Research in Finance, Volume 21

CONTENTS LIST OF CONTRIBUTORS vii INTRODUCTION ix TIME DIVERSIFICATION AND STOCHASTIC DOMINANCE Charles W. Hodges, H...

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CONTENTS LIST OF CONTRIBUTORS

vii

INTRODUCTION

ix

TIME DIVERSIFICATION AND STOCHASTIC DOMINANCE Charles W. Hodges, Haim Levy and James A. Yoder

1

MINORITY EQUITY INVESTMENTS AND INTER-FIRM COLLABORATIONS Su Han Chan, John W. Kensinger, Arthur J. Keown and John D. Martin

17

SIZE AND BOOK-TO-MARKET EFFECTS IN THE RETURNS ON INFORMATION TECHNOLOGY STOCKS Quang-Ngoc Nguyen, Thomas A. Fetherston and Jonathan A. Batten

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IMPLIED VOLATILITIES AND AUDITOR REPUTATION: THE ANDERSEN CASE Jonathan M. Godbey and James W. Mahar

93

SECONDARY EQUITY OFFERINGS: THE CASE OF INSTALLMENTS RECEIPTS Narat Charupat and C. Sherman Cheung

113

A NEW APPROACH TO TESTING PPP: EVIDENCE FROM THE YEN T. J. Brailsford, J. H. W. Penm and R. D. Terrell

135

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CORRELATION AMONG STOCK MARKETS UNDER DIFFERENT EXCHANGE RATE SYSTEMS Paul Sarmas

155

MULTIPLE BANKING AS A COMMITMENT NOT TO RESCUE Paul Povel

175

OPPORTUNITY COST AND PRUDENTIALITY: AN ANALYSIS OF COLLATERAL DECISIONS IN BILATERAL AND MULTILATERAL SETTINGS Herbert L. Baer, Virginia G. France and James T. Moser

201

COLLATERALIZATION AND THE NUMBER OF LENDERS IN PRIVATE DEBT CONTRACTS: AN EMPIRICAL ANALYSIS Gordon S. Roberts and Nadeem A. Siddiqi

229

AN EXAMINATION OF THE EFFICIENCY OF SINGLE VS. MULTIPLE COMMON BOND CREDIT UNIONS James D. Tripp, Peppi M. Kenny and Don T. Johnson

253

LIST OF CONTRIBUTORS Herbert L. Baer

Formerly at Policy Research Department, The World Bank, Washington, DC, USA

Jonathan A. Batten

College of Business Administration, Seoul National University, Seoul, Korea and Graduate School of Management, Macquarie University, Sydney, Australia

T. J. Brailsford

UQ Business School, The University of Queensland, Brisbane, Australia

Su Han Chan

California State University, Fullerton, Fullerton, CA, USA

Narat Charupat

School of Business, McMaster University, Hamilton, Canada

C. Sherman Cheung

School of Business, McMaster University, Hamilton, Canada

Thomas A. Fetherston

School of Business, University of Alabama, Birmingham, Birmingham, AL, USA

Virginia G. France

Department of Finance, University of Illinois at Urbana-Champaign, Champaign Urbana, IL, USA

Jonathan M. Godbey

Auburn University, Auburn, AL, USA

Charles W. Hodges

Department of Accounting and Finance, State University of West Georgia, Carrollton, GA, USA

Don T. Johnson

Western Illinois University, Macomb, IL, USA

Peppi M. Kenny

Western Illinois University, Macomb, IL, USA

John W. Kensinger

College of Business Administration, University of North Texas, Denton, TX, USA vii

viii

Arthur J. Keown

R. B. Pamplin College of Business, VPI & SU, Blacksburg, VA, USA

Haim Levy

Department of Finance, Hebrew University, Jerusalem, Israel

James W. Mahar

Department of Finance, St. Bonaventure University, St. Bonaventure, NY, USA

John D. Martin

Hankamer School of Business, Baylor University, Waco, TX, USA

James T. Moser

Department of Economics & Finance, Louisiana Tech University, Ruston, LA, USA

Quang-Ngoc Nguyen

Jonathan A. Batten College of Business Administration, Seoul National University, Seoul, Korea and Graduate School of Management, Macquarie University, Sydney, Australia

J. H. W. Penm

Faculty of Economics and Commerce, The Australian National University, Canberra, Australia

Paul Povel

Carlson School of Management, University of Minnesota, Minneapolis, MN, USA

Gordon S. Roberts

Schulich School of Business, York University, Toronto, Canada

Paul Sarmas

College of Business Administration, California State Polytechnic University, Pomona, Pomona, CA, USA

Nadeem A. Siddiqi

BearingPoint Inc., Kentwood, MI, USA

R. D. Terrell

National Graduate School of Management, The Australian National University, Canberra, Australia

James D. Tripp

Western Illinois University, Macomb, IL, USA

James A. Yoder

Department of Accounting and Finance, State University of West Georgia, Carrollton, GA, USA

TIME DIVERSIFICATION AND STOCHASTIC DOMINANCE Charles W. Hodges, Haim Levy and James A. Yoder ABSTRACT We use stochastic dominance to test whether investors should prefer riskier securities as the investment horizon lengthens. Simulated return distributions for stocks, bonds, and U.S. Treasury bills are generated for holding periods of one to 20 years and stochastic dominance tests are run to establish preferences among the alternative portfolios. With independent returns, we ﬁnd no evidence that high-risk securities (stocks) dominate low-risk securities (bonds) as the investment horizon lengthens. Under the assumption that security returns are correlated across time, we ﬁnd that common stocks dominate corporate bonds and U.S. Treasury bills for sufﬁciently long investment horizons.

1. INTRODUCTION The issue of time diversification has generated considerable controversy. Theoreticians, most notably Merton and Samuelson, reason that, if markets are efficient and security returns are independent and identically distributed, then lengthening the investment horizon should not reduce risk. Thus, an investor’s optimal mix of securities should be independent of the planned holding period.1 Many market professionals, however, recommend that the proportion of an investor’s holdings of high-risk securities such as equities should increase with Research in Finance Research in Finance, Volume 21, 1–15 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21001-2

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CHARLES W. HODGES ET AL.

the length of the desired investment horizon. Lee (1990) and Reichenstein and Dorsett (1995) offer support for this position by arguing that time diversification will hold true if stock returns are mean reverting across time. In this case, returns have negative autocorrelation so that volatility is reduced, because a positive or negative price movement tends to be followed by a price movement in the opposite direction. While numerous empirical studies employing a mean-variance framework have been conducted on the efficacy of time diversification, they have yielded conflicting results and have failed to resolve the issue.2 We use stochastic dominance (SD) to analyze the issue of time diversification. Data from Ibbotson Associates 2001 Yearbook is used to generate simulated return distributions for portfolios of small stocks, common stocks, long-term corporate bonds, and U.S. Treasury bills for various holding periods. For each holding period, we apply stochastic dominance tests to determine whether preferences can be established among the equity and fixed-income portfolios. Our analysis is first conducted under the assumption that returns are independent across time and then under the assumption that security returns are correlated across time so that potential mean reversion in equity returns is captured. We employ stochastic dominance because it is a more general, analytical technique than mean-variance analysis. Stochastic dominance examines the entire distribution of returns and, thus, considers all the moments of the return distribution. Furthermore, SD does not require any specific distributional assumption such as normality. Empirical studies of time diversification based on mean-variance analysis ignore higher moments, such as skewness and kurtosis, and are not consistent with maximizing expected utility unless the return distributions are normal. Albrecht (1998) demonstrates the pitfalls of applying mean-variancebased performance measures to non-normal security return distributions. In this paper, the stochastic dominance results clearly show that the issue of time diversification is ultimately a question of autocorrelation in security returns. When returns are independent across time, no dominance exists among the stock and bond portfolios, even for long holding periods. This is consistent with the assumptions and analyses by Merton and Samuelson. When autocorrelation across security returns is captured, however, stock portfolios dominate the bond portfolios for sufficiently long holding periods. This is consistent with the practitioner view that stock returns are mean reverting so that lengthening the investment horizon reduces risk.

2. STOCHASTIC DOMINANCE Stochastic dominance has important advantages over the mean-variance framework that underlies other empirical time diversification studies. It is theoretically

Time Diversiﬁcation and Stochastic Dominance

3

unimpeachable, requires no distributional assumptions, and takes all the moments of the return distributions into account. Furthermore, SD requires only very general assumptions about investor behavior. In discriminating between the performance of the stock and bond portfolios, stochastic dominance provides an effective method for placing investment choices into mutually exclusive sets: an efficient set containing desirable investment alternatives and an inefficient set containing the undesirable ones. Return distributions of alternative portfolios are compared against one another to determine which would be preferred (i.e. in the efficient set versus not in the efficient set). The preference criteria is that the investor prefers more return per dollar invested to less, is risk averse, and prefers positive skewness (potential for great gain with limited downside risk) in a return distribution. The basic principle underlying stochastic dominance is quite straightforward.3 Consider the two arbitrary return distributions shown in Fig. 1 and the corresponding cumulative distributions in Fig. 2. In this example, G might correspond to the return distribution of corporate bonds and F might correspond to the return distribution of common stocks. Assuming that investors prefer more return to less (first derivative of the utility function is positive), an investor wanting to maximize expected utility would prefer return distribution F, which lies to the right of distribution G. With distribution F, the chance of earning a higher return is always greater than with G regardless of whether the investor likes or dislikes risk. Formally, investment F dominates G for all utility functions if, and only if, F(r) ≤ G(r) for all r (with at least one strict inequality), where F and G are cumulative distributions. This constitutes first degree stochastic dominance (FSD).

Fig. 1. Return Distributions.

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CHARLES W. HODGES ET AL.

Fig. 2. Cumulative Return Distributions.

In the case where F(r) lies entirely to the right of G(r), preference is readily apparent. When two cumulative distributions cross, other factors than return (e.g. risk aversion) must be considered in order to establish dominance. Further assuming that investors are risk averse (second derivative of the utility function is negative), second degree stochastic dominance (SSD) can be applied. Formally, F dominates G for all risk-averters if and only if:

r −∞

[G(t) − F(t)] dt ≥ 0

(1)

for all values of r, and the inequality is strict for at least one value of r. G(t) is the cumulative distribution associated with G. F(t) is the cumulative distribution associated with F. When F(t) lies to the right of G(t), the integral of G(t) − F(t) is positive. Figure 3 shows that, when the conditions of Eq. (1) are met, F(t) lies far enough to the right of G(t) so that investment F would be preferred to investment G. This is because the expected utility gained from the positive area to the left of R0 is more than the decrease in expected utility lost between R0 and R1 . Analysis of third degree stochastic dominance (TSD) is similar except that it assumes that investors’ absolute risk aversion decreases, which implies that investors prefer positive skewness. Formally, the TSD rule asserts that F dominates G if, and only if:

r

v

−∞ −∞

[G(t) − F(t)] dt dv ≥ 0

(2)

Time Diversiﬁcation and Stochastic Dominance

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Fig. 3. Cumulative Return Distributions – F Preferred to G with Risk Aversion.

for all r and the expected values are: E F (r) ≥ E G (r) with at least one strict inequality. Equation (2) can be interpreted as another measure of how far to the right the cumulative distribution of investment F is relative to that of investment G. The inside integral is merely Eq. (1). If this function is less than zero at any point, second degree stochastic dominance is violated. Third degree stochastic dominance, on the other hand, balances the areas where the function (i.e. the inside integral) is positive against the areas where the function is negative. Hence, there may not be dominance by SSD, even though a dominance by TSD prevails.

3. METHODOLOGY AND RESULTS We now analyze the stock and bond return distributions under the assumption that the returns are independent and then repeat the analysis allowing for autocorrelation in the returns.

3.1. Independent Returns We use simulation to generate sample return distributions for portfolios of small stocks, common stocks, long-term corporate bonds, and U.S. Treasury bills for holding periods of one to 20 years.4 Annual returns for each portfolio from 1926

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CHARLES W. HODGES ET AL.

through 2000 are collected from the Ibbotson Associates data. For a specified holding period of n years and a given portfolio, we randomly select (with replacement) n returns out of the 75 sample returns. We then compute the holdingperiod return (HPR) by: n HPRn = (1 + R i ) − 1 (3) i=1

where: HPRn = return for holding period of n years. Ri = ith return observation. n = number of years in holding period. This procedure is repeated 250 times. Thus, we generate sample return distributions for each portfolio for annual holding periods of one to 20 years. Note that this procedure is consistent with an efficient market because it generates independent returns. To illustrate, consider the case of a five-year holding period and the smallstock portfolio. Five annual returns are selected at random from the 1926 through 2000 historical returns and the five-year holding-period return is computed. This is repeated until a sample distribution of 250 five-year holding-period returns is obtained. Table 1. Mean Returns (Independent Returns). Holding Period (Years)

Small Stocks

Common Stocks

Corporate Bonds

U.S. T-Bills

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.1865 0.4054 0.5815 0.8796 1.2431 1.8269 2.2701 2.7225 3.5033 3.8916 5.1126 6.2349 7.6834 9.1426 9.9900 12.7609 14.0832 16.3932 19.2132 22.3442

0.1396 0.2843 0.4185 0.6009 0.8002 1.0992 1.3921 1.6361 2.0382 2.3164 2.8870 3.3905 4.0060 4.5933 5.1838 6.0751 6.9254 8.0484 9.0971 10.3712

0.0648 0.1278 0.1941 0.2583 0.3331 0.4115 0.4995 0.5898 0.6727 0.7651 0.8718 0.9705 1.0974 1.2477 1.3798 1.5451 1.6772 1.8342 2.0083 2.1812

0.0384 0.0785 0.1218 0.1676 0.2134 0.2609 0.3076 0.3593 0.4123 0.4705 0.5284 0.5863 0.6504 0.7159 0.7828 0.8558 0.9282 1.0045 1.0790 1.1584

Time Diversiﬁcation and Stochastic Dominance

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Table 2. Standard Deviation (Independent Returns). Holding Period (Years)

Small Stocks

Common Stocks

Corporate Bonds

U.S. T-Bills

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.3415 0.6124 0.7956 1.2163 1.5884 2.6733 3.3439 4.0323 5.5973 5.2954 7.1563 10.6047 11.0493 14.0722 13.7674 19.5160 25.6209 31.3195 28.5125 37.1234

0.2033 0.3345 0.4242 0.5871 0.7082 1.0491 1.2709 1.4675 2.0399 2.0537 2.6574 3.3833 3.7438 4.5057 4.8308 5.6614 6.8283 9.1775 8.6184 10.1819

0.0896 0.1249 0.1467 0.1970 0.2279 0.2724 0.3218 0.3602 0.4054 0.4472 0.4706 0.5106 0.5969 0.6794 0.7560 0.9234 0.9225 1.0202 1.1158 1.2254

0.0314 0.0469 0.0604 0.0735 0.0903 0.1057 0.1083 0.1281 0.1339 0.1486 0.1556 0.1798 0.1836 0.1929 0.2115 0.2422 0.2426 0.2637 0.2757 0.2884

Descriptive statistics are computed for each sample return distribution. Tables 1 through 3 list the portfolio means, standard deviations, and skewnesses, respectively. Table 1 shows that the mean return for all portfolios increases with the length of the holding period. The mean return for Treasury bills, for example, grows from 3.84% for a one-year holding period to 115.84% for a 20-year holding period. The corresponding mean returns for small stocks are 18.656% and 2234.42%. One might be tempted to conclude that a long-term (20-year investment horizon) investor should invest in small stocks rather than Treasury bills since the expected return is larger. Risk, however, also increases with the length of the holding period. Table 2 shows that the standard deviation of returns for Treasury bills increases from 3.14% for a one-year holding period to 28.84% for a 20-year holding period. The corresponding standard deviations for small stocks are 34.151% and 3,712.34%. Risk, as measured by the standard deviation, grows much more rapidly with the length of the holding period for small stocks than for Treasury bills. Skewness coefficients given in Table 3 are generally positive and are inconsistent with normally distributed random variables.5 Indeed, the Kolomogorov-D statistics

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CHARLES W. HODGES ET AL.

Table 3. Skewness (Independent Returns). Holding Period (Years)

Small Stocks

Common Stocks

Corporate Bonds

U.S. T-Bills

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.5975 1.1294 1.2845 2.3293 2.2293 3.2641 3.7829 3.2042 3.8482 2.9023 3.2793 4.9828 3.1690 3.8513 2.9038 2.9743 6.0588 6.7478 2.7802 4.5362

−0.4003 0.1592 0.5065 1.0858 0.7606 1.5186 1.3195 1.3104 2.3178 1.4604 1.9264 2.4399 1.8461 2.3279 2.1656 1.9926 2.9756 4.3287 1.9004 2.2607

1.4384 1.0429 0.9985 1.1416 1.1480 1.1102 1.4880 1.4324 1.5495 1.5989 1.1260 0.9811 1.2939 1.2871 1.3420 1.6586 1.1446 1.4233 1.2256 1.5443

0.7029 0.6224 0.5907 0.6260 0.5535 0.4931 0.5776 0.4032 0.3976 0.1392 0.0740 0.4420 0.3889 0.3007 0.4111 0.7835 0.3990 0.5260 0.4745 0.3502

reject normality at the 1% significance level for all the stock and bond portfolios for all holding periods. Thus, preferences established strictly on the basis of a mean-variance analysis would not be valid. Stochastic dominance tests are run to determine whether preferences can be established among the portfolios for each holding period. The SD algorithms for discrete distributions used here are discussed in Levy (1992).6 The results of the 20 tests are summarized in Table 4 which shows membership in the TSD efficient set.7 As the results are the same for all holding periods, we only show the results in five-year increments. The SSD and FSD results are identical to the TSD results. Table 4 shows no evidence that time diversification results in preferences among the portfolios for risk-averse investors who prefer positive skewness. The efficient set for each holding period includes all four portfolios. This means that an investor with a 20-year investment horizon could rationally select any of the stock, bond, or T-bill portfolios. Thus, with independent returns, time diversification fails and Merton and Samuelson are correct.

Time Diversiﬁcation and Stochastic Dominance

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Table 4. Stochastic Dominance Results with Independent Returns.a Holding Period (Years) 1 5 10 15 20

Small Stocks

Common Stocks

Corporate Bonds

U.S. T-Bills

Yes Yes Yes Yes Yes

Yes Yes Yes Yes Yes

Yes Yes Yes Yes Yes

Yes Yes Yes Yes Yes

Note: Yes = Membership in the TSD Efficient Set. a Results for all other holding periods are identical. FSD and SSD results are identical to the TSD results.

3.2. Autocorrelated Returns We now repeat the analysis allowing for autocorrelation across time in the security returns. Mean reversion (negative autocorrelation) in long-run stock returns and mean aversion (positive autocorrelation) in fixed-income securities have been Table 5. Mean Returns Under Autocorrelation. Holding Period (Years)

Small Stocks

Common Stocks

Corporate Bonds

U.S. T-Bills

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.4115 0.6035 0.9260 1.2131 1.5646 1.8780 2.2722 2.7121 3.5052 4.2175 5.1086 6.3226 7.3999 8.5451 9.7845 11.4878 13.7256 15.9648 18.4647

0.2890 0.4144 0.5883 0.7646 0.9903 1.2020 1.4561 1.7393 2.1560 2.5344 2.9976 3.5319 4.1100 4.7234 5.3502 6.1242 7.0687 7.9136 8.9042

0.1397 0.2094 0.2928 0.3829 0.4813 0.5797 0.7024 0.8114 0.9526 1.0765 1.2282 1.3557 1.5001 1.6490 1.8023 1.9380 2.0996 2.2472 2.3592

0.0804 0.1254 0.1714 0.2206 0.2740 0.3308 0.3914 0.4569 0.5291 0.6021 0.6871 0.7770 0.8653 0.9617 1.0657 1.1678 1.2774 1.3985 1.5165

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CHARLES W. HODGES ET AL.

reported by various researchers.8 This autocorrelation may induce preferences among the alternative stock and bond portfolios. Sample return distribution for small stocks, common stocks, long-term corporate bonds, and U.S. Treasury bills are constructed as follows. For a given holding period of n-years, we randomly select an observation (year) from the first 75−(n−1) observations in the sample. The selected return and the next n−1 consecutive returns are then used to compute the n-year holding-period return using equation 1. Since holding-period returns are now computed from consecutive returns, autocorrelation across time in the portfolio returns is now captured. Eliminating the last n−1 observations before selecting the random observation guarantees that the n-year holding-period return can always be computed. This procedure is repeated 250 times. To illustrate, consider a five-year holding period. A return is randomly selected from the first 71 (1926 through 1996) observations and the holding-period return is computed using the next four consecutive returns. This process is repeated until a sample distribution of 250 five-year returns is obtained. Note that if the 71st observation (1996) is selected, then the five-year holding period can be computed from observations 71 through 75 (1996 through 2000 returns). Table 6. Standard Deviations Under Autocorrelation. Holding Period (Years)

Small Stocks

Common Stocks

Corporate Bonds

U.S. T-Bills

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.6034 0.8904 1.3331 1.5134 1.6694 1.7181 2.1213 2.2990 2.8453 3.3260 3.6656 5.0003 5.3469 5.5767 5.3380 6.3668 8.5244 9.6500 10.5444

0.3432 0.3912 0.4963 0.6138 0.7209 0.8417 1.0415 1.1547 1.4077 1.6876 2.0122 2.3484 2.7683 3.2706 3.5738 4.0850 4.7779 5.1602 5.7670

0.1395 0.1818 0.2404 0.3082 0.3884 0.4737 0.5804 0.6620 0.8211 0.9444 1.1133 1.1756 1.3667 1.4700 1.6305 1.7634 1.9361 2.0700 2.1265

0.0675 0.1071 0.1464 0.1899 0.2384 0.2891 0.3433 0.4024 0.4673 0.5315 0.6091 0.6889 0.7669 0.8489 0.9359 1.0213 1.1117 1.2135 1.3112

Time Diversiﬁcation and Stochastic Dominance

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Table 7. Skewness Under Autocorrelation. Holding Period (Years)

Small Stocks

Common Stocks

Corporate Bonds

U.S. T-Bills

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

0.6411 1.7276 2.3218 1.5077 1.2361 1.0215 1.4028 1.7647 1.6208 1.6202 0.8436 1.6289 1.2038 0.9520 0.3263 0.6433 1.0471 0.7733 0.6426

−0.0591 −0.1697 0.3019 0.1419 0.1563 0.2983 0.2872 0.2584 0.2706 0.2465 0.2718 0.2798 0.3750 0.5382 0.5120 0.6806 0.7746 0.6770 0.8457

1.1567 1.0532 1.3166 1.5876 1.4143 1.2562 1.2864 1.1687 1.3682 1.3391 1.4232 1.1737 1.3644 1.1949 1.1597 1.1334 1.1079 1.1268 1.0407

0.8057 0.7869 0.7675 0.7262 0.6951 0.6350 0.6024 0.5690 0.5260 0.4982 0.4755 0.4356 0.4140 0.3793 0.3411 0.3200 0.3024 0.2846 0.2683

Descriptive statistics are computed for each sample return distribution. Tables 5, 6, and 7 give the portfolio means, standard deviations, and skewnesses, respectively. Note that the tables start with a two-year holding period since autocorrelation across time requires at least two holding periods. Tables 5 and 6 show that expected returns and standard deviations increase with the holding period for all portfolios. Table 7 shows that the skewness coefficients remain positive, indicating that the return distributions are not normal. Mean-variance analysis remains inappropriate. A comparison of corresponding standard deviations in Table 2 with those in Table 6 indicates that the portfolio returns are autocorrelated across time. The two equity portfolios exhibit negative autocorrealtion or mean-reverting behavior. Under mean-reversion, a positive return tends to be followed by a negative return so that volatility is dampened. The standard deviations for the small-stock and common-stock portfolios are all less than those for corresponding independent returns for holding periods of five years or longer. For example, the standard deviation for the common-stock portfolio for a 20-year investment horizon is only 576.70% in Table 6 (autocorrelated returns) compared to 1018.19% in Table 2 (independent returns).

