 [ 29.9]
0.3098 [ 3.62] 0.2057 [ 1.64] 0.0543 [0.18] 0.0153 [1.49] 0.0201 [ 1.45] 0.157
Panel C: Long-only leverage Past long lev Past ret 12-Month vol
0.6278 [ 1.60]
3-Month flows
0.0048 [0.33]
Log AUM Adjusted R2
0.127
0.127
the persistence of leverage by past leverage on the righthand side (RHS) absorbs most of the serial correlation effects—when lagged leverage is included as a regressor, there seems to be little gained by making the error terms autocorrelated. Table 7 shows two major differences in sign between the predictive model coefficients and the contemporaneous determinants of leverage in the macro-only specification. First, the coefficient on the S&P 500 return is positive at 0.67 in the predictive model and negative at 0.94 in the contemporaneous model. As the stock market increases, leverage contemporaneously decreases—by definition, as
0.127
0.0236 [ 1.38] 0.127
0.2375 [ 30.6] 0.2258 [ 1.41] 0.7289 [ 1.76] 0.0045 [0.31] 0.0284 [ 1.60] 0.127
asset values increase. But, higher stock returns in the past forecast that hedge fund leverage will increase in the future. Second, the coefficient on LIBOR is contemporaneously positive, at 3.44, but insignificant, in the contemporaneous model compared to a significantly negative coefficient of 6.66 in the predictive model. We expect the coefficient to be negative, which it is in the predictive regression. The unexpected positive sign in the contemporaneous model could be due to lack of power or the fact that true funding costs could have much shorter duration and be more variable than LIBOR. The LIBOR interest rate is, of course, a valid predictor even though it could be an
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Table 7 Contemporaneous relations with gross hedge fund leverage. The table reports regression coefficients for macro and fund-specific variables of the ‘‘Predictive’’ model in Eq. (2) and the ‘‘Contemporaneous’’ model in Eq. (3) for gross hedge fund leverage. Gross leverage is a sum of long and short exposures as a portion of assets under management (AUM). The predictive model coefficients are identical to regression (9) of Table 5 for the macro-only predictors and regression (5) of Table 6 for the fund-specific predictors. The ‘‘Fund-specific variables’’ regressions control for the macro predictors listed in the ‘‘Macro variables’’ regressions: ‘‘IB CDS’’ is the equity market-value weighted cost of CDS protection on defaults on 10-year senior bonds of major investment banks (IB), ‘‘IB ret’’ is the return on the market-value weighted portfolio of IB common stocks, ‘‘S&P 500 ret’’ is the monthly total return on the S&P 500 index, ‘‘Agg HF flows’’ is the past three-month flow on the aggregate hedge fund industry as reported by Barclay Hedge. For the fund-specific variables: ‘‘Past ret’’ is the fund’s return in the past month, ‘‘12-Month vol’’ is the volatility of the hedge fund’s returns computed using monthly data over the past 12 months, ‘‘3-Month flows’’ is the hedge fund flow over the past three months computed using Eq. (1), and ‘‘Log AUM’’ is the logarithm of each hedge fund’s AUM. All variables are described in detail in Appendix B. The table reports posterior means of coefficients and posterior means of t-statistics in square brackets below each coefficient. All estimations have fundfixed effects. Appendix D contains details of the estimation, including the implementation of fixed effects and the calculation of the adjusted R2. The data sample contains 8136 monthly observations that cover 208 hedge funds during a period from December 2004 to October 2009. Predictive
Contemporaneous
Macro variables Past leverage IB CDS IB ret S&P 500 ret VIX LIBOR TED spread Term spread Agg HF flows
Contemporaneous
0.2455 [ 31.1] 0.2151 [ 0.82] 1.4139 [ 2.11] 0.0024 [ 0.10] 0.0414 [ 1.43]
0.1123 [ 0.35] 4.3495 [ 2.35] 0.0530 [ 1.11] 0.2552 [1.75]
0.131
0.5547 [45.5] 0.086
Fund-specific variables 0.2447 [ 32.0] 9.3278 [ 3.54] 0.0436 [ 0.26] 0.6750 [2.09] 0.1010 [ 0.51] 6.6629 [ 2.35] 7.5973 [1.90] 10.32 [ 2.80] 0.0934 [0.38]
fe Adjusted R2
Predictive
0.131
Past leverage 1.3666 [ 0.38] 0.2248 [ 0.90] 0.9419 [ 2.02] 1.4324 [ 4.79] 3.4420 [0.76] 8.7629 [1.49] 12.237 [ 2.09] 1.3419 [3.13] 0.2494 [32.9] 0.080
inferior instrument to proxy for leverage costs in a contemporaneous model. The coefficient on VIX and on aggregate hedge fund flows have the same sign in the predictive and contemporaneous systems, but while their effects are statistically insignificant in predicting hedge fund leverage, they are significantly contemporaneously correlated. In the contemporaneous model, VIX has a coefficient of 1.43 with a posterior t-statistic of 4.79. When VIX increases, it is well known that asset prices fall (the leverage effect), which accounts for the negative contemporaneous coefficient. This finding is also consistent with the prediction of Fostel and Geanakoplos (2008), among others, where leverage decreases during times of high volatility. It is also consistent with hedge funds increasing (decreasing) leverage during less (more) volatile times to achieve a desired target level of volatility. As a predictor, the forecasting ability of VIX for future leverage is largely subsumed by lagged leverage as a regressor. The finding that aggregate hedge fund flows are contemporaneously correlated with hedge fund leverage goes against Stein (2009), who predicts that the entry of new capital should decrease the leverage of arbitrageurs. The last two columns of Table 7 report coefficients for fund-specific variables for the predictive and contemporaneous systems, where both estimations control for the macro variables. The results are similar. The only
Past ret 12-Month vol 3-Month flows Log AUM
fe Adjusted R2
significant variable in both cases is the fund’s rolling 12month volatility of returns. The effect, however, is much stronger contemporaneously (with a coefficient of 4.35 and a posterior t-statistic of 2.35) compared to the predictive model (with a coefficient of 1.41 with a posterior t-statistic of 2.11). While the negative forecasting ability of fund-specific volatility for future leverage is consistent with deleveraging cycle models, the contemporaneous relation is even stronger. Like the effect of VIX, this can be a reflection of the leverage effect, but it is also consistent with hedge funds using leverage to target a desired level of volatility. 5.5. Hedge fund leverage vs. finance sector leverage In this section we compare hedge fund leverage to the leverage of listed financial companies. We focus on aggregate gross hedge fund leverage, but our previous results show that the net and long-only leverage ratios exhibit similar patterns both for all hedge funds and within hedge fund sectors. We define the leverage of listed firms as the value of total assets divided by market value, that is, we study market leverage. Other authors studying the leverage of financial institutions like Adrian and Shin (2009, 2010), among others, use book leverage rather than market leverage. We use market leverage because the market equity value is closest to the NAV of
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
3
50
2.5
40
2 30 1.5
1
Hedge funds Banks Investment banks Finance sector
20
10
0.5
0 2005
2006
2007
2008
2009
119
Table 8 Correlations of hedge fund and finance sector leverage. The table reports correlations of average levels of leverage of hedge funds (HF) and average leverage of their specific strategies—relative value (RV), equity (EQ), event-driven (ED), and credit (CR)—with average leverage of bank holding companies (banks), investment banks (Bear Stearns, Citibank, Credit Suisse, Goldman Sachs, HSBC, JP Morgan, Lehman Brothers, Merrill Lynch, and Morgan Stanley), and the finance sector separately for each definition of hedge fund leverage: Gross leverage (Panel A), Net leverage (Panel B), and Long-only leverage (Panel C) at the monthly frequency. We compute the leverage of finance subsectors following Appendix B. The leverage of hedge funds consists of all observed hedge fund leverage and estimated hedge fund leverage when these are unobserved following Eq. (2) and the estimation method outlined in Appendix D using all macro and fund-specific variables and fund-fixed effects. Gross leverage is a sum of long and short exposures as a portion of assets under management (AUM). Net leverage is a difference of long and short exposures as a portion of AUM. Long-only leverage is the long exposure as a portion of AUM. The data sample is from December 2004 to October 2009.
0 2010
Fig. 7. Hedge fund and finance sector leverage. We compare average gross hedge fund leverage with the leverage of banks, investment banks, and the finance sector. The left-hand axis corresponds to average gross hedge fund leverage and the right-hand axis corresponds to the leverage of banks, investment banks, and the finance sector. The hedge fund leverage ratios consist of all observed hedge fund leverage and estimated hedge fund leverage when these are unobserved following Eq. (2) and the estimation method outlined in Appendix D using all macro and fund-specific variables and fund-fixed effects. The finance sector leverage is constructing following the method described in Appendix B. The data sample is from December 2004 to October 2009.
a hedge fund (see Appendix A). We compare hedge fund leverage to the leverage of banks, investment banks, and the entire finance sector, which we describe in more detail in Appendix B.16 Fig. 7 plots the average level of gross hedge fund leverage in the solid line using the left-hand scale and plots the leverage of the financial sectors in various dashed lines on the right-hand scale. The level of gross hedge fund leverage is the same as in Fig. 4 and starts to decline in mid-2007. Gross hedge fund leverage is modest, between 1.5 and 2.5, compared to the leverage of listed financial firms: the average leverage of investment banks and the whole finance sector over our sample are 14.2 and 9.4, respectively. Fig. 7 shows that leverage in each of the banking and investment banking subsectors and the whole finance sector are highly correlated. Finance sector leverage starts to rise when hedge fund leverage starts to fall in 2007, continues to rise in 2008, and then shoots up in early 2009 before reverting back to more normal levels in late 2009. This counter-cyclical behavior of financial leverage, where market leverage increases during bad times, is consistent with the model of He and Krishnamurthy (2009).17
16 He, Khang and Krishnamurthy (2010) contrast the behavior of commercial and investment bank leverage and show they are different. However, many investment banks were either acquired or became commercial banks during the financial crisis. Since our focus is on hedge fund leverage, we choose to contrast hedge fund leverage with the leverage of all of these institutions. 17 Other authors like Fostel and Geanakoplos (2008), Adrian and Shin (2009, 2010), and Shleifer and Vishny (2010) emphasize the pro-cyclicality
Hedge fund strategies All hedge funds
RV
EQ
ED
CR
0.884 0.823 0.884
0.820 0.734 0.812
0.613 0.536 0.608
0.774 0.733 0.776
0.658 0.586 0.656
0.873 0.845 0.884
0.623 0.525 0.610
0.740 0.766 0.764
0.923 0.891 0.931
0.772 0.765 0.789
0.801 0.712 0.791
0.735 0.680 0.738
0.867 0.828 0.872
0.722 0.667 0.726
Panel A: Gross leverage Banks Investment banks Finance sector Panel B: Net leverage Banks Investment banks Finance sector
Panel C: Long-only leverage Banks Investment banks Finance sector
0.893 0.840 0.896
The remarkable takeaway of Fig. 7 is that hedge fund leverage is counter-cyclical to the market leverage of financial intermediaries. As hedge fund leverage declines in 2007 and continues to fall over the financial crisis in 2008 and early 2009, the leverage of financial institutions continues to inexorably rise. The highest level of gross hedge fund leverage is 2.6 at June 2007, well before the worst periods of the financial crisis. In contrast, the leverage of investment banks is 10.4 at June 2007 and severely spikes upward to reach a peak of 40.7 in February 2009. During this month, the U.S. Treasury takes equity positions in all of the major U.S. banks. In contrast, hedge fund leverage is very modest at 1.4 at that time. Note that hedge fund leverage started to decline at least six months before the financial crisis began in 2008. We show the counter-cyclical behavior of hedge fund leverage to finance sector leverage more completely in Table 8. We report correlation matrices of gross, net, and long-only hedge fund leverage in Panels A–C, respectively, with banks, investment banks, and the finance sector.
(footnote continued) of leverage. Many of these authors focus on accounting or book leverage rather than market leverage. Market leverage increases to very high levels during the financial crisis because stock prices of financial institutions are very low at this time.
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These correlations are very negative. For example, the correlations of gross leverage for all hedge funds with the finance sector are 0.88, 0.82, and 0.88 for banks, investment banks, and the finance sector, respectively. The correlations are very similar for each listed finance sector. The correlations between financial firms and hedge funds are also highly negative for each hedge fund strategy. Clearly, hedge fund leverage moves in the opposite way during the financial crisis to the leverage of regulated and listed financial intermediaries. There are at least two explanations for the countercyclical behavior of hedge fund leverage with respect to listed financial intermediary leverage. First, hedge funds voluntarily reduced leverage much earlier than banks as part of their regular investment process of searching for trades with excess profitability and funding them. An alternative explanation is that the reduction of hedge fund leverage was involuntary. Hedge funds often obtain their leverage through prime brokers which are attached to investment banks and other financial firms. The change in hedge fund leverage could be caused by the suppliers of leverage to hedge funds curtailing funding. Risk managers in the prime brokerage divisions of investment banks could have been prescient in partially forecasting the turbulent periods in 2008 and forced hedge funds to reduce leverage earlier. Only when times were very bad in late 2008 did investment banks adjust their own balance sheet leverage. While this story cannot be refuted, the substantial lead time of six to eight months, shown clearly in Fig. 7, where hedge funds reduced leverage before 2008 makes this unlikely. Furthermore, anecdotal evidence through the Fund’s industry contacts suggests that prime brokers were not substantially increasing funding costs in early to mid-2007. 5.6. Hedge fund vs. finance sector exposure We last attempt to measure the dynamic total exposure of the hedge fund industry. We do this by multiplying leverage by AUM to obtain an estimate of the total exposure. This exercise is, of course, subject not only to the estimation error of our procedure, but also the measurement error of total hedge fund AUM. Since hedge funds are not required to report, the estimates of aggregated hedge fund AUM in the public databases are probably conservative. Thus, our estimated levels of hedge fund exposure have to be interpreted carefully. Fig. 8 plots total hedge fund exposure by taking the estimated gross leverage across hedge funds and aggregated hedge fund AUM reported from the Barclay Hedge database. In the top panel, we plot hedge fund exposure in the solid line (left-hand scale) and hedge fund AUM in the dashed-dot line (right-hand scale) in trillions of dollars. The correlation between the two series is 0.83. Both AUM and exposure increase over 2006 and 2007 and start falling after June 2008. The total hedge fund exposure starts the sample in January 2005 at $2.5 trillion, steadily increases, and then drops from a peak of $4.9 trillion in June 2008 to a low of $1.7 trillion in March 2009. This decrease represents an overall drop of 65% from peak. The correlations of hedge fund AUM and total exposure with gross leverage are only 0.08 and 0.61, respectively. Note that the
6 5
Hedge funds
2.5
Hedge fund exposure Hedge fund AUM
2
4 3
1.5
2 1 2005
2006
2007
2008
2009
1 2010
Investment banks
8
IB assets IB market value
7
0.8 0.7 0.6
6
0.5
5
0.3
0.4 0.2
4 3 2005
0.1 2006
2007
2008
2009
0 2010
Fig. 8. Hedge fund and investment bank gross exposure and leverage. We graph the gross exposure and AUM of hedge funds in Panel A and the gross exposure and market value of equity of investment banks (IB) in Panel B. For hedge funds, we take gross leverage across all hedge funds which consists of observed gross leverage and estimated gross leverage when these are unobserved following Eq. (2) and the estimation method outlined in Appendix D using all macro and fund-specific variables and fund-fixed effects. The hedge fund exposure is computed by multiplying the gross leverage by the aggregated AUM of hedge funds from the Barclays Hedge database. Investment bank exposure is the total amount of assets held by investment banks. The left-hand axes in both panels correspond to AUM or equity. The market value of investment banks is the value of common equity. Appendix B contains further details on these variables. The right-hand axes correspond to gross exposure. The scale of both axes is in trillions of dollars. The data sample is from December 2004 to October 2009.
decrease in hedge fund leverage from 2007 to 2009 is from around 2.3–1.5. Thus, hedge fund exposure is primarily driven by AUM and the dramatic fall in total hedge fund exposure over the financial crisis is caused by investors withdrawing capital from the hedge fund sector. While many studies emphasize the role of leverage cycles, Fig. 8 highlights that inflows and outflows are important components of determining total exposure for hedge funds. The bottom panel of Fig. 8 plots the total exposure and market value for investment banks for comparison. Exposure is defined as the total amount of assets held on the balance sheet. Investment bank and hedge fund exposure have similar patterns in the top and bottom panels of Fig. 8 and have a high correlation of 0.8. There is a sharp drop in investment bank assets in March 2009 which is due to large writedowns in balance sheets during this quarter. Total assets of investment banks decreased from $6.9 trillion in early 2008 to a low of $3.8 trillion in February 2009. Towards the end of the sample, assets rebounded to $5.2 trillion as financial markets stabilized. We graph the relative exposure of hedge funds to investment banks and the finance sector in Fig. 9, which is measured as the ratio of hedge fund exposure to total assets for each of the investment banks and finance
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
0.8
0.35
0.7
0.3
0.6
0.25
0.5
0.2
0.4
0.15 Relative exposure of HF to IB assets Relative exposure of HF to FS assets
0.3 2005
2006
2007
2008
2009
0.1 2010
Fig. 9. Relative gross exposures of hedge funds to investment banks and the finance sector. We plot the ratio of gross exposure of hedge funds (HF) to investment banks (IB) and the finance sector (FS). The gross exposure is computed by multiplying gross leverage and AUM in the case of hedge funds and is total assets in the case of investment banks and the finance sector. For hedge funds, we take gross leverage across all hedge funds which consists of observed gross leverage and estimated gross leverage when these are unobserved following the estimation method outlined in Appendix D using all macro and fund-specific variables and fund-fixed effects. The left-hand axis corresponds to the relative gross exposure of hedge funds to the assets of investment banks, while the right-hand axis corresponds to the relative exposure of hedge funds to the assets of the finance sector. The data sample is from December 2004 to October 2009.
sector. The ratio of hedge fund exposure to investment banks (the finance sector) is approximately 65% (30%) until early 2008. Then, the events of the financial crisis in 2008 cause hedge fund exposure to decline to 40% and 15% of the total asset base of investment banks and the finance sector, respectively. Thus, total exposure of hedge funds is modest compared with the exposure of listed financial intermediaries, especially recently after the financial crisis, and it is modest even before the start of the financial crisis in mid-2007. 6. Conclusion This paper presents, to our knowledge, the first formal analysis of hedge fund leverage using actual leverage ratios. Our unique data set from a fund-of-hedge-funds provides us with both a time series of hedge fund leverage from December 2004 to October 2009, which includes the worst periods of the financial crisis, and a cross-section to investigate the determinants of the dynamics of hedge fund leverage. We uncover several interesting and important results. First, hedge fund leverage is fairly modest, especially compared with the listed leverage of broker/dealers and investment banks. The average gross leverage (including long and short positions) across all hedge funds is 2.1. While there are some funds with large leverage, well above 30, most hedge funds have low leverage partly due to most hedge funds belonging to the equity sector where leverage is low. Gross leverage for other hedge fund
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sectors like relative value is higher, at 4.8, over the sample. Second, hedge fund leverage is counter-cyclical to the market leverage of listed financial intermediaries. In particular, hedge fund leverage decreases prior to the start of the financial crisis in mid-2007, where the leverage of investment banks and the finance sector continues to increase. At the worst periods of the financial crisis in late 2008, hedge fund leverage is at its lowest while the leverage of investment banks is at its highest. We find that the dispersion of hedge fund leverage does not markedly change over the financial crisis and that the leverage of each hedge fund sector moves in a similar pattern to aggregate hedge fund leverage. However, we find that the total exposure of hedge funds is similar to the total exposure of investment banks even though the behavior of leverage is different. The main reason for this similar behavior is not the change in hedge fund leverage, but the withdrawal of assets from the hedge fund industry during 2008. Third, we find that the predictability of hedge fund leverage is mainly from economy-wide, systematic variables. In particular, decreases in funding costs as measured by LIBOR, interest rate spreads, and the cost of default protection on investment banks predict increases in hedge fund leverage over the next month. Increases in asset prices measured by lagged market returns also predict increases in hedge fund leverage. We find the only fundspecific variable significantly predicting hedge fund leverage is return volatility, where increases in fund return volatility tend to reduce leverage. There is little evidence that hedge fund leverage changes are predictable by hedge fund flows or assets under management. Contemporaneously, hedge fund leverage decreases when VIX or fund-specific volatility increase and hedge fund leverage is positively related to aggregate hedge fund flows. An interesting direction for future work is to study hedge fund leverage and returns, since in theory, when managers perceive better investment opportunities, they should increase leverage. Thus, leverage levels can provide a crude measure of a hedge fund manager’s market outlook. Existing empirical work finds little relation at an unconditional level between leverage and returns at the stock level (see, e.g., Bhandari, 1988; Fama and French, 1992), which could be due to not accounting for endogenous leverage and investment choices. Hedge funds are a good laboratory to examine the relation between dynamic leverage management and returns because the underlying asset returns are more easily measured than the asset returns of corporations.
Appendix A. Examples of hedge fund leverage In order to illustrate how our definitions of leverage differ for various portfolios, we present several simple examples off highly stylized hedge funds. In all our examples, we assume no fees are paid so the gross value of the fund is the same as the net value of the fund. All the transactions are done instantaneously and we report the overall balance sheet of the fund at the same date. For
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simplicity, assume there is only one share so the NAV per share is the same as the AUM of the fund. Example 1 (Long-only fund). Consider a hedge fund that has just obtained $10 in cash from investors. The hedge fund manager purchases securities worth $10. In addition, the hedge fund manager borrows $50 and invests those proceeds in a $50 long securities position. The NAV of the hedge fund is the difference between the long and short positions, which is $10, and is the same as the initial investment by investors. The balance sheet of the hedge fund after these transactions can be represented by: Long assets $60 Long securities
Short assets $50 Borrowed cash $10 NAV
In this case, the hedge fund has $60 of Long securities and $0 of Short securities on its balance sheet. As a result, gross leverage is 60/10¼6, net leverage is 60/10¼6, and long-only leverage is also 6. All these leverage measures coincide because there are no risky asset short positions and the long positions are levered by short cash positions. Note that an unlevered long-only fund, which holds long asset positions between zero and one together with cash, has positive leverage ratios less than one. All three leverage ratios – gross, net, and long-only – also coincide. In comparison, a corporate finance definition of leverage where assets are the sum of debt and equity would result in a zero leverage measure. This is because cash is counted as an asset on corporate balance sheets, but in our leverage definitions, only risky assets are included in the leverage measures. Example 2 (Dedicated long–short fund). Suppose a fund with an initial cash endowment of $10 uses that cash to purchase a $10 long security position. In addition, the fund places $50 in long–short bets in risky assets. The balance sheet of the fund is: Long assets $60 Long securities
Short assets $50 Short securities $10 NAV
leverage in Example 2 is equal to one, the combination of short risky and cash positions causes net leverage to be different from one. Example 4 (Dedicated short fund). Our final example is a dedicated short fund. The fund starts with $10 cash, which it pledges as a collateral to borrow $50 worth of assets. This represents a margin (haircut) of 20%. The proceeds from selling the securities result in cash received by the fund. These positions represent $60 of cash on the asset side of the balance sheet and $50 of short securities on the liability side of the fund’s balance sheet: Long assets $60 Long cash
Short assets $50 Short securities $10 NAV
In this case, the hedge fund has $0 of Long securities and $50 of Short securities on its balance sheet. Hence, the fund’s gross leverage is (0þ50)/10 ¼50/10¼ 5, the net leverage is (0 50)/10 ¼ 50/10 ¼ 5, and the long-only leverage is 0/10¼0. In the case when net leverage is negative, the fund is said to be net short, otherwise it is said to be net long. Since the fund is taking only active short positions, the leverage on the long-side of the balance sheet is zero. In the case of a fund buying or selling derivative securities instead of transacting in the physical or cash market, the previous examples hold if the derivatives are decomposed into underlying, but time-varying, positions in physical assets and risk-free securities at the reporting date. At a given time, once the derivatives are decomposed into replicating positions in underlying securities, the same leverage calculations can be performed. Appendix B. Macro data sources This appendix describes data sources of the macro variables and the construction of leverage for investment banks, bank holding companies, and the financial sector. B.1. Macro variables
In this case, gross leverage is (60 þ50)/10¼11, net leverage is (60 50)/10 ¼1, and long-only leverage is 60/10 ¼6. Now all three leverage measures are different because of the presence of the active short position. In particular, the active short bet in this example induces the marked difference between gross and net leverage. Example 3 (General levered fund). Consider a fund with the following balance sheet: Long assets $20 Long securities
Short assets $8 Short securities $2 Borrowed cash $10 NAV
In this example, the fund obtains leverage by both a short cash position as well as a short position in risky assets. The gross leverage is (20þ8)/10¼2.8, net leverage is (20 8)/10¼1.2, and long-only leverage is 20/10¼2. In this example, the long position is leveraged by both short security positions, which could be active bets or passive hedges, and a short cash position. Note that, whereas net
The list of macro variables is: Investment bank (IB) CDS protection. We take credit default swap (CDS) spreads on 10-year senior bonds of the following institutions, with tickers in parentheses: Bear Stearns (BSC), Citigroup (C), Credit Suisse (CS), Goldman Sachs (GS), HSBC (HBC), JP Morgan (JPM), Lehman Brothers (LEH), Merrill Lynch (MER), and Morgan Stanley (MS). While several of these firms are mainly commercial banks with relatively small investment banking and proprietary trading activities compared to other firms in the list, we take these firms as representative of broker/dealer and investment banking activity. Merrill Lynch and Bear Stearns ceased to be independent entities in the sample and Lehman Brothers entered bankruptcy. Data on CDS prices are obtained from Bloomberg and market weights are taken from CRSP. The CDS contract is specified so that a buyer of protection pays premiums specified in percentage points per annum of a notional contract amount to a seller of protection. If the credit event (default) occurs,
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then the seller of protection has to deliver the underlying bond to the buyer of protection. We take CDS on 10-year senior bonds of the listed financial institutions. We market weight the CDS spreads using market capitalization data on common equity for those firms in existence at a given point in time. Investment bank (IB) returns. We take monthly total returns on the investment banks from CRSP. These are market value weighted. S&P 500 returns. This is the total return on the S&P 500 index taken from Standard & Poor’s Index Services. VIX. This is the monthly level of the VIX volatility index taken from Yahoo Finance. LIBOR. We obtain the three-month LIBOR rate from Bloomberg. TED spread. The TED spread is the difference between the three-month LIBOR yield and the three-month T-bill yield. We obtain the three-month T-bill rate from the St. Louis Fed. Term spread. The term spread is defined to be the difference between the 10-year Treasury yield and the three-month T-bill. These are obtained from the St. Louis Fed. Aggregate hedge fund flows. This is the past threemonth flow on the aggregate hedge fund industry, at a monthly frequency, constructed from the Barclays Hedge fund database. This is computed following Section 3.2.2. B.2. Financial sector leverage We construct leverage for investment banks (BSC, C, CS, GS, HBC, JPM, LEH, MER, and MS), bank holding companies, and the entire financial sector using CRSP and Compustat data. Bank holding companies are defined as U.S.-based institutions with Standard Industrial Classification (SIC) codes which fall between 6000 and 6199. We define the financial sector as all U.S.-based companies with SIC codes between 6000 and 6299. Leverage for the listed financial sub-sector is defined to be P A P i2sub-sector i,t ðB:1Þ i2sub-sector MV i,t for firm i at time t, MV i,t is the company i’s market value obtained from CRSP as the product of number of shares outstanding and the closing price at the end of the month t, and Ai,t is the total assets of the company obtained from COMPUSTAT. The assets are reported quarterly and we use the most recent, observable quarterly balance sheet report. Note that Ai,t =MV i,t is the market leverage of company i using the market value of common stock as the value of equity.
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Table A1 A sample hedge fund risk exposure report. This table shows a sample hedge fund risk exposure report. This fund reports exposures monthly broken down by sector. The reported quantities are percentages of net asset value (NAV). Gross leverage is a sum of long and short exposures as a portion of assets under management (AUM). Net leverage is a difference of long and short exposures as a portion of AUM. Sector
Consumer discretionary Consumer staples Energy Financials Health care Industrials Information technology Materials Other assets Telecommunication services Total
Gross leverage ratio (%)
Net leverage ratio (%)
Long market value/ Equity (%)
Short market value/ Equity (%)
16.73
1.93
9.33
(7.40)
9.08 7.84 4.20 5.01 22.14 26.05
5.16 (1.91) (2.87) 2.17 7.28 5.41
7.12 2.97 0.66 3.59 14.71 15.73
(1.96) (4.87) (3.53) (1.42) (7.43) (10.32)
1.31 17.72 0.69
0.46 3.76 0.28
0.89 10.74 0.48
(0.43) (6.98) (0.21)
110.78
21.68
66.23
(44.55)
breaks down its exposure into different sectors and reports a gross leverage of 1.11, a net leverage of 0.22, and a long-only leverage of 0.66. This fund reports both long and short positions in each sector. These numbers are received by the Fund every reporting period. Second, some hedge funds report leverage information in investor letters. An extract of an actual letter is: We made5.3% on the short book and lost3.3% on the long book. Having started the month with7% net long position, we were by mid-month slightly net short for the first time in the fund’s history. Around mid-month we suspected that the market falls, triggered by subprime losses in the financial system, were coming to an end and decided to rebuild a modest18% net long position, which is where we ended the month. From the text of the investor letter, we observe that net leverage at the end of the month is 0.18, but gross leverage and long-only leverage are not reported. However, the Fund is able to obtain more details on leverage, and other risk and performance characteristics of each hedge fund than reported in the investor letters by having analysts visit or call the funds to obtain further information. Thus, although the hedge fund officially does not report size of long and short exposure at this month, our data set contains this information.
Appendix C. Examples of reported hedge fund leverage Appendix D. Estimation Hedge funds report their leverage to investors in several formats, often with several measures of leverage. First, hedge funds periodically send their investors risk reports which list performance and risk statistics over the last reporting period. Table A1 provides an extract of a risk exposure report from an actual hedge fund. This fund
This appendix describes the conditional distributions used in the Gibbs sampler. We treat the unobserved data variables as additional parameters using data augmentation. A textbook exposition of these procedures is Robert and Casella (1999).
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D.1. Predictive model We rewrite the predictive model as Yi,t þ 1 ¼ ci þ b1 Yi,t þ b2 Xi,t þ ei,t þ 1 ,
ðD:1Þ
where Yi,t is leverage of fund i at time t, the vector Xi,t includes both fund-specific variables and economy-wide variables, and ei,t Nð0, s2 Þ and is i.i.d. across funds and time. The constant terms, ci, captures fund-fixed effects. We are especially interested in the predictive coefficients, b ¼ ðb1 b2 Þ. We cast the model in Eq. (D.1) into a measurement equation: n Yi,t þ 1 ¼ Yi,t þ 1 þ wi,t þ 1 ,
ðD:2Þ
where each observation error in fwi,t þ 1 g is equal to zero if Yi,t þ 1 is observed and if Yi,t þ 1 is unobserved is distributed as Nð0, s2w Þ, where the measurement error is i.i.d. across funds and time and is orthogonal to ei,t þ 1 . This extreme form of measurement error follows Sinopoli, Schenato, Franceschetti, Poolla, Jordan, and Sastry (2004) and others and effectively eliminates observations which are observed from the set of measurement equations. This allows us to use a Kalman filter, with extreme heteroskedasticity, in the estimation (see below). We denote
s2v ¼ s2 þ s2w , which is the total variance for observations where leverage is not reported. We denote the parameters y ¼ ðbs2 s2v Þ and partition the data Y ¼ fYi,t g and X ¼ fXi,t g into observed and unobserved sets, X ¼ fX obs X unobs g and Y ¼ fY obs Y unobs g, where we denote the unobserved data with ‘‘unobs’’ superscripts. The set of observed data we denote as Y ¼ fX obs Y obs g. We use y to denote the set of parameters less the parameter currently being drawn. The set of conditional distributions in the Gibbs sampler is: pðb,ci jy ,Y,X unobs ,Y unobs Þ: Conditional on Xunobs and Yunobs being observed, Eq. (D.1) is a regular OLS regression and we can use a conjugate Normal draw. The dependent variable has two variances: if the regressor is observed in data the residuals have variance s2 and if the regressor is unobserved in data the residual variance is s2v . Thus, we can rewrite Eqs. (D.1) and (D.2) as Y ¼ X b þV,
ðD:3Þ
where Y ¼ fYi,t þ 1 ci g, X ¼ fYi,t Xi,t g, and V Nð0, SÞ, where S is a diagonal covariance matrix with entries s2 or s2v depending on whether the regressor is observed in data or not. We estimate the fixed effects in each iteration by appropriately demeaning both sides of Eq. (D.3). For fund-fixed effects we subtract average values of the lefthand side and right-hand side variables for the observations that correspond to that fund. The fixed effects change in each iteration because the missing Yunobs and Xunobs are updated. pðs2 , s2v jy ,Y,X unobs ,Y unobs Þ
We draw s2 using a conjugate Inverse Gamma distribution given the regression (D.3) taking only the entries where the residual variance is s2 . We can draw s2v ¼ s2 þ s2w by taking the entries where the residual variance is s2v . We ensure that s2v 4 s2 in each draw. pðY unobs jy,Y,X unobs Þ We can interpret the system for Yi,t as a state equation (D.1) and a measurement equation (D.2). This allows us to use a forward filtering backward sampling (FFBS) draw following Carter and Kohn (1994), except with (extreme) heteroskedasticity and exogenous variables. For notational simplicity, we suppress dependence on fund i below and use a FFBS draw separately on each fund i with missing values. We run the Kalman filter to determine the conditional distributions of the unobserved variables, Ytjt1 Nðmt,t1 ,Vt,t1 Þ, where Ytjt1 is Yt conditional on the history of observations up to and including t1, which we denote as Ht1 , n mt,t1 ¼ c þ b1 Yt1 þ b2 Xt1
and 2
Vt,t1 ¼ b1 Vt1,t1 þ s2 , treating the Xt values as exogenous. When Ytn is added to the history, we have the joint distribution ! ! !! mt,t1 Vt,t1 Yt Vt,t1 N : ðD:4Þ mt,t1 , Vt,t1 Vt,t1 þ s2w Ytn Note that s2w ¼ 0 if Yt is observed. From the moments of a partitioned normal, we have Ht1 Nðmt,t ,Vt,t Þ,
Ytjt ¼ Yt jYtn ,
ðD:5Þ
where
mt,t ¼ mt,t1 þ
Vt,t1 ðY n mt,t1 Þ, Vt,t1 þ s2w t
and Vt,t ¼ Vt,t1
2 Vt,t1 Vt,t1 s2w ¼ : 2 Vt,t1 þ sw Vt,t1 þ s2w
Note that if b2 ¼ 0, this simplifies to a regular Kalman filter. We assume the initial distribution is ! c þ b2 EX s2 y1 N , , 1b1 1b2 1
which is the stationary distribution for Yt assuming Xt is exogenous. We update as per a normal Kalman filter to obtain the distribution yTjT and the smoothed conditional values ytjT . Once the Kalman filter is run forwards, we backwards sample following Carter and Kohn (1994). pðX unobs jy,Y,Y unobs Þ We assume that the regressand variables, both observed and unobserved, are all jointly normally distributed ~ Þ. To draw the unobserved variables for fund i at Nðm~ , S unobs time t, Xi,t , we have unobs obs jXi,t , y,Y Nðm,v2 Þ, Xi,t
ðD:6Þ
A. Ang et al. / Journal of Financial Economics 102 (2011) 102–126
where m and v2 can be obtained by the mean and variance of a partitioned normal where Xi,t ¼
obs ðXi,t
unobs Xi,t Þ
~Þ Nðm~ , S
has been partitioned into the observed and unobserved components. A similar procedure is used by Li, Sarkar, and Wang (2003), except we recognize that Yi,t is endogenously persistent. ~ each iteration by a We update the values m~ and S conjugate normal distribution and conjugate Wishart draw, respectively. We estimate with a burn-in period of 1,000 observations and 2,000 simulations. Convergence is extremely fast. We report in the tables a posterior mean for each parameter and a posterior t-statistic which is the ratio of the posterior mean and posterior standard deviation. This is to make inference comparable to a classical OLS estimation, which cannot handle missing observations. During each iteration we compute adjusted R2 statistics. We calculate the regular R2 as SS R ¼ 1 residual , SStotal 2
ðD:7Þ
where SSresidual denotes the residual sum of squares, while SStotal denotes the total sum of squares. For our model that predicts values Yi,t by producing estimates Y^ i,t , P P SSresidual ¼ i,t ðYi,t þ 1 Y^ i,t þ 1 Þ2 and SStotal ¼ i,t ðYi,t þ 1 Y Þ2 , where Y is the average value of Yi,t and Y^ i,t þ 1 ¼ ci þ b 1
Yi,t þ b2 Xi,t from Eq. (D.1). We record the adjusted R2: adjusted R2 ¼ 1ð1R2 Þ
nk , npk
ðD:9Þ
where for simplicity we ignore the fund-fixed effects. Fund i’s idiosyncratic error term, ei,t , follows the AR(1) process ðD:10Þ 2
where vi,t Nð0, s Þ. Similar to the predictive model, leverage may be unobserved at time t, so we employ the measurement Eq. (D.2). We follow Chib (1993) in recasting Eqs. (D.9) and (D.10) as a regular OLS equation by defining Y~ i,t ¼ Yi,t fe Yi,t1 X~ i,t ¼ Xi,t fe Xi,t1 :
ðD:12Þ
which now has an i.i.d. error term. The corresponding measurement equation is n Y~ i,t ¼ Y~ i,t þ wi,t ,
ðD:13Þ
where the observation error variance is s2v ¼ s2 þ s2w where Y~ i,t is unobserved and s2 if Y~ t is observed. The set of conditional draws in the Gibbs sampler we use are pðbjy ,Y,Y unobs Þ We draw b using a conjugate normal draw from the regression Eq. (D.12). There are two possible variances, s2 in the case Y~ i,t is observed and s2v in the case it is unobserved. pðfe jy ,Y,Y unobs Þ Chib (1993) notes that Eq. (D.10) is a standard regression draw with et given by Eq. (D.9). We draw fe with a conjugate normal distribution. pðs2 , s2v jy ,Y n ,Y unobs Þ, We draw s2v using a conjugate Inverse Gamma distribution from the regression Eq. (D.12). We ensure that s2v 4 s2 in each draw. pðY unobs jy,YÞ
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The estimation of the contemporaneous model in Eq. (3) is similar to the predictive model in Eq. (2), except that we must now account for serial correlation in the error terms. The model is
ei,t ¼ fe ei,t1 þvi,t ,
0 Y~ i,t ¼ ci þ b X~ i,t þvi,t ,
Same as Section D.1.
D.2. Contemporaneous model
0
This allows us to write
ðD:8Þ
where the number of observations is n, the number of funds is k, and the number of explanatory variables is p. In the tables, we report the posterior mean of the adjusted R2 statistic computed in each iteration.
Yi,t ¼ b Xi,t þ ei,t ,
125
ðD:11Þ
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Journal of Financial Economics 102 (2011) 127–149
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Limits-to-arbitrage, investment frictions, and the asset growth anomaly$ F.Y. Eric C. Lam a, K.C. John Wei b,n a b
Department of Economics and Finance, College of Business, City University of Hong Kong, Kowloon, Hong Kong Department of Finance, School of Business and Management, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
a r t i c l e i n f o
abstract
Article history: Received 8 February 2010 Received in revised form 29 November 2010 Accepted 7 December 2010 Available online 30 March 2011
We empirically evaluate the predictions of the mispricing hypothesis with limits-toarbitrage suggested by Shleifer and Vishny (1997) and the q-theory with investment frictions proposed by Li and Zhang (2010) on the negative relation between asset growth and average stock returns. We conduct cross-sectional regressions of returns on asset growth on subsamples split by a given measure of limits-to-arbitrage or investment frictions. We show that: (i) proxies for limits-to-arbitrage and proxies for investment frictions are often highly correlated; (ii) the evidence based on equalweighted returns shows significant support for both hypotheses, while the evidence from value-weighted returns is weaker; and (iii) in direct comparisons, each hypothesis is supported by a fair and similar amount of evidence. & 2011 Elsevier B.V. All rights reserved.
JEL classification: G14 G31 M41 M42 Keywords: Asset growth Capital investment Stock returns Investment frictions Limits-to-arbitrage
1. Introduction Titman, Wei, and Xie (2004), Fama and French (2006, 2008), and Cooper, Gulen, and Schill (2008), among others,
have shown that companies that invest more or grow their total assets more earn lower subsequent risk-adjusted returns.1 This negative investment-return relation is often referred to as the investment or asset growth anomaly.
$ We appreciate the helpful comments of Santiago Bazdresch, Ling Cen, Edward Chow, Pengjie Gao, Vidhan Goyal, Tony Hou, Jason Karceski, Laura Liu, Alexander Ljungqvist, Welan Qian, Lei Sun, Kevin Wang, Mungo Wilson, Xueping Wu, Chun Xia, Yi Xiang, Guochang Zhang, and seminar participants at the Hong Kong University of Science and Technology, as well as conference participants at the 2009 Western Finance Association meeting in San Diego, the 2009 Asian Finance Association International Conference in Brisbane, the 2009 China International Conference in Finance in Guangzhou, the 2008 Conference on the Theories and Practices of Securities and Financial Markets (SFM) in Kaohsiung, and the 2008 NTU International Conference on Finance in Taipei. We are particularly grateful for the constructive and insightful comments and suggestions from an anonymous referee and Bill Schwert (the editor). This paper won the Best Research Award at the 2008 SMF Conference. Eric Lam acknowledges financial support from a Research Travel Grant from Hong Kong University of Science and Technology (RTG08/09.BM004). John Wei acknowledges financial support from a Research Infrastructure Grant from Hong Kong’s Research Grants Council (RI/93/94.BM02). The authors also thank Alice Cheung, Bill Purves, and Dr. Virginia Unkefer for excellent editorial assistance. All remaining errors are ours. The previous version of the paper was titled, ‘‘The role of limits to arbitrage and the asset growth anomaly.’’ n Corresponding author. Tel.: þ852 2358 7676; fax: þ 852 2358 1749. E-mail addresses:
[email protected] (F.Y.E.C. Lam),
[email protected] (K.C.J. Wei). 1 Similarly, Fairfield, Whisenant, and Yohn (2003) note that future stock returns are negatively related to changes in long-term net operating assets. Hirshleifer, Hou, Teoh, and Zhang (2004) show that stocks of firms with higher levels of net operating assets scaled by lagged total assets earn lower future stock returns.
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.03.024
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There are two prominent explanations for this anomaly: one is behavioral and the other is rational. The behavioral explanation (Titman, Wei, and Xie, 2004; Cooper, Gulen, and Schill, 2008) argues that the anomaly exists because investors are too slow to incorporate the information from firm investment into stock prices, which causes the mispricing. The rational explanation, which is based on the qtheory (see, for example, Zhang, 2005; Xing, 2008; Li, Livdan, and Zhang, 2009; Liu, Whited, and Zhang, 2009; Chen, Novy-Marx, and Zhang, 2010; Li and Zhang, 2010), argues that firms invest more when expected returns (i.e., costs of capital) are lower and invest less when expected returns are higher, inducing the negative relation between investment and subsequent stock returns. In this study, we comprehensively examine the above two explanations. More specifically, we test whether the asset growth anomaly can be explained by the mispricing hypothesis with limits-to-arbitrage put forth by Shleifer and Vishny (1997), or by the q-theory with investment frictions suggested by Li and Zhang (2010), or both. If both explanations can explain the anomaly, we then test whether one subsumes or dominates the other. The limits-to-arbitrage hypothesis argues that arbitrage is risky, costly, and limited. Therefore, if the asset growth anomaly is indeed due to mispricing, the anomaly should be more pronounced for stocks that are difficult to arbitrage than for stocks that are easy to arbitrage. The investment frictions hypothesis predicts that the asset growth anomaly should be stronger for firms with high investment frictions than for firms with low investment frictions. The prediction follows from the fact that for a given change in the cost of capital, the change in investment is smaller when investment frictions are higher. Equivalently, a given magnitude of change in investment predicts a larger magnitude of change in expected returns. As proxies for limits-to-arbitrage and proxies for investment frictions are highly correlated, these two explanations should make similar predictions about the anomaly. If that is the case, the supporting evidence for one explanation drawn from individual tests should support the other explanation as well. It is therefore important to conduct extensive and joint tests to distinguish between these two explanations. We aim to achieve this goal in this paper. To test the limits-to-arbitrage hypothesis, we consider four aspects of limits-to-arbitrage with ten measures: arbitrage risk (measured by idiosyncratic stock return volatility); information uncertainty (measured by analyst coverage, analyst forecast dispersion, and cash flow volatility); shareholder sophistication (measured by the number of institutional shareholders); and potential transaction costs (measured by stock price, bid-ask spread, institutional ownership, the Amihud (2002) illiquidity, and dollar trading volume). Firms with high arbitrage risk, more information uncertainty, less shareholder sophistication, and high transaction costs are more difficult to arbitrage than firms with low arbitrage risk, less information uncertainty, more shareholder sophistication, and low transaction costs. To test the investment frictions hypothesis, we follow Li and Zhang (2010) to use four measures of financing constraints to proxy for investment frictions: firm age,
asset size, payout ratio, and credit rating.2 Firms that are old, large, have high payout ratios, and rated public debt are less financially constrained than firms that are young, small, have low payout ratios, and unrated public debt. As suggested by Li and Zhang (2010), we estimate the Fama and MacBeth (1973) cross-sectional regressions of stock returns against asset growth within subsamples (low, medium, and high) split by a given measure of limits-toarbitrage or financing constraints. The limits-to-arbitrage (investment frictions) hypothesis suggests that the slope of asset growth should be negative and have a higher magnitude for the high limits-to-arbitrage (more financially constrained) subsample than for the low limits-toarbitrage (less financially constrained) subsample. To compare and contrast the two explanations, we examine whether or not the negative slope of asset growth has a higher magnitude when limits-to-arbitrage are more severe after controlling for the level of investment frictions, or when investment frictions are higher after controlling for the level of limits-to-arbitrage. Using Fama and MacBeth (1973) cross-sectional regressions of equal-weighted returns in the sample from July 1971 to December 2009, we show that the negative slope of asset growth has a larger magnitude in the subsample with more severe limits-to-arbitrage or higher investment frictions. Although the measures of limits-toarbitrage and the measures of investment frictions are highly correlated, in the majority of the cases, the negative slope of asset growth still has a higher magnitude when limits-to-arbitrage are more severe even after controlling for investment frictions. Similarly, in the majority of cases, the negative slope still has a larger magnitude when investment frictions are higher even after controlling for limits-to-arbitrage. Furthermore, the effect of limits-to-arbitrage on the asset growth anomaly appears to be stronger when investment frictions are higher, and vice versa. These results suggest that these two effects on the asset growth anomaly are complementary. Overall, the evidence from equal-weighted individual and joint tests provides similar strength of support for both hypotheses. However, some of the results are not robust to controlling for market capitalization, book-tomarket equity, prior stock performance, idiosyncratic stock return volatility, and past equity issuance. In addition, there is relatively less supporting evidence for both explanations from value-weighted tests. Among the ten limits-to-arbitrage proxies, only idiosyncratic stock return volatility demonstrates a reliable effect on the asset growth anomaly. Similarly, among the four financing constraints proxies, only firm age shows a reliable effect on the anomaly. The remainder of this paper proceeds as follows. The next section reviews the relevant literature and develops our hypotheses. Section 3 describes our sample. Section 4 tests the effect of limits-to-arbitrage on the asset growth anomaly. Section 5 tests the effect of investment frictions on the anomaly. Section 6 jointly tests the effect of
2 Note that Li and Zhang (2010) do not consider firm age in their study.
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limits-to-arbitrage on the anomaly after controlling for investment frictions, and vice versa. Finally, Section 7 concludes the paper. 2. Literature review and hypothesis development 2.1. Mispricing with limits-to-arbitrage Titman, Wei, and Xie (2004) attribute the anomaly to investors’ underreactions to overinvestment pursued by managers who are empire building. Cooper, Gulen, and Schill (2008) attribute the phenomenon to investors’ overreactions to changes in firms’ future business prospects implied by asset expansions or reductions. Both studies argue that the investment or asset growth anomaly exists because investors fail or are too slow to incorporate the correct information implied in corporate investment into stock prices, which causes the mispricing.3 If a stock is mispriced, profit opportunities attract rational investors and their arbitrage activities should correct the mispricing. In an ideal setting where arbitrage opportunities are riskless, obvious, and costless to exploit, prices should reflect all available information accurately and mispricing, if any, should be corrected immediately. However, in a realistic market where arbitrage is risky and costly, implementable arbitrage opportunities are limited. Although arbitrageurs may trade against the mispricing, the correction of mispricing will take longer when limits-to-arbitrage are more severe. As arbitrageurs are typically poorly diversified, nonsystematic stock return volatility adds substantially to the total risk of their overall portfolios. Since there is no conclusive evidence that this component of volatility is compensated with higher expected returns, it should be of great concern to arbitrageurs when they arbitrage mispriced stocks.4 De Long, Shleifer, Summers, and Waldmann (1990) point out that the unpredictable actions of noise traders might cause prices to diverge from fundamental values, making arbitrage risky. Shleifer and Vishny (1997) argue that arbitrageurs are typically capital constrained and so might have to prematurely liquidate certain arbitrage positions in response to margin calls and suffer losses. Liu and Longstaff (2004) show that when arbitrage is risky, optimized trades can still be loss-making before prices converge. 3 Titman, Wei, and Xie (2004) show that the negative investmentreturn relation is stronger among firms with greater investment discretion as indicated by larger free cash flow or lower financial leverage. In addition, they find that the abnormal returns cluster around earnings announcements but that there are no significant returns when hostile takeovers are prevalent. Cooper, Gulen, and Schill (2008) find positive earnings surprises for low asset-growth stocks and negative earnings surprises for high asset-growth stocks. Furthermore, Chan, Karceski, Lakonishok, and Sougiannis (2008) report that the anomaly is driven by the underperformance of high asset-growth stocks and it is stronger when past profitability is poorer and corporate governance is weaker. They also find that the anomaly holds whether asset growth was achieved by mergers and acquisitions, increases in plant, property, and equipment, increases in other current assets or increases in other longterm assets, and whether asset growth was financed by equity or debt. 4 Carroll and Wei (1988), Spiegel and Wang (2005), and Fu (2009) all show that stock returns are positively associated with idiosyncratic risk. However, Ang, Hodrick, Xing, and Zhang (2006, 2009) find the opposite.
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Further, investors need information to locate arbitrage opportunities, which may be less obvious when information is imprecise.5 However, sophisticated professionals such as institutional investors are more likely to recognize such opportunities. Transaction costs can be another hindrance. Illiquidity, short-sale constraints, and the risk of short squeezes all might make arbitrage opportunities more difficult to exploit. And of course, trading expenses reduce the profitability of arbitrage trades, which reduces their attractiveness to arbitrageurs.6 When arbitrage is riskier, information is less certain, fewer shareholders are sophisticated, or transaction costs are higher, arbitrage opportunities provided by the mispricing of corporate asset growth are less attractive to arbitrageurs. If information derived from corporate growth is correctly traded into stock prices only gradually, we should observe a stronger asset growth anomaly when arbitrage is more limited. This argument leads to our first hypothesis. H1. The negative relation between asset growth and subsequent stock returns is stronger for firms that are difficult to arbitrage than for firms that are easy to arbitrage. 2.2. The q-theory with investment frictions The q-theory of investment argues that firms make optimal corporate investment choices and dynamically trade off free cash flows. The theory argues that with a time-varying discount rate or expected return to capital, firms tend to invest more when the expected return is lower which results in higher net present value of new investment, and vice versa. As a result, realized investment is negatively associated with subsequent average stock returns in the cross-section (see, for example, Zhang, 2005; Xing, 2008; Li, Livdan, and Zhang, 2009; Liu, Whited, and Zhang, 2009; Chen, Novy-Marx, and Zhang, 2010).7 Li and Zhang (2010) incorporate investment costs or frictions into this q-theory. They show that when investment is frictionless, firm investment is fully responsive to changes in the expected return. On the other hand, when investment has frictions or entails deadweight costs, it becomes less responsive to changes in the expected return. The intuition is that even though the required return is lower and the net present value of new investment is higher, firms may be reluctant to invest, as making new investment also incurs deadweight costs which offset the higher net present value. More importantly, the q-theory 5 Zhang (2006) shows that price momentum and drifts after analysts’ forecast revisions or earnings announcements, which are often attributed to investors’ misreactions, are stronger when information is more uncertain. Verardo (2009) provides additional analysis of the impact of information uncertainty on price momentum. 6 Mashruwala, Rajgopal, and Shevlin (2006) show that transaction costs can constitute a significant barrier for arbitrageurs seeking to exploit the mispricing of accounting accruals documented by Sloan (1996). 7 On the other hand, Cochrane (1991, 1996) derives a time-series relation between investment and future stock returns.
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with investment frictions also predicts that the responsiveness of investment to changes in the discount rate decreases with the amount of frictions. This prediction suggests that the asset growth anomaly should be larger when investment frictions are more serious. Our second hypothesis is thus as follows: H2. The negative relation between asset growth and subsequent stock returns is stronger for firms with high investment frictions than for firms with low investment frictions. Li and Zhang (2010) identify investment frictions by using the measures of financing constraints (asset size, payout ratio, and credit rating). They show that the negative slope of asset growth has a higher magnitude in the more financially constrained subsample than in the less financially constrained subsample. However, they find that the evidence supporting the investment frictions hypothesis becomes very weak or even disappears when standard firm-level asset-pricing characteristics or two preliminary proxies for limits-to-arbitrage are included in the analysis. 2.3. Comparing the two explanations Since the proxies for limits-to-arbitrage are shown to be positively correlated with the proxies for investment frictions (see Table 1 below), the limits-to-arbitrage hypothesis and the investment frictions hypothesis provide similar predictions about the asset growth anomaly. Therefore, supporting evidence for one hypothesis might be interpreted as supporting evidence for the other hypothesis as well. It is only by testing both hypotheses jointly that we might sort out their relative importance in understanding the anomaly. In this study, we estimate the Fama and MacBeth (1973) cross-section regressions of stock returns against asset growth in the subsamples split jointly by measures of limits-to-arbitrage and financing constraints to test the following hypotheses: H3a. Controlling for the level of investment frictions, the negative relation between asset growth and subsequent stock returns is stronger for firms that are difficult to arbitrage than for firms that are easy to arbitrage. H3b. Controlling for the level of limits-to-arbitrage, the negative relation between asset growth and subsequent stock returns is more significant for firms with high investment frictions than for firms with low investment frictions. 3. Variable definitions, sample selection, and summary statistics 3.1. The measure of asset growth Like Cooper, Gulen, and Schill (2008), we use total asset growth (TAG) as a composite measure of overall corporate investment growth and asset expansion. TAGit is defined as the growth rate of firm i’s total assets (TA) from year t 1 to year t. That is, TAGit (TAit/TAit 1) 1. (More
detailed definitions of all the variables are provided in the appendix.) 3.2. The measures of limits-to-arbitrage Following Pontiff (1996), Wurgler and Zhuravskaya (2002), and Mashruwala, Rajgopal, and Shevlin (2006), we use idiosyncratic stock return volatility (IVOL) to measure arbitrage risk. Pontiff (2006) demonstrates that arbitrageurs prefer to hold less of stocks with higher idiosyncratic stock return volatility. Using stock return idiosyncratic volatility as a proxy for arbitrage costs, Duan, Hu, and McLean (2010) and McLean (2010) show that when arbitrage costs are lower, the negative relation between short interest or stock returns of the past 3–5 years and subsequent stock returns is weaker. Shareholder sophistication may also influence the risk of arbitrage. Like Chen, Hong, and Stein (2002), Ali, Hwang, and Trombley (2003), Bartov, Radhakrishnan, and Krinsky (2000), and Bhushan (1994), we use the number of institutional shareholders (INSTN) as a measure of shareholder sophistication. We use three measures of information uncertainty. The first measure is analyst coverage (COV), defined as the number of analysts following a stock. Hong, Lim, and Stein (2000) interpret more analyst coverage as indicating lower information uncertainty. Gleason and Lee (2003) find that the post-earnings-revision price drift is stronger, and Zhang (2006) shows that price momentum is also more pronounced when there is less analyst coverage. The second measure is the dispersion in analysts’ earnings forecasts (DISP), which is defined as the standard deviation of earnings-per-share forecasts divided by the closing stock price at the end of June. DISP is a well-known measure of uncertainty about future earnings or disagreement among market participants (see, for example, Diether, Malloy, and Scherbina, 2002; Zhang, 2006). The third measure is cash flow volatility (CVOL), which is defined as the standard deviation of cash flow from operations. CVOL is likely to capture a firm’s underlying fundamental volatility. Zhang (2006) shows that postearnings-revision price drift and price momentum are stronger when cash flow is more volatile. We use five measures of potential transaction costs. The first measure is the stock price (PRICE). Bhardwaj and Brooks (1992) suggest that the bid-ask spread and the brokerage commission are inversely related to the stock price. Ball, Kothari, and Shanken (1995) use the stock price as an inverse proxy for the bid-ask spread and illiquidity. Stoll (2000) shows that recent stock prices are inversely related to the relative bid-ask spread. The second measure is the effective bid-ask spread (BIDASK), which is two times the difference between the transaction price and the midquote (which is the average of the bid price and the ask price) divided by the transaction price. BIDASK is used to measure the trading expenses for arbitrageurs who have to compensate dealers for making markets and providing liquidity. The third measure of transaction costs is institutional ownership (INSTH), which is the percentage of outstanding shares held by institutional investors. It is easier for
Panel A: Summary statistics of asset growth, limits-to-arbitrage measures, and investment frictions measures Mean TAG IVOL COV DISP CVOL INSTN PRICE BIDASK INSTH ILLIQ DVOL AGE ASSET PAYOUT RATING
Standard deviation
0.147 0.120 8.006 0.139 0.082 90.285 20.309 0.012 0.405 4.517 10 7 1.839 108 18.258 1.478 109 1.967 0.231
0.778 0.061 7.277 3.824 0.199 119.673 23.452 0.012 0.264 3.127 10 6 7.398 108 15.259 5.533 109 0.839 0.419
Minimum
Maximum
0.697 0.027 1.000 0.000 0.003 0.000 0.356 0.000 0.000 4.775 10 11 1.441 104 2.235 3.791 106 1 0
27.935 0.791 38.675 143.2967 7.587 961.267 551.649 0.156 1.472 0.133 10 3 1.875 1010 62.718 1.258 1011 3 1
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Table 1 Summary statistics, firm characteristics, and sample correlations. Panel A reports time-series averages of the means, standard deviations, minimums, and maximums of the annual overall corporate growth measure (TAG), the measures of limits-to-arbitrage including idiosyncratic volatility (IVOL), analyst coverage (COV), dispersion in analyst forecast (DISP), cash flow volatility (CVOL), shareholder sophistication (INSTN), share price (PRICE), bid-ask spread (BIDASK), institutional ownership (INSTH), the Amihud (2002) illiquidity (ILLIQ), and dollar trading volume (DVOL), as well as the measures of investment frictions including firm age (AGE), asset size (ASSET), payout ratio ranking (PAYOUT), and credit rating (RATING). Panel B reports the time-series averages of equal-weighted and value-weighted one-year (six months for year 2009) post-formation monthly percentage returns (RETEW and RETVW), median firm characteristics including the market value of equity (SIZE), book-to-market equity ratio (BM), prior six-month stock return (PRET), net share issuance (NS), lagged net share issuance (NSlag), limits-to-arbitrage, and investment frictions of decile portfolios sorted by TAG at the end of June each year. (1 –10) is the difference in the measures and characteristics between the bottomgrowth portfolio (Decile 1) and the top-growth portfolio (Decile 10). t(1–10) is the corresponding t-statistic based on Newey and West (1987) standard errors. See the Appendix for detailed definitions of variables. Panel C reports the time-series averages of the correlations between asset growth, measures of limits-to-arbitrage, and measures of investment frictions. The measures and characteristics are calculated with information available at the end of June each year between 1971 and 2009 (from 1976 when COV and DISP are involved; from 1980 when INSTN and INSTH are involved; from 1993 when BIDASK is involved). The data set is related to U.S. domestic firms traded on the NYSE, Amex, and Nasdaq exchanges. Their financial statements are taken from Compustat. Stock market data come from the Center for Research in Security Prices (CRSP). Analyst data are from the Institutional Brokers’ Estimate System (I/B/E/S). Institutional holdings records are from CDA/Spectrum Institutional (13f) Holdings. Correlations significant at the 5% level are in bold.
Panel B: Firm characteristics, limits-to-arbitrage measures, and investment frictions measures across asset growth deciles TAG rank 2
3
4
5
6
7
8
9
0.174 1.559 1.398 4.235 1.128 0.082
0.058 1.458 1.094 8.604 1.184 0.091
0.008 1.430 1.240 14.723 1.120 0.094
0.025 1.378 1.101 20.547 1.081 0.085
0.055 1.382 1.100 23.669 0.973 0.084
0.087 1.190 1.010 26.187 0.898 0.082
0.126 1.197 1.076 29.683 0.797 0.081
0.180 1.189 0.975 27.602 0.701 0.082
0.279 0.962 1.017 24.002 0.615 0.074
10 (high) 0.615 0.374 0.683 21.745 0.557 0.053
1–10
t(1–10)
0.789 1.185 0.715 17.510 0.571 0.029
[ 18.56] [6.54] [3.34] [ 6.61] [9.45] [2.34]
131
TAG RETEW RETVW SIZE( 107) BM PRET
1 (low)
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Table 1 (continued ) Panel B: Firm characteristics, limits-to-arbitrage measures, and investment frictions measures across asset growth deciles TAG rank 2
3
4
5
6
7
8
9
10 (high)
0.003 0.006 0.151 2.794 0.003 0.098 27.517 5.334 0.289 0.015 2.654 3.952 10.897 7.048 1.256 0
0.001 0.003 0.120 4.735 0.003 0.068 44.700 9.281 0.399 0.009 1.035 8.695 12.95 14.696 1.974 0
0.001 0.003 0.103 5.765 0.002 0.054 50.967 13.473 0.396 0.007 0.606 14.111 15.000 22.458 2.026 0
0.002 0.003 0.093 5.941 0.002 0.047 53.567 16.902 0.408 0.007 0.371 19.116 15.705 30.821 2.077 0
0.003 0.004 0.089 6.235 0.002 0.045 55.900 18.442 0.414 0.006 0.239 21.095 16.308 32.278 2.051 0
0.003 0.004 0.091 6.500 0.001 0.047 61.283 19.460 0.440 0.006 0.206 27.189 14.667 31.932 2.000 0
0.006 0.005 0.095 6.882 0.001 0.049 62.450 20.101 0.461 0.007 0.202 32.673 14.205 31.212 2.000 0
0.008 0.008 0.102 6.588 0.001 0.057 61.950 19.479 0.470 0.007 0.208 35.925 12.436 25.684 1.923 0
0.015 0.011 0.115 5.882 0.001 0.066 57.650 18.658 0.439 0.008 0.265 37.883 10.667 19.385 1.667 0
0.076 0.019 0.134 5.603 0.002 0.086 52.567 15.680 0.411 0.008 0.286 43.313 8.821 17.623 1.179 0
1–10
t(1–10)
0.073 0.013 0.017 2.809 0.001 0.012 25.050 10.346 0.122 0.007 2.368 39.361 2.076 10.575 0.077 0
[ 7.57] [ 9.58] [6.03] [10.52] [4.42] [3.61] [ 6.53] [ 20.21] [ 9.91] [8.42] [2.87] [ 4.35] [4.99] [ 6.37] [0.77] [0.00]
Panel C: Correlations among asset growth, measures of limits-to-arbitrage, and measures of investment frictions TAG IVOL COV DISP CVOL INSTN PRICE BIDASK INSTH ILLIQ DVOL AGE ASSET PAYOUT RATING
0.049 0.029 0.013 0.105 0.001 0.068 0.064 0.016 0.065 0.057 0.080 0.008 0.092 0.011
IVOL
0.355 0.045 0.351 0.323 0.390 0.395 0.211 0.201 0.178 0.378 0.214 0.424 0.311
COV
0.023 0.199 0.628 0.434 0.443 0.259 0.218 0.554 0.341 0.455 0.199 0.393
DISP
0.028 0.032 0.043 0.042 0.058 0.004 0.014 0.007 0.008 0.024 0.025
CVOL
0.167 0.194 0.212 0.118 0.092 0.086 0.187 0.114 0.181 0.175
INSTN
0.440 0.371 0.492 0.138 0.573 0.378 0.469 0.204 0.336
PRICE
0.407 0.279 0.148 0.401 0.310 0.258 0.216 0.316
BIDASK
0.387 0.418 0.183 0.269 0.195 0.223 0.299
INSTH
0.177 0.089 0.074 0.001 0.042 0.094
ILLIQ
0.067 0.080 0.051 0.096 0.102
DVOL
0.258 0.584 0.110 0.260
AGE
0.339 0.320 0.312
ASSET
0.160 0.265
PAYOUT
0.205
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
NS NSlag IVOL COV DISP CVOL INSTN PRICE INSTH BIDASK ILLIQ ( 10 7) DVOL( 106) AGE ASSET ( 107) PAYOUT RATING
1 (low)
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investors to borrow shares of stocks that have higher institutional ownership. In addition, these stocks are also less exposed to the risk of short squeezes (Dechow, Hutton, Meulbroek, and Sloan, 2001). Nagel (2005) uses higher institutional ownership to indicate low short-sale constraints. Edmans (2009) shows that by trading on private information, blockholders can cause prices to reflect fundamental value rather than current earnings. Managers are thus encouraged to invest for long-run growth rather than short-term profits. The fourth measure is the Amihud illiquidity (ILLIQ), which is defined as the absolute value of daily stock returns dividend by daily dollar trading volume (Amihud, 2002). ILLIQ measures the impact of order flow on the stock price. Following Bhushan (1994), the final measure is dollar trading volume (DVOL), which is the number of shares traded multiplied by the stock price. DVOL is used to inversely measure price pressure and time required to fill an order or to trade a large block of shares. 3.3. The measures of investment frictions We use four measures of financing constraints to proxy for investment frictions. Like Li and Zhang (2010), we use asset size, payout ratio, and credit rating as the first three measures of financing constraints. Asset size (ASSET) is the book value of total assets. Payout ratio ranking (PAYOUT) is the tercile ranking based on payout ratio, which is defined as total dividends (including repurchases) divided by earnings. Credit rating (RATING) is a dummy variable, which is equal to zero if a firm’s public debt has never been rated during our sample period, and one otherwise. Asset size (e.g., Erickson and Whited, 2000; Almeida and Campello, 2007), payout ratio (e.g., Fazzari, Hubbard, and Peterson, 1988; Almeida, Campello, and Weisbach, 2004; Almeida and Campello, 2007), and credit rating (e.g., Almeida, Campello, and Weisbach, 2004; Almeida and Campello, 2007) are widely used as the measures of financing constraints. Barry and Brown (1985) argue that more established firms (i.e., firms with older age) have more information available to the market. Zhang (2006) uses firm age as an inverse measure of information uncertainty. In this study, however, we follow Hadlock and Pierce (2010) to use firm age (AGE) as our final measure of financing constraints.