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CHARLES W. HODGES ET AL.

The corporate bond and Treasury bill portfolios, however, exhibit positive autocorrelation or mean aversion. Under mean aversion, a positive return tends to be followed by another positive return so that volatility is enhanced. The standard deviation of the corporate bond and Treasury bill portfolios in Table 6 are greater than those for corresponding independent returns given in Table 2 for all holding periods. For example, the standard deviation for the corporate bond portfolio for a 20-year investment horizon is 212.65% in Table 6 (autocorrelated returns) but only 122.54% in Table 2 (independent returns). These results suggest that time diversification may hold with autocorrelated returns. Mean reversion in the stock portfolios combined with mean aversion in the fixed-income portfolios imply that the relative risk of the equity portfolios compared to the fixed-income portfolios should decline as the holding period lengthens. Thus, equities would be preferred to fixed-income securities for sufficiently long holding periods as investment professionals claim. Stochastic dominance tests are run to determine if preferences can be established when autocorrelation in the return generating process is captured. The results given in Table 8 show membership in the TSD efficient set. As predicted, preferences Table 8. Stochastic Dominance Results Under Autocorrelation.a Holding Period (Years) 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Small Stocks

Common Stocks

Corporate Bonds

U.S. T-Bills

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No No No No No

Yes Yes Yes Yes Yes Yes No No No No No No No No No No No No No

Note: Yes = Membership in the TSD Efficient Set. a SSD results are identical.

Time Diversiﬁcation and Stochastic Dominance

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for the equity portfolios are now established. Common stocks and small stocks dominate Treasury bills for holding periods of eight years or longer and corporate bonds for holding periods of 16 years or longer. Common stocks are preferred over small stocks for holding periods of 18 years or longer. The SSD results are identical to the TSD results.

4. CONCLUDING COMMENTS The results in this paper reconcile the views of theoreticians and market professionals. With independent security returns, no dominance exists between the equity and fixed-income portfolios. All portfolios are in the efficient set for all holding periods. This is consistent with the arguments of Merton and Samuelson that time diversification does not reduce risk and that asset allocation should not be influenced by the intended holding period. However, when autocorrelation in security returns is considered, we find that the stock portfolios dominate the fixed-income portfolios given sufficiently long holding periods. Mean reversion in stock returns combined with mean aversion in bond returns makes equities more attractive as the holding period lengthens. This is consistent with the practitioner view that the proportion of equity holdings should increase with the intended holding period. Thus, the issue of time diversification is ultimately a debate about the degree to which security returns are autocorrelated across time.

NOTES 1. See Merton and Samuelson (1974) and Samuelson (1990, 1994). 2. See, for example, Lloyd and Haney (1980), Lloyd and Modani (1983), McEnally (1985), Butler and Domian (1991), Levy and Gunthorpe (1993), Gunthorpe and Levy (1994), Thaler and Williamson (1994), Thorley (1995), Asness (1996), Ferguson and Simaan (1996), Hodges, Taylor and Yoder (1997), Olsen and Khaki (1998), Hansson and Persson (2000) and Siegel (2002). 3. For a review of stochastic dominance rules, see Levy (1992). 4. This sampling approach is similar to the bootstrapping methodology introduced by Efron (1979). 5. Kurtosis coefficients are generally positive and are inconsistent with normally distributed random variables. Kurtosis results are available from the authors upon request. 6. Computer programs for stochastic dominance with discrete distributions are given in Levy and Sarnat (1984). 7. Similar results are obtained by Hodges and Yoder (1996).

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8. See, for example, Fama and French (1988), Poterba and Summers (1988), Reichenstein and Dorsett (1995), Lewellen (2001), and Strong and Taylor (2001).

REFERENCES Albrecht, T. (1998). The mean-variance framework and long horizons. Financial Analysts Journal, 54, 44–49. Asness, C. S. (1996). Why not 100% equities? Journal of Portfolio Management, 22, 29–34. Butler, K. C., & Domian, D. L. (1991). Risk, diversification, and the investment horizon. Journal of Portfolio Management, 17, 41–47. Efron, B. (1979). Bootstrap methods: Another look at the jack-knife. Annals of Statistics, 7, 1–12. Fama, E., & French, K. (1988). Permanent and temporary components of stock prices. Journal of Political Economy, 96, 246–273. Ferguson, R., & Simaan, Y. (1996). Portfolio composition and the investment horizon revisted. Journal of Portfolio Management, 22, 62–67. Gunthorpe, D., & Levy, H. (1994). Portfolio composition and the investment horizon. Financial Analysts Journal, 50, 51–55. Hansson, B., & Persson, M. (2000). Time diversification and estimation risk. Financial Analysts Journal, 56, 55–62. Hodges, C., Taylor, W., & Yoder, J. A. (1997). Stocks, bonds, the Sharpe ratio, and the investment horizon. Financial Analysts Journal, 53, 74–80. Hodges, C., & Yoder, J. A. (1996). Time diversification and security preferences: A stochastic dominance approach. Review of Quantitative Finance and Accounting, 7, 289–298. Ibbotson, R. (2001). Stocks, bonds, bills, and inﬂation: 2001 yearbook. Chicago, IL: Ibbotson. Lee, W. (1990). Diversification and time: Do investment horizons matter? Journal of Portfolio Management, 16, 21–26. Levy, H. (1992). Stochastic dominance and expected utility: Survey and analysis. Management Science, 38, 555–593. Levy, H., & Gunthorpe, D. (1993). Optimal investment proportions in senior securities and equities under alternative holding periods. Journal of Portfolio Management, 19, 30–36. Levy, H., & Sarnat, M. (1984). Portfolio investment selection: Theory and practice. Englewood Cliffs, NJ: Prentice-Hall. Lewellen, J. (2001). Temporary movements in stock prices. Working Paper, MIT. Lloyd, W. P., & Haney, R. L., Jr. (1980). Time diversification: Surest route to lower risk. Journal of Portfolio Management, 6, 5–9. Lloyd, W. P., & Modani, N. K. (1983). Stocks, bonds, bills, and time diversification. Journal of Portfolio Management, 9, 7–11. McEnally, R. W. (1985). Time diversification: Surest route to lower risk? Journal of Portfolio Management, 11, 24–26. Merton, R. C., & Samuelson, P. A. (1974). Fallacy of the Log-Normal approximation to optimal portfolio decision-making over many periods. Journal of Financial Economics, 1, 67–95. Olsen, R. A., & Khaki, M. (1998). Risk, rationality, and time diversification. Financial Analysts Journal, 54, 58–63. Poterba, J., & Summers, L. (1988). Mean reversion in stock prices: Evidence and implications. Journal of Financial Economics, 22, 27–59.

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Reichenstein, W., & Dorsett, D. (1995). Time diversiﬁcation revisted. Charlottesville, VA: Research Foundation of the Institute of Chartered Financial Analysts. Samuelson, P. A. (1990). Asset allocation could be dangerous to your health. Journal of Portfolio Management, 16, 5–8. Samuelson, P. A. (1994). The long-term case for equities. Journal of Portfolio Management, 21, 15–26. Siegel, J. J. (2002). Stocks for the long run. New York, NY: McGraw-Hill. Strong, N., & Taylor, N. (2001). Time diversification: Empirical tests. Journal of Business Finance and Accounting, 28, 263–302. Thaler, R. H., & Williamson, J. P. (1994). College and university endowment funds: Why not 100% equities? Journal of Portfolio Management, 23, 27–37. Thorley, S. R. (1995). The time-diversification controversy. Financial Analysts Journal, 51, 68–76.

MINORITY EQUITY INVESTMENTS AND INTER-FIRM COLLABORATIONS Su Han Chan, John W. Kensinger, Arthur J. Keown and John D. Martin ABSTRACT We examine the beneﬁts for ﬁrms participating in collaborations funded via minority equity placements. Selling ﬁrms, on average, realize signiﬁcant increases in share value – strongly correlated with the size of the equity stake, its beta, and the relatedness of the two ﬁrms (by industry). Shares of purchasing ﬁrms, though, show neutral responses on average (but positive response for R&D intensive alliances). Further, purchasing ﬁrms have better ﬁnancial performance than their industry peers in the years surrounding the announcement (suggesting, unlike joint ventures, that poor performance is not their motivation). Selling ﬁrms, however, may be motivated by poor operating performance.

1. INTRODUCTION The use of interfirm collaborations or business alliances has grown dramatically over the last decade as firms have sought to improve performance by pooling corporate resources to engage in joint design, production, marketing, or distribution of products and services. Interfirm collaborative agreements can manifest themselves in one of several organizational forms including complex contracts, strategic

Research in Finance Research in Finance, Volume 21, 17–44 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21002-4

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alliances, joint ventures, and mergers. We focus on strategic alliances which are an intermediate form of collaboration. Specifically, we study strategic alliances that involve a minority equity investment by one of the partnering firms (the purchaser) in the other (the seller).1 These agreements are particularly interesting because the minority equity stake not only provides an infusion of cash to the seller but gives the purchaser partial control over the seller’s resources without creating a new entity as in a joint venture. In addition, the partial ownership interest provides a mechanism for bonding the partnering firms to the alliance agreement. We examine investor reactions to the announcement of corporate purchases of minority equity stakes associated with the formation of strategic alliances. Despite the prevalence of minority equity investments among partners to interfirm collaborations, especially in high-tech industries, there is little empirical evidence as to their valuation consequences. Previous studies of interfirm equity investments (see Choi, 1991; Mikkelson & Ruback, 1985) or block shareholdings (see Bethel, Liebeskind & Opler, 1998; Hertzel & Smith, 1993; Wruck, 1989) have not focused on the use of minority equity stakes as a bonding mechanism for a strategic alliance.2 Prior research on interfirm collaboration has examined joint ventures (Johnson & Houston, 2000; McConnell & Nantell, 1985), non-equity strategic alliances (Chan, Kensinger, Keown & Martin, 1997), and equity alliances (Allen & Phillips, 2000). The results of the joint venture and alliance studies suggest that interfirm collaborations, in general, benefit the partnering firms. Our study is most closely related to a recent study by Allen and Phillips (2000) who investigate long-term block ownership by corporations and performance changes in firms with corporate block owners. Using a sample of 150 corporate equity purchases that accompany explicit product market relationships and 252 equity stakes that are not associated with business relationships during the 1980–1991 period, Allen and Phillips examine three potential reasons for block ownership: accruing the benefits of product market relationships, the alleviation of financing constraints, and improved board monitoring by corporate owners. They find that the largest increases in the sellers’ stock prices, investment, and operating profitability occur when the equity ownership is accompanied by alliances, joint ventures, and other product market relationships between the purchasing and selling firms. Furthermore, their findings were strongest in industries with high R&D expenditures. The study concludes that block ownership has significant benefits in product market relationships. We provide additional evidence as to the sources of value creation in inter-firm collaborations supported by equity participation. Our study focuses exclusively on minority equity alliances and adds to the findings of the Allen and Phillips (2000) study in the following ways.

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First, we examine firms that announce strategic alliances or collaborative agreements contemporaneously with a minority equity participation.3 Our sample permits us to examine not only the value effects of these minority-equity participation cum alliance announcements to the participating firms but also events immediately following the announcement to see how these relationships evolve over time. Furthermore, we exclude joint ventures since they have been studied extensively elsewhere. Joint ventures also differ fundamentally from minority equity alliances in that all joint venture partners generally contribute funding or other resources to the joint project that forms the basis for the venture, whereas in a minority equity alliance one partner buys and the other sells equity. The equity investment aligns the interests of the partnering firms and thus serves as a bonding mechanism for the partners to the alliance. The clear distinction of buyer and seller firm in a minority-equity relationship permits us to separately test the value effect of the alliance on the value of the purchasing and selling firms. Similar to Allen and Phillips’s finding for their subsample of equity purchases where alliances or joint ventures are formed, we find that selling firms in minority equity alliances during the 1981–1992 period realize significant increase in share value while purchasing firms garner neutral share price responses. In addition we document that the majority of the alliances are strengthened or extended in the period up to three years following the initial announcement of the tie-up. Second, we conduct multiple regression tests to provide additional insight into the determinants of wealth gains for the purchasing and selling firms that announce minority equity tie-ups. Allen and Phillips (2000) do not provide such evidence; they focus on the determinants of investment and operating performance changes following corporate block equity purchases. Our analysis reveals that purchasing firms that are more R&D intensive seem to reap higher returns from a minority equity alliance than their less R&D intensive counterparts. For selling firms, we find that increases in their share values are strongly correlated with the size of the equity stake, their riskiness, and the relatedness of the industries to which the partnering firms belong. These results are consistent with the hypotheses discussed in Section 2 of the paper. Finally, we document the yearly operating performance of both purchasing firms and selling firms in the six-year period surrounding the announcement of the minority equity purchase to see whether the firms’ operating performance motivates them to enter into such arrangements and how the firms perform following the formation of the alliance. Our findings suggest that purchasing firms have cash flows to invest while selling firms may be motivated to enter into such alliances because of poor operating performance. The selling firms show

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significant improvement in their operating performance in the third year following the alliance. The paper is organized as follows: Section 2 elaborates on the sources of value creation from collaboration involving minority equity investments. Section 3 describes the data collection procedures and the resulting test sample as well as the test methodology. Section 4 discusses the findings, and Section 5 concludes.

2. MINORITY EQUITY STAKES AND INTERFIRM COLLABORATIONS Collaboration using minority equity investments is an essential strategy especially for firms in high tech industries such as biotechnology and computer hardware and software. By banding together the allied firms hope to benefit from reduced investment risks, improved access to new technologies and product markets, and the accelerated development of new products. Furthermore, cash starved firms might gain access to capital under more favorable terms than would be available in the capital market. Where the buyer possesses specific knowledge relevant to the seller’s business, it may possess skill in evaluating the seller’s investment opportunities that is superior to investors in the public capital market and thus be willing to invest under terms more favorable to the seller than would be the case with a public equity offering.4 Furthermore, the specialized knowledge of the purchaser combined with the bonding effects of common ownership may help deter opportunistic behavior by the selling firm.5 This, in turn, reduces the cost of raising capital compared to the public capital market (resulting from asymmetric information).

2.1. Pooling Resources and Lowering Transactions Costs In an equity alliance one or more of the participating firms purchases common stock from an allied firm. The purchase provides more than a cash infusion to the selling firm; it also bonds the firms’ joint efforts by providing the purchasing firm with access to information concerning the seller’s cost structure and often a voice in management. (See Kensinger and Martin (1991), for a further discussion of minority equity stakes as a means for financing network organizations.) Harrigan (1985) argues that a minority investment by a larger firm may be the only way for the purchasing firms’ managers to obtain access to the assets and

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capabilities of smaller, knowledge-intensive firms. A case in point is provided by Hewlett-Packard which purchased an equity stake in Conductus Inc., a closelyheld Silicon Valley startup that produces superconducting chips. Conductus invented new equipment for forming brittle superconducting ceramics into the thin films needed to make micro-chips. A Hewlett-Packard official was quoted as saying, “Research in superconductors is better done by small companies such as Conductus. It’s a very valuable relationship for us.” Another case in point to illustrate the role minority equity stakes plays and the potential benefits to firms in this mode of collaboration is the relationship between IBM and Hogan Systems, Inc. (a leading developer and provider of integrated banking applications software and services). In September 1990, IBM took a 5% equity stake in Hogan Systems, Inc. to strengthen and cement a marketing relationship that began in 1986. At the same time, it also amended and extended agreements that granted IBM exclusive rights to license, market and provide support for Hogan’s banking software product in North America. In addition, IBM will also provide funding to Hogan for the joint development of some projects. In return, Hogan will receive 50% of revenues from IBM’s sales of its products. This pooling of resources appears to benefit both parties because Hogan was having problems selling its software to the larger banks and IBM needed an integrated banking software package for its banking hardware. Psychologically, the alliance gives the impression that IBM, the leading hardware company has just identified Hogan as the leading bank software company. This helps bolster Hogan’s reputation. The agreement also gives Hogan access to IBM’s deep pockets, a unique competition over its competitors, and access to certain areas of IBM’s technology and planning. On the downside, however, Hogan will be put in a precarious position without a distribution capability but there is a clause in the contract that provides Hogan with a certain amount of protection. The benefit that IBM gets is that Hogan’s banking software package will help it sell its mainframe computers to financial institutions. These examples illustrate how the allied firms benefit from synergy in production, distribution, and sourcing of inputs. Note, however, that the purchasing firm would gain even more if it purchases the seller’s shares at a discounted price. However, Wu (2001) shows that private placements to strategic partners (including suppliers and customers) are at a premium as opposed to private equity sales to informed investors (such as managers or directors, block shareholders, venture capitalists, and institutional investors) that are generally at a discount. Therefore the benefits to the purchasing firm, if any, will come mainly from future collaborative opportunities. For deeper discussion of the role of knowledge, see Jensen and Meckling (1991).

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2.2. Mitigating Adverse Selection and Information Problems Wruck (1989) shows that a private sale of equity results in a shift to more concentrated holdings by non-managers and this generally increases firm value if the blockholder uses his votes to see that corporate resources are managed more efficiently or if the existence of the block increases the probability of a valueincreasing takeover. In the case of the equity alliances we study, the purchasing partner generally does not intend to take over control or restructure the selling firm. Therefore, any shift in assessment of the value of the seller is more likely to come from a more efficient use of corporate resources. Also, the purchase of a minority equity stake to form an alliance by an informed purchaser is an endorsement of the selling firm’s management and its future prospects (e.g. the value of the seller’s option to develop and market its new technology). Therefore, a reassessment of the seller’s value could also be a result of the revelation of new information to the market concerning the seller’s future prospects (which the market is incapable of evaluating without this signal). Following the above reasoning, we expect that the formation of an equity alliance will create value for both the purchasing and selling firms. This value arises from a lowering of transaction costs through pooling of resources while outsourcing non-core functions and taking advantage of the capabilities of the allied firms. It also arises from the mitigation of adverse selection and information asymmetry problems regarding the seller’s future prospects. However, we expect that the value creation will vary across the partnering firms in predictable ways. For example, Mody (1993) suggests that the flexibility inherent in alliances facilitates experimentation with new combinations of participants in the pursuit of new technologies or marketing strategies. Therefore, we expect firms that are highly R&D intensive or that have high growth opportunities will gain more value from experimentation as well as from the pooling of resources. Also we expect firms facing higher risks in their operations to benefit more from the pooling of resources with a partner firm in an alliance. Given information asymmetry problems, we expect more value added for alliances involving firms in related industries (see also Balakrishnan & Koza, 1993).