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years in order to minimize the survivorship and selection biases inherent in the way Compustat adds firms to its database (Banz and Breen, 1986). Following Titman, Wei, and Xie (2004), we remove firms with less than $10 million in sales (Compustat item REVT) to exclude firms at an early stage of development. We also delete firms for which we do not have all the data necessary to compute the variables. The data set covers annual firm characteristics from 1970 to 2009 and monthly stock returns from July of 1971 to December of 2009.8 Due to limitations in the databases, analyses involving analyst features, institutional features, and bid-ask spreads start from 1976, 1980, and 1993, respectively. Panel A of Table 1 reports summary statistics of our sample. The mean of total asset growth (TAG) is 14.7% with a standard deviation of 77.8%, suggesting a significant variation in TAG across firms and over time. Panel B presents the median values of firm characteristics, measures of limits-to-arbitrage, as well as measures of investment frictions for portfolios sorted into total asset-growth deciles. Similar to the findings of previous studies, high asset-growth stocks have lower average subsequent stock returns than low asset-growth stocks. The return spread between low- and high-growth firms is larger for the equal-weighted portfolio (1.185% per month) than for the value-weighted portfolio (0.715% per month). High-growth stocks have larger market values of equity (SIZE), lower book-to-market equity ratios (BM), lower prior six-month stock returns (PRET), higher past net share issuance (NS, NSlag), and lower idiosyncratic volatility (IVOL) than low-growth firms. As these characteristics might be associated with lower subsequent returns for high-growth firms, we control for them in the tests.9 Relative to low-growth firms, high-growth firms also have uniformly lower limits-to-arbitrage. Investment frictions are more or less the same for both the low- and high-growth deciles. Panel C presents the sample correlations among our measures of asset growth, limits-to-arbitrage, and investment frictions. Total asset growth (TAG) is significantly correlated with the measures of limits-to-arbitrage and the measures of investment frictions, except for the number of institutional shareholders (INSTN), asset size (ASSET), and credit rating (RATING). As expected, most of the measures of limits-to-arbitrage are significantly correlated with most of the measures of investment frictions.
3.4. Sample selection and summary statistics The data set used to test the hypotheses is related to U.S. domestic firms traded on the NYSE, Amex, and Nasdaq exchanges. Their financial statements are taken from Compustat. Stock market data come from the Center for Research in Security Prices (CRSP). Analyst data are from the Institutional Brokers’ Estimate System (I/B/E/S). Institutional holdings records are from CDA/Spectrum Institutional (13f) Holdings. Like Fama and French (1992, 1993), certificates, American depositary receipts (ADRs), shares of beneficial interest (SBIs), unit trusts, closed-end funds, real estate investment trusts (REITs), and financial firms are excluded. We also require a firm to have been in the Compustat time series for at least two
8 Our sample seems comparable to those used in previous studies. For example, we observe that only stocks of firms in the highest total asset-growth rank (i.e., decile 10) subsequently underperform. This is consistent with the findings of Chan, Karceski, Lakonishok, and Sougiannis (2008) but is in contrast to those of Cooper, Gulen, and Schill (2008), who find that stocks of low-growth firms subsequently outperform. The sample of Chan, Karceski, Lakonishok, and Sougiannis differs from that of Cooper, Gulen, and Schill in that the former excludes the decile of smallest stocks. Our sample also differs from that of Cooper, Gulen, and Schill because we exclude firms at an early stage of development. 9 See, for example, Fama and French (1992), Ikenberry, Lakonishok, and Vermaelen (1995), Daniel and Titman (1997), Daniel, Titman, and Wei (2001), Daniel and Titman (2006), Fama and French (2008), and Pontiff and Woodgate (2008) for the effects of these firm characteristics on the cross-sectional stock returns.
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For example, the correlations between idiosyncratic volatility (IVOL) and firm age (AGE), asset size (ASSET), payout ratio ranking (PAYOUT), and credit rating (RATING) are 37.8%, 21.4%, 42.4%, and 31.1%, respectively. The correlation between asset size (ASSET) and dollar trading volume (DVOL) is 58.4%. The correlation between credit rating (RATING) and analyst coverage (COV) is 39.3%. These high and significant correlations suggest that both limits-to-arbitrage and investment frictions explanations have similar empirical predictions on the asset growth anomaly. It is therefore important to conduct extensive and joint tests to distinguish between these two explanations. 4. The effect of limits-to-arbitrage on the asset growth anomaly The first regression tests whether or not the mispricing with limits-to-arbitrage can explain the asset growth anomaly while controlling for the increased dispersion in total asset growth which goes with limits-to-arbitrage (H1). More specifically, we follow the methods of Li and Zhang (2010) to examine the slope coefficient of asset growth (c1,j, j ¼1, 2, or 3) in the following Fama and MacBeth (1973) cross-sectional regression of stock returns across the tercile subsamples (Low, Medium, and High) split by a given measure of limits-to-arbitrage. Ri,t ¼ c0,j þ c1,j lnð1 þ TAGi,t1 Þ þbj Controlsji,t1 þ eji,t1 ,
ð1Þ
where Ri,t is the monthly raw return between July of year t and June of year t þ1 (or between July and December for 2009). When j ¼1 (i.e., c1,1), it indicates a baseline regression with no control variables. We test the robustness of the baseline regression slope of asset growth (c1,1) to the inclusion of existing assetpricing characteristics by adding the following controls. The first set of controls is {lnSIZE, lnBM, lnPRET} with j¼2 (i.e., c1,2). The second set of controls is {lnSIZE, lnBM, lnPRET, IVOL, NS, NSlag} with j ¼3 (i.e., c1,3). ln SIZE is the natural logarithm of the market value of equity at the end of June of year t. As in Fama and French (1993), ln BM is the natural logarithm of the book value of equity at the end of the fiscal year ending in calendar year t 1 divided by the market value of equity at the end of December of year t 1. lnPRET is the natural logarithm of the gross stock return of the previous six months at the end of May of year t. NS is share issuance and is defined as the natural logarithm of the ratio of split-adjusted shares outstanding at the end of the previous fiscal year to those at the beginning of that year. NSlag is just NS lagged by one year. We then test the difference in the slope coefficients of asset growth (c1,1, c1,2, or c1,3) between the High and Low limits-to-arbitrage subsamples for significance. Table 2 reports the slope coefficients of asset growth across the tercile subsamples for each of the ten measures of limits-to-arbitrage. The reported slopes are the timeseries averages of the monthly estimated slope coefficients from ordinary least squares (OLS) Fama and MacBeth (1973) cross-sectional regressions. The corresponding t-statistics are calculated with Newey and West
(1987) robust standard errors. To check whether the results are driven by small firms, we also report the estimated slope of asset growth from weighted least squares (WLS) Fama and MacBeth (1973) regressions with market capitalization as the weighting. The subsample with the lowest (highest) limits-to-arbitrage is denoted as the Low (High) group, while the middle subsample is labeled as the Medium group. Using OLS or WLS with or without controls, the regression slopes of asset growth are always negative across all tercile subsamples for all ten measures of limits-to-arbitrage. In addition, the slope spreads between the High and Low subsamples (reported in the last row labeled as High–Low) are all negative except for ten cases. Of the negative cases, 20 are significant at the 5% level or better. We apply two-tailed tests for the significance throughout. The baseline OLS regression without controls generates the slope coefficients of asset growth (c1,1(OLS)) which are all negative and have a higher magnitude when arbitrage is more limited except for dollar trading volume (DVOL). Six of the nine cases with a negative slope spread are statistically significant at the 5% level or better. The three insignificant cases are when analyst forecast dispersion (DISP), cash flow volatility (CVOL), and illiquidity (ILLIQ) are used as the measure of limits-to-arbitrage. When the first set of control variables is included in the regressions, the negative regression slopes of asset growth (c1,2(OLS)) have a higher magnitude when limits-to-arbitrage are more severe for all ten measures of limitsto-arbitrage. In addition, when idiosyncratic return volatility (IVOL), analyst coverage (COV), stock price (PRICE), or institutional ownership (INSTH) is used as the measure of limits-to-arbitrage, the negative regression slope of asset growth (c1,2(OLS)) has a significantly higher magnitude in the High subsample than in the Low subsample. When investor sophistication (INSTN) or bid-ask spread (BIDASK) is used as the measure of limits-to-arbitrage, the slope spreads between the High and Low subsamples are significant at the 10% level (t-statistic¼ 1.91 or 1.92). When the second set of controls is included in the regressions, the results are almost the same (although slightly weaker) as with the first set of controls. The slope coefficients of asset growth (c1,3(OLS)) are negative and have a higher magnitude as limits-to-arbitrage are more severe for all ten measures of the limits. In addition, when idiosyncratic volatility (IVOL), analyst coverage (COV), stock price (PRICE), or bid-ask spread (BIDASK) is used as the measure of limits-to-arbitrage, the negative regression slope of asset growth has a significantly higher magnitude when limits-to-arbitrage are more severe. When the cross-sectional regressions are estimated using the WLS method, the baseline negative regression slopes without controls (c1,1(WLS)) or the negative slopes with controls (c1,2(WLS) or c1,3(WLS)) have a significantly higher magnitude when limits-to-arbitrage are more severe with seven of the ten measures of limits-toarbitrage. Cash flow volatility (CVOL), investor sophistication (INSTN), and institutional ownership (INSTH) are the only exceptions. However, only when idiosyncratic volatility (IVOL) is used as the measure of limits-to-arbitrage, does the negative slope in the High subsample have a
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
135
Table 2 Slopes from the regressions of stock returns against past asset growth in the subsamples split by limits-to-arbitrage measures. This table reports the estimated slopes of asset growth (c1,j, j ¼ 1, 2, or 3) from the following Fama and MacBeth (1973) cross-sectional regression for each tercile subsample (Low, Medium, or High) split by a given measure of limits-to-arbitrage. The measures of limits-to-arbitrage include idiosyncratic volatility (IVOL), analyst coverage (COV), dispersion in analyst forecast (DISP), cash flow volatility (CVOL), shareholder sophistication (INSTN), share price (PRICE), bid-ask spread (BIDASK), institutional ownership (INSTH), Amihud (2002) illiquidity (ILLIQ), and dollar trading volume (DVOL). Ri,t ¼ c0,j þ c1,j lnð1 þ TAGi,t1 Þ þ Control si,j þ ei,j,t , where Ri is monthly raw stock return (%) between July of year t and June of year tþ 1 (or between July and December for 2009). For j ¼1 (c1,1), no control variable is included. For j ¼2 (c1,2) the control variables are natural logarithms of market value of equity (SIZE), book-to-market equity ratio (BM), and prior six-month stock return (PRET). For j¼ 3 (c1,3) the extra control variables are idiosyncratic volatility (IVOL), net share issuance (NS), and lagged net share issuance (NSlag). See the Appendix for detailed definitions of variables. The regressions are estimated cross-sectionally every month between July 1971 and December 2009 (from 1976 when COV and DISP are involved; from July 1980 when INSTN and INSTH are involved; from July 1993 when BIDASK is involved) for each tercile subsample using ordinary least squares (OLS) or weighted least squares (WLS) with SIZE as the weights. The data set is related to U.S. domestic firms traded on the NYSE, Amex, and Nasdaq exchanges. Their financial statements are taken from Compustat. Stock market data come from the Center for Research in Security Prices (CRSP). Analyst data are from the Institutional Brokers’ Estimate System (I/B/E/S). Institutional holdings records are from CDA/Spectrum Institutional (13f) Holdings. The reported slopes are time-series averages of the monthly estimated slope coefficients of asset growth. High–Low is the time-series average of the differences in slope between the High and Low limits-to-arbitrage subsamples. The corresponding t-statistics based on Newey and West (1987) standard errors are in brackets. N is the number of stock-month observations. Coefficients significant at the 5% level are in bold. Limits-to-arbitrage Low (Low IVOL) Medium High (High IVOL) High–Low t(High–Low) Low (High COV) Medium High (Low COV) High–Low t(High–Low) Low (Low DISP) Medium High (High DISP) High–Low (High–Low) Low (Low CVOL) Medium High (High CVOL) High–Low t(High–Low) Low (High INSTN) Medium High (Low INSTN) High–Low t(High–Low) Low (High PRICE) Medium High (Low PRICE) High–Low t(High–Low) Low (Low BIDASK) Medium High (High BIDASK) High–Low t(High–Low) Low (High INSTH) Medium High (Low INSTH)
c1,1(OLS)
c1,2(OLS)
c1,3(OLS)
c1,1(WLS)
c1,2(WLS)
c1,3(WLS)
N
0.325 1.235 1.637
0.025 1.005 1.358
0.112 0.952 1.169
0.600 1.026 1.381
0.241 0.707 1.262
0.304 0.675 1.079
359,654 360,425 359,791
1.312 [ 5.33]
1.333 [ 5.59]
1.281 [ 5.08]
0.782 [ 2.09]
1.021 [ 2.98]
1.383 [ 3.72]
0.673 1.013 1.572
0.576 0.832 1.390
0.474 0.698 1.221
0.603 0.675 1.146
0.517 0.605 0.913
0.312 0.408 0.845
0.899 [ 2.85]
0.815 [ 2.98]
0.747 [ 2.78]
0.543 [ 1.58]
0.396 [ 1.42]
0.534 [ 1.86]
1.010 0.996 1.451
0.904 0.838 1.163
0.796 0.736 1.076
0.208 1.062 1.011
0.072 0.834 0.669
0.043 0.581 0.612
0.442 [ 1.73]
0.259 [ 1.14]
0.280 [ 1.14]
0.803 [ 1.98]
0.596 [ 1.72]
0.568 [ 1.60]
1.215 1.264 1.431
0.800 1.027 1.193
0.632 0.933 1.057
1.327 0.701 0.553
1.192 0.264 0.421
0.749 0.208 0.305
0.217 [ 0.84]
0.393 [ 1.36]
0.425 [ 1.52]
0.774 [1.62]
0.771 [1.68]
0.444 [0.99]
0.951 1.351 1.633
0.819 1.125 1.270
0.760 0.943 1.027
0.600 1.230 0.598
0.558 1.033 0.450
0.330 0.784 0.100
0.681 [ 2.46]
0.452 [ 1.91]
0.267 [ 1.24]
0.002 [0.00]
0.108 [0.26]
0.230 [0.56]
0.642 1.446 1.446
0.539 1.193 1.261
0.429 0.960 1.062
0.689 1.195 1.355
0.514 0.908 1.024
0.276 0.645 0.722
0.804 [ 2.61]
0.722 [ 2.60]
0.633 [ 2.65]
0.666 [ 1.57]
0.510 [ 1.46]
0.446 [ 1.32]
0.642 1.166 1.786
0.644 0.988 1.595
0.485 0.776 1.334
0.271 1.219 1.402
0.321 1.018 1.266
0.198 0.407 0.952
1.144 [ 2.09]
0.952 [ 1.92]
0.849 [ 2.11]
1.132 [ 2.22]
0.945 [ 2.03]
0.754 [ 1.67]
0.968 1.270 1.646
0.806 1.024 1.293
0.688 0.887 1.034
0.860 0.015 0.673
0.766 0.066 0.512
0.453 0.255 0.345
231,114 237,529 225,029
231,716 230,746 231,210
333,323 333,321 333,348
301,586 297,504 305,277
359,791 360,425 359,654
186,804 186,825 186,796
301,454 298,081 304,832
136
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
Table 2 (continued ) Limits-to-arbitrage
c1,1(OLS)
c1,2(OLS)
c1,3(OLS)
c1,1(WLS)
c1,2(WLS)
c1,3(WLS)
High–Low t(High–Low)
0.678 [ 2.56]
0.487 [ 2.01]
0.345 [ 1.44]
0.186 [0.49]
0.254 [0.65]
0.107 [0.25]
1.212 1.325 1.467
0.934 0.992 1.407
0.817 0.779 1.250
0.923 1.173 1.426
0.617 0.833 1.230
0.392 0.628 0.978
0.254 [ 0.73]
0.473 [ 1.56]
0.433 [ 1.57]
0.503 [ 1.22]
0.612 [ 1.49]
0.586 [ 1.63]
1.387 1.185 1.300
1.091 1.018 1.120
0.927 0.964 0.940
0.926 0.926 1.003
0.649 0.689 0.802
0.414 0.567 0.587
0.087 [0.26]
0.028 [ 0.10]
0.013 [ 0.05]
0.077 [ 0.19]
0.153 [ 0.42]
0.173 [ 0.53]
Low (Low ILLIQ) Medium High (High ILLIQ) High–Low t(High–Low) Low (High DVOL) Medium High (Low DVOL) High–Low t(High–Low)
significantly higher magnitude than in the Low subsample in all three model specifications (i.e., c1,1(WLS), c1,2(WLS), and c1,3(WLS)). When no controls are included in the regressions (c1,1(WLS)), the slope spread between the High and Low subsamples is also significant when earnings forecast dispersion (DISP) is used as the measure of limits-to-arbitrage. With no controls (i.e., c1,1(WLS)) or only the first set of controls (i.e., c1,2(WLS)), bid-ask spread (BIDASK) also gives a significant difference. To summarize the results from Table 2, equalweighted results from the individual tests of the effect of limits-to-arbitrage on the asset growth anomaly provide a fair amount of support for the limits-to-arbitrage hypothesis. In contrast, value-weighted results provide only limited support. 5. The effect of investment frictions on the asset growth anomaly We next examine whether or not the q-theory with investment frictions can explain the asset growth anomaly while controlling for the increased dispersion in total asset growth which goes with investment frictions (H2). This time, we examine the slopes of asset growth (c1,1, c1,2, or c1,3) in regression (1) across the tercile subsamples split by a given measure of investment frictions. We then test the difference in the slope coefficients between the High and Low investment frictions subsamples. Table 3 reports the results. The evidence from both OLS and WLS regressions with or without controls indicates that the regression slopes of asset growth are all negative across all tercile subsamples (or across both the High and Low RATING subsamples) with all four measures of investment frictions. In addition, the slope spreads between the High and Low investment frictions subsamples are all negative, and nine (out of 24) are significant at the 5% level or better. More specifically, the baseline results from the OLS regressions without controls indicate that the negative slope coefficient of asset growth (i.e., c1,1(OLS)) has a significantly higher magnitude as investment frictions become more severe when firm age (AGE) or credit rating (RATING) is used as the measure of investment frictions.
N
341,422 341,543 341,418
359,926 359,704 360,240
When asset size (ASSET) is used as the measure of investment frictions, the slope spread between the High and Low subsamples is significant at the 10% level (t-statistic¼1.89). When controls are included in the regressions, these negative slopes of asset growth (c1,2(OLS) and c1,3(OLS)) maintain a significantly higher magnitude in the subsample of younger firms (AGE) or firms with unrated public debt (RATING) than in the subsample of older firms or firms with rated public debt. Further, these negative slopes become higher in magnitude in the subsample of firms with small asset size (ASSET) than in the subsample of firms with big asset size. When the cross-sectional regressions are estimated using the WLS method with market capitalization as the weighting, the negative slope of asset growth (c1,3(WLS)) with the second set of controls has a significantly higher magnitude at the 1% level when investment frictions are more severe only when firm age (AGE) is used as the measure of investment frictions. When the first or the second set of controls is included in the regression, the slope spread between the High and Low subsamples is significant at the 10% level (t-statistic¼ 1.94) when asset size (ASSET) is used as the measure of investment frictions. To summarize the results from Table 3, equalweighted results from individual tests of the effect of investment frictions on the asset growth anomaly provide a fair amount of support for the investment frictions hypothesis. However, value-weighted results provide relatively weak support. These results are similar to those analyzing limits-to-arbitrage. Comparing the results in Table 2 with those in Table 3, we find that the number of cases providing support for each hypothesis is similar. In the equal-weighted regressions, of the 30 asset growth slope differences between the High and Low limits-to-arbitrage subsamples in Table 2, 14 (47%) are significantly negative. Of the 12 slope differences between the High and Low financing constraints subsamples in Table 3, eight (67%) are significantly negative. The results from the value-weighted regressions are much weaker. Only six (20%) cases provide significant support for the limits-to-arbitrage hypothesis, while only one (8.3%) does so for the investment frictions hypothesis. Nevertheless, there are no
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
137
Table 3 Slopes from the regressions of stock returns against past asset growth in subsamples split by investment frictions measures. This table reports the estimated slopes of asset growth (c1,j, j ¼ 1, 2, or 3) from the following Fama and MacBeth (1973) cross-sectional regression for each tercile subsample (Low, Medium, or High) split by a given measure of investment frictions. The measures of investment frictions include firm age (AGE), asset size (ASSET), payout tercile ranking (PAYOUT), and credit rating (RATING). Ri,t ¼ c0,j þ c1,j lnð1 þ TAGi,t1 Þ þ Control si,j þ ei,j,t , where Ri is monthly raw stock return (%) between July of year t and June of year t þ 1 (or between July and December for year 2009). For j¼ 1 (c1,1), no control variable is included. For j¼ 2 (c1,2) the control variables are natural logarithms of market value of equity (SIZE), book-to-market equity ratio (BM), and prior six-month stock return (PRET). For j ¼3 (c1,3) the extra control variables are idiosyncratic volatility (IVOL), net share issuance (NS), and lagged net share issuance (NSlag). See the Appendix for detailed definitions of variables. The regressions are estimated cross-sectionally each month between July 1971 and December 2009 (from 1976 when COV and DISP are involved; from July 1980 when INSTN and INSTH are involved; from July 1993 when BIDASK is involved) for each tercile subsample using ordinary least squares (OLS) or weighted least squares (WLS) with SIZE as the weights. The data set is related to U.S. domestic firms traded on the NYSE, Amex, and Nasdaq exchanges. Their financial statements are taken from Compustat. Stock market data come from the Center for Research in Security Prices (CRSP). Analyst data are from the Institutional Brokers’ Estimate System (I/B/E/S). Institutional holdings records are from CDA/Spectrum Institutional (13f) Holdings. The reported slopes are time-series averages of the monthly estimated slope coefficients of asset growth. High–Low is the time-series average of the differences in slope between the High and Low investment frictions subsamples. The corresponding t-statistics based on Newey and West (1987) standard errors are in brackets. N is the number of stock-month observations. Coefficients significant at the 5% level are in bold. Investment frictions Low (High AGE) Medium High (Low AGE) High–Low t(High–Low) Low (High ASSET) Medium High (Low ASSET) High–Low t(High–Low) Low (High PAYOUT) Medium High (Low PAYOUT) High–Low t(High–Low) Low (RATING¼ Yes) High (RATING¼ No) High–Low t(High–Low)
c1,1(OLS)
c1,2(OLS)
c1,3(OLS)
c1,1(WLS)
c1,2(WLS)
c1,3(WLS)
N
0.670 1.212 1.563
0.394 0.961 1.266
0.202 0.836 1.137
0.646 0.788 1.125
0.422 0.480 0.949
0.068 0.212 0.900
371,565 351,421 356,884
0.893 [ 3.47]
0.871 [ 3.66]
0.936 [ 3.75]
0.478 [ 1.28]
0.526 [ 1.64]
0.832 [ 2.81]
1.051 1.150 1.600
0.682 0.985 1.312
0.546 0.843 1.095
0.828 1.099 1.434
0.533 0.763 1.294
0.310 0.697 0.966
0.549 [ 1.89]
0.630 [ 2.23]
0.549 [ 2.12]
0.606 [ 1.48]
0.760 [ 1.94]
0.656 [ 1.94]
1.195 1.420 1.357
1.013 1.139 1.070
0.760 1.005 0.972
0.646 0.954 1.087
0.491 0.382 0.816
0.204 0.293 0.586
0.162 [ 0.59]
0.057 [ 0.24]
0.213 [ 0.97]
0.441 [ 0.99]
0.325 [ 0.82]
0.381 [ 1.02]
0.458 1.047
0.189 1.212
0.191 1.005
0.772 0.903
0.419 0.767
0.349 0.571
1.015 [ 3.54]
1.023 [ 2.97]
0.813 [ 2.24]
0.132 [ 0.40]
0.348 [ 1.16]
0.222 [ 0.78]
cases against either hypothesis in either equal-weighted or value-weighted regressions. 6. The joint effects of limits-to-arbitrage and investment frictions on the asset growth anomaly As discussed earlier, the supporting evidence from the individual tests does not allow us to disentangle the limits-to-arbitrage explanation from the investment frictions explanation. To achieve this, we extend the analyses in Sections 4 and 5 by independently sorting firms into terciles based on each of the ten measures of limits-toarbitrage and each of the four measures of investment frictions. The intersection of the three-by-three sorted sub-groups results in nine subsamples for each set of combinations. To examine H3, we test the differences in the slopes of asset growth (c1,1, c1,2, or c1,3) in regression (1) between the High and Low limits-to-arbitrage subsamples across different investment frictions sub-groups or alternatively between the High and Low investment frictions subsamples across different limits-of-arbitrage
359,942 359,964 359,964
409,287 307,547 363,036
835,119 250,572
sub-groups. Equivalently, we test the limits-to-arbitrage hypothesis while controlling for investment frictions and vice versa. Panels A to C of Table 4 report the differences in the regression slopes of asset growth (c1,1, c1,2, or c1,3) between the High and Low limits-to-arbitrage subsamples for High, Medium, and Low investment frictions subgroups. In the equal-weighted regressions, negative differences in the regression slope of asset growth outnumber positive differences by 268 to 62. In other words, the differences in the regression slope of asset growth are negative in 81.2% of the cases. Among these negative differences in slope, 72 of them are statistically significant at the 5% level or better. In addition, when limits-to-arbitrage are measured by idiosyncratic return volatility (IVOL), analyst coverage (COV), stock price (PRICE), or bid-ask spread (BIDASK), there are at least some cases where the differences in the slope of asset growth are significantly negative at the 5% level across each of the investment frictions sub-groups. Further, there are more significant differences in the slope of asset
138
Table 4 Differences in the regression slope of asset growth between the high and low limits-to-arbitrage subsamples controlling for investment frictions. This table reports the time-series averages of the differences in the regression slope of asset growth (c1,1, c1,2, or c1,3) between the High and Low limits-to-arbitrage subsamples across tercile subgroups sorted by a given measure of investment frictions. See Table 2 for regression specifications, the definition of differences in slope, and the sample periods. The measures of limits-to-arbitrage are idiosyncratic volatility (IVOL), analyst coverage (COV), dispersion in analyst forecast (DISP), cash flow volatility (CVOL), shareholder sophistication (INSTN), share price (PRICE), bid-ask spread (BIDASK), institutional ownership (INSTH), the Amihud (2002) illiquidity (ILLIQ), and dollar trading volume (DVOL). The measures of investment frictions are firm age (AGE), asset size (ASSET), payout ratio ranking (PAYOUT), and credit rating (RATING). See the Appendix for detailed definitions of variables. The data set is related to U.S. domestic firms traded on the NYSE, Amex, and Nasdaq exchanges. Their financial statements are taken from Compustat. Stock market data come from the Center for Research in Security Prices (CRSP). Analyst data are from the Institutional Brokers’ Estimate System (I/B/E/S). Institutional holdings records are from CDA/Spectrum Institutional (13f) Holdings. The t-statistics based on Newey and West (1987) standard errors are in brackets. Coefficients significant at the 5% level are in bold. Panel A: High investment frictions sub-group Differences in
Low AGE
Low ASSET
Low PAYOUT
RATING ¼0
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
1.549 1.444 1.275 0.706 1.344 1.607
[ 3.84] [ 3.48] [ 2.89] [ 1.20] [ 2.31] [ 2.15]
2.917 2.427 3.113 2.786 2.356 2.893
[ 3.64] [ 2.82] [ 2.33] [ 3.15] [ 2.57] [ 2.64]
1.311 1.174 1.269 0.489 0.257 0.270
[ 2.31] [ 1.73] [ 1.63] [0.75] [ 0.33] [ 0.33]
1.423 1.404 1.171 0.716 0.941 0.808
[ 5.43] [ 5.44] [ 4.17] [ 1.32] [ 2.07] [ 1.66]
COV
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.867 0.486 0.032 0.463 0.152 0.230
[ 1.77] [ 1.02] [ 0.06] [ 0.82] [0.29] [0.42]
0.718 1.344 0.582 0.372 1.099 0.777
[ 0.88] [ 1.38] [ 0.43] [ 0.37] [ 1.10] [ 0.58]
0.820 0.530 0.429 0.958 0.482 0.618
[ 2.06] [ 1.33] [ 1.04] [ 1.78] [ 0.96] [ 1.16]
0.557 0.331 0.233 0.366 0.022 0.053
[ 1.63] [ 1.10] [ 0.77] [ 0.88] [0.06] [ 0.13]
DISP
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.353 0.186 0.250 1.189 0.613 0.578
[ 0.94] [ 0.52] [ 0.60] [ 1.97] [ 1.08] [ 1.04]
0.355 0.190 0.080 0.075 0.270 0.519
[ 1.07] [ 0.60] [ 0.23] [ 0.16] [0.62] [1.16]
0.506 0.459 0.483 0.768 0.703 0.659
[ 1.58] [ 1.35] [ 1.30] [ 1.40] [ 1.56] [ 1.30]
0.425 0.186 0.201 0.813 0.757 0.994
[ 1.63] [ 0.75] [ 0.77] [ 1.72] [ 1.87] [ 2.40]
CVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.216 1.120 0.122 0.806 0.761 0.388
[0.55] [ 0.30] [ 0.30] [1.24] [1.32] [0.65]
0.056 0.132 0.274 0.161 0.054 0.119
[0.10] [ 0.21] [ 0.44] [0.22] [ 0.07] [ 0.17]
0.066 0.385 0.252 0.774 0.149 0.655
[ 0.17] [ 0.92] [0.72] [0.97] [0.18] [ 0.81]
0.053 0.227 0.478 0.884 0.863 0.646
[ 0.18] [ 0.69] [ 1.47] [1.43] [1.65] [1.22]
INSTN
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.566 0.121 0.075 1.074 0.243 0.360
[ 1.76] [ 0.36] [ 0.22] [ 2.19] [ 0.48] [0.63]
1.512 4.337 5.458 1.937 4.242 5.490
[ 0.93] [ 1.41] [ 1.40] [ 1.17] [ 1.38] [ 1.41]
0.504 0.069 0.031 0.433 0.197 0.455
[ 1.54] [ 0.20] [ 0.08] [ 0.86] [0.40] [0.96]
0.739 0.506 0.216 0.473 0.360 0.197
[ 2.41] [ 1.81] [ 0.87] [ 1.05] [ 1.04] [ 0.50]
PRICE
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.980 0.955 0.721 1.021 0.776 0.568
[ 2.73] [ 2.49] [ 2.05] [ 1.89] [ 1.37] [ 1.01]
0.938 0.360 0.018 0.745 0.481 0.440
[ 1.41] [ 0.54] [ 0.02] [ 0.97] [0.63] [0.48]
0.850 0.958 1.017 0.859 0.907 0.720
[ 2.13] [ 2.45] [ 2.56] [ 1.57] [ 1.72] [ 1.40]
0.726 0.646 0.544 0.960 0.739 0.694
[ 2.33] [ 2.23] [ 2.02] [ 2.02] [ 1.87] [ 1.68]
c1,1(OLS)
1.501
[ 2.34]
0.631
[0.61]
1.205
[ 2.07]
1.142
[ 2.02]
BIDASK
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
IVOL
1.392 1.389 1.083 1.048 1.186
[ 2.28] [ 2.42] [ 1.61] [ 1.62] [ 1.84]
0.114 0.160 0.244 0.089 0.600
[0.11] [0.16] [ 0.26] [0.09] [0.49]
0.833 0.856 1.059 0.862 1.212
[ 1.57] [ 1.63] [ 1.59] [ 1.37] [ 1.84]
0.900 0.746 1.735 1.276 1.244
[ 1.89] [ 1.88] [ 2.72] [ 2.41] [ 2.11]
INSTH
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.693 0.237 0.127 0.999 0.495 0.075
[ 2.47] [ 0.82] [ 0.42] [ 2.03] [ 1.04] [0.14]
0.558 0.106 0.035 0.435 0.007 0.053
[ 1.71] [ 0.30] [ 0.09] [ 0.80] [0.01] [0.10]
1.378 0.940 0.835 1.742 0.720 0.369
[ 2.54] [ 1.77] [ 1.48] [ 2.76] [ 1.06] [ 0.52]
0.698 0.465 0.239 0.157 0.137 0.040
[ 2.46] [ 1.73] [ 0.90] [ 0.41] [ 0.42] [ 0.10]
ILLIQ
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.276 0.484 0.318 0.622 0.595 0.550
[ 0.61] [ 1.05] [ 0.68] [ 1.16] [ 1.11] [ 1.05]
0.629 4.015 5.822 1.220 4.104 7.270
[ 0.13] [0.64] [0.89] [ 0.25] [0.65] [1.10]
0.008 0.161 0.254 0.589 0.555 0.641
[ 0.02] [ 0.38] [ 0.62] [ 1.11] [ 0.96] [ 1.10]
0.242 0.300 0.218 0.743 0.557 0.521
[ 0.65] [ 0.92] [ 0.73] [ 1.80] [ 1.42] [ 1.36]
DVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.034 0.103 0.145 0.185 0.238 0.202
[ 0.09] [0.29] [0.40] [0.39] [0.51] [0.44]
1.356 1.538 0.720 1.446 1.897 0.607
[1.24] [1.28] [ 0.54] [1.41] [1.61] [ 0.45]
0.063 0.036 0.120 0.031 0.013 0.295
[ 0.16] [ 0.09] [ 0.33] [ 0.06] [0.03] [ 0.57]
0.188 0.085 0.096 0.067 0.083 0.081
[0.53] [0.27] [0.33] [ 0.16] [ 0.22] [ 0.22]
Panel B: Medium investment frictions sub-group Differences in
Medium AGE
Medium ASSET
Medium PAYOUT
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
1.308 1.502 1.579 1.913 1.827 1.936
[ 2.93] [ 3.73] [ 3.57] [ 2.99] [ 3.04] [ 3.14]
0.976 1.142 1.049 1.108 1.464 1.409
[ 2.33] [ 2.67] [ 2.19] [ 2.52] [ 3.26] [ 3.07]
1.370 1.402 1.138 0.842 1.425 1.168
[ 2.31] [ 3.44] [ 2.65] [ 1.54] [ 2.44] [ 1.82]
COV
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.810 0.722 0.723 0.974 0.693 0.587
[ 1.86] [ 1.58] [ 1.66] [ 1.82] [ 1.26] [ 1.16]
0.112 0.163 0.358 0.043 0.163 0.463
[ 0.23] [ 0.38] [0.79] [ 0.08] [0.37] [1.04]
0.657 1.011 0.796 0.488 0.812 0.547
[ 1.32] [ 1.98] [ 1.49] [ 0.79] [ 1.45] [ 0.93]
DISP
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.480 0.342 0.660 1.229 1.069 1.112
[ 1.20] [ 0.88] [ 1.49] [ 1.76] [ 1.62] [ 1.53]
1.216 0.940 1.153 1.987 1.360 1.640
[ 2.56] [ 1.95] [ 2.33] [ 3.12] [ 2.12] [ 2.39]
0.731 0.222 0.244 0.270 0.700 0.049
[ 1.39] [ 0.38] [ 0.39] [0.37] [1.08] [0.07]
CVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS)
0.617 0.724 0.855 0.329 0.216
[ 1.45] [ 1.51] [ 1.80] [0.53] [0.41]
0.394 0.860 0.821 0.233 0.623
[ 0.90] [ 1.78] [ 1.56] [0.44] [ 1.13]
0.439 0.441 0.456 1.802 1.053
[ 1.05] [ 1.05] [ 1.03] [2.80] [1.68]
139
IVOL
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
140
Table 4 (continued ) Panel B: Medium investment frictions sub-group Differences in
Medium AGE
Medium ASSET
Medium PAYOUT
0.310
[0.53]
0.613
[ 1.18]
1.048
[1.42]
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.667 0.493 0.556 0.554 0.037 0.042
[ 1.61] [ 1.27] [ 1.35] [0.89] [ 0.07] [0.08]
0.132 0.008 0.333 0.984 0.781 0.199
[ 0.36] [0.02] [0.83] [ 1.99] [ 1.59] [ 0.37]
0.284 0.189 0.071 0.507 0.962 1.099
[ 0.80] [ 0.54] [0.19] [0.86] [1.67] [1.63]
PRICE
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.501 0.471 0.691 0.173 0.167 0.471
[ 1.16] [ 1.15] [ 1.53] [ 0.29] [ 0.31] [ 0.82]
0.059 0.044 0.033 0.434 0.383 0.494
[ 0.12] [ 0.09] [ 0.06] [0.86] [0.76] [0.89]
1.109 1.234 1.139 0.785 1.070 0.857
[ 2.19] [ 2.54] [ 2.24] [ 1.10] [ 1.46] [ 1.14]
BIDASK
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.393 0.088 0.206 0.273 0.031 0.040
[ 0.70] [0.17] [ 0.42] [ 0.44] [0.05] [ 0.06]
1.512 1.149 1.060 1.945 1.583 1.441
[ 2.22] [ 2.27] [ 2.32] [ 2.71] [ 2.85] [ 2.51]
0.796 0.739 0.461 1.272 0.315 0.189
[ 1.23] [ 1.23] [ 0.75] [ 1.80] [ 0.35] [ 0.21]
INSTH
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.669 0.509 0.597 1.190 0.331 0.449
[ 1.51] [ 1.24] [ 1.36] [1.80] [0.56] [0.73]
0.458 0.451 0.283 0.574 1.024 1.138
[ 1.18] [ 1.20] [ 0.69] [0.92] [1.79] [1.87]
0.167 0.078 0.022 1.133 1.050 0.375
[ 0.46] [ 0.23] [0.06] [ 2.45] [ 2.23] [ 0.71]
ILLIQ
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.108 0.051 0.339 0.452 0.331 0.363
[ 0.22] [ 0.11] [ 0.73] [ 0.79] [ 0.57] [ 0.60]
0.096 0.499 0.534 0.003 0.341 0.338
[ 0.17] [ 0.82] [ 0.86] [ 0.00] [ 0.56] [ 0.57]
0.796 1.218 1.085 0.811 1.305 1.088
[ 1.69] [ 2.75] [ 2.30] [ 1.57] [ 2.52] [ 2.02]
DVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.093 0.379 2.734 1.085 0.312 2.611
[0.13] [0.46] [0.94] [ 1.31] [ 0.35] [0.97]
0.073 0.111 0.083 0.086 0.042 0.109
[ 0.14] [ 0.21] [ 0.17] [0.18] [ 0.08] [0.22]
0.226 0.465 0.316 0.542 0.962 0.708
[ 0.51] [ 1.24] [ 0.81] [ 1.31] [ 2.52] [ 1.68]
Panel C: Low investment frictions sub-group Differences in
IVOL
c1,1(OLS) c1,2(OLS)
High AGE
0.138 0.120
High ASSET
[0.27] [ 0.23]
1.383 1.359
High PAYOUT
[ 3.14] [ 3.26]
1.315 1.531
[ 2.82] [ 3.17]
RATING ¼1
0.775 0.238
[ 1.27] [ 0.30]
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
c1,3(WLS) INSTN
[0.14] [ 0.66] [ 0.00] [ 0.14]
1.381 1.332 1.342 1.900
[ 2.92] [ 2.22] [ 2.50] [ 3.42]
1.428 0.914 1.034 1.379
[ 2.92] [ 1.44] [ 1.85] [ 2.21]
0.449 0.966 0.515 0.197
[0.55] [ 1.35] [ 0.64] [0.24]
COV
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.787 0.879 0.866 0.144 0.335 0.446
[ 1.40] [ 1.67] [ 1.68] [ 0.19] [ 0.57] [ 0.73]
0.588 0.258 0.017 0.808 1.167 0.965
[ 0.93] [ 0.40] [0.03] [1.05] [1.65] [1.36]
1.177 0.911 0.730 0.720 0.235 0.000
[ 2.33] [ 2.02] [ 1.41] [ 1.13] [ 0.42] [0.00]
1.103 0.837 0.646 0.187 0.327 0.011
[ 1.99] [ 1.63] [ 1.18] [ 0.32] [ 0.60] [ 0.02]
DISP
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.065 0.010 0.076 0.069 0.496 0.525
[0.12] [0.02] [ 0.15] [ 0.10] [ 0.86] [ 0.81]
0.481 0.363 0.234 0.604 0.546 0.418
[ 1.03] [ 0.84] [ 0.51] [ 1.00] [ 1.07] [ 0.78]
0.159 0.176 0.166 1.266 1.470 0.685
[ 0.35] [ 0.42] [ 0.38] [ 1.75] [ 2.30] [ 1.05]
0.902 1.086 1.023 1.001 0.624 0.787
[ 1.92] [ 2.60] [ 2.25] [ 1.59] [ 1.25] [ 1.29]
CVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.319 0.409 0.184 0.815 0.955 0.813
[0.76] [0.80] [0.36] [1.19] [1.33] [1.09]
0.393 0.590 0.403 1.199 1.177 1.197
[0.99] [1.41] [1.00] [2.04] [2.06] [2.04]
0.251 0.511 0.184 0.302 0.543 0.714
[ 0.50] [ 0.88] [ 0.44] [0.37] [0.71] [0.93]
0.376 0.562 0.700 0.567 0.479 0.671
[0.59] [0.88] [1.05] [0.79] [0.76] [0.85]
INSTN
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.463 0.452 0.000 0.745 0.415 0.670
[ 1.19] [ 1.27] [ 0.00] [1.15] [0.68] [1.03]
0.096 0.027 0.039 0.410 0.381 0.595
[ 0.20] [0.06] [ 0.08] [0.75] [0.75] [1.02]
1.341 1.243 0.914 0.513 0.353 0.285
[ 3.28] [ 3.25] [ 2.46] [0.62] [0.48] [0.43]
0.033 0.446 0.176 0.473 0.461 0.145
[0.06] [0.85] [0.33] [0.73] [0.81] [0.22]
PRICE
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.099 0.047 0.342 0.216 0.049 0.044
[0.20] [0.10] [0.63] [0.30] [0.08] [ 0.07]
1.229 0.812 1.517 1.340 0.767 1.336
[ 2.08] [ 1.31] [ 2.16] [ 1.85] [ 1.19] [ 1.85]
0.517 0.602 0.479 0.341 0.510 0.837
[ 1.23] [ 1.43] [ 1.06] [ 0.57] [ 0.92] [ 1.41]
0.595 0.723 0.345 2.453 1.959 1.007
[0.56] [0.64] [0.26] [1.17] [1.06] [0.63]
BIDASK
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
1.097 0.884 0.091 1.945 1.337 1.139
[ 1.41] [ 1.12] [ 0.11] [ 2.17] [ 1.62] [ 1.17]
0.048 0.138 0.237 0.022 1.013 1.370
[ 0.06] [ 0.16] [0.23] [ 0.02] [0.84] [1.23]
1.385 1.496 1.281 2.689 2.663 2.151
[ 2.52] [ 2.71] [ 2.55] [ 3.35] [ 3.58] [ 2.79]
1.629 1.486 1.530 0.888 0.023 0.206
[ 1.92] [ 1.98] [ 1.79] [ 0.78] [ 0.02] [0.20]
INSTH
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.412 0.453 0.137 0.816 0.505 0.478
[ 0.96] [ 1.15] [ 0.35] [1.29] [0.77] [0.70]
1.293 1.261 1.015 0.875 0.788 0.456
[ 2.99] [ 2.98] [ 2.59] [1.33] [1.29] [0.69]
0.016 0.081 0.089 0.622 0.595 0.499
[ 0.04] [0.19] [0.17] [1.27] [1.14] [0.79]
0.020 0.227 0.186 0.682 0.723 0.399
[ 0.04] [0.52] [ 0.37] [1.16] [1.41] [0.65]
ILLIQ
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS)
1.399 0.761 1.019 0.775
[1.81] [1.12] [1.44] [1.03]
4.348 5.990 6.405 6.127
[ 1.21] [ 1.21] [0.64] [ 1.73]
0.354 0.833 0.859 0.231
[ 0.76] [ 1.66] [ 1.84] [ 0.42]
0.141 1.127 0.627 0.348
[0.15] [1.13] [0.53] [0.35]
141
0.078 0.572 0.002 0.107
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.383 0.074 0.441 0.016 0.237 0.010 [0.44] [ 0.57] [ 0.95] [0.44] [0.45] [0.17] 0.216 0.281 0.466 0.239 0.239 0.090 [ 1.09] [ 0.53] [0.92] [ 0.99] [0.08] [1.06]
[ 0.71] [ 0.63]
1.720 1.331 4.989 1.384 0.207 5.675 [ 0.63] [ 1.02] [ 1.15] [ 0.61] [ 1.23] [ 1.17] 1.293 10.601 13.908 1.513 18.030 14.170 c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS) DVOL
0.331 0.460 c1,2(WLS) c1,3(WLS)
Differences in
Panel C: Low investment frictions sub-group
Table 4 (continued )
High AGE
[0.53] [0.69]
6.814 5.840
High ASSET
[ 1.43] [0.59]
0.376 0.340
High PAYOUT
0.972 0.685
RATING ¼1
[ 0.44] [ 0.08] [ 0.47] [ 0.02] [ 0.28] [0.01]
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
[0.97] [0.59]
142
growth among the High investment frictions sub-groups than among the Low investment frictions sub-groups when limits-to-arbitrage are measured by idiosyncratic volatility (IVOL), stock price (PRICE), or bid-ask spread (BIDASK). In the value-weighted regressions, negative differences in the regression slope of asset growth also outnumber positive differences by 205 to 125. In other words, the differences are negative in 62.1% of the cases. Among these negative differences in slope, 47 of them are statistically significant at the 5% level. In addition, there are at least some cases where the differences in slope are significant across all investment frictions sub-groups when limits-to-arbitrage are measured by idiosyncratic volatility (IVOL), analyst forecast dispersion (DISP), or bidask spread (BIDASK). There are more significant differences in the slope of asset growth among the High investment frictions sub-groups than among the Low investment frictions sub-groups when limits-to-arbitrage are measured by idiosyncratic volatility (IVOL) or analyst forecast dispersion (DISP). Overall, the results from double split-sample regressions reported in Table 4 show that after controlling for investment frictions, the negative slope coefficients of asset growth have in general a higher magnitude when limits-to-arbitrage are more severe. In addition, the value-weighted results are weaker than the equalweighted results. It appears that the effect of limits-toarbitrage on the asset growth anomaly is stronger when investment frictions are higher. Finally, we test the investment frictions hypothesis while controlling for limits-to-arbitrage. Panels A to C of Table 5 report the differences in the slope coefficient of asset growth between the High and Low investment frictions subsamples for High, Medium, and Low limitsto-arbitrage sub-groups. In the equal-weighted regressions, negative differences in the regression slope of asset growth outnumber positive differences by 274 to 86. That is, the difference in the regression slope is negative in 76.1% of the cases. Among these negative differences in slope, 93 are statistically significant at the 5% level or better. Further, there are at least some cases where the differences in slope are significant across each of the tercile limits-to-arbitrage sub-groups when investment frictions are measured by firm age (AGE), asset size (ASSET), or credit rating (RATING). There are more significant differences in slope among the High limits-to-arbitrage sub-groups than among the Low limits-to-arbitrage sub-groups when investment frictions are measured in terms of firm age (AGE) or asset size (ASSET). In the value-weighted regressions, negative differences in the regression slope of asset growth also outnumber positive differences by 275 to 85, which is little different from the equal-weighted regressions. Now, however, among the negative differences in slope, only 49 are statistically significant. Further, only when investment frictions are proxied by firm age (AGE) are there at least some cases where the differences in slope are significant across each of the tercile limits-to-arbitrage sub-groups. There are also more significant differences in slope among
Table 5 Differences in the regression slope of asset growth between the high and low investment frictions subsamples controlling for limits-to-arbitrage. This table reports the time-series averages of the differences in the regression slope of asset growth (c1,1, c1,2, or c1,3) between the High and Low investment frictions subsamples across tercile subgroups sorted by a given measure of limits-to-arbitrage. See Table 3 for regression specifications, the definition of differences in slope, and the sample periods. The measures of investment frictions are firm age (AGE), asset size (ASSET), payout ratio ranking (PAYOUT), and credit rating (RATING). The measures of limits-to-arbitrage are idiosyncratic volatility (IVOL), analyst coverage (COV), dispersion in analyst forecast (DISP), cash flow volatility (CVOL), shareholder sophistication (INSTN), share price (PRICE), bid-ask spread (BIDASK), institutional ownership (INSTH), the Amihud (2002) illiquidity (ILLIQ), and dollar trading volume (DVOL). See the Appendix for detailed definitions of variables. The data set is related to U.S. domestic firms traded on the NYSE, Amex, and Nasdaq exchanges. Their financial statements are taken from Compustat. Stock market data come from the Center for Research in Security Prices (CRSP). Analyst data are from the Institutional Brokers’ Estimate System (I/B/E/S). Institutional holdings records are from CDA/Spectrum Institutional (13f) Holdings. The t-statistics based on Newey and West (1987) standard errors are in brackets. Coefficients significant at the 5% level are in bold. Panel A: High limits-to-arbitrage sub-group Differences in
AGE
ASSET
PAYOUT
RATING
1.274 0.965 1.122 0.090 1.068 1.149
[ 2.73] [ 2.05] [ 2.30] [0.11] [ 1.59] [ 1.75]
0.015 0.000 0.101 0.344 0.162 0.700
[0.03] [0.00] [0.21] [0.54] [0.26] [1.20]
0.252 0.482 0.242 0.052 0.174 0.047
[0.59] [1.16] [0.57] [0.09] [0.32] [0.08]
0.540 1.049 1.582 0.183 0.571 1.365
[ 0.91] [ 1.23] [ 1.76] [0.26] [ 0.65] [ 1.60]
Low COV
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.464 0.322 0.237 0.377 0.169 0.432
[ 0.80] [ 0.61] [ 0.44] [ 0.57] [ 0.28] [ 0.65]
0.457 0.659 1.102 1.829 1.894 1.845
[ 0.71] [ 0.95] [ 1.64] [ 2.51] [ 2.72] [ 2.56]
0.336 0.296 0.424 0.217 0.134 1.008
[0.84] [0.76] [ 0.97] [ 0.41] [ 0.26] [ 1.76]
0.249 0.375 0.397 0.112 0.127 0.384
[ 0.50] [ 0.79] [ 0.75] [ 0.22] [ 0.25] [ 0.74]
High DISP
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.774 0.824 0.851 0.689 0.539 0.575
[ 1.98] [ 2.10] [ 1.98] [ 1.13] [ 1.00] [ 1.01]
0.475 0.446 0.596 0.175 0.104 0.025
[ 1.12] [ 1.14] [ 1.46] [ 0.31] [ 0.22] [ 0.05]
0.090 0.151 0.689 0.243 0.134 0.727
[ 0.28] [ 0.44] [ 1.71] [ 0.38] [ 0.24] [ 1.25]
0.525 0.301 0.256 0.259 0.475 0.169
[ 1.17] [ 0.74] [ 0.59] [0.48] [ 1.03] [ 0.35]
High CVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.835 0.803 0.794 0.742 0.815 0.874
[ 2.28] [ 2.13] [ 2.16] [ 1.37] [ 1.69] [ 1.63]
0.643 0.832 0.770 1.299 1.292 1.419
[ 1.82] [ 2.44] [ 2.16] [ 2.64] [ 2.64] [ 3.10]
0.137 0.252 0.129 0.319 0.382 0.786
[0.41] [0.72] [0.38] [ 0.56] [ 0.73] [ 1.41]
1.056 1.455 1.576 0.169 0.355 0.839
[ 2.25] [ 2.51] [ 2.62] [0.33] [ 0.73] [ 1.39]
Low INSTN
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.640 0.449 0.737 1.572 0.887 0.781
[ 1.58] [ 1.26] [ 1.83] [ 3.00] [ 1.93] [ 1.60]
0.999 0.828 0.592 1.607 1.017 1.180
[ 1.74] [ 1.51] [ 1.09] [ 2.95] [ 1.86] [ 1.92]
0.302 0.581 0.230 1.541 0.765 0.378
[0.85] [1.81] [0.69] [ 1.80] [ 1.10] [ 0.58]
1.426 1.533 1.077 1.064 1.127 0.822
[ 2.57] [ 3.22] [ 2.06] [ 2.01] [ 2.63] [ 1.33]
Low PRICE
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
1.486 1.287 1.641 1.407 0.981 0.910
[ 3.06] [ 2.73] [ 3.14] [ 2.04] [ 1.63] [ 1.35]
0.192 0.256 0.405 0.321 0.132 0.371
[0.34] [ 0.44] [0.59] [0.45] [ 0.19] [0.50]
0.250 0.053 0.402 0.217 0.254 0.246
[ 0.61] [ 0.13] [ 0.94] [ 0.37] [0.47] [0.42]
1.890 1.795 1.210 3.219 2.760 1.671
[ 1.84] [ 1.58] [ 0.90] [ 1.54] [ 1.40] [ 0.99] 143
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
High IVOL
144
Table 5 (continued ) Panel A: High limits-to-arbitrage sub-group Differences in
AGE
ASSET
PAYOUT
RATING
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.848 1.026 1.530 0.135 0.416 0.775
[ 1.32] [ 1.58] [ 2.04] [0.16] [ 0.54] [ 0.98]
0.976 0.692 0.871 1.524 2.110 2.383
[ 1.21] [ 0.77] [ 0.87] [ 1.33] [ 1.80] [ 2.39]
0.401 0.572 0.025 1.190 1.462 0.812
[1.27] [1.68] [ 0.06] [1.84] [2.07] [1.11]
0.328 0.430 0.885 0.355 1.225 1.233
[0.48] [0.68] [1.03] [ 0.34] [ 1.40] [ 1.30]
Low INSTH
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.742 0.522 0.675 1.553 1.168 0.818
[ 1.98] [ 1.57] [ 1.78] [ 2.49] [ 2.10] [ 1.37]
1.118 0.908 0.642 1.605 1.050 0.853
[ 2.20] [ 1.87] [ 1.28] [ 2.85] [ 1.80] [ 1.24]
0.475 0.747 0.365 1.268 0.828 0.439
[1.21] [2.00] [1.08] [ 1.72] [ 1.49] [ 0.70]
1.266 1.260 0.729 1.139 1.263 0.939
[ 3.00] [ 3.35] [ 1.61] [ 2.20] [ 2.99] [ 1.49]
High ILLIQ
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
2.334 1.972 2.305 1.910 1.534 1.753
[ 3.53] [ 3.48] [ 3.85] [ 2.72] [ 2.61] [ 3.00]
4.012 5.395 7.023 5.634 6.276 6.411
[1.11] [1.09] [ 0.70] [1.58] [1.30] [ 0.64]
0.217 0.055 0.306 0.843 0.592 1.059
[ 0.50] [0.12] [ 0.69] [ 1.48] [ 1.09] [ 2.01]
1.008 2.008 1.330 1.160 1.751 1.275
[ 1.22] [ 2.29] [ 1.19] [ 1.29] [ 1.94] [ 1.18]
Low DVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.541 9.889 13.113 1.157 17.682 13.64
[0.26] [0.95] [1.08] [0.45] [1.20] [1.12]
1.678 1.124 5.167 1.422 0.319 5.845
[1.97] [0.45] [ 0.95] [1.08] [ 0.13] [ 1.07]
0.293 0.088 0.089 0.782 0.617 0.834
[ 0.62] [0.19] [ 0.19] [ 1.59] [ 1.19] [ 1.61]
0.366 0.661 0.057 0.159 0.166 0.269
[ 0.46] [ 0.78] [ 0.06] [ 0.20] [ 0.20] [ 0.32]
Panel B: Medium limits-to-arbitrage sub-group Differences in
AGE
ASSET
PAYOUT
RATING
Medium IVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.359 0.270 0.512 1.383 1.123 1.287
[ 1.04] [ 0.62] [ 1.11] [ 2.65] [ 2.04] [ 2.13]
0.003 0.092 0.039 0.077 0.117 0.029
[ 0.01] [ 0.24] [ 0.09] [ 0.14] [ 0.23] [ 0.06]
0.289 0.164 0.182 0.279 0.645 0.987
[ 0.72] [ 0.40] [ 0.41] [0.42] [1.00] [1.52]
0.723 0.848 0.904 0.320 0.073 0.002
[ 2.33] [ 2.38] [ 2.33] [0.76] [0.13] [0.00]
Medium COV
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.774 0.777 0.900 0.573 0.695 0.650
[ 1.97] [ 2.16] [ 2.45] [ 1.32] [ 1.67] [ 1.54]
0.454 0.283 0.521 0.046 0.348 0.674
[ 1.10] [ 0.69] [ 1.13] [ 0.09] [ 0.80] [ 1.39]
0.613 0.435 0.616 0.327 0.239 0.428
[ 1.47] [ 1.01] [ 1.36] [ 0.73] [ 0.78] [ 0.93]
0.982 0.625 0.783 0.505 0.372 0.391
[ 2.77] [ 1.65] [ 1.88] [ 1.38] [ 1.02] [ 1.02]
Medium DISP
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS)
0.280 0.326 0.448 0.130
[ 0.70] [ 0.79] [ 1.05] [0.21]
0.844 0.722 0.736 0.204
[ 2.23] [ 2.00] [ 1.75] [ 0.58]
0.612 0.078 0.157 0.024
[ 1.48] [ 0.19] [ 0.38] [0.04]
0.742 0.513 0.346 0.020
[ 2.61] [ 1.81] [ 1.16] [0.04]
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
High BIDASK
0.322 0.648
[ 0.59] [ 1.19]
0.418 0.746
[ 0.97] [ 1.45]
0.535 0.189
[0.89] [0.29]
0.171 0.152
[ 0.37] [ 0.33]
Medium CVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
1.509 1.883 2.094 0.847 1.352 1.339
[ 3.00] [ 3.64] [ 3.84] [ 1.21] [ 2.11] [ 2.08]
0.519 0.810 0.766 1.096 1.170 1.137
[ 1.29] [ 1.59] [ 1.39] [ 1.45] [ 1.81] [ 1.88]
0.777 0.800 0.947 0.428 0.231 0.644
[ 1.40] [ 1.42] [ 1.58] [ 0.54] [ 0.33] [ 0.83]
0.865 1.085 1.155 0.715 0.784 0.860
[ 1.97] [ 2.04] [ 2.02] [ 1.32] [ 1.55] [ 1.55]
Medium INSTN
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
1.453 1.110 1.203 0.495 0.741 0.823
[ 2.69] [ 2.21] [ 2.43] [ 0.75] [ 1.26] [ 1.43]
0.444 0.360 0.070 0.143 0.141 0.602
[ 0.79] [ 0.58] [ 0.09] [ 0.23] [0.21] [0.74]
0.172 0.087 0.333 0.067 0.013 0.149
[ 0.40] [ 0.20] [ 0.76] [0.14] [ 0.03] [ 0.29]
0.540 0.611 0.413 0.314 0.499 0.692
[ 1.15] [ 1.28] [ 0.78] [ 0.57] [ 0.97] [ 1.18]
Medium PRICE
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.562 0.389 0.374 0.562 0.532 0.808
[ 1.59] [ 1.17] [ 1.07] [ 1.03] [ 1.13] [ 1.64]
0.404 0.172 0.072 0.273 0.343 0.052
[ 0.87] [ 0.38] [0.17] [ 0.42] [ 0.59] [0.09]
0.263 0.020 0.070 1.196 1.249 1.373
[ 0.72] [ 0.06] [ 0.19] [ 1.96] [ 2.38] [ 2.47]
1.239 1.259 1.380 1.230 1.181 1.304
[ 3.34] [ 3.16] [ 3.00] [ 2.45] [ 2.33] [ 2.73]
Medium BIDASK
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.491 0.397 0.442 0.304 0.450 0.845
[ 1.07] [ 0.87] [ 0.85] [ 0.41] [ 0.59] [ 1.13]
0.833 0.729 0.583 0.356 0.333 0.884
[ 1.67] [ 1.41] [ 1.03] [ 0.52] [ 0.54] [ 1.55]
0.574 0.459 0.430 0.311 1.037 0.910
[2.05] [1.44] [1.16] [0.47] [1.77] [1.56]
0.256 0.234 0.598 0.821 0.944 0.131
[ 0.61] [ 0.56] [ 1.10] [1.39] [1.80] [ 0.22]
Medium INSTH
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
1.367 1.146 1.242 0.565 1.059 1.259
[ 3.13] [ 2.96] [ 3.06] [ 0.77] [ 1.70] [ 2.02]
0.351 0.420 0.641 1.969 1.396 1.250
[ 0.80] [ 0.83] [ 1.24] [ 2.68] [ 2.31] [ 2.12]
0.266 0.298 0.358 2.304 2.146 1.688
[ 0.67] [ 0.79] [ 0.97] [ 3.30] [ 3.52] [ 3.09]
0.658 0.594 0.460 0.321 0.847 0.722
[ 1.60] [ 1.38] [ 1.00] [ 0.45] [ 1.48] [ 1.22]
Medium ILLIQ
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.633 0.474 0.276 0.556 0.384 0.303
[ 1.49] [ 1.12] [ 0.61] [ 1.13] [ 0.84] [ 0.66]
0.696 0.515 0.172 0.337 0.117 0.124
[ 1.51] [ 1.07] [ 0.31] [ 0.63] [ 0.23] [0.22]
0.326 0.625 0.436 0.364 0.818 0.864
[0.82] [1.68] [1.12] [0.79] [2.02] [2.06]
1.899 1.549 1.538 2.320 1.937 1.879
[ 3.54] [ 2.55] [ 2.36] [ 4.64] [ 3.46] [ 2.88]
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS) Panel C: Low limits-to-arbitrage sub-group
0.998 0.943 0.750 0.830 0.823 0.779
[ 2.56] [ 2.60] [ 1.86] [ 1.85] [ 1.92] [ 1.93]
1.112 1.099 0.783 0.596 0.506 0.464
[ 2.00] [ 2.09] [ 1.31] [ 0.99] [ 0.89] [ 0.79]
0.118 0.242 0.079 0.085 0.151 0.059
[0.26] [0.55] [0.18] [ 0.18] [0.32] [0.12]
1.759 1.670 1.731 1.830 1.457 1.548
[ 3.09] [ 2.79] [ 2.82] [ 4.23] [ 3.21] [ 2.96]
Medium DVOL
Differences in Low IVOL
0.425 0.358
ASSET [0.97] [0.89]
1.548 1.068
PAYOUT [1.89] [1.24]
0.248 0.124
RATING [0.40] [0.17]
0.108 0.117
[0.36] [0.36]
145
c1,1(OLS) c1,2(OLS)
AGE
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
c1,2(WLS) c1,3(WLS)
146
Table 5 (continued ) Panel C: Low limits-to-arbitrage sub-group Differences in
AGE
ASSET
PAYOUT
RATING
0.231 0.225 0.275 0.352
[0.50] [0.39] [0.53] [0.53]
1.833 1.798 1.177 1.694
[1.34] [2.07] [1.38] [1.55]
0.084 1.350 0.603 1.062
[0.10] [ 1.82] [ 0.75] [ 1.16]
0.037 0.067 0.145 0.360
[0.12] [ 0.12] [ 0.34] [ 0.84]
High COV
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.384 0.716 1.071 0.058 0.656 1.108
[ 0.85] [ 1.69] [ 2.27] [ 0.11] [ 1.33] [ 2.16]
0.327 0.428 0.503 0.648 0.372 0.102
[ 0.43] [0.45] [ 0.38] [ 0.64] [0.37] [ 0.08]
0.021 0.085 0.726 0.021 0.113 0.389
[ 0.04] [ 0.19] [ 1.64] [0.03] [0.21] [ 0.66]
0.795 0.880 0.810 0.067 0.476 0.341
[ 2.93] [ 2.98] [ 2.37] [0.17] [ 1.47] [ 0.98]
Low DISP
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.356 0.628 0.677 0.431 0.422 0.523
[ 0.63] [ 1.15] [ 1.24] [0.63] [ 0.65] [ 0.84]
0.600 0.619 0.750 0.704 0.921 0.962
[ 1.32] [ 1.47] [ 1.76] [ 1.45] [ 1.80] [ 1.76]
0.256 0.132 0.373 0.742 0.901 0.753
[0.63] [0.73] [ 0.91] [ 1.09] [ 1.31] [ 1.10]
1.001 1.201 1.078 0.071 0.343 0.038
[ 3.23] [ 3.59] [ 2.86] [0.14] [ 0.82] [0.07]
Low CVOL
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.731 0.274 0.489 0.732 0.622 0.449
[ 1.50] [ 0.55] [ 0.97] [ 0.94] [ 0.80] [ 0.56]
0.306 0.110 0.094 0.261 0.061 0.103
[ 0.48] [ 0.17] [ 0.15] [ 0.30] [ 0.07] [ 0.12]
0.048 0.126 0.118 0.792 0.013 0.582
[ 0.10] [0.23] [ 0.21] [ 0.78] [0.01] [0.69]
0.627 0.667 0.398 0.148 0.739 0.813
[ 1.31] [ 1.55] [ 0.87] [ 0.20] [ 1.49] [ 1.52]
High INSTN
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.537 0.779 0.662 0.247 0.229 0.561
[ 1.66] [ 2.54] [ 2.02] [0.47] [ 0.47] [ 1.17]
0.417 3.535 4.830 0.723 3.588 4.899
[0.26] [1.16] [1.25] [0.42] [1.18] [1.27]
0.535 0.594 0.652 0.596 0.610 0.548
[ 1.48] [ 1.64] [ 1.86] [ 1.09] [ 1.10] [ 0.93]
0.654 0.581 0.685 0.118 0.306 0.480
[ 2.44] [ 2.17] [ 2.39] [ 0.28] [ 0.83] [ 1.18]
High PRICE
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.406 0.285 0.578 0.170 0.156 0.386
[ 1.29] [ 0.95] [ 1.78] [ 0.33] [ 0.32] [ 0.73]
0.098 0.709 1.094 0.274 1.380 1.405
[ 0.15] [ 1.05] [ 1.36] [ 0.35] [ 1.84] [ 1.61]
0.084 0.303 0.135 0.301 0.651 0.130
[0.20] [0.75] [0.32] [0.49] [1.16] [0.22]
0.568 0.426 0.321 0.194 0.062 0.030
[ 2.14] [ 1.47] [ 1.14] [0.48] [ 0.18] [0.09]
Low BIDASK
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
0.444 0.518 0.231 0.728 0.704 0.728
[ 1.03] [ 1.33] [ 0.58] [ 1.44] [ 1.52] [ 1.71]
1.655 0.945 0.794 1.302 1.186 1.613
[ 2.32] [ 1.30] [ 0.93] [ 1.30] [ 1.13] [ 1.31]
0.221 0.091 0.451 0.440 0.339 0.127
[0.52] [ 0.20] [ 0.94] [ 0.67] [ 0.55] [ 0.19]
0.160 0.157 0.101 0.492 0.028 0.217
[ 0.54] [ 0.61] [0.32] [1.01] [0.07] [0.50]
High INSTH
c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS)
0.462 0.738 0.686 0.262
[ 1.41] [ 2.34] [ 2.08] [0.60]
0.244 0.113 0.282 0.758
[0.45] [0.20] [0.47] [1.12]
0.260 0.409 0.684 0.043
[ 0.80] [ 1.18] [ 1.77] [0.07]
0.587 0.568 0.675 0.300
[ 2.09] [ 2.08] [ 2.19] [ 0.73]
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS)
[ 2.84] [ 2.06] [ 1.53] [ 0.28] [ 0.97] [ 0.54] 0.937 0.819 0.594 0.108 0.321 0.178 [ 0.04] [ 0.44] [ 1.17] [ 0.92] [ 0.78] [ 0.91] [ 1.36] [ 1.51] [0.42] [ 1.46] [ 1.71] [0.33] 1.398 1.745 0.542 1.407 2.009 0.437
0.015 0.157 0.435 0.512 0.392 0.449
[ 1.66] [ 1.34] [ 1.14] [ 0.18] [ 0.65] [ 0.21] 0.625 0.581 0.485 0.069 0.222 0.069 [ 1.35] [ 1.44] [ 2.09] [ 0.85] [ 0.77] [ 1.34] [0.06] [ 0.74] [ 0.99] [0.15] [ 0.75] [ 1.19] 0.294 4.610 6.440 0.727 4.642 7.842
0.563 0.617 0.911 0.485 0.414 0.758
[0.36] [0.02] 0.265 0.015
0.047 0.036
[ 0.07] [ 0.05]
0.402 0.500
[ 1.05] [ 1.12]
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
147
the High limits-to-arbitrage sub-groups than among the Low limits-to-arbitrage sub-groups when investment frictions are proxied by firm age (AGE). Overall, the results from the double split-sample regressions reported in Table 5 show that the negative slope coefficients of asset growth in general have a higher magnitude in the financially more constrained subsample than in the financially less constrained subsample, even after controlling for the level of limits-to-arbitrage. Further, the equal-weighted results are stronger than the value-weighted results. It also seems that the effect of investment frictions on the asset growth anomaly is stronger when limits-to-arbitrage are more severe. Comparing the results presented in Table 4 with those in Table 5, we find that there is a fair and similar amount of evidence supporting each hypothesis in explaining the asset growth anomaly. Of the 660 differences in the asset growth slope between the High and Low limits-to-arbitrage subsamples in Table 4, 119 (18%) are significantly negative while only four (0.6%) contradict the predictions of the limits-to-arbitrage explanation by being significantly positive. Similarly, of the 720 differences in the asset growth slope between the High and Low investment frictions subsamples in Table 5, 142 (19.7%) are significantly negative while only seven (1.0%) contradict the predictions of the q-theory with investment frictions explanation. In addition, the significant support (at the 5% level or better) from the equal-weighted results is much stronger (22% for the limits-to-arbitrage hypothesis and 26% for the investment frictions hypothesis) than that from the value-weighted results (14% for both hypotheses). In contrast, the evidence against either hypothesis is very small, representing no more than 1% of the cases.
0.719 0.825 0.940 0.540 0.586 0.730 c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS) High DVOL
[ 2.01] [ 2.51] [ 2.47] [ 1.18] [ 1.44] [ 1.66]
0.660 0.726 0.968 0.513 0.608 0.743 c1,1(OLS) c1,2(OLS) c1,3(OLS) c1,1(WLS) c1,2(WLS) c1,3(WLS) Low ILLIQ
[ 1.81] [ 2.13] [ 2.45] [ 1.04] [ 1.46] [ 1.73]
0.168 0.416 c1,2(WLS) c1,3(WLS)
[ 0.39] [ 0.90]
7. Conclusion In this study, we comprehensively test and compare the predictions of the mispricing hypothesis with limits-toarbitrage suggested by Shleifer and Vishny (1997) and the q-theory with investment frictions proposed by Li and Zhang (2010) on the asset growth anomaly (i.e., the negative asset growth-return relation). We test the hypotheses based on the Fama and MacBeth (1973) cross-sectional regressions of future stock returns against asset growth conducted on subsamples split by a given measure of limits-to-arbitrage or investment frictions. We find that the slope of asset growth is in general negative and has a significantly higher magnitude in the High limits-to-arbitrage (or investment frictions) subsample than in the Low limits-to-arbitrage (or investment frictions) subsample. Based on equal-weighted returns, the negative asset growth-return relation is stronger when limits-to-arbitrage are more severe, even after controlling for the level of investment frictions. Similarly, the negative relation is more pronounced when investment frictions are higher, even after controlling for the level of limits-to-arbitrage. Moreover, it appears that the effect of limits-to-arbitrage is stronger when investment frictions are higher, and vice versa. The results suggest that limits-to-arbitrage and investment frictions play complementary roles in explaining the asset growth anomaly. However, the evidence
148
F.Y.E.C. Lam, K.C.J. Wei / Journal of Financial Economics 102 (2011) 127–149
from value-weighted returns is much weaker in supporting either hypothesis. In addition, idiosyncratic return volatility appears to be the only measure of limits-toarbitrage that has a reliable effect on the asset growth anomaly. Similarly, firm age seems to be the only measure of investment frictions with a reliable effect on the anomaly. The main objective of Li and Zhang (2010) is to test the investment frictions hypothesis while controlling for limits-to-arbitrage. They therefore do not study many important aspects of limits-to-arbitrage as this study does. In this study, we extensively examine whether the limits-to-arbitrage hypothesis or the investment frictions hypothesis can better explain the asset growth anomaly. Our tests also control for important firm characteristics and employ value-weighted regressions, which have been omitted previously. Li and Zhang (2010) find that the effect of limits-to-arbitrage seems to dominate the effect of investment frictions in explaining the asset growth anomaly. However, our comprehensive analysis shows that this may not be the case. There is indeed a similar amount of evidence supporting each explanation. In addition, the two explanations appear to complement each other in explaining the asset growth anomaly when small and large firms are given equal weight. However, the evidence is substantially weakened when firm characteristics are controlled for, or when larger firms are given more weight. Appendix. Definition of variables TAG:
IVOL:
Growth in total assets, measured as the net percentage change in total book assets (Compustat item AT) over the previous fiscal year. Data source: Compustat Idiosyncratic stock return volatility, measured as the standard deviation of the residual values from the following time-series market model: Ri,t ¼ bi0 þ bi1 RM,t þ ei,t ,
COV:
DISP:
CVOL:
INSTN:
PRICE:
BIDASK:
where Ri,t is the monthly individual stock return and RM,t is the monthly market index return. The model is estimated with 36 months of returns (requiring a full 36month history) ending in June of year t. Data source: CRSP Analyst coverage, measured as the number of analysts following the firm at the end of June of year t. Data source: I/B/E/S Dispersion in analyst forecasts, measured as the standard deviation of analysts’ earnings-per-share forecasts scaled by the closing stock price at the end of June of year t. Data source: I/B/E/S and CRSP Cash flow volatility, measured as the standard deviation of cash flow from operations over the previous 5 years (requires a minimum of 3 years). Cash flow is earnings before extraordinary items (item IB) minus total accruals, divided by average total book assets (item AT) over a fiscal year. Total accruals is the change in current assets (item ACT) less the change in cash (item CHE), the change in current liabilities (item LCT), and depreciation (item DP) plus the change in short-term debt (item DLC). Data source: Compustat Shareholder sophistication, which is the number of institutional investors holding a firm’s shares at the end of June of year t. Data source: CDA/Spectrum Institutional Share price, measured as the closing stock price (the average of bid-and-ask prices if the closing price is not available) at the end of June of year t. Data source: CRSP Bid-ask spread, which is measured as the time-series average of 2 9Price–(Askþ Bid)/29/Price at the end of each
month over the 12 months ending in June of year t, where Price is the closing stock price and Ask (Bid) is the ask (bid) quote. Data source: CRSP INSTH: Institutional ownership, which is the percentage of outstanding shares held by institutional investors at the end of June of year t. Data source: CDA/Spectrum Institutional ILLIQ: The Amihud (2002) illiquidity measure, which is defined as the time-series average of absolute daily returns divided by daily dollar trading volume over the past one year ending in June of year t. Data source: CRSP DVOL: Dollar trading volume, defined as the time-series average of monthly share trading volume multiplied by the monthly closing price over the past 12 months ending in June of year t. Data source: CRSP ASSET: Asset size, which is the book value of total assets (item AT) at the end of the previous fiscal year. Data source: Compustat AGE: Firm age, which is the number of years a stock has appeared in the CRSP database at the end of the previous fiscal year. Data source: CRSP PAYOUT: Payout ratio tercile ranking, ranked according to all distributions to equity holders, including share repurchases (item PRSTKC), dividends to preferred stock (items DVP), and dividends to common stock (item DVC), scaled by operating income before depreciation (item OIBDP) over the previous fiscal year. Firms with zero or negative earnings but positive distributions are put into the high payout ratio tercile, while firms with zero or negative earnings and zero distributions are put into the low payout ratio tercile. Data source: Compustat RATING: Credit rating dummy, which is zero if a firm has never had a Standard & Poor’s (S&P) long-term credit rating in the Compustat database in the sample period and one otherwise. Data source: Compustat SIZE: Market value of equity, which is the closing stock price multiplied by the number of shares outstanding at the end of June of year t. Data source: CRSP BM: Book-to-market equity ratio, which is the book value of equity at the end of the previous fiscal year divided by the market value of equity at the end of December of the previous year. As in Fama and French (1993), book equity is total assets (item AT) minus liabilities (item LT), plus balance sheet deferred taxes (item TXDB) and investment tax credits (item ITCI), minus preferred stock liquidation value (item PSTKL) if available, or redemption value (item PSTKRV) if available, or carrying value (item PSTK) if available. Data source: Compustat PRET: Prior return, which is the past 6-month gross stock return at the end of May of year t. Data source: CRSP NS: Net share issuance, which is the natural logarithm of the ratio of split-adjusted shares outstanding (item CSHO multiplied by item ADJEX_C) at the end of the previous fiscal year to those at the beginning of that year. Data source: Compustat NSlag: Lagged net share issuance, which is NS lagged by a year. Data source: Compustat
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Journal of Financial Economics 102 (2011) 150–166
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Creditor rights and corporate risk-taking$ Viral V. Acharya a,b,c,d, Yakov Amihud a,n, Lubomir Litov e a
New York University, Stern School of Business, United States CEPR, United Kingdom c ECGI, Belgium d NBER, United States e Washington University in St. Louis, Olin Business School, United States b
a r t i c l e in f o
abstract
Article history: Received 5 March 2008 Received in revised form 5 April 2010 Accepted 12 April 2010 Available online 27 May 2011
We propose that stronger creditor rights in bankruptcy affect corporate investment choice by reducing corporate risk-taking. In cross-country analysis, we find that stronger creditor rights induce greater propensity of firms to engage in diversifying acquisitions that are value-reducing, to acquire targets whose assets have high recovery value in default, and to lower cash-flow risk. Also, corporate leverage declines when creditor rights are stronger. These relations are usually strongest in countries where management is dismissed in reorganization and are also observed over time following changes in creditor rights. Our results thus identify a potentially adverse consequence of strong creditor rights. & 2011 Elsevier B.V. All rights reserved.
JEL classification: G31 G32 G33 G34 Keywords: Bankruptcy code Corporate reorganization Investment Diversification
1. Introduction Throughout history, defaulting on debt has incurred harsh punishment. In Biblical times and in ancient Greece,
creditors would enslave their debtors-in-default until they fully repaid their debt. During some periods in Rome, creditors could use physical punishment for debtors in default.1 The United Kingdom had debtor’s prisons until
$ Acharya is C.V. Starr Professor of Finance. Amihud is Ira Leon Rennert Professor of Finance. We acknowledge with gratitude comments and suggestions that helped improve the paper by Barry Adler, Kenneth Ahern, Reena Aggarwal, Franklin Allen, Heitor Almeida, Meghana Ayyagari, Moshe Barniv, Bo Becker, Sreedhar Bharath, Bernie Black, Long Chen, Sid Chib, Jonathan Cohn, Jeff Coles, Phil Dybvig, Espen Eckbo, Alex Edmans, Isil Erel, Mara Faccio, Mike Faulkender, Julian Franks, Radha Gopalan, Todd Gormley, Bill Greene, Todd Henderson, Joel Houston, Kose John, Lutz Johanning, Ohad Kadan, Sandy Klasa, Anzhela Kniazeva, Diana Kniazeva, William Megginson, Todd Milbourn, Natalie Moyen, Ed Morrison, Holger Mueller, Harold Mulherin, Paige Ouimet, Troy Paredes, Katharina Pistor, Amiyatosh Purnanandam, Stefano Rossi, Antoinette Schoar, Alan Schwartz, Oren Sussman, Anjan Thakor, Rohan Williamson, Daniel Wolfenzon, Jeff Wurgler, David Yermack, Bernie Yeung, the seminar participants at Washington University in Saint Louis, NYU Salomon Center corporate governance seminar, University of Michigan, Tel Aviv University, Bar Ilan Iniversity, Hebrew University, Interdisciplinary Center in Herzliya, the 2008 Conference on Law and Economics at the University of Pennsylvania, Cornell University’s Empirical Legal Studies Conference, 2008 UNC-Duke Corporate Finance Conference, the University of Gent 2008 Bankruptcy and Reorganization Conference, University of California at San Diego, University of Arizona, and especially two anonymous referees. We thank Simeon Djankov for providing access to the creditor rights data. Rong Leng provided excellent research assistance. A part of this paper was completed while Acharya was at London Business School. Acharya is grateful for research support from the ESRC (Grant no. R060230004) awarded to the London Business School Corporate Governance Research Center. n Corresponding author at: New York University, Stern School of Business, 44 West 4th Street, New York, NY 10012, United States. E-mail addresses:
[email protected] (V.V. Acharya),
[email protected] (Y. Amihud),
[email protected] (L. Litov). 1 In 450 BC: The Twelve Tablets, Section III, Debt. Penalties ranged from imprisonment to removing parts of the body.
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.04.001
V.V. Acharya et al. / Journal of Financial Economics 102 (2011) 150–166
their abolition by the 1869 Debtors Act. In contrast, the modern-day norm of limited liability in bankruptcy reduces creditor rights by limiting their ability to pursue debtors who default on promised payments.2 The question is: how strong should state-mandated creditor rights-indefault be, given that stockholders and creditors are limited in their ability to contract around them? Schwartz (1997, p. 127) points out: ‘‘When a firm becomes insolvent, however, the state-supplied dispute resolution procedure—the bankruptcy system and court—is mandatory; parties cannot contract in the lending agreement for an alternative procedure.’’ Because bankruptcy laws apply uniformly to all firms and have precedence over private firm-specific contracts, they may lead to inefficient outcomes for some firms.3 We examine the effect of creditor rights on corporate risk-taking. In particular, we ask: what effect does the strength of creditor rights have on firm investment decisions? While a harsh penalty in default reduces fraud and opportunistic behavior by debtors, it might also discourage bona-fide risky investment. This paper henceforth examines the link between creditor rights and corporate investment policy. It thus differs from research on creditor rights that mainly analyzes their effect on financing policies, such as the suggestion by Djankov, McLeish, and Shleifer (2007) that stronger creditor rights encourage increase in the supply of credit.4 We propose that stronger creditor rights induce risk-reducing investments. Strong creditor rights in default may lead to inefficient liquidation, which extinguishes the continuation option of a firm’s enterprise and thus hurts shareholder value. Also, creditor rights that mandate the dismissal of management in bankruptcy impose private costs on managers. To avoid these costs, shareholders and managers lower the likelihood of distress by reducing cash-flow risk. Such risk reduction can result in value loss due to foregoing profitable investments, or from undertaking value-decreasing diversifying investments; strong creditor rights can thereby result in dead-weight costs to firms and to the economy at large. Further, while strengthening creditor rights increases the propensity to lend, it may reduce firms’ demand for credit, resulting in lower overall levels of corporate debt. Our empirical analysis examines the effects of creditor rights on corporate risk-taking. We use variation of creditor rights across countries as an explanatory variable. La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998)
2 Europe still has effective and strict penalties upon bankruptcy, as noted in The Economist, 23 March 2002, Fear of failure—Europe’s fear of bankruptcies: ‘‘In Europe, by contrast [to the United States], failed firms face bigger hurdles. First, in the continent that created the debtor’s prison, insolvency is still tainted with moral failure. In some countries, company directors are personally liable for bankruptcy. That steeply raises the penalties for failure—and so deters entrepreneurs from taking risks.’’ 3 This is why Schwartz (1997) proposes that the state makes available to firms a menu of bankruptcy procedures. Then, allowing parties flexibility in contracting for preferred bankruptcy procedures alleviates undesirable effects on investment arising from strong creditor rights. 4 This analysis contends that stronger creditor rights reduce the dead-weight cost due to debtor-creditor conflict (Jensen and Meckling, 1976).
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suggest that creditor rights are largely a function of national legal origin. While some variation in creditor rights may be an endogenous response of the legal system to the characteristics of the national economy, it is reasonable to assume for our empirical analysis that creditor rights are predetermined. We employ several measures of corporate risk-taking and examine their relation to creditor rights across countries and over time. Our primary analysis focuses on the effect of creditor rights on the nature of mergers and acquisitions (M&A) in a country. We focus on M&A because these transactions provide an opportunity to observe a major corporate investment and its effect on corporate risk—whether the acquisition is diversifying across industries and thereby risk-reducing, or focusing within-industry. In M&A, we can also identify whether the assets in which the firm invests are of high or low recovery value. Further, corporate investment in the form of M&A decisions is not tainted by the cross-country differences in reporting practices that affect other measures of investment (such as capital expenditures and research and development (R&D) expenses). We find the following: (1) In countries with stronger creditor rights, firms have greater propensity to do diversifying acquisitions across industries. This is observed when estimating the likelihood of diversifying acquisitions at the level of single acquisitions as well as at the level of a country or at the level of an industry in a country. Also, geographically diversifying (cross-border) acquisitions are more likely in countries with stronger creditor rights. Further, in countries with stronger creditor rights, firms have segments in a greater number of lines of business, a measure of diversification. (2) In countries with strong creditor rights, acquirers whose assets have low recovery value in distress are more likely to acquire target firms with high-recovery assets.5 This is because high asset recovery values enable firms in distress to defer default by liquidating some assets and by using the proceeds to service debt. Thus, by acquiring a high-recovery target, a low-recovery firm reduces or defers the likelihood of default in case of distress. (3) The effect of diversifying acquisitions on the acquirer’s value is more negative in countries with stronger creditor rights. In such countries, acquirer profitability, measured by return on assets (ROA), is significantly lower post-acquisition, and the acquirer’s abnormal stock return is also lower. In contrast, in focusing (sameindustry) acquisitions, there is no adverse effect of stronger creditor rights on the acquirer’s value.
5 Assets with high recovery value have lower costs of liquidation. These incur lower loss of value in distressed sales and, following the definition of Shleifer and Vishny (1992), have lower specificity in that they are fungible across industries and hence trade at prices that are closer to their value in best use. Our measure of high-recovery industries is based on the realized recovery rates of debts of defaulted firms in various industries, documented by Acharya, Bharath, and Srinivasan (2007).
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Our results on the choice of corporate risk through mergers and acquisitions are further corroborated with alternative measures of corporate risk. We present two additional findings on the creditor rights-corporate risk relation: (4) In countries with stronger creditor rights, firms choose to reduce cash-flow risk, as measured by the standard deviation of firm ROA. We obtain this result at the level of a single firm, a country, or an industry in a country. (5) In countries with stronger creditor rights, corporate leverage is lower. This finding is notable, as it contradicts the argument that stronger creditor rights brings about a greater level of lending.
(2009a) find that in countries with stronger creditor rights, technologically innovative industries innovate less, employ lower financial leverage, and grow more slowly.6 Chava and Roberts (2008) and Nini, Smith, and Sufi (2009) find that restrictive debt covenants and enforcement of covenant violations, which provide firm-specific creditor rights, inhibit capital investment. These findings point out potentially harmful effects of creditor rights with respect to risky investment. This paper proceeds as follows. Section 2 discusses the data, the empirical design, and the test results and Section 3 offers concluding remarks.
Findings (1) and (2) above are generally stronger for creditor rights that correspond to whether management is dismissed in bankruptcy, reflecting an effect of managerial self-interest on corporate policies, as well as whether there is automatic stay in bankruptcy. Finally, all of the above effects are also observed over time, as a result of strengthening (and, vice versa, weakening) of a country’s creditor rights. To control for a potential dependence of creditor rights on the country’s characteristics, we include in our models country-level variables that may be related to creditor rights, such as legal origin, macroeconomic risk, the extent of the rule of law, flexibility to fire employees, the size of the capital market, accounting disclosure standards, and percapita gross domestic product (GDP). We also perform robustness tests using variables that measure the propensity to avoid risk (cultural and religious variables), and we present direct comparisons between the U.S. and the U.K. which arguably are similar in economic and financial development as well as in culture, but are quite different in their creditor rights (much stronger in the U.K. than in the U.S.). Our results on the role of managerial self-interest in the decision to diversify when faced with stronger creditor rights is consistent with evidence from Amihud and Lev (1981), who find that diversifying acquisitions and lower risk of return on equity are more pervasive in manager-controlled firms than in stockholder-controlled firms. Further, Tufano (1996) proposes that managerial risk-aversion induces corporate hedging in public gold mining firms. Tufano (1998) proposes that hedging reduces the need to access external capital markets and thus lessens the discipline that market scrutiny imposes on corporate insiders. Among theoretical studies on the effects of creditor rights, Adler (1992) suggests that while strong creditor rights induce the manager to increase firm risk as the firm approaches default, their ex ante effect is to reduce risk to avoid insolvency. Manso (forthcoming) proposes that penalizing failing entrepreneurs through tough bankruptcy procedures inhibits innovation, and Acharya and Subramanian (2009b) argue that strong creditor rights can deter financial leverage and risk-taking in more innovative industries. Adler, Capkun, and Weiss (2007) propose that the recent strengthening of creditor rights in the U.S. induces firms to delay default and to waste assets in the process. Empirically, Acharya and Subramanian
We test whether stronger creditor rights across countries cause firms to undertake lower risk. Our main analysis pertains to reduction of risk via diversifying acquisitions, which lower the likelihood of default (after controlling for leverage). We test the following:
2. Hypotheses, data, and empirical design
Hypothesis Ia. The propensity to undertake diversifying acquisitions is greater in countries with stronger creditor rights. We test this hypothesis by examining diversifying acquisitions across industries at three different levels: individual acquisitions, average country-level acquisitions, and average industry-level acquisitions. We also test the hypothesis by examining geographic diversification, measured by cross-border acquisitions. Acquisitions can help reduce the likelihood of default when an acquirer whose assets have low recovery value in bankruptcy acquires a target with high-recovery assets, which lose less of their value in distressed sales and fetch prices that are closer to their value in best use (using the notion of asset specificity from Shleifer and Vishny, 1992). A firm in financial distress can liquidate some of its highrecovery assets and use the proceeds to service its debt, thus deferring default. Also, Eckbo and Thorburn (2003) suggest that it is in the manager’s interest to increase the recovery rate of debt in default (which is related to asset characteristics), because the probability of rehiring managers who are automatically dismissed in bankruptcy in Sweden is increasing in the recovery rate of the firm’s debt. Our hypothesis is: Hypothesis Ib. In countries with stronger creditor rights, firms in industries whose assets have low recovery value are more likely to acquire firms in industries whose assets have high recovery value. Firms can diversify across industries by means alternate to acquisitions. We therefore test a related hypothesis: Hypothesis Ic. The number of lines of business in which a firm engages is higher in countries with stronger creditor rights. 6 There is an inverse relation between the strictness of personal bankruptcy laws and entrepreneurship, as reflected in the extent of selfemployment. See Fan and White (2003) and Armour and Cumming (2005) for details.
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Next, we conjecture that creditor rights induce corporate managers to trade off corporate value for lower risk when undertaking diversifying acquisitions. Hypothesis II. In countries with stronger creditor rights, diversifying acquisitions are followed by lower profitability (measured by return on assets), and their announcement induces more negative stock price reaction. Creditor rights have no such effects on firm performance in focusing (same industry) acquisitions. Our remaining hypotheses test whether firms reduce two additional measures of risk—operating risk and financial risk—in countries with stronger creditor rights: Hypothesis III. In countries with stronger creditor rights, firms have lower cash-flow risk, measured by the standard deviation of the annual EBITDA-to-assets ratio.
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2.1. Creditor rights We use the data on creditor rights from La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998), who record creditor rights components in a cross-country sample as of 1994. The variable CRIGHTS is the sum of four provisions: AUTOSTAY, REORG, SECURED, and MANAGES (see Table 1 for details). Each of these components takes a value of one if it is present in the country’s bankruptcy code, or of zero if it is absent. Consequently, the range of values for CRIGHTS is zero through four. In our 38-country sample (see Table 2), the mean of CRIGHTS is 2.08 with standard deviation of 1.28. As a robustness check, we use the creditor rights data of Djankov, McLeish, and Shleifer (2007) to re-estimate our models and to examine the effects of changes in creditor rights.
2.2. Creditor rights and diversification in M&A activity Hypothesis IV. Corporate leverage (debt-to-assets ratio) is decreasing in the strength of creditor rights. These hypotheses are tested in a cross-section of countries, as well as over time, accounting for changes in creditor rights. The data in our analysis include legal and economic country variables, as well as data on individual companies and acquisition transactions. Table 1 describes the construction and the data sources for all variables.
The tests of risk reduction through cross-industry diversifying acquisitions employ data from the Securities Data Corporation (SDC) Platinum Mergers & Acquisitions database for the period 1994–2004. Our sample consists of acquisitions in 38 countries with data on creditor rights as of 1994, which satisfy the following requirements. We include only mergers where both the acquirer and the target are under the same jurisdiction. (Later, we present evidence on the
Table 1 Variable definitions. Definition Dependent variables Pr(same-industry merger) SAME
Probability of an acquisition being in the same industry. It equals one if acquirer and target are in the same two-digit industry, and zero otherwise The ratio of the number of mergers in the same two-digit SIC code to the number of all domestic mergers in a country or in an industry in the country ROA EBITDA/Assets. All data are annual. EBITDAj,c,t is earnings before interest, taxes, and depreciation and amortization (the sum of data items #14 and #11), which is unaffected by methods of accounting depreciation that differ across countries, and Assetsi,c,t is contemporaneous total assets (data item #89). ROA is winzorized at 1% in both tails Cumulative abnormal return computed over the seven-day window surrounding CAR—Cumulative the event date, from day -3 to day þ 3, where day 0 is the announcement day. The abnormal return daily abnormal return is the difference between the daily stock return and the ( 3 to þ3) market model expected return, where the market model parameters are estimated from a regression of weekly stock returns on the country’s stock return index. The parameter estimation employs up to 105 weeks of data and no less than 52 weeks, up to nine weeks before the week of the acquisition announcement. The cumulative abnormal return is calculated over the seven days surrounding the announcement day. The resulting sample of firms’ CAR is then winsorized at 1% at both tails Firm risk (RISK) RISKj,c is the standard deviation of firm j in country c of industry-adjusted ROAj,c,t, where ROAj,c,t ¼ EBITDAj,c,t/Assetsj,c,t. t is the year, and we require at least eight years of data. Here, ROA is industry adjusted by subtracting in each year the sample-wide median ROA for the firm’s industry (using 2-digit SIC code). Data are for the period 1992–2005. The entire data of ROAi,c,t are winsorized at 0.5% in both tails to account for extreme observations. The entire firm sample of RISKi,c is then winsorized at 1% in both sides of the sample distribution. The measure is similar to the one used in John, Litov, and Yeung (2008) Country risk (RISKn) The median of RISKj,c across firms in country c Leverage (also used Ratio of total debt-to-total assets in book value. Debt is total liabilities minus as a control variable) equity and minus deferred taxes. Leverage data are winsorized in the entire population at 1% in both tails. Industry-adjusted leverage is calculated as the firm’s leverage minus the respective industry’s sample-wide median leverage (using two-digit SIC code)
Source
SDC Platinum Mergers & Acquisitions SDC Platinum Mergers & Acquisitions Compustat Global Vantage
Datastream
Compustat Global Industrial/ Commercial Annual Database
Compustat Global Vantage
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Table 1 (continued ) Definition
Source
Creditor-rights variables Creditor rights An index aggregating creditor rights, following La Porta, Lopez-de-Silanes, Shleifer, (CRIGHTS) and Vishny (1998). It is the sum of the four indexes that follow. CRIGHTS then ranges between zero and four No automatic stay Equals one if the reorganization procedure does not impose an automatic stay on (AUTOSTAY) the assets of the firm upon filing the reorganization petition, creditors are able to seize their collateral after the reorganization petition is approved. It equals zero if such restriction does exist in the law Reorganization Equals one if the reorganization procedure imposes restrictions, such as creditors’ (REORG) consent or minimum dividend for a debtor to be able to file for reorganization. It equals zero for countries without such restriction Secured debt first Equals one if secured creditors are ranked first in the distribution of the proceeds (SECURED) that result from the disposition of the assets of a bankrupt firm, as opposed to other creditors such as employees or government. Equals zero if non-secured creditors, such as the government and workers, are given absolute priority No management Equals one if an official appointed by the court, or by the creditors, is responsible stay (MANAGES) for the operation of the business during reorganization, that is, management does not retain administration of its property pending the resolution of the reorganization. Equivalently, this variable equals 1 if the debtor does not keep the administration of its property pending the resolution of the reorganization process, and zero otherwise Control variables Shareholder rights (SHRIGHTS)
An index that aggregates shareholder rights. ‘‘The index is formed by adding one when: (1) the country allows shareholders to mail their proxy vote to the firm, (2) shareholders are not required to deposit their shares prior to the general shareholders’ meeting, (3) cumulative voting or proportional representation of minorities in the board of directors is allowed, (4) an oppressed minorities mechanism is in place, (5) the minimum percentage of share capital that entitles a shareholder to call for an extraordinary shareholders’ meeting is less than or equal to 10% (the sample median), or (6) shareholders have preemptive rights that can be waived only by a shareholders’ vote. The index ranges from zero to six’’ Log(GDP per capita) Natural logarithm of the average real GDP per capita in US dollars, 1994–2000 Macroeconomic risk The standard deviation of the quarterly growth in real industrial production for (Macro risk) each country in the period 1990–2004. For some countries, we use instead the index of manufacturing production: Argentina, Chile, Greece, Hong Kong, Indonesia, New Zealand, Peru, Philippines, Singapore, and South Africa. For Argentina, Canada, Taiwan, and Thailand, data are from the international database of Global Insight. The variable is measured in decimal points Rule of law The assessment of the law and order tradition of the country. Calculated as ‘‘average of the months of April and October of the monthly index between 1982 and 1995. Scale from zero to ten, with lower scores for less tradition for law and order’’ Legal origins A dummy variable that identifies the legal origin of the Company law or Commercial Code of each country. The detailed origins are French, German, Nordic (default is Common) Accounting disclosure An index created by the examination of the annual report in 1994 of companies across countries on their inclusion or omission of 90 line items Emerging markets Flexibility to fire Country corporate tax rate Log(Market cap) Transaction value Tangibility
La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998); Djankov, McLeish, and Shleifer (2007) La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998)
La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998) La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998)
La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998)
Quotation is from La Porta, Lopez-deSilanes, Shleifer, and Vishny (1998)
Penn World Tables, Version 6.1 International Financial Statistics of International Monetary Fund (IMF)
International Country Risk Guide; La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998)
La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998); and the CIA Factbook 2003 International Accounting and Auditing Trends, Center for International Financial Analysis and Research Dummy variable equal to one if the country’s per capita GDP (in US$, average over Penn World Tables, Version 6.1 1994–2000) is less than the median for the sample of countries An index of the ease to fire workers based on a study of the employment laws Doing Business Report, 2004, The (divided by 100) World Bank The annual top corporate tax rate for 1992–2002, per country. It is then applied for World Tax Database at the University 2003–2005 when necessary of Michigan The logarithm of the stock market capitalization in U.S. dollars in 1994 World Market Indicators database, The World Bank The amount paid in U.S. dollars. SDC Platinum Mergers & Acquisitions. Net fixed (tangible) assets/Total assets Compustat Global Vantage
effect of creditor rights on geographic diversification, using cross-border transactions.) We exclude acquisitions where the acquirer is in the financial industry (Standard Industry Classification (SIC) header 6), which include leveraged buyouts (LBOs), or a regulated industry (SIC headers 48 and 49), transactions where the acquirer and the target are the same company (repurchases recorded as acquisitions),
transactions where the acquirer is a mutual company, investment company, subsidiary, or state-owned enterprise, and transactions in which the equity ownership stake acquired from the target is less than 20%. Finally, we include only countries with at least 50 transactions that satisfy the above criteria, though additional data requirements on transaction value reduce the sample size for some countries.
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Table 2 Overall descriptive statistics. The table describes the total number of domestic mergers in the sample countries for 1994–2004 that enter Table 3 regressions. The sample presented consists of the countries for which we have La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998) data on creditor rights. We exclude countries that have less than 50 qualified transactions in the sample period (before imposing additional data requirements). A transaction is qualified if the percentage of acquired shares is at least 20%. We exclude financial industry (SIC header 6) and regulated industry companies (SIC headers 48 and 49) from the country transaction count. The mergers and acquisition data are from SDC Platinum Mergers and Acquisitions database. The year of creditor rights change is the one from the Djankov, McLeish, and Shleifer (2007) study. We also present data on the median country cash-flow risk proxy, RISKn. Refer to Table 1 for variable definitions. Acquirer’s country
Argentina Australia Austria Belgium Brazil Canada Chile Denmark Finland France Germany Greece Hong Kong India Indonesia Ireland Israel Italy Japan Malaysia Mexico Netherlands New Zealand Norway Peru Philippines Portugal Singapore South Africa South Korea Spain Sweden Switzerland Taiwan Thailand Turkey United Kingdom United States
No. of mergers Count
Proportion of sameindustry mergers (%) SAME
Cash-flow risk proxy RISK*
Shareholder rights SHRIGHTS
Creditor rights CRIGHTS
Macroeconomic volatility Macro risk
$ GDP per capita GDP
66 1,618 14 49 143 2,071 41 80 154 434 201 70 190 236 39 92 73 333 1,771 369 82 101 98 130 26 42 56 243 372 198 338 186 38 52 83 17 5,624 17,491
55.33 61.72 64.52 57.54 70.26 61.37 61.84 56.47 54.60 59.79 55.31 47.22 34.11 57.87 60.53 63.59 45.45 53.31 46.80 25.27 62.59 57.80 57.73 58.94 68.63 56.00 65.31 32.19 49.84 32.48 64.08 58.53 57.67 44.90 43.95 50.00 58.61 59.07
0.058 0.121 0.036 0.043 0.070 0.094 0.033 0.049 0.054 0.045 0.057 0.043 0.064 0.051 . . 0.075 0.038 0.022 0.066 0.049 0.059 0.073 0.079 0.058 0.080 0.036 0.064 0.061 0.051 0.040 0.067 0.046 0.065 0.097 0.071 0.088
4 4 2 0 3 5 5 2 3 3 1 2 5 5 2 4 3 1 4 4 1 2 4 4 3 3 3 4 5 2 4 3 2 3 2 2 5 5
1 1 3 2 1 1 2 3 1 0 3 1 4 4 4 1 4 2 2 4 0 2 3 2 0 0 1 4 3 3 2 2 1 2 3 2 4 1
0.07 0.04 0.09 0.08 0.03 0.01 0.04 0.07 0.08 0.10 0.04 0.06 0.13 0.07 0.07 0.08 0.02 0.12 0.03 0.05 0.03 0.11 0.06 0.07 0.07 0.18 0.06 0.06 0.02 0.06 0.08 0.16 0.07 0.06 0.05 0.07 0.05 0.01
$7,801 $20,948 $26,220 $24,649 $4,143 $20,647 $4,604 $32,434 $23,856 $24,033 $26,443 $11,219 $23,850 $423 $868 $21,376 $16,391 $19,814 $36,616 $3,982 $4,421 $24,802 $15,528 $33,844 $2,296 $1,041 $10,782 $22,916 $3,413 $9,545 $14,535 $26,812 $37,908 $12,580 $2,396 $2,810 $21,767 $30,899
We test Hypothesis Ia by estimating the likelihood of same-industry acquisition in a country as a function of the strength of creditor rights, controlling for other variables. A diversifying acquisition is one where the acquirer and the target are not in the same industry (using two-digit SIC code).7 The main explanatory variable in our analysis is CRIGHTS, the aggregate measure of creditor rights from La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998), and its components, AUTOSTAY, REORG, SECURED, and MANAGES. We predict that the coefficient of CRIGHTS is negative; that is, there is lower likelihood of same-industry mergers in countries with stronger creditor rights.
7 The results are qualitatively similar when we employ industry classification at the three-digit SIC level.
The univariate relation between the country’s creditor rights and diversifying mergers is observed in Fig. 1, which plots the country variable SAMEc, the proportion of same-industry acquisitions in country c, as a function of the country’s CRIGHTS. The pattern shows a negative relation between these two variables; that is, stronger creditor rights lead to greater diversification. Next, to test our Hypothesis Ia, we do a detailed transaction-level analysis in which we estimate the likelihood of a same-industry acquisition as a function of creditor rights and control variables. The country-level control variables include shareholder rights index, SHRIGHTS (obtained from La Porta, Lopez-de-Silanes, Shleifer, and Vishny, 1998); its effect should be positive if same-industry acquisitions, which produce synergies and retain the same level of asset risk, are in shareholders’
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Proportion of same-industry mergers
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0.7 0.6 0.5 0.4 0.3 0.2 0
1
2
3
4
Creditor rights Fig. 1. The fraction of same-industry mergers and acquisitions (two-digit SIC code) out of all mergers and acquisitions in a country, SAME, and creditor rights, CRIGHTS. The vertical axis represents the share of same-industry mergers in a country. The horizontal axis represents creditor rights. The fitted line represents the slope from a Tobit regression of the fraction of same-industry mergers in a country on a constant and the creditor rights index. The slope coefficient is 0.043 with t-statistic¼ 3.94.
interest (after controlling for creditor rights). To control for the effects of level of development and of efficiency of the capital market (see La Porta, Lopez-de-Silanes, Shleifer, and Vishny, 1997), we include the following variables (details on the construction of these variables are in Table 1): Log(Market cap),8 Accounting disclosure, and Rule of law. These variables should positively affect the likelihood of same-industry acquisitions if the internal capital markets in conglomerates substitute for lessefficient outside capital markets. Similarly, the Emerging market dummy variable should have a negative coefficient if internal capital markets in conglomerates are valuable. Flexibility to fire proxies for the efficiency of the labor market, which may affect merger type. Legal origin influences a number of national institutional variables, including creditor and shareholder rights (La Porta, Lopez-de-Silanes, Shleifer, and Vishny, 1998); this variable also interacts with the likelihood of bankruptcies (Claessens and Klapper, 2005). These three legal control variables are obtained from Levine and Demirguc-Kunt (2001) and La Porta, Lopez-de-Silanes, Shleifer, and Vishny (1998). The country-level control variables include Macro risk and the country’s average real GDP per capita, which is a proxy for the degree of economic development. The effect of Macro risk should be negative if managers in riskier countries carry out more diversifying mergers. We control for GDP per capita because developed and developing countries may have different investment opportunity sets. The transaction-related control variables are Transaction value and Leverage of both acquirer and target firms. Leverage represents the financial distress risk, which the acquirer should take into account. This risk induces diversifying mergers, and therefore, we expect the coefficients of leverage to be negative. In estimation, we face a
8 Our results are robust to an alternative definition of capital market development, using the ratio of market capitalization-to-GDP as of 1994. However, by this definition, Malaysia, Hong Kong, and South Africa rank at the top, while the U.S. ranks in eighth place, after Chile; Japan is ranked thirteenth, after Thailand and the Philippines.
data limitation. Over 45% of the acquirers in our sample and 88% of the target firms have no accounting information. Consequently, leverage data on both acquirer and target are available for only 2,586 transactions, about 8% of the sample (without the U.S. and the U.K., we have only 746 transactions with leverage data). In addition, leverage in any country is partly endogenous to the country’s creditor rights. We therefore use estimated leverage variables, derived from an instrumental variables regression. For all transactions with data on leverage (see Table 1 for definition), we estimate a regression for both acquirer and target firm leverage as follows: We regress the acquiring (target) firm’s leverage on all country-level control variables and on two exogenous variables, the ranks (in quartiles) of U.S. median leverage and U.S. median tangibility (the ratio of fixed assets-to-total assets) for the industry of the acquiring (target) firm over the period 1992–2004. The U.S. has a low level of creditor rights (CRIGHTS¼1), which implies under our hypotheses a lessconstrained choice of leverage, and it has the most data on all industries, making the estimation more reliable. Accordingly, we impute the leverage of an acquirer (target) firm in any industry in any country as the leverage in that country and industry estimated from a model of the acquirer’s (target’s) leverage as a function of two exogenous industry variables, using U.S. data, and of the acquirer’s own country’s exogenous control variables. For our main test, we estimate a probit model for each transaction j in country c, Prðsame industry mergerÞj,c ¼ a0 þ a1 CRIGHTSc þcontrol variables:
ð1Þ
The dependent variable equals one if acquirer and target are in the same two-digit SIC industry, and zero otherwise. Hypothesis Ia implies that a1 o0. The model includes year dummy variables and estimation-cluster standard errors by country. The results in Table 3 are consistent with Hypothesis Ia. The coefficient of CRIGHTS is negative and statistically significant (column 1), meaning that stronger creditor
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rights are associated with greater propensity to diversify (lower probability of same-industry merger). The results are similar when we exclude the U.S. (column 6) or both the U.S. and the U.K. (column 7), which account for by far the largest number of acquisitions. All four creditor rights components have negative and significant coefficients. The component with the most negative effect is MANAGES, underscoring the importance of managerial dismissal in bankruptcy as an incentive to diversify. Based on columns 1 and 7 of Table 3, the marginal effect of CRIGHTS on the propensity to acquire same-industry target, evaluated at
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mean CRIGHTS (‘‘local elasticity’’), is 9.49%, and 16.48% when excluding the U.S. and the U.K. Notably, the effect of shareholder rights is opposite to that of creditor rights. The positive and significant coefficient of SHRIGHTS when excluding the U.S. suggests that shareholder interests induce focusing acquisitions, after controlling for the effect of creditor rights. The evidence on the effect of internal capital markets in conglomerates is mixed. While the positive coefficient of Log(Market cap) implies that in countries with developed capital markets there is a lesser need for conglomerate mergers, this
Table 3 Merger-level analysis: proportion of same-industry mergers. The table presents the coefficient estimates from probit regressions. The dependent variable equals one if both acquirer and target are in the same industry, using two-digit SIC code. A country is included in our sample if it has at least 50 qualified transactions over the sample period. A transaction is included if the percentage of acquired shares is at least 20%. Excluded are transactions where the acquirer is from the financial industry (SIC header 6) or regulated industry (SIC headers 48 and 49). CRIGHTS are as of 1994. The control variables include shareholder rights, rule of law, macroeconomic risk, legal origins, the logarithm of the stock market capitalization, the index of flexibility to fire, the quality of accounting disclosure, an emerging market indicator, the logarithm of average real per capita GDP (1994–2000) in US$, the logarithm of transaction value, and the imputed leverage for the acquirer and the target (the predictors are the U.S. industry quartile rank of the median leverage and median tangibility, and all exogenous control variables). All variables are defined in Table 1. The regressions include year fixed effects (not reported). Models (1) through (5) include all countries. Model (6) excludes the U.S. Model (7) excludes both the U.S. and the U.K. The t-statistics in parentheses are based on robust estimation of standard errors with errors clusteradjusted at the country level. nnn, nn, and n indicate significance at the 1%, 5%, and 10% levels, respectively. Sample period is 1994–2004. Variable
All countries (1)
CRIGHTS
(2)
(3)
(4)
Emerging market Rule of law French legal origin German legal origin Nordic legal origin Macro risk Log(GDP per capita) Log(Transaction value) Acquirer’s leverage (imputed) Target’s leverage (imputed) Number of countries Observations Chi-squared
0.420nnn (3.56)
0.524nnn (5.18) 0.318nnn (3.78)
0.022 (0.91) 0.293nnn (6.48) 0.836nn (2.15) 0.026nnn (4.46) 0.661nnn (5.99) 0.375nnn (5.79) 0.388nnn (2.87) 0.613nnn (9.32) 1.167nnn (5.3) 0.207 (0.22) 0.178nnn (3.37) 0.086nnn (5.41) 1.746n (1.69) 7.647nnn (6.13)
0.002 (0.08) 0.247nnn (5.94) 1.077nnn (2.68) 0.033nnn (5.23) 0.421nnn (4.75) 0.544nnn (7.85) 0.189n (1.71) 0.86nnn (9.96) 0.903nnn (4.49) 2.945nnn (3.18) 0.199nnn (3.71) 0.090nnn (5.47) 1.755 (1.68) 7.861nnn (6.14)
0.012 (0.46) 0.266nnn (6.01) 1.37nnn (3.32) 0.030nnn (4.82) 0.505nnn (5.27) 0.362nnn (5.66) 0.305nn (2.52) 0.950nnn (10.58) 1.245nnn (5.33) 1.841nn (1.96) 0.097nn (2.04) 0.091nnn (5.47) 1.734 (1.64) 8.062nnn (6.17)
0.029 (1.16) 0.207nnn (5.56) 0.993nn (2.41) 0.047nnn (6.26) 0.303nnn (4.25) 0.445nnn (6.87) 0.224nn (2.10) 0.968nnn (10.49) 1.097nnn (5.10) 6.312nnn (6.76) 0.055 (1.20) 0.096nnn (5.52) 1.737 (1.64) 8.251nnn (6.17)
0.848nnn (6.89) 0.143nnn (5.38) 0.225nnn (6.20) 0.262 (0.67) 0.011nn (2.21) 0.653nnn (6.08) 0.026 (0.34) 0.0004 (0.01) 0.101 (1.00) 1.212nnn (5.70) 0.803 (0.97) 0.152nnn (3.09) 0.083nnn (5.30) 1.754n (1.70) 7.584nnn (6.09)
38 33,221 4,449.7
38 33,221 4,279.3
38 33,221 1,696.8
38 33,221 1,375.8
38 33,221 5,870.4
MANAGES
Accounting disclosure
(7)
0.415nnn (5.74)
SECURED
Flexibility to fire
(6) 0.411 (3.66)
REORG
Log (Market cap)
Exclude U.S. and U.K.
nnn
0.245 (6.33)
AUTOSTAY
SHRIGHTS
(5)
nnn
Exclude U.S.
0.218nnn (4.00) 0.134nnn (3.09) 0.503 (1.17) 0.024nnn (3.09) 1.932nnn (3.42) 0.952nnn (4.13) 0.213 (1.61) 1.087nn (2.35) 2.458nnn (3.33) 4.755nn (2.15) 0.423nnn (3.13) 0.083nn (2.29) 0.486 (0.35) 13.957nnn (3.51)
0.112nnn (2.88) 0.035 (0.87) 0.449 (0.94) 0.035nnn (4.31) 0.956nn (2.58) 0.600nnn (4.33) 0.009 (0.07) 0.673n (1.69) 1.393nn (2.58) 1.765 (1.13) 0.354nnn (3.35) 0.064nnn (2.85) 1.376n (1.75) 7.700nn (2.57)
37 15,730 1,838.4
36 10,106 2,079.4
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coefficient becomes negative and insignificant when excluding the U.S. and the U.K. While internal capital markets in diversified firms are claimed to be of greater value in poorer countries, we obtain that the coefficient of Emerging market is positive (i.e., greater likelihood of focusing acquisitions), and that of GDP per capita is negative (i.e., greater likelihood of diversifying acquisitions in richer countries). Accounting disclosure, an aspect of a developed capital market, has a negative coefficient, implying a greater degree of diversification in such markets. On the other hand, Rule of law, which is associated with capital market development, has a positive coefficient, consistent with the importance of internal capital markets in countries with underdeveloped markets. Target’s leverage has a significant negative effect on the propensity to do same-industry mergers, suggesting that higher financial distress risk induces diversifying acquisitions. The elasticity of target leverage (evaluated at the mean of Target’s leverage) is 2.96, meaning that a 1% increase in the target leverage ratio reduces the likelihood of same-industry merger by nearly 3%. Reinforcing this effect, Acquirer’s leverage also has a negative and marginally significant coefficient when excluding the U.S. and the U.K.9 The effects of Flexibility to fire, Macro risk, and French legal origin and German legal origin are inconclusive, given that their coefficients switch signs and change significance depending on whether the U.S. and the U.K. are included. 2.2.1. Robustness tests We briefly review some robustness tests that we perform. Details on these tests are available in an Appendix at the Journal of Financial Economics (JFE) Web site. First, to address the concern that both creditor rights and corporate strategy might be driven by culture-based factors, we add to the model culture-based variables: the religious composition of the country’s population, following Stulz and Williamson (2003), and the Uncertainty avoidance index of business people in the country, due to Hofstede (2001). Still, CRIGHTS retains its negative and highly significant coefficient. We also compare the U.S. and the U.K. alone, which are similar in culture and financial institutions but differ in their creditor rights. We find that the probability of diversifying mergers is significantly higher in the U.K., whose CRIGHTS equals four versus one in the U.S. Second, we address the concern that the propensity to do same-industry acquisitions is affected by the country’s antitrust laws. We control for that, using data from Hylton and Deng (2007), and find that the coefficient of CRIGHTS remains negative and significant. Third, we test our hypothesis at the aggregate country level, in which each country—large and small alike—is one observation. We regress SAMEc (proportion of same-industry acquisitions) on CRIGHTSc and 9 The fact that both target and acquirer leverage are associated with diversifying acquisitions is consistent with our focus on the managerial agency problem, and potentially inconsistent with the view of agency problems between creditors and shareholders being of importance for corporate risk-taking. The latter would imply that higher acquirer leverage leads to stronger risk-taking incentives, and thereby, would be associated with focusing acquisitions.
country-level control variables. The coefficient of CRIGHTS remains negative and significant. Geographic diversification: We estimate a model similar to that in Table 3, where the dependent variable equals one for domestic acquisition, or zero for cross-border acquisition. The creditor rights pertain to the acquirer’s country (among the 38 countries in our sample; the target firms can be from any country). The coefficient of CRIGHTS is again negative and statistically significant ( 0.111, t ¼5.23), and remains so even if we exclude the U.S. and the U.K. (over 60% of the acquisitions). This is also consistent with our hypothesis that stronger creditor rights induce diversifying acquisitions. Industry-level analysis: Because countries differ in the composition of their industries, we estimate our model at the industry level, following the methodology in Rajan and Zingales (1998). We measure the inherent propensity in an industry to do same-industry acquisitions by the propensity to do that in the U.S., whose acquisition market is the most active and whose relatively low level of creditor rights (CRIGHTS¼1) makes firms less constrained. We estimate the following model: SAMEk,c ¼ g0 þ g1 SAMEk,US þ g2 CRIGHTSdm c SAMEk,US þCountry fixed effects:
ð2Þ
SAMEk,US is the proportion of same-industry acquisitions in the U.S. in industry k out of all acquisitions where the acquirer is in industry k (using two-digit SIC code during the period 1994–1997), and SAMEk,c is defined similarly as the proportion of same-industry acquisitions of acquirers in industry k in country c for the subsequent period, dm 1998–2004. CRIGHTSc is the demeaned value of CRIGHTSc, obtained by subtracting the overall sample mean of CRIGHTS. We include an industry from a given country if it has at least six qualified transactions during the period 1998–2004. We estimate model (2) by the Tobit method. We obtain that g1 ¼1.310 (t¼9.83) and g2 ¼ 0.263 (t¼7.56). That is, across industries, strong creditor rights in a country reduce the tendency to engage in same-industry acquisitions relative to the inherent tendency in these industries. 2.2.2. Risk reduction in acquisitions and industry recovery rates The next test, Hypothesis Ib, examines the effect of creditor rights on the choice of target in acquisitions in terms of the recovery rate of its assets in default (henceforth, recovery). Recovery is the extent to which the price of the assets sold in distress is close to the value of the assets in their best use, following the inverse of the definition of asset specificity in Shleifer and Vishny (1992). We propose that a firm with high-recovery assets can better accommodate financial distress, by partially liquidating such assets, using the proceeds to service debt and thus deferring default. Such a deferment increases the value of the call option embedded in the firm’s equity, increasing its value.10 This assumes that the firm’s 10 Berger, Ofek, and Swary (1996) find that a high recovery value of assets (imputed from book value items) is particularly valuable for firms in financial distress.
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volatility does not appreciably change following the sale of an asset and that the proceeds from such sale are used to service debt. If, however, the cash obtained from liquidating risky assets is retained, for example—to satisfy a working capital covenant restriction, the firm’s volatility declines and the net effect on the equity value is uncertain. But such risk reduction may serve the interests of a risk-averse manager who chooses to reduce volatility in response to strong creditor rights that may threaten managerial job security. In this scenario, high-recovery assets become attractive. This scenario would motivate managers of bidder firms with low-recovery assets to acquire targets with high-recovery assets to enhance their chances of survival. We test the effect of creditor rights on the type of target that a low-recovery bidder seeks. Denote the event of lowrecovery acquirer (AL) buying a high-recovery target (TH) by AL \ TH, and the probability of this event occurring among all such acquisitions by Pr(AL \ TH9TH). We estimate the determinants of Pr(AL \ TH9TH) in the model PrðAL \ TH9THÞj,c ¼ d0 þ d1 CRIGHTSc þcontrol variables:
ð3Þ
We hypothesize that d1 40: stronger creditor rights induce acquirers in low-recovery industries to buy target firms in high-recovery industries. We assign to firms the recovery level of the industry in which they operate, using the data in Acharya, Bharath, and Srinivasan (2007, Table 2), which employ historical experience on defaults in the U.S. over the period 1982–1999.11 In the estimation model, the universe is all targets with high recovery, and the bidders are either low recovery (dependent variable¼1), or high recovery (dependent variable¼ 0). The control variables are those from Table 3. The results in Table 4 support Hypothesis Ib. The coefficient of CRIGHTS is positive and significant for the entire sample as well as when excluding the U.S. and the U.K., which constitute more than half the sample (columns 6–10). That is, stronger creditor rights induce greater likelihood of acquisition of high-recovery targets by low-recovery firms. All components of creditor rights have positive coefficients, and except for the component that secured creditors are paid first (SECURED), they are all statistically significant. The relatively large coefficient of the managerial dismissal component (MANAGES) underscores the evidence in Eckbo and Thorburn (2003) cited above. Macro risk has a positive effect on the likelihood of low-recovery firms acquiring highrecovery firms, which is consistent with the view that such acquisitions are chosen as means to reduce risk.12 This test provides additional evidence that creditor rights affect the 11 Low-recovery industries (in terms of two-SIC code headers) include: transportation (37, 40, 41, 42, 44, 45, 46, 47), high technology and office equipment (35, 36, 38), consumer/service sector (52, 53, 54, 55, 56, 57, 58, 59, 72, 73, 75, 76, 78, 79), and leisure time/media (27, 48, 70). Highrecovery industries include: energy and natural resources (10, 12, 13, 14, 24), building products/homebuilders (8, 15, 17, 24, 28, 29, 32, 34), and healthcare/chemicals (28, 80). We alternatively follow Dyck and Zingales (2004), characterizing as low recovery rate industries the following: mining, manufacturing, and transportation. Our results are similar. 12 We also estimate the model as a country-level regression, where the dependent variable is the proportion of all high-recovery targets in the country acquired by low-recovery bidders (we use logistic
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nature of corporate investment—the choice of an acquisition target—in an attempt to mitigate the likelihood of default. 2.2.3. Diversification across industry lines of business In addition to diversifying through acquisitions, firms can develop internally a portfolio of lines of business in different industries. We now test Hypothesis Ic, on the relation between creditor rights and the number of segments that firms have. The data, obtained from the Compustat North America Segment file, are confined to firms that file such reports by U.S. rules.13 These include non-U.S. firms whose stock is traded in the U.S. through American Depository Receipts, or that are listed in the U.S., or report by U.S. rules to conform to securities laws, as well as Canadian firms. Surely, this sample is limited to firms from countries whose characteristics (such as size, visibility, or type of business) cause their securities to trade in the U.S., or to non-U.S. firms that choose to be covered by U.S. financial reporting rules. With this caveat in mind, we analyze the data on the effect of creditor rights on firms’ tendency to diversify across lines of business. The sample consists of 836 firms in the manufacturing industries (SIC codes 1000 through 3999) from 21 countries, excluding the U.S. (which has overwhelmingly more firms than any country in this sample), with 4,520 firmyears of reporting between 1992 and 2005. We also require that firms have leverage data in either the Compustat North America or the Compustat Global Vantage databases, and as before, we include a country only if at least six firms have data in that country. Because Canadian firms constitute about half of the firm-years in our sample, we repeat our estimation for a sample of 20 countries with 2,132 firmyears that excludes Canadian firms. We estimate a probit regression, where the dependent variable equals one if the firm has more than one business segment, and zero otherwise. CRIGHTS is the main explanatory variable in our model, which includes all other explanatory variables that appear in Table 3, with firm leverage estimated and instrumented with the same variables. We hypothesize that the coefficient of CRIGHTS is positive, i.e., stronger creditor rights induce firms to diversify across lines of business (internally or by acquisition). Indeed, the coefficient of CRIGHTS is positive, 0.346 (t¼ 2.94); excluding Canada: 0.236 (t¼ 3.45). In an ordinary least squares regression, where the dependent variable is Log(number of segments), the coefficient of CRIGHTS is 0.110 (t ¼3.72); excluding Canada: 0.106 (t ¼2.51).14 These results further support our hypothesis that stronger creditor rights induce firms to reduce their risk through diversification across industries. (footnote continued) transformation). The coefficient of CRIGHTS is positive, 0.288, with t ¼3.37, consistent with the results for the single-acquisition regression. 13 Foreign firms listing in the U.S. are required to file with the Securities Exchange Commission (SEC) and reconcile with U.S. Generally Accepted Accounting Principles (GAAP) and Financial Accounting Standards Board (FASB) rules (in particular, Statements of Financial Accounting Standards (SFAS) 131 and its predecessor, SFAS 14, regarding the reporting of segments data) in their annual reports. 14 Standard errors are clustered by country, and the model includes year dummy variables.