2.3. Controlling Opportunistic Behavior Via Minority Equity Ownership On the downside, alliances carry risks not incurred in the fully integrated corporation. These include a variety of uncertainties arising out of dependence on another party for resources or services. (See Klein, Crawford and Alchian (1978), for a discussion of this general class of problems.) Furthermore, such

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partnerships are inherently less stable than fully integrated (merged) firms because the contracts used to form them cover a limited scope of activities, and residual rights to profits are sometimes purposefully left ambiguous. According to Murray and Siehl (1989) these agreements constitute “complex contracts” for which it is difficult to identify a priori the potential outcomes of the relationship, the factors causing those outcomes, the appropriate responses to the outcomes, or which party is responsible for each response. Due to this ambiguity, a relationship of mutual interest (bonding) replaces legalistic enforcement mechanisms. Typically, the bond takes one of two basic forms: an equity investment by one of the partnering firms (a minority equity stake) or hostage assets.6 For example, Mody (1993) points out that alliances have weak incentives to curb opportunistic behavior on the part of the partnering firms when compared to the fully integrated firm that arises out of a merger. Equity ownership in an equity alliance helps create an ownership structure that safeguards investments (and other claims to future income) while aligning the incentives of the partners for cooperative behavior (Pisano, 1989). Opportunism by an equity partner is penalized through reductions in the value of its equity investment. Thus a higher minority equity stake ensures greater bonding of the firm’s efforts and reduces the possibility of opportunstic behavior as it helps align the incentives of the partners. Furthermore, in the event of termination, equity ownership protects the acquiring partner by providing an enforceable mechanism for dissolving the alliance. That is, the proportionate ownership interest of the acquiring partner provides a ready basis for determining exactly what is due to each partner to the agreement should the alliance be terminated. We hypothesize, therefore, that the larger the size of the minority equity stake relative to the total shares the seller has outstanding the lower is the risk of opportunism and the greater the potential value created by the alliance. Pisano (1989) argues that R&D is inherently more costly to govern through contracts and is subject to incentive losses when internalized completely. For R&D activities partial equity ownership is preferred to pure contractual governance. Based on this argument, we would expect equity alliances involving R&D to be more prevalent than those involving non-R&D activities. In summary, because minority equity investments benefit the allied firms from a lowering of transaction costs through the pooling of resources, we expect stock market gains for both the purchasing and the selling firm. However, the wealth gains will vary across the partnering firms in predictable ways. We expect more gains to accrue to firms that are highly R&D intensive, that have high growth opportunities, and that face high risks in their operations. Also given information asymmetry problems experienced by selling firms, we expect more value added

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for selling firms that form alliances with purchasing firms from related industries. We also hypothesize that the larger the size of the minority equity stake relative to the total shares the seller has outstanding, the lower is the risk of opportunism and the greater the potential value created by the alliance.

3. DATA AND METHODOLOGY 3.1. Sample Description To obtain the sample of firms entering into alliances involving the purchase of minority equity stakes, we searched both the Lexis/Nexis database (including the Business Wire, PR Newswire, Southwest Newswire Reuters and United Press International) and the Dow Jones News Retrieval Service database (including the Dow Jones News Wire and the Wall Street Journal) for the 1981–1992 period. We combine various keywords including “alliance,” “minority-equity” and “minority stake” with the different agreement types (licensing, marketing, distribution, supply, production, manufacturing, development, research, and technology). Unlike some previous studies of interfirm equity investments (see Choi, 1991; Madden, 1981; Mikkelson & Ruback, 1985), we did not use the SEC Schedule 13D filings to identify our initial set of firms. This was done for the following reasons: (1) equity alliances often involve small, non-publicly traded seller firms (13D filings are required only when 5% or more of a publicly traded firm’s stock is acquired); (2) 13D filings do not give information as to the purpose of the investment; and (3) previous studies have noted that the 13D filings are often preceded by press releases or WSJ reports that reveal plans to acquire a minority stake in another firm.7 We found 93 announcements of minority-equity investments that meet the following sample selection criteria: (1) the purpose of the buy-in is to form an alliance to pool knowledge and resources to achieve a common objective; (2) the equity stake creates a minority position (does not exceed 50% of the selling firm’s outstanding shares); (3) at least one of the partners in the alliance has stock return data available in the CRSP daily returns file for NYSE, AMEX, or NASDAQ firms during the period of analysis;8 and (4) at the time of the buy-in, the purchasing firm gave no indication of an intention to acquire the seller firm. The following announcement by Hewlett-Packard is an example of an announcement of a minority-equity investment: Hewlett-Packard Co. announced that it had entered into a letter of intent with Santa Barbara Laboratories Inc. providing for a multi-faceted relationship between the two companies, as part of which Hewlett-Packard will acquire a minority-equity position in Santa Barbara Laboratories

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for an undisclosed amount of cash. . . . The company said the proposed relationship includes arrangements for technical collaboration (Dow Jones News Wire, 9/24/84).

Of the firms involved in the minority-equity alliances, stock return data was available in the CRSP file for 85 purchasing firms and 29 selling firms (two of these announcements involve multiple firms purchasing the same seller firm).9 The minority equity stake (as reported by the purchasing/selling firm in the news article) averages 15%, ranging from 3% up to 32% of the selling firm’s outstanding shares (59 of the announcements reported precise figures on the size of the minorityequity position, while the others simply reported that a minority-equity position was taken). Mikkelson and Ruback (1985) in their study of the value effects of accumulation of large blocks report an average equity position of 37% for 13D filings associated with an outstanding takeover proposal and 9.8% where the equity purchase is for investment purposes. In Wruck’s (1989) study of private sales of equity securities she reports that after taking into account the purchasers’ stockholdings prior to the sale, the stake averages 26%, and ranges from about 2 to 84%. The higher stakes reported by Wruck may reflect the fact that her sample includes cases where the purchaser intends to gain control of the selling firm, obtain the right to elect or nominate directors, or help impede a takeover of the selling firm by another firm. Allen and Phillips (2000) report that the average size of the equity stakes in their sample was 20% (median 14%) which is very similar to our sample. Thus, it appears that the average equity stake in minority equity alliances lies somewhere between that associated with a takeover proposal and a passive investment. Panel A of Table 1 presents the sample observations classified by the year of their announcement. While the sample spans twelve years, approximately 45% of the sample is concentrated in 1989 and 1990. The concentration of minority equity alliance announcements in these two years is consistent with a report indicating that acquisitions and minority equity investments rose in 1989 as the U.S. hightechnology industry restructured (Electronic Business, July 9, 1990, pp. 42–44). According to the same report the number of foreign firms acquiring equity interests in U.S. electronics firms also rose in that year. In our sample we find four incidences of buy-ins by foreign firms, one in 1988, two in 1989 and one in 1990. For the foreign purchasing firms, the primary motive is to tap an existing infrastructure and to establish an international working partnership.10 Panel B of Table 1 classifies the alliances by the purpose of the agreement. We find that 26% of the announcements (24 cases) involve development or research alliances followed by 23 cases of marketing alliances (25%). There are 25 cases (27%) that involve combinations of the four types of agreement and 9 cases (10%) that did not specify the purpose for forming the equity alliance. The above

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Table 1. Distribution of Announcements of Interfirm Alliances Involving Minority Equity Investments. Panel A: Annual Distribution of Announcements Year of Announcement

Number of Announcements

% of Total

1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

2 4 5 4 3 10 6 8 22 20 2 7

2.2 4.3 5.4 4.3 3.2 10.8 6.5 8.6 23.7 21.5 2.2 7.5

Total

93

100.0

Panel B: Distribution of Announcements by Type of Cooperative Agreement Type of Cooperative Agreement

Number of Announcements

By Purchasing Firms

By Selling Firms

I. Licensing II. Marketing III. Development or Research IV. Technology V. Combination of II and III VI. Other combinations of I–IV VII. Not Specified

4 23 24 8 14 11 9

3 19 24 8 12 11 8

1 7 7 2 9 1 2

Total

93

85

29

Note: The table reports the distribution by year and by type of cooperative agreement for the 93 alliance announcements involving the purchase/sale of minority equity stakes by NYSE, AMEX, and NASDAQ firms in the 1981–1992 period. The sample of announcements (identified by searching the Lexis-Nexis database) reported below include only cases where at least one of the partnering firms in the alliance is publicly traded with return data available on the CRSP tape. Panel A reports the number of announcements in each year during the 1981–1992 period. Panel B classifies the announcements by the type of cooperative agreement as stated in the news article containing the announcement of the alliance. It also reports the number of announcements under each type made by purchasing firms and selling firms.

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distribution of equity alliances by purpose of the agreement is consistent with our conjecture that equity alliances encompassing R&D activities would be more prevalent relative to the other types of activities (consistent with Chan et al., 1990). Table 2 classifies the observations by industry affiliation based on SIC codes. The table also groups the purchasing and selling firms into high-technology and lowtechnology groups. This grouping is based on both the SIC code and information in CorpTech (a database containing information about high-tech manufacturing, development and service companies). About 86% of the purchasing firms and 93% of the selling firms belong to the high-technology industries. Furthermore, the minority-equity buy-ins are most prevalent in the computer and software industries (45 purchasing firms and 13 seller firms). The largest group of low-technology firms

Table 2. Industry Affiliation of Purchasing and Selling Firms. Industry

Panel A: High-technology group Aircraft engine and parts Computer programming, systems design and software Computer equipment and industrial machinery Medical or biotech Pharmaceuticals Chemical and thermoplastics Instruments Semi-conductors and electrical equipment Telecommunications

Purchasing Firms

1 5 40

Selling Firms

6 4 5 5 7

9 4 2 2 1 1 7 1

73

27

1 3 5 1 2

1 1

Low-tech sub-total

12

2

Grand total

85

29

High-tech sub-total Panel B: Low-technology group Air transportation Farm machinery and equipment Motor vehicle and parts Paper and allied products Rubber and miscellaneous plastic products services

Note: The table classifies the purchasing and selling firms in our sample into a high-technology group or a low-technology group. We classify a firm as being in the high-technology group if its operations are primarily hitech as described in CorpTech, a database containing information about hightech manufacturing, development and service companies in the U.S. Both the Purchasing and selling firms reported below are publicly-traded firms with return data available on the CRSP tape.

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(5 purchasing firms and 1 seller) comes from the motor vehicle and parts industry. We also find that of the 93 announcements of minority-equity purchase, 38 (41%) involve combinations between firms in related industries (the same three-digit SIC industry).11 Most of the buy-ins involve larger firms acquiring the shares of a smaller firm. Furthermore, roughly 69% of the purchasing firms bought into private firms. There are only 23 cases where both purchasing and selling firms are publicly-traded with data available on the CRSP tapes. (Note that there are 29 cases if we include 6 cases in which one of the partnering firms is a foreign-listed firm.) Note that those sellers that are publicly-traded are relatively young in terms of the number of years since listing. The average as well as the median age since listing is about 6 years. Table 3 presents sample statistics to show the basic characteristics of both the purchasing and selling firms that collaborate using a minority equity stake. The purchasing firms are much larger, about 85 times, than the selling firms (as measured by the market value of equity 21 days prior to the announcement). It Table 3. Profile of Purchasing and Selling Firms. Summary Statistics

Purchasing firms Mean Standard deviation Median Sample size Sellers firms Mean Standard deviation Median Sample size

Market Value of Equity ($M)

RD/Sales

BV/MV

Leverage

Variance

21,369

0.08 0.04 0.07 76

0.58 0.37 0.55 83

0.49 0.16 0.46 84

0.07% 0.19% 0.03% 84

0.95 2.32 0.17 23

0.40 0.28 0.38 27

0.50 0.26 0.48 28

0.16% 0.11% 0.12% 29

85 252

29

Note: The table provides summary statistics for the Purchasing and selling firms in our sample. The market value of equity is the market value of the firm’s common stock 21 trading days before the initial announcement of the equity alliance. RD/Sales is the ratio of research and development expenditures divided by firm sales in the year prior to the announcement of the minority equity investment. BV/MV is the ratio of the book value of the firm’s assets to their market value (measured as the sum of the market value of the firm’s equity plus the book value of its liabilities). Leverage is the ratio of the total firm liabilities to total assets. Variance is the variance in daily stock returns over the two years preceding the announcement of the minority equity investment. Except for the stock returns which are obtained from CRSP tapes, all the other variables are taken from the Compustat tapes in the year prior to the announcement. The number of observations for each variable varies depending on the availability of data from the Compustat tapes.

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is noteworthy that the average size of the selling firm sample ($252 million) is similar to that of Wruck’s (1989) private equity sales sample ($234 million). Purchasing firms’ R&D/sales ratio averages 8% with a median of 7% while selling firms’ R&D/sales ratio is much higher, averaging 95% with a median of 17%. The t-statistic for the difference in the mean R&D/sales between the two samples is significant (t-statistic = 1.80). The high average R&D/sales ratio for the seller sample is driven mainly by four high-tech selling firms for which the R&D/sales ratios exceed 100%. Even when comparing the purchasing and selling samples using the median R&D/sales ratio, the selling firms are still at least twice as R&D intensive as the purchasing firms. Although both purchasing and selling firms exhibit growth opportunities measured using the book-to-market value (BV/MV) ratio, the selling firms exhibit a significantly lower mean BV/MV ratio than the purchasing firms (t-statistic of difference in mean BV/MV = 2.67). (BV/MV is the ratio of the book value of the firm’s assets to their market value, where market value is equal to the sum of the market value of the firm’s equity plus the book value of its liabilities.) This suggests that the selling firms in general exhibit higher growth opportunities than the purchasing firms. The lower BV/MV ratio for the selling firms could also suggest that the fraction of market value of the selling firms’ assets attributable to tangible assets is lower than that for the purchasing firms. The above observations about the differences in size, R&D intensity and growth opportunities between the purchasing and selling firms are consistent with the argument that the larger and relatively less R&D intensive firms with lower growth prospects use minority equity alliances to gain access to the capabilities of smaller, knowledge-intensive firms with attractive growth prospects. Although both purchasing and selling firms exhibit similar levels of financial leverage, the selling firms exhibit significantly higher stock return volatility (as measured by the variance in daily stock returns) than their purchasing firm counterparts (t-statistic of difference in mean variance = 3.09). The higher variance in the selling firms’ stock returns could be largely due to the higher risk of their operations. We also examine the ownership concentration in our sample firms using the percentage of insider ownership information from CDA/Spectrum. CDA/Spectrum defines an insider as an officer, director or beneficial owner (holder of 10% or more) of a company’s stock. We measure the total direct insider ownership as a percentage of the number of shares outstanding for the quarter just prior to the announcement of the equity alliance. The mean (median) insider holdings for the purchasing firms and sellers are 14.6% (5%) and 17.5% (17.5%), respectively. These data are consistent with evidence reported in other studies (Morck, Shleifer & Vishny, 1988; Wruck, 1989) that ownership is more concentrated in smaller

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firms. The ownership concentration, however, is not significantly different between the purchasing firm and selling samples (t-statistic of difference = 0.98).

3.2. Outcomes of the Minority-Equity Relationships The purchasing firms in our sample use a minority-equity buy-in as a means to enter into a collaborative relationship with a selling firm. Hence we expect the outcomes of this form of interfirm investment to differ from those buy-in situations where the purchasing firm is considering a takeover or making a passive investment. In the study of interfirm investment by Mikkelson and Ruback (1985) they report (see their Table 1) that for those investments where the purchasing firm is considering a takeover, about 49% of the selling firms were taken over by the purchasing firm within three years of the initial buy-in while for passive investments only about 8% of the selling firms were taken over by the purchasing firm. Also for passive investments, about 44% ended in a targeted repurchase or a sale of shares to a third party. It is also interesting to see how these relationships evolve when compared to non-equity strategic alliances and joint ventures. In Chan et al.’s (1997) study of non-equity strategic alliances, they find that in the eight year period following the announcement of the alliances, only a small percentage (around 6%) of the alliances resulted in early termination of the agreement. The majority of them (about 83%) involve the signing of new agreements to strengthen or expand the relationship. Only a small percentage of the alliances (around 6%) evolved into a more permanent form of relationship, such as a joint venture or a merger. This is in contrast to joint ventures in which roughly 80% end in a takeover by one of the partners (see Bleeke & Ernst, 1995). Since minority equity alliances lie somewhere in between non-equity alliances and joint ventures in terms of the integration of the allied firms, we would expect to find the outcomes of the minority equity alliances falling somewhere between the other two modes of interfirm relationships. To track the evolution of the minority-equity alliances we examine the Wall Street Journal (WSJ) index and news articles from the wire services for any related news reports related to these investments. We track these news reports starting from the date of the announcement of the minority-equity relationship and terminating three full years after the announcement. Table 4 summarizes the results of this analysis. We find a total of 41 outcome events reported for our sample firms in the WSJ and newswire services within three years. More than 70% of them relates to the strengthening or extension of the initial collorative agreement (categories A–E).12 There are nine instances where the purchasing firm increases stake in the sellers, fifteen incidences of formation of new pact, two incidences where the partnering

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Table 4. Outcomes of Interfirm Alliances Involving Minority Equity Investment. Outcome Within Three Years After the Initial Announcement

Alliance strengthened or extended A. Purchasing firm increases stake in the selling firm B. Formation of new pact, expansion or strengthening of alliance D. Formation of joint venture E. Purchasing firm agrees to buy selling firm

Number of Occurrences

9 15 2 4 30

Alliance reduced in scope or terminated F. Involvement in a legal dispute G. Purchasing firm reduces stake in the seller or loosen ties with selling firm H. Purchasing firm sells its entire stake in the seller (targeted repurchase or sale of shares to a third party) I. Termination of partnership

2 2 3 5 11

Total number of announced outcomes within 3 years

41

Note: This table reports the outcomes of the interfirm alliances in our sample. The table only reports the outcomes involving both purchasing and selling firms that are announced in either the Dow Jones News Retrieval Service or the Lexis/Nexis database. The outcomes span the period between the initial announcement of the alliance and the end of the third full year following the initial announcement made during the 1981–1992 period.

firms decide to form a joint venture, and four instances (about 10% of the total announced outcomes) where a purchasing firm agrees to acquire the selling firm. (In two of the acquisition cases the purchasing firm agreed to acquire the selling firm a year after purchasing a minority equity stake.) The later finding is in contrast to that for interfirm investments with a takeover intention in which about 49% of the selling firms were taken over (see Mikkelson & Ruback, 1985) or to that for joint ventures in which roughly 80% end in a takeover by one of the partners (see Bleeke & Ernst, 1995). Table 4 also shows a total of eleven outcomes (about 27% of the total announced outcomes) in which the alliance agreement was reduced in scope or terminated (categories F–I). There are two cases in which the partnering firms were involved in legal disputes over violation by one of the partners of some key elements of the partnering agreement. There are two cases where the purchasing firm reduces its stake in the seller and three cases (about 7% of total announced outcomes) where a purchasing firm sells its entire equity interest in the selling firm either back to the selling firm or to a third party.13 This contrasts with passive investments in

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which about 44% ended in a targeted repurchase or a sale of shares to a third party as reported by Mikkelson and Ruback (1985). Finally, there are five cases in the sample where the alliance was dissolved because one of the partnering firms was acquired by a third party. In summary, the evidence in Table 4 indicates that for many firms the formation of an alliance represents the beginning of a dynamic relationship between the partnering firms. This evidence provides some limited support for Mody’s (1993) conjecture that alliances can be used as a learning experiment. Changes in the relationship may also be the result of adaptation to evolving market conditions as well.

3.3. Methodology for Assessing Abnormal Stock Performance A standard event study procedure is used to measure the immediate stock price response associated with the announcement of minority-equity alliances. Specifically, we use a methodology similar to Dodd and Warner (1983). Abnormal performance for each firm is estimated using the market model and daily stock returns obtained from the CRSP files. Defining the announcement day as day 0, the estimation period for the market model estimate begins on day −170 and ends with day −21. Abnormal stock returns are estimated as the prediction errors from the market model. We calculate abnormal returns for the event days −20 through +10 and average them across firms for each of the 31 event days. Significance tests are based on a standardized test statistic constructed to determine whether the mean abnormal return is significantly different than zero (see Dodd & Warner, 1983, for a detailed description of the test statistics and their calculation).