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Table 4 Recovery rates and mergers and acquisitions. The table presents coefficient estimates of probit models. The dependent variable equals one if Pr(TH\AL9TH) ¼1, i.e., if the target is in a high-recovery industry and the acquirer is in a low-recovery industry. The universe is all target firms in a high-recovery industry. Included are all transactions where the percentage of acquired shares is at least 20%. Excluded are transactions involving acquirers that are financial industry (SIC header 6) or regulated industry companies (SIC headers 48 and 49). The following industries are classified as low recovery (two-SIC code headers): transportation (37, 40, 41, 42, 44, 45, 46, 47), high technology and office equipment (35, 36, 38), consumer/service sector (52, 53, 54, 55, 56, 57, 58, 59, 72, 73, 75, 76, 78, 79), or leisure time/media (27, 48, 70). The following industries are classified as high recovery (two -SIC code headers): energy and natural resources (10, 12, 13, 14, 24), building products/ homebuilders (8, 15, 17, 24, 28, 29, 32, 34), or healthcare/chemicals (28, 80). This classification follows Acharya, Bharath, and Srinivasan (2007). All variables are defined in Table 1. The leverage of acquirer and target is calculated as in Table 3. The sample period is 1994–2004. The absolute values of the t-statistics are shown in parentheses below the coefficients and are based on robust standard errors that are cluster-adjusted at the country level. We include year fixed effects (not reported). nnn, nn, and n indicate significance at the 1%, 5%, and 10% levels, respectively. Variables
All countries (1)
CRIGHTS
(2)
(3)
Excluding the U.S. & U.K. (4)
0.128nn (2.45)
(6)
(7)
(8)
SECURED
0.492nnn (2.64) 0.51nn (2.33)
0.124 (0.60)
MANAGES 0.107n (1.65) Log (Market cap) 0.083 (1.17) Flexibility to fire 1.250 (1.34) Accounting disclosure 0.05nnn (3.73) Emerging markets 0.162 (1.02) Rule of law 0.190 (1.01) French legal origin 0.405 (1.44) German legal origin 0.257nn (2.08) Nordic legal origin 0.733nn (2.00) Macro risk 5.734n (1.94) Log(GDP per capita) 0.249n (1.75) Log (Transaction value) 0.015 (1.49) Acquirer’s leverage (imputed) 12.99nnn (9.47) Target’s leverage (imputed) 5.838nnn (9.03) 38 6,495 28,376.0
(10)
0.425nn (2.38) 0.277n (1.93)
REORG
SHRIGHTS
(9)
0.354nnn (4.56) 0.915nnn (6.30)
AUTOSTAY
No. of countries Observations Chi-squared
(5)
0.016 0.114n 0.118 (0.22) (1.71) (1.54) 0.615nnn 0.12n 0.165nn (6.49) (1.86) (2.27) 2.379nn 1.716 1.305 (2.32) (1.52) (0.99) 0.018 0.045nnn 0.034nnn (1.15) (3.38) (3.05) 1.138nnn 0.059 0.027 (5.69) (0.49) (0.21) 0.56nn 0.225 0.161 (2.33) (1.18) (0.76) 0.317 0.418 0.538 (1.04) (1.52) (1.59) nnn 1.483 0.099 0.084 (9.38) (0.94) (0.62) 2.317nnn 0.817nn 0.982nn (4.46) (2.26) (2.08) 9.374nnn 6.488nn 9.048nnn (3.01) (2.42) (3.92) 0.600nnn 0.173 0.156 (3.47) (1.29) (0.99) nnn n 0.136 0.017 0.019n (6.45) (1.70) (1.95) 26.83nnn 12.88nnn 12.71nnn (7.03) (9.25) (9.08) 32.688nnn 5.658nnn 5.342nnn (14.58) (8.66) (7.66) 38 6,495 6,360.2
38 6,495 43,325.1
38 6,495 13,403.8
2.3. Value effects of creditor rights in diversifying cross-industry acquisitions Hypothesis II suggests that stronger creditor rights induce managers to undertake diversifying acquisitions even when they harm corporate performance. To some extent, creditor rights may be desirable because they reduce the dead-weight cost that results from the conflict of interests between debtors and creditors (see Jensen and Meckling, 1976). For example, debtors may choose to continue the operation of a distressed firm even if it erodes
0.619nnn (3.50) 0.22nnn 0.18nnn (2.71) (3.32) 0.116n 0.283nnn (1.90) (2.94) 0.274 0.497 (0.33) (0.67) 0.056nnn 0.035nnn (4.51) (3.23) 0.259 0.453 (1.68) (1.47) 0.424nn 0.186 (2.05) (0.81) 0.72nnn 0.330 (2.69) (1.09) nnn 0.871 1.118nnn (3.57) (3.65) 0.670n 0.156 (1.79) (0.35) 4.761 3.149 (1.68) (1.15) nn 0.272 0.3nn (1.98) (2.32) 0.017n 0.073nnn (1.7) (3.11) 12.96nnn 15.25nnn (9.4) (12.8) 5.762nnn 10.807nnn (8.83) (7.75) 38 6,495 12,529.0
36 2,599 27,974.7
0.191nnn 0.165nn 0.211nnn (2.81) (2.33) (3.35) 0.25nn 0.205nn 0.081 (2.13) (2.05) (0.66) 1.108 1.496 1.456 (1.12) (1.67) (1.21) nnn nnn 0.039 0.039 0.036nnn (3.12) (3.6) (3.45) 0.492 0.345 0.84nn (1.44) (0.99) (2.31) 0.209 0.107 0.145 (0.8) (0.44) (0.55) 0.849nn 0.579 0.707nn (2.49) (1.63) (2.14) 1.017nnn 0.578 0.868n (2.70) (1.32) (1.90) 0.289 0.112 0.218 (0.58) (0.25) (0.48) 5.129n 5.223nn 5.228n (1.7) (1.99) (1.79) 0.363nn 0.211 0.222 (2.09) (1.57) (1.25) nnn nnn 0.076 0.077 0.074nnn (3.23) (3.22) (3.14) 14.80nnn 14.84nnn 14.72nnn (12.65) (12.04) (11.71) 10.217nnn 10.046nnn 9.833nnn (7.22) (6.62) (6.93) 36 2,599 6,449.9
36 2,599 15,708.8
36 2,599 9,494.0
1.466nnn (5.25) 0.357nnn (5.81) 0.416nnn (3.47) 1.86nn (2.16) 0.048nnn (5.23) 0.157 (0.49) 0.909nnn (3.15) 0.774nn (2.57) 2.025nnn (6.15) 0.279 (0.57) 4.462 (1.6) 0.249nn (2.05) 0.085nnn (3.65) 15.17nnn (12.37) 10.133nnn (7.45) 36 2,599 13,115.9
firm value in order to retain the option of a rebound. Then, diversification that reduces this conflict may be beneficial. However, we hypothesize that in countries with stronger creditor rights, diversifying acquisitions are associated with worse firm performance. In testing this hypothesis, we present as a benchmark the relation between firm performance and creditor rights in focusing (same industry) acquisitions, which are likely to be undertaken for economic reasons, such as synergy. In focusing acquisitions, we do not expect that the strength of creditor rights is negatively associated with firm performance.
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The effect of diversification on corporate performance is subject to debate, but much of the evidence suggests that diversification is value-reducing.15 In countries with underdeveloped capital markets, diversified conglomerates may be beneficial by enabling internal capital markets that substitute for the costly outside capital market. However, Scharfstein and Stein (2002) point out that internal capital markets can have a ‘‘dark side’’ if they cause inefficient subsidization of poorly performing groups.16 We test the consequences of diversifying acquisitions as a function of a country’s creditor rights using two measures of firm performance: (1) the change in the acquiring firm’s return on assets, ROA, in the three years after the acquisition compared to the ROA in the year prior to acquisition, and (2) the acquirer’s stock price change, measured as the cumulative abnormal return, CAR, over a seven-day window surrounding the acquisition announcement. (Details on the calculation of ROA and CAR are in Table 1.) We estimate the following model separately for focusing and for diversifying acquisitions: Performancej,c ¼ Z0 þ Z1 CRIGHTSc þ control variables:
ð4Þ
In the first test, Performancej,c is DROA(k)j,c ¼ROAj,c(t þk) ROAj,c(t 1), the change in the return on assets of acquirer firm j in country c, k year(s) after the acquisition compared to one year before its announcement, t is the effective year of the acquisition, and k ¼1, 2, 3. We use ROA as a performance measure, following Healy, Palepu, and Ruback (1992), who suggest that this measure is unaffected by the method of accounting used in mergers. The control variables include all the country variables used in the previous analyses and Log(transaction value). To control for the endogeneity of the decision to diversify, we add the inverse Mills ratio from the probit regression presented in Table 3. The model includes acquirer industry fixed effects to control for industry-wide changes in profitability, and year fixed effects. We estimate the model separately for one, two, and three years after the merger (k¼1, 2, 3). The coefficient Z1 measures the extent to which the post-merger change in the acquirer’s ROA is affected by the country’s creditor rights. Our hypotheses are: For diversifying acquisitions: Z1 o0, because managers may sacrifice corporate performance to attain lower corporate risk. For focusing (same industry) acquisitions: Z1 Z0. The results in Table 5, columns 1–6, support our hypothesis. The coefficient Z1 is negative and highly 15 See (among others) Morck, Shleifer, and Vishny (1990), Berger and Ofek (1995), Comment and Jarrell (1995), Moeller and Schlingemann (2005), Campa and Kedia (2002), Villalonga (2004), Ammann, Hoechle, and Schmid (2008), Laeven and Levine (2007), and Schmid and Walter (2009). 16 Related literature on the dark side of internal capital markets also includes Berger and Ofek (1995), Lamont (1997), Scharfstein (1998), Shin and Stulz (1998), Rajan, Servaes, and Zingales (2000), Lamont and Polk (2002), Comment and Jarrell (1995), Khanna and Palepu (2000), Lins and Servaes (2002), and Lee, Peng, and Lee (2008).
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significant in diversifying mergers for all three postmerger horizons. That is, the acquirer’s post-merger performance declines significantly in countries with stronger creditor rights up to three years after the merger, relative to its performance in the pre-merger year. For focusing (same industry) acquisitions, the coefficient Z1 is not significantly different from zero, again consistent with Hypothesis II. We conclude that diversifying acquisitions that seem to occur in response to stronger creditor rights are followed by deterioration in corporate performance.17 When we exclude the U.S. and the U.K. (which have by far the largest number of observations within the sample), the results remain qualitatively the same. For the sample of diversifying acquisitions, the coefficient of CRIGHTS in model (4) is 0.015 (t ¼3.43) for dROA(1)j,c, for dROA(2)j,c it is 0.017 (t¼4.07), and for dROA(3)j,c it is 0.013 (t¼ 4.17). In contrast, for focusing (same industry) acquisitions, the coefficients of CRIGHTS are all insignificantly different from zero. In the second test, Performancej,c is the acquirer’s CAR over the seven days surrounding the announcement day.18 The results on the effect of creditor rights on the acquirer’s CAR support our hypothesis and are consistent with the results on post-acquisition changes in the acquirer’s ROA. As presented in Table 5 columns 7–8, diversifying acquisitions lower the acquirer’s value in countries with stronger creditor rights: the coefficient Z1 of CRIGHTS in model (4) is negative and significant for diversifying acquisitions (column 8), 0.013 (t ¼5.14), meaning a value loss of 1.3% upon the announcement of such deals for any unit of CRIGHTS, whereas for focusing (same industry) acquisitions (column 7) it is positive and marginally significant, 0.011 (t¼1.65).19 Excluding the U.S. and the U.K., the coefficient of CRIGHTS in diversifying acquisitions is 0.011 (t¼2.40), significant, while in focusing acquisitions it is 0.002 (t ¼0.26), insignificant. When estimating the model for the U.S. and the U.K. alone, which are similar in culture and financial institutions but different in creditor rights (CRIGHTS ¼4 for the U.K. and one for the U.S), the results are similar. Acquirers in the U.K. lose significantly more in diversifying acquisitions, whereas in focusing acquisitions they gain more.20 These results suggest that stronger creditor rights induce
17 As a robustness check, we re-estimate the model using the creditor rights variable from Djankov, McLeish, and Shleifer (2007), which varies over time for five countries. The results are qualitatively similar. 18 We use this time window because in some countries, low stock liquidity causes a slower adjustment of stock prices to information, and lax enforcement of insider trading rules may cause trading on the information some days prior to the formal announcement. Our results are qualitatively similar for smaller event windows, such as 1 to þ 1. 19 The results are qualitatively similar when we use Djankov, McLeish, and Shleifer (2007) on CRIGHTS. The coefficient of CRIGHTS in the diversifying acquisitions model is 0.007 (t ¼3.36) and it is 0.004 (t¼ 0.53) for same-industry acquisitions. 20 We estimate a regression of CAR as a dependent variable in a model similar to that in Table 5, with data from these two countries alone. We set a dummy variable UK¼ 1 for an acquirer in the U.K., where creditor rights are stronger, and UK¼0 for a U.S. acquirer, and we exclude country-related variables. We obtain that for diversifying acquisitions, the coefficient of UK
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Table 5 Effects of creditor rights on performance for focusing and diversifying mergers. The table includes two performance variables: (1) DROA(k) ¼ ROA(tþ k) ROA(t 1), where ROA is return on assets ¼ EBITDA/Assets, and t is the year of the merger; (2) Cumulative abnormal returns on the acquirer’s stock, CAR, from three days before the merger announcement to three days after the merger announcement. Abnormal returns are calculated from a market model whose parameters are estimated from weekly returns and market model for each country using 105 weeks but not less than 52 weeks, up to nine weeks before the week of the merger announcement. We include year and industry fixed effects (not reported). To account for the choice of type of acquisition, we add the inverse Mills ratio, computed using probit model (1) in Table 3 for regressions that include all countries. The t-statistics (in parentheses) are based on robust standard errors cluster-adjusted at the country level. The nnn, nn, and n indicate significance at the 1%, 5%, and 10% levels, respectively. Refer to Table 1 for variable definitions. ROA(t þ1) ROA(t 1)
CRIGHTS SHRIGHTS Log(Market cap) Flexibility to fire Accounting disclosure Emerging markets Rule of law French legal origin German legal origin Nordic legal origin Macro risk Log(GDP per capita) Log(Transaction value) Dummy: Target is public Inverse Mills Ratio Observations R-squared (%)
ROA(t þ2) ROA(t 1)
ROA(tþ 3) ROA(t 1)
CAR (t 3 to t þ3)
Focusing (1)
Diversify (2)
Focusing (3)
Diversify (4)
Focusing (5)
Diversify (6)
Focusing (7)
Div. (8)
0.0003 (0.02) 0.004 (0.37) 0.001 (0.11) 0.124 (0.77) 0.001 (0.44) 0.025 (0.47) 0.021 (0.44) 0.037 (0.86) 0.055 (1.35) 0.020 (0.42) 0.105 (0.27) 0.001 (0.13) 0.002 (0.37) 0.004 (0.63) 0.082 (0.21)
0.028nnn (8.20) 0.009 (1.44) 0.007 (0.93) 0.041 (0.76) 0.0001 (0.06) 0.006 (0.38) 0.019 (0.69) 0.026 (1.34) 0.003 (0.27) 0.024 (0.85) 0.169 (1.0) 0.013 (0.85) 0.003 (0.95) 0.005 (1.57) 0.040 (1.08)
0.026 (1.30) 0.008 (0.61) 0.019 (0.90) 0.258 (1.03) 0.002 (0.76) 0.078 (0.94) 0.079 (1.06) 0.034 (0.50) 0.079 (1.13) 0.145n (1.84) 0.780 (1.09) 0.022 (1.06) 0.009 (0.93) 0.011 (1.29) 0.573 (0.9)
0.031nnn (10.28) 0.007 (1.27) 0.003 (0.49) 0.042 (0.79) 0.0003 (0.26) 0.008 (0.48) 0.019 (0.92) 0.021 (1.34) 0.005 (0.44) 0.026 (1.02) 0.619nnn (4.08) 0.012 (0.95) 0.003 (0.72) 0.001 (0.39) 0.053 (1.08)
0.017 (0.98) 0.012 (1.03) 0.030 (1.49) 0.237 (1.11) 0.004n (1.79) 0.103 (1.43) 0.062 (1.02) 0.065 (1.35) 0.062 (1.16) 0.093 (1.23) 0.427 (1.04) 0.006 (0.4) 0.009 (1.21) 0.006 (1.25) 0.618 (1.25)
0.030nnn (8.84) 0.003 (0.45) 0.002 (0.26) 0.041 (0.79) 0.001 (0.79) 0.002 (0.13) 0.016 (0.82) 0.025 (1.39) 0.006 (0.53) 0.021 (0.72) 0.161 (0.92) 0.009 (0.73) 0.001 (0.3) 0.003 (0.78) 0.092n (1.96)
0.011 (1.65) 0.008n (1.74) 0.017nn (2.31) 0.173nn (2.41) 0.002 (1.62) 0.051nn (2.2) 0.058 (1.53) 0.032 (1.28) 0.049n (1.96) 0.047nn (2.32) 0.279 (1.45) 0.015 (1.10) 0.005 (1.32) 0.016nnn (5.01) 0.434nn (2.01)
0.013nnn (5.14) 0.002 (0.56) 0.004 (1.49) 0.033 (1.13) 0.0001 (0.18) 0.022nnn (2.89) 0.02n (1.87) 0.019 (1.66) 0.013nn (2.34) 0.047nnn (2.98) 0.058 (0.63) 0.02nn (2.22) 0.002nnn (2.66) 0.017nn (2.48) 0.014 (0.65)
8,788 8.8
5,752 11.7
8,198 8.5
5,491 15.0
7,742 4.2
4,770 13.6
7,500 1.6
5,725 2.0
firms to undertake diversifying acquisitions, even in the presence of a post-acquisition decline in profitability and value, perhaps as a response to the threat of default. 2.4. The effects of changes in creditor rights Thus far, we have analyzed the cross-country relation between creditor rights and two sets of variables: type of acquisition (focusing or diversifying) and post-acquisition performance. We now test the effect of creditor rights on these variables over time, exploiting seven changes in creditor rights that occurred in six countries: Indonesia, Israel, Japan (two changes), Sweden, Thailand, and Russia,21 (footnote continued) is 0.017 (t¼34.52) while for focusing acquisitions, the coefficient of UK is 0.071 (t¼ 5.89). 21 Russia is included only in this table’s regressions, not in any other estimation, because it has a unique legal origin. Its inclusion with a
documented in Djankov, McLeish, and Shleifer (2007). These changes decreased CRIGHTS by one unit—that is, they weakened creditor rights—except for the 2002 change in Japan that raised CRIGHTS by one unit. We estimate the following regression, a variant of model (1): DepVarj,c ¼ y0 þ y1 DCRIGHTSc þcontrol variables:
ð5Þ
DepVar is the dependent variable in the regression: (i) the probability of same-industry acquisition, Pr(same industry); (ii) the probability of same-country acquisition, Pr(same country); (iii) the probability of a low-recovery acquirer buying a high-recovery target, Pr(AL\TH9TH)j,c; (iv) the change in acquirer’s ROA k years after the (footnote continued) unique dummy variable for its legal origin does not change any of the reported results.
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acquisition, DROA(k)¼ ROA(tþk) ROA(t 1); and (v) the cumulative abnormal return on the acquirer’s stock from three days before the acquisition announcement to three days thereafter, CAR (t 3 to tþ 3). In cases where creditor rights became weaker, we set DCRIGHTSc ¼0 for the years that follow the year of change and set DCRIGHTSc ¼1 for the period that precedes it (including the change year). Analogously, if creditor rights were strengthened, DCRIGHTSc ¼ 1 during the period following the year of the change and DCRIGHTSc ¼0 beforehand. As discussed, all changes in CRIGHTSc during the sample period, but for one case, made creditor rights weaker. For the 32 countries in our sample with no changes in creditor rights, DCRIGHTS¼0 for the entire sample period. The control variables are Transaction value (in logarithm) and, importantly, country fixed effects, which account for all country-based variables, in line with the difference-indifferences methodology. We also include year fixed effects and industry fixed effects (except for dependent variable (iii), where the classification is done by industry). We estimate the regressions for the dependent variables (i)–(iii) above by the probit method and for the dependent variables (iv)–(v) by OLS, with standard errors clustered at the country level to account for potential within-country correlation in the residuals.
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In accordance with our hypotheses, we expect that in model (5), y1 o0 for all dependent variables except for Pr(AL\TH9TH)j,c, where we expect y1 40. The regression results in Table 6 support our hypothesis, as follows: (i) DepVar¼Pr(same industry): The coefficient of DCRIGHTSc is negative and statistically significant: y1 ¼ 0.145 (t ¼6.19). This means that weakening of creditor rights significantly increases the likelihood of same-industry mergers and reduces the extent of diversifying, risk-reducing mergers. The marginal effect from this regression is 0.057, i.e., an increase in the strength of creditor rights by one (on a scale of zero to four) is associated with a statistically significant drop in the probability of a same-industry merger by 5.7%. (ii) DepVar¼Pr(same country): y1 ¼ 0.213 (t ¼2.83). Weakening of creditor rights reduces the likelihood of cross-country mergers. (iii) DepVar¼Pr(AL \ TH9TH) (the likelihood of a highrecovery target being acquired by a low-recovery firm): y1 ¼0.147 (t ¼1.08). The strengthening of creditor rights increases the propensity of firms with lowrecovery assets to seek and buy target firms with
Table 6 The effect of changes in creditor rights. The creditor rights change dummy, DCRIGHTS, equals one after the year of change from a period of stronger creditor rights, and zero otherwise, and it equals zero after the year of change from a period of weaker creditor rights, and one otherwise. It equals zero for the control sample of no change in creditor rights. Included are all mergers and acquisitions where the acquired percentage shares is at least 20%, the transaction has a disclosed value, and the time changes in creditor rights are available in Djankov, McLeish, and Shleifer (2007). We exclude transactions where the acquirer is in the financial industry (SIC header 6) or regulated industry (SIC headers 48 and 49). The sample period is 1994–2004. Models (1), (2) and (3) are estimated by the probit method and the rest are estimated by OLS. The dummy variable to measure the probability of same-industry acquisition, Pr(Same industry), equals one when bidder and target are in the same industry. The dummy variable to measure the probability of an acquisition of high-recovery target by a lowrecovery acquirer, Pr(AL\TH9TH), equals one when, among all acquisitions of target firms whose assets have high recovery value, the bidder firm’s assets have low recovery value. For regression (2) only, we include all cross-country and within-country mergers that meet the requirements above. The postacquisition change in return on assets is DROA(k) ¼ROA(t þk) ROA(t 1), where k ¼1, 2, or 3, calculated for each merger with available data, where t is the effective year of the merger. CAR is the cumulative abnormal returns on the acquirer stock from three days before the acquisition announcement to three days after it. The standard errors are cluster-adjusted at the country level. Included (but not reported for brevity) are fixed effects for country, year, and industry (two-digit SIC code—acquirer’s industry), following the difference-in-differences methodology of Bertrand, Duflo, and Mullainathan (2004). Model (3) does not include industry fixed effects, in line with Table 4. nnn, nn, and n indicate significance at the 1%, 5%, and 10% levels, respectively. Refer to Table 1 for variable definitions. Part I. Mutivariate analysis Variable Pr(Same industry) (1)
DCRIGHTS
c,t
Log (Transaction value) Fixed effects Observations
0.145nnn (6.19) 0.028n (2.52) Country, year, industry 33,221
Pr(Same country) (2)
Pr(TH \ AL9TH) (3)
0.213nnn (2.83) 0.07nn (2.22) Country, year, industry 52,756
0.147 (1.08) 0.057 (7.73) Country, year 6,495
DROA(1)
DROA(2)
DROA(3)
(4)
(5)
(6)
0.042nnn 0.051nnn 0.023nnn (5.78) (9.22) (4.93) 0.002n 0.002 0.001n (1.75) (1.03) (1.73) Country, year, Country, year, Country, year, industry industry industry 14,540 13,689 12,512
CAR (t 3 to t þ 3) (7) 0.005nn (3.31) 0.001 (1.07) Country, year, industry 13,225
Part II. Details of changes Country
Year of law change
Detail of change
Indonesia Israel Japan
1998 1995 2000 and 2002
Russia Sweden Thailand
1998 1995 1999
Change to SECURED ¼ 0 Change to AUTOSTAY ¼0 2000: Change to SECURED ¼ 0 2002: Change to AUTOSTAY ¼ 1 1998: Change to MANAGES ¼ 0 Change to REORG ¼0 Change to REORG ¼0
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high-recovery assets. In this case, however, the coefficient is not statistically significant. (iv) DepVar¼ DROA(1), DROA(2), and DROA(3): The coefficients of DCRIGHTSc are, respectively, y1 ¼ 0.042 (t¼ 5.78), y1 ¼ 0.051 (t ¼9.22), and y1 ¼ 0.023 (t¼ 4.93). All coefficients are negative, as expected, and significant. These results mean that in countries where creditor rights were weakened, acquirers made more profitable acquisitions than they did beforehand. Notably, in this regression we include all acquisitions, not only the diversifying ones, because of the self-selection in diversification. When including only diversifying acquisitions, the three coefficients of DCRIGHTSc are slightly more negative: 0.062 (t ¼6.87), 0.069 (t¼ 9.24), and y1 ¼ 0.027 (t¼ 4.30), all statistically significant. (v) DepVar¼CAR(t 3 to t þ3): The negative and significant coefficient of DCRIGHTSc, y1 ¼ 0.005 (t ¼3.31), means that after creditor rights were weakened, acquisitions became more value-enhancing, the improvement being 0.5% of the acquirer’s value. When estimating the model with diversifying acquisitions only (which are subject to selection), the coefficient of DCRIGHTSc is again slightly more negative, 0.008 (t ¼3.08).
CRIGHTS AUTOSTAY REORG SECURED MANAGES
Firm-level model
Country-level model
0.005 0.010 0.003 0.006 0.023
0.010 0.024 0.003 0.005 0.036
(t ¼2.60) (t ¼1.44) (t ¼0.59) (t ¼1.00) (t ¼ 3.91)
These results support our hypothesis: the coefficient
k1 on CRIGHTSc is negative and statistically significant. As in Table 3, the component of CRIGHTS with the most negative effect on RISK is managerial dismissal in reorganization (MANAGES). When we exclude the U.S. and the U.K., the effect of CRIGHTS is similar, 0.005 with t ¼2.50.22 We estimate again the model at the industry level. Following the methodology of Rajan and Zingales (1998) discussed above, the inherent risk for an industry k is the median risk level of that industry in the U.S., RISKk,US, calculated for the 1992–1998 period. RISKk,c is the median risk in the same industry in country c, calculated over the subsequent period, 1999–2005. The model is: RISKk,c ¼ l0 þ l1 RISKk,US þ l2 CRIGHTSdm c RISKk,US þ Country fixed effects:
In summary, the results on the effects of changes in creditor rights are consistent with those obtained in the cross-section analysis and thus support Hypothesis II on the effects of creditor rights on types of firm investments and on value. 2.5. Creditor rights and firms’ cash-flow risk We now test Hypothesis III, whether the level of corporate cash-flow risk is lower in countries with stronger creditor rights. We test this hypothesis because, in addition to undertaking diversifying acquisitions (Hypotheses Ia–Ic), firms can reduce their risk by other means that are not directly observed. We define RISKj,c as the standard deviation of the yearly ROAj,c,t of firm j in country c during the period 1992–2005. (Details are in Table 1.) The sample includes only firms in the manufacturing industries with data for at least eight years and excludes utilities and financial firms, which are regulated in many countries. We require at least six firms in a country, thus having a sample of 5,394 firms in 35 countries. The estimation model is: RISKj,c ¼ k0 þ k1 CRIGHTSc þcontrol variables:
ð6Þ
Our hypothesis implies k1 o0. The control variables are those used in Table 3, adding firm size (logarithm of firm’s assets at the beginning of its data in our sample), which negatively correlates with risk, and industry (onedigit SIC) dummy variables. In the country-level regressions, the dependent variable is the median for each country of the variable RISKj,c, and the expalanatory variables are the country’s creditor rights and all country variables. The results are as follows: (complete tables are available in an appendix at the JFE Web site).
(t ¼2.95) (t ¼2.71) (t ¼0.36) (t ¼0.56) (t ¼4.10)
ð7Þ
Hypothesis III implies that l2 o0. We indeed obtain that l2 ¼ 0.158 with t¼ 2.16, supporting our hypothesis. Creditor rights have a negative effect on corporate cashflow risk, relative to the industry’s inherent risk level, RISKk,US. Also, the result l1 ¼0.862 (t ¼4.49) (R2 ¼30.2%) supports the use of risk in a U.S. industry to represent the inherent level of that industry’s risk in other countries. 2.6. Creditor rights and financial leverage For any given level of corporate activity, corporate managers can reduce the likelihood of bankruptcy and its associated costs by lowering financial leverage. Thus, strong creditor rights should reduce corporate demand for leverage. On the other hand, La Porta, Lopez-deSilanes, Shleifer, and Vishny (1998) suggest that strong creditor rights increase the supply of credit, which would raise overall leverage if demand for borrowing is unaffected.23 By our Hypothesis IV, strong creditor rights may reduce leverage if the cost imposed by such rights 22 Among the control variables, the instrumented leverage has a negative and significant coefficient. Large firms have lower risk. Macro risk has a positive effect on RISKj,c, but is insignificant. Including Hofstede’s (2001) Uncertainty avoidance index as a control variable, we obtain that its coefficient is negative and insignificant ( 0.0001 with t ¼ 0.032) in the single-firm regression, and 0.0004 (t¼ 2.39) in the country-level regression. In the latter regression, the coefficient of CRIGHTS is 0.007 (t ¼ 4.18), highly significant. 23 Haselmann, Pistor, and Vig (2010) find that the improvement in enforcement of creditor rights in Central and East European countries, through creation of a collateral registry, boosted lending. Acharya, Sundaram, and John (2011) show theoretically and empirically that the effect of creditor rights on corporate leverage depends on the asset specificity of the firm. Vig (2007) finds that in India, strengthening creditor rights reduced leverage.
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outweighs the beneficial effect on the supply of credit. We test the effect of creditor rights on leverage via the model: Leveragej,t,c ¼ m0 þ m1 CRIGHTSc þcontrol variables:
ð8Þ
Here, Leveragej,c,t is the industry-adjusted leverage (in book value) of firm j in country c in year t (details are in Table 1). The sample of firms is the same as in the tests of cash-flow risk; it includes 36,237 firm-years with leverage data, of which 17,304 are in countries excluding the U.S. and the U.K. The regression includes the country variables and firm-specific variables that appear in Table 3, adding variables that are used in studies of leverage: country corporate tax rate in each year, firm asset tangibility, firm size, and firm ROA. The firm control variables and the country tax rate are lagged one year. The regression includes year fixed effects, and standard errors are clustered by country. Our hypothesis is that in model (8), m1 o0, i.e., stronger creditor rights induce corporate managers to reduce financial risk by reducing corporate leverage. We estimate the model at both the single firm-year level and the country level. For the country-level regression, we calculate the yearly average industry-adjusted leverage ratio for the country and then regress that country’s average annual leverage on the creditor rights in the country, as well as on all country variables and on year dummy variables. The results are as follows (complete tables are available at the JFE Web site):
CRIGHTS AUTOSTAY REORG SECURED MANAGES
Firm-level model
Country-level model
0.022 0.037 0.049 0.042 0.041
0.019 0.015 0.027 0.032 0.018
(t ¼5.20) (t ¼2.45) (t ¼4.66) (t ¼2.61) (t ¼3.10)
(t ¼9.32) (t ¼3.01) (t ¼6.92) (t ¼6.06) (t ¼3.05)
Supporting our hypothesis that stronger creditor rights reduce leverage, the coefficient of CRIGHTS is negative and significant at both the single-firm level and the country level. When we exclude the U.S. and the U.K. in the singlefirm regressions, the coefficient of CRIGHTS is 0.018 with t ¼3.42. All four categories of creditor rights have consistently negative coefficients that are statistically significant.24 Finally, we estimate the effect of changes in creditor rights on the leverage of the firms in our sample. We estimate model (5) above with DepVar¼Leverage. The specification of the model is as described in Section 2.4. We also add leverage-related, firm-specific variables: Tangibility, Log(assets), and Earnings Before Interest, Tax, Depreciation and Amortization (EBITDA)/Assets. We expect 24 We obtain similar results in a robustness test that employs Djankov, McLeish, and Shleifer’s (2007) data on creditor rights. In the sample of all countries, the coefficient of CRIGHTS is 0.018 with t ¼3.52, and after excluding the U.S. and the U.K., it is 0.013 with t ¼4.59. When we add to the single-firm regression the culture-based Uncertainty avoidance index of Hofstede (2001), its coefficient is negative but insignificant, 0.0001 (t¼ 0.56), while the negative and significant effect of CRIGHTS is unaltered: its coefficient is 0.0221 (t ¼ 5.54).
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the coefficient of DCRIGHTSc to be negative; that is, weakening of creditor rights increases corporate leverage because the costs of financial distress to debtors are lower. Indeed, we obtain that the coefficient of DCRIGHTSc is 0.035 with t ¼2.53. That is, weakening of creditor rights causes firms to increase their leverage. 3. Conclusion and discussion We find that having strong creditor rights in a country leads firms to reduce risk. They do so by undertaking diversifying acquisitions, both across industries in the domestic market and across national borders, and they increase the number of lines of business in which they participate. In response to strong creditor rights, firms also implement policies that reduce cash-flow risk, and they become reluctant to borrow, which results in lower leverage in countries with strong creditor rights. Thus, creditor rights have effects on real as well as financial corporate policies. Further, we find that to avoid the higher costs associated with stronger creditor rights, firms make diversifying acquisitions even if they hurt corporate performance, measured by return on assets post-acquisition and by stock price reaction to the acquisition announcement. Both measures of performance show declines resulting from diversifying acquisitions, with the decline being greater in countries with stronger creditor rights. No such relation between corporate performance in acquisitions and creditor rights is observed in focusing (same industry) acquisitions. Stronger creditor rights are one way to mitigate stockholder expropriation or risk-shifting tendencies that benefit them at the expense of bondholders; they thereby facilitate raising external capital. Our findings thus confirm that creditor rights do what they are expected to do: inhibit risk-taking by companies. However, it may well be that stronger creditor rights may induce managers to reduce risk and to stifle even non-opportunistic risk-taking that would be beneficial to all claimholders. In this paper, we provide evidence of this downside from strong creditor rights. This tradeoff suggests that the existence of stronger creditor rights is not always desirable. The optimal level of creditor rights should balance their positive effect on the supply of credit against their negative effect on corporate risk-taking and on operating performance, as well as on the demand for debt. In future work, it would be interesting to assess directly this important tradeoff. Appendix A. Supporting information Supplementary data associated with this article can be found in the online version at doi:10.1016/j.jfineco.2011. 04.001.
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Journal of Financial Economics 102 (2011) 167–182
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Tracking down distress risk$ Nishad Kapadia n Jones Graduate School of Business, Rice University, Houston 77030, United States
a r t i c l e i n f o
abstract
Article history: Received 9 November 2009 Received in revised form 14 June 2010 Accepted 24 June 2010 Available online 27 May 2011
This paper shows that exposure to aggregate distress risk is the underlying source of the premiums for the Fama-French size (SMB) and value (HML) factors. Using a unique data set of aggregate business failures of both private and public firms from 1926 to 1997, I build portfolios that track news about future firm failures. These tracking portfolios optimally hedge aggregate distress risk and earn a Capital Asset Pricing Model (CAPM) alpha of approximately 4% a year. Both HML and SMB predict changes in future failure rates. Small stocks have lower returns than large stocks and value stocks have lower returns than growth stocks when the market expects an increase in future failure rates. Finally, a two-factor model with the market and the tracking portfolio for aggregate distress as factors does as well as the Fama-French three-factor model in pricing the 25 size and book-to-market sorted portfolios. & 2011 Elsevier B.V. All rights reserved.
JEL classification: G11 G12 G32 G33 Keywords: Distress risk Bankruptcy Risk factors
1. Introduction This paper tests the hypotheses in Chan and Chen (1991) and Fama and French (1996) that distress risk is responsible for the size and value premiums in the crosssection of expected stock returns. Chan and Chen (1991) argue that small firms are ‘marginal’ (in the sense that they are less likely to survive adverse economic conditions than are large firms), and hence have higher expected returns than predicted by their unconditional market betas. Fama and French (1996) hypothesize that distress risk is also the
$ I would like to thank the referee, Eugene Fama, and the editor, William Schwert, for their invaluable feedback and suggestions. I am also grateful to Valery Polkovnichenko and Francesco Franzoni (discussants), Kerry Back, James Weston, Jennifer Conrad, Jefferson Duarte, Alex Butler, John Campbell, and workshop participants at Rice University, the Lone Star Finance Conference, and the FIRS 2010 conference for helpful comments. n Tel.: þ1 713 348 5392. E-mail address:
[email protected]
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.05.004
underlying cause of the value premium. In particular, they argue that if the human capital of individuals is tied to the firms they work for, and distress is correlated across firms, individuals will require a premium to hold stocks with high exposure to distress risk. Thus, they suggest that aggregate distress is a state variable in the context of the Merton (1973) Inter-temporal Capital Asset Pricing Model (ICAPM), and portfolios that have greater covariances with aggregate distress should have higher expected returns. Subsequent research (Dichev, 1998; Griffin and Lemmon, 2002; Vassalou and Xing, 2004; Garlappi, Shu, and Yan, 2008), however, provides conflicting results about the existence, sign, and magnitude of the distress risk premium and its relation to size and value. Campbell, Hilscher, and Szilagyi (2008) show that firms with high default probabilities have abnormally low expected returns and hence, argue that distress risk cannot explain the size and value premiums. The common methodology to analyze the effect of distress risk on the cross-section of expected stock returns is to estimate default probabilities for individual firms and then test whether firms with high default probabilities
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N. Kapadia / Journal of Financial Economics 102 (2011) 167–182
have higher subsequent returns.1 The characteristic of high default probability, however, may not be a good proxy for covariance with aggregate distress risk because it does not take into account the cost of distress. George and Hwang (2010) show that in a model with endogenous leverage, firms with low costs of distress will optimally choose greater leverage and therefore have high default probabilities. Thus, sorting firms based on their default probability may not capture their expected losses due to distress or exposures to aggregate distress risk. This paper proposes a novel covariance-based approach to estimating the distress risk premium. I construct portfolios with maximal correlation to a measure of aggregate distress and analyze their properties. The aggregate distress measure is from Dun & Bradstreet and contains the number and aggregate liabilities of businesses that close with a loss to creditors. These data are well-suited as a measure of aggregate distress because they cover both private and public firms and are available at the monthly frequency from 1894 to 1997. I construct tracking portfolios for aggregate distress based on the methodology in Lamont (2001), by projecting future business-failure growth rates on a set of basis assets. These tracking portfolios are maximally correlated with changes in market expectations of future business failure rates and therefore have two uses. First, they allow us to use information in current market returns to forecast future business failure rates. Second, they act as hedging portfolios for economy-wide distress risk by having positive returns when the market expects failures to increase. Equipped with the Dun & Bradstreet data and the tracking portfolio methodology, I test the hypothesis that exposure to distress risk is the underlying cause of the size and value premiums. For distress risk to be a credible explanation, it must pass three tests. First, the Fama-French factors, SMB and HML, must be negatively correlated with unexpected increases in aggregate distress; second, distress risk must have a positive premium, with greater exposure to distress resulting in higher expected returns and CAPM alphas; and third, a pricing model with distress risk must be able to explain the expected returns of portfolios sorted on the basis of size and value (HML, SMB, and the 25 size and book-to-market sorted portfolios). These three tests generate the three key results in this paper. First, I find that returns on HML and SMB predict changes in future business failure rates. Second, I show that the tracking portfolio for aggregate distress earns low average returns and significantly negative CAPM alphas. Finally, I find that a two-factor model with a tracking portfolio for aggregate distress and the market as factors does as well as the Fama-French three-factor model in pricing size and book-to-market sorted portfolios. My first finding, that returns on HML and SMB predict changes in future business failure rates, implies that when there is news about an increase in future business failures, not only does the market as a whole decline, but small
1 See, for example, Dichev (1998), Griffin and Lemmon (2002), Campbell, Hilscher, and Szilagyi (2008).
stocks do worse than large stocks and value stocks do worse than growth stocks. A good way for an investor to hedge against an unexpected increase in future failure rates is therefore to short HML and SMB. Liew and Vassalou (2000) and Vassalou (2003) show that HML and SMB predict aggregate Gross Domestic Product (GDP) growth. I refine this result by showing that HML and SMB predict only the component of GDP growth correlated with aggregate distress, and that both continue to predict aggregate distress even after controlling for GDP growth. In the second set of tests, I form a tracking portfolio for future failure rate growth using a subset of the 25 size and book-to-market sorted portfolios as basis assets. The tracking portfolio also has large and significant unconditional and conditional CAPM alphas of approximately 4% per year, showing that investors are willing to pay a substantial premium to hedge against economy-wide distress. This result is robust to the choice of basis assets in that using the statistically constructed cluster portfolios of Ahn, Conrad, and Dittmar (2009) as basis assets results in similar risk premiums for the failure-rate tracking portfolio and similar exposures to HML and SMB. Third, I find that the tracking portfolio for distress effectively summarizes the information in HML and SMB that is relevant to pricing assets. In particular, a twofactor model (with the market and the tracking portfolio for business failures as factors) results in statistically insignificant and economically small intercepts for HML and SMB in time-series regressions. The two-factor model also results in similar alphas as the Fama-French threefactor model, with both the 25 size and book-to-market sorted portfolios and the Fama-French 30 industry sorted portfolios as test assets. This finding suggests that we do not need two separate factors. A single linear combination of size and book-to-market sorted portfolios does as well in pricing test portfolios as HML and SMB. It is reassuring that this linear combination has an economic meaning—it is chosen to optimally predict aggregate future distress. An advantage of the tracking portfolio approach is that it is relatively model-free. Different default prediction models lead to conflicting results on the sign of the default risk premium. For example, using a structural model based on Merton (1974), Vassalou and Xing (2004) report that stocks with high default probabilities have higher subsequent returns. However, papers that use reduced-form models such as Dichev (1998) that uses the Altman (1968) Z-score, or Campbell, Hilscher, and Szilagyi (2008) that uses a hazard model, report that stocks with high modelimplied default probabilities earn low returns. The tracking portfolio approach sidesteps the problem of determining which model best predicts individual firm defaults by allowing the data in the cross-section of returns and actual defaults to determine the premium for distress risk. Another difference from prior research on the distress risk premium is that the Dun & Bradstreet data used in this paper include private firms in the aggregate failure measure. The Fama-French hypothesis that distress risk is priced because it is related to human capital implies that including data on private firm failures may be critical in constructing a variable for aggregate distress for two reasons. First, private firms employ over two-thirds of the
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US workforce (Davis, Haltiwanger, Jarmin, and Miranda, 2006). Also, Heaton and Lucas (2000) show that individuals who derive income from entrepreneurial undertakings hold a substantial fraction of the stock market. This proprietary business income is likely to be most at risk when businesses fail across the economy, and these investors may wish to hedge this risk through their investment portfolios. The difference in the sign of the distress risk premium between the characteristic-based approach in Campbell, Hilscher, and Szilagyi (2008) and the covariance-based approach in this paper is puzzling. A surprising result reconciles our findings: firms with high default probabilities do not co-vary with news about aggregate firm failures. This lack of co-variation is not due to differences in data underlying the aggregate distress measure and individual default probabilities. The returns of the highest decile probability portfolio do not co-vary with changes in an alternate measure of aggregate distress—the median default probability of all firms from the model in Campbell, Hilscher, and Szilagyi (2008). In fact, going short HML and SMB to hedge increases in this measure dominates going short the highest default probability decile. This result suggests that the low returns to high default probability stocks, although interesting in their own right, are not due to exposure to aggregate distress risk. This paper is related to the extensive body of research focused on understanding the rationale for the size and value premiums. Prior explanations include the conditional CAPM (Jagannathan and Wang, 1996), real optionbased explanations (Berk, Green, and Naik, 1999; Petkova and Zhang, 2005), and multi-factor models based on the Merton (1973) ICAPM (e.g., Campbell and Vuolteenaho (2004) or macroeconomic variables—Vassalou (2003). Also, Guo and Jiang (2010) consider aggregate distress risk as an additional factor in the ICAPM framework. Their results are complementary to this paper—they show that the median default probability of all firms forecasts the market risk premium, while I focus on the risk premium for distress and its relation to the size and value factors. This paper is organized as follows: Section 2 describes the data and summarizes the Lamont (2001) tracking portfolio methodology. My analysis is organized around three key themes: the relation between the Fama-French factors and future business failure rate growth (Section 3); the sign and magnitude of the distress risk premium (Section 4); and the tracking portfolio for future failure rates as an asset-pricing factor (Section 5). Section 6 analyzes the relation between the results in this paper and those in Campbell, Hilscher, and Szilagyi (2008). Section 7 concludes.
2. Data and methodology Since the Dun & Bradstreet data have not been used extensively in the financial economics literature, I provide a broad overview of the data below. This section describes the data (Section 2.1), reviews the tracking portfolio methodology and discusses some of the modeling choices made in this paper (Section 2.2), and provides descriptive statistics (Section 2.3).
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2.1. Business failure data The primary data used in this paper are from Dun & Bradstreet. They define business failure as: yall businesses that ceased operations following assignment or bankruptcy; ceased with loss to creditors after such action as execution, foreclosure, or attachment; voluntarily withdrew leaving unpaid obligations; were involved in court actions such as receivership, reorganization or arrangement; or voluntarily compromised with creditors y Voluntary discontinuances involving no loss to creditors are excluded. This definition of failure does not include all business closures. For example, businesses that close voluntarily because of inadequate profits, ill-health, retirement, etc. are not included. The failure data are available from January 1894 through December 1997. The data from 1894 to 1965 are from the Macrohistory database of the National Bureau of Economic Research (NBER), while the post-1965 data are from monthly publications of Dun & Bradstreet.2 Dun & Bradstreet provides both the failure rate (number of failures per 10,000 firms) and the aggregate liabilities of firms that fail at the monthly frequency. The data unfortunately end in 1997 when Dun & Bradstreet stopped publishing business failure data. The data typically used in studying distress risk are based on public bond defaults. Public bond data start much later than the Dun & Bradstreet data and have far fewer bankruptcies. For example, the bankruptcy data in Chava and Jarrow (2004), as shown in Campbell, Hilscher, and Szilagyi (2008), have on average fewer than one bankruptcy per month in the 1960s and 1970s, rising to an average of four per month in the 1990s. The low number of public bond defaults means that the aggregate default rate is very sensitive to small variations in the number of defaults per month. In contrast, aggregate firm failures from Dun & Bradstreet have over 1,000 firm failures per month in the 1960s, rising to an average of over 6,000 per month in the 1990s. Fig. 1 plots the monthly failure rate from 1926 to 1997, with gray bars showing NBER-dated recessions. There is substantial time-series variation in failure rates. Failure rates are high in the 1920s and increase to peak levels during the Great Depression. Failure rates drop during World War II and steadily increase until 1980. They dramatically rise in the next decade, from an average of 2.97 per thousand firms per month in the 1970s to 7.56 per thousand firms per month in the 1980s. There are three major determinants of the time-series variation in failure rates: macroeconomic conditions, the age distribution of firms, and bankruptcy laws. First, as is evident from the chart, failure rates are high during
2 The exact name of the publication has changed over time. The names include ‘Monthly Failures’ (1959–1975), ‘News from Dun & Bradstreet, Inc., Business Economics Division. K, Monthly Failures’ (1975–1981), and ‘The Dun & Bradstreet Record of Business Closings’ (1981–1997).
N. Kapadia / Journal of Financial Economics 102 (2011) 167–182
18 16 14 12 10 8 6 4 2 48
42
37
53 19 59 19 64 19 70 19 75 19 81 19 86 19 91 19 97
19
19
19
19
19
19
31
0 26
Business failures per 10,000 firms
170
Fig. 1. The monthly business failure rate from 1926 to 1997. The failure rate is defined as the number of businesses that fail with a loss to creditors every month divided by the total number of firms in the database. NBER dated recessions are shown as gray bars.
recessions. Second, Lane and Schary (1991) find that young firms have higher failure rates and argue that the age distribution of firms in the economy affects aggregate failure rates. For example, they suggest that the decline in failure rates in the 1940s can be partially attributed to the low rate of business formation during World War II. Third, changes in bankruptcy law affect incentives to file for bankruptcy. The Dun & Bradstreet data are less sensitive than the number of bankruptcy filings to changes in law, as Dun & Bradstreet captures business failures with loss to creditors even outside of the bankruptcy process.
Rt. News is defined as a change in expectations in the month t about future realizations of the macroeconomic variable:
2.2. The tracking portfolio methodology
where Zt 1 is a vector of instruments known at time t 1. The tracking portfolio is a linear combination of basis asset returns defined by the portfolio weights b estimated above:
Adverse economic information can take several months to translate into firm failures, as firms assess the impact of the economic change on their business, draw down their cash balances, and explore legal options for bankruptcy. However, the stock market reacts today to news about higher failure rates in the future. Assessing covariances of stock returns with contemporaneous changes in failure rates may miss valuable information already incorporated into prices. The tracking portfolio methodology in Lamont (2001) provides a framework to incorporate information on changes in expected future failures. It also allows the econometrician to use information which is known to market participants but is not a part of past realizations of the failure rate (or other known macroeconomic) series to predict future failure rates. Thus, this methodology delivers two useful outputs: (1) a forecasting engine for future failure rates that uses information in current market prices and (2) portfolios whose returns are maximally correlated with innovations in future failure rates. My focus will be on the latter, as returns of these portfolios serve to hedge against unexpected increases in distress risk, and their risk premium provides an estimate of the distress risk premium. However, I will also test whether market information helps improve failure rate forecasts in out-of-sample tests. In the terminology of Lamont (2001), we wish to construct a tracking portfolio for news about a macroeconomic variable yt þ k, using returns on a series of basis assets
DEt ½yt þ k ¼ Et ½yt þ k Et1 ½yt þ k :
ð1Þ
In our context, for example, this change in expectations could be because of information that the market learns in March 1990 about firm failure rates between April 1990 and March 1991. Lamont (2001) shows that this tracking portfolio can be constructed using the following regression: yt þ k ¼ b0 Rt þc0 Zt1 þ et,t þ k ,
Tracking portfoliot ¼ b0 Rt :
ð2Þ
ð3Þ
The primary function of the instruments in Z is to model changes in expected returns of the basis assets. To mitigate any potential misspecification of expected returns, Lamont (2001) advocates using monthly returns, as predictability at the monthly frequency is very low. The instruments also help provide more precise estimates of b by isolating innovations in the macroeconomic variable yt þ k. I describe the data underlying the three key components of the tracking portfolio formation regression (Eq. (2)), the dependent variable y, the instruments Z, and the basis asset returns R below. 2.2.1. The dependent variable The dependent variables are annual failure rate growth, annual growth in real aggregate liabilities of firms that fail, or annual GDP growth. Following Lamont (2001) and Vassalou (2003), I use annual growth rates (differences in logs) as the dependent variable in tracking portfolio formation regressions. I use growth rates because the raw monthly failure rate series is highly auto-correlated (0.96 at 1 lag), and returns on the basis assets are related to innovations, rather than levels of the failure rate series. Annual growth rates are reasonably
N. Kapadia / Journal of Financial Economics 102 (2011) 167–182
robust to seasonality3 and a change in Dun & Bradstreet’s data collection procedure in 1984 to include additional sectors.4 To construct annual growth rates, I first aggregate monthly failure data to the annual frequency. For the failure rate series, annual failure rates (AFRATE) are AFRATEt þ 1,t þ 12 ¼
t þ 12 1 i ¼X f, Nt i ¼ t þ 1 i
ð4Þ
where fi is the number of failures in month i, and Nt is the total number of firms covered by the data set in month t. Since N is available only at the annual frequency, I use the number of firms in the year prior to month t þ1 in constructing AFRATEt þ 1,t þ 12. Then I construct annual failure rate growth (AFRATEGRTH) using differences in log annual failure rates: AFRATEt þ 1,t þ 12 AFRATEGRTHt þ 12 ¼ ln : ð5Þ AFRATEt11,t Annual growth in real aggregate liabilities of firms that failed and annual GDP growth are constructed in a similar manner, except that aggregate liabilities of firms that failed are deflated by Consumer Price Index (CPI) to get real aggregate liabilities before computing growth rates. 2.2.2. The instruments The instruments control for expected returns of the basis assets. They are (1) the risk-free rate (1-month Treasury bill rate), (2) the default spread (difference in yield between BAA and AAA bonds) from the Federal Reserve Board’s Federal Reserve Economic Data (‘FRED’) database, and (3) the term spread (the difference in yields of long-term government bonds from Ibbotson Stocks, Bonds, Bills & Inflation Yearbook (2009) and the risk-free rate). Another purpose of the instruments is to isolate innovations in the y series. Since both the annual failure rate growth and annual liability growth exhibit significant autocorrelation (0.52 and 0.55, respectively, at one lag for the non-overlapping January–December series), I also include a lagged value of these variables when they are chosen as the y series. The lagged value is constructed, as are other instruments, with information known up to t 1 (yt 12,t 1 for the annual series). 2.2.3. The basis assets A crucial decision in the tracking portfolio methodology is the choice of basis assets. Basis asset returns should 3 The monthly failure rate data exhibit seasonality, with firstquarter failure rates much higher than the rest of the year. Annual failure rate growth does not exhibit seasonality. 4 The new sectors include agriculture, forestry, fishing, finance, insurance, real estate, and miscellaneous service sectors. The addition of the new sectors significantly increased the aggregate liabilities of failed firms as the new firms were added in, but only marginally affected the average failure rate. Naples and Arifaj (1997) estimate that the published data with the expanded sample has a failure rate that is 3% lower, on average, than what it would have been without the new sectors. Furthermore, any effects of the changes in the data-collection procedure should affect only 1 year of the annual growth rate series. Because this mainly affects liability growth, all regressions involving liability growth contain a year dummy for 1984.
171
be informative about changes in market expectations of future business failures. For example, it is likely that the market as a whole will decline when there is news that economy-wide failures are expected to increase over the next year, suggesting that the market is a good basis asset candidate. Since Fama and French (1996) and Chan and Chen (1991) hypothesize that the size and value premiums are related to distress risk, I use portfolios sorted on the basis of size and book-to-market as basis assets. These include (1) HML and SMB, and (2) a subset of the 25 size and book-to-market sorted portfolios (described in Section 3 below). I also use two bond portfolios, DEF and TERM. DEF is the excess return of longterm corporate bonds over long-term government bonds from Ibbotson Stocks, Bonds, Bills & Inflation Yearbook, while TERM is the excess return of long term government bonds over the risk-free rate. Following Lamont (2001), all basis asset returns are in excess of the risk-free rate. This ensures that the resulting tracking portfolio is zero investment, and that the weights b do not need to be rescaled or restricted to sum up to one.5 2.3. Descriptive statistics Table 1 contains the means, standard deviations, and correlations of key variables. The variables include annual (January–December) failure rate growth, aggregate liability growth, one-year lagged values of these two series, GDP growth, 1-year lagged GDP growth, and 1-year lagged returns on HML and SMB. Since GDP data are available from 1947 to 2008 and failure data from 1926 to 1997, the number of non-overlapping annual observations for these series is less than that for the Fama-French factors, which are available from 1927 to 2008. Panel A presents univariate statistics and Panel B presents pairwise correlations. The correlation between the failure rate growth and growth in aggregate liabilities of firms that failed is 77%, suggesting that these variables capture similar phenomena. One way of thinking about these two variables is that the failure rate is an equally weighted measure of business failures while aggregate liabilities are a value-weighted measure. However, since one large failure affects aggregate liabilities significantly more than it does the failure rate, unlike most valueweighted measures, aggregate liability growth is more volatile than failure rate growth. Since the two series are highly correlated, for the sake of brevity I only present results for the failure rate growth series in this paper. Results for aggregate liability growth are similar and are available on request. The next set of correlations foreshadows the major results of this paper. First, failure rate growth is significantly 5 The risk-free rate from t 1 to t is considered to be known at time t 1 and is part of the set of instruments (i.e., is not a basis asset). Most recent papers (e.g., Lamont, 2001; Vassalou, 2003) follow this methodology. However, Breeden, Gibbons, and Litzenberger (1989) do not, instead including the 90-day T-bill rate as part of the set of basis assets. I have tried this alternative and found similar results. Further details are available upon request.
172 Table 1 Descriptive statistics. This table reports descriptive statistics for key variables used in the paper. The variables include annual failure rate growth, growth in annual (real) aggregate liabilities of failed firms, annual GDP growth, lagged values of these three series, and lagged annual returns for the market in excess of the risk free rate (MKTRF), HML, and SMB (in % per month). All annual variables in this table are non-overlapping, for the calendar year (January–December), and use all available data for each variable from 1926 to 2008. Panel A reports the number of observations (‘N’), means, standard deviations, medians, minima and maxima of each variable. Panel B reports pairwise correlations and ‘p-values’ for the null of no correlation. Panel A: Univariate statistics Mean
Std. dev.
Median
Min
Max
71 71 61 82 82 82
0.51% 2.56% 3.28% 0.44% 0.33% 0.18%
28.5% 34.0% 2.3% 1.7% 1.1% 1.1%
1.6% 2.0% 3.4% 0.8% 0.4% 0.2%
103.4% 85.6% 2.0% 5.0% 2.6% 3.3%
103.0% 100.4% 8.4% 3.8% 2.7% 2.9%
Panel B: Pairwise correlations Failure rate growth
Liability growth
Lagged failure rate growth
Lagged liability growth
GDP growth
Lagged GDP growth
Lagged MKTRF
Lagged HML
Lagged SMB
Failure rate growth
1
0.77 o 0.01
0.52 o 0.01
0.55 o0.01
0.56 o0.01
0.13 0.36
0.32 0.01
0.36 0.01
0.36 0.01
Liability growth
1
0.21
0.37 0.08
0.44 o0.01
0.11 o0.01
0.34 0.45
0.24 o 0.01
0.37 0.05
o 0.01
1
0.77
0.01 o0.01
0.56 0.96
0.14 o 0.01
0.17 0.23
0.28 0.15
0.02
1
0.07
0.44 0.64
0.20 o 0.01
0.16 0.10
0.35 0.15
o 0.01
1
0.04
0.62 0.78
0.12 o 0.01
0.24 0.37
0.06
0.02
0.10 0.89
0.15 0.43
0.25
1
0.12
0.35 0.27
0.00
Lagged failure rate growth Lagged liability growth GDP growth Lagged GDP growth Lagged MKTRF Lagged HML
1
1
0.02 0.86
Lagged SMB
1
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Failure rate growth Liability growth GDP growth Lagged market returns Lagged HML Lagged SMB
N
N. Kapadia / Journal of Financial Economics 102 (2011) 167–182
correlated with lagged annual returns on the market ( 32%), HML (36%), and SMB ( 36%). Aggregate liabilities have similar correlations at 34%, 24%, and 37%, respectively. This suggests that when market participants expect high failure rates in the future, the market portfolio has low returns. News on future failures has differing effects across the cross-section of stocks as well: small stocks and value stocks have much lower returns than large stocks and growth stocks when subsequent failure rates are high. Table 1, Panel B also shows that GDP growth is negatively correlated with both annual failure rate growth ( 56%) and annual liability growth (44%). Amongst the return series, GDP growth is most correlated with lagged market returns (62%). GDP growth has a much smaller correlation with HML (12% and not statistically significant), while its correlation with SMB is 24%.
3. Do the Fama-French factors predict business failure rate growth? This section tests whether the Fama-French factors predict changes in future business failure rates. If the size and value premiums are related to exposure to distress risk, unexpected increases in business failures should result in more negative returns for small stocks than for large stocks and for value stocks than for growth stocks. Fig. 2 charts annual returns of each factor with growth in failure rates in the subsequent year. The negative correlation of each of the factors with failure rate growth is visible in the chart, with lower returns typically accompanying an increase in future failures. To confirm the intuition from Fig. 2, I use the market, HML, and SMB as basis assets and test if they predict future failure rate growth in tracking portfolio formation regressions. Failure rate growtht þ 1,t þ 12 ¼ a þ b MKTRFt 0
þ l HMLt þ t SMBt þ d Zt1
ð6Þ
where MKTRF is the excess return of the market over the risk-free rate. These regressions are run on overlapping annual failure rates with monthly basis asset returns. All t-statistics are based on Newey and West (1987) standard errors (with 12 lags) to correct for the moving-average error structure induced by the overlapping nature of the data and also for any residual autocorrelation in the failure rate growth series. If the underlying cause of the premiums for HML and SMB is distress risk, l and t should be negative. In the first specification in Table 2, Panel A, the only instrument in Z is lagged failure rate growth (from t 12 to t 1). All three portfolios significantly predict the future failure rate growth series over the 1926–1997 period. The coefficients of the market ( 0.45), HML ( 0.65), and SMB ( 0.74) are all negative and significant. That is, the tracking portfolio is short the market, HML, and SMB. These results support the hypothesis that the Fama-French factors predict changes in future business failure rates. Value stocks and small stocks have lower returns than do
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growth stocks and large stocks when there is news about an increase in future business failures. The next specification includes other instruments—the risk-free rate, term spread, and default spread. Adding the instruments leaves the inference from the first specification largely unchanged. A higher risk-free rate predicts greater future defaults, which is consistent with Altman (1993). A flat or inverted term structure typically predicts lower GDP growth (see, for example, Estrella and Hardouvelis, 1991), and not surprisingly, also predicts greater failure rates. The negative sign on the coefficient on default spreads is surprising, as higher default spreads should predict higher defaults. Note, however, that this coefficient is not statistically significant. Specification 3 adds in the two bond portfolios, DEF and TERM, as basis assets. Although both variables have the expected sign, neither is statistically significant. The lack of significance for DEF is surprising, as one might expect that corporate bond returns will be lower when the market expects an increase in economy-wide business failures. A potential reason for not finding a stronger relation may lie in the nature of the corporate bond data. The Ibbotson series is the only available long time-series of corporate bond returns and consists of high-grade bonds, which may not be as sensitive to future defaults as low-grade bonds. The mean return for the DEF series over the entire time period is 0.03% a month, and we cannot reject the hypothesis that the mean is zero, suggesting that the high-grade bonds in the Ibbotson data do not have a significant default premium. Since business failures are higher in bad economic times, one possible explanation for my results is that they are driven by the correlation between GDP growth and the Fama-French factors reported by Liew and Vassalou (2000). Table 2, Panel B tests this alternate hypothesis. Specification 1 tests whether the failure-rate tracking portfolio results are the same in the sample where GDP growth data are available (every quarter from 1947 onwards). The annual failure rate variable rolls forward every quarter, corresponding to the quarters for which GDP data are available. Specification 1 shows that the results are robust in the quarterly 1947–1997 sample as well. Specification 2 adds in GDP growtht þ 1, t þ 12 as a control, resulting in an insignificant coefficient on the market. The coefficient on HML drops from 1.25 to 0.82, but remains statistically significant. The coefficient on SMB is not affected. Thus, the FamaFrench factors predict aggregate business failure rates even after controlling for GDP growth. Specifications 3 and 4 in Table 2, Panel B test the converse: do Fama-French factors predict GDP growth after controlling for failure rate growth? Specification 3 forms a tracking portfolio for GDP growth using the FamaFrench factors as basis assets. The market has positive returns when there is news about an increase in GDP growth. HML also positively predicts GDP growth, although the coefficient is not significant. The coefficient on SMB is small and is also statistically insignificant. On controlling for failure rate growth, the coefficient on HML drops by almost 75%, from 0.11 to 0.02. This suggests that at best, HML predicts the component of GDP growth that is correlated with aggregate business failures.
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150%
10% Annual failure-rate growth Lagged annual market returns
8% 6% 4%
50%
2% 0%
0% -2%
-50%
-4% -6%
-100%
Returns (in % per month)
Annual failure rate growth
100%
-8% -10% 1992
1987
1982
1977
1972
1967
1962
1957
1952
1947
1942
1937
1932
1927
-150%
6% Annual failure-rate growth Lagged annual HML returns
4%
50%
2%
0%
0%
1992
1987
1982
1977
1972
1967
1962
1957
-6% 1952
-150% 1947
-4%
1942
-100%
1937
-2%
1932
-50%
Returns (in % per month)
100%
1927
Annual failure-rate growth
150%
150%
5% Annual failure-rate growth
Annual failure-rate growth
4% 3%
50%
2% 1%
0% 0% -50%
-1%
Returns (in % per month)
Lagged annual SMB returns
100%
-2% -100% -3% -150% 1992
1987
1982
1977
1972
1967
1962
1957
1952
1947
1942
1937
1932
1927
-4%
Fig. 2. Business failure rate growth and lagged annual returns. This figure plots the annual growth in the business failure rate from 1927 to 1997 along with the prior year’s annual returns for the market (in excess of the risk-free rate) in Panel A, HML in Panel B, and SMB in Panel C. Panel A: Annual business failure rate growth and lagged annual market returns. Panel B: Annual business failure rate growth and lagged annual HML returns. Panel C: Annual business failure rate growth and lagged annual SMB returns.
The results in this section show that distress risk is a plausible explanation for the size and value premiums. Both SMB and HML predict changes in business failure rates even after controlling for aggregate market returns. This shows that news about future failure rates affects the
cross-section of returns differently. Value stocks and small stocks are impacted more severely than are growth stocks and large stocks. Thus, investments in HML and SMB have an exposure to aggregate distress, which could result in their risk premiums.