4. RESULTS 4.1. Gains to Purchasing and Selling Firms in a Minority-Equity Alliance Table 5 presents the abnormal returns and the distribution of wealth gains between firms participating in alliances involving a minority-equity commitment. For the sample of 85 acquiring firms, 55% experience positive abnormal returns on the announcement day; however, the average abnormal return is an insignificant 0.07%. The two-day results are similar. This evidence indicates that on average the purchasing firms neither pay too much nor too little.14 For the sample of 29 selling firms, 76% of these firms experience positive abnormal returns on the announcement day and the average abnormal return

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Table 5. Average and Cumulative Abnormal Returns for Purchasing and Selling Firms. Statistics Pre-announcement period (−20, −1) Cumulative average abnormal return (Z-statistic) Day 0 average abnormal return (Z-statistic and % positive) Two-day (Day 0, +1) cumulative abnormal return (Z-statistic and % positive) Post-announcement period (2, 10) Cumulative average abnormal return (Z-statistic) Mean market value of equity ($M) Mean change in wealth ($M)

Purchasing Firms (N = 85)

Selling Firms (N = 29)

0.44% (0.04)

4.69% (1.13)

0.07% (0.56; 55%)

5.42% (7.84; 76%)*

0.17% (0.24; 54%)

8.15% (8.24; 83%)*

0.31% (1.03)

−2.87% (1.86)∗∗

21,369 119.36

252 20.04

Note: The table reports the announcement day as well as pre- and post-announcement returns for both the purchasing and selling firms forming an alliance involving the purchase/sale of a minority equity stake. The market value of equity as well as the dollar change in equity value is also reported for both purchasing and selling firms. The market value of equity is the market value of the firm’s common stock 21 trading days before the initial announcement of the equity alliance. The mean dollar change in wealth is computed by first multiplying each participating firm’s market value of equity by its two-day (0, +1) cumulative abnormal return and then averaging the product across firms in the Purchasing firm or selling firm sample. ∗ Significant at the 5% level for a two-tailed test.

is 5.42% (Z-statistic = 7.84). The average abnormal return over the two-day announcement period is a statistically significant 8.15% with a Z-statistic of 8.24. This evidence indicates that significant value is created for the stockholders of the selling firms when a minority equity buy-in to form an alliance is announced. For both the purchasing and selling firms, we find that the cumulative average abnormal return (CAAR) in the pre-announcement period (−20, −1) is insignificant. In the post-announcement period (2, 10) the CAAR is insignificant for the purchasing firms, but is a significant −2.87% for the selling firms. This suggests that the market may have overreacted to the news of the minority equity alliance for the selling firms when it was announced. However, considering that the CAAR on days 0 and +1 is a significant 8.15%, the selling firms still garner a net gain. The finding that the gains accrue to selling firms but not to purchasing firms is consistent with prior studies of mergers and acquisitions. The result is also in line with findings for joint-ventures and non-equity strategic alliances in which the

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smaller strategic partner (analogous to the selling firm) reaps a higher abnormal return compared to the larger partner (analogous to the purchasing firm). Similarly, in the subset of their sample that involved the announced formation of alliances and joint ventures, Allen and Phillips (2000) find that the stock prices of selling firms respond positively while purchasing firms do not. For their entire sample of block equity purchases they find that the cumulative average excess stock returns to sellers over a 21-day (−10, +10) interval is a significant 6.9%. The response is greater (9.1%) for the subset of their sample where the equity purchase is accompanied by the announced formation of a product market relationship in the form of joint ventures or alliances. Similarly, we find that for the same 21day period the selling firms involved in minority equity alliances the cumulative average excess stock returns is a significant 8.35%. In their study of accumulations of 5% or more of another company’s shares Mikkelson and Ruback (1985) find that, in general, the share prices of both the acquiring and selling firms increase in response to the initial disclosure of the investment position. In contrast, we find that where the motive of the equity buy-in is to form an alliance, only the stock prices of the selling firms respond favorably. It is possible that our inability to detect a significant abnormal return for the acquirer is due to the large size differential between the purchasing and the selling firms in our sample. Table 5 shows that purchasing firms are significantly larger (85 times the market capitalization of) than the selling firms. To investigate this possibility we investigate dollar returns corresponding to the announcement period abnormal returns. To obtain a measure of the dollar change in wealth for the purchasing and the selling firms, we first multiply each participating firm’s market value of equity by its two-day cumulative abnormal return and then average the product across firms in the sub-samples. We find that the mean dollar change in wealth (based on two-day abnormal returns) for the sellers is $20.04 million while that experienced by the purchasing firms is $119.36 million. These dollar returns suggest that on average the formation of a minority equity alliance benefits both the purchasing and selling firms. The average excess stock returns for selling firms in our sample are higher than that obtained by Mikkelson and Ruback (1985) in their study of interfirm investment and by Wruck (1989) who examines private equity sales. Mikkelson and Ruback report a two-day excess return of 3.24% while Wruck reports an excess return of 4.5%.15 One possible explanation for this result is that the alliances we study are expected to generate improvements in the utilization of corporate resources or to mitigate information asymmetry problems such that they create greater value than the sale of equity to a passive investor. The purchasing firm results are different from those of Mikkelson and Ruback (1985). They find statistically significant two-day abnormal returns (1.27%,

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35

see their Table 4, p. 535) for purchasing firms while our sample produces an insignificant two-day abnormal return (0.33%).16 This result may be due to differences in sample composition for the two studies. Interfirm equity purchases can also be made as a part of a passive investment strategy wherein the acquiring firm does not intend to become involved in the business of the selling firm and only hopes to reap its proportionate share of the selling firm’s returns. The Mikkelson and Ruback sample may include alliances formed with both active and passive investment motives whereas we study only those cases in which the acquirer plans to engage in an active investment strategy involving the selling firm. It is also noteworthy that the majority of selling firms in equity alliances are small entreprenuerial firms, and consequently the relative size of the purchasing firm compared to the seller may be much larger in our sample than in Mikkelson and Ruback’s sample. Thus the lack of significance in the returns to the purchasing firms in our study may simply be due to the relative size of the event’s valuation impact relative to the size of the firm. We test for the possibility of a wealth transfer between the purchasing and selling firms by estimating the correlation between the two-day announcement period abnormal returns for the subsample of 23 equity alliances for which both the purchasing and selling firms are in our sample. If sellers were benefiting at the expense of purchasing firms or vice versa, then we would expect this correlation to be negative and significant. The resulting coefficient was −0.03 and was not statistically different from zero. Consequently, we find no evidence of wealth transfers between purchasing and selling firms.

4.2. Determinants of Value Effects We conduct multiple regression tests to explain cross-sectional differences in abnormal returns for purchasing and selling firms using variables related to attributes that may lead to greater value creation. The explanatory variables include the technology status of the firm (HITECH = 1 for firms in high tech industries and 0 otherwise), R&D intensity (R&D/sales), growth opportunities as measured by the ratio of book to market value equity (BV/MV), riskiness as measured by the variance in daily stock returns over the two years prior to the formation of the alliance (Variance), the proportionate control that changes hands in the transaction as measured by the percentage of equity that the purchasing firm intends to purchase from the selling firm (Stake), and the relatedness of the industry affiliation of the partnering firms (Related Industry = 1 if the allied firms are from a similar industry, and 0 otherwise). The rationales for including these explanatory variables were discussed earlier in Section 2.

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We include the logarithm of the market value of firm equity (on event day −21) in the regression to control for the influence of firm size (Firm Size). We also construct an indicator variable that equals 1 if the alliance agreement involves research and/or development to test whether there is a difference in share price response between alliances where the stated purpose of the agreement involves research and/or development versus non-R&D types of agreements (such as marketing agreements). Since we do not find the type of agreement to be a differentiating factor we do not report this regression result. Panels A and B of Table 6 present the estimated coefficients from the crosssectional regressions involving the two-day cumulative abnormal return for the purchasing and selling samples, respectively. Panel A shows that the valuation effect for the purchasing firms is positively correlated with their R&D intensity. In other words, purchasing firms that are more R&D intensive seem to reap higher returns from forming a minority equity alliance than their less R&D intensive counterparts. Panel B shows that the abnormal returns for the selling firms have significant positive relationship with the Variance, Stake and Related Industry variables. A positive coefficient for the Variance variable indicates that selling firms with more volatile stock returns enjoy higher abnormal returns from forming the alliance. The positive and significant coefficient for the Stake variable suggests that the larger the minority stake purchased by the purchasing firm, the higher the abnormal returns for the selling firms. This result supports the hypothesis that the larger the size of the minority equity stake relative to the seller’s outstanding shares, the lower is the risk of opportunism and consequently the greater the potential value that is created by the alliance. Finally, selling firms that tie-up with purchasing firms that are in a related industry are associated with significantly higher abnormal returns. This result conforms to the hypothesis that purchasing firms from a related industry are better able to evaluate the selling firm’s assets-in-place and its growth options thus mitigating the information asymmetry problems regarding the selling firms. Although the BV/MV variable has a negative coefficient (suggesting that firms with higher (lower) growth opportunities tend to get a higher (lower) payback from forming an alliance), it is not significant.

4.3. Operating Performance of Firms that Form Equity Alliances In this section we examine the operating performance of both purchasing and selling firms that engage in minority equity alliances. We compare the relative operating performance of these firms to their peers in the two years preceding and three years following the announcement of the formation of an alliance to

Dependent Variable

Intercept

Firm Size

HITECH

R&D Intensity

Panel A: Results for publicly-traded purchasing firms (N = 46) CAR(0,1) −0.058 0.003 −0.012 0.262 (−1.64)** (1.306) (−1.104) (1.87)** Panel B: Results for publicly-traded selling firms (N = 21) CAR(0,1) −0.046 0.001 −0.002 −0.100 (−0.60) (0.06) (−0.063) (−1.74)

BV/MV

Variance

STAKE

Related Industry

R2

Adjusted R2

F-value

0.011 (0.76)

−2.54 (−1.57)

0.001 (1.07)

−0.001 (−0.136)

17.8%

2.6%

1.17

0.006 (3.09)*

0.062 (2.42)*

68.5%

51.48%

4.03

−1.102 (−1.72)

49.995 (3.52)*

Note: This table reports the cross-sectional regression results obtained by regressing the two-day (0, +1) cumulative abnormal return for investing (and sellers) firms on selected variables representing firm size, technology status of firm (HITECH), R&D intensity, growth opportunities (BV/MV), riskiness of firm (variance), percentage of equity stake in the selling firm (STAKE), and industry relatedness (RELATED INDUSTRY). Firm size is measured by the logarithm of the market value of equity 21 days prior to the announcement of the alliance. Hitech is a dummy variable that takes a value of one if the firm is classified as a high tech firm. R&D intensity is the ratio of the firm’s R&D expenditures to its net sales. BV/MV measures a firm’s growth options and is computed as the ratio of book value of the firm’s assets to the market value of the firm’s assets (measured as the sum of the market value of the firm’s equity plus the book value of its liabilities). Variance, a measure of the riskiness of the firm, is the variance in daily stock returns (from CRSP tapes) over the two years preceding the announcement of the minority equity investment. Stake is the percentage of equity of the selling firm reported in the news article that the investing firm says it will purchase. RELATED INDUSTRY is a dummy variable that takes a value of one if the investing and selling firm are from the same 3-digit SIC industry. R&D intensity and BV/MV are computed using data from the Compustat tapes the year prior to the announcement of the formation of the equity alliance. There are 46 observations from the investing firm sample and 21 observations from the seller sample that have complete data on all the variables used in the regression. ∗ Significant at the 5% level for a two-tailed test. ∗∗ Significant at the 10% level for a two-tailed test.

Minority Equity Investments and Inter-Firm Collaborations

Table 6. Determinants of Abnormal Returns for Purchasing and Selling Firms Engaged in Alliances Involving Minority-Equity Investments in the 1981–1992 Period.

37

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gain insight into the circumstances under which managers choose to engage in such alliances. There are two issues addressed in this analysis. First, do firms that enter into alliances do so because they are performing poorly or simply because the purchasing firms have the cash flow to invest? Mohanram and Nanda (1996) observe that firms entering into joint ventures tend to be experiencing deteriorating performance. Second, does the operating performance of alliance partners improve or deteriorate following the equity tie-up? Data on operating performance spanning the six-year period surrounding (two years before to three years after) the announcement of the minority equity alliance is obtained from the COMPUSTAT. We measure operating performance using operating cash flow return on assets (OCF-ROA) which is computed by dividing the earnings before interest, taxes, depreciation, amortization, and extraordinary items (COMPUSTAT mnemonic EBITDA) by the book value of total assets. To adjust for industry influences we calculate industry-adjusted performance measures as the difference between the announcing firm value in a given year and the median value for all firms on COMPUSTAT with the same four-digit SIC code.17 The number of observations in each year varies depending on the availability of COMPUSTAT data. Panels A and B of Table 7 report the operating performance results for the set of purchasing and selling firms. These results indicate that firms that acquire equity shares in an alliance partner, on average, have higher operating cash flow to assets than their industry peers over the entire six year period beginning two years before the announcement of the formation of an alliance. This suggests that purchasing firms that engage in minority equity alliances tend to be cash rich firms and therefore their participation in such alliances is not motivated by poor performance. Furthermore, Panel A shows that when firm performance relative to its industry peers is analyzed for three years following the formation of the alliance, the purchasing firm’s relative cash flow position is reduced significantly (although it is still above the industry) when compared to its cash flow position in the year preceding the equity participation. This evidence suggests that purchase of a minority equity stake is a way for the cash-rich firms to spend their cash. Selling firms, on the other hand, show negative operating cash flow-to-asset position in most of the years surrounding the announcement of the minority equity alliance. Furthermore, the selling firms perform significantly worse than their industry peers in the two years leading up to the equity tie-up announcement. Unlike the purchasing firms, however, the operating cash flow-to-asset position of the sellers show significant improvement in the third year following the equity tieup when compared to the year preceding the alliance announcement. The above results suggest that poor performance may be a motivation for selling firms to enter into interfirm collaborations involving minority equity participation by the

Year Relative to Minority Equity Purchase Announcement −2

−1

Panel A: Operating performance of purchasing firms Number of observations 77 82 18.0* Average of firm-level OCF-ROA (%) 18.7* Industry-adjusted OCF-ROA Average (%) 8.0* 7.8* % Positive 83 80 Change in industry-adjusted OCF-ROA Year −2 vs. Year −1: −0.40% Panel B: Operating performance of selling firms Number of observations 26 29 Average of firm-level OCF-ROA −5.0 −4.0 Industry-adjusted OCF-ROA Average (%) −12.1* −9.7* % Positive 46 45 Change in industry-adjusted OCF-ROA Year −2 vs. Year −1: 2.20%

0

82 17.8* 8.0* 82

27 −9.6 −16.2 41

1

83 16.6*

2

82 15.8*

7.5* 7.7* 82 83 Year −1 vs. Year +3: −1.2%** 24 3.6

23 −1.5

−3.0 −8.2 46 43 Year −1 vs. Year +3: 5.7%**

3

81 15.6* 6.9* 81

20 3.6 −2.7 50

Minority Equity Investments and Inter-Firm Collaborations

Table 7. Operating Performance of Purchasing and Selling Firms in Minority Equity Alliances Surrounding Minority Equity Purchase Announcements.

Note: Performance is measured using operating cash flow return on asset (OCF-ROA). OCF-ROA is computed using the earnings before interest, taxes, depreciation, amortization, and extraordinary items (EBITDA) divided by total assets. The industry-adjusted performance measure equals the difference between the announcing firm’s measure in a given year and the median value for all firms on COMPUSTAT with the same four-digit SIC code. The number of observations in each year varies depending on the availability of COMPUSTAT data. ∗ Significant at the 5% level for a two-tailed test. ∗∗ Significant at the 10% level for a two-tailed test.

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partnering firm. In addition, the alliance and equity stake seem to help improve the operating performance of the selling firms. In summary, the above results suggest that, unlike joint venture agreements, poor performance is not a motivation for purchasing firms to enter into interfirm collaborative agreements involving a minority equity stake. For selling firms, however, poor operating performance may be a motivation for them to enter into minority equity alliances. In addition, the post-performance results for both the purchasing firms and selling firms seem to be in line with the evidence we present on the market’s response to the announcement of minority equity tie-ups by purchasing and target firms.

5. CONCLUSIONS Minority-equity investment in a strategic partner’s common stock is frequently used to finance an alliance and to bond the partnering firms to the agreement. The partner that sells the equity stake gets an immediate cash infusion, while the purchasing partner gets a percentage of the seller’s profits plus access to the seller’s skills and technology as prescribed in the alliance agreement. Based on 93 announcements of companies making minority-equity commitments in strategic partners who indicate no intention to seek control of the partnering firm, we find that the average stock price response is neutral for the acquiring firms, but positive and significant for the selling firms. Further, we find no evidence that the gains to the selling firms are a result of a wealth transfer from the purchasing firms. The finding of significant positive wealth gain for the selling firms is consistent with Mikkelson and Ruback’s (1985) study of interfirm equity investments, Wruck’s (1989) study of private equity sales, and Allen and Phillips’ (2000) study of corporate equity ownership associated with product market relationships. Our cross-sectional analysis reveals that the twoday announcement abnormal returns for the selling firms are positively related to the amount of equity invested by the purchasing firms, their riskiness as reflected in the variability of their stock returns, and the relatedness of the industry to which the purchasing firm belongs. The analysis also reveals that purchasing firms that are more R&D intensive seem to reap higher returns from a minority equity alliance than their less R&D intensive counterparts. The evidence from this study suggests that the pooling of resources in a minority equity alliance benefits the selling firms. The change in the selling firm’s value could be derived from enhanced financing flexibility, a lowering of transactions costs, and a more efficient use of corporate resources under the minority equity arrangement. In addition, the purchase of minority equity stake by a sophisticated

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purchasing firm solely for the purpose of forming a strategic alliance can constitute an endorsement of the selling firm’s management and future prospects. Therefore, the positive valuation observed for the selling firm’s stock could also be due to this revelation of new information to the market concerning the seller’s future prospects. Within three years of the announced formation of an alliance the majority of the agreements continue unchanged. Of those that do change, the largest number are expanded or strengthened. The result is an increase in the equity stake, formation of a joint venture or merger of the partnering firms. A very small percentage of the alliances terminate within three years of their formation. These results provide evidence that firms engaging in minority equity alliances often take advantage of the flexibility afforded in alliances to alter their relationships, possibly to adapt to evolving market conditions. Finally, firms that acquire minority stakes in alliance partner firms tend to have better operating performance than their peers during the period two years before through three years following the announcement of the agreement. The cash flow position of the purchasing firms, however, deteriorates somewhat in the three years following the announcement, compared with their own prior cash flow position (although still better than industry peers). Selling firms, on the other hand, tend to perform worse than their industry peers in the two years before the announcement of their engaging in the formation of an equity alliance. Their performance in the three years following the announcement, however, improves significantly when compared to their pre-alliance performance. This evidence on the selling firms differs from that observed for non-equity alliances and suggests that poor performance may be a motivator for selling firms to participate in alliances that involves equity participation by a cash rich partner.

NOTES 1. See Chan et al. (1997) for an analysis of non-equity strategic alliances. 2. Mikkelson and Ruback (1985) and Choi (1991) observe positive stock market responses to the announcement of interfirm equity investments, while Wruck (1989) and Hertzel and Smith (1993) observe positive abnormal returns to announcement of private sales of equity mainly to institutions. Wruck notes that the change in firm value depends on the level of ownership concentration after the sale of equity and the purchaser’s current or anticipated future relationship with the firm. Also Bethel et al. (1998) show the effectiveness of activist block owners in helping restructure selling firms and in improving their operating performance. Note that although these studies distinguish between toehold investments (in anticipation of a takeover) and all other investment motives, they do not delineate between passive investment motives and the strategic (or collaborative) motives that we examine in this paper.

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3. Allen and Phillips (2000) examine a sub-sample of block equity purchases that are accompanied by alliances and joint ventures formed within a two-year interval either prior to or subsequent to the purchase. 4. Morck et al. (1988) find that smaller firms find information asymmetry problems to be particularly acute, which would make minority equity alliances particularly attractive for these firms. For more about public versus private equity offerings, see Wu (2000). 5. For more discussion on this issue, see Parkhe (1993) and Chan et al. (1997). 6. See Pisano (1989) for a discussion of the role of equity financing in reducing the incentives for opportunism by partners in an equity alliance. Williamson (1985, p. 191) describes a double hostage system for bonding an alliance “. . . reciprocity involves the sale of specialized product to B conditioned on the procurement of specialized product from B. The argument here is that reciprocity can serve to equalize the exposure of the parties, thereby reducing the incentive of the purchaser or seller to defect from the exchange – leaving the supplier to redeploy specialized assets at greatly reduced value.” 7. Madden (1981) found that the Wall Street Journal date preceded the Insider’s Chronicle date (that reports Schedule 13D filings) by an average of 37 days. The average delay between the filing date of the Schedule 13-D and the date of the Insider’s Chronicle was 23 days. 8. Minority equity purchases have been used extensively to forge alliances between large publicly-held firms and smaller privately-held firms and also between domestic U.S. and foreign firms. Therefore, we include publicly-traded firms (with returns data available on the CRSP) regardless of whether they form minority equity alliances with a publicly traded firm, a private firm or a foreign firm. 9. The number of purchasing (selling) firms in the final sample excludes four (two) publicly-traded foreign firms that do not have stock return data in the CRSP file. 10. For example, in 1989, the Ascom Group of Switzerland (the largest communications and services automation equipment company in Switzerland) made a $6 million direct investment in New York based Comverse Technology Inc. (one of the leading international suppliers of computerized message management systems) for 17 million shares, giving it an ownership position of 13.7% (Business Wire, August 17, 1989). The investment was made as part of a multi-faceted strategic alliance formed by the two companies to distribute message management systems to organizations that provide subscriber services in selected markets of Western Europe. Under the pact, Ascom will also market Comverse’s defense and related communications processing systems in Switzerland, West Germany and other markets. 11. For those firms that are not publicly-traded, we read the news articles describing the minority equity alliance to find out the industry in which those firms are operating. 12. Since we rely on press releases for information we recognize the possibility that firms may simply not announce changes in the status of their alliances following the initial announcement. 13. For example, in October, 1993 IBM sold its entire equity interest in Hogan Systems Inc. back to Hogan in a private market transaction. IBM has bought approximately 5% of Hogan’s system’s stock since September 1990 to strengthen a strategic partnership that has existed between the two companies since 1986. The sale was profitable for IBM due to the strong increase in price of Hogan’s stock. For Hogan, the sale was potentially profitable because it hopes to make a better return from the repurchase of those shares than from holding cash. A Hogan senior vice president said it is not clear yet if Hogan and IBM will

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extend the current exclusive marketing agreement after it expires in 1995 (Business Wire, 10/4/93). 14. We also compare the excess returns for firms that purchase equity stakes in private firms with those that purchase equity stakes in public firms and find no significant difference. 15. The results for the Mikkelson and Ruback (1985) study reflect the abnormal returns for a sample of 106 firms that sold shares to other firms who stated that their purchase objective was for investment purposes. Similar results for selling firms that were the target of a takeover attempt were much higher (7.74%). 16. As in Mikkelson and Ruback, we also evaluated the abnormal returns of the purchasing firms based on whether they are frequent (appearing in our sample six or more times) or infrequent purchasers of minority equity. As for the full sample, the abnormal returns for both sub-samples are insignificant. 17. Allen and Phillips (2000) use a similar technique to examine operating income changes surrounding corporate equity purchases. See also Barber and Lyon (1996).