N. Kapadia / Journal of Financial Economics 102 (2011) 167–182
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Table 2 The Fama-French factors, future failure rate growth, and GDP growth. This table presents tracking portfolio formation regressions for annual failure rate growth and GDP growth: yt þ 1,t þ 12 ¼ aþ b0 Rt þ c0 Zt1 : y is either failure rate growth or GDP growth, R is a vector of basis assets (MKTRF, HML, SMB, DEF, and TERM), and Z is a vector of instruments (lagged failure rate growth, the risk-free rate, term spread, and default spread). Panel A estimates this regression for failure rate growth for the full sample (every month, from 1926 to 1997). Panel B estimates the regression for failure rate growth (Specifications 1 and 2) and GDP growth (Specifications 3 and 4) for the sample where GDP growth data are available (every quarter, from 1947 to 1997). All standard errors are Newey-West (12 lags for monthly, 4 for quarterly data). Panel A: Predicting failure rate growth using the Fama-French factors (1926–1997) (1)
(2)
(3)
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
0.00 0.45 0.65 0.74
0.30 3.06 2.01 3.23
0.06 0.39 0.63 0.44
0.86 2.48 1.64 1.93
0.06 0.43 0.83 0.49 0.40 0.34
0.92 2.22 2.27 2.08 0.72 0.94
Lag failure rate growth Risk-free rate Term spread Default spread
0.49
4.84
0.46 45.10 2.81 0.37
5.01 3.93 2.94 1.36
0.46 45.10 2.80 0.38
4.99 3.90 2.88 1.36
N R2
846 0.27
Intercept MKTRF HML SMB DEF TERM
846 0.34
846 0.34
Panel B: Do the Fama-French factors predict future failure rate growth or GDP growth? Failure rate growth (1947–1997) (1)
GDP growth (1947–1997)
(2)
(3)
(4)
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
Intercept MKTRF HML SMB DEF TERM
0.01 0.30 1.25 1.40 0.48 0.94
0.16 0.99 2.05 3.05 0.71 1.77
0.15 0.15 0.82 1.40 0.27 1.07
2.73 0.62 1.77 3.15 0.37 2.06
0.04 0.12 0.11 0.00 0.05 0.03
5.15 2.37 1.37 0.01 0.38 0.34
0.04 0.10 0.02 0.11 0.02 0.10
6.15 2.3 0.3 2.15 0.14 1.12
Lag failure rate growth Risk-free rate Term spread Default spread
0.42 46.34 2.42 0.15
4.61 5.6 2.38 0.33
0.39 26.50 1.20 0.37
6.74 2.93 1.06 0.85
0.01 5.34 0.33 0.06
0.50 3.64 1.60 1.01
0.03 1.86 0.15 0.07
2.01 1.17 0.69 1.24
3.71
5.73 0.08
4.94
GDP growth Failure rate growth N R2
197 0.37
197 0.55
4. Tracking portfolios for future business failures This section builds tracking portfolios for news about failure rates using size and book-to-market sorted portfolios as basis assets. I include a subset of the 25 size and book-to-market sorted portfolios rather than just HML and SMB to better span failure rate growth. However, including all 25 size and book-to-market sorted portfolios in the tracking portfolio formation regression risks adding too much noise, as they are highly correlated with each other. I therefore choose nine of the 25 portfolios: S1B1, S1B3, S1B5, S3B1, S3B3, S3B5, S5B1, S5B3, S5B5, where ‘S’ stands for size and ‘B’ for book-to-market, and 1 is the smallest and 5 the largest. All portfolio returns are in
197 0.20
197 0.42
excess of the risk-free rate, so the resultant tracking portfolio is a zero-investment portfolio. Table 3 presents coefficients for the basis assets and the instruments for tracking portfolios for future failure rate growth. Since these are overlapping regressions with monthly returns for basis assets and annual dependent variables, all standard errors are Newey-West (with 12 lags). The coefficients of the tracking portfolio display a clear pattern: within each size quintile, coefficients decline as you move from growth to value.6 Note as well
6 As with other papers that use this methodology (e.g., Vassalou, 2003), individual coefficients are not significant due to multicollinearity.
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Table 3 Tracking portfolios for failure rate growth. This table forms and analyzes tracking portfolios for annual failure rate growth. These portfolios are linear combinations of basis assets (R), with weights defined by the coefficients b in the following regression, reported in Panel A: Failure rate growtht þ 1,t þ 12 ¼ a þ b0 Rt þ c0 Zt1 : The basis assets are a subset of the 25 size and book-to-market sorted (value-weighted) portfolios: S1B1, S1B3, S1B5, S3B1, S3B3, S3B5, S5B1, S5B3, S5B5 (where S stands for size and B for book-to-market and 1 is the smallest and 5 the largest). The regression also includes instruments in Z (lagged annual failure rate growth, the risk-free rate, lagged default spread, and lagged term spread) as controls which are not reported for brevity. All standard errors are Newey-West (12 lags). Panel B reports time-series regressions on the tracking portfolio formed in Panel A. Three specifications are reported: an unconditional CAPM, a conditional CAPM (using the default spread, term spread, and dividend yield as instruments), and a Fama-French three-factor regression. Panel A: Tracking portfolio formation
Intercept S1B1 S1B3 S1B5 S3B1 S3B3 S3B5 S5B1 S5B3 S5B5 N R2
Estimate
t-Value
0.06 0.21 0.06 0.33 0.00 0.15 0.46 0.29 0.17 0.17
0.87 1.86 0.35 1.44 0.01 0.44 1.32 0.98 0.45 0.78
834 0.34
Panel B: Time-series regressions for the tracking portfolio formed in Panel A (1)
Alpha MKTRF
(2)
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
0.38% 0.60
3.29 9.58
0.34% 0.41
3.66 3.39
0.13% 0.39
2.30 20.37
6.49 0.22 4.05 3.22
0.51 1.13 2.22 1.19 0.79 0.31
14.24 5.95
Default spreadnMKTRF Lagged annual MKTRFnMKTRF Term spreadnMKTRF Dividend yieldnMKTRF HML SMB R2
(3)
0.47
that none of the coefficients represent extreme positions (whether short or long) in any of the basis assets despite not imposing any restrictions during the estimation. I form a tracking portfolio for future failure rates as a linear combination of the basis asset portfolios with the coefficients b estimated above as portfolio weights. This tracking portfolio has average returns of 0.77% per month ( 9.2% per year) and a standard deviation of 4.74%. The negative sign is what we expect, since the tracking portfolio for business-failure growth is the portfolio most positively correlated with news about future distress. In other words, it has high returns when an
(footnote continued) Note, however, that we know that HML and SMB are significant in predicting future failures from the previous section. Also, a tracking portfolio constructed using a ‘tradable’ strategy significantly predicts future failure rates out-of-sample. Further details of this test are available from the author.
0.54
0.85
increase in future business failures is expected. This portfolio serves to hedge against an increase in failure rates and therefore has low expected returns. The first specification of Table 3, Panel B reports CAPM time-series regressions. Specification 1 shows that the tracking portfolio has an economically and statistically significant CAPM alpha of 4.6% per year. As a comparison, the CAPM alpha for HML in the same time period is 3.5% per year. Furthermore, the CAPM alpha for businessfailure tracking portfolios is robust with respect to which specific set of size and book-to-market portfolios are used as basis assets. For example, using the Fama-French six size and book-to-market sorted portfolios or adding TERM and DEF gives similar results.7 7 On including TERM and DEF as basis assets, the monthly CAPM alpha (t-value) for the failure-rate growth tracking portfolio is -0.28% ( 2.99). Since the bond returns are not jointly significant, I do not present these as my primary results. Using the six size and B/M sorted
N. Kapadia / Journal of Financial Economics 102 (2011) 167–182
One possible explanation of the CAPM alpha for distress risk is that the tracking portfolios have time-varying betas. If the beta for the distress-risk tracking portfolio is correlated with the market risk premium, unconditional CAPM alphas will be biased. To determine whether the conditional CAPM explains the expected returns of these portfolios, I perform conditional regressions [see Shanken (1990) and Petkova and Zhang (2005) for a description of the methodology] where b is allowed to vary linearly with instruments in the investor’s information set: rtrack ¼ a þ b0 rm þb0 Zrm ,
ð7Þ
where all returns are in excess of the risk-free rate, b is a vector of coefficients [b1 b2 b3 b4], and Z is a set of four instruments (the term spread, default spread, dividend yield, and average return on the market over the prior year). Table 3, Panel B, Specification 2 reports conditional CAPM alphas for the tracking portfolio for distress risk. The alpha remains significant and similar in magnitude to its unconditional value. This suggests that given the instruments selected, the premium for distress is unlikely to be explained by a conditional CAPM. The next step is to test the premium using a multifactor model. Specification 3 shows results of FamaFrench three-factor models. The failure-rate tracking portfolio is significantly negatively correlated with HML and SMB. An increase in expected future failures is associated with lower returns for value stocks than for growth stocks and for small stocks than for large stocks. The Fama-French model does substantially better in explaining the returns of the distress-risk tracking portfolio than the CAPM, with R2 increasing from 47% to 85%. The Fama-French alpha is economically small, but statistically significant at 0.13% per month. To ensure that the sign of the distress risk premium is not sensitive to the choice of size and book-to-market sorted portfolios as basis assets, I also construct a tracking portfolio for aggregate failure rates using the cluster portfolios of Ahn, Conrad, and Dittmar (2009) as basis assets. I find that this tracking portfolio has a statistically significant CAPM alpha of 0.39% per month (t-value 2.53) and a conditional CAPM alpha of 0.37% per month (t-value 2.49). The tracking portfolio has significant exposures to HML and SMB and the Fama-French three factor model alpha is economically small and statistically insignificant at 0.15 (t-value of 1.07).8 The results of this section show that covariance with aggregate distress commands a risk premium beyond that predicted by the CAPM. The tracking portfolio for aggregate firm failures, which is constructed to be maximally correlated with news about future failure rates, has significant negative unconditional and conditional CAPM alphas. The tracking portfolio for aggregate distress is also strongly related to the Fama-French factors.
(footnote continued) portfolios as basis assets results in monthly CAPM alpha (t-value) of 0.186% ( 2.04) per month. 8 These results are available from the author.
177
5. Distress risk as an asset-pricing factor The previous section shows that distress risk commands a risk premium. This section investigates whether co-variation with the aggregate distress-tracking portfolio is sufficient to explain the size and value premiums. Cochrane (2006) argues that the central point in Fama and French (1996) is that all the important information in the 25 size and book-to-market portfolios is captured by just three factors and that ‘macro-modelers’ should therefore focus on explaining why HML and SMB have nonzero abnormal returns. Hence, I first examine whether using the distress-risk tracking portfolio as an explanatory variable results in a zero intercept for HML and SMB in time-series regressions. I then compare the performance of a two-factor model (with the distress-risk tracking portfolio and the market as factors) with the Fama-French three-factor model using the 25 size and book-to-market sorted portfolios as test assets. 5.1. Can distress risk explain the risk premiums of HML and SMB? Table 4 reports results of the time-series regression: rfact ¼ a þ b MKTRF þ d TRACK,
ð8Þ
where rfact is the returns to HML (Panel A) or SMB (Panel B) and TRACK is the return of the tracking portfolio for annual failure rates formed from nine of the 25 size and book-to-market sorted portfolios in Section 4. Panel A, Specification 1 reports that the unconditional CAPM alpha for HML for the sample period (1926–1997) is 0.28% per month. On adding TRACK, the alpha reduces to a statistically and economically insignificant 0.0004% a month. The two-factor model therefore explains the high expected returns of HML. As a further check, Specifications 3 and 4 examine the 1963–1997 period, when the value premium is larger. Again, the CAPM alpha reduces from 0.576% to 0.05% per month once TRACK is added in. Panel B reports similar specifications for SMB, whose CAPM alpha reduces from a statistically insignificant 0.07% to 0.04%. Although SMB does not have a significant CAPM alpha for the full sample, TRACK is significant as an explanatory variable and the R2 doubles to almost 24% once TRACK is included. The results are similar for the1963–1997 period. The results of this section suggest that TRACK is able to price both HML and SMB. TRACK also adds to the explanatory power of the CAPM in terms of an increase in R2. Since HML and SMB effectively summarize the information in the size and book-to-market sorted portfolios, it is possible that TRACK will do as well as HML and SMB in pricing these portfolios. 5.2. How does the distress-risk tracking portfolio compare with the Fama-French three-factor model in pricing other assets? If distress risk is the underlying source of the premiums for HML and SMB, a two-factor model with the market and TRACK as factors should perform as well as the three-factor model in pricing other assets. I therefore
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N. Kapadia / Journal of Financial Economics 102 (2011) 167–182
Table 4 Explaining HML and SMB. This table presents results of time series regressions of HML (Panel A) and SMB (Panel B) on a two-factor model. The two factors are excess returns on the market (MKTRF) and the distress risk tracking portfolio (TRACK) constructed in Table 3 from nine of the 25 size and book-to-market sorted portfolios. Each panel has two specifications: the full 1926–1997 sample and the 1963–1997 subsample. Panel A: Time series regressions for HML Full sample (1926–1997)
Subsample (1963–1997)
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
Intercept MKTRF TRACK
0.28% 0.20
2.35 2.77
o 0.01% 0.28 0.78
0.01 6.74 22.98
0.58% 0.21
4.51 5.46
0.06% 27.40 32.41
0.01 6.74 22.98
R2
0.09
0.67
0.13
0.79
Panel B: Time-series regressions for SMB Full sample (1926–1997)
Intercept MKTRF TRACK R2
Subsample (1963–1997)
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
0.08% 0.21
0.76 4.96
0.04% 0.02 0.31
0.45 0.45 4.77
0.11% 0.21
0.78 4.91
0.07% 0.12 0.31
0.52 2.63 4.32
0.12
0.24
compare the performance of a two-factor model (with the tracking portfolio for distress and the market as factors) to the Fama-French three-factor model in pricing a set of test assets. Another interpretation of the tests in this section is that they help us determine whether TRACK captures all of the pricing-related information in HML and SMB. In other words, do we need two separate factors to be able price size and book-to-market sorted portfolios, or would one factor that is chosen to optimally predict aggregate distress suffice? Table 5 reports intercepts from time-series regressions for the Fama-French three-factor and the distress risk twofactor model. Panel A reports alphas and factor loadings from the two-factor model and alphas from the FamaFrench three-factor model as a benchmark. Factor loadings for the three-factor model are not reported for reasons of brevity. The alphas for both models appear to be similar across the 25 portfolios. The distress-risk tracking portfolio does better than the three-factor model on the small growth portfolio (alpha of 0.62 versus 0.88 for the three-factor model), but does a little worse on the adjoining portfolios. Overall, the average absolute alphas for the two models are almost identical. The two-factor model’s average absolute alpha is 0.1411% per month, while the three-factor model’s is 0.1409% per month. Gibbons, Ross, and Shanken (1989) (GRS) derive the finite sample distribution for the statistic that tests the hypothesis that the intercepts are jointly zero.9 The GRS statistics for both models are very similar (3.07 for the
9 Since the tracking portfolio is a linear combination of a subset of the test asset portfolios, the cross-equation error covariance matrix, which needs to be inverted to construct the GRS statistic, is singular. I therefore exclude the middle portfolio (size 3, book-to-market 3) in constructing the GRS statistic for the case where the test assets are the 25 size and book-to-market portfolios. Alternate approaches, such as using a generalized inverse, excluding another portfolio (size 3, book-to-
0.10
0.17
three-factor and 2.91 for the two-factor) and both models are rejected with p-values o0.01. The GRS statistic can also be interpreted as a measure of the distance between the factors and the ex post mean variance frontier formed from the test assets and the factors. The two models perform equally well with regards to this metric. The results are similar when the 30 industry portfolios as classified by Fama and French (1997) are used as test assets. In unreported results, I find that alphas are similar across the 30 portfolios, with an average absolute alpha of 0.18% per month for both models. The GRS statistics at 2.72 for both models also differ only in the third decimal place. Taken together, the results presented so far show that distress risk is sufficient to explain the risk premium for HML and SMB and is a credible explanation for the success of the Fama-French three-factor model in explaining the cross-section of stock returns. In particular, the two-factor model with the distress-risk tracking portfolio and the market as factors does as well as the three-factor model in pricing test assets.
6. Relation to results in Campbell, Hilscher, and Szilagyi (2008) Campbell, Hilscher, and Szilagyi (2008) (henceforth CHS) find that stocks with high default probabilities have low subsequent returns. Since this paper finds that stocks with high exposure to default risk have high expected returns, the difference between our results is puzzling. Although both papers investigate distress risk, there is an important difference between our methodologies: CHS (footnote continued) market 4), or adding TERM and DEF as basis assets in constructing TRACK (but not including them as test assets), result in similar inferences.
Table 5 Time series regressions on 25 size and b/m and 30 industry portfolios. This table reports intercepts (in % per month) from time-series regressions with the 25 Fama-French size and book-to-market-sorted portfolios as test assets. Results are presented for the Fama-French threefactor model and a two-factor model (with the tracking portfolio for future failure rate growth, TRACK, formed as in Table 3, and the market as factors). The Gibbons, Ross, Shanken (1989) (GRS) test statistic for the joint significance of the intercepts is also reported. The sample period is from 1926 to 1997. Fama-French 3 factor model Alpha
t-Value
2
3
4
Value
Small 2 3 4 Big
0.88 0.25 0.18 0.05 0.07
0.52 0.03 0.12 0.06 0.03
0.14 0.07 0.09 0.08 0.02
0.02 0.08 0.11 0.01 0.21
0.10 0.01 0.13 0.22 0.05
GRS p-Value
3.0753 o 0.01
Small 2 3 4 Big
Growth
2
3
4
Value
3.35 2.69 2.50 0.85 1.64
3.04 0.46 2.04 1.07 0.69
1.27 1.08 1.44 1.24 0.30
0.20 1.38 1.85 0.20 3.16
1.14 0.13 1.72 2.50 0.47
Two-factor tracking portfolio model Alpha
t-Value
Growth
2
3
4
Value
Small 2 3 4 Big
0.62 0.31 0.21 0.04 0.08
0.63 0.09 0.09 0.08 0.03
0.20 0.03 0.09 0.06 0.02
0.03 0.06 0.10 0.01 0.20
0.01 0.04 0.20 0.24 0.08
GRS p-Value
2.9101 o 0.01
Small 2 3 4 Big
Growth
2
3
4
Value
2.05 2.09 1.90 0.64 1.86
2.78 0.71 1.13 1.25 0.59
1.20 0.30 1.09 0.88 0.24
0.22 0.60 1.19 0.07 2.25
0.07 0.33 2.29 2.25 0.65
TRACK
Small 2 3 4 Big
t-Value
Growth
2
3
4
Value
0.04 0.15 0.11 0.21 0.27
0.91 0.46 0.18 0.15 0.09
0.71 0.51 0.31 0.27 0.18
0.82 0.61 0.47 0.47 0.47
1.27 0.91 0.97 0.89 0.73
Small 2 3 4 Big
Growth
2
3
4
Value
0.41 3.61 3.52 11.17 21.57
14.05 13.26 7.83 8.62 6.36
15.37 16.79 14.07 14.33 9.39
19.39 20.57 20.27 19.89 18.94
29.89 27.15 40.01 28.78 20.86
Market
t-Value
Growth
2
3
4
Value
1.64 1.15 1.21 1.17 1.13
0.98 1.03 1.02 1.02 0.99
0.98 0.93 1.00 0.95 0.88
0.86 0.90 0.88 0.92 0.90
0.67 0.86 0.86 0.96 0.76
Small 2 3 4 Big
Growth
2
3
4
Value
21.65 31.58 44.95 70.96 104.20
17.32 33.92 50.75 65.57 81.48
24.13 35.36 51.43 57.47 51.75
23.39 34.80 43.26 45.18 41.40
18.20 29.29 40.24 35.88 25.01
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Small 2 3 4 Big
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Growth
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aggregate distress. The loading on the highest default-risk portfolio is statistically and economically insignificant, while the portfolio with lowest default-risk loads positively. I obtain similar results by using real liability growth as the dependent variable, or by using the 2nd and 9th decile default-risk portfolios as basis assets. (For purposes of brevity, I do not report these results.) These results show that firms with a high probability of default do not have high exposures to aggregate failure rates. A potential reason for the insignificance of the highest default probability decile in predicting future failures is that the data underlying the two are different. Firm failures are economy-wide, while the default deciles are only based on listed firms. To control for differences in data and methodology, I compute an aggregate measure of distress based on CHS. This allows us to focus on the difference between firm-specific characteristic of high default probability and covariance with aggregate distress, while keeping everything else the same.
examine the returns of stocks with high probabilities of distress, while this paper looks at stocks whose returns co-vary with news about economy-wide defaults. A natural question, therefore, is why is there a wedge between these two approaches? In particular, do firms with high default probabilities have high exposures to distress risk? 6.1. Business failure news and the characteristic of high default probability I first replicate CHS’s results by sorting stocks into deciles based on default probability as computed by CHS, using coefficients from the 12-month-ahead prediction model in Table IV of their paper. The sample runs from 1963 to 1997, since they estimate their model starting in 1963, while the Dun & Bradstreet data end in 1997. As in CHS, I find that the highest default probability decile has extremely low returns—the CAPM alpha is 0.8% per month, while the four-factor alpha (the Fama-French three factors and momentum) is 0.6% per month. Table 6 reports results of tracking portfolio formation regressions for failure rate growth using the market and the two extreme deciles of default risk as basis assets. This regression is designed to test whether stocks with high default probabilities have high exposures to
6.2. Covariances with innovations in median default probability In order to compute an aggregate measure of distress based on CHS, I compute the default probability for each
Table 6 Default probability and distress risk. This table examines whether firms with different default probabilities have different exposures to aggregate distress risk. Default probability is based on the 12 month-ahead model in Table IV in Campbell, Hilscher, and Szilagyi (2008). Panels A and B report portfolio formation regressions: y ¼ a þ b0 Rt1,t þ c0 Zt1 : In Panel A, y is failure rate growtht þ 1,t þ 12, the basis assets in R are MKTRF, the highest default probability decile (DP10) and the smallest default probability decile (DP1). Panel B reports factor mimicking portfolio formation regressions, where y is Dmdpt 1,t the change in the log median default probability of all firms. The basis assets include (1) DP1 and DP10; (2) size (S) and book-to-market (B) sorted portfolios, where 1 is the smallest and 5 the largest and; (3) HML, SMB. All specifications also include MKTRF and three instruments in Z—the risk-free rate, lagged term spread and lagged default spread. Panel A: The exposure of default risk sorted portfolios to distress risk Failure rate growth
Intercept MKTRF DP10 DP1
Real liability growth
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
0.16 0.06 0.11
1.78 0.28 0.84
0.17 0.78
1.83 2.09
0.27 0.45 0.07
1.98 1.38 0.45
0.30 1.19
2.13 2.58
0.65
1.7
0.67
1.91
Panel B: Forming factor mimicking portfolios for Dmdp (1)
Intercept MKTRF DP1 DP10 S1B1 S1B5 S5B1 S5B5 DP1 minus DP10 HML SMB R2
(2)
(3)
Estimate
t-Value
Estimate
t-Value
Estimate
t-Value
0.00 0.49 0.31 0.30
0.17 2.24 1.53 5.24
0.01 0.10 0.27 0.09 0.03 0.90 0.68 0.18
2.33 0.34 1.69 1.14 0.30 6.15 4.03 2.11
0.01 0.27
2.37 1.82
0.11 1.28 0.74
1.84 7.34 4.95
0.12
0.38
0.39
N. Kapadia / Journal of Financial Economics 102 (2011) 167–182
firm every month using the model in CHS (Table IV). I then use the median default probability of all firms each month as an aggregate measure of distress risk. The correlations between the median default probability and the 25th and 75th percentiles of default probability are 84% and 94%, respectively, which means that the results shown below are not sensitive to the choice of median as a summary measure. The high correlation also suggests that there is substantial common time-series variation in default probabilities across firms. Because the median default probability is highly auto-correlated (95% at lag 1), I use changes in logs of this series for all subsequent tests. This measure is also intuitive, as the change in default probability (rather than the level of the series) is likely to be correlated with returns. Using the median default probability rather than actual defaults means that we can examine the contemporaneous rather than the predictive relation between aggregate distress and returns. Table 6, Panel B investigates whether the returns of stocks with high default probability co-vary with changes in median default probability by using factor-mimicking portfolio formation regressions. Breeden, Gibbons, and Litzenberger (1989) describe the methodology of creating factor-mimicking portfolios, which is also the foundation for the tracking portfolio methodology used in this paper. I use the term ‘factor-mimicking portfolios’ for projections of contemporaneous changes in the target variable on the space of returns to distinguish from ‘tracking portfolios’ which are projections of future changes in the target variable. If innovations in median default probability are an aggregate risk that an investor would like to hedge, one obvious strategy would be to do so through investments in portfolios sorted by default probability. The first specification in Table 6, Panel B, tests the appropriateness of this strategy by regressing innovations in median default probability on the market and returns of the two extreme default probability deciles. The coefficient on the returns of the highest decile of default probability is significant and negative; however, the coefficient on returns of the lowest default probability decile is also negative and of a similar magnitude, but insignificant. A Wald test cannot reject the hypothesis that the two coefficients are equal (p-value 0.9). Note as well that the resulting mimicking portfolio would go short both the lowest and the highest default-risk decile by similar amounts. Finally, the R2 of this regression is relatively low at 12%. This regression shows that the two extreme default-risk deciles do not have significantly different exposures to innovations in aggregate default probability. Specification 2 in Table 6, Panel B adds on the four extreme size and book-to-market-sorted quintile portfolios as basis assets with the following results. First, the regression’s R2 triples to 38%. Second, the coefficient on the highest default-probability decile portfolio switches sign and becomes insignificant. The factor-mimicking portfolio is long growth stocks and long large stocks, with the four size and book-to-market portfolios jointly significant (p-value o 0.001). These results suggest that HML and SMB are important in hedging innovations to aggregate distress risk. Specification 3 makes this clear by
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regressing innovations in median default probability on the market, the difference between the returns of the smallest and largest default probability deciles, HML, and SMB. The coefficient on the difference between the returns of the smallest and largest default probability deciles is significant, but in the wrong direction. The coefficients on HML and SMB are large and significantly negative, consistent with the evidence in this paper that investments in large stocks and growth stocks serve to hedge against increases in distress risk. I find, in other words, that firms with high default probabilities are not sensitive to aggregate distress risk, which is consistent with the intuition that default probability is not a good measure of distress risk since it ignores variation in the costs of financial distress. The results in this section also confirm the importance of HML and SMB in hedging innovations in aggregate distress, since both are much more important in hedging changes in median default probability than are returns to portfolios formed from sorts on default probability. 7. Conclusion This paper resurrects distress risk as an explanation of the size and value premiums. The key innovation in the paper is to build tracking portfolios for future economywide business failures that hedge against news about increases in business failures. My first result is that HML and SMB predict future failure rates. Second, tracking portfolios for future failure rates built using different sets of basis assets have significant CAPM alphas. These portfolios have high returns when there is news about an increase in business failures and are rewarded with high valuations and low expected returns when benchmarked against the conditional and unconditional CAPM. Third, the tracking portfolio for distress risk results in insignificant intercepts for both HML and SMB when it is added as an additional explanatory variable to marketmodel time-series regressions. Also, the two-factor model with the tracking portfolio for distress and the market does as well in pricing the 25 size and book-to-market sorted portfolios and industry portfolios as the FamaFrench three-factor model. This result shows that distress risk by itself is sufficient to explain the premiums associated with the Fama-French factors—the tracking portfolio for aggregate firm failures captures the information contained in HML and SMB that is relevant in explaining the expected returns of other assets. Thus, a state variable that reflects aggregate distress risk explains the premiums for HML and SMB. References Ahn, D., Conrad, J., Dittmar, R., 2009. Basis assets. Review of Financial Studies 22, 5133–5174. Altman, E., 1968. Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance 23, 589–609. Altman, E., 1993. Corporate Financial Distress and Bankruptcy. John Wiley & Sons, New York. Berk, J., Green, R., Naik, V., 1999. Optimal investment, growth options, and security returns. Journal of Finance 54, 1553–1607. Breeden, D., Gibbons, M., Litzenberger, R., 1989. Empirical test of the consumption-oriented CAPM. Journal of Finance 44, 231–262.
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Campbell, J., Hilscher, J., Szilagyi, J., 2008. In search of distress risk. Journal of Finance 63, 2899–2939. Campbell, J., Vuolteenaho, T., 2004. Bad beta, good beta. American Economic Review 94, 1249–1275. Chan, K., Chen, N., 1991. Structural and return characteristics of small and large firms. Journal of Finance 46, 1467–1484. Chava, S., Jarrow, R., 2004. Bankruptcy prediction with industry effects. Review of Finance 8, 537–569. Cochrane, J., 2006. Financial markets and the real economy. In: Cochrane, J. (Ed.), International Library of Critical Writings in Financial Economics, vol. 18. Edward Elgar Publishing, pp. 239–314 (Chapter 7). Davis, S., Haltiwanger, J., Jarmin, R., Miranda, J., 2006. Volatility and dispersion in business growth rates: publicly traded versus privately held firms. NBER Macroeconomics Annual 21, 107–156. Dichev, I., 1998. Is the risk of bankruptcy a systematic risk? Journal of Finance 53, 1131–1147 Estrella, A., Hardouvelis, G.A., 1991. The term structure as a predictor of real economic activity. Journal of Finance 46, 555–576. Fama, E.F., French, K.R., 1996. Multifactor explanations of asset pricing anomalies. Journal of Finance 51, 55–84. Fama, E.F., French, K.R., 1997. Industry costs of equity. Journal of Financial Economics 43, 153–193. Garlappi, L., Shu, T., Yan, H., 2008. Default risk, shareholder advantage, and stock returns. Review of Financial Studies 21, 2743–2778. George, T., Hwang, C., 2010. A resolution of the distress risk and leverage puzzles in the cross section of stock returns. Journal of Financial Economics 96, 56–79. Gibbons, M., Ross, S., Shanken, J., 1989. A test of the efficiency of a given portfolio. Econometrica 57, 1121–1152. Griffin, J., Lemmon, M., 2002. Book-to-market equity, distress risk, and stock returns. Journal of Finance 57, 2317–2336.
Guo, H., Jiang, X., 2010. Aggregate distress risk is priced with a positive premium. Working Paper, University of Cincinnati. Heaton, J., Lucas, D., 2000. Portfolio choice and asset prices: the importance of entrepreneurial risk. Journal of Finance 55, 1163–1198. Ibbotson Associates, 2009. Stocks, Bonds, Bills, and Inflation: 2009 Yearbook. Ibbotson Associates, Chicago, IL. Jagannathan, R., Wang, Z., 1996. The conditional CAPM and the crosssection of expected returns. Journal of Finance 51, 3–53. Lamont, O., 2001. Economic tracking portfolios. Journal of Econometrics 105, 161–184. Lane, S., Schary, M., 1991. Understanding the business failure rate. Contemporary Economic Policy 9, 93–105. Liew, J., Vassalou, M., 2000. Can book-to-market, size and momentum be risk factors that predict economic growth? Journal of Financial Economics 57, 221–245 Merton, R., 1973. An intertemporal capital asset pricing model. Econometrica 41, 867–887. Merton, R., 1974. On the pricing of corporate debt: the risk structure of interest rates. Journal of Finance 29, 449–470. Naples, M., Arifaj, A., 1997. The rise in us business failures: correcting the 1984 data discontinuity. Contributions to Political Economy 16, 49–59. Newey, W., West, K., 1987. A simple positive-definite heteroskedasticity and autocorrelation consistent covariance matrix. Econometrica 55, 703–708. Petkova, R., Zhang, L., 2005. Is value riskier than growth? Journal of Financial Economics 78, 187–202 Shanken, J., 1990. Intertemporal asset pricing: an empirical investigation. Journal of Econometrics 45, 99–120. Vassalou, M., 2003. News related to future GDP growth as a risk factor in equity returns. Journal of Financial Economics 68, 47–73. Vassalou, M., Xing, Y., 2004. Default risk in equity returns. Journal of Finance 59, 831–868.
Journal of Financial Economics 102 (2011) 183–198
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Corporate cash holdings and CEO compensation incentives$ Yixin Liu a, David C. Mauer b,n a b
Whittemore School of Business and Economics, University of New Hampshire, Durham, NH 03824, United States School of Management, University of Texas at Dallas, 800 West Campbell Road, SM31, Richardson, TX 75080-3021, United States
a r t i c l e i n f o
abstract
Article history: Received 16 October 2009 Received in revised form 26 October 2010 Accepted 23 November 2010 Available online 30 May 2011
We examine the effect of chief executive officer (CEO) compensation incentives on corporate cash holdings and the value of cash to better understand how compensation incentives designed to enhance the alignment of manager and shareholder interests could influence stockholder-bondholder conflicts. We find a positive relation between CEO risk-taking (vega) incentives and cash holdings, and we find a negative relation between vega and the value of cash to shareholders. The negative effect of vega on the value of cash is robust after controlling for corporate governance, is stronger in firms with high leverage, is reversed for unlevered firms, and is not present in financially constrained firms. We also find that the likelihood of liquidity covenants in new bank loans is increasing in CEO vega incentives. Our evidence primarily supports the costly contracting hypothesis, which asserts that bondholders anticipate greater risk-taking in high vega firms and, therefore, require greater liquidity. & 2011 Elsevier B.V. All rights reserved.
JEL classification: G30 G32 G34 Keywords: Cash holdings Value of cash Managerial incentives
1. Introduction A fundamental principle of finance is that managers should make financing and investment decisions that maximize the market value of equity. In reality, however, riskaverse and under-diversified managers could eschew risky positive net present value policy choices in favor of riskreducing choices that in some cases have negative net present values. Equity-based compensation can help overcome managers’ aversion to risk and thereby more closely align their interests with those of shareholders, but such compensation can also aggravate stockholder-bondholder conflicts. As originally argued by Jensen and Meckling (1976), equity-based compensation and especially stock options can exacerbate risk-shifting incentives, encouraging managers to adopt risky policy choices that increase the market value of equity at the expense of bondholders. $ We thank Matt Billett, Yuqian Wang, Yue Ying, and Yilei Zhang for helpful comments and suggestions. Yixin Liu is grateful for financial support from the Graduate School at the University of New Hampshire. n Corresponding author. Tel.: þ1 972 883 5844. E-mail address:
[email protected] (D.C. Mauer).
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.05.008
Given the possible adverse incentive effects of equitybased compensation, researchers have long been interested in the questions of how compensation incentives influence corporate policy choices and how bondholders endeavor to mitigate or protect themselves from the possible negative consequences of these choices. Corporate liquidity policy would seem to be an ideal although heretofore largely overlooked policy in which to explore the links between compensation incentives and stockholder-bondholder conflicts. This is especially true given the evidence that US firms hold increasingly more assets in the form of cash.1 On the one hand, because the decision to hold and deploy cash is to a large extent at the discretion of management with little outside scrutiny, the cash policy of risk-averse and underdiversified managers could differ from that preferred by shareholders. As such, an efficient compensation structure that aligns the interests of managers and shareholders could limit investment in cash to funds needed to support operations. On the other hand, equity-based compensation such
1 Bates, Kahle, and Stulz (2009) report that the average cash-toassets ratio more than doubles from 10.5% in 1980 to 23.2% in 2006.
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as options that encourage greater risk-taking could exacerbate stockholder-bondholder conflicts. Accordingly, bondholders could choose to protect themselves by requiring covenants that impose minimum liquidity standards or firms could choose to maintain excess liquidity to blunt the effects of incentive compensation on the cost of debt.2 These differing perspectives on how managerial compensation incentives influence investment in cash suggest that liquidity policy can serve as an interesting and useful backdrop with which to study how managerial compensation incentives affect firm stakeholders. In this paper, we first examine how compensation incentives influence cash holdings. We find a robust positive relation between the sensitivity of chief executive officer (CEO) compensation to stock price volatility (vega) and cash holdings. To uncover whether this positive relation is consistent with shareholder wealth maximization or is more reflective of a stockholderbondholder conflict, we next examine how CEO compensation incentives influence the marginal value of cash to shareholders. Our evidence shows that vega has a negative effect on the marginal value of cash to shareholders, which suggests that excess cash balances mitigate the risk to bondholders from risk-taking incentives induced by high vega compensation. Additional evidence on the positive relation between vega and liquidity covenants in bank loans supports this conclusion. We use compensation data from ExecuComp to compute the sensitivities of a CEO’s own-firm wealth (i.e., stock and option compensation) to a change in the stock price (delta) and the stock price volatility (vega). We then match this data with Compustat and Center for Research in Security Prices (CRSP) data, which results in a sample of 20,439 firm-years over the period from 1992 to 2006. After controlling for firm characteristics and corporate governance measures, we find that cash holdings are positively related to vega. Because vega is a measure of CEO risk-taking incentives and cash is essentially a riskfree asset, this positive relation is perhaps unexpected. There are, however, at least two explanations. The first is that the greater risk-taking incentives induced by high vega compensation could increase the cost of external funds, which encourages the firm to hold excess cash balances to hedge future funding needs.3 We call this the costly external finance hypothesis.4 The other explanation is that the greater risk-taking incentives induced by high
2 Recent empirical work shows a positive relation between the cost of debt (as measured by credit spreads) and managerial stock ownership (Ortiz-Molina, 2006) and the volatility sensitivity (vega) of chief executive officer (CEO) compensation (Daniel, Martin, and Naveen, 2004; Brockman, Martin, and Unlu, 2010). Billett, Mauer, and Zhang (2010) find negative (positive) bond price reactions to the change in the volatility (stock price) sensitivity of the CEO’s wealth induced by firsttime option or restricted stock grants. 3 For the hedging and closely related precautionary savings motives for cash holdings, see, respectively, Kim, Mauer, and Sherman (1998) and Opler, Pinkowitz, Stulz, and Williamson (1999). 4 From a slightly different perspective, firms that face costly external financing and uncertain future investment opportunities might choose to hold excess cash balances and conserve cash by compensating managers with stock and options. This, too, could drive the positive vega-cash relation in our data. We include this explanation under the costly external finance hypothesis.
vega compensation exacerbate stockholder-bondholder conflicts. Debtholders could protect themselves by requiring liquidity covenants or firms could choose to hold larger cash balances to moderate a higher cost of debt. Following Smith and Warner (1979), we refer to this as the costly contracting hypothesis. To help disentangle which effect is the driving force behind the positive relation between vega and cash holdings, we examine the relation between vega and the value of cash. We employ the Faulkender and Wang (2006) approach, which uses excess equity returns to estimate the marginal value of cash from equityholders’ perspective. The costly external finance hypothesis predicts a positive relation between vega and the value of cash, because additional cash allows the firm to make profitable investments when they might otherwise be passed over. In contrast, the costly contracting hypothesis predicts a negative relation, because an additional dollar of cash in a high vega firm is more likely to benefit bondholders. Consistent with the costly contracting hypothesis, we find a negative and economically significant relation between vega and the value of cash to equityholders. This negative relation between vega and the value of cash is robust after controlling for the effects of corporate governance on the value of cash, is stronger in firms with high leverage, and is reversed for unlevered firms. Although this is strong evidence for the costly contracting hypothesis, we also find some support for the costly external finance hypothesis. In particular, the effect of vega on the marginal value of cash is insignificantly different from zero for financially constrained firms. This suggests that for high vega, financially constrained firms the benefit to equityholders from an additional dollar of cash compensates for the benefit that greater liquidity provides to bondholders. Finally, we examine the relation between CEO compensation incentives and the incidence of liquidity covenants in new bank loans, to get a better understanding of the mechanism by which debtholders might influence liquidity policy. We collect information on liquidity covenants in new bank loans taken out by our sample firms from the Dealscan database of the Loan Pricing Corporation (LPC). We find a positive and economically significant relation between the vega of a CEO’s compensation and the likelihood of liquidity covenants in new bank loans. This evidence suggests that debtholders actively play a role in the liquidity policy of high vega firms. Our paper makes several contributions to the literature. First and most general, our focus on liquidity policy provides a new perspective on how managerial compensation incentives can influence relations among firm stakeholders. Second, our analysis establishes that the volatility or risk-taking incentive of a CEO’s compensation significantly affects both the level and value of cash holdings. Third, our results suggest a more nuanced relation between cash and compensation incentives than what could be predicted from the existing literature. In particular, because cash is typically viewed as negative debt and because leverage is found to be strongly positively related to managerial risk-taking (i.e., vega) incentives (e.g., Coles, Daniel, and Naveen, 2006), one might be
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tempted to conclude that a negative relation exists between cash holdings and vega. Our analysis establishes, however, that the relation is positive, which is consistent with Acharya, Almeida, and Campello (2007), who argue that cash should not be viewed as negative debt when there are realistic financing frictions. Finally, our analysis of how the value of cash to shareholders is influenced by managerial compensation incentives highlights an important and yet unrecognized factor influencing the level and marginal value of cash. In particular, our analysis suggests that bondholder concerns over managerial risk-taking incentives help drive the positive relation between vega and cash holdings. The remainder of the paper is organized as follows. We develop our hypotheses in Section 2 and describe our data in Section 3. Section 4 contains our results, and Section 5 concludes. 2. Hypotheses Following a large body of literature (e.g., Guay, 1999; Core and Guay, 2002; Coles, Daniel, and Naveen, 2006), we measure CEO compensation incentives by the sensitivity of CEO wealth to stock return volatility (vega) and the sensitivity of CEO wealth to stock price (delta). Our primary focus is on vega, and so in this section we first present three hypotheses for why vega might influence firm cash policy. We then provide a brief discussion of the likely influence of delta on firm cash policy. 2.1. Vega and cash There are three testable hypotheses for the influence of vega on firm cash holdings. Alignment hypothesis: As originally argued by Jensen and Meckling (1976), firms can align the interests of risk-averse and under-diversified managers with equityholders by compensating them with equity-based compensation such as stock options. As shown by Coles, Daniel, and Naveen (2006), the resulting increase in the vega of a CEO’s compensation motivates her to pursue riskier investment and financing policies. Because investment in cash lowers overall firm risk, an increase in CEO vega would decrease cash holdings. Thus, the alignment hypothesis predicts a negative relation between vega and cash holdings of a firm. Costly external finance hypothesis: Firms that encourage greater risk-taking with high vega compensation could have difficulty raising external capital or face a higher cost of external funds. This would suggest that firms build cash to hedge future funding needs and thereby predicts a positive relation between vega and cash. Similarly, Kim, Mauer, and Sherman (1998) and Opler, Pinkowitz, Stulz, and Williamson (1999) find that companies with substantial growth opportunities have significantly larger cash balances. If high growth option firms tend to face higher costs of external funds and if these firms tend to compensate managers with stock and options to conserve cash, then this would also predict a positive relation between cash balances and vega.
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Costly contracting hypothesis: Creditors could rationally anticipate that managers with high vega compensation will pursue riskier policy choices and, therefore, require covenants to limit excessive risk-taking or moderate risk by maintaining sufficient liquidity. Examples of the latter include minimum working capital requirements and minimum cash flow coverage ratios, which effectively force firms to build over time a pool of internal funds. Thus, the costly contracting hypothesis predicts a positive relation between vega and cash holdings of a firm. Furthermore, because covenants are the likely channel through which debtholders require larger cash balances, we might also expect a higher likelihood of liquidity covenants in lending agreements when managers have high vega compensation.5 The costly contracting hypothesis and the costly external finance hypothesis have opposite predictions about the influence of vega on the value of cash.6 This will allow us to distinguish between the two hypotheses if vega and cash holdings are positively related. The costly contracting hypothesis predicts that vega decreases the value of cash to equityholders, because debtholders are more likely to benefit from an additional dollar of cash in high vega firms. Alternatively, the costly external finance hypothesis predicts that vega increases the value of cash. The reason is that cash balances in high vega firms are used to hedge costly external financing and thereby allow the firm to make profitable investments when they might otherwise be passed over. These predictions can be sharpened by examining the effect of vega on the value of cash by leverage status and by whether the firm is financially constrained. Thus, if the costly contracting hypothesis is true, we would not expect a negative relation between vega and the value of cash for unlevered firms, and we would expect the negative relation between vega and the value of cash to be stronger for high leverage firms than for low leverage firms. Similarly, if the costly external finance hypothesis is true, we would expect that the positive relation between vega and the value of cash would be stronger for financially constrained firms than for firms that are not financially constrained. Finally, to test the relation between vega and the value of cash, we need to estimate the value of cash to equityholders, because the costly external finance and costly contracting hypotheses make different predictions about how equityholders and debtholders view the value of cash.7 We estimate
5 This prediction assumes that firms do not voluntarily maintain higher levels of liquidity to avoid restrictive covenants. In this case, although vega would have a negative effect on the value of cash to equityholders, there would be no relation between vega and the incidence of liquidity covenants. 6 It is unclear how vega will influence the value of cash under the alignment hypothesis. One might argue that because high vega compensation aligns the interests of managers and shareholders, vega increases the value of cash. Alternatively, because managers with high vega compensation eschew excess cash holdings, it is plausible that vega reduces the value of cash to shareholders. 7 Thus, for example, we cannot use a total firm value approach to estimate the value of cash as in Pinkowitz and Williamson (2004) and Pinkowitz, Stulz, and Williamson (2006), because our hypotheses give different predictions about how equityholders and debtholders view the marginal value of cash. A total firm value approach yields a net value
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the value of cash using the Faulkender and Wang (2006) methodology, which focuses on the value of cash to equityholders in regressions in which excess equity returns are regressed on the change in cash and other corporate policy variables. 2.2. Delta and cash Although the stock price sensitivity (delta) and stock return volatility sensitivity (vega) of a CEO’s incentive compensation are derived from stock and options and tend to be positively correlated, they are mathematically distinct sensitivity measures and, more important, could have different economic implications for policy choices. As a result, it is generally of interest to examine the influence of delta (or pay-for-performance) incentives on corporate policy choices, and it could be prudent to assess the robustness of our findings on the effect of vega on cash policy by controlling for delta. The effect of delta on the level of cash holdings can be either positive or negative. On the one hand, Lambert, Larcker, and Verrecchia (1991), Carpenter (2000), and Ross (2004) argue that a risk-averse and under-diversified manager has a strong incentive to adopt risk-reducing policy choices if her compensation has high pay-for-performance sensitivity. This suggests a positive relation between delta and cash holdings.8 On the other hand, if high delta compensation enhances the alignment between managers and shareholders, then we would expect a negative relation between delta and cash holdings. Similarly, the effect of delta on the value of cash can be positive or negative. The alignment hypothesis suggests that delta increases the value of cash because managers with high pay-for-performance incentives are more likely to efficiently deploy cash (see, e.g., Jensen, 1986). Conversely, delta might reduce the value of cash if managers with high delta compensation are more cautious and, therefore, tend to hold too much cash (see, e.g., Guay, 1999). 3. Data and descriptive statistics We use the ExecuComp database to construct a sample of US firms from 1992 to 2006. The ExecuComp database provides yearly data on salary, bonus, stock option and restricted stock grants, and managerial stock and option holdings for the top executives of firms in the Standard & Poor’s (S&P) 500, S&P Midcap 400, and S&P Smallcap 600. Consistent with the previous literature, we exclude firms in the financial service industries in which liquidity is hard to assess [Standard Industrial Classification (SIC) codes 6000 6999] and in the utility sector due to their special regulatory environment (SIC codes 4900 4999). (footnote continued) of cash, which combines the assessments of equityholders and debtholders. 8 Harford, Mansi, and Maxwell (2008) find a positive relation between the fraction of manager pay in the form of stock options and firm cash holdings, which is consistent with the notion that managers with higher pay sensitivity adopt lower risk policies.
Firm-specific accounting variables are obtained from Compustat, and stock returns are obtained from CRSP. Following Faulkender and Wang (2006), we eliminate firm-years for which net assets are negative, the market value of equity is negative, or dividends are negative. We further require sample firm-years to have the necessary data to compute CEO delta and vega incentives. Our final sample consists of 20,439 firm-years. Panel A of Table 1 reports descriptive statistics for variables used in our cash holdings regressions. The variables are defined as follows. Cash: Following Opler, Pinkowitz, Stulz, and Williamson (1999), we measure corporate cash holdings as the ratio of cash and marketable securities to net assets, where net assets are total assets minus cash and marketable securities. Compensation incentives: For a firm-year, Vega is the dollar change in the value of the CEO’s option grants and any option holdings for a 0.01 change in the annualized standard deviation of stock returns. Delta is the dollar change in the value of the option or restricted stock grants, share holdings, and any restricted stock and option holdings for a 1% change in the stock price. The vega and delta computations follow the methods in Core and Guay (2002), who use the dividend-adjusted version of the Black and Scholes model to compute the value of executive stock options. We also follow Coles, Daniel, and Naveen (2006) in assuming that the vega of any stockholdings, including restricted stock, is zero. Finally, the vega and delta calculations include all of the CEO’s option or restricted stock grants reported in the proxy statement. In our regressions, we scale Vega and Delta by total CEO compensation, Vega/TC and Delta/TC, where total compensation in a year includes bonus, restricted stock and option grants, long-term incentive payouts, and any other compensation. In general, it is appropriate to scale compensation incentives because a CEO might have a relatively large dollar value for vega or delta, which is small relative to her total compensation. Instruments: We use instruments for vega and delta in some of our regression models. The instruments we use include firm age, CEO age, and CEO tenure.9 A firm’s age in a given sample year is the number of years since the first year that the firm is reported in Compustat; CEO age is the age of the CEO as reported in the ExecuComp database; and CEO tenure is the number of years that the current CEO has served in that capacity as reported in the ExecuComp database. Governance variables: Following Dittmar and MahrtSmith (2007), we measure corporate governance using the indices examined in Gompers, Ishii, and Metrick (2003) and Bebchuk, Cohen, and Ferrell (2009) and institutional block and pension holdings. The Gompers, Ishii, and Metrick index is the number of antitakeover provisions in the firm’s charter as reported by the Investor Responsibility Research Center (IRRC) and varies from zero to 24. The Bebchuk, Cohen, and Ferrell index records
9 These instruments for vega and delta are used by, for example, Coles, Daniel, and Naveen (2006) and Brockman, Martin, and Unlu (2010).
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Table 1 Descriptive statistics and correlations of firm characteristics and chief executive officer (CEO) compensation incentives. The sample includes all firm-years in the ExecuComp database during the period 1992 to 2006 where data are available to compute CEO compensation incentives and where accounting data are available on Compustat. The sample excludes financial and utility firms. Panel A reports descriptive statistics, and Panel B reports Pearson correlation coefficients. Cash is the ratio of cash plus marketable securities to net assets (Compustat items #1/(#6 #1)). Vega is the change in the value of the CEO’s option grant in a year and any accumulated option holdings for a 0.01 change in the annualized standard deviation of stock returns. Delta is the change in the value of the option or restricted stock grants in a year, share holdings, and any accumulated restricted stock and option holdings for a 1% change in the stock price. Vega/TC and Delta/TC are the ratios of vega and delta to total compensation, where total compensation in a year includes salary, bonus, restricted stock and option grants, long-term incentive payouts, and any other compensation. Option vega and delta are computed using the dividend-adjusted Black and Scholes model. A firm’s age in a given sample year is the number of years since the first year that the firm is reported in Compustat. CEO age is the age of the CEO as reported in the ExecuComp database. CEO tenure is the number of years that the current CEO has served in that capacity as reported in the ExecuComp database. The Gompers, Ishii, and Metrick index is the number of antitakeover provisions in the firm’s charter as reported by the Investor Responsibility Research Center (IRRC) and varies from zero to 24. The Bebchuk, Cohen, and Ferrell index records the incidence of six out of the 24 antitakeover provisions and varies from zero to six. Institutional blockholdings is the sum of all ownership positions greater that 5% held by institutional investors as reported in the Thompson Financial database. Pension holdings is the sum of all ownership positions by public pension funds as reported in the Thompson Financial database. Log firm size is the natural logarithm of net assets (#6 #1). Market-to-book is the ratio of the market value of net assets to the book value of net assets ((#6 #1 #60 þ#25 #199)/(#6 #1)). Cash flow/net assets is the ratio of earnings after interest, dividends, and taxes but before depreciation to the book value of net assets ((#13 #15 #16 #21)/(#6 #1)). NWC/net assets is the ratio of net working capital minus cash plus marketable securities to the book value of net assets ((#179 #1)/(#6 #1)). Capex/net assets is the ratio of capital expenditures to the book value of net assets (#128/(#6 #1)). Leverage is the ratio of long term debt plus debt in current liabilities to the book value of net assets ((#9 þ#34)/(#6 #1)). Industry sigma is the mean of the standard deviations of cash flow/net assets over ten years for firms in the same industry, as defined by two-digit Standard Industrial Classification codes. Dividend dummy is a dummy variable equal to one if the firm paid a common dividend and zero otherwise. R&D/sales is the ratio of research and development expense to sales (#46/#12). R&D/sales is set equal to zero when research and development expense is missing. Acquisition activity is the ratio of expenditures on acquisitions to the book value of net assets (#129/(#6 #1)). All variables in dollars (including vega and delta) are inflation-adjusted to 2006 dollars using the Consumer Price Index. Inflation-adjusted vega and delta and all ratio variables are winsorized at the 1st and 99th percentiles. nnn nn , , and n in Panel B denote significance at the 1%, 5%, and 10% levels, respectively. Panel A: Descriptive statistics Variable
Mean
1st quartile
Median
3rd quartile
Standard deviation
N
Cash
0.275
0.020
0.075
0.271
0.537
20,290
141.997 803.246 0.033 0.468
19.701 70.826 0.011 0.035
53.678 204.691 0.021 0.076
144.056 602.001 0.039 0.200
250.155 2048.720 0.041 1.568
17,214 20,439 17,204 20,395
17.591 64.677 7.876
6.000 58.000 3.000
13.000 65.000 5.000
26.000 71.000 10.000
15.533 9.083 7.578
18,886 20,260 17,026
Governance variables Gompers, Ishii, and Metrick index Bebchuk, Cohen, and Ferrell index Institutional blockholdings Pension holdings
9.206 2.157 0.165 0.028
7.000 1.000 0.064 0.016
9.000 2.000 0.148 0.027
11.000 3.000 0.243 0.036
2.687 1.295 0.126 0.020
14,373 14,373 17,260 17,260
Control variables Log firm size Market to book Cash flow/net assets NWC/net assets Capex/net assets Leverage Industry sigma Dividend dummy R&D/sales Acquisition activity
6.872 2.827 0.093 0.097 0.079 0.245 0.110 0.478 0.057 0.033
5.747 1.294 0.060 0.013 0.033 0.064 0.039 0.000 0.000 0.000
6.776 1.770 0.096 0.095 0.058 0.225 0.074 0.000 0.002 0.000
7.911 2.819 0.144 0.220 0.099 0.359 0.143 1.000 0.051 0.030
1.711 3.275 0.151 0.196 0.070 0.214 0.105 0.500 0.150 0.071
20,290 20,249 18,774 19,691 20,064 20,215 20,436 20,439 20,273 18,970
CEO compensation incentives Vega (thousands of dollars) Delta (thousands of dollars) Vega/TC Delta/TC Instruments Firm age CEO age CEO tenure
Panel B: Correlations between cash, CEO incentives, and firm characteristics Variable Cash Vega Delta Vega/TC Delta/TC Firm age CEO age CEO tenure Gompers, Ishii, and Metrick index
Cash
Vega
Delta
Vega/TC
Delta/TC
1.00 0.03nnn 0.06nnn 0.00 0.10nnn 0.19nnn 0.17nnn 0.00 0.17nnn
1.00 0.44nnn 0.50nnn 0.08nnn 0.20nnn 0.01 0.03nnn 0.03nnn
1.00 0.19nnn 0.64nnn 0.01 0.10nnn 0.25nnn 0.10nnn
1.00 0.27nnn 0.10nnn 0.02n 0.02nnn 0.02nn
1.00 0.07nnn 0.07nnn 0.23nnn 0.13nnn
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Table 1 (continued ) Panel B: Correlations between cash, CEO incentives, and firm characteristics Variable Bebchuk, Cohen, and Ferrell index Institutional blockholdings Pension holdings Log firm size Market to book Cash flow/net assets NWC/net assets Capex/net assets Leverage Industry sigma Dividend dummy R&D/sales Acquisition activity
Cash nnn
0.13 0.01 0.03nnn 0.46nnn 0.64nnn 0.22nnn 0.27nnn 0.16nnn 0.12nnn 0.22nnn 0.27nnn 0.57nnn 0.06nnn
Vega nnn
0.03 0.10nnn 0.03nnn 0.49nnn 0.07nnn 0.08nnn 0.18nnn 0.07nnn 0.02nnn 0.02nn 0.12nnn 0.03nnn 0.00
the incidence of six out of the 24 antitakeover provisions and varies from zero to six. Institutional blockholdings is the sum of all ownership positions greater that 5% held by institutional investors, and pension holdings is the sum of all ownership positions by public pension funds, where both sums are scaled by total outstanding shares. Data on institutional and pension ownership positions are from the Thompson Financial database. Control variables: The control variables in the cash holdings regressions are motivated by the variables used in Bates, Kahle, and Stulz (2009). Firm size is measured by the logarithm of net assets. Market-to-book asset ratio is computed as the book value of net assets minus the book value of equity plus the market value of equity, all divided by the book value of net assets. Cash flow/net assets is the ratio of earnings after interest, dividends and taxes but before depreciation divided by the book value of net assets. NWC/net assets is the net working capital-to-net assets ratio. Capex/net assets is the ratio of capital expenditures to the book value of net assets. Leverage is the sum of long-term debt and debt in current liabilities divided by the book value of net assets. Industry sigma is the mean of the standard deviations of cash flow/net assets over ten years for firms in the same industry, as defined by two-digit SIC codes. Dividend dummy is a dummy variable equal to one in years in which a firm pays a common dividend and is zero otherwise. R&D/sales is the ratio of research and development expense to sales. This ratio is set equal to zero when research and development expense is missing. Acquisition activity is measured by the ratio of expenditures on acquisitions to the book value of net assets. All variables in dollars are inflation-adjusted to 2006 dollars using the consumer price index. Inflation-adjusted vega and delta and all ratio variables are winsorized at the 1st and 99th percentiles to mitigate the impact of outliers. As seen in Panel A, the average cash holding is large at 27.5% of net assets. The median cash holding, however, is much smaller at 7.5% of net assets. CEOs in the sample appear to have nontrivial vega and delta incentives. In particular, a 0.01 increase in stock return volatility increases the average (median) CEO’s wealth by about $142,000 ($54,000); and a 1% increase in the stock price
Delta nnn
0.17 0.14nnn 0.04nnn 0.21nnn 0.22nnn 0.10nnn 0.09nnn 0.04nnn 0.06nnn 0.01n 0.00 0.02nnn 0.00
Vega/TC
Delta/TC
0.01 0.01 0.07nnn 0.22nnn 0.02nnn 0.05nnn 0.10nnn 0.05nnn 0.01 0.06nnn 0.04nnn 0.00 0.00
0.19nnn 0.11nnn 0.08nnn 0.00 0.20nnn 0.08nnn 0.02nnn 0.09nnn 0.09nnn 0.01 0.04nnn 0.01 0.02nnn
increases the average (median) CEO’s wealth by about $803,000 ($205,000). Focusing on the means (medians) of Vega/TC and Delta/TC, these dollar vega and delta incentives represent about 3% (2%) and 47% (8%) of total annual compensation, respectively. Panel B of Table 1 reports Pearson correlation coefficients among the variables. As seen in the panel, cash holdings are negatively related to vega and positively related to delta. These relations are consistent with the alignment hypothesis. One must be careful not to draw conclusions from these simple correlations, because a quick perusal of Panel B reveals that cash holdings and CEO compensation incentives are strongly correlated (and not always in the same direction) with firm size and growth opportunities, and they are generally correlated with virtually all of the other control variables. A number of other noteworthy correlations are evident in the panel. First, the positive correlation between vega and delta (0.44) is lower when these incentive variables are scaled by total compensation (0.27). This suggests that part of the correlation between vega and delta is driven by their common correlation with the size of the total compensation package, which tends to be highly correlated with firm size. Second, the instruments for compensation incentives (firm age, CEO age, and CEO tenure) have reasonable correlations with vega and delta and their scaled counterparts.10 We motivate our choice of instruments for vega and delta in the next section. Finally, poorly governed firms tend to have smaller cash holdings. Thus, for example, the correlation between the Gompers, Ishii, and Metrick index and cash is 0.17. Harford, Mansi, and Maxwell (2008) find a similar result and argue that it is consistent with their spending hypothesis (i.e., self-interested managers spend excess cash reserves).
10 One might be tempted to be alarmed by the nontrivial correlations between our dependent variable (cash holdings) and two of our instruments (firm age and CEO age). This is perfectly acceptable and essential. As illustrated, for example, in Kennedy (2003, pp. 167–168), an instrument must be correlated with the dependent variable, but a perfect instrument must not be correlated with the unobserved determinants of the dependent variable.
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4. Results In this section, we first report regressions of corporate cash holdings on CEO compensation incentives. We subsequently report regressions that estimate the marginal value of a dollar of cash to equityholders. In these regressions, we estimate the effect of CEO compensation incentives on the value of cash for the full sample and for sample categories based on degree of leverage and financial constraints. In both the cash holdings and value of cash regressions we report results with and without controls for corporate governance. Finally, we examine how CEO compensation incentives influence the likelihood of liquidity covenants in new bank loan lending agreements. 4.1. Cash holdings and CEO compensation incentives Table 2 reports regressions of cash holdings on CEO compensation incentives and controls. All of the regressions include industry and time effects (i.e., two-digit SIC code dummies and year dummies), and the t-statistics in parenthesis below parameter estimates are computed using heteroskedastic-consistent standard errors, which are corrected for correlation across observations of a given firm. Models 1–3 include Vega/TC and Delta/TC, Models 4–6 include only Vega/TC, and Models 7–10 separately control for each of the four governance variables. Model 1 in Table 2 reports the contemporaneous relation between cash holdings and managerial incentives. The regression reveals that cash holdings are positively related to vega. In other words, firms that encourage CEO risk-taking hold more cash, all else equal. The control variables generally have expected signs. Firms with low cash holdings tend to be large, have high working capital, and have greater acquisition activity. In contrast, higher growth firms as measured by the marketto-book ratio and the ratio of R&D to sales hold more cash. In their study of corporate governance and firm cash holdings, Harford, Mansi, and Maxwell (2008) lag their governance variables and argue that lagging helps control for potential endogeneity of governance. To control for potential endogeneity of compensation incentives, Model 2 in Table 2 reports the relation between cash holdings and lagged CEO compensation incentives. A positive and statistically significant effect of vega is seen on cash holdings. While lagging CEO vega and delta helps to alleviate endogeneity concerns, Model 3 in Table 2 explicitly accounts for endogeneity using two-stage least squares (2SLS) estimation. In the first stage, we separately regress vega (delta) on all of the variables used in Table 2 along with the instruments CEO age and CEO tenure (firm age).11 To check whether the instruments are weak, we compute the F-statistics of the reduced form equations (i.e., the additional explanatory power of the instruments 11 In unreported regressions, we check the robustness of our twostage least squares (2SLS) results by using a variety of additional instruments (e.g., CEO cash compensation and various measures of risk) for CEO compensation incentives and by using various subsets of instruments in the first stage regressions. In all cases, the results are similar to those reported in Table 2.
189
in the first-stage regressions for Vega/TC and Delta/TC). Following standard convention (see, e.g., Stock and Watson, 2003), because the computed F-statistics of 16.17 and 15.16 in the reduced form equations for Vega/ TC and Delta/TC, respectively, exceed 10, we could conclude that our instruments are not weak. Similarly, the Sargan test (see, e.g., Hill, Griffiths, and Lim, 2008) for the validity of the instruments fails to reject the null hypothesis that the (surplus) instrument(s) are uncorrelated with the regression error term in the cash regression.12 We report in Model 3 the second-stage regression in which vega and delta are replaced by their predicted values from their respective first-stage regressions. As seen in Model 3, CEO vega continues to have a positive and significant impact on cash holdings, consistent with the findings in Models 1 and 2. The positive relation between cash holdings and vega is not only statistically significant, but also reasonably economically significant. For example, using the coefficient estimate on Vega/TC in Model 1 and the statistics for the sample used to estimate Model 1, a one standard deviation increase in Vega/TC increases cash holding by 0.012 or about 5.5% (based on a regression sample mean for cash holdings of about 0.22). Models 4–6 in Table 2 report cash regressions analogous to Models 1–3, except that we take Delta/TC out of the models. The results without Delta/TC are very similar to those in Models 1–3. In particular, in all three specifications, we find a positive and statistically significant effect of vega on cash holdings. Overall, this suggests that although vega and delta incentives tend to be positively correlated (see Panel B of Table 1), they measure different aspects of CEO compensation incentives. Models 7–10 separately re-estimate Model 1 with each of the four corporate governance variables. Controlling for corporate governance has no effect on the relation between vega and cash holdings; all of the coefficients on vega continue to be significantly positive. The coefficients on the governance variables are consistent with the results reported in Harford, Mansi, and Maxwell (2008). In particular, firms with higher governance indices have lower cash holdings and firms with higher institutional and pension holdings have higher cash holdings. Finally, across all models in Table 2, no reliable relation exists between delta and cash holdings. As such, the remainder of the paper focuses primarily on the results for CEO vega incentives. 4.2. Value of cash and CEO compensation incentives So far we show a consistently positive relation between cash holdings and CEO vega. This result could seem surprising at first glance if one views cash simply as negative debt (see, e.g., Acharya, Almeida, and Campello, 2007), because 12 Because there are two endogenous right-hand-side variables (Vega/TC and Delta/TC) and three instruments (CEO age, CEO tenure, and firm age), the Sargan statistic tests the validity of one extra, or surplus, moment condition. A rejection of the null hypothesis that the surplus moment condition is valid indicates that one or more of the instruments is invalid.
Independent variable
Vega/TC
Lagged incentives (2)
2SLS (3)
Contemporaneous incentives (4)
Lagged incentives (5)
2SLS (6)
GIM index (7)
BCF index (8)
Institutional block holding (9)
Pension holdings (10)
0.262 (2.60)nnn 0.002 ( 0.25)
0.229 (2.39)nn 0.006 (0.93)
7.516 (3.44)nnn 0.075 ( 1.17)
0.249 (2.30)nn
0.270 (2.52)nnn
3.563 (2.54)nnn
0.220 (2.22)nn 0.005 (0.56) 0.003 ( 1.90)n
0.222 (2.26)nn 0.005 (0.52)
0.254 (2.33)nn 0.002 ( 0.27)
0.238 (2.16)nn 0.003 ( 0.30)
Gompers, Ishii, and Metrick index Bebchuk, Cohen, and Ferrell index Institutional Blockholdings Pension holdings Log firm size Market to book Cash flow/net assets NWC/net assets Capex/net assets Leverage Industry sigma Dividend dummy R&D/sales Acquisition activity Industry dummies Year dummies Number of observations Adj. R2
0.007 ( 1.97)nn 0.097 (2.53)nnn
0.072 ( 13.15)nnn 0.063 (15.27)nnn 0.122 (1.35) 0.429 ( 8.18)nnn 0.101 ( 0.92) 0.010 ( 0.22) 0.093 ( 1.72)n 0.010 ( 0.95) 1.058 (11.39)nnn 0.310 ( 6.67)nnn
0.073 ( 12.99)nnn 0.062 (13.53)nnn 0.158 (1.61) 0.408 ( 7.67)nnn 0.208 ( 1.72)n 0.010 (0.21) 0.010 ( 0.19) 0.009 ( 0.90) 1.090 (11.08)nnn 0.315 ( 6.68)nnn
0.121 ( 8.47)nnn 0.058 (26.03)nnn 0.058 (1.27) 0.398 ( 12.07)nnn 0.087 ( 0.98) 0.011 (0.48) 0.143 ( 2.22)nn 0.003 ( 0.30) 0.975 (16.50)nnn 0.286 ( 4.78)nnn
0.072 ( 13.15)nnn 0.063 (15.36)nnn 0.122 (1.35) 0.429 ( 8.19)nnn 0.102 ( 0.93) 0.009 ( 0.21) 0.093 ( 1.72)n 0.010 ( 0.93) 1.059 (11.40)nnn 0.311 ( 6.69)nnn
0.073 ( 13.00)nnn 0.062 (13.60)nnn 0.158 (1.61) 0.408 ( 7.66)nnn 0.205 ( 1.70)n 0.008 (0.18) 0.010 ( 0.20) 0.010 ( 0.95) 1.088 (11.08)nnn 0.313 ( 6.66)nnn
Yes Yes 14,215 0.55
Yes Yes 13,226 0.55
Yes Yes 11,102 0.54
Yes Yes 14,215 0.55
Yes Yes 13,226 0.54
0.094 0.073 0.074 ( 9.52)nnn ( 13.16)nnn ( 13.28)nnn 0.060 0.066 0.066 (32.84)nnn (10.25)nnn (10.28)nnn 0.089 0.009 0.011 (2.62)nnn (0.09) (0.11) 0.398 0.463 0.462 ( 16.03)nnn ( 8.10)nnn ( 8.09)nnn 0.116 0.250 0.248 ( 1.83)n ( 2.03)nn ( 2.00)nn 0.031 0.004 0.004 (1.64)n ( 0.08) ( 0.07) 0.096 0.015 0.015 ( 1.99)nn ( 0.32) ( 0.32) 0.005 0.018 0.019 ( 0.59) ( 1.46) ( 1.57) 0.994 0.993 0.994 (25.31)nnn (7.08)nnn (7.08)nnn 0.314 0.293 0.294 ( 6.81)nnn ( 6.00)nnn ( 6.03)nnn Yes Yes 11,940 0.46
Yes Yes 10,309 0.50
Yes Yes 10,309 0.50
0.077 ( 13.56)nnn 0.066 (15.58)nnn 0.095 (1.01) 0.485 ( 8.61)nnn 0.258 ( 2.18)nn 0.003 ( 0.06) 0.080 ( 1.49) 0.003 ( 0.30) 1.074 (11.25)nnn 0.333 ( 6.41)nnn
0.206 (3.65)nnn 0.080 ( 14.00)nnn 0.066 (15.56)nnn 0.103 (1.09) 0.487 ( 8.66)nnn 0.254 ( 2.15)nn 0.006 (0.13) 0.082 ( 1.50) 0.006 ( 0.57) 1.060 (11.09)nnn 0.325 ( 6.27)nnn
Yes Yes 11,979 0.56
Yes Yes 11,979 0.56
Y. Liu, D.C. Mauer / Journal of Financial Economics 102 (2011) 183–198
Delta/TC
Contemporaneous incentives (1)
190
Table 2 Regressions of cash holdings on chief executive officer (CEO) compensation incentives and controls. The dependent variable is the ratio of cash plus marketable securities to net assets, where net assets is the book value of total assets minus cash plus marketable securities. All independent variable are defined in Table 1. Models 1–3 regress cash holdings in fiscal year t on CEO vega and delta incentives in year t, CEO vega and delta incentives in year t 1, and predicted CEO vega and delta incentives, respectively. The predicted values are computed from first-stage regressions of vega (delta) on all independent variables plus the instruments CEO age and CEO tenure (firm age). 2SLS refers to two-stage least squares estimation. Models 4–6 are the same except we exclude delta and we use the instruments CEO age and CEO tenure in the first-stage regression for vega in Model 6. Models 7–10 report regressions of cash holdings in fiscal year t on CEO vega and delta incentives in year t and the Gompers, Ishii, and Metrick index (GIM index), Bebchuk, Cohen, and Ferrell index (BCF index), institutional block holdings, and pension holdings, respectively. Industry dummies are based on two-digit Standard Industrial Classification codes. t-Statistics are in parentheses below parameter estimates. The t-statistics for Models 1, 2, 4, 5, and 7–10 are based on heteroskedastic-consistent standard errors, corrected for correlation across observations of a given firm. nnn, nn, and n denote significance at the 1%, 5%, and 10% levels, respectively.
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Coles, Daniel, and Naveen (2006) find a strong positive relation between leverage and CEO vega. Although the positive relation between vega and cash is inconsistent with the alignment hypothesis, it is consistent with the costly contracting hypothesis and the costly external finance hypothesis. The costly contracting hypothesis argues that debtholders could demand (or firms could rationally choose) greater cash reserves at firms that encourage CEO risk-taking to reduce firm risk and to provide a cushion in case of distress. Alternatively, the costly external finance hypothesis highlights the difficulty of obtaining external funds for firms that encourage risk-taking with high vega compensation. In this case, firms hold more cash to hedge future external funding needs. To differentiate between the two hypotheses and to get a better understanding of what drives the positive relation between vega and cash holdings, we turn to an examination of the value of cash and, in particular, the influence of CEO compensation incentives on the value of cash to equityholders. The costly contracting hypothesis predicts that the value of cash to equityholders is decreasing in vega, because cash benefits bondholders. Alternatively, the costly external finance hypothesis predicts that the value of cash to equityholders is increasing in vega, because cash is used to hedge costly external financing and thereby benefit equityholders. Both hypotheses could be present in the data, so the effect of vega on the value of cash reflects a net effect. We use the methodology developed in Faulkender and Wang (2006) to estimate the influence of CEO compensation incentives on the value of an additional dollar of cash to equityholders. We estimate the following Faulkender and Wang regression augmented to include CEO compensation incentives:
DCi,t DEi,t DNAi,t DRDi,t þ g2 þ g3 þ g4 Mi,t1 Mi,t1 Mi,t1 Mi,t1 DIi,t DDi,t Ci,t1 NFi,t þ g5 þ g6 þ g7 þ g8 Li,t þ g9 Mi,t1 Mi,t1 Mi,t1 Mi,t1
ri,t RBi,t ¼ g0 þ g1
þ g10
Ci,t1 DCi,t DCi,t þ g11 Li,t Mi,t1 Mi,t1 Mi,t1
DCi,t Mi,t1 DCi,t þ g14 ðDelta=TCÞi,t þ g15 ðDelta=TCÞi,t þ ei,t , Mi,t1 þ g12 ðVega=TCÞi,t þ g13 ðVega=TCÞi,t
ð1Þ where the dependent variable is the difference between firm i’s stock return over year t 1 to year t ðri,t Þ (computed using monthly returns from CRSP) and the Fama and French (1993) size and book-to-market matched portfolio return from year t 1 to year t (RBi,t ).13 For the 13 Specifically, for each year, we group every firm in our sample into one of 25 size and book-to-market portfolios based on the intersection between size and book-to-market independent sorts. So stock i’s benchmark return in year t is the return to which stock i belongs at the beginning of fiscal year t. Returns on these 25 portfolios are from Kenneth R. French’s website http://mba.tuck.dartmouth.edu/pages/ faculty/ken.french/data_library.html. We thank Professor French for graciously providing these data. For more details, please refer to Faulkender and Wang (2006).
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right-hand-side variables, DXi,t indicates a change in variable X for firm i over year t 1 to year t, where the scaling variable, Mi,t 1, is firm i’s market value of equity at time t 1. The right-hand-side variables include cash and marketable securities (Ci,t), earnings before extraordinary items (Ei,t), net assets (NAi,t), research and development expense (RDi,t) (set equal to zero if missing), interest expense (Ii,t), common dividends (Di,t), long-term debt plus debt in current liabilities divided by the market value of equity at time t 1 (Li,t), and net new finance (NFi,t).14 The coefficients on the incentive variables (g12 and g14 ) measure the direct effect of compensation incentives on excess equity returns, and the coefficients on the interactions of the incentive variables with the change in cash (g13 and g15 ) measure the effect of compensation incentives on the value of an additional dollar of cash. We are most interested in the coefficient on ðVega=TCÞi,t ðDCi,t =Mi,t1 Þ (i.e., g13 ), which measures the effect of CEO risk-taking incentives on the marginal value of cash. The costly contracting hypothesis predicts that g13 is negative, because an additional dollar of cash is more likely to benefit bondholders. In contrast, the costly external finance hypothesis predicts that g13 is positive, because an additional dollar of cash helps to alleviate financial constraints. The coefficient on ðDelta=TCÞi,t ðDCi,t =Mi,t1 Þ (i.e., g15 ) is similarly interpreted, in that it measures the effect of CEO pay-for-performance incentives on the marginal value of cash. A positive value for g15 is consistent with the view that delta enhances managerstockholder alignment, while a negative value for g15 is consistent with the view that high delta compensation induces greater CEO risk-aversion, which in turn induces suboptimal cash holdings. Finally, we estimate our value of cash regressions with and without Delta/TC and ðDelta=TCÞi,t ðDCi,t =Mi,t1 Þ as a robustness check to ensure that our inferences about ðVega=TCÞi,t ðDCi,t =Mi,t1 Þ are not unduly influenced by having delta also in the equation.15 4.2.1. The marginal value of cash Table 3 reports regressions of excess stock returns on CEO compensation incentives, governance variables, and 14 Net new finance, NFi,t, is computed as sales of common and preferred stock net of stock repurchases, plus issuance of long-term debt net of long-term debt reduction (i.e., Compustat items #108 #115 þ#111 #114). 15 Because delta and vega are computed using stock and option compensation, they tend to be positively correlated (see Panel B of Table 1). This might induce a multicollinearity problem if both are in the equation, which would increase the standard errors of the coefficient estimates on variables constructed from delta and vega. However, the estimated coefficients would still be unbiased. Another potentially more serious problem is a left-out variables bias for any coefficients of variables involving vega when delta is not in the equation. Thus, for example, if g13 o 0 and g15 4 0, because ðVega=TCÞ ðDC=MÞ and ðDelta=TCÞ ðDC=MÞ are positively correlated (r ¼ 0.35), it is straightforward to show that not including ðDelta=TCÞ ðDC=MÞ in the equation will bias upward the coefficient estimate on ðVega=TCÞ ðDC=MÞ (i.e., g13 will be less negative). Thus, the left-out variables problem argues that both delta and vega and their interactions with the change in cash should be in the equation. Because it is not clear which problem is of greater concern for our case, we report estimation results either with and without delta or report estimation results without delta and comment on whether results are materially different if delta is also in the equation.
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Table 3 The impact of chief executive officer (CEO) compensation incentives on the value of cash. This table reports regressions of excess stock returns, rit RBit , on CEO compensation incentives and changes in firm characteristics over the fiscal year. The dependent variable is the stock return for firm i during fiscal year t, rit , minus stock i’s benchmark return in year t, RBit , where the benchmark return is the return of the Fama and French size and book-to-market portfolio to which stock i belongs at the beginning of fiscal year t. All variables except Vega/TC, Delta/TC, and GOV are scaled by the lagged market value of equity, Mt1 . Model 1 is the benchmark Faulkender and Wang (2006) specification. Models 2 and 3 use the continuous values of Vega/TC and Delta/TC (i.e., the values reported in Table 1 and used in the cash holdings regressions of Table 2). Models 4 and 5, and the models controlling for corporate governance, 6–9, use dummy variable incentives, where Vega/TC and Delta/TC are equal to one if their respective continuous measures are above their sample medians and zero otherwise. Following Dittmar and Mahrt-Smith (2007), the governance dummy variable GOV in Model 6–9 takes a value of one if the firm is in the bottom tercile of the Gompers, Ishii, and Metrick index (GIM index), bottom tercile of the Bebchuk, Cohen, and Ferrell index (BCF index), top tercile of institutional blockholders, and top tercile of pension holdings, respectively. In all cases, the benchmark group is the top or bottom governance tercile, so all sample observations in the middle governance tercile are eliminated from these regressions. In the regressions, Ct is cash plus marketable securities, Et is earnings before extraordinary items plus interest, deferred tax credits, and investment tax credits, NAt is total assets minus cash holdings, RDt is research and development expense (which is set equal to zero if missing), It is interest expense, Dt is common dividends, Lt is the ratio of long-term debt plus debt in current liabilities to the market value of equity at time t 1, and NFt is total equity issuances minus repurchases plus debt issuances minus debt redemption. DXt is notation for the one-year change, Xt Xt1 , where t (t 1) denotes end of fiscal year t (t 1). t-Statistics in parentheses below parameter estimates are computed using heteroskedastic-consistent standard errors, corrected for correlation across observations of a given firm. nnn, nn, and n denote significance at the 1%, 5%, and 10% levels, respectively. Independent variable
DCt
FW model
Continuous incentives
Dummy variable incentives
(1)
(2)
(3)
(4)
(5)
1.246 (21.47)nnn
1.357 (17.29)nnn 0.464 ( 4.90)nnn 5.670 ( 2.26)nn 0.042 (5.86)nnn 0.320 (2.39)nn
1.389 (17.50)nnn 0.193 ( 2.18)nn 2.540 ( 1.86)n
1.082 (15.45)nnn 0.067 ( 8.18)nnn 0.729 ( 4.69)nnn 0.149 (16.95)nnn 1.007 (6.22)nnn
1.477 (18.11)nnn 0.033 ( 4.09)nnn 0.442 ( 2.83)nnn
Vega/TC Vega/TC DCt Delta/TC Delta/TC DCt GOV GOV DCt
DEt DNAt DRDt DIt DDt Ct 1 Lt NFt Ct 1 DCt Lt DCt Intercept Number of observations Adj. R2
0.701 0.725 (14.64)nnn (13.94)nnn 0.344 0.311 (14.42)nnn (12.88)nnn 1.464 1.669 (3.46)nnn (3.72)nnn 5.503 5.256 ( 12.19)nnn ( 10.66)nnn 3.594 3.325 (4.12)nnn (3.56)nnn 0.486 0.506 (10.91)nnn (10.49)nnn 0.005 0.005 ( 0.52) ( 0.48) 0.158 0.132 ( 3.32)nnn ( 2.58)nnn 0.658 0.813 ( 2.51)nnn ( 2.79)nnn 0.416 0.426 ( 5.67)nnn ( 5.27)nnn 0.044 0.040 ( 7.38)nnn ( 5.24)nnn 16,719 0.19
14,432 0.20
0.731 0.713 0.727 (13.96)nnn (13.93)nnn (13.93)nnn 0.316 0.297 0.313 (12.96)nnn (12.51)nnn (12.89)nnn 1.681 1.230 1.654 (3.71)nnn (2.80)nnn (3.65)nnn 5.240 5.321 5.248 ( 10.59) ( 10.79)nnn ( 10.58)nnn 3.433 2.117 3.476 (3.68)nnn (2.26)nn (3.71)nnn 0.517 0.491 0.510 (10.74)nnn (10.17)nnn (10.56)nnn 0.009 0.006 0.009 ( 0.87) (0.56) ( 0.82) 0.129 0.148 0.133 ( 2.51)nnn ( 2.91)nnn ( 2.59)nnn 0.865 0.827 0.864 ( 2.95)nnn ( 2.81)nnn ( 2.94)nnn 0.430 0.380 0.426 ( 5.10)nnn ( 4.82)nnn ( 5.08)nnn 0.038 0.085 0.027 ( 5.08)nnn ( 9.13)nnn ( 3.20)nnn 14,432 0.19
14,432 0.22
changes in firm characteristics over the fiscal year. Model 1 reports a baseline regression similar to Model II in Table II of Faulkender and Wang (2006). Though our sample covers a more recent time period and is restricted to firms on ExecuComp, the two estimations are similar. Using the coefficient estimates in Model 1, an extra dollar of cash increases shareholder wealth by $1.246 if the firm has zero
14,432 0.19
Controlling for corporate governance
GIM index (6)
BCF index Institutional block (7) (8)
Pension (9)
0.803 (7.76)nnn 0.052 ( 5.06)nnn 0.584 ( 2.87)nnn 0.119 (10.73)nnn 0.833 (3.82)nnn 0.007 ( 0.71) 0.470 (2.41)nn 0.733 (10.80)nnn 0.238 (8.06)nnn 0.924 (1.29) 4.390 ( 7.09)nnn 5.221 (5.20)nnn 0.352 (6.05)nnn 0.000 ( 0.01) 0.318 ( 4.78)nnnn 0.813 ( 2.21)nn 0.141 ( 1.48) 0.072 ( 5.37)nnn
0.776 (8.10)nnn 0.051 ( 5.20)nnn 0.432 ( 2.10)nn 0.118 (11.57)nnn 0.590 (2.60)nnn 0.009 ( 0.96) 0.374 (1.89)n 0.670 (11.48)nnn 0.209 (7.46)nnn 0.985 (1.52) 4.141 ( 6.45)nnn 4.417 (4.53)nnn 0.336 (6.79)nnn 0.006 (0.41) 0.212 ( 3.38)nnn 1.185 ( 3.80)nnn 0.121 ( 1.36) 0.077 ( 5.89)nnn
1.326 (11.18)nnn 0.054 ( 5.23)nnn 0.707 ( 3.39)nnn 0.134 (11.69)nnn 0.914 (4.31)nnn 0.034 ( 3.17)nnn 0.406 ( 1.96)nn 0.667 (9.12)nnn 0.311 (8.79)nnn 1.493 (2.64)nnn 5.850 ( 9.02)nnn 2.603 (2.02)nn 0.481 (7.92)nnn 0.019 (1.14) 0.222 ( 3.09)nnn 0.654 ( 1.59) 0.463 ( 4.33)nnn 0.079 ( 6.65)nnn
1.305 (12.23)nnn 0.048 ( 4.34)nnn 0.520 ( 2.54)nnn 0.144 (12.19)nnn 0.951 (4.71)nnn 0.061 ( 5.77)nnn 0.535 ( 2.91)nnn 0.681 (10.09)nnn 0.350 (10.13)nnn 1.083 (1.88)n 5.275 ( 8.52)nnn 2.678 (2.08)nn 0.526 (8.88)nnn 0.012 (0.74) 0.243 ( 3.45)nnn 0.956 ( 2.68)nnn 0.392 ( 3.98)nnn 0.069 ( 4.85)nnn
6,815 0.17
8,206 0.16
8,351 0.22
8,324 0.24
cash and no leverage at the beginning of the fiscal year. The mean firm, however, has cash holdings of 10.71% of the market capitalization of equity at the beginning of the fiscal year and a debt to equity ratio of 40.2%. Therefore, the value of an additional dollar of cash to shareholders in the mean firm is 1.246 0.658 0.1071 0.416 0.4020¼$1.01. In comparison, Model II in Table II of Faulkender and Wang
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(2006) yields a slightly smaller marginal value of cash to shareholders of $0.94. Models 2 and 3 augment the specification in Model 1 by including CEO compensation incentives. Regardless of whether delta is in the equation (Model 2) or whether delta is not in the equation (Model 3), the coefficient on vega interacted with the change in cash is negative.16 This supports the costly contracting hypothesis, which posits that the positive relation between cash holdings and CEO vega is largely driven by liquidity covenants or, in their absence, by a desire on the part of the firm to hold greater amounts of liquid assets to moderate the cost of debt. According to this hypothesis, an extra dollar of cash benefits bondholders more than equityholders when the CEO has high vega compensation. In Model 2, the coefficient on delta interacted with the change in cash is positive. Thus, evidence also exists that high delta compensation enhances the alignment of management and shareholder interests, which has a positive influence on equityholders’ assessment of the value of cash. Using Model 2, we compute the value of an additional dollar of cash for a firm with average compensation incentives as $0.99. A one standard deviation increase in Vega/TC decreases the value of an additional dollar of cash by 0.23 (from 0.99 to 0.76) or 23%.17 A similar calculation for delta shows that a one standard deviation increase in Delta/TC increases the value of an additional dollar of cash by 0.27 or 27%. Thus, it appears as if CEO compensation incentives have a significant economic effect on the marginal value of cash. Models 4 and 5 repeat Models 2 and 3 using dummy variables for CEO compensation incentives, and Models 6– 9 use these dummy variable incentives in conjunction with the Dittmar and Mahrt-Smith (2007) value of cash specifications, which include effects of corporate governance. Thus, we set Vega/TC and Delta/TC equal to one if vega scaled by total compensation and delta scaled by total compensation are above their sample medians. As seen in Models 4 and 5, the signs of the coefficients on the dummy variable compensation incentives interacted with the change in cash are the same as those for the continuous measures in Models 2 and 3. We then use these dummy variable incentive measures along with dummy variable governance variables in Models 6–9 to assess the robustness of our results after controlling for corporate governance. Following Dittmar and Mahrt-Smith (2007), the governance dummy variable GOV in Models 6–9 takes a value of one if the firm is in the bottom tercile of the Gompers, Ishii, and Metrick index, bottom tercile of the Bebchuk, Cohen, and Ferrell index, top tercile of institutional blockholders, and top tercile of Pension holdings, respectively. In all cases, the benchmark group is the top
16 Comparing Models 2 and 3, the coefficients on vega and vega interacted with the change in cash are smaller in absolute value when delta is excluded from the regression. As noted in footnote 15, this is consistent with a left-out variables problem. 17 Using Model 3, the corresponding numbers are a value of cash for a firm with average compensation incentives of $1.04 and a decrease in the value of an additional dollar cash for a one standard deviation increase in Vega/TC of 0.11 or 11%.
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or bottom governance tercile, so all sample observations in the middle governance tercile are eliminated from these regressions. The addition of the corporate governance variables does not affect our inferences about CEO compensation incentives. In particular, in each of Models 6–9 the coefficients on Vega/TC interacted with the change in cash are significantly negative and the coefficients on Delta/TC interacted with the change in cash are significantly positive. As in Dittmar and Mahrt-Smith (2007), corporate governance also influences the marginal value of cash. Thus, in Models 6 and 7, firms in the bottom tercile of their respective governance indices have positive coefficients on the governance dummy interacted with the change in cash, which suggests that good governance enhances the marginal value of a dollar of cash. However, we find opposite results to Dittmar and Mahrt-Smith (2007) for institutional blockholdings (Model 8) and pension holding (Model 9), in which the coefficients on the governance dummy interacted with the change in cash are negative, not the positive values that they report.18 4.2.2. The marginal value of cash at leverage extremes The regression results in Table 3 that vega decreases the marginal value of cash to shareholders are strongly supportive of the costly contracting hypothesis for the positive relation between vega and cash holdings. Vega has a negative effect on the marginal value of cash to equityholders because an additional dollar of cash is more likely to benefit debtholders at the expense of equityholders. This suggests that we can sharpen our tests by focusing on the effect of vega on the marginal value of cash after subdividing our sample by the firm’s degree of leverage. If the costly contracting hypothesis is the driving force behind the negative relation between vega and the marginal value of cash, we would expect that this negative relation is more pronounced when the firm has high leverage than when the firm has low leverage, and it should disappear when the firm has zero leverage (i.e., unlevered firms). The reason is that, as leverage increases, debtholders could exert greater influence on firm liquidity policy to protect their investment (e.g., by requiring liquidity covenants). We test these leverage predictions in Table 4 by estimating value of cash regressions that include triple interactions between vega, change in cash, and a leverage dummy variable. We specify two leverage dummy variables: HighLev takes a value of one if the firm has an above sample median leverage ratio, and PosLev take a value of one if the firm has non-zero leverage.19 In these specifications, the coefficients on the triple interaction variables Vega=TC DCt HighLev and Vega=TC DCt PosLev 18 This could be because of differences in the samples of the two papers. In particular, our sample has the requirement that firms have compensation data on ExecuComp and also covers a slightly different time period (i.e., their sample period is 1990 to 2003 and our sample period is 1992 to 2006). 19 There are 2,398 firm-year observations with PosLev ¼0. Thus, about 17% (2,398/14,432) of our regression observations are unlevered.
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Table 4 The impact of chief executive officer (CEO) compensation incentives interacted with leverage on the value of cash. This table reports regressions of excess stock returns, rit RBit , on CEO compensation incentives and changes in firm characteristics over the fiscal year. The dependent variable is the stock return for firm i during fiscal year t, rit , minus stock i’s benchmark return in year t, RBit , where the benchmark return is the return of the Fama and French size and book-to-market portfolio to which stock i belongs at the beginning of fiscal year t. All variables except Vega/TC, Delta/TC, and GOV are scaled by the lagged market value of equity, Mt1 . Model 1 is the benchmark Faulkender and Wang (2006) specification. Models 2 and 3 use the continuous values of Vega/TC and Delta/TC (i.e., the values reported in Table 1 and used in the cash holdings regressions of Table 2). Models 4 and 5, and the models controlling for corporate governance, 6–9, use dummy variable incentives, where Vega/TC and Delta/TC are equal to one if their respective continuous measures are above their sample medians and zero otherwise. Following Dittmar and Mahrt-Smith (2007), the governance dummy variable GOV in Model 6–9 takes a value of one if the firm is in the bottom tercile of the Gompers, Ishii, and Metrick index (GIM index), bottom tercile of the Bebchuk, Cohen, and Ferrell index (BCF index), top tercile of institutional blockholders, and top tercile of pension holdings, respectively. In all cases, the benchmark group is the top or bottom governance tercile, so all sample observations in the middle governance tercile are eliminated from these regressions. In the regressions, Ct is cash plus marketable securities, Et is earnings before extraordinary items plus interest, deferred tax credits, and investment tax credits, NAt is total assets minus cash holdings, RDt is research and development expense (which is set equal to zero if missing), It is interest expense, Dt is common dividends, Lt is the ratio of long-term debt plus debt in current liabilities to the market value of equity at time t 1, and NFt is total equity issuances minus repurchases plus debt issuances minus debt redemption. DXt is notation for the one-year change, Xt Xt1 , where t (t 1) denotes end of fiscal year t (t 1). t-Statistics in parentheses below parameter estimates are computed using heteroskedastic-consistent standard errors, corrected for correlation across observations of a given firm. nnn, nn, and n denote significance at the 1%, 5%, and 10% levels, respectively. Independent variable
DCt HighLev
(1)
(2)
(3)
(4)
1.320 (16.96)nnn 0.032 ( 3.17)nnn
1.339 (17.12)nnn
1.341 (17.13)nnn 0.038 ( 3.78)nnn
1.367 (17.32)nnn
PosLev Vega/TC Vega/TC DCt Vega/TC DCt HighLev
0.451 ( 4.80)nnn 0.436 (0.16) 10.226 ( 2.36)nn
Delta/TC DCt Ct 1 DCt Lt DCt Controls Number of observations Adj. R2
0.191 ( 2.22)nn 4.568 (1.71)n 12.340 ( 2.82)nnn
0.052 ( 2.95)nnn 0.190 ( 2.17)nn 9.815 (2.22)nn
0.040 (5.70)nnn 0.295 (2.27)nn 0.844 ( 2.90)nnn 0.378 ( 4.61)nnn
11.140 ( 2.49)nnn 0.040 (5.64)nnn 0.315 (2.40)nn 0.847 ( 2.89)nnn 0.407 ( 5.02)nnn
0.898 ( 3.06)nnn 0.372 ( 4.36)nnn
0.904 ( 3.07)nnn 0.408 ( 4.82)nnn
Yes 14,432 0.20
Yes 14,432 0.20
Yes 14,432 0.19
Yes 14,432 0.19
Vega/TC DCt PosLev Delta/TC
0.044 ( 2.47)nnn 0.452 ( 4.76)nnn 4.623 (1.10)
capture the difference in the effects of vega on the marginal value of cash between high and low leverage firms and positive and zero leverage firms, respectively. Equally important, the coefficients on the interaction variable Vega=TC DCt capture the effects of vega on the value of cash for low and zero leverage firms, respectively. We expect the coefficients on the interaction variables for low and zero leverage firms to be much smaller in absolute value than the coefficients on the triple interaction variables, and we expect the coefficient on the triple interaction variables to be significantly negative. As reported in Table 4, the relation between vega and the marginal value of cash is more negative for high leverage firms (versus low leverage firms) and for positive leverage firms (versus zero leverage firms). The coefficients on Vega=TC DCt are positive in all regressions and are significantly positive in the specifications comparing the effect of vega on the marginal value of cash for firms with positive and zero leverage. Thus, for example, using
13.460 ( 2.88)nnn
Model 4, the value of an additional dollar of cash for a firm with positive leverage and average CEO vega incentives is $0.98, and the value of an additional dollar of cash for a firm with zero leverage and average CEO vega incentives is $1.43. A one standard deviation increase in Vega/TC decreases the value of cash for the former by $0.15 (from $0.98 to $0.83) and increases the value of cash for the latter by $0.41 (from $1.43 to $1.84). This is strong evidence for the costly contracting hypothesis and further illustrates that vega incentives could increase the value of cash when cash cannot benefit debtholders (i.e., when the firm is unlevered). This suggests that the costly external finance hypothesis, and in particular the role that cash might play in relieving financial constraints in high vega firms, also influences the marginal value of cash. 4.2.3. The marginal value of cash for firms facing financial constraints Although our results for the effect of vega on the value of cash support the costly contracting hypothesis, we
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cannot rule out the costly external finance hypothesis. The reason is that the effect of vega on the value of cash could depend on whether a firm is financially constrained. In particular, this relation could be positive or at least non-negative in financially constrained firms. To determine whether financial constraints influence the relation between vega and the value of cash, we interact vega and the change in cash with variables that proxy for the degree to which a firm is financially constrained. Positive coefficients on these triple interaction variables would imply that the negative effect of vega on the value of cash is less negative for financially constrained firms than for firms that are not financially constrained. We can then add these coefficients to the coefficients on vega interacted with the change in cash to compute the effect of vega on the value of cash for financially constrained firms. The literature employs a number of financial constraint proxies. Among others, Gertler and Gilchrist (1994) use firm
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size as a measure of financial constraint based on the argument that small firms are more vulnerable to capital market imperfections. Lamont, Polk, and Saa-Requejo (2001) consider the market-to-book ratio in their financial constraint index. They contend that to be constrained, a firm needs to have good investment opportunities. Dividend payout as an indicator of costly external finance is used by Fazzari, Hubbard, and Peterson (1988), motivated by the idea that low payout firms have insufficient internal cash flow to fund investments and thus have to rely on external sources. Lastly, Whited (1992) and Kashyap, Lamont, and Stein (1994) use the absence of a bond rating as a proxy for financial constraints. Table 5 reports value of cash regressions in which we interact Vega/TC and the change in cash with two different dummy variables for small firm size (SmallSales and SmallNA) in Models 1 and 2, a dummy variable for high market-to-book (HighMB) in Model 3, a dummy variable
Table 5 The impact of chief executive officer (CEO) compensation incentives interacted with financial constraint proxies on the value of cash. The table reports regressions of excess stock returns on CEO compensation incentives and changes in firm characteristics over the fiscal year. Except where noted, the dependent variable and the independent variables are defined in Table 3. SmallSales is a dummy variable equal to one if a firm’s sales is below the sample median and zero otherwise. SmallNA is a dummy variable equal to one if a firm’s net assets (total assets minus cash plus marketable securities) is below the sample median and zero otherwise. HighMB is a dummy variable equal to one if the firm’s market to book asset ratio is above the sample median and zero otherwise. LowPayout is a dummy variable equal to one if the firm’s payout ratio is below the sample median and zero otherwise. The payout ratio in a given year is computed as the ratio of common dividends plus share repurchases to earnings before extraordinary items plus interest, deferred tax credits, and investment tax credits. NoRating is a dummy variable equal to one if the firm does not have a bond rating but reports positive debt. t-Statistics in parentheses below parameter estimates are computed using heteroskedastic-consistent standard errors, corrected for correlation across observations of a given firm. nnn, nn, and n denote significance at the 1%, 5%, and 10% levels, respectively. Independent variable
D Ct Vega/TC Vega/TC DCt Vega/TC DCt SmallSales
(1)
(2)
(3)
(4)
(5)
1.380 (17.72)nnn 0.148 ( 1.60) 2.441 ( 0.69) 0.101 ( 0.03)
1.361 (17.54)nnn 0.126 ( 1.37) 3.524 ( 1.05)
1.283 (18.85)nnn 0.437 ( 5.08)nnn 12.088 (-5.67)nnn
1.392 (17.82)nnn 0.170 ( 1.93)nn 8.719 ( 4.38)nnn
1.208 (15.41)nnn 0.079 ( 0.81) 3.783 ( 1.17)
2.549 (0.64)
Vega/TC DCt SmallNA
16.273 (5.66)nnn
Vega/TC DCt HighMB
8.349 (2.80)nnn
Vega/TC DCt LowPayout
4.045 (0.90)
Vega/TC DCt NoRating SmallSales
0.026 (3.22)nnn
SmallNA
0.027 (3.21)nnn
HighMB
0.340 (34.86)nnn
LowPayout
0.032 (3.84)nnn
NoRating Ct 1 D Ct Lt DCt Controls Number of observations Adj. R2
0.845 ( 2.88)nnn 0.429 ( 5.07)nnn
0.854 ( 2.90)nnn 0.419 ( 4.90)nnn
0.831 ( 3.09)nnn 0.382 ( 4.93)nnn
0.890 ( 3.01)nnn 0.431 ( 5.12)nnn
0.043 (4.65)nnn 0.846 ( 2.69)nnn 0.362 ( 4.04)nnn
Yes 14,432 0.19
Yes 14,432 0.19
Yes 14,430 0.28
Yes 14,430 0.19
Yes 13,169 0.18
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for whether the firm has low payouts (LowPayout) in Model 4, and a dummy variable for firms that do not have a long-term bond rating but report positive amounts of debt (NoRating) in Model 5. We use the sample medians of sales, total assets minus cash and marketable securities, market-to-book asset ratio, and common dividends plus repurchases to earnings to construct the dummy variables SmallSales, SmallNA, HighMB, and LowPayout, respectively. In the table, the coefficients on the constraint proxies interacted with Vega/TC and the change in cash are generally positive and the coefficients for HighMB and LowPayout are statistically significant. This indicates that the effect of vega on the value of cash tends to be less negative for financially constrained firms than for financially unconstrained firms. We can uncover the effect of vega on the marginal value of cash for financially constrained firms by adding the coefficient on Vega=TC DCt to the coefficient on Vega=TC DCt interacted with the financial constraint dummy variable (e.g., Vega=TC DCt LowPayout). Although these sums range in value from 2.542 ( 2.441þ 0.101) in Model 1 to 4.185 ( 12.088þ16.273) in Model 3, none is significantly different from zero. This evidence is consistent with the costly external finance hypothesis, because it suggests that for high vega, financially constrained firms the benefit to equityholders of an additional dollar of cash compensates for the benefit that greater liquidity provides to bondholders (i.e., the net effect is zero).20
Table 6 The impact of chief executive officer (CEO) compensation incentives on the probability of observing liquidity covenants in bank loans. The table reports the marginal effects on the probability of a liquidity covenant in a bank loan for a one standard deviation change in explanatory variables. The marginal effects are computed from probit regressions, which estimate the determinants of the decision to include liquidity covenants in bank loans taken out by our sample firms. We collect bank loan data from the Dealscan database of the Loan Pricing Corporation, which contains information on the commercial loan issuance market and focuses primarily on bank debt with longer maturities. We classify a bank loan as including a liquidity covenant if the loan document specifies a minimum current ratio, minimum quick ratio, or a minimum interest, debt service, or fixed charge coverage ratio. All explanatory variables are defined in Tables 1 and 2 except log of maturity, which is the natural logarithm of the loan maturity in months. We report z-values, which test whether the underlying probit coefficient estimates are equal to zero, in parentheses below the marginal effects. The z-values are computed using robust standard errors. nnn, nn, and n denote whether the underlying probit coefficient estimate is significantly different from zero at the 1%, 5%, and 10% levels, respectively. Independent variable Vega/TC Delta/TC Log of firm size Market to book Industry sigma
4.3. Liquidity covenants and CEO compensation incentives Although our evidence suggests that the positive vega and cash holdings relation is largely explained by the costly contracting hypothesis, our conclusion would be strengthened if we could demonstrate a positive relation between the vega of a CEO’s compensation and the incidence of liquidity covenants in debt contracts. The search for such a relation, however, can easily be short-circuited by the possibility that high vega firms might choose to side-step costly liquidity covenants by voluntarily holding excess cash reserves. In this way, high vega firms that pursue risky policies might be able to avoid additional restrictive covenants and yet moderate the cost of borrowing. One clear advantage to this voluntary solution is that the firm would have the flexibility to use the cash balance without potentially violating a liquidity covenant. Ultimately, however, it is an empirical question whether there is any evidence of a positive relation between vega and the incidence of liquidity covenants. To test whether a relation exists between compensation incentives and liquidity covenants, we collect bank loan issuance data for the firms in our sample from the Dealscan database of the Loan Pricing Corporation over our sample period from 1992 to 2006. The Dealscan database contains information on the commercial loan market and focuses primarily on bank debt with longer 20 The positive effect of vega on the value of cash for unlevered firms that we show in Table 4 would be consistent with the costly external finance hypothesis if unlevered firms in our sample are financially constrained. In unreported results, however, we find no evidence that unlevered firms in our sample are more (or less) financially constrained than levered firms in our sample.
Leverage Log of maturity Pseudo R2 Observed probability of a liquidity covenant Predicted probability of a liquidity covenant Number of observations
(1)
(2)
0.517 0.436 (2.35)nn (2.07)nn 0.013 ( 1.28) 0.071 0.071 ( 11.71)nnn ( 11.68)nnn 0.006 0.007 ( 1.15) ( 1.37) 0.148 0.147 ( 1.68)n ( 1.67)n 0.308 0.308 (6.44)nnn (6.45)nnn 0.086 0.086 (7.62)nnn (7.63)nnn 0.07 0.707
0.07 0.707
0.711
0.711
3,185
3,185
maturities. We identify 3,185 firm-years in which the firm issued a new bank loan, and the Dealscan database reports the covenants in the loan. We classify a bank loan as including a liquidity covenant if the loan document specifies a minimum current ratio, minimum quick ratio, or a minimum interest, debt service, or fixed charge coverage ratio.21 The current and quick ratios are direct measures of the stock of liquid assets relative to current liabilities. Coverage ratios, however, have a more subtle relation to corporate liquidity. Because coverage ratios place restrictions on the spread between firm cash flows or earnings and fixed changes (i.e., interest and principal payments on debt), minimum coverage ratios imply that the firm adds to the stock of liquidity over time. In our sample of 3,185 bank loans, 13% require a minimum
21 Although loans are sometimes observed to contain a covenant requiring minimum cash and equivalents, none of the loans in our sample contains such a covenant.
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current ratio, 9% require a minimum quick ratio, and 38%, 3%, and 33% require a minimum interest, debt service, or fixed charge coverage ratio, respectively. We estimate probit regressions in which the dependent variable is equal to one if the loan contains any of the five liquidity covenants and the independent variables include CEO compensation incentives and control variables. Table 6 reports marginal effects from these probit regressions, which are the effects on the probability of a liquidity covenant for a one standard deviation change in the explanatory variables. Model 1 includes both Vega/TC and Delta/TC in the probit, and Model 2 includes only Vega/TC. As seen in the table, Vega/TC has a significant effect on the likelihood of observing a liquidity covenant in a loan. For example, using Model 2, a one standard deviation increase in Vega/TC increases the likelihood of observing a liquidity covenant in a bank loan by about 0.44, which represents a 62% increase in the observed probability of a liquidity covenant in the regression sample. In contrast, in Model 1, Delta/TC has an insignificant effect on the likelihood of a liquidity covenant. Overall, this evidence supports the notion that the positive relation between vega and cash holdings is at least in part driven through the imposition of liquidity covenants in debt contracts. 5. Conclusions This paper examines how CEO compensation incentives intended to align the interests of managers and shareholders influence the conflict between stockholders and bondholders by examining the effects of managerial compensation incentives on corporate cash holdings and the value of cash. We find that the vega of a CEO’s compensation is significantly positively related to cash holdings, which suggests that greater CEO risk-taking incentives encourage greater liquidity. This positive relation is consistent with two possible explanations. The costly contracting hypothesis asserts that firms with high vega incentives hold more cash because bondholders, anticipating more risk-taking behavior by the CEO, require additional cash as a cushion against possible losses. The costly external finance hypothesis asserts that firms with high vega incentives are more likely to face financial constraints and, therefore, build excess cash holdings as a hedge. These two hypotheses have opposite predictions for the value of cash to equityholders, which allows us to distinguish between them. Using the Faulkender and Wang (2006) approach to measure the marginal value of cash to equityholders, we find that high CEO vega is associated with a lower value of cash. We further find that this negative relation is robust after controlling for corporate governance, is stronger in firms with high leverage, and is reversed for unlevered firms. We also find evidence that high vega compensation increases the likelihood of liquidity covenants in loan documents. Overall, the evidence is consistent with the costly contracting hypothesis, which asserts that bondholders anticipate greater risk-taking in high vega firms and, therefore, require greater liquidity. However, we do find some support for the costly external finance
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hypothesis, because vega does not influence the value of cash for financially constrained firms. This suggests that the benefit of cash to equityholders of high vega, financially constrained firms compensates for the benefit that greater liquidity provides bondholders. References Acharya, V., Almeida, H., Campello, M., 2007. Is cash negative debt? A hedging perspective on corporate financial policies. Journal of Financial Intermediation 16, 515–554. Bates, T.W., Kahle, K.M., Stulz, R., 2009. Why do US firms hold so much more cash than they used to? Journal of Finance 64, 1985–2021 Bebchuk, L., Cohen, A., Ferrell, A., 2009. What matters in corporate governance. Review of Financial Studies 22, 783–827. Billett, M.T., Mauer, D.C., Zhang, Y., 2010. Stockholder and bondholder wealth effects of CEO incentive grants. Financial Management 39, 463–487. Brockman, P., Martin, X., Unlu, E., 2010. Executive compensation and the maturity structure of corporate debt. Journal of Finance 65, 1123–1161. Carpenter, J.N., 2000. Does option compensation increase managerial risk appetite? Journal of Finance 55, 2311–2331 Coles, J.L., Daniel, N.D., Naveen, L., 2006. Managerial incentives and risktaking. Journal of Financial Economics 79, 431–468. Core, J., Guay, W.R., 2002. Estimating the value of employee stock option portfolios and their sensitivities to price and volatility. Journal of Accounting Research 40, 613–630. Daniel, N.D., Martin, J.S., Naveen, L., 2004. The Hidden Cost of Managerial Incentives: Evidence from the Bond and Stock Markets. Unpublished Working Paper. Georgia State University, Atlanta, GA. Dittmar, A., Mahrt-Smith, J., 2007. Corporate governance and the value of cash holdings. Journal of Financial Economics 83, 599–634. Fama, E.F., French, K.R., 1993. Common risk factors in the returns on stocks and bonds. Journal of Financial Economics 33, 3–56. Faulkender, M., Wang, R., 2006. Corporate financial policy and the value of cash. Journal of Finance 61, 1957–1990. Fazzari, S., Hubbard, R.G., Peterson, B., 1988. Financing constraints and corporate investment. Brookings Papers on Economic Activity 1, 144–195. Gertler, M., Gilchrist, S., 1994. Monetary policy, business cycles and the behavior of small manufacturing firms. Quarterly Journal of Economics 109, 309–340. Gompers, P., Ishii, J., Metrick, A., 2003. Corporate governance and equity prices. Quarterly Journal of Economics 118, 107–155. Guay, W., 1999. The sensitivity of CEO wealth to equity risk: an analysis of the magnitude and determinants. Journal of Financial Economics 53, 43–71. Harford, J., Mansi, S.A., Maxwell, W.F., 2008. Corporate governance and firm cash holdings in the US. Journal of Financial Economics 87, 535–555. Hill, R.C., Griffiths, W.E., Lim, G.C., 2008. Principles of Econometrics. John Wiley & Sons, Hoboken, NJ. Jensen, M.C., 1986. Agency costs of free cash flow, corporate finance, and takeovers. American Economic Review 76, 323–329. Jensen, M.C., Meckling, W.H., 1976. Theory of the firm: managerial behavior, agency costs, and ownership structure. Journal of Financial Economics 3, 305–360. Kashyap, A.K., Lamont, O.A., Stein, J.C., 1994. Credit conditions and the cyclical behavior of inventories. Quarterly Journal of Economics 109, 565–592. Kennedy, P., 2003. A Guide to Econometrics. MIT Press, Cambridge, MA. Kim, C., Mauer, D.C., Sherman, A.E., 1998. The determinants of corporate liquidity: theory and evidence. Journal of Financial and Quantitative Analysis 33, 305–334. Lambert, R.A., Larcker, D.F., Verrecchia, R.E., 1991. Portfolio considerations in valuing executive compensation. Journal of Accounting Research 29, 129–149. Lamont, O.A., Polk, C., Saa-Requejo, J., 2001. Financial constraints and stock returns. Review of Financial Studies 14, 529–554. Opler, T., Pinkowitz, L., Stulz, R., Williamson, R., 1999. The determinants and implications of cash holdings. Journal of Financial Economics 52, 3–46. Ortiz-Molina, H., 2006. Top-management incentives and the pricing of corporate public debt. Journal of Financial and Quantitative Analysis 41, 317–340. Pinkowitz, L., Stulz, R., Williamson, R., 2006. Does the contribution of corporate cash holdings and dividends to firm value depend
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Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
The CEO pay slice$ Lucian A. Bebchuk a,b, K.J. Martijn Cremers c, Urs C. Peyer d,n a
Harvard Law School, USA NBER, USA c Yale School of Management, USA d INSEAD - The Business School for the Worlds Europe Campus, Boulevard de Constance, Fontainebleau 77305, France b
a r t i c l e i n f o
abstract
Article history: Received 12 May 2008 Received in revised form 23 June 2010 Accepted 20 July 2010 Available online 30 May 2011
We investigate the relation between the CEO Pay Slice (CPS)—the fraction of the aggregate compensation of the top-five executive team captured by the Chief Executive Officer—and the value, performance, and behavior of public firms. The CPS could reflect the relative importance of the CEO as well as the extent to which the CEO is able to extracts rents. We find that, controlling for all standard controls, CPS is negatively associated with firm value as measured by industry-adjusted Tobin’s q. CPS also has a rich set of relations with firms’ behavior and performance. In particular, CPS is correlated with lower (industry-adjusted) accounting profitability, lower stock returns accompanying acquisitions announced by the firm and higher likelihood of a negative stock return accompanying such announcements, higher odds of the CEO receiving a lucky option grant at the lowest price of the month, lower performance sensitivity of CEO turnover, and lower stock market returns accompanying the filing of proxy statements for periods when CPS increases. Taken together, our results are consistent with the hypothesis that higher CPS is associated with agency problems and indicate that CPS can provide a useful tool for studying the performance and behavior of firms. & 2011 Elsevier B.V. All rights reserved.
JEL classification: D23 G32 G38 J33 J44 K22 Keywords: Executive compensation Corporate governance CEO Options Tobin’s q Entrenchment CEO turnover Independent directors CEO chair Acquisitions Empire-building Opportunistic timing Backdating
$ This paper is a substantial revision of our earlier discussion paper ‘‘CEO Centrality’’ (Bebchuk, Cremers, and Peyer, 2007). We benefited from many valuable suggestions made by our referee, Kevin Murphy. We also benefited substantially from the helpful comments of Rajesh Aggarwal, Alma Cohen, Wayne Ferson, Will Goetzmann, Yaniv Grinstein, Dirk Jenter, Steve Kaplan, Felix Meschke, Mitchell Petersen, Paul Oyer, Charu Raheja, Eric Rasmusen, Catherine Schrand, Anil Shivdasani, Anand Venkateswaran, and seminar and conference participants at the University of Amsterdam, the University of Arizona, Columbia Business School, ESCP-EAP Paris, the University of Frankfurt, Harvard University, INSEAD, the University of Lausanne, the University of Oslo, the University of St. Gallen, the University of Southern California, the New York University, the University of Zurich–University of Pennsylvania Law and Finance conference, the annual Conference on Finance and Accounting 2007, the third Annual Conference on Empirical Legal Studies at Cornell Law School in 2007, the conference on Corporate Governance at Washington University in St. Louis, the American Finance Association annual meeting, the American Law and Economics Association annual meeting, the Conference on Corporate Governance Research at Drexel University, and the National Bureau of Economic Research Corporate Finance meeting. We are also grateful to Ronald Masulis for sharing with us his data on acquirer returns. For financial support, we would like to thank the Guggenheim Foundation, the John M. Olin Center for Law, Economics, and Business, and the Harvard Law School Program on Corporate Governance. n Corresponding author. Tel.: þ33 (0)1 60 72 4178; fax: þ 33 (0)1 60 72 4045. E-mail address:
[email protected] (U.C. Peyer).
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.05.006
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CEO turnover Variability of returns Pay distribution Internal pay equity
1. Introduction The inner workings of the top executive team, and their importance for firm performance, are hard to observe or quantify. In this paper, we aim to contribute to the subject by introducing a new measure pertaining to the relationship between the Chief Executive Officer (CEO) and the other members of the top executive team, as well as studying the relation between this measure and the performance and behavior of firms. Our new measure is CEO Pay Slice (CPS), which is defined as the fraction of the aggregate compensation of the firm’s top-five executive team captured by the CEO. By basing CPS on compensation information from executives that are all at the same firm, we control for any firm-specific characteristics that affect the average level of compensation in the firm’s top executive team. We find that CPS has a rich set of relations with a wide range of aspects of firms’ performance and behavior. In particular, higher CPS is associated with lower firm value as measured by Tobin’s q, lower accounting profitability, lower quality of acquisition decisions, higher odds of opportunistically timed option grants to the CEO, lower CEO turnover, and lower stock market returns accompanying the filing of proxy statements for periods when CPS increases. Our findings thus unearth a rich set of systematic relations between CPS and the value and outcomes of firms. Taken as a whole, our results indicate that CPS can provide a useful tool for research on firm performance and behavior, and that its relation with the value and behavior of firms is an important issue for study by financial economists. Our investigation of the relation between CPS levels and firm outcomes and behavior has two parts. The first part examines the relation between lagged CPS and firm value as measured by industry-adjusted Tobin’s q. We find a strong empirical relation between CPS and q. Controlling for the various factors that prior work has used in q regressions, a significant—and economically meaningful— negative correlation exists between CPS and industryadjusted q. We also find that the association between CPS and q is robust to the inclusion of several factors that might affect both q and CPS, such as the CEO’s tenure and status as founder or large owner or chair of the board, the size of the company’s aggregate top-five compensation relative to peer companies, the extent to which the CEO’s compensation is more incentive-based than the compensation of the other top executives, and the compensation inequality among the executives in the top team other than the CEO. We find that the identified negative correlation between CPS and Tobin’s q is robust to the addition of all of these controls as well as to controlling for lagged q, adding firm fixed effects, and trying to incorporate the
endogenous choice of CPS. The negative association between CPS and q exists both among firms whose aggregate top-five compensation is higher and for those where it is lower than their peers. The negative association between q and CPS is further concentrated among firms whose boards are entrenched (using measures of shareholder rights as in Gompers, Ishii, and Metrick, 2003; Bebchuk, Cohen, and Ferrell, 2009). In the second part of our analysis, we examine how CPS is associated with other dimensions of company behavior and performance, including ones that are commonly viewed as reflecting governance problems. These tests help to understand why CPS and firm value might be negatively related. First, CPS is negatively correlated with accounting profitability. Firms with high CPS tend to have a lower industry-adjusted operating income to assets ratio. Second, high-CPS firms tend to make worse acquisition decisions as judged by the market’s reaction to their acquisition announcements, using the data set of Masulis, Wang, and Xie (2007). If the acquiring firm has higher CPS, the stock return accompanying the acquisition announcement is lower and more likely to be negative. Third, firms with higher CPS are more likely to provide their CEO with opportunistically timed option grants. High CPS is associated with an increased likelihood of the CEO receiving a lucky option grant with an exercise price equal to the lowest price of the grant month. Fourth, CPS is associated with CEO turnover. The probability of a CEO turnover after bad performance is lower if CPS is higher controlling for the CEO’s length of service. Fifth, stock market returns accompanying the filing of proxy statements tend to be lower for periods when CPS increases.1 In interpreting our rich set of results, one should keep in mind that firms might differ in their CPS levels for two reasons. First, firms might differ in their optimal (or appropriate) CPS level, as the optimal CPS level for any given firm might depend on the CEO’s relative ability and contribution, as well as on the extent to which it is optimal for the firm to provide tournament incentives to executives. Second, firms might differ in how their CPS levels depart (if at all) from the optimal level for the firm. To the extent that the CEO has power and influence over the company’s decision making, the CEO might use this power and influence to raise CPS above its optimal level. In this case, the excess CPS—that is, the excess of the
1 Our earlier discussion paper (Bebchuk, Cremers, and Peyer, 2007) provides evidence that high CPS is also associated with greater tendency to reward the CEO for luck due to positive industry-wide shocks.
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actual CPS over the optimal CPS—reflects rents captured by the CEO and can be viewed as a product of agency (governance) problems. This separation of CPS into two components, optimal (or appropriate) CPS and excess CPS, is relevant for interpreting any identified association of CPS with firm characteristics or behavior. A correlation of a given variable with firm differences in observed CPS levels could be due to a correlation of the variable with the optimal level of CPS for a given firm or with excess CPS (or a correlation with both). Whether the second component exists at all depends on whether CPS is optimally selected. Under an optimal selection hypothesis, CPS is generally optimally selected and the second component is thus nonexistent. Under an agency (governance) hypothesis, CPS might not always be optimally chosen and CPS has a component that reflects rent-seeking and agency problems. The negative correlation we find between CPS and q rules out the joint hypothesis that CPS is chosen optimally to reflect the relative importance of the CEO in the top team and that firm value as measured by q is either uncorrelated or positively correlated with the optimal CPS level. Instead, this finding has two, not mutually exclusive, explanations. One is an optimal selection explanation: The optimal level of CPS or the relative importance of the CEO could be higher for lower value firms, and the identified pattern could be due to the tendency of such firms to choose high CPS levels. This possibility calls for further study, including the development of a formal theoretical framework for studying optimal levels of CPS. A second explanation for the negative correlation between CPS and firm performance is an agency (governance) problem explanation: High excess CPS could reflect agency and governance problems, which in turn bring about the identified pattern between lower firm value and higher CPS. While the identified correlation between CPS and Tobin’s q can theoretically be fully explained by optimal selection alone, some of our other results are supportive or at least consistent with the possibility that the association between CPS and lower q is at least partly driven by CPS reflecting governance problems. In particular, this is the case with respect to our findings that CPS is associated with opportunistic timing of CEO grants, worse acquisition decisions, more CEO luck-based pay, and lower probability of turnover in the event of bad performance, as well as our result that the negative association between q and CPS is concentrated among firms whose boards are entrenched. We should stress that, even if some firms have excessive CPS levels and actual CPS levels are correlated with excess CPS levels and agency problems, this is a mere correlation and it does not imply that firms with high (observed) CPS levels have governance problems and are made better off by reducing these levels. In some highCPS firms, an observed high level of CPS might be optimal given the firm’s circumstances and a reduction in the CPS level would make the firm worse off. Our work is related to several bodies of literature. To begin, some recent work has shown that the fraction of the top-five compensation received by CEOs has been trending up over time (Bebchuk and Grinstein, 2005;
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Frydman, 2005; Murphy and Zabojnik, 2007; Frydman and Saks, 2010). In contrast, we focus on the relations of this fraction with the performance and behavior of firms at any given time. Our work also relates to the literature examining how firm value as measured by Tobin’s q is associated with governance arrangements. For example, studies show that Tobin’s q is negatively correlated with the presence of staggered boards (e.g., Bebchuk and Cohen, 2005), the weakness of shareholder rights more generally (see e.g., Gompers, Ishii, and Metrick, 2003; Bebchuk, Cohen, and Ferrell, 2009; Cremers and Nair, 2005), and the presence of a large board (Yermack, 1996). We contribute to this literature by identifying yet another aspect of the firm’s governance arrangements—the CPS level—that is associated with Tobin’s q. In addition, this paper relates to work on stock market reaction to acquisition announcements. Financial economists have paid close attention to buyers’ willingness to make acquisitions, which, as measured by the stock market returns accompanying the acquisition announcement, the market views as value-decreasing (see, e.g., Lang, Stulz, and Walkling, 1991; Morck, Shleifer, and Vishny, 1990; Qiu, 2004; Moeller, Schlingemann, and Stulz, 2005). Masulis, Wang, and Xie (2007) show that the magnitude of the announcement returns are related to governance characteristics and, in particular, entrenchment provisions. We extend their work by showing that these returns are also negatively correlated with CPS even after controlling for entrenchment provisions. Similarly, our work is related to the literature on opportunistic timing of option grants and its relation to firm governance and structure (see, e.g., Yermack, 1997; Lie, 2005; Bebchuk, Grinstein, and Peyer, 2010). We extend this work by showing that, controlling for other governance provisions, firms with higher CPS are more likely to grant opportunistically timed options to the CEO. Our work is further related to the substantial literature on CEO turnover (see, e.g., Jenter and Kanaan, 2006; Kaplan and Minton, 2006). We extend this literature by showing that high CPS is associated with a lower CEO turnover controlling for performance.2 Two earlier studies have used different measures of CEO dominance within the top executive team. Morck, Shleifer, and Vishny (1989), in a study of alternative mechanisms for transfer of corporate control, define CEOs as powerful when no other person holds the title of president or chairman and no other person co-signs the letter to shareholders in the annual report. They find that more powerful CEOs are less likely to be replaced by the board but more likely to be replaced through a hostile takeover. More recently, in investigating whether CEO dominance is correlated with firm-specific variability of stock returns, Adams, Almeida, and Ferreira (2005) assume CEOs to be more powerful when they serve as chair of the board, when they are the only insider on the 2 While our analysis focuses on the relation between CPS and CEO turnover, Chang, Dasgupta, and Hilary (2010) examine a complementary question of whether abnormal stock returns around managerial departure announcements are related to CPS.
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board, and when they have the status of a founder. In this paper, we put forward CPS as a measure of CEO dominance that captures more than the formal status variables. CPS is positively correlated with such variables, but they explain only a small part of the variability in CPS. Finally, a growing literature is studying how the type and style of a CEO affects firm outcomes (see, e.g., Malmendier and Tate, 2009; Bertrand and Schoar, 2003). Our work seeks to highlight the importance for firm outcomes of another dimension concerning the CEO: the CPS. Our analysis is organized as follows. Section 2 describes our data and presents summary statistics. Section 3 analyzes the relation between CPS and Tobin’s q. Section 4 examines the relation between CPS and accounting profitability, abnormal acquirer returns, opportunistic timing of CEO grants, the probability of turnover in the event of bad performance, and abnormal returns around announcements of CPS changes. Finally, Section 5 concludes.
2. Data and summary statistics 2.1. The CEO Pay Slice (CPS) The CEO Pay Slice is defined as the percentage of the total compensation to the top five executives that goes to the CEO. In this section, we discuss our computation of CPS and give summary statistics. We compute the CPS using data from Compustat’s ExecuComp database from 1993 to 2004. Our main measure is based on the total compensation to each executive, including salary, bonus, other annual pay, the total value of restricted stock granted that year, the Black and Scholes value of stock options granted that year, longterm incentive payouts, and all other total compensation (as reported in ExecuComp item TDC1). While CPS can be computed for every firm-year, we restrict our sample to firm-years in which the CEO was in office for the entire year. This avoids observations with artificially low CPS due to the fact that a CEO has received compensation only for part of the year. Also, for some firm-years more than five executives are listed in ExecuComp. In such cases, we use only the five executives with the highest compensation.3 Because CPS is likely the product of many observable and unobservable dimensions of the firm’s top executives and management model, CPS could enable us to capture dimensions of the CEO’s role in the top team beyond the ones captured by other, previously examined variables such as whether the CEO also chairs the board. CPS is positively correlated with dummy variables for whether the CEO also chairs the board and whether the CEO is the 3 In our sample period, firms were required to report the compensation for anyone holding the office of CEO during the year, plus the four highest paid executive officers not including the CEO. Some firms voluntarily report the compensation for more executives than required. When restricting the sample to firms that report compensation for only five executives, our results continue to hold (not reported). If the firm reports compensation for fewer than five executives (uncommon), we exclude the firm to ensure that CPS remains comparable across firms.
only executive of the firm who is a member of the board.4 However, a regression of CPS on these two variables results in an adjusted R-squared of only 0.9%, which indicates that CPS captures other information not contained in those two variables.5 In addition, because CPS is calculated using the compensation figures for the top executives at the same firm, it directly controls for any firm-specific characteristics that affect the average level of executive compensation at the firm level. 2.2. Summary statistics Univariate statistics for the average CPS and the main variables used in this paper are shown in Table 1. The statistics are computed based on a panel data set of 12,011 firm-year observations that represent 2,015 different firms and 3,256 different CEOs between 1993 and 2004. In this time period, the average CPS was 35% and its standard deviation equals 11.4%. For the pertinent firm characteristics, we use various Compustat, Center for Research in Security Prices (CRSP), IRRC, and ExecuComp variables: Tobin’s q is defined as the market value of equity plus the book value of assets minus the sum of book value of common equity and deferred taxes, all divided by the book value of assets. Industry adjustments are made at the four-digit standard industrial classification (SIC) level, by subtracting the industry median Tobin’s q. Our definition of Tobin’s q is the one used by Kaplan and Zingales (1997) and subsequently also by Gompers, Ishii, and Metrick (2003).6 Industry-adjusted ROA is the return on assets computed as operating income divided by book value of assets minus the median ROA of the firms in Compustat in a given four-digit SIC industry and year. It is expressed in percentage terms. We report results in which both variables are winsorized at the 1 and 99 percentile, though results are robust to not winsorizing. The entrenchment index (Eindex) consists of six of the governance/shareholder rights provisions that are identified as those most relevant for shareholder value by Bebchuk, Cohen, and Ferrell (2009). The six provisions in the Eindex are classified boards, poison pills and golden parachutes, and supermajority voting requirements for charters, by-laws, and mergers. Eindex ranges between 0 and 6, where higher values indicate weaker shareholder 4 We use information from the Investor Responsibility Research Center (IRRC) to identify the chairman. If the item is missing we use the annual title from ExecuComp to identify whether the CEO is also holding the chairman position. 5 The rank correlation of CPS with a dummy variable for whether the CEO also chairs the board is 0.062 (significant at the 1% level) and the correlation of CPS with a dummy whether the CEO is the only executive of the firm who is a member of the board is 0.099 (significant at the 1% level). The second variable is related not only to the relative importance of the CEO within the top executive team but also to the relative importance of the executive team on the board (Raheja, 2005). 6 Tobin’s q is equal to the market value of assets divided by the book value of assets (Compustat item 6), where the market value of assets is computed as the book value of assets (item 6) plus the market value of common stock (item 199nitem 25, or if item 199 is missing, then item 24nitem 25) less the sum of book value of common stock (item 60, set to zero if missing) and balance sheet deferred taxes (item 74, set to zero if missing).