ACKNOWLEDGMENTS We thank Marshall Bloom, Andrew Chen, David Denis, Diane Denis, Ning Gong, Mike Impson, Paul Laux, Ray Miles, Ko Wang as well as participants at the Texas Finance Symposium and the Financial Management Association Meeting for comments on previous versions of this paper. We are also grateful to Yajat Bindal and Jaafar Salwani for their research assistance.

REFERENCES Allen, J. W., & Phillips, G. M. (2000). Corporate equity ownership and product market relationships. Journal of Finance, 25, 2791–2815. Balakrishnan, S., & Koza, M. P. (1993). Information asymmetry, adverse selection and joint ventures. Journal of Economic Behavior and Organization, 20, 99–117. Barber, B., & Lyon, J. (1996). Detecting abnormal operating performance: The empirical power and specification of test-statistics. Journal of Financial Economics, 3, 359–400. Bethel, J. E., Liebeskind, J. P., & Opler, T. (1998). Block share purchases and corporate performance. Journal of Finance, 53, 605–634. Chan, S. H., Keown, A. J., Kensinger, J. W., & Martin, J. D. (1997). Do strategic alliances create value? Journal of Financial Economics, 46, 199–221. Chan, S. H., Martin, J. D., & Kensinger, J. W. (1990). Corporate research and development expenditures and share value. Journal of Financial Economics, 26, 255–276. Choi, D. (1991). Toehold acquisitions, shareholder wealth, and the market for corporate control. Journal of Financial and Quantitative Analysis, 26, 391–407. Dodd, P., & Warner, J. B. (1983). On corporate governance. Journal of Financial Economics, 11, 401–438. Harrigan, K. R. (1985). Strategies for joint ventures. Lexington, MA: Lexington Books.

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Hertzel, M., & Smith, R. L. (1993). Market discounts and shareholder gains for placing equity privately. Journal of Finance, 48, 459–485. Jensen, M. C., & Meckling, W. (1991). Specific and general knowledge, and organizational structure. In: L. Werin & H. Wijkander (Eds), Main Currents in Contract Economics. Oxford: Blackwell. Johnson, S., & Houston, M. B. (2000). A reexamination of the motives and gains in joint ventures. Journal of Financial and Quantitative Analysis, 35, 67–85. Kensinger, J. W., & Martin, J. D. (1991). Financing network organizations. Journal of Applied Corporate Finance, 4, 66–76. Klein, B., Crawford, R., & Alchian, A. (1978). Vertical integration, appropriable rents, and the competitive contracting process. Journal of Law and Economics, 21, 297–326. Madden, G. P. (1981). Potential corporate takeovers and market efficiency: A note. Journal of Finance, 36, 1191–1197. McConnell, J., & Nantell, T. (1985). Common stock returns and corporate combinations: The case of joint ventures. Journal of Finance, 40, 519–536. Mikkelson, W. H., & Ruback, R. S. (1985). An empirical analysis of the interfirm equity investment process. Journal of Financial Economics, 523–553. Mody, A. (1993). Learning through alliances. Journal of Economic Behavior and Organization, 20, 151–170. Mohanram, P., & Nanda, A. (1996). When do joint ventures create value? Academy of Management Proceedings, 36–40. Morck, R., Shleifer, A., & Vishney, R. (1988). Management ownership and market valuation: An empirical analysis. Journal of Financial Economics, 20, 293–315. Murray, A. I., & Siehl, C. (1989). Joint venture and other alliances: Creating a successful cooperative linkage. Morristown, NJ: Financial Executives Institute. Parkhe, A. (1993). Strategic alliance structuring: A game theoretic and transaction cost examination of interfirm cooperation. Academy of Management Journal, 36, 794–829. Pisano, G. (1989). Using equity participation to support exchange: Evidence from the biotechnology industry. Journal of Law, Economics, and Organization, 5, 109–126. Williamson, O. (1985). The economic institutions of capitalism. New York, NY: Free Press. Wruck, K. H. (1989). Equity ownership concentration and firm value: Evidence from private equity financings. Journal of Financial Economics, 23, 3–28. Wu, Y. (2000). The choice between public and private equity offerings. Unpublished Working Paper, University of Chicago.

SIZE AND BOOK-TO-MARKET EFFECTS IN THE RETURNS ON INFORMATION TECHNOLOGY STOCKS Quang-Ngoc Nguyen, Thomas A. Fetherston and Jonathan A. Batten ABSTRACT This paper explores the relationship between size, book-to-market, beta, and expected stock returns in the U.S. Information Technology sector over the July 1990–June 2001 period. Two models, the multivariate model and the three-factor model, are employed to test these relationships. The risk-return tests conﬁrm the relationship between size, book-to-market, beta and stock returns in IT stocks is different from that in other non-ﬁnancial stocks. However, the sub-period results (the periods before and after the technology crash in April 2000) show that the nature of the relationship between stock returns, size, book-to-market, and market factors, or the magnitude of the size, book-to-market, and market premiums, is on average unchanged for both sub-periods. This result suggests the technology stock crash in April 2000 was not a correction of stock prices.

Research in Finance Research in Finance, Volume 21, 45–91 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21003-6

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1. INTRODUCTION One of the most important debates among financial economists, as well as financial practitioners, in recent years concerns the valuation of information technology (IT) stocks. The valuation of IT stocks is not an easy task as many of these firms do not have, or have only a short history of stock performance. Even for those few firms that do have a long history of performance, the prediction of future earnings is extremely difficult due to unique features of the sector. Future earnings of firms in the IT sector depend on the opportunity, the company, the management, or the future outcome of the research and development activity, which are as difficult to estimate as predicting future earnings themselves (Trueman, Wong & Zhang, 2001). Empirical studies investigating IT stock valuation have used options (Franklin, 2000) or web traffic (for internet stocks, Rajgopal, Kotha & Venkatachalam, 2000), while Sadorsky (2003) finds that the conditional volatilities of oil prices, the term premium, and the consumer price index each have a significant impact on the conditional volatility of technology stock prices. An implicit feature of these studies is the assumption that IT stocks are “special” and consequently traditional valuation models – such as the discounted cash flow model – may argued to be inappropriate. However, no single paper has empirically explained why IT stocks are special, except for those that cite the abnormal price-earnings ratios (P/E) associated with these stocks as evidence for their “specialty” (Shiller, 2000). The objective of this paper is to investigate why IT stocks are special by utilizing a comparative perspective which tests the relation between size, book-to-market equity, beta, and stock returns and then compares the magnitude of this relationship with that found in earlier studies (Fama & French, 1992, 1993). The paper also tests the difference in the risk-return relationship for IT stocks before and after the technology stock crash in April 2000. Investigating IT stocks in a comparative perspective can lead to evidence that would help financial academics as well as practitioners differentiate IT stocks from other stocks, as well as providing further insight into questions concerning valuation. There is one obvious benefit arising from the distinction between IT stocks and “old economy” stocks.1 It is logical that a new valuation model for IT stocks should be developed if IT stocks are radically different from “old economy’ stocks. It is equally reasonable a priori that the extant discounted cash flows model should be sufficient to produce accurate measurements of IT stock prices, if there is no distinction between IT stocks and “old economy” stocks. In the case of no distinction, looking for a new model for the valuation of IT stocks would be pointless. The evidence on the relation between size, book-to-market equity, beta, and stock returns in the IT sector is investigated in this paper using two alternative

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risk-return testing models. In the first model, or the multivariate model, direct measurements of firm size, book-to-market ratio, and market betas are applied. The model is then used in the Fama and MacBeth (1973) cross-sectional regressions to test the significance of the coefficients on the size, book-to-market, and beta variables. This is the simplest approach and was widely used prior to the introduction of the three-factor model by Fama and French (1993). In the threefactor model, firm size, book-to-market ratio, and market beta are not applied directly. In contrast, these variables are represented by the returns on the three portfolios formed in a way that closely mimics firm size, book-to-market ratio, and market beta. The time-series regressions are applied to the three-factor model. To address any biases introduced by the impact of the technology crash in April 2000 on the behavior of stock prices, this analysis is carefully divided into two sub-periods: one before the crash and one after the crash. Thus the paper provides an insight into how IT stocks behave in the lead-up to the crash, after the crash as well as how they behave over the whole sample period, from July 1990 to June 2001. The paper improves the regression approaches used by Fama and French (1992, 1993). This paper employs the Fama and MacBeth (1973) procedure to estimate the coefficient slopes on the size, book-to-market, and beta variables. Another improvement, is that the paper uses the Seemingly Unrelated Regressions (SUR) methodology to estimate the coefficients for the three-factor model. This procedure runs time-series regressions for all portfolios as a whole, and gives estimators of the coefficients after adjusting for cross-correlation between the portfolios’ residuals. Individually the results are robust. However the two models, the multivariate model and the three-factor model, produce different results. In tests using the multivariate model, the book-to-market ratio is the only significant factor that explains variation in stock returns. However, the book-to-market effect is only significant at the 10% level, in contrast to Fama and French (1992) who find that the effect is very robust (at the 5% level) for all non-financial stocks listed on the NYSE, AMEX, and NASDAQ over the 1963–1991 period. Another difference is that this paper finds no relationship between size and stock returns. Nevertheless, the paper does discover that beta has weak explanatory power, which is similar to their earlier finding. In tests using the three-factor model, all the returns on the portfolios that are designed to mimic the size, book-to-market, and market (beta) factors are strongly related to returns on size – book-to-market sorted portfolios. This evidence is in favor of the three-factor model. The different results produced by the multivariate model and the three-factor model suggest that the two models might not be comparable. The excess returns on the size – book-to-market portfolios and the market portfolios before the technology crash in April 2000 (the pre-crash excess

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returns) are negative while the excess returns on those portfolios after the crash (the post-crash excess returns) are indistinguishable from zero. However, this paper finds that the relation between size, book-to-market, beta, and portfolio returns (using the three-factor model) is similar for the periods before and after the crash. The remainder of this paper is organized as follows. Section 2 describes the differing empirical evidence on the risk-return relation as well as summarizes alternative explanations for the size and book-to-market anomaly. Specific hypotheses are then proposed. The data, its source, and the measurements of variables for the risk-return tests are presented in Section 3. Section 4 discusses the multivariate model and the three-factor model as well as the reasons for their uses. Section 5 provides the regression results. Section 6 concludes the paper and suggests the direction for future research.

2. LITERATURE REVIEW 2.1. Background Sharpe (1964) and Lintner (1965) suggest a positive linear relation between individual security risk and its expected return. This relationship is expressed by the well-known Capital Asset Pricing Model (CAPM) where: E(R i ) = E(R f ) + [E(R m ) − E(R f )]␤i

(1)

The symbols in Eq. (1) are defined as follows: E(R i ) is the expected return on security i for the period and is equal to the change in the price of the security, plus any dividends, interest, or other distributions, divided by the price of the security at the start of the period; E(R m ) is the expected return on the market portfolio of all securities taken together; E(R f ) is the return on the riskless security for the period; ␤i is the contribution of security i to the risk of the market portfolio and is often called the “systematic risk” of security i. is defined algebraically by: ␤i =

Cov(R i , R m ) Var(R m )

(2)

Nevertheless, the applicability of the CAPM has been questioned with a number of studies in the asset-pricing literature demonstrating a weak relationship between beta and stock returns. Many findings show that market ␤s of stocks are not sufficient to explain stocks returns (e.g. Banz, 1981), or more bluntly the relationship between market ␤s and average stock returns is flat (e.g. Fama & French, 1992). Additional factors, such as firm size, book-to-market equity, have been introduced to accommodate actual stock return behavior. The failure

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of the CAPM to explain empirical evidence, or the deviation from the CAPM is considered as an “anomaly” in the risk-return relationship and is attributed to the following two anomalies. 2.1.1. Firm Size Anomaly Banz (1981) discovered the firm size anomaly in a sample of common stocks listed on the NYSE between 1926 and 1975. After forming stocks into 25 sizebeta portfolios containing similar numbers of securities he ran month-by-month cross-sectional regressions of portfolio returns on their betas and market values and found that in addition to portfolio ␤, the market proportion of a security was statistically significantly related to the security’s expected return. This relationship is negative: stocks of firms with large market values have smaller returns than stocks of small firms of equal market betas. The negative relationship between firm size and stock return was confirmed by Keim (1983) who controlled for possible bias in ␤ estimates, using three different estimators of beta: the OLS betas, Scholes-William (1977) betas and Dimson (1979) betas. Fama and French (1992) also demonstrated a negative relationship between stock returns and firm size. The robustness of the size effect and the absence of a relationship between ␤s and average returns was also true for the extended 1941–1990 period (Fama & French, 1992). Interestingly, Fama and French claim that if Black, Jensen and Scholes (1972) and Fama and MacBeth (1973) had controlled for the size effect, the relationship between ␤s and average returns would have disappeared. 2.1.2. Book-to-Market Anomaly Along with the size effect, Fama and French (1992) also find that book-to-market equity (ratio of book equity (BE) to market equity (ME)) captures variation in the cross-section of average returns. Firms with high ratios of book value to the market value of common equity have higher average returns than firms with low book-to-market ratios; a result consistent with earlier findings Rosenberg, Reid and Lanstein (1985). Barber and Lyon (1997a) supplement Fama and French’s (1992) with supporting empirical evidence for stocks in the financial sector. Empirical evidence for the extended period, the 1940–1962 period, also reveals a strong relationship between book-to-market ratio and stock returns (Davis, 1994).

2.2. Explanations for These Anomalies The apparent violations of the CAPM have inspired financial academics to find plausible explanations for these violations. The reasons for the failure of the CAPM

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could be classified into three categories: risk-based explanations, psychologybased explanations, and characteristics-based explanations. 2.2.1. Risk-Based Explanations The risk-based category generally focuses on the possible errors in tests of the CAPM, or the missing risk factors that are not captured by market betas.According to Fama and French (1992), one of the possibilities for the failure of ␤ in predicting average returns is that other explanatory variables (i.e. size, book-to-market equity, leverage) are correlated with true ␤s, and this obscures the relationship between average returns and measured ␤s. Another is that there is a positive relationship between ␤ and average return, but the relationship is obscured by noise in the ␤ estimates. However, Chan and Chen (1988) argue that the observed size effect is just a risk effect in disguise. They posit firm size is a good instrument for risk, therefore if ␤s are measured in such a way that captures the size variable, ␤ itself is sufficient to explain average returns. In other words, Chan and Chen believe the SLB model works if ␤s are estimated more precisely. Chan and Chen propose that the size-sorted portfolios’ ␤s follow a stationary distribution: ¯ + ␩˜ it ␤˜ it = ␤¯ i + ␪˜ t (␤¯ i − ␤)

(3)

where ␤¯ i is the time-series mean of security i’s betas; ␤¯ is the cross-sectional mean of ␤¯ i s; ␪˜ t has zero mean and ␩˜ it is a random noise independent of all other parameters. With ␤s being estimated under this stochastic assumption, Chan and Chen find the size premium, in tests including ␤s and firm size variables, is not statistically different from zero. In contrast, they observe a strong positive relationship between their adjusted ␤s and average returns. The data they use are for the 1954–1983 period. This argument was rejected by Jegadeesh (1992), who shows that Chan and Chen’s (1988) result is obscured by a high correlation between ␤s and the size factors. Thus, it is not surprising that their ␤s explain most of the cross-sectional differences in average returns even if the average returns are related to firm size. When the test portfolios are constructed so that the market betas have low crosssectional correlation with firm size (i.e. ln(size)), Jegadeesh (1992) finds the size effect still exists. Another approach argues that the relationship between size and average return proxies for a more fundamental relationship between expected returns and economic risk factors. The empirical evidence in Fama and French’s (1995) paper further supports the risk-based explanations for the size and book-to-market effects. Fama and French (1995) find that BE/ME is related to earnings. Low BE/ME is typical of firms with high average returns on capital, whereas high BE/ME is typical of firms that are relatively distressed. Size is also related to profitability.

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Controlling for BE/ME, small stocks tend to have lower earnings on book equity than do big stocks. A third risk based explanation concerns the presence of “data-snooping statistics” as used by Aldous (1989, p. 252) to describe the situation “where you have a family of test statistics T(a) whose null distribution is known for fixed a, but where you use the test statistic T = T(a) for some a chosen using the data.” Lo and MacKinlay (1990b) argue that if the choice of a is based on the data, then the sampling distribution of the resulting test statistic is generally not the same as the null distribution with a fixed a; hence, the actual size of the test may differ substantially from its nominal value under the null. Other possible biases related to the data-snooping bias are also suggested by many financial academics. Black (1993) and MacKinlay (1995) say that the deviations from the CAPM are sample-specific results that are unlikely to be observed in various sets of data. However, other studies do not support the datasnooping bias, sample-specific bias, and the selection bias explanations for the deviations from the CAPM. Chan, Hamao and Lakonishok (1991), Capaul, Rowley and Sharpe (1993), and Fama and French (1998) document strong relationships between average return and BE/ME in markets outside the U.S. Davis (1994) finds that the relationship between average return and BE/ME observed in recent U.S. returns extends back to 1941. Even the relationship exists for data back to 1926 with the pre-1963 value premium is close to that observed for the subsequent period in earlier work. 2.2.2. Psychology-Based Explanations This explanation proposes that the value premium is due to investor overreaction to firm performance. Investors overreact to performance and assign irrationally low values to weak firms and irrationally high values to strong firms. When the overreaction is corrected, weak firms have high stock returns and strong firms have low returns. Proponents of this view include DeBondt and Thaler (1987), Lakonishok, Shleifer and Vishny (1994), and Haugen (1995). For instance, according to Lakonishok, Shleifer and Vishny (1994), investors extrapolate past performance too far into the future: stocks that have performed poorly in the past (“value” stocks) are expected by investors to continue to perform poorly in the future, and vice versa, stocks that have done well in the past (“growth” or “glamour” stocks) are expected by investors to continue to do well in the future. This leads to “value” stocks being underpriced and “glamour” stocks being overpriced. Lakonishok, Sheleifer and Vishny (1994) conjecture that those investors who employ value strategies, i.e. buying “value” stocks and selling “glamour” stocks, could earn superior returns given the same level of risk involved.

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2.2.3. Characteristics-Based Explanations Proponents of the characteristics-based explanation suggest that it is the characteristics (i.e. high or low book-to-market firms, small or big firms) and not risk that determines stock returns (Daniel & Titman, 1997). These authors argue that not all high book-to-market firms are in financial distress, there are many firms that are not in financial distress but still have high ratios of book-equity to marketequity, such as firms in related lines of businesses, in the same industries, or from the same region. Daniel and Titman (1997) conjecture that if these characteristics drive expected returns, there should be firms with characteristics that do not match their risk loadings (on SMB and HML in the three-factor model). For example, there should be some strong firms in distressed industries. In the characteristics model, these firms have low returns because they are strong. But they can have high loadings on a distress risk factor if the factor is in part due to covariance of returns within industries. Thus, the returns on these firms will be too low, given their risk loadings. Conversely, there are distressed firms in strong industries. Because they are distressed, they have high returns, but in terms of risk loadings they look like strong firms. If characteristics drive prices, their returns will be too high given their risk loadings. In short, the characteristics hypothesis says that the characteristics (high BM versus low BM) drive stock returns. Low BM produces low stock returns, irrespective of risk loadings. Similarly, high BE/ME stocks have high returns, regardless of risk loadings. Davis, Fama and French (2000) reexamine Daniel and Titman’s (1997) findings with a similar approach but for a larger sample period and find that the results from the characteristics model is unique to the short sample period of 1973–1993. The characteristics model is not able to explain the relationship between BM and average return for the extended period 1929–1997. Interestingly, Davis, Fama and French’s (2000) result provides support for the risk model. Given the contradictory results provided by empirical evidence, this paper investigates three simple null hypotheses: (1) There is no relationship between size and stock returns; (2) There is no relationship between book-to-market ratio and stock returns; and (3) There is no relationship between beta and stock returns. The alternative hypotheses are: (1) Size is related to stock returns; (2) Book-tomarket is related to stock returns; and (3) Beta is related to stock returns. The multivariate model and the three-factor model will be used to test the null hypotheses. The null hypotheses are similar to the hypotheses that the coefficients on the size, book-to-market, and market variables (in those two models) are indistinguishable from zero. Similarly, the alternative hypotheses are similar to the hypotheses that the coefficients on those variables are statistically different from zero. The coefficients on the size, book-to-market, and market variables will be determined by running the Fama and MacBeth cross-sectional regressions on

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the multivariate model and the time-series regressions on the three-factor model. These regressions techniques will be described in the Method section.