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Table 1 Descriptive statistics. CEO Pay Slice (CPS) is the fraction of the total compensation (ExecuComp item TDC1) to the group of top-five executives that is received by the Chief executive officer (CEO). Industry Median CPS is the median CPS in the four-digit standard industrial classification (SIC) group. Tobin’s q is defined as the market value of equity plus the book value of assets minus the book value of equity, all divided by the book value of assets. The industry adjustment is made at the four-digit SIC level using all Compustat firms. ROA is the return on assets computed as operating income divided by book value of assets. Eindex is the entrenchment index of Bebchuk, Cohen, and Ferrell (2009). Log Book Value is the log of the book value of assets. Insider Ownership is the fraction of shares held by all insiders as reported by ExecuComp. Capex/Assets is the ratio of capital expenditures to assets. Leverage is the long-term debt to assets ratio. R&D is the ratio of R&D to sales. If R&D is missing, it is set to zero and the dummy variable R&D Missing is set to one. Company Age is computed as the current year minus the year in which the company was first listed on the Center For Research in Security Prices (CRSP). Founder is a dummy equal to one if the CEO was already CEO when the firm first appeared on CRSP. CEO Outsider is a dummy equal to one if the CEO was working at the firm for less than one year before becoming CEO. Log Abnormal Total Compensation is the residual of a regression of total compensation of the topfive executives on Log Book Value with industry and year fixed effects. Relative Equity Compensation is the ratio of the fraction of equity compensation of the CEO to the average fraction of equity compensation of the other four top executives. The fraction of equity compensation is defined as EBC/TDC1, where EBC is the equity-based compensation calculated as the sum of the value of the restricted shares granted plus the Black and Scholes value of options granted and TDC1 is the total compensation from ExecuComp. CEO Ownership Z 20% is a dummy equal to one if the CEO holds at least 20% of outstanding shares. CEO Tenure is the number of years since becoming CEO. Diversification is a dummy variable equal to one if the firm reports more than one segment on Compustat’s segment database. CEO Is Chair is a dummy equal to one if the CEO is also the chairman of the board using Investor Responsibility Research Center (IRRC) and ExecuComp data. CEO Is Only Director is a dummy variable equal to one if the CEO is the only executive officer on the board. Number of VPs is the number of vice presidents among the top-five executives. We present the number of observations, the overall sample mean, and standard deviation, as well as the minimum and maximum values. Variable
CPS Industry Median CPS Industry-adjusted Tobin’s q Eindex Log Book Value Insider Ownership Insider Ownership2 ROA Capex/Assets Leverage R&D R&D Missing Company Age Founder CEO Outsider Abnormal Total Compensation (Log) Relative Equity Compensation CEO Ownership Z 20% CEO Tenure Diversified CEO Is Chair CEO Is Only Director Number of VPs
Number of observations
Mean
Standard deviation
Minimum
Maximum
8,659 8,683 8,557 8,683 8,663 8,683 8,683 8,662 8,662 8,647 8,683 8,683 8,683 8,683 8,680 8,651 8,683 8,683 8,139 8,662 8,683 8,683 8,683
0.357 0.336 0.339 2.227 7.689 0.061 0.009 0.037 0.183 0.196 0.121 0.517 25.992 0.144 0.153 0.115 1.106 0.045 7.736 0.580 0.729 0.507 2.577
0.114 0.035 1.095 1.294 1.699 0.070 0.030 0.090 1.997 0.164 4.616 0.500 18.805 0.351 0.360 0.672 0.710 0.206 7.172 0.494 0.444 0.500 1.273
0 0.089 1.32 0 0.644 0.000 0.000 0.475 19.9 0 0 0 0 0 0 3.84 0 0 0 0 0 0 0
1 0.587 5.77 6 13.9 0.825 0.681 0.238 132 1.87 0.31 1 78 1 1 5.03 6 1 52 1 1 1 4
rights or more entrenched management. As a robustness test, we have also used the Gompers, Ishii, and Metrick (2003) governance index (Gindex), which is based on a broader set of 24 governance provisions, and the results are qualitatively similar (not shown). Log Book value is the book value of assets. Insider Ownership is the fraction of shares held by insiders as reported by ExecuComp.7 Capex/Assets is the ratio of capital expenditures to assets. Leverage is the ratio of long-term debt to assets. R&D is the ratio of research and development to sales. If R&D is missing, it is set to zero and the dummy variable R&D Missing is set to one. Company age is computed as the current year minus the year in which the company was first listed on CRSP.
Next, we include several variables capturing CEO and top team compensation characteristics. Founder CEO is a dummy equal to one if the CEO’s tenure reported in ExecuComp started prior to the firm’s first listing in CRSP, which is assumed to be the initial public offering (IPO) year. There are 1,661 firm-year observations with a founder CEO, consisting of 284 different founder CEOs in our sample. CEO Is Outsider is a dummy equal to one if the CEO was at the firm less than one year before becoming CEO.8 Abnormal Total Compensation is the residual of the following industry and year fixed effects regression: log(total compensation to the top five executives combined) on a constant and log(book value of assets). The inclusion of this variable can thus be viewed
7 Just using CEO ownership, we find very similar results in the CPS regressions in Table 2. For the q regressions (Tables 3 and 4), CEO ownership and its square are less significant than Insider Ownership (not shown).
8 We use ExecuComp information on ‘‘joined company’’ and ‘‘became CEO.’’ A CEO is classified as an insider if the CEO has joined the company more than a year before becoming CEO and if either one data item is missing.
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as controlling for the aggregate quality or outside opportunities of the firm’s top executive team. We report results using industry classifications at the four-digit SIC level, but the results are robust to using two- or threedigit levels (not shown). Relative Equity Compensation captures the difference in pay-performance sensitivity between the CEO and other top executives, measured as the ratio of the fraction of equity compensation of the CEO to the average fraction of equity compensation of the other four top executives. Here, the fraction of equity compensation is defined as EBC/TDC1, where EBC is the equity-based compensation calculated as the sum of the value of the restricted shares granted plus the Black and Scholes value of options granted and TDC1 is the total compensation from ExecuComp. CEO OwnershipZ20% is a dummy equal to one if the CEO owns a stake of at least 20%. CEO Tenure is the number of years since becoming CEO. Diversification is a dummy variable equal to one if the firm reports more than one segment on Compustat’s segment database. The last three variables capture board characteristics. CEO Is Chair is a dummy based on ExecuComp and equal one if the CEO also chairs the board, in which case the CEO is likely to be more powerful. CEO Is Only Director is a dummy variable equal to one if the CEO is the only executive officer on the board. Finally, Number of VPs is the number of vice presidents among the top five executives using ExecuComp data. The latter two variables proxies are related to the firm’s organizational structure, e.g., whether or not the firm has more CEO-like executives who could run corporate divisions. The rank order correlation between contemporaneous and lagged CPS equals 44.2%. Other variables with high correlations with CPS are Industry Median CPS (25%), Relative Equity Compensation (35.3%), and Number of VPs (19.2%) (not reported). In Table 2, we report CPS regressions using a pooled panel with firm and year fixed effects and standard errors clustered at the firm level. We find that CPS is positively associated with Industry Median CPS, the Number of VPs on the board, the CEO Is Chair dummy, ROA, R&D expenses, Company Age, and Relative Equity Compensation, and that it has a non-linear relation to Insider Ownership.9 The CEO Is Only Director variable is not significant. The specification in Column 1 later is used as first-stage regressions in a system of equations, in which we try to incorporate the endogenous choice of CPS. The three variables assumed as instruments for CPS, i.e., variables that only affect firm value through CPS but not directly, are Industry Median CPS, Number of VPs, and CEO Is Only Director (the first three variables in Table 2). The first two are clearly the most important in Table 2, while the third has been used by previous literature as a proxy for the relative importance of the CEO (e.g., Adams, Almeida, and Ferreira, 2005).
9 We find that CEO Is Chair duality is related both to higher total CEO compensation and to lower total compensation of the other top four executives (controlling for industry, size, and year effects).
Abnormal Total Compensation of the top-five executive group has a negative coefficient that is marginally significant. To understand this further, in Column 2 we decompose this variable into cases in which the group is relatively highly paid (positive values) versus poorly paid (negative values). We find that the negative association between CPS and Abnormal Total Compensation is driven by firms with top teams that are relatively poorly paid. Specifically, CPS and Abnormal Total Compensation are negatively related only for firms in which the top executive team as a whole receives relatively low compensation. For firms with relatively high compensation for the top team, we find a significantly positive association. Thus, any deviation from the median total compensation seems to be related to a higher CPS. Finally, being a new CEO (tenure equal to one year) also has a negative association with CPS. 3. CPS and firm performance 3.1. How could CPS and firm performance be expected to correlate? Before proceeding, we first discuss alternative hypotheses as to how CPS can be expected to correlate with firm value and behavior. In thinking about this question, we distinguish two assumptions under which this question could be analyzed. 3.1.1. Optimal selection hypotheses Consider a case in which there are no agency problems and firms therefore generally set CPS at the optimal level according to the relative importance of the CEO in the top executive team. Absent agency costs, the compensation of the top executive team is set by the board without any undue influence by the CEO. In this optimal selection scenario, by definition, no firm would be able to increase its value by changing its CPS level. Still, CPS levels could relate to firm value to the extent that the optimal CPS level differs across firms. Optimal CPS levels can be expected to vary among firms, depending on several considerations. First, the optimal CPS level for any given firm depends on the pool of candidates from which the members of the top executive team are drawn, and the quality and outside opportunities of these candidates clearly differ from firm to firm. Second, the optimal CPS level depends on the extent to which it is desirable to provide tournament incentives to top executives other than the CEO.10 Third, the optimal CPS level depends on the extent to which it is desirable for the firm to have a dominant player model based on one especially important player rather than a management
10 A tournament environment can provide both positive and negative incentives to top executives other than the CEO (Milgrom and Roberts, 1992). On the one hand, a tournament could provide executives other than the CEO with incentives to excel to increase their chances of succeeding the CEO. On the other hand, a tournament could produce deadweight costs by, for example, causing executives vying for the CEO position to cooperate less with, or even seek to undermine, their rivals. These benefits and costs are likely to vary across firms.
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Table 2 CEO Pay Slice (CPS) regressions. Firm fixed effects regressions with t-statistics based on robust standard errors clustered at the firm level. Each regression includes year dummy variables (not shown). The dependent variable is CPS. CPS is the ratio of CEO total compensation to the sum of all top executives’ total compensation. Total compensation is data item TDC1 from ExecuComp. We limit the sample to firms with five or more executives listed in ExecuComp and use only the top-five executives determined by total compensation to form the denominator. We also require that the CEO is the same as last year and that last year he was in office for a full year. Industry Median CPS is computed as the median CPS of the same four-digit SIC industry in a given year. Number of VPs is determined based on ExecuComp data that identify the main position of the executive listed. See Table 1 for further variable descriptions. n, nn, and nnn indicate significance at 10%, 5%, and 1% level, respectively. Variables
CPS (1)
Industry Median CPS Number of VPs CEO Is Only Director CEO Is Chair Industry-adjusted Tobin’s q Eindex Log Book Value Insider Ownership Insider Ownership2 ROA Capex/Assets Leverage R&D R&D Missing Company Age Founder Abnormal Total compensation Abnormal Total Compensation (dummy¼ 1 if Abnormal Total Compensationo 0) Abnormal Total Compensation (dummy¼ 1 if Abnormal Total CompensationZ 0) Relative Equity Compensation CEO OwnershipZ20% CEO Tenure¼ 1 CEO Tenure¼ 2 CEO Tenure¼ 3 or 4 CEO Tenure¼ 5 or 6 CEO Tenure Missing Diversified CEO Outsider Number of observations R-squared Firm fixed effects Year dummies
nnn
0.492 (8.246) 0.0179nnn (10.59) 0.00442 (1.212) 0.0105nn (2.031) 0.00389 (1.431) 0.000231 ( 0.0815) 0.000548 ( 0.0911) 0.167nn ( 2.228) 0.275n (1.907) 0.0568nn (2.498) 0.000343 ( 0.801) 0.0223 ( 1.344) 0.00214nnn (14.27) 0.00195 ( 0.126) 0.00267nnn (3.081) 0.00111 (0.110) 0.00672n ( 1.785)
0.0537nnn (19.90) 0.00455 ( 0.415) 0.00747 ( 1.382) 0.000304 ( 0.0619) 0.00105 (0.246) 0.00476 (1.280) 0.00773 (0.617) 0.00688 ( 1.580) 0.00192 ( 0.215) 8,129 0.246 Yes Yes
(2) 0.491nnn (8.270) 0.0176nnn (10.51) 0.00454 (1.247) 0.0103nn (1.984) 0.00410 (1.521) 0.000347 ( 0.123) 4.70e-05 (0.00775) 0.168nn ( 2.233) 0.276n (1.915) 0.0556nn (2.436) 0.000320 ( 0.752) -0.0217 ( 1.304) 0.00216nnn (13.95) 0.00232 ( 0.151) 0.00261nnn (3.009) 0.00149 (0.149)
0.0125nn ( 2.047) 0.000204 ( 0.0353) 0.0537nnn (19.94) 0.00516 ( 0.470) 0.00747 ( 1.381) 0.000381 ( 0.0777) 0.000989 (0.232) 0.00477 (1.287) 0.00776 (0.619) 0.00688 ( 1.589) 0.00174 ( 0.196) 8,129 0.246 Yes Yes
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model based on a team of top executives.11 Fourth and related, the optimal CPS level reflects whether it is desirable to concentrate dollars spent on incentive generation on the CEO instead on other top executives. Existing theory does not provide an unambiguous prediction as to how the above considerations relate to firm value, allowing three different optimal selection hypotheses: Hypothesis O1. Optimal CPS is positively correlated with firm performance. It might be argued that a dominant player model and powerful tournament incentives are especially valuable for high value firms with high growth opportunities that need to be decisively and vigorously pursued. It might also be that high value firms are especially likely to attract star CEOs. Hypothesis O2. Optimal CPS is negatively correlated with firm performance. A dominant player model and powerful tournament incentives might be especially needed for low value firms in distress that need to be turned around. It might also be that low value firms are unlikely to be able to attract a good executive bench. Hypothesis O3. Optimal CPS is uncorrelated with firm performance. It might be that the factors making high or low CPS optimal vary in ways that are distributed independently of firm value. Thus, to the extent that the association between CPS and firm performance is determined by optimal selection, an empirical investigation is necessary to choose among the competing Hypotheses O1–O3. 3.1.2. Agency (governance) hypotheses The discussion above assumed that all CPS levels are optimally set and that CPS measures the relative importance of the CEO in the top executive team. However, because choices are partly made by agents whose decisions are influenced by private interests and thus involve agency costs, some CPS choices could depart from their optimal level. Under this alternative hypothesis, CPS could reflect the extent to which a CEO’s power and influence is used to push for a dominant player model and an increase in CEO compensation, leading to a higher CPS than optimal for the firm. In this case, CPS would (partly) reflect rents that the CEO has been able to extract by influencing the pay-setting process to allocate a larger slice of the aggregate compensation of the top executive to himself or herself.12 11 A dominant player model has both benefits and costs. On the one hand, a dominant player model could provide clarity, steadiness, and reduction in the cost of decision making. On the other hand, a large body of literature, starting with Shaw (1932), extolls the benefits of group instead of individual decision making, and some experimental data show that groups often outperform individuals in decision making (see Bainbridge, 2002, for a survey). Furthermore, a dominant player model and the high CPS coming with it can lead to resentment on the part of the other members of the top team (Brill, 1993; Cook, 1990). All of these benefits and costs are unlikely to be invariant across firms. 12 In the management literature, there is related work on the psychology of managerial decisions that uses the pay of the CEO relative to other top executives as a measure of CEO self-importance or narcissism. For example, Hayward and Hambrick (1997) and Chatterjee and Hambrick (2007) use the CEO cash compensation divided by the cash
Assuming that some CPS levels depart from the optimum, let ‘‘excess CPS’’ denote the excess (if any) of a given observed CPS level over the optimal level. As long as excess CPS levels are not perfectly negatively correlated with optimal CPS levels, observed CPS levels can be expected to be positively correlated with excess CPS levels. In this case, a correlation between excess CPS levels and a given variable (e.g., Tobin’s q) can produce a correlation between observed CPS levels and this variable. A high level of excess CPS—that is, a substantial departure from the optimal CPS level—can be viewed as a reflection of significant governance problems. It could reflect a state of affairs in which the CEO is making significant use of the CEO’s power. Accordingly, high levels of excess CPS, and the governance problems they reflect, would be correlated with low firm value. Thus, to the extent that observed CPS levels do contain a potentially significant component of excess CPS, such presence can be expected to produce a negative correlation between CPS and firm value, which provides the following agency (governance) hypothesis: Hypothesis G. Excess CPS levels, and in turn also observed CPS levels, are negatively correlated with firm performance. 3.1.3. Firm performance and endogenously determined CPS In this section, our primary empirical proxy for firm performance is the industry-adjusted Tobin’s q. This follows a substantial literature on the association between firm value and various corporate arrangements, which extensively used Tobin’s q as a measure of firm value (e.g., Demsetz and Lehn, 1985; Morck, Shleifer, and Vishny, 1988; Lang and Stulz, 1994; Yermack, 1996; Gompers, Ishii, and Metrick, 2003). In studying the empirical association between CPS and Tobin’s q, it is critical to recognize that CPS is an endogenously determined variable, which itself could be determined by factors that are also related to firm value. We try to account for this in several different ways when relating CPS to Tobin’s q. First, we use lagged not contemporaneous CPS.13 Second, we industry-adjust CPS by deducting the median CPS in each firm’s industry at the four-digit SIC level in that year. Third, we control for lagged Tobin’s q. Fourth, we add firm fixed effects, effectively considering how changes in CPS are associated with changes in firm value (Table 3). In addition, in later parts of this paper, we take additional steps. To begin, we add controls that could affect the endogenous choice of CPS (Section 3.2). We also use the CEO changes in our sample to investigate whether we can find evidence for optimal selection, i.e., whether a low level of Tobin’s q is associated with an increase in the level of CPS for the new relative to the old CEO (footnote continued) compensation of the second-highest-paid officer in a small sample of firms (about one hundred companies) as one among a set of indicators for CEO self-importance, and they find some evidence of a negative association between CEO self-importance and firm performance. 13 As we use lagged CPS, we require that the CEO remains in place the following year. The results are qualitatively similar without this constraint (not shown).
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Table 3 Tobin’s q and CEO Pay Slice (CPS). This table presents ordinary least squares regressions in Columns 1 and 2 and firm fixed effects regressions in Columns 3 and 4. Regression 4 reports the second-stage results for a system of equations estimation, using a firm fixed effects instrumental variable regression. The first-stage CPS regression equals CPS, t 1 ¼a þb X þc Zþ ui þeit, and corresponds to Column 1 of Table 2. The instruments in the first stage are (all measured at t 1): industry median CPS, the number of vice presidents in the top-five executives, and a dummy variable for CEO is the only director. The Hansen J statistic is a test of overidentifying restrictions, where the p-value is reported between parentheses. t-statistics are based on robust standard errors clustered at the firm level. In all regressions, we include year dummies (not shown). The dependent variable is the four-digit SIC industry-adjusted Tobin’s q. Tobin’s q is defined as the market value of equity plus the book value of assets minus the sum of book value of equity and deferred taxes, all divided by the book value of assets. The industry adjustment is done by subtracting the industry median Tobin’s q from the firm Tobin’s q. The dependent variable is winsorized at the 1% and 99% level. CPS is the ratio of CEO total compensation to the sum of all top executives’ total compensation and is expressed as decimals. Total compensation is data item TDC1 from ExecuComp. See Table 1 for further variable descriptions. The sample size is smaller for data availability reasons related to the board membership of the CEO. n, nn, and nnn indicate significance at 10%, 5%, and 1% level, respectively. Variables
CPS, t 1
Industry-adjusted Tobin’s q (1)
(2)
(3)
0.475nnn ( 3.226)
0.177nn ( 2.470)
0.229nn ( 2.347)
CPS, t 1 (endogenous) 0.287nnn (11.10) 0.00855 (0.459) 0.399nnn ( 9.949) 0.564 (1.284) 0.850 ( 1.535) 1.470nnn (5.841) 0.00387 (1.412) 0.402nnn ( 3.070) 0.00357 (0.622) 0.0193 (0.301) 0.0322nnn (6.672) 0.0187 ( 0.302) 0.0113 (0.611) 0.00131 (0.126) 0.0569 ( 1.140) 0.0766nn ( 2.216) 0.0545n ( 1.678) 0.0497 ( 1.478) 0.0415 ( 1.540) 0.0578 ( 0.786) 0.0162 ( 0.521) 0.0304 (0.438) 0.0249 ( 0.737)
1.013nnn (7.227)
0.767nnn (48.03) 0.00377 ( 0.738) 0.00901n ( 1.686) 0.0773 (0.333) 0.118 ( 0.286) 0.851nnn (5.342) 0.000583 (0.163) 0.186n ( 2.519) 0.0101n (1.708) 0.00287 ( 0.215) 0.000962nn (2.342) 0.00540 ( 0.249) 0.0183 (1.417) 0.00211 ( 0.232) 0.0463 ( 1.203) 0.00733 ( 0.290) 0.00930 (0.414) 0.00516 ( 0.250) 0.0215 ( 1.119) 0.0508nn ( 1.967) 0.0623nnn ( 4.179) 0.0140 (0.609) 0.0214 ( 1.218) 0.111n (1.820)
8,661 0.192 No Yes
8,077 0.702 No Yes
8,077 0.273 Yes Yes
Industry-adjusted Tobin’s q, t 1 Eindex Log Book Value Insider Ownership Insider Ownership2 ROA, t Capex/Assets Leverage R&D R&D Missing Company Age
0.0966nnn ( 5.874) 0.0379nn ( 2.408) 0.413 (0.633) 2.113n ( 1.655) 4.089nnn (10.95) 0.00584 (1.374) 0.739nnn ( 3.759) 0.0169nnn (2.745) 0.192nnn ( 4.396) 0.00328nn ( 2.358)
Founder Abnormal Total Compensation, t 1 Relative Equity Compensation, t 1 CEO Ownership Z 20% CEO Tenure ¼ 1 CEO Tenure ¼ 2 CEO Tenure ¼ 3 or 4 CEO Tenure ¼ 5 or 6 CEO Tenure Missing Diversified CEO Outsider CEO Is Chair Constant
Number of observations R-squared Firm fixed effects Year dummies Hansen J statistic
(4)
0.649nn ( 1.981) 0.290nnn (31.60) 0.00884 (0.542) 0.397nnn ( 15.87) 0.463 (1.262) 0.693 ( 1.038) 1.468nnn (12.52) 0.00427 (1.231) 0.393nnn ( 4.297) 0.00374nn (2.533) 0.0105 (0.163) 0.0325nnn (6.305) 0.0201 ( 0.372) 0.00207 (0.131) 0.00408 ( 0.367) 0.0552 ( 1.059) 0.0848nn ( 2.525) 0.0594nn ( 2.110) 0.0495nn ( 2.018) 0.0417n ( 1.673) 0.0493 ( 0.726) 0.0164 ( 0.611) 0.0408 (0.943) 0.0215 ( 0.773)
8,077 0.270 Yes Yes 1.31 (25%)
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(Section 3.3). In addition, we analyze a system of equations to simultaneously estimate the associations between firm value and CPS, using a two-stage procedure (Section 3.3). Furthermore, we examine whether the association between Tobin’s q and lagged CPS is different in subsamples, where optimal selection or agency problems or both could differ (Section 3.5). Finally, to shed light upon the identified association between Tobin’s q and CPS, we investigate in Section 4 whether CPS is related to a host of other firm outcomes and behavior. These include accounting profitability as measured by industry-adjusted ROA (Section 4.1), acquirer stock market returns when the firm announces a takeover (Section 4.2), opportunistic timing of CEO stock option grants (Section 4.3), CEO turnover (Section 4.4), and abnormal stock returns around announcements of CPS changes (Section 4.5). In all of these settings, we discuss the extent to which the relation between CPS and firm behavior is consistent with either of the two main hypotheses or interpretations of CPS. 3.2. Association between CPS and Tobin’s q In this subsection, we discuss our empirical results concerning the association between lagged CPS and firm performance as measured by industry-adjusted Tobin’s q.14 Our regressions include the standard controls used in the literature. In particular, we control for firm size (logs of book value of assets), insider ownership and insider ownership squared (see McConnell and Servaes, 1990), profitability (ROA), the ratio of capital expenditures to assets (Capex/Assets), leverage, the ratio of R&D expenditures to sales (R&D), a dummy for missing R&D data, log of the age of the firm (see Shin and Stulz, 2000), and year dummies. We also include the entrenchment index (Eindex) of Bebchuk, Cohen, and Ferrell (2009). The pooled panel regression result with year dummies, displayed in Column 1 of Table 3, indicates that higher CPS has a strong association with lower firm value. All standard errors are clustered at the firm level to account for correlations within firm observations. The economic significance is strongest for lagged CPS: A one standard deviation change in the value of CPS (equal to 11.73%) is associated with a reduction in next year’s Tobin’s q of 5.5% ( ¼11.73% 0.475). In further tests (not included to save space, available upon request), we find that the results are 14 Tobin’s q is the ratio of market-to-book of the firm. Specifically, we calculate Tobin’s q as (data199ndata25þdata6 data60 data74)/data6, where data199 is the stock price at the end of the fiscal year, data25 is the number of shares outstanding, data6 is the book value of total assets, data60 is the book value of equity, and data74 is the amount of deferred taxes. If data199 is missing, we use data24 instead. If data74 is missing, it is set to zero. We winsorize q at 1%, but our main results are robust when we do not do so. The results are also robust to using [ln(Tobin’s q) ln(industry median of Tobin’s q)] or ln[Tobin’s q (industry median of Tobin’s q)], and when we remove the bubble years of 1999 and 2000. An alternative specification of our regressions, with log TQ as the dependent variable and SIC codes as industry fixed effects, yields similar results throughout. Using the Fama and French classification of 48 industry groups, instead of four-digit SIC codes, yields similar results throughout (not shown).
robust to using lagged industry-adjusted CPS (i.e., deducting the median CPS each year of all firms with the same four-digit SIC code). In subsequent columns, we add lagged Tobin’s q as a control, effectively considering changes in firm value. We further add seven other controls that could be related to the choice of CPS under the optimal selection hypothesis. In particular, we examine whether the negative association between q and CPS is driven by factors not included in standard q regressions that are correlated both with CPS and with a lower q.15 3.2.1. Founder CEO Founder CEOs could have relative importance in the top team in ways not expressed by their annual executive compensation. In addition, Amit and Villalonga (2006) find that Fortune 500 firms that are founder-managed have a higher value. If CPS was lower when the CEO is a founder, then the relation between CPS and Tobin’s q could be due to the omitted founder effect. 3.2.2. Abnormal Total Compensation CPS could be related to the level of the firm’s aggregate top-five compensation relative to peer companies, and this aggregate top-five compensation could be related to firm value. For example, a firm with a CEO whose compensation is on par with peer companies could have a high CPS to the extent that its other top executives have abnormally low compensation due to low quality and poor outside opportunities. In such a firm, firm value likely is low, and so is the aggregate compensation of the top executives other than the CEO as well as of the top-five team. The inclusion of this variable can thus be viewed as controlling for the aggregate quality or outside opportunities of the firm’s top executive team. 3.2.3. Relative Equity Compensation This captures the difference in pay-performance sensitivity between the CEO and other top executives. Aggarwal and Samwick (2003) show that CEOs capture a substantial fraction of the aggregate incentive pay awarded to the top-five executive team. When an executive is paid an especially large fraction of compensation in equity, the executive’s compensation level could increase to compensate the executive for the risk-bearing costs involved. Thus, CPS might be high because the CEO receives a compensation package that is more performance-based relative to that of the other top executives. 3.2.4. CEO OwnershipZ20% CPS could be related to whether the CEO has a large ownership, whereas previous literature has identified that CEO ownership and firm value are correlated. There are 525 firm-year observations of 61 different CEOs owning at least a 20% stake in the company. 15 In addition, in untabulated results, we use both lagged Equity-CPS and lagged Non-Equity-CPS in the Tobin’s q regressions. We find that there is a negative and significant coefficient for both variables and that the coefficient on Non-Equity-CPS tends to be more negative (or larger in absolute value).
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3.2.5. CEO Tenure CPS could increase with the CEO’s tenure, and the CEO’s tenure could be related to the firm’s value. Therefore, we include dummy variables for different levels of the CEO tenure, with tenure of 7 years and more being the hold-out group. 3.2.6. Diversification When a firm is diversified, some of the top executives might be heads of divisions. CPS thus could be related to whether the firm has a diversified structure, which has been found to affect firm value (e.g., Lang and Stulz, 1994), and thus our results could be driven by this relation. 3.2.7. CEO Outsider Parrino (1997) examines the characteristics of new CEOs who enter their job at the firm, finding that firms with insider CEOs could be more heterogeneous in nature, implying that CEO talent from inside the firm is harder to replicate. Further, Murphy and Zabojnik (2007) show that outsider CEOs receive more compensation, which could increase their CPS and could indicate unique skills. 3.2.8. CEO Is Chair Adams, Almeida, and Ferreira (2005) use this as a proxy for the relative importance of the CEO to the firm. The result in Column 2 of Table 3 indicates that the negative association between industry-adjusted Tobin’s q and lagged CPS is robust to adding these controls. The coefficient of lagged CPS is significant at 5%, albeit with a reduced magnitude. The main effect comes from adding lagged Tobin’s q, which greatly increases the R-squared and renders many of the standard controls insignificant or much less significant than before. Most of the additional controls are not statistically significant, with the main exception being the Diversification dummy. In Column 3, we add firm fixed effects to the specification with the additional controls of Column 2, thus considering how changes in Tobin’s q are related to changes in lagged CPS. The association between q and lagged CPS remains robustly negative, though again statistical significance is reduced (the coefficient for lagged CPS has a t-statistic of 2.35). 3.3. Optimal selection and firm value: CEO changes and a system of equations The negative correlation between CPS and Tobin’s q identified in Section 3.2 is inconsistent with two of the optimal selection hypotheses discussed in Section 3.1. In particular, our findings are inconsistent with the hypothesis that firms’ optimal CPS levels are positively correlated with firm value (Hypothesis O1) or that firms’ optimal CPS levels are uncorrelated with firm value (Hypothesis O3). Thus, to the extent that CPS levels are largely optimally set, our findings are consistent only with the second optimal selection Hypothesis O2. In addition to the optimal selection Hypothesis O2, our findings are consistent with the agency (governance) hypothesis (Hypothesis G) that CPS levels are correlated with excess CPS levels which are in turn negatively correlated with firm value due to agency problems.
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It is worth stressing that the two remaining hypotheses are not mutually exclusive. The agency (governance) hypothesis does not assume that all firms depart from optimal CPS levels, only that some do. The negative correlation between CPS and q might thus be due to a negative correlation between optimal CPS levels and q as well as a correlation between actual CPS levels and excess CPS. Therefore, we frame our investigation below as an examination of whether the identified pattern is fully driven by optimal selection or is at least partly due to agency (governance) problems. To this end, in the firm fixed effects regression in Column 4 of Table 3 we try to instrument for CPS using a two-staged estimation process in which we specify a system of equations to explicitly estimate the association between endogenously determined lagged CPS and Tobin’s q. In the first stage (results presented in Column 1 of Table 2), we use CPS as the dependent variable to estimate how it is related to various firm characteristics. Three instruments are used to identify variation in CPS that only affects Tobin’s q through CPS: Industry Median CPS, the number of vice presidents on the board, and whether the CEO is the only director. We also add contemporaneous Tobin’s q as an explanatory variable, next to the various controls and firm fixed effects. Column 1 in Table 2 shows that only the first two (Industry Median CPS and the Number of VPs) are significantly related to CPS. We use the Industry Median CPS, as the optimal CPS is likely to be different across industries and the choice of industry is to a large extent exogenous. Murphy (1999), for example, shows that executive compensation has important industry-wide components. The use of the number of VPs is motivated by two observations: First, Kale, Reis, and Venkateswaran (2009) identify this as an important determinant of tournament incentives, i.e., the more executives with an equal job title, the more the tournament incentives. Second, if the number of VPs is higher, the more likely it is that the other four executives are similar, which might allow the CEO to clearly differentiate himself or herself from others and thus justify taking a larger slice of the top-five pie. The results of the second-stage estimation of Tobin’s q on the (estimated) endogenously determined lagged CPS are presented in Column 4 of Table 3. We also include lagged Tobin’s q, the standard and additional controls in Columns 2 and 3 of Table 3, and firm fixed effects.16 The coefficient of lagged CPS is negative and significant at 5% (t-statistic of 1.98), suggesting that the negative association between Tobin’s q and CPS is robust to incorporating the endogenous choice of CPS. We report the results from the Sargan and Hansen test of overidentifying restrictions (see, e.g., Hayashi, 2000, pp. 227–228, 407 and 417), which tests the null hypothesis that the instruments are valid instruments (i.e., uncorrelated with the error term in the second stage) and that the excluded instruments are correctly excluded from the estimation second-stage regression. A rejection would cast
16 The regressions are estimated using Stata 9’s extra command xtivreg2 written by Schaffer (2007).
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doubt on the validity of the instruments. Using robust standard errors, this null hypothesis is not rejected. Furthermore, we verify that no strong evidence for reverse causality exists, i.e., that firms with low q tend to hire CEOs with high CPS. Specifically, we investigate all 1,326 CEO changes indentified from ExecuComp in the universe of firms in our sample and compare the CPS of CEOs joining low q versus high q firms. If low value firms are more optimally run by CEOs with a high CPS, then we would expect to find that the new CEOs of low value firms have, on average, a significantly higher CPS than new CEOs of high value firms. However, we find neither significant differences in CPS, measured in the first full fiscal year after taking office, nor industry-adjusted CPS between newly hired CEOs in lower valued (with an industry-adjusted Tobin’s q that is negative or with a Tobin’s q below one) versus higher valued firms (results not included to save space, available upon request). We note that no significant difference exists between low and high value firms in terms of the increase in CPS that the new CEO receives relative to the predecessor. The p-value of the difference in the change of CPS from the old CEO to the new CEO across firms with Tobin’s q above versus below one has a p-value of 11%, and using negative versus positive industry-adjusted Tobin’s q the p-value is 82%. Thus, this analysis does not support the hypothesis that the identified negative correlation between CPS and q can be explained by a tendency of low value firms to provide new CEOs with relatively high levels of CPS. In further unreported results, we separately consider CEOs hired from the outside versus inside CEOs. We find that CPS increases significantly if the new CEO is hired from outside the firm, but this is not related to the firm’s level of (industry-adjusted or not) q. The negative correlation between Tobin’s q and lagged CPS is thus robust to controlling for lagged Tobin’s q and for many other additional factors introduced in this subsection. It is also robust to adding firm fixed effects and incorporating the endogenous choice of CPS. In the most extensive specification with firm fixed effects without instruments, Column 3 in Table 3, the coefficient of lagged CPS equals 0.229 with a t-statistic of 2.3. That means that the economic significance of a one standard deviation increase in the value of CPS is associated with a reduction in next year’s Tobin’s q of about 2.7% (¼11.73% 0.229).17 Meanwhile, the coefficient on the instrumented CPS in Column 4 of Table 3 equals 0.649, such that one standard deviation increase in CPS is associated with a 7.6% lower Tobin’s q (¼11.73% 0.649).
3.4. Firm value and CPS versus Gini Top 5 The recent study of Kale, Reis, and Venkateswaran (2009) finds a positive contemporaneous association between Tobin’s q and another measure of compensation inequality in the top executive team, Gini Top 5, which is 17 In addition, all results in Table 3 are robust to excluding firm-year observations with a founder CEO or when the CEO holds at least 20% equity ownership.
defined as the Gini coefficient for the top five executives including the CEO. A higher Gini Top 5 is viewed by Kale, Reis, and Venkateswaran (2009) as reflecting greater inequality and thus stronger tournament incentives. Because Gini Top 5 is naturally positively correlated with CPS, it is worth investigating the robustness of our result to including lagged Gini Top 5 and, more generally, to reconcile our respective results. Gini Top 5 is a product of both (i) the extent to which the CEO’s compensation differs from the average compensation of the other members of the top executive team, a factor captured by CPS, and (ii) the extent to which compensation is unequal among these other members of the team. In particular, CPS captures only the pay inequality between the CEO and the average pay of the other top executives, while Gini Top 5 (used by Kale, Reis, and Venkateswaran, 2009) is driven by the inequality between all top five executives and thus by both factors (i) and (ii). To separately capture factor (ii), we use the variable Gini Other 4, which is defined as the Gini coefficient for the four executives in the top team other than the CEO.18 Table 4 presents q regressions to which the Gini variables are added (including many controls but not reporting their coefficients to save space). In Column 1, we include only lagged Gini Top 5 to replicate the results for Kale, Reis, and Venkateswaran (2009), and we find a positive and significant coefficient. In Column 2, we use both lagged CPS and lagged Gini Top 5, and find that both are significant with a negative coefficient for CPS and a positive coefficient for Gini Top 5. However, once the additional controls from Table 3 plus firm fixed effects are added in Column 3, lagged Gini Top 5 is significant only at the 10% level with a coefficient that is about half the coefficient in Column 1, while CPS remains significant (t-statistic of 2.10).19 Thus, the negative correlation between CPS and q is robust to the inclusion of Gini Top 5. How does one reconcile the negative correlation between q and CPS with the positive correlation between q and Gini Top 5? In Columns 4 and 5 of Table 4, we use lagged Gini Other 4 in conjunction with lagged CPS, with firm fixed effects used in Column 5 but not in Column 4. In both regressions, lagged CPS remains negative and significant, which reinforces the conclusion that, putting aside how compensation is distributed among the other four, CPS, our chief variable of interest, is negatively correlated with q. 18 Gini Top 5 is positively correlated with CPS and Gini Other 4. When compensation among the four top executives other than the CEO is equal, CPS and Gini Top 5 would give an identical rank ordering. Across firms with identical CPS, differences in Gini Top 5 are driven by differences in Gini Other 4. The correlation between CPS and Gini Top 5 (Gini Top 4) is 62% ( 10%), between Gini Top 5 and Gini Top 4 equals 54%, and their averages (standard deviations) are 0.32 (0.15) and 0.27 (0.20), respectively, such that the slightly lower Gini Top 4 average indicates that the compensation of the top four non-CEO executives is a bit more similar relative to the top five executives including the CEO. 19 Kale, Reis, and Venkateswaran (2009) use contemporaneous specifications and find a positive correlation between Gini and firm value. Our finding that lagged Gini is positively (albeit less significantly) related to firm value supports the importance of tournament incentives and suggests that CPS captures a different effect.
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Table 4 Tobin’s q and CEO Pay Slice (CPS) with additional control variables. This table presents ordinary least squares (OLS) regressions in Columns 1, 2 and 4, and firm fixed effects regressions in Columns 3 and 5, with t statistics based on robust standard errors clustered at the firm level. The dependent variable is the four-digit SIC industry-adjusted Tobin’s q. The dependent variable is winsorized at the 1% and 99% level. Gini Top 5 is the Gini coefficient of the top-five executives, including the CEO, while Gini Other 4 is the gini coefficient of the top team excluding the CEO. See Table 1 for a description of the other variables. Included in the regression, but not displayed for brevity, are the following variables: Constant (in OLS regressions), Eindex, Log Book Value, Insider Ownership, ROA, Capex/Assets, R&D, R&D Missing, Company Age, Diversified, CEO Outsider, CEO is Chair, CEO Tenure missing, CEO Tenure¼ 5 or 6, CEO Tenure ¼3 or 4, and year dummies. n, nn, and nnn indicate significance at 10%, 5%, and 1% level, respectively. Variables
Industry-adjusted Tobin’s q (1)
(3) nnn
CPS, t 1 Gini Top 5, t 1
(2)
0.2075nn (1.986)
0.804 ( 4.757) 0.353nn (2.182)
(4) nn
0.172 ( 2.102) 0.104n (1.744)
Gini Other 4, t 1
0.489 ( 3.434)
-0.147nn (-2.089)
0.225nn (2.497)
0.0619 (1.056) 0.293nnn (11.42)
7,828 0.193 No Yes Yes No
7,300 0.273 Yes Yes Yes Yes
nnn
Tobin’s q, t 1
Number of observations R-squared Firm fixed effects Year dummies Standard control variables (Column 1 of Table 3) Additional control variables (Columns 2–4 of Table 3)
(5) nnn
0.291 (10.08) 7,828 0.194 No Yes Yes No
At the same time, Gini Other 4 is positive in both regressions, though it is significant only in the regression without firm fixed effects in Column 4. Thus, the positive correlation between q and Gini Top 5 seems to come from a positive correlation between Gini Other 4 and q. Thus, the results in Kale, Reis, and Venkateswaran (2009) seem to be driven by Gini Other 4, the pay inequality among the group of top executives other than the CEO. Investigating the relation between Gini Other 4 and firm performance and behavior could be a worthwhile subject for future research. 3.5. Interaction of CPS with shareholder rights and compensation levels This subsection considers whether the negative association between q and CPS is more prevalent in certain subsets of firms. We run firm fixed effects regressions as in Column 3 of Table 3 with additional interaction terms but report only the interaction variables to conserve space. 3.5.1. Shareholder Rights We first investigate whether firms with high versus low entrenchment levels, as measured by the Eindex (Bebchuk, Cohen, and Ferrell, 2009), display different sensitivities between CPS and firm value. In firms with higher entrenchment levels, the CEO and the board are relatively insulated from market discipline and the threat of removal. For those firms, the potential for agency problems in general, and departures from optimal levels of CPS in particular, could be higher. The first column of Table 5 displays the results of replacing lagged CPS with two variables to the specifications of Table 3: the interactions of lagged CPS with dummies of high versus low Eindex, where high (low)
7,828 0.198 No Yes Yes No
7,300 0.281 Yes Yes Yes Yes
Eindex is a dummy equal to one if the firm’s Eindex is above (below or equal to) the sample median’s Eindex in a given year. The lower value for firms with higher CPS is driven by firms with high entrenchment as measured by the Eindex. This suggests a complementary relation, as it is only firms with both entrenchment and high CPS that have lower firm values. Thus, the data suggest that the negative correlation between CPS and firm value is more pronounced in firms with high entrenchment levels. In such firms, the potential for departures from optimal CPS levels may well be more significant, and as a result the distribution of actual CPS levels could be influenced to a greater extent by the distribution of excess CPS levels and the governance problems they reflect. Thus, the finding reported in this subsection is consistent with the hypothesis that the negative correlation between CPS and q is at least partly due to CPS levels, including a component that reflects agency problems. 3.5.2. Quality of the pool of executive candidates We create two more subsets of firms: one in which the abnormal compensation paid to the top five executives (including the CEO) is positive or negative, and another in which the abnormal compensation to the top four executives (excluding the CEO) is positive or negative. Firms with relatively high abnormal compensation of the topfive executives as a group could be in a particularly challenging business environment and need to attract or retain valuable talent. Firms that pay the top executives other than the CEO more than peer companies could face a pool of executive candidates that has a different quality. For example, the negative association between q and CPS could be driven by firms with lower value having trouble attracting enough talent to their top executive team, thus
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Table 5 CEO Pay Slice (CPS) and Tobin’s q in different subsamples. The table shows firm fixed-effects regressions with year dummies and t-statistics based on robust standard errors clustered at the firm level. The dependent variable is the four-digit SIC industry-adjusted Tobin’s q. Tobin’s q is defined as the market value of equity plus the book value of assets minus the sum of the book value of equity and deferred taxes, all divided by the book value of assets. The dependent variable is winsorized at the 1% and 99% level. CPS is the ratio of CEO total compensation to the sum of all top executives’ total compensation and is expressed as decimals. Total compensation is data item TDC1 from ExecuComp. The industry adjustment in CPS and Tobin’s q are made at the four-digit SIC level. Low Eindex is defined as a firm with Eindex ¼ 0 or 1. High Eindex are firms with Eindex from 2 to 6. Abnormal Total Compensation is the residual of the following industry and year fixed effects regression: log (total compensation to the top five executives)¼ constant and log (book value of assets), with year and industry fixed effects. Abnormal compensation other 4 is the residual of the following industry and year fixed effects regression: log (total compensation to the four non-CEO executives) ¼constant and log (book value of assets), with year and industry fixed effects. Abnormal Total Compensation Pos (Neg) and Abnormal compensation other 4 Pos (Neg) are dummy variables equal to one if Abnormal Total Compensation or Abnormal compensation other 4 is positive (negative). For additional variable definitions, see Table 1. Included in the regression, but not displayed for brevity, are the following variables: lagged Industry-adjusted Tobin’s q, Eindex, Log Book Value, Insider Ownership, Insider Ownership2, ROA, Capex/Assets, Leverage, R&D, R&D Missing, Company Age, Founder, CEO Ownership Z 20%, CEO Tenure, Diversified, CEO Is Chair, and year dummies. n, nn, and nnn indicate significance at 10%, 5%, and 1% level, respectively. Variables
Industry-adjusted Tobin’s q (1)
CPS, t 1 High Eindex CPS, t 1 Low Eindex High Eindex
(2)
(3)
0.270 ( 2.14) 0.111 ( 1.1) 0.096 (1.17)
0.241nnn ( 2.19) 0.055 ( 0.43) 0.121 (2.03)nnn
CPS, t 1 Abnormal Total Compensation Pos CPS, t 1 Abnormal Total Compensation Neg Abnormal Total Compensation Pos
0.168nn ( 2.01) 0.145nn ( 1.96) 0.014 ( 0.16)
CPS, t 1 Abnormal compensation other 4 Pos CPS, t 1 Abnormal compensation other 4 Neg Abnormal compensation other 4 Pos
0.163n ( 1.76) 0.222nn ( 2.02)
CPS, t 1 CEO Outsider CPS, t 1 CEO Not Outsider Firm fixed effects Additional control variables Year dummies Number of observations R-squared
(4)
nn
Yes Yes Yes 8,100 0.27
by necessity focusing on attracting the best possible CEO. In other words, the CPS may be high because the firm’s bench has relatively lower quality. The interaction of CPS with whether or not the other four top executives (excluding the CEO) are paid better or worse relative to their peers can directly investigate this possibility. Column 2 (3) of Table 5 shows the interactions of lagged CPS with dummy variables indicating whether the abnormal total compensation of the top-five (top-five team other than the CEO) executives is positive or negative. The negative association between lagged CPS and q is present among both subsets of firms that pay their topfive executives more than peer companies and firms that pay these executives less than peer companies. However, the coefficient estimate is significant only for those firms whose abnormal total compensation is positive. This finding is consistent with the interpretation that high CPS is particularly negatively associated with firm
Yes Yes Yes 8,077 0.27
Yes Yes Yes 8,096 0.27
Yes Yes Yes 8,100 0.27
value if total compensation to the top-five executives is in excess of what comparable firms in the industry and of similar size pay. The findings in Column 3 do not provide support for the hypothesis that the negative association between lagged CPS and q is driven by the quality of the pool of executive candidates (poor bench) faced by firms with lower industry-adjusted value because both interaction terms are significant. Finally, we investigate whether the negative relation between lagged CPS and firm value is particular to firms with outside versus inside CEOs. Research stressing the difference between firms with inside and outside CEOS include Murphy (2002), Murphy and Zabojnik (2007), and Cremers and Grinstein (2009). Column 4 shows that both types of firms display a negative, and at least marginally significant, association between lagged CPS and q. This suggests that it is unlikely that our finding of a negative correlation is driven by firms in which performance is bad
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and that have to recruit a CEO from the outside who needs to be compensated more highly. 4. CPS and company decisions and behavior Thus far we have focused on the relation between CPS and one measure of firm outcomes and performance: Tobin’s q. We now turn to examining whether CPS is associated with several other significant aspects of firms’ decisions and behavior. This section provides a critical counterpart to Section 3, which focuses on the association between CPS and firm value. In particular, this section can shed light on the reasons that high-CPS firms seem to have lower value. As such, this inquiry can help in assessing whether cross-sectional differences in CPS could be at least partly due to agency (governance) problems instead of just differences in optimal CPS levels. While a low Tobin’s q could be due to such problems, an optimally governed firm might also have low Q due to its circumstances. In contrast, some of the aspects of firm outcomes and behavior considered in this section, such as the poor quality of acquisition decisions, are likely to be correlated with suboptimal decision making and thus can help to further test the agency (governance) explanation. We consider in turn five aspects of firms’ decisions and outcomes: accounting profitability (Section 4.1), quality of acquisition decisions as judged by the stock market’s reaction to their announcement (Section 4.2), opportunistic timing of CEO option grants (Section 4.3), CEO turnover (Section 4.4), and the stock market returns accompanying the filing of proxy statements for periods with changes in CPS (Section 4.5). 4.1. Accounting profitability and CPS The first dimension of firm outcomes and performance we consider is that of accounting profitability. Our dependent variable is accounting profitability as proxied by ROA, defined as net income divided by the book value of assets, industry-adjusted using the median profitability of the four-digit SIC industry in a given year using all firms in Compustat, and winsorized at the 1 and 99 percentiles. Table 6 reports pooled panel regressions using robust standard errors that are clustered at the firm level, and all specifications include year dummies. In Column 1, we use lagged CPS next to lagged Tobin’s q and the various standard controls we used in the q regressions (see Table 3). In the second column, we add the additional controls from Table 3 plus firm fixed effects to Column 1. Finally, in Column 3, we use the instrumented lagged CPS from Column 1 of Table 2 together with firm fixed effects. In the specifications without firm fixed effects, the coefficient on lagged (industry-adjusted) CPS is negative and clearly significant throughout. The effect of CPS is also economically meaningful. Using the estimate in Column 1, a one standard deviation increase in CPS (0.1172) is associated with a decrease of industry-adjusted ROA by 0.48% (¼ 0.1172n 4.094). Given the average ROA of 3.7%, the impact of a one standard deviation change in CPS corresponds to a change of about 10% of the mean value. If
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we include firm fixed effects in column 2, the coefficient on lagged CPS remains negative but is less significant with a t-statistic of about 1.8, while the coefficient on the instrumented CPS in Column 4 is again significant with a t-statistic of 2.0. The negative association of CPS with (industryadjusted) accounting profitability is consistent with and reinforces our earlier finding that high CPS is associated with lower firm value as measured by Tobin’s q. 4.2. CPS and acquirer returns To gain insight into our finding that high-CPS firms display a lower firm value, we ask whether such firms are more likely to make suboptimal acquisition decisions. In studying this issue, we follow the study of Masulis, Wang, and Xie (2007). This study investigates the negative correlation between firm value and shareholder rights, measured by the Gindex [the governance index of Gompers, Ishii, and Metrick (2003), consisting of 24 shareholder rights provisions] or the Eindex, by asking whether weaker shareholder rights are associated with lower levels for the stock returns accompanying bidders’ announcements. The Masulis, Wang, and Xie study finds that announcement returns for acquirers with high entrenchment levels are significantly lower, and it concludes that the low value of high-entrenchment firms could be at least partly due to the bad acquisition decisions they make. Using the same data, we add CPS in the year prior to the acquisition announcement as another explanatory variable. Our test asks whether, controlling for the level of entrenchment, high CPS is associated with lower stock returns upon the announcement of an acquisition as well as with a higher likelihood of a negative stock return upon such an announcement. We start with the 3,333 events from Masulis, Wang, and Xie (2007).20 The sample is based on acquisitions recorded by the Securities Data Corporation (SDC) between January 1, 1990 and December 31, 2003. Because we require that CPS is available at the fiscal year-end prior to the takeover bid, our sample is reduced to 1,241 events.21 For this subsample, we find an average (standard deviation) abnormal announcement return in the 11 days around the announcement date of 0.26% (6.60). These are very similar to the values of 0.22% (6.59) reported by Masulis, Wang, and Xie (2007) for the full sample, and it is thus unlikely that the restrictions imposed by the availability of CPS introduce any particular bias. Table 7 shows the results for two sets of regressions. Columns 1 and 2 are ordinary least squares (OLS) regressions with the abnormal announcement return of the bidder in the 11 days around the initial announcement as the dependent variable (cumulative abnormal return, CAR[ 5, þ5]). Columns 3 and 4 are logit regressions in 20 For a detailed description of the sample and the selection process, see Masulis, Wang, and Xie (2007), pp. 5 6. We thank Ronald Masulis for sharing these data. 21 We have CPS data from 1993 onward and only use CPS when the CEO is not changing during the year.
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Table 6 Return on assets (ROA). The dependent variable is the industry-adjusted operating income divided by book value of asset ratio. The industry adjustment is made at the fourdigit SIC level by year and by subtracting the industry median (using all firms in Compustat) ROA from the firm’s ROA. The dependent variable is winsorized at the 1% and 99% level and is expressed in percentage terms. All regressions include year dummies (not shown) and standard errors are clustered at the firm level. Regression 1 is ordinary least squares (OLS). Regressions 2 and 3 are firm fixed effects regressions. Regression 3 reports the second-stage results for a system of equations estimation, using a firm fixed effects instrumental variable regression. The first-stage CEO Pay Slice (CPS) regression equals CPS, t 1¼ aþb X þc Zþ ui þeit, and corresponds to Column 1 of Table 2. The instruments in the first stage are (all measured at t 1): industry median CPS, the number of vice presidents in the top-five executives, and a dummy variable for CEO is the only director. Included in the regression, but not displayed for brevity, are the following variables: Constant, Diversified, CEO Is Chair, CEO Tenure Missing, CEO Tenure ¼5 or 6, CEO Tenure ¼3 or 4, and year dummies. t-statistics are based on robust standard errors clustered at the firm level. n, nn, and nnn indicate significance at the 10%, 5%, 1% level, respectively. Variables
CPS, t 1
Industry-adjusted ROA (1)
(2)
4.094nnn ( 3.174)
2.388n ( 1.787)
CPS, t 1 (instrumented) Industry-adjusted Tobin’s q, t 1 Eindex Log Book Value Insider Ownership, t 1 Insider Ownership2, t 1 Capex/Assets Leverage R&D R&D Missing Company Age
1.899nnn (10.73) 0.218n (1.728) 0.480nnn (3.452) 7.544nn (1.999) 0.760 ( 0.109) 0.00947 (0.162) 8.629nnn ( 6.383) 0.184nnn ( 8.485) 0.673n ( 2.062) 0.0205n (2.399)
Founder Abnormal Total Compensation, t 1 Relative Equity Compensation, t 1 CEO OwnershipZ 20% CEO Tenure¼ 1 CEO Tenure¼ 2 CEO Outsider Number of observations R-squared Firm fixed effects
8,672 0.130 No
which the dependent variable is equal to one if the CAR was negative and zero otherwise. Both types of regressions use robust standard errors that are clustered at the firm level to account for correlations if firms make multiple acquisitions. The main variable of interest is the CPS of the bidder, computed at the fiscal year-end prior to the takeover bid. In Columns 1 and 2, we find that the coefficient is negative and significant at the 10% level even after controlling for other determinants found to be significant in Masulis, Wang, and Xie (2007). In particular, CPS has
1.490nnn (7.640) 0.154 ( 0.693) 1.083n (1.796) 2.956 (0.507) 0.885 ( 0.116) 0.0231 ( 1.021) 13.01nnn ( 6.401) 0.0192n ( 2.056) 0.595 (0.657) 0.0930 ( 1.357) 1.249n ( 1.724) 0.0500 (0.221) 0.663nnn ( 4.464) 1.201 ( 1.529) 0.390 ( 0.891) 0.447 ( 1.088) 1.113 (1.273) 8,181 0.081 Yes
(3)
3.192nn (1.962) 1.458nnn (13.56) 0.156 ( 0.797) 1.056nnn (3.553) 3.931 (0.893) 2.436 ( 0.303) 0.0271 ( 0.647) 13.10nnn ( 12.23) 0.0208 ( 1.169) 0.681 (0.893) 0.0964 ( 1.567) 1.244n ( 1.920) 0.143 (0.761) 0.610nnn ( 4.562) 1.218n ( 1.960) 0.306 ( 0.758) 0.394 ( 1.165) 1.012n (1.949) 8,181 0.077 Yes
additional explanatory power over and above the entrenchment Eindex (Column 1) or the governance Gindex (Column 2) and over and above additional proxies for power such as the CEO also being the chair and the CEO being the only director among the top-five executives. Economically, the coefficient on the CPS variable of 0.023 indicates that a one standard deviation increase in CPS (in this sample that is 0.12) is associated with a reduction of the announcement return of 0.276% (0.12 2.30). Given the average market value of the bidder in our sample of $6,358 million, a one standard
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Table 7 CEO Pay Slice (CPS) and acquirer returns. The sample consists of 1,241 takeover announcement events from the sample of Masulis, Wang, and Xie (2007). The dependent variable is the cumulative abnormal announcement return (CAR) of the bidder in the 11 days around the announcement (CAR[ 5,þ 5]) in Regressions 1, and 2 and a dummy equal to one if the CAR is negative in Regressions 3 and 4. Regressions 1 and 2 (3 and 4) are OLS (logit) regressions with t-statistics based on robust standard errors and errors clustered at the firm level. Robust t-statistics are in parentheses. CPS is the ratio of CEO to the sum of all top executives’ compensation. CPS is based on total compensation as measured by data item TDC1 from ExecuComp containing salary, bonus, other annual compensation, total value of restricted stock granted, Black and Scholes value of stock options granted, long-term incentive payouts, and all other total incentive compensation. Gindex is the governance index of Gompers, Ishii, and Metrick (2003). Eindex is the entrenchment index of Bebchuk, Cohen, and Ferrell (2009). Fraction Blockowners is the fraction of the shares outstanding owned by institutional blockholders. Log Book Value (Bidder) is the book value of the bidder at the end of the fiscal year prior to the takeover. Relative Deal Size is the ratio of the deal value (from SDC) to the market value of equity of the bidder at the fiscal year-end prior to the takeover. Tobin’s q is the market-to-book ratio of the bidder at the fiscal year-end prior to the takeover. Leverage is the ratio of book value of long-term debt to assets. Herfindahl is based on sales of firms in the same four-digit SIC industry. Run-up is the cumulative stock return in the year prior to the takeover. High-Tech Dummy is equal to one if the firm operates in an industry with four-digit SIC code of 3570, 3571, 3572, 3576, 3577, 3661, 3674, 4812, 4813, 5045, 5961, 7370, 7371, 7372, or 7373. Cash Used (Stock Only) Dummy is equal to one if the bidder pays at least a part in cash (all in equity). The status of the target is private, public, or subsidiary indicated by the respected dummy variables. CEO Is Chair is a dummy equal to one if the CEO is also the chairman and zero otherwise. Year dummies are included but omitted to save space. The R-squared reported for the logit regression is a pseudo R-square. n, nn, and nnn indicate significance at 10%, 5%, and 1% level, respectively. Variables
CPS (Bidder) Eindex (Bidder)
CAR[ 5,þ 5] (1)
(2)
(3)
(4)
0.0230n ( 1.784) 0.493nnn ( 4.106)
0.0227n ( 1.769)
0.0113nn (2.177) 0.0959nn (2.141)
0.0111nn (2.146)
0.0254 (0.978) 0.251n ( 2.153) 0.750 ( 0.598) 0.0229 ( 0.146) 2.196n (1.678) 5.306n (1.954) 1.368n ( 2.284) 1.084n ( 1.724) 0.00530 (1.152) 0.925n ( 1.828) 1.648 (0.445) 2.214 (0.599) 0.187 (0.0504) 0.290 ( 0.711) 3.248 (0.820)
0.179nnn ( 2.755) 0.0285 (1.090) 0.217n ( 1.882) 0.764 ( 0.602) 0.0129 (0.0815) 2.150 (1.633) 5.939n (2.118) 1.380n ( 2.318) 1.020 ( 1.621) 0.00571 (1.235) 0.917n ( 1.799) 1.182 (0.289) 1.790 (0.439) 0.292 ( 0.0715) 0.323 ( 0.792) 3.912 (0.896)
0.0131 ( 1.219) 0.0614 (1.415) 0.231 (0.756) 0.00564 ( 0.128) 0.163 ( 0.351) 2.164 ( 1.630) 0.196 (1.276) 0.244 (1.441) 0.000366 ( 0.220) 0.523nnn (2.913) 0.341 ( 0.226) 0.511 ( 0.338) 0.0207 (0.0137) 0.187 (1.323) 1.067 ( 0.675)
0.0285 (1.270) 0.0138 ( 1.291) 0.0554 (1.276) 0.233 (0.758) 0.0133 ( 0.303) 0.144 ( 0.308) 2.292n ( 1.717) 0.195 (1.289) 0.224 (1.318) 0.000438 ( 0.264) 0.518nnn (2.882) 0.243 ( 0.152) 0.420 ( 0.262) 0.123 (0.0770) 0.193 (1.372) 1.141 ( 0.680)
1,241 0.098
1,241 0.094
1,241 0.053
1,241 0.051
Gindex (Bidder) Fraction Blockholders (Bidder) Log Book Value (Bidder) Relative Deal Size Tobin’s q (Bidder) Leverage (Bidder) Herfindahl (Bidder) Run-up (Bidder) High-Tech Dummy (Bidder) Cash Used Dummy Stock Only Dummy Private (Target) Subsidiary (Target) Public (Target) CEO Is Chair Constant Number of observations R-squared
Dummy¼1 if CAR Negative
deviation increase in CPS results in a loss of about $18 million per acquisition announcement. The effect of a one standard deviation change in CPS is thus in the same order of magnitude as the effect from adding one more provision in the Eindex (the coefficient on the Eindex in Column 1 is 0.493) and is more than twice the effect from adding one more provision in the Gindex (the coefficient on the Gindex in Regression 2 is 0.179).
The coefficients on CPS in Columns 3 and 4 are positive and significant at the 5% level, indicating that high-CPS firms are more likely to make acquisitions judged by the market to be value-destroying, i.e., acquisitions in which the bidder announcement return is negative. Economically, the coefficient of 0.0113 implies that a one standard deviation increase in CPS increases the chances of an acquisition being judged to be value-destroying by the
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market by 15% (exp(0.12 1.13) ¼1.15). This is again of similar magnitude to increasing Eindex by one and of substantially higher magnitude than increasing Gindex by one. From this analysis, we conclude that one potential reason for the lower valuation of firms with high CPS is that high-CPS firms make acquisitions viewed less favorably by the market and, in particular, are more likely to make acquisitions viewed as value-destroying by the market. These findings are consistent with the hypothesis that cross-sectional differences in CPS levels are at least partly due to and reflective of differences in agency (governance) problems. 4.3. CPS and opportunistic option grant timing This subsection considers the relation between CPS and the occurrence of opportunistically timed option grants to the CEO. Yermack (1997) shows that option grants are opportunistically timed, being systematically followed by abnormal positive stock returns, and Lie (2005) shows that the abnormal stock returns around CEO option grants are at least partly due to backdating. The literature on opportunistic timing has also shown an association between such timing and the quality of firm governance (see, e.g., Bizjak, Lemmon, and Whitby, 2009; Heron and Lie, 2009; Yermack, 1997). We examine in this subsection whether opportunistic timing is related in any systematic fashion to CPS. We use the standard data in current work on opportunistic timing—the Thomson Financial’s insider trading database, which is available from 1996 onwards We focus on lucky grants, at-the-money grants awarded on a date with a stock price equal to the lowest price of the month. Bebchuk, Grinstein, and Peyer (2010) show that lucky grants occur with a substantially higher frequency than could be explained by pure luck and that they provide a useful proxy for opportunistically timed grants. We start with a sample of 11,712 firm-year observations from Bebchuk, Grinstein, and Peyer (2010), from which we use only those where the CEO did receive an option grant, leaving a sample of 8,823 firm-year observations (though results are robust to using all observations). We also consider a sample in which all five top executives receive an option grant, which further reduces to sample to 7,243 firm-year observations. We run four logit regressions in which the dependent variable is a dummy variable called Lucky, which is equal to one if the firm granted its CEO a lucky option grant during the year and zero otherwise. The first and fourth regressions are pooled logit regressions with the robust standard errors clustered at the firm level, using the sample in which the CEO receives an option grant in the first logit and the sample in which all top-five executives receive an option grant in the fourth logit. The second and third regressions include firm and CEO fixed effects, respectively, and use the sample in which the CEO receives an option grant. The controls included are Insider Ownership, Size, Industry (High-Tech Dummy), and a proxy for stock return volatility (computed as the standard deviation of daily stock returns over a year) to
account for the fact that opportunistic timing is more profitable when stock return volatility is high. All four regressions include year dummies as well. The results are displayed in Table 8. In all four specifications, the coefficient of the CPS variable is positive and significant (at 95% confidence), indicating that a higher CPS is positively correlated with opportunistic timing of option grants. In unreported regressions, we replace CPS with industry-adjusted CPS and find that the coefficient is also positive and significant. Overall, our findings indicate that high CPS is correlated with opportunistic timing of option grants, which is consistent with the notion that high CPS is correlated with agency (governance) problems. Finally, we consider whether the probability of Lucky grants for top executives other than the CEO is related to CPS. To that end, we construct a variable termed Sumlucky, which is the number of lucky grants among the top-five executives (including the CEO). As shown in Regression 5, this is strongly negatively related to CPS, suggesting that high-CPS CEOs are more generous to themselves than to their close colleagues when it comes to opportunistically timed options. This findings is consistent with high CPS being associated with CEOs with more self-importance or narcissism (Hayward and Hambrick, 1997; Chatterjee and Hambrick, 2007).22 4.4. CPS and CEO turnover We have seen that firms with higher CPS have lower firm value and accounting profitability and make acquisition decisions that are viewed less favorably by the market. It could thus be expected that the CEOs of such firms are replaced more often unless the high CPS is at least partly due to agency problems in the first place, which could make CEO replacement more difficult and unlikely. We explore this possibility by testing whether, controlling for performance, CEO turnover is related to CPS. Table 9 displays the results of logit regressions where the dependent variable is equal to one if there is a CEO turnover in year t. We use the ExecuComp data set to identify CEO turnover, which we define as taking place if the CEO title in this data set has changed from one person to another. We find 1,326 turnovers in our sample of 9,571 firm-years with available data on the prior-year CPS. The independent variables of interest in Column 1 are the CPS at the end of the preceding year and the interaction between CPS and the stock return. The control variables include the stock return of the company during the year and dummies for the year of the CEO’s service (we do not use tenure as a continuous variable because its 22 The sample is considerably smaller here, as it relies on matching all top executives by name from Thompson Financial’s insider trading database to ExecuComp. A match requires that the last names and initials of the first names are the same and no other such combination existed in the company in the year. However, many names are written differently in the databases that are likely the same (e.g., Robert and Bob), such that our match is of limited quality. However, there is unlikely to be a bias in how names are reported in the various places and CPS or Lucky. Finally, alternative specifications in which we count only the other top four lucky grants as the dependent variable result in very similar results, as does an ordered logit regression.
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Table 8 CEO Pay Slice (CPS) and opportunistic timing of option grants. The sample consists of 8,823 firm-year observations between 1996 and 2004 in which the CEO did receive an option grant during the year (Regressions 1 3) or 7,243 observations in which all top-five executives have received an option grant during the year (Regression 4). The dependent variable, Lucky, is a dummy equal to one if the firm has provided at least one option grant to the CEO during the year in which the grant day was the day with the lowest stock price of the month. Option grant information is from Thompson Financial’s insider trading database. For details on the definition of the variable and the sample, see Bebchuk, Grinstein, and Peyer (2010). Regression 5 further restricts the sample to firms in which all five top executives grants could be identified in Thompson Financial. The dependent variable, Sumlucky, is the number of lucky grants among the top-five executives (including the CEO). The independent variables are CPS, the ratio of CEO to the sum of all top executives’ total compensation, is based on total compensation as measured by data item TDC1 from ExecuComp containing salary, bonus, other annual compensation, total value of restricted stock granted, Black and Scholes value of stock options granted, long-term incentive payouts, and all other total incentive compensation; High Tech Dummy is a dummy equal to one if the firm operates in an industry with four-digit SIC code of 3570, 3571, 3572, 3576, 3577, 3661, 3674, 4812, 4813, 5045, 5961, 7370, 7371, 7372, or 7373; Insider Ownership is the fraction of shares held by insiders as reported by ExecuComp; Log Book Value is the log of the book value of assets; Eindex is the entrenchment index of Bebchuk, Cohen, and Ferrell (2009); Stdev Stock Return is the standard deviation of daily stock return over a calendar year. The first and forth regressions are logit regressions with errors clustered at the firm level with no firm or CEO fixed effects. The second regression is a firm fixed effects logit regression, the third is a CEO fixed effects logit regression, and the fifth is an OLS regression with errors clustered at the firm level. n, nn, and nnn indicate significance at 10%, 5%, and 1% level, respectively. Year dummies and a constant (in Regressions 1, 4, and 5) are included but omitted to save space. Variables
CPS High-Tech Dummy Insider Ownership Insider Ownership2 Log Book Value Eindex Stdev Stock Return
Lucky
Sumlucky
(1)
(2)
(3)
(4)
(5)
3.706nnn (14.08) 0.192 (1.638) 2.127 (1.548) 3.047 ( 0.839) 0.0293 (1.237) 0.0256 (0.944) 0.068n ( 1.797)
7.322nnn (13.99)
9.885nnn (13.81)
2.564 (1.132) 2.390 ( 0.475) 0.443nnn (3.082) 0.132 (1.440) 0.100 ( 1.484)
0.623 ( 0.214) 6.429 (0.841) 0.456nn (2.327) 0.168 (1.424) 0.058 ( 0.740)
3.873nnn (12.42) 0.227n (1.753) 2.248 (1.288) 4.670 ( 0.844) 0.040 (1.477) 0.024 (0.773) 0.086n ( 1.890)
8,823 No No Yes No
8,823 Yes No Yes No
8,823 No Yes Yes No
7,243 No No Yes Yes
0.755nn ( 2.109) 0.193 (1.428) 2.225 ( 1.573) 4.427 (1.440) 0.004 ( 0.183) 0.003 (0.0954) 0.050 (1.300) 0.315nnn (3.48) 1,529 No No Yes Yes
Lucky Number of observations Firm fixed effects CEO fixed effects CEO receives option grant All five top executives receive option grant
effect on turnover might not be monotonic). The coefficient on CPS is negative and significant, indicating that CEOs with high CPS are less likely to be replaced. The interaction can answer the question whether high-CPS CEOs are less likely to experience turnover even if their stock performance is bad. The coefficient on the interaction variable is positive, and marginally significant, indicating that turnover is less performance-sensitive for high-CPS CEOs.23 To assess the economic significance of the result in Column 1, we consider the effect of a 10% increase in CPS on the performance sensitivity of CEO turnover. The coefficient on stock return is 0.350, implying that with a 50% stock return, CEO turnover probability increases
23 Powers (2005) suggests computing the marginal effect (basically the local derivate at the mean of the variables) to get the correct test statistic. Doing so confirms and strengthens the significance of our results. For example, in Regression 2 we find that the marginal effect is positive (0.144) with a standard error of 0.033, making it significant at the 1% level, with similar results for the other interaction variables.
by 19% (exp( 0.5 0.350) 1). The coefficient on the interaction term between the stock return and industryadjusted CPS is 2.201, implying a reduction in the performance sensitivity of 10% (exp( 0.5 1.684 0.1) 1), about a one-third reduction in the performance sensitivity of turnover. Results are robust to adding firm fixed effects in Column 2. Following Jenter and Kanaan (2006), Column 3 splits the stock return into firm-specific and market returns, where firm specific returns are defined as the difference between the overall stock return and the market return. Consistent with Jenter and Kanaan (2006) we also find that CEO turnover is sensitive to market returns, albeit not significantly so. The main conclusion is that CEO turnover is less sensitive to firm-specific returns for CEOs with a high industry-adjusted CPS. If a lower performance sensitivity is an indication of more agency problems (e.g., Kaplan and Minton, 2006), then our findings here are consistent with the notion that cross-sectional differences in CPS are associated with differences in the magnitude of agency problems. These findings could also help to
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Table 9 CEO turnover and CEO Pay Slice (CPS). The sample consists of 9,571 firm-year observations with available data on CEO turnover in year t and independent variables the year prior to the turnover. Regressions 1 and 3 (2 and 4) are logit (firm fixed effects) regressions with t-statistics based on robust standard errors clustered at the firm level. We display the coefficients and t-statistics in brackets underneath. The dependent variable is a dummy equal to one if the CEO for firm i in year t 1 is not the same as in year t (there are 1,326 turnovers). CPS is based on total compensation as measured by data item TDC1 from ExecuComp containing salary, bonus, other annual compensation, total value of restricted stock granted, Black and Scholes value of stock options granted, long-term incentive payouts, and all other total incentive compensation. The tenure dummies are equal to one if a CEO has exactly that number of years of tenure. Zero is the hold-out group, i.e., CEOs who in year t 1 just joined the company. Stock return, t 1 is the return over the calendar year prior to the CEO turnover. Market Return is the value-weighted CRSP return. Firm-Specific Return is the difference between the firm and the market return. CEO Age 460 Dummy is a dummy equal to one if the CEO’s age is above 60 using data from ExeuComp and IRRC. CEO Is Chair is a dummy equal to one if the CEO is also the chairman and zero otherwise. n and nnn indicate significance at 10% and 1% level, respectively. Variables
CPS, t 1 Stock Return, t 1 Stock Return, t 1 CPS, t 1
CEO turnover dummy (1)
(2)
(3)
(4)
2.550nnn ( 5.613) 0.350 (1.141) 2.201n (2.348)
4.121nnn ( 10.37) 0.372 (1.442) 2.379nnn (2.947)
2.346nnn ( 4.810)
4.028nnn ( 9.60)
0.250 ( 0.778) 1.910n (1.894) 0.926 ( 1.120) 2.456 (0.991) 7.644nnn (7.517) 5.468nnn (5.442) 0.297 (0.256) 0.645 ( 0.455) 0.272 (0.222) 0.515 (0.420) 0.985 (0.924) 0.489n (1.781) 0.541nnn 0.541nnn 5.033nnn ( 4.524)
0.330 ( 1.228) 2.364nnn (2.776) 0.598 ( 0.903) 0.828 (0.427)
Firm-Specific Return, t 1 Firm-Specific Return, t 1 CPS, t 1 Market Return, t 1 Market Return, t 1 CPS, t 1 CEO Tenure¼ 1, t 1 CEO Tenure¼ 2, t 1 CEO Tenure¼ 3, t 1 CEO Tenure¼ 4, t 1 CEO Tenure¼ 5, t 1 CEO Tenure¼ 6, t 1 CEO Tenure46, t 1 CEO Age460 Dummy CEO Is Chair Constant
Number of observations Pseudo R-squared Firm fixed effects
7.645nnn (7.525) 5.470nnn (5.447) 0.294 (0.254) 0.648 ( 0.457) 0.275 (0.224) 0.520 (0.424) 0.985 (0.925) 0.493n (1.804) 0.537nnn ( 4.918) 4.956nnn ( 4.491) 9,571 0.64 No
explain the overall negative association between CPS and firm value. Results are again robust to adding firm fixed effects (see Column 4).
4.5. Stock market reactions to proxy statement releases Companies’ proxy statements disclose the compensation of the firm’s top executives during the preceding year, as well as other types of new information. In this subsection we study the relation between these abnormal returns and the changes in CPS levels disclosed in the proxy statements.
1.174nnn (7.751) 2.284nnn ( 18.08)
9,571 Yes
9,571 0.64 No
1.176nnn (7.768) 2.283nnn ( 18.08)
9,571 Yes
Our event study uses the data on proxy filing dates collected by Dlugosz, Fahlenbrach, Gompers, and Metrick (2006). They collect those dates for 1,916 companies for the years 1996–2001. We examine whether the release of information about changes in CPS is associated with abnormal stock returns. New information about the elements necessary for calculating CPS is provided in firms’ proxy statements, which are the source of public information about executive compensation. Using the date of the proxy filing as the event date, we calculate the cumulative abnormal return around each event date using the market model. The event window is 10 to þ10 days around the event. We use a 21-day
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Table 10 Abnormal returns around announcements of CEO Pay Slice (CPS). We use the date of the proxy filing as the event date, in which the proxy dates are from Dlugosz, Fahlenbrach, Gompers, and Metrick (2006), who collect proxy dates in the years 1996 2001 for 1,916 companies. We find 4,062 firm-years with available data to compute the change in CPS from year t 1 to year t and with sufficient data available on CRSP to compute abnormal returns. We calculate the cumulative abnormal return (CAR) around the event using the market model. The event window is 10 to þ 10 days around the event, using a 21-day window because the proxy date and the filing date are not always the same. CPS is based on total compensation and is expressed as a percentage. Panel A presents mean comparisons between samples that increase (top quartile) or decrease (lowest quartile) their CPS from one year to the next. Panel B reports a weighted least squares regression where the dependent variable is CAR. The independent variables are the change in CPS from year t 1 to year t, Log Book Value (of assets) and the Book-toMarket ratio. Observations are weighed by the inverse of the variance of the estimate of the cumulative abnormal return. n, nn, and nnn indicate significance at 10%, 5%, and 1% level, respectively. The regression in panel B also reports t-statistics in parentheses. Panel A: Mean comparisons Average CAR
Number of observations
For Firms increasing CPS For Firms decreasing CPS Difference (decrease-increase)
0.699%nnn 1.028%nnn 0.329%
2,062 2,000
Top quartile change in CPS Lowest quartile change in CPS Difference (lowest-top)
0.531% 1.691%nnn 1.160%nnn
1,015 1,015
Panel B: Regression analysis CAR[ 10,þ10] in percent Variables Change in CPS (t 1, t)
(1)
(2)
0.0328 (2.03)nn
0.0044 (0.21) 0.0525 (1.86)n 0.3907 (1.24) 0.1014 (0.89) 0.1514 (2.02)nnn 1.357 (1.56) 0.003 3763
Change in CPS Dum(Eindex4 median) Dum(Eindex 4median) Log Book Value, t Book-to-Market, t Constant R-squared Number of observations
window because the filing date often time precedes the distribution of the proxy.24 We assign events to groups according to the change in CPS in the event year relative to the previous year. We also weigh the observations by the inverse of the variance of the estimate of the cumulative abnormal return to incorporate estimation risk. Table 10 Panel A presents the comparison of the average CAR for firms with decreasing versus increasing CPS, as well as the average CAR for the 25% of firms with the biggest reduction in CPS versus the 25% of firms with the biggest increase in CPS. Comparing across groups, the 25% of firms with the biggest decreases in CPS had a significantly higher CAR than the 25% of firms with the biggest increases in CPS. The difference in the 21-day event window of 1.2% is statistically and economically significant. Comparing firms with decreasing versus increasing CPS, we again find a positive difference in CAR equal to 0.3%, but it is not statistically significant.
24 For example, Dell filed its proxy on October 31, 2007 while the letter says that the proxy statement is distributed on or about November 5, 2007. Similarly, SUN Bankcorp filed on April 30, 2007, but the letter in the proxy statement is dated May 11. Focusing on a shorter event window of 7 one day, the results go in the same direction but become statistically insignificant (not shown).
0.1299 (1.07) 0.1448 (1.61) 1.610 (1.79)n 0.002 4062
We also find a small but strongly statistically significant correlation of 3.5% between the change in CPS and the CAR. As reported in Panel B of Table 10, this correlation survives after controlling for differences in firm size and book-to-market characteristics. In particular, the second regression of CAR also includes the interaction of the change in CPS with a dummy indicating whether or not the firm has an Eindex above the sample median. The negative relation between news about increases in CPS and abnormal returns is driven by firms with high entrenchment. This is consistent with the previous result that the negative correlation of CPS with q is concentrated in firms with high entrenchment. One interpretation of our results is that the market reacts negatively to news about increases in CPS. An alternative interpretation, consistent with the view that CPS levels are correlated with worse governance, is that increases in CPS are also correlated with other information released in firms’ proxy statements that investors view unfavorably. 5. Conclusion In this paper, we conduct an empirical investigation of CPS, the fraction of top-five compensation captured by the
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CEO. We show that CPS has a rich set of relations with the performance, value, and behavior of firms. In particular, cross-sectional differences in CPS are associated with lower Tobin’s q, lower accounting profitability, less favorable market reaction to acquisition announcements made by the firm, more opportunistic timing of CEO option grants, more luck-based CEO pay, less CEO turnover controlling for performance and tenure, and lower stock market returns accompanying the filing of proxy statements for periods with increases in CPS. The identified negative correlation between CPS and Tobin’s q is especially concentrated among firms with higher entrenchment levels. To the extent that our results are fully or partly driven by firms’ optimal CPS choices, they indicate that high CPS is optimal for low value firms and thus call for developing a theoretical explanation for such an association. Furthermore, some of our findings are consistent with the possibility that CPS levels of some firms are excessive and that cross-sectional differences in CPS levels provide a tool for studying cross-sectional differences in agency problems. Beyond our particular findings and their interpretation, our general conclusion is that CPS is an aspect of firm governance and management that deserves the attention of researchers. Future research on the effects of governance arrangements and management processes, as well as research on a wide range of aspects of firm behavior and decision making, could consider using CPS as a useful control or a subject of investigation. We hope that our work can provide a framework and a starting point for this line of work. References Adams, R., Almeida, H., Ferreira, D., 2005. Powerful CEOs and their impact on corporate performance. Review of Financial Studies 18, 1403–1432. Aggarwal, R.K., Samwick, A., 2003. Performance incentives within firms: the effect of managerial responsibility. Journal of Finance 58, 1613–1649. Amit, R., Villalonga, B., 2006. How do family ownership, control and management affect firm value? Journal of Financial Economics 80, 385–417. Bainbridge, S.M., 2002. Why a board? Group decision making in corporate governance. Vanderbilt Law Review 55, 1–55. Bebchuk, L.A., Cohen, A., 2005. The cost of entrenched boards. Journal of Financial Economics 78, 409–433. Bebchuk, L.A., Cohen, A., Ferrell, A., 2009. What matters in corporate governance. Review of Financial Studies 22, 783–827. Bebchuk, L.A., Cremers, M., Peyer, U., 2007. CEO centrality. Discussion paper no. 13701. National Bureau of Economic Research, Cambridge, MA. Bebchuk, L.A., Grinstein, Y., 2005. The growth in executive pay. Oxford Review of Economic Policy 21, 283–303. Bebchuk, L.A., Grinstein, Y., Peyer, U., 2010. Lucky CEOs and lucky directors. Journal of Finance 65, 2363–2402. Bertrand, M., Schoar, A., 2003. Managing with style: the effect of managers on firm policies. Quarterly Journal of Economics 118, 1169–1208. Bizjak, J., Lemmon, M., Whitby, R., 2009. Option backdating and board interlocks. Review of Financial Studies 22, 4821–4847. Brill, J.M., 1993. Stock ownership guidelines for executives. Corporate Executive (March–April), 381–385. Chang, Y.Y., Dasgupta, S., Hilary, G., 2010. CEO ability, pay, and firm performance. Management Science 56, 1633–1652. Chatterjee, A., Hambrick, D.C., 2007. It’s all about me: narcissistic CEOs and their effects on company strategy and performance. Administrative Science Quarterly 52, 351–386. Cook, F.W., 1990. How much stock should management own? Compensation and Benefits Review (September/October), 20–28.
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Journal of Financial Economics 102 (2011) 222–232
Contents lists available at ScienceDirect
Journal of Financial Economics journal homepage: www.elsevier.com/locate/jfec
Structural breaks, parameter uncertainty, and term structure puzzles$ George Bulkley a,, Paolo Giordani b a b
University of Bristol, United Kingdom Swedish Central Bank, Swedan
a r t i c l e in f o
abstract
Article history: Received 24 June 2010 Received in revised form 28 October 2010 Accepted 2 November 2010 Available online 31 May 2011
We show that uncertainty about parameters of the short rate model can account for the rejections of the expectations hypothesis for the term structure of interest rates. We assume that agents employ Bayes rule to learn parameter values in the context of a model that is subject to stochastic structural breaks. We show that parameter uncertainty also implies that the verdict on the expectations hypothesis varies systematically with the term of the long bond and the particular test employed, in the same way that is found in empirical tests. & 2011 Elsevier B.V. All rights reserved.
JEL classification: G12 G17 Keywords: Change-point Learning Expectations hypothesis
1. Introduction The expectations hypothesis (EH) states that the yield on a long bond is determined by the expectation of short yields over the term of the bond plus a risk premium. Campbell and Shiller (1991) develop two testable implications of this model that have been the focus of much subsequent empirical work. They show that under the EH the yield spread between long and short bonds should forecast: (1) the change in the yield on the long bond over the term of the short bond and (2) changes in short yields over the term of the long bond. The first prediction is decisively rejected in empirical tests. It is often found that even the sign of the regression coefficient is the opposite of that predicted by the EH. However, the implication that
$ We thanking Vivek Nawosah for help with data handling. George Bulkley gratefully acknowledges financial support from the ESRC under research Grant ACRR2784. Corresponding author. E-mail address:
[email protected] (G. Bulkley).
0304-405X/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.jfineco.2011.05.009
the yield spread forecasts changes in the short yield is often not rejected, and when it is rejected at least the sign of the coefficient on the spread is invariably correct. See, for example, Campbell and Shiller (1991) and Bekaert, Hodrick, and Marshall (1997, 2001). Campbell and Shiller (1991) and Campbell (1995) note that the fact that the verdict on the EH differs significantly according to the test that is employed is a puzzle. A further interesting feature of the empirical work is that the strength of the rejections of the EH in the first test increases systematically with the term of the long bond. Potential rational explanations for these results, which might save the EH, have been thoroughly explored. The first question is whether inference is reliable in these regressions. Stambough (1988) notes that measurement error in the long yield rate enters both sides of a model of changes in the long yield and shows that this might result in the negative coefficients in this regression. Campbell and Shiller (1991) address this by using instrumental variables, but they still find negative slope coefficients in the first regression. Bekaert, Hodrick, and Marshall
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(1997) show how small sample biases arise in these regressions and that, once allowance is made for small sample problems, the puzzle that different tests deliver different verdicts is explained. However, both tests now deliver decisive rejections of the EH. For further discussion of the statistical properties of tests of the EH, see Lanne (1999) and Bekaert and Hodrick (2001). Another possibility is that the rejections of the EH could be explained by the assumption in the standard tests that there is a fixed term premium. Could a time varying risk premium lead to changes in the long rate that could account for the rejections of the EH using the first regression, where changes in the long rate are the dependent variable? It turns out that the scale of the rejections is simply too large to be fully explained by plausible movements in a term premium. See, for example, Backus, Gregory, and Zin (1994), Dai and Singleton (2000) and Duffee (2002). Different data-generating processes for the short rate have also been studied. Bekaert, Hodrick, and Marshall (2001) consider a Hamilton-type regime-switching model but find that this cannot explain the rejection of the EH using Campbell-Shiller regressions (although a partial explanation is possible if interaction with a time varying term premium is introduced). Bansal and Zhou (2002) also fit a Hamilton-type model and find that this can explain a number of puzzling features of the data, but they do not address the rejections of the EH using CampbellShiller regressions. In this paper we continue the search for a rational explanation for this apparent rejection of the EH and pursue the idea that the puzzles might be explained if different data-generating processes for the short rate are assumed. We assume that the short rate process is subject to repeated stochastic structural breaks, in which the break points are not observed but have to be inferred in real time from short rate data. This presents agents with the problems of judging at any date whether or not an interest rate surprise denotes a break and of estimating new parameter values conditional on that inference. We show that Bayesian learning in this context induces changes over time in rational expectations and hence changes in long yields, so that negative slope coefficients are obtained in the first regression. In this way we offer a model that formalizes the insight of Campbell (1995) that changing rational expectations of the long yield have the potential to explain negative slope coefficients in the regression that forecasts changes in long yields. Whether this explanation can account for the empirical rejections of the EH is critically dependent on the frequency and size of the breaks. We investigate this using Monte Carlo methods with a model of breaks calibrated to US data. The idea that the rejections of the EH could be explained by a different assumption about the data-generating process, so that expectations do not conform to the model assumed in standard tests, also offers one explanation why Froot (1989) finds that changes in the term spread do reflect changes in expected future rates if investor survey data on expectations are used. The assumption that parameters are subject to multiple periodic shifts has attracted increasing interest in
223
modelling many macro-economic time series. In the context of interest rates, Garcia and Perron (1996), Gray (1996), Ang and Bekaert (2002), Bansal and Zhou (2002) and Pesaran, Pettenuzzo, and Timmermann (2006) have fitted models with parameter shifts. Pesaran, Pettenuzzo, and Timmermann (2006) identify seven distinct regimes in 55 years of data on US Treasury bill rates. Kozicki and Tinsley (2001a, 2001b) do not explicitly model shifts in the short rate process but show that movements in long rates in the US are consistent with expectations of multiple shifts in the short rate process. We report in subsection 4.1 our own results from fitting a model of stochastic breaks to US short rate data, and this provides the estimates for our calibrations. The idea that any systematic patterns might be detected in changes in expectations about the long yield seems at first sight surprising because changes in Bayesian expectations should be unforecastable. However, Brav and Heaton (2002) and Lewellen and Shanken (2002) show how uncertainty about a model parameter introduces what appears to the econometrician, with hindsight, to be systematic changes in expectations even though agents are Bayesian and changes in expectations are unforecastable in real time. The implications of this process of learning for patterns in historic series of equity returns are explored in these two papers. We show that a similar process of learning leads to systematic changes in short rate expectations and these can explain the rejections of the EH in the first Campbell-Shiller regression. The key to these systematic patterns, identified by Brav and Heaton (2002) and Lewellen and Shanken (2002), is the fact that in the sequence of expectations about an unknown parameter each successive expectation is dependent on the same realization of the parameter. The series of expectations that the econometrician will observe are driven by additional independent drawing of the signal, but these signal realizations have all been generated by the same single parameter realization, which serves as an (unobserved) attractor for the sequence. The gradual convergence of Bayesian beliefs to the true parameter value can explain how evidence of in-sample return predictability can be reconciled with the absence of out-of-sample predictability. See, for example, Bossaerts and Hillion (1999). Lewellen and Shanken (2002) show how this ex post systematic convergence can result in return reversals, and Brav and Heaton (2002) show how returns could appear ex post to exhibit underreaction. In this paper we show that learning introduces systematic patterns into movements in long yields that can explain these puzzles in the term structure of interest rates. Under the EH, long rates reflect current beliefs about the short rate process, so that the spread contains a term that reflects these beliefs and changes in the long rate, the dependent variable in the first Campbell-Shiller regression, contains a term that reflects the revision of beliefs. We show that these additional terms result in much more substantial biases in the first Campbell-Shiller regression than in the second. This explains why one regression could reject the EH much more decisively than the other.
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To develop a preliminary intuition for the role these new terms play, we start with a simple example to show how systematic components appear, with hindsight, in a sequence of Bayesian expectations, conditional on successive signals about a single fixed realization of a variable to be forecast. Assume a single individual is subjected to repeated independent intelligence quotient (IQ) tests. Tests are a noisy but unbiased measure of IQ, and the observer’s priors are that IQ is drawn from a normal distribution with mean 100 and a known variance. A Bayesian expectation after the first test is a convex combination of the prior and the test score. The test score on average equals their true IQ and therefore if their IQ is actually higher (lower) than the prior, the Bayesian will on average underestimate (overestimate) their true IQ. Second, as more test scores arrive, Bayesian expectations will on average converge to the individual’s true IQ, as less weight is given to the prior and more to the accumulating test scores. Therefore, Bayesian expectations will on average rise (fall) over time if the individual’s IQ is actually higher (lower) than the prior. These statements about changes are conditional on whether the new mean is higher or lower than the agents’ prior. They are of no value to an agent in real time who does not know whether the new mean is higher or lower than their prior. These two features imply that someone looking back at historical data will see agents either initially making forecasts that are lower than test scores and their forecasts subsequently rising or initially making forecasts that are higher than test scores and their forecasts subsequently falling. Expectations are rational but the econometrician observes a negative correlation between a change in expectations and public information at the date of the forecast (the difference between the Bayesian expectation and the test score). Consider now a model of the short rate in which a parameter is subject to stochastic structural shifts. We assume agents form rational expectations and have correct priors over the model of the short rate and the meta distribution from which new parameters are drawn. In this context the problem of learning the value of the unknown parameter, following a structural break, shares these two systematic features of the IQ example. Current short rates are a noisy measures of the new parameter of the short rate model. They correspond to IQ scores, and long yields, the forecast of short rates, correspond to Bayesian expectations about IQ, conditional on test results. If the new mean for the short rate following a break is actually higher (lower) than agents’ priors, short rates will on average be higher (lower) than the prior, so the Bayesian forecast of short rates, the long rate, will be typically be lower (higher) than the observed short rate, since it is a weighted average of prior and short rate. Thus, yield spreads (measured as long rate minus short rate) will typically be negative if the new mean for the short rate following a break is higher than agents’ priors and, conversely if the new mean is lower than agents’ priors. If the new mean for the short rate following a shift is higher than agents’ priors, long yields will subsequently rise on average (just as do IQ forecasts) and, conversely, if the new mean is lower than agents’ priors. Thus when the new mean is higher (lower) than the prior, spreads are negative (positive) but long
yields are typically rising (falling), exactly the opposite of the conventional account in the absence of learning, where negative spreads forecast decreasing long yields. In this way, these new terms in the spread and changes in long yields, as a result of learning, exhibit negative covariance, explaining why the spread fails to predict changes in long rates in the way that is expected under the EH when model parameters are known. We show that the new terms will be relatively larger for longer term bonds, explaining why the empirical tests deliver more decisive rejections of the EH for longer bonds. In the regression of subsequent changes in short rates on the spread, learning affects the independent but not the dependent variable. This introduces a milder error-invariable bias and less frequent rejections. We assess the empirical importance of this model of learning for estimation of the Campbell-Shiller regressions using Monte Carlo methods. We generate synthetic data on short rates under a piece-wise stationary autoregressive (AR) model of the short rate, which has stochastic structural shifts that are calibrated to evidence on the frequency of shifts in US short rate data. We then construct data on short rate expectations at each date assuming that agents form rational expectations applying Bayesian inference, using only observations on the short rate available up to the same date that the expectation is formed. Long rates are then generated from these expectations under the EH. We then apply the two standard regression tests of the EH to this generated data. The average point estimate of the coefficient on the spread that should be unity under the EH is substantially less than unity when the tests are applied to the synthetic data, under a range of plausible calibrations. For longer bonds, we find that the coefficient on the spread is of the opposite sign to that predicted by the EH. We also find that, consistent with empirical evidence, the prediction of the EH that the yield spread should forecast short rates fares much better in our simulated data. From the perspective of a forecaster, a critical difference exists between learning of parameter shifts in the context of a regime-switching model of the kind popularized by Hamilton (1989) and models with stochastic shifts examined here. In the former class of models, agents know the parameters of a small fixed set of regimes and have to estimate at any date only the probabilities of the short rate being in each of these known regimes. In models with stochastic shifts, the parameter following each shift is unique. Agents have to estimate the parameters of each new regime, knowing only the distribution from which any new parameters are drawn, which explains why our model can account for the empirical results when they could not be explained in a conventional regime shifting environment of the kind studied by Bekaert, Hodrick, and Marshall (2001). The paper is organized as follows. Section 2 sets out the expectations hypothesis and the two regression tests introduced by Campbell and Shiller (1991). In Section 3 we set out a model in which the short rate is subject to structural shifts and show how learning affects the Campbell and Shiller regressions. In Section 4 we estimate a regression with stochastic mean shifts on US monthly short interest rate data and use the resulting parameter
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estimates to calibrate a large simulation on synthetic data. Section 5 concludes. 2. The expectations hypothesis and regression tests In this section we set out the expectations hypothesis and derive the two key regression tests employed by Campbell and Shiller (1991) and investigated by Bekaert, Hodrick, and Marshall (1997, 2001). Consider the claim to a zero coupon bond with a single certain payment at date (tþ n) of vðt þ nÞ ¼ 1. We write the log yield on the one period bond at t as rt and define log yield to maturity at date t on zero coupon bond with a final log payment of zero and of maturity n to be yðn,tÞ. Then, the EH states that continuously compounded zero coupon bond yields are an average of expected continuously compounded short rates over the term of the bond, plus a term premium. The log price pðn,tÞ then satisfies pðn,tÞ ¼ nyðn,tÞ
ð1Þ
and yðn,tÞ ¼
n1 1X Et ðrt þ i Þ þ cn : ni¼0
ð2Þ
We assume the term premium to be time invariant and hence normalize it to zero for brevity. Define the log return on a bond with maturity n, in the interval ðt,t þ 1Þ, to be Rðn,t þ 1Þ, Rðn,t þ 1Þ ¼ pðn1,t þ1Þpðn,tÞ,
ð3Þ
Therefore, Rðn,t þ 1Þ ¼ nyðn,tÞðn1Þyðn1,t þ1Þ:
ð4Þ
The EH implies that the expected return on the long bond at date t,Et ðRðn,t þ 1ÞÞ, over the term of the short bond, equals the yield on the short bond, rt (normalizing the risk premium to zero). Therefore, rt ¼ nyðn,tÞðn1ÞEt ½yðn1,t þ 1Þ:
ð5Þ
CS1: Rearranging Eq. (5) and replacing expected values with realized values gives the first regression test yðn1,t þ 1Þyðn,tÞ ¼ a þ b
1 ðyðn,tÞrt Þ þ ut þ 1 n1
rt þ i ðn1Þrt ¼ a þbnðyðn,tÞrt Þ þ ut þ n1
premium is reflected in the constant, a. This is the second of the regressions introduced by Campbell and Shiller (1991), and we refer to this regression as CS2. Campbell and Shiller (1991) and Bekaert, Hodrick, and Marshall (1997) report overwhelming rejections of the hypothesis that b¼1 in CS1 but considerably weaker rejections of the hypothesis that b¼1 in CS2. Furthermore for the long maturity bonds, the EH is not rejected using CS2. In the next section we show how parameter uncertainty and the process of learning introduce new terms into both CS1 and CS2. 3. Structural shifts and tests of the expectations hypothesis In this section we show that the parameter uncertainty associated with the potential for structural shifts implies that the slope coefficient on the (scaled) spread in CS1 and CS2 is less than unity under rational expectations, with CS1 coefficients having the largest expected deviations from unity. The critical question is how rational expectations are formed when agents believe that there could be structural shifts in the short rate process. Allowance for shifts introduces two distinct problems: The potential for future shifts has to be considered, and current parameter values have to be estimated from a data set when there could have been a recent shift. Both problems are elegantly solved by explicitly modeling the shifting process and assuming that Bayesian agents integrate over uncertainty about all unknown values. This section makes use of a very stylized process that is amenable to analytical treatment. Sections 4.1 and 4.2 employ Monte Carlo methods to deal with more complex inferential problems. We first examine how learning affects the coefficients that we would expect to estimate in CS1 and CS2 in a stylized model of the short rate that serves to isolate the implications of the process of learning a parameter value on spreads and changes in long rates. Assume short rates, rt, are i.i.d. drawings from a distribution, the mean of which, mt, is unobserved and is subject to stochastic structural shifts. The short rate, rt is given by rt ¼ m t þ e t ,
ð6Þ mt ¼ mt1 þ kt vt ,
The hypothesis that expected excess returns on the long bond, over the life of the short bond, are zero implies that the value of b in regression Eq. (6) is unity. The constant, a, reflects any term premium. This is one of the regression tests introduced by Campbell and Shiller (1991), and we refer to this regression as CS1. CS2: The second regression follows directly from rearranging Eq. (2) and replacing expected values with actual values n1 X
225
ð7Þ
i¼1
Regression equation (7) tests the EH prediction that the spread is an unbiased prediction of changes in short rates over the life of the long bond, which implies a slope coefficient of unity on the spread. Again, any fixed term
kt BernoulliðpÞ,
ð8Þ
where et HNð0, s and vt HNð0, s Following a shift, the gradual convergence of beliefs about the new mean to its true value drives the results obtained below so we assume that shifts are infrequent ðp is small). To gain some analytic insights into this problem, we assume that the shift date is observed so the only problem for agents is to estimate the new mean. The possibility of structural shifts means that agents are continually revising their beliefs about the unobserved mean mt. The spread reflects current beliefs about the mean, and changes in long yields reflect the changing beliefs about the value of mt. We identify the additional terms that this introduces into the CS1 regression. We show that these terms exhibit negative covariance and so 2 eÞ
2 v Þ.
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explain why the slope coefficient on the scaled spread, under the EH, is less than unity, once parameter uncertainty is allowed. We also show that these learning terms become bigger, relative to the conventional terms, for longer bonds and hence explain why the rejections of the EH appear to be more significant when longer bonds are used in CS1. Finally, we show that only the right hand side (RHS) of CS2 is affected by learning and, hence, this test is not as strongly biased toward rejection of the EH. To identify the new terms that are introduced by learning, first consider estimating CS1 and CS2 on data generated by this model if both shift dates and realized values of mt were observed. Assume that the mean of the distribution from which short rates are drawn following a shift is known to be m1. Then, under the EH, substituting into Eq. (2) at date t yields yðn,tÞ ¼ m1 þ
ðrt m1 Þ n
For large n, this is approximately equal to n1 m1 rt et þ 1 fEðm1 jr 1,t þ 1 ,m0 ÞEðm1 jr 1,t ,m0 Þg þ þ : n n n n1 ð15Þ Comparing Eqs. (11) and (15), the last three terms are those expected under full information. The first term reflects the process of learning. The RHS of CS1, measured at t, is 1 ðn1Þ 1 Eðm1 jr 1,t ,m0 Þ þ ðrt Eðm1 jr 1,t ,m0 ÞÞrt ðn1Þ n n
ð9Þ ¼
and ðrt þ 1 m1 Þ : yðn1,t þ 1Þ ¼ m1 þ n1
ð10Þ
The left hand side (LHS) of CS1 is therefore, from regression equation (6), m1 rt et þ 1 þ n n n1
m1 rt Eðm1 jr 1,t ,m0 Þm1 þ : n n n
ð16Þ
Comparing Eqs. (12) and (16) the first two terms are the same as those identified under full information. The third term on the RHS of CS1 is the result of learning. Hypothesis 1. The additional terms introduced by learning into both the RHS and LHS of CS1 exhibit negative covariance.
ð11Þ Proof. See Appendix.
and the RHS of CS1 is 1 1 m1 rt m1 þ ðrt m1 Þrt ¼ : ðn1Þ n n n
ð12Þ
From Eqs. (11) and (12) it can be seen that the LHS of CS1 is equal to the RHS plus the scaled white noise error, yielding the conventional expectation of a slope coefficient of unity. Now assume that the shift date is observed but that m1 is not. The problem is to estimate the new mean from observed drawings of short rates from the new distribution, knowing the meta distribution from which the new mean is drawn. The prior beliefs of agents following a known shift date are that the new mean is their last estimate of the old mean before the shift, which we call m0, and the precision of this prior reflects both the variance of the shift process and the precision of their estimate of the old mean. Following a shift at date t, agents apply Bayes rule to form expectations about the new mean, given knowledge of m0 and sm and observations of the short rate, r1 , . . . ,rt . If the old mean were known with certainty, s2m ¼ s2v . If there is uncertainty about the old mean, this increases s2m . We study the process of learning the value of the parameter m1 in the window before another shift is observed. To see the consequences of parameter uncertainty, substitute the investor’s expectation in place of a known m1 so the yield on an n month bond at date t is yðn,tÞ ¼ Eðm1 jr 1,t ,m0 Þ þ
where we use the notation r 1,t ¼ fr1 ,r2 , . . . ,rt g. The LHS of CS1, measured at tþ 1, is 1 ðrt þ 1 Eðm1 jr 1,t þ 1 ,m0 ÞÞ Eðm1 jr 1,t þ 1 ,m0 Þ þ n1 1 ð14Þ Eðm1 jr 1,t ,m0 Þ þ ðrt Eðm1 jr 1,t ,m0 ÞÞ : n
1 ðrt Eðm1 jr 1,t ,m0 ÞÞ, n
ð13Þ
An intuition for why negative covariance exists between the two new terms builds on the ideas in the IQ example set out in the introduction. Consider what an econometrician expects to observe. At date 1 a shift occurs and Bayesian expectations of the new mean are a weighted sum of the prior, m0, and the first observation of the new short rate, r1, where the weights sum to unity. On average (over the error in the short rate model, et Þ the first realization of the short rate from the new distribution is the new mean, m1, and therefore on average the Bayesian expectation is less (greater) than the new mean if m1 4 m0 ðm1 o m0 Þ. Because the long rate approximately equals the expectation of the new mean, the spread (measured as long yield minus short yield) typically is negative (positive) if m1 4m0 ðm1 om0 Þ. With successive drawings from the new distribution, beliefs gradually converge to the new parameter value as investors give increasing weight to the realizations that are drawn from the new distribution and less weight to their priors. Expectations of the mean, i.e., approximately long rates, are observed to gradually increase (decrease) if m1 4 m0 ðm1 om0 Þ. Thus, when m1 4 m0 ðm1 o m0 Þ, a negative (positive) spread and long rates increasing (decreasing) in the subsequent period are typically observed. These are statements on what is expected conditional on the actual (unobserved) drawing of the parameter. For example, it is not true that the unconditional expectation of long rate changes is positive when the spread is negative. This is opposite to the conventional expectation under the EH, when parameters are known, which is that a negative (positive) spread implies long yields will fall (rise). We show
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227
in the Appendix that this is one of the factors driving the negative covariance between the two new learning terms.
scale mixture of normal distributions for the innovations: rt ¼ mt þ rðrt1 mt Þ þ se et ,
ð19Þ
Hypothesis 2. Introduction of parameter uncertainty implies that the parameter b in CS1 is on average (over realizations of e1 , . . . , et þ 1 Þ decreasing in the term of the long bond.
mt ¼ mt þ kt sm vt ,
ð20Þ
Proof. See Appendix
Hypothesis 3. Introduction of parameter uncertainty induces an error-in-variable downward bias in the test of the EH under CS2. Referring to Eq. (7), and making the substitution rt ¼ m1 þ et , the LHS of CS2, for an n period bond at date t, is ðm1 þ et þ i Þðn1Þðm1 þ et Þ ¼
i¼1
where jrj o1, vt is Nð0,1Þ and et is Nð0,1Þ with probability 2
1px and Nð0, x Þ with probability px . Shifts to the local mean mt occur as Bernoulli events with probability pm in each period and variance s2m . As in Giordani and Villani
The result is driven by the fact that the size of the learning term on the LHS of CS1 increases in n relative to the other terms.
n X
kt Bernoulliðpm Þ,
n X
et þ i ðn1Þet ,
ð17Þ
i¼1
and the RHS is ðn1Þðet þ Eðm1 jr 1,t ,m0 Þm1 Þ:
ð18Þ
If m1 is known, the last two terms cancel out, resulting in the standard prediction of a slope coefficient of unity. If m1 is not known, the difference ðEðm1 jr 1,t ,m0 Þm1 Þ induces an error-in-variable downward bias toward zero of the slope coefficient in CS2 regressors. However, ðEðm1 jr 1,t ,m0 Þm1 Þ P is uncorrelated with ni¼ 1 et þ i , so there is not the bias that was identified for CS1. In particular errors-in-variables cannot imply a CS2 slope coefficient that has a negative expected value (although negative values can occur in any given sample). CS1 tests how expectations change over time. Although the expectation of the change in expectation is zero, the average change in expectation observed with hindsight and conditional on a single actual realization of m1 is not zero, and this is what accounts for the rejection of the EH in CS1. Expectations about the mean of the short rate change in a way that appears with hindsight to be systematic but is unforecastable to investors in real time. This is the same process that arises in equity markets (Lewellen and Shanken, 2002; Brav and Heaton, 2002) when a series of signals about the value of an asset is received by investors, each conditional on the same underlying asset value. Although unobserved, the true value serves as an attractor for the sequence of Bayesian expectations. 4. A model of stochastic mean shifts To obtain simple analytical results, we assume in the model set out in Section 3 that the shift date is known, that there is no persistence in short rates for a given mean, and that the innovations are Gaussians. We now relax these assumptions and formulate a more realistic model that can be estimated on US data and then used for simulation exercises. The model is an AR(1) process with shifts in the conditional mean at unknown dates and a
(2010), we model changes in mean (instead of, as is more common, changes in intercept) because this facilitates formulating a prior and interpreting posterior results. However, because mt, rather than mt1 , appears in the right-hand side of Eq. (19), the dynamics following a change in m are those of an intercept shift: If r is positive, the transition to the new mean is gradual, not sudden. This is arguably the more realistic alternative and, importantly in this context, it greatly complicates the forecaster’s problem of detecting a change in mean. At monthly or higher frequencies the interest rate is often nearly unchanged from one period to the next as several periods could elapse between Federal Reserve monetary policy meetings. This results in a highly non-normal distribution of the innovations. This feature is less pronounced in quarterly data, but the excess kurtosis of the innovations is still evident and motivates us to use a scale mixture of two normal distributions for et . 4.1. Estimation of the stochastic mean shifts model on US data In this subsection the model equations (19)–(20) is estimated with Bayesian methods on quarterly US threemonth Treasury bill interest rates. The model, although complex in certain dimensions, is still univariate and piece-wise linear, and we do not suggest that it is an accurate description of all aspects of the data. However, the evidence of parameter shifts is strong in this and similar models estimated on US and international data. Simpler (i.e., continuous instead of in jumps) forms of parameter variations are widely used by practitioners. Marcellino (2008) finds that a simple AR model with continuous parameter variation performs very well on US inflation and interest rates. Kozicki and Tinsley (2001a) infer from their estimated model that shifts in US short interest rates might be expected once or twice a decade, and Pesaran, Pettenuzzo, and Timmermann (2006) find evidence of several parameter shifts in US short interest rates. Giordani and Villani (2010) conclude that allowing for shifts in mean and variance improves both point and interval forecasts for quarterly short interest rates. We model quarterly US three-month Treasury bill interest rates covering the period 1984Q1–2010Q2.1 The starting date of 1984, common in the monetary policy literature, is chosen to exclude periods in which the short 1 The data is from the FRED database, series ID TB3MS. The series has monthly averages aggregated from daily and is further aggregated from monthly to quarterly by averaging. All numerical results in this paper are little changed if end period interest rates are used instead of averages.
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rate was highly volatile from month to month. In contrast, the post-1984 series exhibits a far smoother pattern, with short interest rates closely following the federal funds rate set in Federal Reserve meetings and changed in small increments from one meeting to the next. We set pm ¼ ð4 7Þ1 , implying on average approximately seven years between shifts, as found by Pesaran, Pettenuzzo, and Timmermann (2006). The implied prior distribution for the number of shifts in any given period is binomial with mean npm and variance npm ð1pm Þ, with n the sample size. The prior for s2m is a weakly informative inverse gamma
s2m IGð3 32 ,3Þ,
Table 1 Parameter estimates for the US short interest rate model, 1984Q1– 2010Q2. The table reports posterior means and (in parenthesis) posterior standard deviations for the parameters of the model of US short interest rates of Section 4.1. Parameters
Posterior mean (posterior std)
r sm se px
0.913 3.966 0.135 0.286 4.537
x
(0.036) (0.868) (0.030) (0.109) (1.245)
ð21Þ
which can be interpreted as three prior observations of breaks with variance 32. The prior on r is Nð0:95,0:52 Þ, truncated to the region r 2 ð0:995 0:995Þ. The prior distribution for m0 (that is, 1983 Q4) is N(10,4) to capture the period of high interest rates in the few years prior to our sample. The probability of the second mixture component, px , has a beta prior distribution, with prior probability 0.2 and prior sample size 10 (see Gelman, 2 Carlin, Stern, and Rubin, 2004) while the variance x is IGð3 32 ,3Þ. Inference is carried out by Markov chain Monte Carlo methods as in Giordani and Kohn (2008). Results: Table 1 and Fig. 1 summarize posterior inference. On the full sample, r has a mean estimate of 0.91. The posterior means of px and x are 0.29 and 4.54, respectively, resulting in a highly non-normal distribution for the innovations. The posterior variance of sm is much smaller than the prior variance, indicating that the data are informative on the presence of shifts. The short rate and the average smoothed mean mt are shown in Fig. 1.2 4.2. CS1 and CS2 on US data We start by estimating the regression coefficients for CS1 and CS2 using the actual US short interest rates rt and long rates at each date constructed under the EH, using the model described by Eqs. (19) and (20) to form expectations about future short interest rates. Short rate expectations are formed by optimal Bayesian updating given values of the parameters r, sm , se , pm , px , and x, which are set at the posterior means given in Table 1. The timing and size of the shifts Dmt ¼ sm vt are unknown. The assumption of known parameter values simplifies the agent’s filtering problem and minimizes departures from the standard strong form of rational expectations in which all values of mt are also known. It also greatly reduces computing complexity because on-line particle filtering methods are fast and reliable for this type of problem when parameters are known. Much more expensive Markov chain Monte Carlo methods are in general required when parameters are unknown, as in Section 4.1. We use the auxiliary particle filter of Pitt and Shephard (1999), with ten thousand particles and resampling of all particles at each time point. At each point, the filtering distribution 2 The average smoothed mean mt is the average across draws of mt jr1 , . . . ,rt , . . . ,rT , with T the sample size. This is not available to a forecaster in real time unless t¼ T.
Fig. 1. US short interest rate (three months) rt and smoothed Eðmt jr 1,t Þ.
pðmt jr1 , . . . ,rt Þ is then approximated by a sample of ten thousand draws (or particles). Because r is assumed known, the expected value of rt þ h at time t is given by Et ðrt þ h Þ ¼ Et ðmt þ rh ðrt mt ÞÞ ¼ Et ðmt Þð1rh Þ þ rh rt ,
ð22Þ
where Et ðmt Þ is estimated by averaging values across all particles. In the first two columns of Table 2 we summarize the results of estimating the two regressions, 1984Q1– 2010Q2, using long yield data constructed under the EH from short rate expectations calculated as described in the previous paragraph. In the second two columns of Table 2 we report the results from estimating the original Campbell-Shiller regressions using actual long yield data, on a data set updated to 2010.3 The key features of the original empirical work are evident in the extended data set. In the regressions that employ constructed long yield data, the features of the empirical work that have been widely described as puzzles can be clearly seen. The slope coefficients in CS1 are not just substantially less than unity, but they are negative for longer bonds. In addition, 3 The regressions that use actual long yield data employ the data set of Bulkley, Harris, and Nawosah (2010), which extends the zero coupon data set of McCulloch and Kwon (1993) up to 2010Q2. This data set followed McCulloch and Kwon and did not include data for bonds between 60 and 120 months. Hence, results are not reported in Table 2 for bonds between 60 and 120 months.
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Table 2 CS1 and CS2 on US data, 1984Q1–2010Q2, simulated and real long rates (quarters). Maturity is in quarters. For CS1m and CS2m multi-period interest rates are not actual US rates but are computed from actual oneperiod (three-month) T-bill rates assuming the expectations hypothesis holds and using the model of Section 4. Correlation consistent standard errors are in parentheses. For CS1r and CS2r actual multi-period yields (monthly, converted into quarterly) are used in computing CS1 and CS2 coefficients. Maturity
CS1m
CS2m
CS1r
4 8 12 16 20 24 28 32 40
0.03 (0.53) 0.41 (0.77) 0.85 (1.02) 1.29 (1.27) 1.74 (1.54) 2.18 (1.80) 2.64 (2.06) 3.09 (2.33) 4.00 (2.86)
0.38 (0.23) 0.10 (0.28) 0.28 (0.31) 0.45 (0.28) 0.49 (0.26) 0.53 (0.24) 0.44 (0.21) 0.39 (0.20) 0.37 (0.24)
0.95 0.95 1.43 1.81 2.08
CS2r (0.36) (0.51) (0.61) (0.69) (0.76)
2.35 (1.02)
0.44 0.56 0.58 0.62 0.65
(0.17) (0.21) (0.24) (0.24) (0.23)
0.50 (0.24)
Table 3 CS1 and CS2 simulated data, break dates unknown. CS1 and CS2 mean parameter estimates on simulated data. The first number in parenthesis is the standard deviation. The second is the standard deviation of the corresponding coefficient when the probability of breaks is set to zero (fixed parameters, rational expectations case). Point estimates under no breaks are not reported (they differ from one only because of small sample bias). Maturity of long bond
CS1
CS2
4 8 12 16 20 24 28 32 40
0.80 (1.02, 1.22) 0.55 (1.33, 1.15) 0.30 (1.68, 1.09) 0.06 (2.079, 1.04) 0.19 (2.48, 0.99) 0.43 (2.90, 0.95) 0.68 (3.31, 0.92) 0.92 (3.74, 0.89) 1.41 (4.55, 0.84)
0.94 0.89 0.86 0.80 0.76 0.72 0.67 0.62 0.53
(0.44, (0.45, (0.48, (0.52, (0.56, (0.59, (0.64, (0.68, (0.76,
0.57) 0.49) 0.42) 0.37) 0.33) 0.29) 0.27) 0.25) 0.23)
the absolute size of the slope coefficient in CS1 declines monotonically with bond duration. Finally, the slope coefficients in CS2 are much closer to unity and offer much weaker evidence against the EH. The coefficient estimates are robust in that they are not strongly affected by doubling or halving the standard deviation or the probability of a break, or by setting r to 0.95 or 0.85. Our choice of sample is also not critical in that similar results are obtained if the sample is extended to start in 1974 or 1964 or shortened to start in 1994. 4.3. CS1 and CS2 on simulated data Table 3 reports the mean and standard deviation of slope coefficients of CS1 and CS2 estimated on five thousand samples of one hundred quarters (net of a burn-in of one hundred quarters), a sample period broadly comparable to those typically used in the empirical literature. The model parameters are again fixed at the posterior means of US data estimates given in Table 1 and shifts in mt occur at unknown dates. Again, all three of the features of the empirical work,
229
which have been widely described as puzzles, can be clearly seen. First, the slope coefficients in CS1 are not just substantially less than unity but are negative for longer bonds. Second, the absolute size of the slope coefficient in CS1 declines monotonically with bond duration. Finally, the slope coefficients in CS2 are much closer to unity, and of the correct sign, suggesting that it delivers much weaker evidence against the EH. The quantitative results can change sizably with the size and frequency of the breaks. For example, deviations from one are substantially larger (smaller) if the standard deviation of the breaks is set to 6 (2) instead of 4. This suggests that deviations from the EH could be larger in countries (or periods) with less stable monetary policy. However, the qualitative results of CS1 coefficients decreasing with the horizon and larger deviations for CS1 than for CS2 are remarkably robust. The standard deviations of CS1 and CS2 parameter estimates in the simulations of the estimated model are reported in Table 3. We also report the standard deviations of the same parameters under the assumption of no breaks ðpm ¼ 0Þ.4 It is evident that the presence of breaks greatly increases the variability of CS1 (especially) and of CS2 estimates, particularly for long maturity bonds. Fig. 2 provides some insights into the filtering problem faced by agents. Panel A shows a simulated sample, with the true mean mt (subject to shifts) and the filtered mean Et ðmt Þ. Due to its persistence, rt can be above or below its mean for long periods, making inference on mt difficult. Panel B shows the standard deviation of the filtered mt, which is volatile. As suggested by the analysis of Section 3, the assumption of unknown break dates is not essential to the results. If we assume that agents know the break dates and have only to infer the break size, deviations from unity are somewhat smaller than in the case of unknown break dates, but all qualitative results are unaffected (not reported).
5. Summary and conclusions The expectations hypothesis makes specific predictions about how the term structure of interest rates should forecast both changes in long yields and changes in short yields. In empirical work the former predictions are decisively rejected, with the forecast often being in the wrong direction. However, the EH is not always rejected for short rate forecasts, and these are typically in the right direction. In this paper we show that the assumption that agents are uncertain about the parameters of the short rate model has the potential to explain these apparently contradictory verdicts. The key to this is that, once parameter uncertainty is allowed, changes in long yields reflect the updating of beliefs about the unknown parameter as additional draws of the short rate arrive. We show that there is a systematic component to these revisions in beliefs, which can explain why long yields do not change in the way expected under the EH, when the parameters of the short rate model are known. Future changes in short rates are not affected by the process of 4 The CS1 and CS2 parameters in the case of no breaks are not reported. We find, as shown by Bekaert, Hodrick, and Marshall (1997), that the coefficients are sizably biased upward.
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Fig. 2. Simulated data: true mt, Eðmt jr 1,t Þ and stdðmt jr1,t Þ.
learning, so introducing learning affects the spread but not the dependent variable in the CS2 regression. Noise is introduced into the RHS of CS2 by learning, so introducing an errors-in-variables problem, but this is a milder problem than that identified in CS1. Biases introduced by learning are sometimes dismissed as small sample problems. However, if uncertainty is periodically renewed, as implied by the evidence cited above for the structural shifts in the US postwar short rate process, then learning is important regardless of sample size. A final interesting feature of the evidence on the EH is that rejections are stronger in the US than in the other G7 countries (Hardouvelis, 1994). If the rejections of the EH are explained by behavioral biases, it is puzzling why these should be any greater in the US, especially because the US markets are the most liquid, a point noted by Hardouvelis (1994). Rooting the explanation for the rejections of the EH in the short rate process opens up a potential rational explanation for different results across different countries, if structural breaks vary in size or frequency or both. We can confirm from simulations, not reported here, that the scale of the rejections does vary, sometimes substantially, with the size and frequency of breaks. In general, larger breaks translate into smaller CS1 and CS2 coefficients, but point estimates of the coefficients in CS1 and CS2 do not always vary monotonically with break frequency and standard deviation. The impact of any particular change in the distribution of breaks is also sensitive to the persistence parameter for the short rate. Bayesian learning is complex in this problem, particularly when the timing of the breaks is unknown, with subtle interactions between the different parameters. A thorough investigation of this explanation for different verdicts on the EH across countries is therefore a substantial topic for further research.
When expectations are formed in any environment in which occasional structural breaks are known to occur, agents who observe a surprise in the data have to determine whether this is due to one or several outliers, under unchanged model parameters, or to a structural break, in which case the new parameters have to be estimated. We show that Bayesian forecasts of short rates in this case result in patterns in long yields that might otherwise be attributed to behavioral biases. Another topic for future work is, therefore, to investigate whether the assumption of stochastic structural breaks might also explain other puzzling patterns in expectations data, for example, in the foreign exchange market. Appendix A A.1. Proof of hypothesis 1 The short rate, following a known shift a date 1, is drawn from a distribution in which the new mean m1 is fixed until some future date T when another shift occurs. Whether T is known or not is not important given our assumptions of random walk type shifts. We consider a sequence of market forecasts at dates t ¼ 1, . . . T before there is any further shift. The investor’s expectation of the new mean at date t, 1 r t o T, is ! g t 1 X 1,t Eðm1 jr1, ,m0 Þ ¼ m0 þ r , ð23Þ g þt g þt t i ¼ 1,...t i where g ¼ s2e =s2m . Consider the sequence of investor forecasts about the new mean following a known shift at date 1: Eðm1 jr1 ,m0 Þ,Eðm1 jr 1,2 ,m0 Þjm1 Þ, Eðm1 jr 1,3 ,m0 Þ . . .
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The values of rt that determine this series of expectations depend on the realization of both m1 and et . Denote by EðEðm1 jr11,t ,m0 Þjm1 Þ the value that the econometrician expects to observe (i.e. over draws of et Þ for the investor’s expectation, conditional on any given drawing of m1. Applying the law of iterated expectations, we study the series
conditional on a realized single drawing of the new mean: EðEðm1 jr 1,t ,m0 Þjm1 ÞEðEðm1 jr 1,t1 ,m0 Þjm1 Þ !! g t 1 X m0 þ ¼E rt g þt g þ t t t ¼ 1,...t E
EðEðm1 jr1 ,m0 Þjm1 Þ,EðEðm1 jr 1,2 ,m0 Þjm1 Þ, . . . : What is critical in the following analysis is that each element in the series is conditional on the same drawing of the new parameter m1. Typically when we examine the properties of a series of forecasts, it is assumed that each forecast is for an independently drawn realization of both the signal (in this case, rt)and the random variable to be forecast (in this case m1). The problem here is different in that each forecast in the series is for a new drawing of the signal but the same drawing of the parameter realization. For further discussion of the consequences of this distinction for a sequence of Bayesian forecasts in equity markets, see Lewellen and Shanken (2002). We need two sets of results on this series to establish the negative covariance of the new terms in the dependent variable and the spread in CS1. Lemma 1. EðEðm1 jr
1,t
,m0 Þm1 Þjm1 Þ is
1. Decreasing in ðm1 m0 Þ given t. 2. Increasing in t given ðm1 m0 Þ, IF ðm1 m0 Þ 4 0 AND decreasing in t given ðm1 m0 Þ, IF ðm1 m0 Þ o 0. Proof. EðEðm1 jr 1,t ,m0 Þjm1 Þm1 ¼E ¼
g t m0 þ g þt g þt
g ðm1 m0 Þ: g þt
1 X r t i ¼ 1,...t i
!! ! m1 m1
&
Lemma 2. The expected change in investor expectations between any two dates, conditional on the realization of the new mean, EðEðm1 jr 1,t ,m0 Þjm1 ÞEðEðm1 jr 1,t1 ,m0 Þjm1 Þ, is 1. Increasing in ðm1 m0 Þ, given t and ei , 1 o io t. 2. Decreasing in t given ðm1 m0 Þ, IF ðm1 m0 Þ 40 AND increasing in t given ðm1 m0 Þ, IF ðm1 m0 Þ o0. Proof. Lemma 2 states that a sequence of investor expectations on average rises if m1 4 m0, converging in expectation to the new mean from below, and if m1 o m0 , then a sequence of investor expectations on average falls, converging in expectation to the new mean from above. Consider the average change in investor expectations that are observed
231
¼
X g t1 1 m0 þ rt g þt1 g þ t1 t1 t ¼ 1,...t1
g ðm1 m0 Þ: ðg þtÞðg þ t1Þ
!!
&
Lemmas 1 and 2 taken together establish the negative covariance of the new terms that are introduced by learning. The assumption that m1 is the same for each element in the series is critical, and this argument would fail if m1 were redrawn between two consecutive dates.
A.2. Proof of Hypothesis 2 CS1 equation (6) states (setting the risk premium to zero) yðn1,t þ 1Þyðn,tÞ ¼ b
1 ðyðn,tÞrt Þ þ ut þ 1 , n1
ð24Þ
1 ðyðn,tÞrt Þ: n1
ð25Þ
implying Et ðyðn1,t þ 1ÞÞyðn,tÞ ¼ b
We can, therefore, denote by bt the expected value conditional on information available at time t of the LHS divided by the RHS: bt ¼
Et ðyðn1,t þ 1ÞÞyðn,tÞ : 1 ðyðn,tÞrt Þ n1
ð26Þ
Under the assumption of m1 known, bt is constant and equal to one. If m1 is not known, using Eqs. (15) and (16), and for large n, this expression becomes 1 ðm1 rt Þ þ Et fEðm1 jr 1,t þ 1 ,m0 ÞEðm1 jr 1,t ,m0 Þg bt ¼ n , 1 1 ðm1 rt Þ þ ðEðm1 jr 1,t ,m0 Þm1 Þ n n
ð27Þ
which decreases with n if, and only if, the ratio Et fEðm1 jr 1,t þ 1 ,m0 ÞEðm1 jr 1,t ,m0 Þg 1 ðEðm1 jr 1,t ,m0 Þm1 Þ n
ð28Þ
also decreases with n. This ratio (and hence bt) is a function of realizations of the errors e1 , . . . , et . Using results from the proof of Hypothesis 1, the average value of this ratio (integrating over e1 , . . . , et Þ is given by (for t large) g ðm1 m0 Þ n ðg þ tÞ2 , ¼ 1 g ðg þtÞ ðm1 m0 Þ n g þt which decreases linearly in n.
ð29Þ
232
G. Bulkley, P. Giordani / Journal of Financial Economics 102 (2011) 222–232
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