3. DATA 3.1. Data Description This study investigates Information Technology (IT) stocks that are listed on the New York Stock Exchange (NYSE), the American Stock Exchange (AMEX) and the NASDAQ from July 1990 to June 2001 as provided by the COMPUSTAT Database. Not all stocks are chosen for the risk-return tests in the paper; only those who have the market equity and book-to-market data as described in Section 3.2.2. are included. In addition, only stocks that have monthly beta for every month during a testing year (12 months) are selected for the tests conducted during that year. Due to the fact that new firms enter the IT sector and existing firms exit the sector each year, there are circumstances that a stock might be selected in a particular period but might not be selected in a later period. Thus, the number of stocks satisfying the testing conditions varies year by year. Table 1 shows the total number of stocks available for the risk-return tests in each year from July 1990 to 2000. The number of stocks in each portfolio during a testing year (from July of year t to June of year t + 1) is also reported. For simplicity the formation of portfolios is described in the next section. From Table 1, it can be seen that the total number of stocks that satisfy the required conditions increases nearly four fold over the 1990–2001 period, starting from 379 stocks for the testing year July 1990–June 1991 to 1474 stocks for the testing year July 2000–June 2001. This reflects the “technology boom” during the 1990s. According to Kothari, Shanken and Sloan (1995), there are at least two aspects of COMPUSTAT selection procedures that appear to impart a survivorship bias. First, prior to 1978 COMPUSTAT routinely included historical financial statement information for as many years as available going back to 1946 on firms added to their database in a given year. In 1978 COMPUSTAT launched a major database expansion project from about 2700 NYSE-AMEX and high-profile NASDAQ companies to about 6,000 companies. Five years of annual data from 1973 to 1978 was added for most of these firms. Consider a firm in 1973, with substantial assets but relatively poor earnings prospects, considerable uncertainty, and correspondingly low market value. Suppose this high BM (book-to-market ratio) firm performed poorly over the next five years, with earnings even lower than expected and negative stock returns. If this company was not on COMPUSTAT to begin with, it might not be added to the database in 1978, either because of

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Table 1. Year-by-Year Numbers of Stocks Available for Testing from July 1990 to June 2001. Portfolios

July 1990

July 1991

July 1992

July 1993

July 1994

July 1995

July 1996

July 1997

July 1998

July 1999

July 2000

Big-High Big-BM2 Big-ME3 Big-Low ME2-High ME2-BM2 ME2-BM3 ME2-Low ME3-High ME3-BM2 ME3-BM3 ME3-Low Small-High Small-BM2 Small-BM3 Small-Low

12 25 44 28 23 37 22 28 23 25 21 20 33 14 11 13

8 25 37 47 20 32 33 24 35 22 18 17 32 23 14 7

3 41 37 42 20 24 34 37 39 26 17 25 43 19 18 5

16 32 47 43 15 25 35 40 35 34 26 29 58 27 17 8

17 44 53 50 28 41 38 39 38 39 26 38 62 29 29 19

18 39 59 60 24 42 56 42 50 45 29 41 71 37 24 22

21 50 64 93 29 65 72 50 64 51 44 41 97 42 29 26

22 68 87 103 50 81 69 54 76 65 56 59 107 38 41 36

24 59 106 113 48 84 81 73 95 81 51 60 111 54 40 29

12 46 98 142 47 100 88 73 107 89 70 54 133 62 39 31

24 77 122 170 51 100 108 101 107 119 94 59 183 75 48 36

Total

379

394

430

487

590

659

838

1012

1109

1191

1474

The table reports the number of stocks in each portfolio at the beginning of July of each year t from July 1990 to June 2001. At the end of June of each year t, all Information Technology stocks on the NYSE, AMEX, and NASDAQ are grouped into 16 portfolios based on their market capitalization (ln(ME)) and book-tomarket ratio (ln(BM)). The size breakpoints are the first (25%), second (50%) and third (75%) quartiles of ln(ME) of all information technology stocks on the NYSE, AMEX, and NASDAQ. Similarly, the book-to-market breakpoints are the first, second, and third quartiles of ln(BM) of all information technology stocks on these exchanges. Stocks with negative BM are excluded so that ln(BM) is calculable. A portfolio’s ln(ME), ln(BM), and beta are the value-weighted averages of stocks’ ln(ME), ln(BM), and beta, respectively. The weights are determined by stocks’ ln(ME). Big, ME2, ME3, and Small represent the biggest size quartile, second largest size quartile, third largest size quartile and smallest size quartile, respectively. High, BM2, BM3, and Low represent the highest book-to-market quartile, second highest book-to-market quartile, third highest book-to-market quartile, and the lowest high book-to-market quartile, respectively. Big-High means the size – bookto-market portfolio whose stocks belong to the biggest size quartile and the highest book-to-market quartile.

delisting or failure to meet minimum asset or market value requirements. On the other hand, if this high BM company performed unexpectedly well over the next five years, it could very well be included in 1978. The high ex post returns over this period and the high initial BM ratio could give the appearance of a positive relationship between BM and expected returns even when no such relationship existed.

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Second, even in recent years, COMPUSTAT’s procedures for inclusion of financial data on firms favor surviving firms. Alford, Jones and Zmijewski (1994) report that firms experiencing unfavourable economic conditions have a high propensity to delay the filing of their financial statements to the Securities and Exchange Commission (SEC) and the stock exchanges. Eventually some of these firms’ stocks are delisted from the exchanges because of failure to comply with disclosure requirements, thin trading activity, or financial distress. Financial statement information for these firms during the distress period is less likely to be available and included in the COMPUSTAT database. Some of the firms that delay filing of financial statements due to financial distress subsequently improve their performance. They then file their previously delayed financial statements and COMPUSTAT incorporates data on these firms. Thus, COMPUSTAT’s selection procedures may induce an upward bias in the average return on COMPUSTAT firms, particularly the high BM firms, even the later period. The sample period of July 1990–June 2001 is free of the first case of survivorship bias, although the sample is not free of the second case of survivorship bias. However, it is believed that the (second case of) survivorship bias is not serious for the information technology stocks in this period. This is due to the fact that the July 1990–June 2000 period is the “glorious” period for firms in the technology sector. Firms that file for bankruptcy in this period are not in large number to make the survivorship bias significant. In addition, firms that went into liquidation from July 2000 to June 2001 have not yet recovered so that their company information could be backfiled into the COMPUSTAT database.

3.2. Measurement of Variables This section briefly describes how various variables such as firm size, book-tomarket ratio, market beta, and stock returns are measured. 3.2.1. Firm Size A firm’s market equity (ME, denominated in millions of U.S. dollars) at the end of June of year t is used to measure its size. December-end ME is also mentioned in the measure of book-to-market ratio section but this quantity is solely for the purpose of calculating the book-to-market ratios. The reason for the use of Juneend ME and December-end ME is discussed in the measure of book-to-market ratios section. The natural logarithm of ME instead of the absolute value of ME is used to proxy for the size variable. This is due to the fact that market value of equity is highly skewed towards small firms, while there are very few firms that have high market capitalization. Using ln(ME) will transform the distribution of

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ME, making it more normally distributed and facilitating the portfolio selection procedures. Most of previous authors also use ln(ME) in their tests of capital asset pricing model. (e.g. Chan & Chen, 1998; Fama & French, 1992; Jegadeesh, 1992). 3.2.2. Book-to-Market Ratios The book-to-market ratio (BE/ME or BM) is the ratio of BE to ME where ME is the market value of a firm at the end of December in year t − 1, BE is the book value of common equity of the same firm at the fiscal year-end that falls in calendar year t − 1. For the same reason that is discussed above, the risk-return test in this paper also uses the natural logarithm of BM (ln(BM)) as a proxy for the BM variable (Fama & French, 1992). Stocks with negative BE are excluded so that ln(BM) is calculable. Fama and French (1992) also use December market equity and fiscal yearend book equity in the BM ratio. They argue that because firms do not have the same fiscal yearends, using ME at fiscal yearends would result in the BMs whose crosssectional variations in a given year are partly due to market-wide variation during the year. For example, if there is a general fall in stock prices during the year, ratios measured early in the year will tend to be lower than ratios measured later. Some confusion might arise due to the use of different periods to measure the size variable and the book-to-market variable. June-end ME of year t is used to calculate firm size, yet December-end ME and fiscal yearend book equity in year t − 1 are used to gauge book-to-market ratios. The reason is that the returns to be used in the risk-return tests will be for the July of year t to June of year t + 1 period. This creates a six-month gap between the ME and BM variables and the returns they are used to explain. Many financial economists follow this measurement procedure, such as Fama and French (1992) and Kothari, Shanken and Sloan (1995). The six-month (minimum) gap between fiscal yearend and the return tests is arbitrary. Nevertheless, this is motivated from Alford, Jones and Zmijewski’s (1994) paper. These authors report that on average 19.8% of firms do not comply with the Securities and Exchange Commission (SEC) requirement that firms must file their 10-K reports with the SEC within 90 days of their fiscal yearends. In addition, more than 40% of the December fiscal yearend firms that do comply with the 90-day rule file on March 31, and their reports are not made public until April. Thus, a six-month gap is expected to be sufficient for all accounting data to be made publicly available. Table 2 presents the descriptive statistics for the size (ln(ME)) and book-to-market ratio (ln(BM)) variables for the July 1990–June 2000 period. 3.2.3. Market Beta Annual beta is used in the multivariate model to test the relationship between stock returns, size, book-to-market ratio, and beta. Monthly beta is used to calculate

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Table 2. Descriptive Statistics for the Size – Book-to-Market Portfolios: July 1990–June 2001. Portfolios

Mean

Median

Standard Deviation

Minimum

Panel A. Portfolios’ book-to-market ratios and descriptive statistics. Big-High −0.03 −0.18 0.35 −0.39 Big-BM2 −0.63 −0.72 0.37 −1.25 Big-ME3 −1.20 −1.24 0.40 −2.01 Big-Low −2.15 −2.18 0.48 −3.26 ME2-High 0.00 −0.11 0.32 −0.35 ME2-BM2 −0.62 −0.70 0.36 −1.21 ME2-BM3 −1.20 −1.26 0.41 −2.02 ME2-Low −2.25 −2.12 0.44 −3.15 ME3-High 0.11 0.01 0.32 −0.25 ME3-BM2 −0.59 −0.68 0.38 −1.18 ME3-BM3 −1.19 −1.23 0.40 −1.99 ME3-Low −2.32 −2.38 0.37 −3.00 Small-High 0.28 0.11 0.30 0.05 Small-BM2 −0.56 −0.60 0.36 −1.08 Small-BM3 −1.19 −1.27 0.39 −1.96 Small-Low –2.39 −2.40 0.55 −3.44 Panel B. Portfolios’ size (ME) and descriptive statistics. Big-High 6.94 7.29 0.86 Big-BM2 7.19 7.33 0.60 Big-ME3 7.41 7.46 0.48 Big-Low 7.31 7.11 0.71 ME2-High 4.63 4.75 0.60 ME2-BM2 4.74 4.94 0.58 ME2-BM3 4.77 4.96 0.61 ME2-Low 4.79 4.89 0.61 ME3-High 3.40 3.50 0.51 ME3-BM2 3.50 3.62 0.50 ME3-BM3 3.51 3.63 0.52 ME3-Low 3.46 3.70 0.55 Small-High 2.02 2.05 0.34 Small-BM2 2.17 2.27 0.42 Small-BM3 2.17 2.17 0.45 Small-Low 2.16 2.27 0.45

4.96 5.86 6.75 6.49 3.67 3.96 3.93 3.99 2.61 2.75 2.81 2.55 1.43 1.43 1.40 1.41

Maximum

Observations

0.71 0.09 −0.50 −1.44 0.66 0.08 −0.45 −1.43 0.82 0.15 −0.43 −1.71 0.99 0.16 −0.44 −1.54

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

7.88 8.05 8.46 8.80 5.87 5.90 5.97 6.00 4.33 4.43 4.42 4.37 2.72 2.85 2.92 2.86

11 11 11 11 11 11 11 11 11 11 11 11 11 11 11 11

The table reports the descriptive statistics for the 16 size – book-to-market portfolios from July 1990 to June 2001. At the end of June of each year t, all Information Technology stocks on the NYSE, AMEX, and NASDAQ are grouped into 16 portfolios based on their market capitalization (ln(ME)) and book-tomarket ratio (ln(BM)). ME is common equity, which is denominated in millions of U.S. dollars and is measured at the end of June of year t. BM is the ratio of book equity to market equity, with book equity measured at fiscal yearend falling in year t − 1, and market equity measured at the end of

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Table 2. (continued ) December of year t − 1. ln(ME) and ln(BM) are the natural logarithms of ME and BM, respectively. The ME breakpoints are the first (25%), second (50%), and third quartiles (75%) of the stocks’ ln(ME). Similarly, the BM breakpoints are the first, second, and third quartiles of the stocks’ ln(BM). Big, ME2, ME3, and Small represent the biggest largest size quartile, second largest size quartile, third largest size quartile and smallest size quartile, respectively. High, BM2, BM3, and Low represent the highest book-to-market quartile, second highest book-to-market quartile, third highest book-to-market quartile, and the lowest high book-to-market quartile, respectively. Panel A shows the time-series averages of book-to-market ratios (ln(BM)) and the associated statistics for the 16 size – book-to-market portfolios. A portfolio’s book-to-market ratio is the value-weighted average of the ln(BM) of all stocks in the portfolio, with the weights calculated based on the stocks’ ln(ME). Panel B shows the time-series averages of market equity (ln(ME)) and the associated statistics for the 16 size – book-to-market portfolios. A portfolio’s market equity is the value-weighted average of the ln(ME) of all stocks in the portfolio, with the weights calculated based on the stocks’ ln(ME).

annual beta. Annual beta from July of year t to June of year t + 1 is the arithmetic average of monthly betas during the same period. That is: Betai,t =

beta(Jult ) + beta(Augt ) + · · · + beta(Jant+1 ) + · · · + beta(Junt+1 ) 12 (4)

where betai,t is the annual stock beta for the testing year beginning in July of year t and ending in June of year t + 1; beta(Jult ), . . ., beta(Junt+1 ) are the monthly stock betas for months from July of year t to June of year t + 1. Monthly stock betas are extracted from the COMPUSTAT database. COMPUSTAT calculates monthly stock beta by regressing monthly stock returns of the previous 60 months since the calculation month (inclusive) on monthly S&P 500 index returns of the same period. If less history is available, COMPUSTAT uses a minimum of 24-month data to measure monthly beta. Thus, firms that do not have at least 24 consecutive monthly returns will not have beta available on the COMPUSTAT database and will not included in this paper’s tests.2 Due to the fact that firms in the information technology sector do not usually have a long history of stock prices, calculating annual beta using annual returns of the past five years (at least two years) would leave very few firms with available beta. This would result in too few observations for the tests of the risk-return relationship and could give rise to spurious inferences. The use of monthly returns in the calculation of annual beta though not producing very precise estimates of annual beta, would work better than the use of annual returns given the short history of stock prices for firms in the IT sector. The procedure that COMPUSTAT uses to measure monthly beta is different from that employed by Fama and French (1992). In this last paper (monthly) beta

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is measured using the Scholes and Williams (1977) procedure, which accounts for the degree of stock trading infrequency. Scholes-Williams beta estimates are defined as ␤i =

+1 k=−1

B ik (1 + 2r)

(5)

where r is the autocorrelation of the value-weighted monthly market returns and the B ik are the slope coefficients from three separate OLS regressions. R it = ␣ik + B ik R m,t+k + vt ,

k = −1, 0, 1

(6)

Although trading frequency of stocks does affect a stocks’ beta, the effect of trading frequency on Info-Tech stocks is believed to be small as these stocks are highly traded. Furthermore, the use of annual beta will reduce the possible bias that is inherent in the estimation of monthly beta. Possible bias might arise from the systematic cross-temporal covariance in short-interval returns that are used to estimate monthly beta (e.g. Lo & MacKinlay, 1990a; Mech, 1993) or seasonality in returns (see, Kothari, Shanken & Sloan, 1995). 3.2.4. Returns Annual returns from July of year t to June of year t + 1 are calculated in the COMPUSTAT database; they are the percentage increase (or decrease) in the closing stock prices in June of year t and June of year t + 1, adjusted for dividends payments and the compounding effect of reinvested dividends. Similarly, monthly returns are the percentage increase (or decrease) in the closing stock prices on the last days of two consecutive months. Monthly returns are also adjusted for the effect of dividend payments. One-year Treasury bill rate and three-month Treasury bill rate will respectively be used to calculate annual returns and monthly returns. Table 3 reports the time-series averages of the portfolios’ excess returns (i.e. the spreads of portfolio’s annual returns over the one-year Treasury Bill rates), betas, book-to-market ratios (ln(BM)), and market equity (ln(ME)) for the July 1997–June 2001 period. The summary statistics for these variables are used in the multivariate model. There seems to be no relationship between portfolios’ excess returns and size (or ln(ME)). Across each book-to-market quartile, the excess returns show no particular pattern when moving from big- to small-stock portfolios. The relationship between the excess returns and ln(BM) is somewhat stronger, with the excess returns increasing from high- to low-BM portfolios within the biggestsize quartile. Within the second biggest-size quartile (ME2) the excess returns decrease from high-BM to low-BM portfolios. Beta is highly positively correlated

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Table 3. Time-Series Averages of Portfolios’ Excess Returns, Book-to-Market Ratios, and Market Equity: July 1997–June 2001. Book-to-Market Quartiles

Size Quartiles Excess Returns

High BM2 BM3 Low

Big

ME2

ME3

0.51 15.92 19.13 24.63

44.38 31.20 11.34 −4.22

17.98 25.75 28.74 8.79

Book-to-Market Quartiles

Beta Small 45.33 31.46 42.05 3.72

ME2 ME3

Small

1.26 1.35 1.49 1.56

1.19 1.26 1.32 1.28

0.65 0.69 0.55 0.87

0.96 1.02 1.15 1.25

Size Quartiles Book-to-Market Ratio (ln(BM))

High BM2 BM3 Low

Big

Market Equity (ln(ME))

Big

ME2

ME3

Small

Big

ME2 ME3

Small

−0.23 −0.89 −1.53 −2.49

−0.16 −0.85 −1.50 −2.60

−0.07 −0.83 −1.49 −2.65

0.12 −0.82 −1.50 −2.82

7.34 7.53 7.92 8.34

5.13 5.25 5.30 5.21

2.20 2.40 2.41 2.43

3.76 3.85 3.87 3.90

The table reports the time-series averages of portfolios’ excess returns, beta, book-to-market ratio (ln(BM)), and market equity (ln(ME)) for the July 1997–June 2001 period. At the end of June of each year t, all Information Technology stocks on the NYSE, AMEX, and NASDAQ are grouped into 16 portfolios based on their market capitalization (ln(ME)) and book-tomarket ratio (ln(BM)). The size breakpoints are the first (25%), second (50%) and third (75%) quartiles of ln(ME) of all information technology stocks on the NYSE, AMEX, and NASDAQ. Similarly, the book-to-market breakpoints are the first, second, and third quartiles of ln(BM) of all information technology stocks on these exchanges. Stocks with negative BM are excluded so that ln(BM) is calculable. A portfolio’s ln(ME), ln(BM), and beta are the value-weighted averages of stocks’ ln(ME), ln(BM), and beta, respectively. The weights are determined by stocks’ ln(ME). Big, ME2, ME3, and Small represent the biggest size quartile, second largest size quartile, third largest size quartile and smallest size quartile, respectively. High, BM2, BM3, and Low represent the highest book-to-market quartile, second highest book-to-market quartile, third highest book-to-market quartile, and the lowest high book-to-market quartile, respectively. Big-High means the size – bookto-market portfolio whose stocks belong to the biggest size quartile and the highest book-to-market quartile. Annual stock returns for the period July of year t to June of year t + 1 are adjusted for monthly stock price appreciation plus reinvestment of monthly dividends and the compounding effect of dividends paid on reinvested dividends. A portfolio’ return is the value-weighted average of the returns on individual stocks in the portfolio. A portfolio’s excess return is the difference between the portfolio’ return and the 1-year U.S. Treasury bill rate in the same testing year. A testing year is from July of year t to June of year t + 1.

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with ln(ME). Across each book-to-market quartile, beta decreases monotonically from big- to small-stock portfolios.

4. METHOD This section consists of two parts. Section 4.1. describes the multivariate model that is traditionally used in tests of the size and book-to-market effects. Section 4.2. describes the three-factor model, proposed by Fama and French (1993). Detailed portfolio formation procedures for each model are also discussed in each part.

4.1. Multivariate Model 4.1.1. The Model Previous researchers form stocks into portfolios based on stock characteristics, such as a stocks’ market ␤, size, book equity-to-market equity ratio (BM) and then run Fama and MacBeth (1973) cross-sectional regressions of portfolio returns on the portfolios’ characteristics using the following model (for example, Banz, 1981; Chan & Chen, 1988; Chui & Wei, 1998; Fama & French, 1992; Jegadeesh, 1992): R pt − R ft = ␣0t + ␣1t ln(ME)pt + ␣2t ln(BM)pt + ␣3t ␤pt + ␧pt

(7)

where R pt is the monthly return on a portfolio in month t; R ft is the monthly risk free rate; ␣0t , ␣1t , ␣2t , and ␣3t are the intercept and the coefficients, respectively; ␤pt is the portfolio market beta in month t; ln(ME)pt is the portfolio size variable in month t; ln(BM)pt is the portfolio book-to-market variable in month t; and ␧pt is the residual in month t of the regression. Model 7 or the multivariate model, as it will be called throughout this paper, will be used to test the size and book-to-market effects in the returns on the Information Technology stocks for the July 1997–June 2001 period. Although the choice of the independent variables in Model 7 is arbitrary, it is motivated by the results of previous studies. Fama and French (1992) report that ME and BM are sufficient to capture variation in stock returns while market beta, whose effect on stock prices is the center of the risk-return controversy, has no explanatory power vis-`a-vis stock returns. This paper assumes that the three factors in the multivariate model are general enough and no additional factors are more significant than these factors. One of the weaknesses associated with the multivariate model is the problem of multicollinearity. In other words, the possible high correlation between any

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pair of the three variables would lead to spurious results and render any inference from the results meaningless. To overcome this problem, various combinations of these three factors will be used in regressions. Fama and French (1992) use the Fama and MacBeth (1973) cross-sectional approach to estimate the coefficients and residuals in the model. This paper improves the Fama and MacBeth procedure, which use Ordinary Least Squares (OLS) method, by adopting the Newey-West (1987) technique. The OLS methodology will give best, linear, unbiased estimates of the coefficients of a model only when the residuals have constant variance, (i.e. homoskedasticity), and are independent of each other (i.e. not autocorrelated). If the residuals show patterns of heteroskedasticity (non-constant variance), the variances, and therefore the standard deviations of the coefficients, will be biased. Because the Newey-West (1987) procedure accounts for the problems of hetoroskedasticity and autocorrelation, it is more efficient and produces more accurate t-statistics than the OLS. 4.1.2. Data for the Multivariate Model It has been discussed in Section 3 that the period to be covered for testing will be from July 1990 to June 2001. However, this is achievable only when all the necessary data for stocks are available. For instance, stocks without ln(ME), ln(BM), beta, and returns data (with these variables calculated as described in Part B of the Data section) as at end of June of year t would not be included in the tests based on the multivariate model. (Monthly) beta data for IT stocks in COMPUSTAT is only available from August 1996. Thus, annual beta for IT stocks could not be calculated for testing years3 before July 1997. Therefore, the sample period chosen for the tests based on the multivariate model is from July 1997 to June 2001. Also, annual data rather than monthly data are used. Kothari, Shanken and Sloan (1995) argue that annual data are free of any seasonality effects and therefore is more likely to give a better picture of the relationship between size, book-to-market ratio, beta, and stock returns. 4.1.3. Portfolio Selection Procedure In June of each year, all IT stocks that satisfy our selection criteria are sorted by size (ln(ME)) to determine the quartile breakpoints for ME. These stocks are then allocated to four size portfolios based on the breakpoints. We subdivide each size portfolio into four portfolios on the basis of book-to-market equity (ln(BM)) for individual stocks. The book-to-market breakpoints are determined based on all available stocks in our sample, not on stocks in each size portfolio. As a result, we obtain sixteen size – book-to-market portfolios with stocks independently sorted into portfolios according to their ln(ME) and ln(BM).

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4.1.4. Estimating Portfolios’ Size, Book-to-Market Ratio, Beta, and Returns After assigning firms to the size – book-to-market portfolios in June, we calculate the value-weighted annual returns on the portfolios with the weights based on the natural logarithms of individual stocks’ market equity (ln(ME)). Algebraically, a portfolio’s annual returns are calculated as: n i=1 R i × |ln(MEi )| Rp = (8) n i=1 |ln(MEi )| where R p is the return on portfolio p; |ln(MEi )| is the absolute value of the natural logarithm of stock i’s market equity; n is the number of stocks in portfolio p. We obtain the value-weighted market equity, value-weighted book-to-market ratio, and value-weighted market beta for each portfolio in a similar way: A portfolio’s market equity is calculated as: n |ln(MEi )| × ln(MEi ) ln(MEp ) = i=1 (9) |ln(MEi )| A portfolio’s book-to-market ratio is calculated as: n |ln(MEi )| × ln(BMi ) ln(BMp ) = i=1n i=1 |ln(MEi )| and a portfolio’s beta is calculated as: n |ln(MEi )| × betai n betap = i=1 i=1 |ln(MEi )|

(10)

(11)

4.2. Three-Factor Model 4.2.1. The Model Many financial economists suspect that the relation between size and average return is not due to investors’ irrational behavior but is representative of a more fundamental relationship between expected returns and economic risk factors (Chan & Chen, 1991; Fama & French, 1992). In an attempt to produce more evidence on the rational asset-pricing story, Fama and French (1993) propose a so-called three-factor model. They use the Black, Jensen and Scholes’ (1972) timeseries regression approach. Monthly returns on stocks are regressed on the returns to a market portfolio of stocks and mimicking portfolios for size and book-tomarket equity (BM). The three-factor model is expressed: R(t) − RF(t) = a + b[RM(t) − RF(t)] + sSMB(t) + hHML(t) + e(t)

(12)

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where RM(t) is the value-weighted monthly returns on the market portfolio that consists of all IT stocks; RF(t) is the risk free rate; SMB(t) is the difference between returns on small stocks and returns on big stocks; HML(t) is the difference between returns on high book-to-market stocks and low book-to-market stocks. 4.2.2. Why Employ a Three-Factor Model? We employ the three-factor model in addition to the multivariate model (Model 7) because firstly, we want to examine whether the size and book-to-market effects is a function of the estimation technique. If the two models produce different or conflicting results, there are three possibilities: (1) the two models describe different aspects of the size and book-to-market effect and thus they are incomparable; (2) either one of the model is wrong; and (3) both models are wrong and the size and book-to-market effects might be the results of data-snooping biases as conjectured by Lo and MacKinlay (1990b). Thus, a test of the size and bookto-market effects is also a test of these two models. Secondly, the multivariate model does not tell us why size and book-to-market factors are related to stock returns. It might be that these factors proxy for common risk factors in returns. The three-factor model goes a step towards finding new factors that capture firm size and book-to-market equity. Because SMB and HML factors can be used for any stock, if we can establish that SMB and HML are related to some kind of risk,4 the question of why there is a relationship between stock returns, firm size, and book-to-market equity would be solved. Thirdly, the three-factor model has an advantage over the multivariate model in that the former uses the pattern of returns, i.e. the return on small stocks minus the return on big stocks (SMB), the return on high book-to-market stocks minus the return on low book-to-market stocks (HML), in determining average stock returns (Barber & Lyon, 1997a). These authors argue that the use of pattern of returns is good because there are cases where larger firms or low book-to-market firms may have common stock returns that more closely mimic those of small firms or high book-to-market firms. The three-factor model allows for this possibility since the pattern of returns, rather than the explicit measurement of size and book-to-market equity, is used. Finally, Fama and French (1993, 1995, 1996, 1997) find that empirical evidence supports the three-factor model. They suggest that this model is an equilibriumpricing model. It would be interesting to see whether the model works well for firms in the information technology sector. 4.2.3. Data for the Three-Factor Model As the three-factor model does not require beta data for individual stocks, the sample period used for the risk-return tests based on the three-factor model will

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cover the full July 1990–June 2001 period as described in the Data section. Whereas annual data is used for the multivariate model, we use monthly data for the threefactor model. In Section 4.1. we argue that annual data is better than monthly data because the effect of seasonal change in returns will be minimized when annual data are used. This is true if the multivariate model is used. However, for the threefactor model, it is not necessary to eliminate the seasonal effect. The reason is that the explanatory variables, SMB, HML, and RM–RF are themselves returns, in which the seasonal effect is inherent. The dependent variable is also return and as such contains in itself the seasonal effect. When the time-series regressions of the dependent variable on the explanatory variables are run, the seasonal effects in two sides of the three-factor model will be canceled out. Thus, the period (month versus annual) used to measure returns is appropriate and also has the advantage of providing more observations, which would lead to more precise estimates of the coefficients for the model. 4.2.4. Inputs for the Three-Factor Model We mimic the procedure employed by Fama and French (1993). In June of each year t from 1985 to 2000, all Information Technology stocks on the NYSE, AMEX, and NASDAQ which have the ME and BM data at the start of each testing year are size-sorted into two groups based on stocks’ ln(ME). The size breakpoint is the median of all IT stocks’ ln(ME). The two groups are called small (S) and big (B). All the selected IT stocks are also sorted into three book-to-market portfolios based on the breakpoints for the bottom 30% (Low), middle 40% (Medium), and top 30% (High) of the ranked values of ln(BM) for the stocks. BM is defined as in the “measure of book-to-market equity” section. The size-sort and BM-sort are conducted independently. Six portfolios (S/L, S/M, S/H, B/L, B/M, B/H) from the intersections of the three BM and two ME groups are obtained. For example, the S/L portfolio contains the stocks in the small-ME group that are also in the low-BM group, and the B/H portfolio contains the big-ME stocks that also have high BMs. Monthly value-weighted returns on the six portfolios are calculated from July of year t to June of t + 1, and the portfolios are reformed in June of t + 1. Fama and French (1993) say that the calculation of returns beginning in July to year t will allow for the possibility that book equity of year t − 1 is not known until June of year t. (1) The Explanatory Variable: Size or (SMB) The portfolio SMB (small minus big), mimics the risk factor in returns related to size, is the difference, each month, between the simple average of the returns on the three small-stock portfolios (S/L, S/M, and S/H) and the simple average of the returns on the three big-stock portfolios

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(B/L, B/M, and B/H): R s/l + R s/m + R s/h R b/l + R b/m + R b/h − (13) 3 3 Equation (13) can be expressed as: R s/l − R b/l + R s/m − R b/m + R s/h − R b/h (14) SMB = 3 From Eq. (14), it can be seen that SMB is the difference between the returns on small- and big-stock portfolios with about the same weighted-average bookto-market equity. This difference should be largely free of the influence of BM, focusing instead on the difference return behaviors of small and big stocks. (2) The Explanatory Variable: BM or (HML) The portfolio HML (high minus low) mimics the risk factor in returns related to book-to-market equity, is defined similarly. HML is the difference, each month, between the simple average of the returns on the two high-BM portfolios (S/H and B/H) and the average of the returns on the two low-BM portfolios (S/L and B/L): SMB =

HML =

R s/h + R b/h R s/l + R b/l − 2 2

(15)

or (R s/h − R s/l ) + (R b/h − R b/l ) (16) 2 The two components of HML are returns on high- and low-BM portfolios with about the same weighted-average size. Thus the difference between the two returns should be largely free of the size factor in returns, focusing instead on the different return behaviors of high- and low-BM firms. (3) The Explanatory Variable: Market or (RM–RF) Finally, the proxy for the market factor in stock returns is the excess market return, RM–RF. RM is the return on the value-weighted portfolio of the stocks in the six size-BM portfolios. RF is the three-month bill rate. Fama and French (1993) use the one-month Treasury bill rate to proxy for the RF. However, due to the lack of information for the one-month Treasury bill rate, the three-month Treasury bill rate is used.5 Nevertheless, the use of the three-month bill rate does not result in any substantial difference in the risk-return tests’ results. This paper will later prove this statement empirically. (4) The Dependent Variables (the Returns on the Size–Book-to-Market Portfolios) The excess returns on 16 portfolios, formed on size and book-to-market equity, are used as dependent variables in the time-series regressions. The HML =

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reason for the use of the size – book-to-market portfolios is to determine whether the mimicking portfolios SMB and HML capture common factors in stock returns related to size and book-to-market equity. The 16 size-BE/ME portfolios are formed much like the six size-BE/ME portfolios discussed earlier. In June of each year t all Information Technology stocks are sorted by size (ln(ME) and (independently) by book-to-market equity (ln(BM)). For the size sort, ME is measured at the end of June. For the book-to-market sort, ME is market equity at the end of December of t − 1, and BE is book common equity for the fiscal year ending in calendar year t − 1. The first (25%), second (50%), and third (75%) quartiles of stocks’ ln(ME) and ln(BM) are used as the breakpoints for the allocation of stocks into four size quartiles and four book-to-market quartiles. Sixteen portfolios are formed from the intersections of the size and BM quartiles. Value-weighted monthly returns on the portfolios from July of year t to June of year t + 1 are used as dependent variables in the time-series regressions. Table 4 shows the descriptive statistics for SMB, HML, RM–RF, and the excess returns on sixteen size – BM portfolios from July 1990 to June 2001. The timeseries mean of SMB is 1.12%, with a t-statistic of 1.63 (less than 1.98). This suggests that over the sample period, small stocks do not outperform big stocks. However, the returns on high book-to-market stocks do exceed those on low book-to-market stocks over the same period. The time-series mean for HML is a positive 1.48%, with a t-statistic of 2.37. The excess returns on the market portfolio (RM–RF) are significant in the negative territory (a mean of −2.71%, with a t-statistic of −3.04). Except for the portfolios in the smallest-size quartile and the ME3-BM2 portfolio, other portfolios have mean excess returns that are distinguishable from zero. These portfolios have negative mean excess returns with −2.53% being the highest (the ME3-High portfolio). This fact, coupled with a negative mean excess return on the market portfolio (RM–RF), indicates that IT stocks on average produce negative returns over the July 1990–June 2001 period. It is also clear that the mean excess return on each of the size – book-to-market portfolio is very low in practical terms. For instance, the ME3-High portfolio, which has the highest mean excess return compared with other size – BM portfolios, produces a mean excess return of −2.53% per month, which is translated into approximately −30.36% per year. That is not to mention the ME2-Low portfolio, which loses nearly 51.12% (−4.26 × 12) per year. The lowest mean excess return on a size – book-to-market portfolio reported by Fama and French (1993) was 0.32% per month or 3.84% per year. Even after accounting for slight differences in research design, the positive 3.84% is still significantly different to the negative −30.36%. Table 4 also reports low correlations between SMB, HML, and RM–RF. The correlation coefficients between SMB and HML, SMB and RM–RF, and HML

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Table 4. Descriptive Statistics for the Dependent and Explanatory Variables for the Three-Factor Model: July 1990–June 2001. Panel A. Descriptive Statistics for SMB, HML, and RM–RF Mean

St. dev

Correlations SMB

SMB (t-statistic) HML (t-statistic) RM–RF (t-statistic)

1.12 (1.63) 1.48 (2.37) −2.71 (−3.04)

HML

7.87

1

7.17

0.34

1.00

10.27

0.36

−0.13

RM–RF

1

Panel B. Descriptive Statistics for Portfolios’ Excess Returns Book-to-Market Quartiles

Size Quartiles Means Big

High (t-statistic) BM2 (t-statistic) BM3 (t-statistic) Low (t-statistic)

−3.09 (−3.62) −2.55 (−3.30) −2.95 (−3.55) −3.41 (−3.78)

ME2

ME3

Standard Deviations Small

−2.66 −2.53 −0.04 (−2.87) (−2.90) (−1.29) −2.84 0.08 −1.29 (−3.34) (0.03) (−1.09) −3.07 −3.17 −1.15 (−3.13) (−2.65) (−0.88) −4.26 −3.35 0.85 (−3.77) (−2.51) (0.51)

Big

ME2

ME3 Small

9.81

10.65 10.06 11.92

8.89

9.76 32.91 13.66

9.56

11.28 13.70 15.08

10.36

12.98 15.33 19.35

The table reports the descriptive statistics for the returns that mimic size (SMB), book-to-market (HML), and market (RM–RF) factors (panel A), and the excess returns on the 16 size – book-to-market portfolios (panel B) for the July 1990–June 2001 period. SMB, HML, and RM–RF are used as the explanatory variables, and the portfolios’ excess returns are used as the dependent variable for the three-factor model. R(t) − RF(t) = a + b[RM(t) − RF(t)] + sSMB(t) + hHML(t) + e(t) Panel A shows the descriptive statistics for SMB, HML, and RM–RF. SMB (small minus big) is the difference between the returns on small-stock and big-stock portfolios with about the same weighted average book-to-market equity. HML (high minus low) is the difference between the returns on high and low book-to-market equity portfolios with about the same weighted average size. RM is the valueweighted monthly% return on the stocks in the 16 size-BM portfolios. RF is the three-month Treasury bill rate, observed at the beginning of each month. Panel B shows the descriptive statistics for the excess returns on the 16 size – book-to-market portfolios. Three-month Treasury bill is used to calculate the excess returns. The portfolios are formed as follows. At the end of June of each year t, all Information Technology stocks on the NYSE, AMEX, and NASDAQ are grouped into 16 portfolios based on their market capitalization (ln(ME)) and

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Table 4. (Continued ) book-to-market ratio (ln(BM)). ME is common equity, which is denominated in millions of U.S. dollars and is measured at the end of June of year t. BM is the ratio of book equity to market equity, with book equity measured at fiscal yearend falling in year t − 1, and market equity measured at the end of December of year t − 1.The ME breakpoints are the first (25%), second (50%), and third (75%) quartiles of the stocks’ ln(ME). Similarly, the BM breakpoints are the first, second, and third quartiles of the stocks’ ln(BM). Stocks with negative BM are excluded so that ln(BM) is calculable. The reported means (in percentage) are the time-series averages of the monthly values of the corresponding variables. The sample period ranges from July 1990 to June 2001. A value with a t-statistic being less than –1.98 or greater than 1.98 is considered significant at the 5% level.

and RM–RF are 0.34, 0.36, and −0.13, respectively. All these figures are well below 0.50.

5. RESULTS This section contains three parts. Section 5.1. presents the empirical results of the Fama and MacBeth (1973) regressions on the multivariate model. Section 5.2. presents the empirical results of the time-series regressions on the three-factor model. Section 5.3. compares the behavior of information technology stocks’ price before and after the technology stock crash in April 2000.

5.1. Regressions Using the Multivariate Model This section consists of two sub-sections. Section 5.1.1. discusses the results from the FM (Fama & MacBeth) regressions on individual stocks. Section 5.1.2. discusses the results from the FM regressions on the size – book-to-market portfolios. 5.1.1. The FM Regressions on Individual Stocks Table 5 reports the time-series averages of the slope from year-by-year FM regressions of the cross-section of stock returns on size, book-to-market ratio, and beta. The average slope provides standard FM tests for determining which explanatory variables on average have non-zero expected premiums during the July 1997 to June 2001 period. From Table 5, it can be seen that the significance (at the 0.10 level) of the slope coefficient of the book-to-market variable, ln(BM), is consistent in three out of the four models when ln(BM) is present (Models 1, 2, and 7). When the book-to-market variable is alone in

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Table 5. Results from the (Improved) Fama and MacBeth Regressions with Stock Data: July 1997–June 2001. Models

Variables

Intercept (%)

Coefficients (%) a3t ␤it

a1t ln(ME)it

a2t ln(BM)it

−4.18 (−1.25)

5.03 (2.56)*

5.05 (1.39)

8.42 (3.08)*

4.48 (1.40)

Model 1

ln(ME), ln(BM), and Beta (t-statistic)

46.02 (1.11)

Model 2

ln(BM) and Beta (t-statistic)

30.75 (1.04)

Model 3

ln(ME) and Beta (t-statistic)

44.53 (1.06)

−5.11 (−1.61)

Model 4

ln(ME) and BM (t-statistic)

48.51 (1.13)

−3.62 (−1.21)

Model 5

Beta (t-statistic)

21.81 (0.75)

Model 6

ln(ME) (t-statistic)

47.12 (1.08)

Model 7

ln(BM) (t-statistic)

34.65 (1.07)

4.89 (1.32) 4.82 (2.22) 4.05 (1.27)

−4.25 (−1.45) 7.51 (2.68)*

The table reports the time-series average coefficient slopes and the associated t-statistics (in brackets) from the (improved) Fama and MacBeth regressions of stock returns on size, book-to-market ratio, and beta for the July 1997–June 2001 period. The reported intercepts and slopes are in percentage. R it − R ft = a 0t + a 1t ln(ME)it + a 2t ln(BM)it + a 3t ␤it + ␧it The multivariate model above is a general model. There is a total of seven models where the explanatory variables are combined in various ways. For instance, model 1 includes all three variables, ln(ME), ln(BM), and beta while model 2 consists of only two variables, ln(BM) and beta. The aim is to separate the effect of the multicollinearity problem. ME is common equity, which is denominated in millions of U.S. dollars and is measured at the end of June of year t. BM is the ratio of book equity to market equity, with book equity measured at fiscal yearend falling in year t − 1, and market equity measured at the end of December of year t − 1. ln(ME) and ln(BM) are the natural logarithms of ME and BM, respectively. Beta is the average of monthly stock betas during the period July of year t to June of year t + 1. Monthly stock beta is calculated for a 5-year (60-month) time period, ending in the current month. If less history is available, beta will be calculated for as few as 24 months. Month-end closing prices (including dividends) are used in the calculation. A testing year (for each yearly cross-sectional regression) is from July of year t to June of year t + 1. There are four yearly cross-sectional regressions for the July 1997–June 2001 period. ∗ Significant at the 0.10 level.

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the regressions, the average slope on ln(BM) is 7.51%, with a t-statistic of 2.68 (Model 7). The magnitude of the book-to-market coefficient increases to 8.42% (t-statistic of 3.08) when beta is added (Model 2). This change might be caused by a slight negative correlation coefficient of −0.08 (Table 7) between book-tomarket ratio and beta. In the regressions where ln(ME), ln(BM), and beta are included (Model 1), the slope on ln(BM) decreases to 5.03%, with a t-statistic of 2.56. The slope coefficient on ln(BM) is indistinguishable from zero in Model 4, where stock returns are regressed on the size and book-to-market variables. This lack of explanatory power from ln(BM) is due to the fact that ln(BM) is highly negatively correlated with ln(ME). The time-series average of the correlation coefficient between ln(BM) and ln(ME) is reported at −0.37 (Table 7). Nevertheless, Model 7 provides strong evidence that the book-to-market ratio is statistically related to variation in stock returns. The strong explanatory power of book-to-market ratio sharply contrasts the weak relationship between size, ln(ME), beta, and stock returns. In univariate regressions where either beta or size is included, the t-statistics for the slopes on the size and beta variables are just −1.45 (Model 6) and 1.27 (Model 5), respectively. Models 1, 2, 3, and 4 say that size and beta have no power to explain average returns in FM regressions that use various combinations of beta with size and book-to-market ratio. It should be noticed that our interpretation of the results in Table 5 might be affected by an extremely low adjusted R-squared for each model; the values of the adjusted-R2 never exceeds 0.05 across models and across years. Thus, the book-to-market variable is significant in explaining stock returns but it is not the only significant variable; some unknown variable(s) are more significant and more powerful in explaining variation in stock returns. 5.1.2. The FM Regressions on the Size – Book-to-Market Portfolios Table 6 reports the results from the FM regressions on portfolios formed on size and book-to-market ratios. Similar to Table 5, Table 6 also reports a strong bookto-market effect (higher book-to-market stocks have higher average returns) in three out of the four models where ln(BM) is present (Models 2, 4, and 7). In the yearly regressions of returns on book-to-market ratio alone, the t-statistic for the coefficient on ln(BM) scores an impressive 2.77 (Model 7). The book-to-market effect is thus robust in the 1997–2001 annual returns on NYSE, AMEX, and NASDAQ Info-Tech stocks. Like the weak size effect reported in Table 5, the results reported in Table 6 suggest that the size effect in the size – book-to-market portfolios’ returns is insignificant over the July 1997 to June 2001 period. When firm size, ln(ME), is the only explanatory variable in the regressions, the t-statistic for the average

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Table 6. Results from the (Improved) Fama and MacBeth Regressions with Portfolio Data: July 1997–June 2001. Models

Variables

Intercept (%)

Coefficients (%) a1t ln(ME)pt a2t ln(BM)pt

Model 1

ln(ME), ln(BM), and Beta (t-statistic)

46.15 (1.09)

0.35 (0.27)

Model 2

ln(BM) and Beta (t-statistic)

44.77 (1.07)

Model 3

ln(ME) and Beta (t-statistic)

45.65 (1.15)

0.96 (0.50)

Model 4

ln(ME) and BM (t-statistic)

41.12 (1.01)

−2.14 (−0.90)

Model 5

Beta (t-statistic)

44.26 (1.12)

Model 6

ln(ME) (t-statistic)

32.92 (0.79)

Model 7

ln(BM) (t-statistic)

31.56 (1.05)

a 3t b pt

6.07 (2.15)

−17.13 (−1.72)

6.85 (2.39)*

−14.15 (−1.07) −25.60 (−2.14)

7.23 (2.72)* −21.14 (−1.92)

−2.44 (−1.04) 7.42 (2.77)*

The table reports the time-series average coefficient slopes and the associated t-statistics (in brackets) from the (improved) Fama and MacBeth regressions of stock returns on size, book-to-market ratio, and beta for the July 1997–June 2001 period. The reported intercepts and slopes are in percentage. R pt − R ft = a 0t + a 1t ln(ME)pt + a 2t ln(BM)pt + a 3t ␤pt + ␧pt The multivariate model above is a general model. There is a total of seven models where the explanatory variables are combined in various ways. For instance, model 1 includes all three variables, ln(ME), ln(BM), and beta while model 2 consists of only two variables, ln(BM) and beta. The aim is to separate the effect of the multicollinearity problem. ME is common equity, which is denominated in millions of U.S. dollars and is measured at the end of June of year t. BM is the ratio of book equity to market equity, with book equity measured at fiscal yearend falling in year t − 1, and market equity measured at the end of December of year t − 1. ln(ME) and ln(BM) are the natural logarithms of ME and BM, respectively. Beta is the average of monthly stock betas during the period July of year t to June of year t + 1. Monthly stock beta is calculated for a 5-year (60-month) time period, ending in the current month. If less history is available, beta will be calculated for as few as 24 months. Month-end closing prices (including dividends) are used in the calculation. A testing year (for each yearly cross-sectional regression) is from July of year t to June of year t + 1. There are four yearly cross-sectional regressions for the July 1997–June 2001 period. Portfolios are reformed based on stocks’ market equity, ln(ME), and book-to-market ratio, ln(BM) at the end of June of each year t. Portfolios’ ln(ME), ln(BM), and beta are the value-weighted averages of individual stocks’ ln(ME), ln(BM), and beta, respectively. The weights are determined by stocks’ ln(ME). ∗ Significant at the 0.10 level.

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slope on ln(ME) is only −1.04 (Model 6). With the presence of other explanatory variables, such as ln(BM) and beta, the average slopes on the firm size variable are even smaller and have smaller t-statistics. The risk premiums on ␤ in Models 1, 2, 3, and 5 are interestingly also negative. This could indicate that portfolios with lower ␤ earn higher returns than portfolios with higher ␤. Nevertheless, the evidence on the negative relationship between portfolios’ ␤ and returns is not conclusive because all the premiums on the beta variable are indistinguishable from 0. The largest t-statistic (in absolute value) for the premium on ␤ is −2.14, which is insignificant at the 0.10 level. 5.1.3. Comparison between the FM Regressions on Individual Stocks and the FM Regressions on the Size – Book-to-Market Portfolios The book-to-market effect exists regardless of whether portfolio data or stock data are used. In addition, the magnitudes of this effect are similar in both cases. When portfolio data are used, the slope on ln(BM) in Model 7 is 7.42%, with a t-statistic of 2.77 (Table 6). When stock data are used, the slope on ln(BM) in Model 7 is 7.51%, with a t-statistic of 2.68 (Table 5). These results confirm the significance of the book-to-market ratio in explaining stock returns. Although the slope on ln(ME) and beta in Table 5 is different from the slope on ln(ME) and beta in Table 6, both tables report that size and beta are not related to stock returns. Instead, both tables suggest that ln(BM) is the only variable that explains variation in stock returns. Table 7 shows that when stocks are formed into size – book-to-market portfolios, the correlation between the size variable and the book-to-market variable is reduced to −0.08 (−0.37 if stock data are used). However, the achieved low correlation between size and book-to-market ratio comes at the expense of the correlation between size and beta, which is increased to 0.75. The change in the correlation coefficients between ln(ME), ln(BM), and beta due to alternative uses of stock data and portfolio data is one of the reasons for the differing slopes on ln(ME) and beta in Table 5 and Table 6. Nevertheless, the advantage of sorting stocks into portfolios is that the return-generating process is more correctly specified by the multivariate model, which assumes portfolio size, book-to-market ratio, and beta are the three most important factors that explain variation in portfolio returns. This is indicated by the fact that the values of R2 in regressions using portfolio data are higher than the values of R2 obtained in regressions using stock data, with the (average) values of adjusted R2 in the cross-sectional regressions using portfolio data are as high as 0.20. 5.1.4. Comparison with Fama and French’s (1992) results Similar to Fama and French’s (1992) paper, this paper finds no relationship between beta and stock returns. Whether beta is used alone or in various combinations with size and book-to-market ratio, the slopes on beta is indistinguishable from 0. This

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Table 7. Correlation Matrices. ln(ME)

ln(BM)

Beta

Stocks data ln(ME) ln(BM) Beta

1 −0.37 0.13

1 −0.08

1

Portfolios data ln(ME) ln(BM) Beta

1 −0.08 0.75

1 −0.24

1

The table reports the time-series averages of the correlation coefficients between ln(ME), ln(BM), and beta for individual stocks as well as for the size – book-to-market portfolios. ME is common equity, which is denominated in millions of U.S. dollars and is measured at the end of June of year t. BM is the ratio of book equity to market equity, with book equity measured at fiscal yearend falling in year t − 1, and market equity measured at the end of December of year t − 1. ln(ME) and ln(BM) are the natural logarithms of ME and BM, respectively. Beta is the average of monthly stock betas during the period July of year t to June of year t + 1. Monthly stock beta is calculated for a 5-year (60-month) time period, ending in the current month. If less history is available, beta will be calculated for as few as 24 months. Month-end closing prices (including dividends) are used in the calculation. Portfolios are reformed at the end of June of each year t, using size and book-to-market quartile breakpoints. The size breakpoints are the first (25%), second (50%) and third (75%) quartiles of ln(ME) of all information technology stocks on the NYSE, AMEX, and NASDAQ. Similarly, the book-tomarket breakpoints are the first, second, and third quartiles of ln(BM) of all information technology stocks on these exchanges. Stocks with negative BM are excluded so that ln(BM) is calculable. A portfolio’s ln(ME), ln(BM), and beta are the value-weighted averages of stocks’ ln(ME), ln(BM), and beta, respectively. The weights are determined by stocks’ ln(ME).

result confirms the weak explanatory power of beta reported by many financial economists (e.g. Barber & Lyon, 1997b; Davis, 1994; Jegadeesh, 1992). However, the results in this paper provide a different picture to those found by Fama and French (1992). First, Fama and French (1992) find that the book-to-market effect is robust at the 5% level of significance while the book-to-market effect in this study is only significant at the 10% level. Secondly, the combination of size and book-to-market ratio captures variation in stock returns, whereas this paper finds no relationship between size and stock returns regardless of whether size is alone or in combination with book-to-market ratio. 5.2. Regressions Using the Three-Factor Model This section contains six sub-Sections 5.2.1., 5.2.2. and 5.2.3. reports the results on the one-factor model, with HML, SMB, and RM–RF in turn plays the role of the

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explanatory variable. 5.2.4. discusses the results on the two-factor model, in which SMB and HML are the two explanatory variables. 5.2.5. discusses the results on the three-factor model, in which SMB, HML, and RM–RF are the three explanatory variables. And finally, 5.2.6. considers the use of the three-month Treasury bill rate as an alternative to the one-month Treasury bill rate. 5.2.1. Regressions with One Explanatory Variable: HML Inspired by a strong relationship between the book-to-market factor and stock returns in Section 5.1, we do a preliminary test on the relationship between the 16 size – book-to-market portfolios’ returns and the HML returns, which mimic the book-to-market factor. Panel A in Table 8 shows the results of the Seemingly Unrelated Regression (SUR) of the size – BM portfolios’ returns on HML. Except for the highest book-to-market quartile and the top three portfolios in the smallest size quartile, all the portfolios in other size and book-to-market quartiles have HML coefficients that are statistically different from zero. Even within the smallest size quartile and the highest book-to-market quartile, the slopes on HML for the ME2High and Small-BM3 portfolios have t-statistics of −1.97, which is very close to –1.98 – the critical value at the 5% level of significance. More interestingly, the coefficient slopes on HML are related to the book-to-market factor: (with the exception of the ME3–BM2 portfolio) within each size quartile, the slopes decrease monotonically from higher- to lower – book-to-market quartiles. The HML variable therefore is significant to explain stock returns. However, the values of the intercepts and the SUR value for the adjusted R2 seem to suggest that other factors, in addition to HML, are needed to capture all variation in stock returns. More than half of the sixteen size – book-to-market portfolios have intercepts that are statistically different from zero. Particularly, all portfolios in the biggest and second biggest size quartiles have intercepts that are statistically different from zero. Moreover, the adjusted R2 recorded is only 0.16. Thus, the one-factor model where HML is the only explanatory variable leaves 84% of variation in stock returns unexplained. 5.2.2. Regressions with One Explanatory Variable: SMB Different from a weak size effect reported in Section 5.1., SMB proves to be a significant factor that explains the shared variation in expected returns. Panel B in Table 8 reports the intercepts and the coefficient slopes on SMB in the SUR regression of the size – book-to-market portfolios’ returns on SMB alone. Only five of the 16 size – book-to-market portfolios, four from the biggest size quartiles and one from the second biggest size quartiles (the ME2-BM2 portfolio), produce coefficients that are indistinguishable from zero. The remaining 11 portfolios have SMB slopes that are either equal to or greater than 2.83 standard errors from zero.

76

Table 8. Seemingly Unrelated Regressions of Portfolios’ Excess Returns on SMB, HML, and RM–RF in the One-Factor and Two-Factor Models: July 1990–June 2001. Book-to-Market Quartiles

Size Quartiles (Intercepts) Panel A. SUR Results for One-Factor Model: HML

Adjusted R2

Big

ME2

ME3

Small

Big

ME2

ME3

Small

−2.89 (−3.34) −2.14 (−2.79) −2.43 (−2.98) −2.74 (−3.14) −0.13 (−1.13) −0.28 (−2.64) −0.35 (−3.13) −0.46 (−3.82)

−2.29 (−2.46) −2.41 (−2.85) −2.44 (−2.53) −3.36 (−3.10) −0.25 (−1.97) −0.29 (−2.51) −0.43 (−3.24) −0.61 (−4.10)

−2.28 (−2.58) −4.20 (−1.86) −2.43 (−2.07) −2.29 (−1.79) −0.17 (−1.40) 2.90 (9.34) −0.50 (−3.11) −0.72 (−4.10)

0.04 (0.04) −0.86 (−0.72) −0.62 (−0.47) 1.58 (0.94) −0.06 (−0.39) −0.29 (−1.78) −0.36 (−1.97) −0.49 (−2.14)

−3.05 (−3.55) −2.60 (−3.34) −2.95 (−3.52) −3.42 (−3.76) −0.03 (−0.28) 0.04 (0.43) 0.00 (0.00) 0.00 (0.02)

−3.05 (−3.38) −3.00 (−3.54) −3.45 (−3.60) −4.80 (−4.41) 0.35 (3.04) 0.15 (1.41) 0.34 (2.83) 0.48 (3.48)

−3.15 (−3.95) −3.36 (−1.73) −4.01 (−3.70) −4.43 (−3.79) 0.55 (5.44) 3.08 (12.55) 0.75 (5.51) 0.96 (6.53)

−0.95 (−1.07) −2.36 (−2.36) −2.22 (−1.95) −0.81 (−0.60) 0.81 (7.23) 0.95 (7.56) 0.96 (6.68) 1.49 (8.75)

0.16

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QUANG-NGOC NGUYEN ET AL.

High (t-statistic) BM2 (t-statistic) BM3 (t-statistic) Low (t-statistic) High (t-statistic) BM2 (t-statistic) BM3 (t-statistic) Low (t-statistic)

Panel B. SUR Results for One-Factor Model: SMB

Size Quartiles (Intercepts) Panel C. SUR Results for One-Factor Model: RM–RF Panel D. SUR Results for Two-Factor Model: SMB and HML

High (t-statistic) BM 2 (t-statistic) BM 3 (t-statistic) Low (t-statistic) High (t-statistic) BM 2 (t-statistic) BM 3 (t-statistic) Low (t-statistic) High (t-statistic) BM 2 (t-statistic)

Big

ME2

ME3

Small

Big

ME2

ME3

Small

−1.12 (−1.96) −0.45 (−1.26) −0.66 (−1.83) −0.95 (−2.33) 0.73 (13.42) 0.77 (23.02) 0.85 (25.01) 0.91 (23.45) −0.14 (−1.10) −0.33 (−2.99)

−0.05 (−0.14) −0.45 (−1.35) −0.25 (−0.76) −1.02 (−2.66) 0.96 (28.36) 0.88 (28.17) 1.04 (33.16) 1.19 (32.84) −0.43 (−3.38) −0.39 (−3.26)

−0.10 (−0.28) 4.64 (1.84) 0.15 (0.31) 0.22 (0.35) 0.90 (26.05) 1.68 (7.06) 1.22 (26.30) 1.32 (21.67) −0.43 (−3.82) 1.97 (8.53)

2.48 (3.87) 1.73 (2.59) 1.71 (1.82) 4.06 (3.01) 0.93 (15.35) 1.11 (17.68) 1.05 (11.84) 1.18 (9.27) −0.41 (−3.26) −0.74 (−5.55)

−2.89 (−3.34) −2.22 (−2.91) −2.50 (−3.07) −2.83 (−3.27) 0.01 (0.11) 0.15 (1.44) 0.12 (1.15) 0.16 (1.43)

−2.56 (−2.92) −2.56 (−3.09) −2.74 (−3.06) −3.78 (−3.92) 0.48 (4.13) 0.27 (2.50) 0.54 (4.55) 0.76 (5.92)

−2.66 (−3.48) −5.59 (−3.53) −3.00 (−3.13) −3.04 (−3.28) 0.68 (6.70) 2.47 (11.76) 1.03 (8.09) 1.34 (10.92)

−0.48 (−0.56) −1.53 (−1.67) −1.30 (−1.24) 0.54 (−0.46) 0.93 (8.18) 1.18 (9.78) 1.22 (8.74) 1.86 (12.07)

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Book-to-Market Quartiles

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Table 8. (Continued ) BM 3 (t-statistic) Low (t-statistic)

−0.40 (−3.35) −0.52 (−4.10)

−0.63 (−4.83) −0.89 (−6.37)

−0.89 (−6.35) −1.23 (−9.06)

−0.81 (−5.32) −1.20 (−7.06)

Adjusted R2 = 0.56 Adjusted R2 = 0.44 The table reports the Seemingly Unrelated Regressions (SUR) results for the following model: Panel A.

R(t) − RF(t) = a + hHML(t) + e(t)

Panel B. R(t) − RF(t) = a + sSMB(t) + e(t) Panel C.

R(t) − RF(t) = a + b[RM(t) − RF(t)]e(t)

Panel D.

R(t) − RF(t) = a + sSMB(t) + hHML(t) + e(t)

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At the end of June of each year t, all Information Technology stocks on the NYSE, AMEX, and NASDAQ are grouped into 16 portfolios based on their market capitalization (ln(ME)) and book-to-market ratio (ln(BM)). Ln(ME) and ln(BM) are the natural logarithms of ME (market equity) and BM (book-to-market ratio), respectively. The ME breakpoints are the first, second, and third quartiles of the stocks’ ln(ME). Similarly, the BM breakpoints are the first, second, and third quartiles of the stocks’ ln(BM). Big, ME2, ME3, and Small represent the biggest size quartile, second largest size quartile, third largest size quartile and smallest size quartile, respectively. High, BM2, BM3, and Low represent the highest book-to-market quartile, second highest book-to-market quartile, third highest book-to-market quartile, and the lowest high book-to-market quartile, respectively. Big-High means the size – book-to-market portfolio whose stocks belong to the biggest size quartile and the highest book-to-market quartile. SMB (small minus big) is the difference between the returns on small-stock and big-stock portfolios with about the same weighted average bookto-market equity. HML (high minus low) is the difference between the returns on high and low book-to-market equity portfolios with about the same weighted average size. RM is the value-weighted monthly% return on the stocks in the 16 size-BM portfolios. RF is the three-month Treasury bill rate, observed at the beginning of the month. A value with a t-statistic being greater than 1.98 or less than −1.98 is considered significant at the 5% level.

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In addition, the SMB coefficient slopes increase monotonically from bigger to smaller size quartiles within each book-to-market quartiles, except for the second biggest book-to-market (BM2) quartile. Although the adjusted R2 for the one-factor model where SMB is the only explanatory variable is nearly twice as high as that of HML (0.30 for SMB compared with 0.16 for HML), it is still far short of the ideal value of one. In addition, the majority of the intercepts in Panel B are statistically distinguishable from zero. Thus, SMB is significant in explaining variation in returns, but like HML, it leaves much variation in returns that might be explained by other factors.

5.2.3. Regressions with One Explanatory Variable: RM–RF In this section the covariance between the returns on the market portfolio with the excess returns on the 16 size – book-to-market portfolios is considered. Panel C in Table 8 shows that the excess return on the market portfolio of stocks, RM–RF, captures variation in stock returns very well. The t-statistics on the slope coefficient of RM–RF are all above seven, far greater than the critical value of approximately 1.98 at the 5% level of significance. It seems that RM–RF does not need an intercept to explain expected stock returns. Only five out of the 16 size – book-to-market portfolios have intercepts that are statistically different from zero (three from the smallest size quartile and three from the lowest book-to-market quartile, the SmallLow portfolio is the intersection between the smallest size quartile and the lowest BM quartile). The adjusted R2 is 0.56, higher than those for SMB and HML. However, the market still leaves much variation in stock returns that might be explained by other factors.

5.2.4. Regressions with Two Explanatory Variables: SMB and HML The combination of SMB and HML proves to explain stock returns very well. Only one portfolio, Big-High, has the HML coefficient that is indistinguishable from 0. Only four portfolios from the biggest size quartile have SMB coefficients that are not statistically different from zero. These results are a significant improvement from the one-factor model: when SMB is the only explanatory variable, five portfolios have SMB coefficients that are indistinguishable from zero; and when HML is the only explanatory variable, six portfolios have HML coefficients that are indistinguishable from zero. However, SMB and HML together could not capture all variation in stock returns. The adjusted R2 from the SUR regression of the size – book-to-market portfolios’ returns on SMB and HML is only 0.44, leaving 56% of variation in returns unexplained. That unexplained variation is captured by the market factor, as we shall see in the next section.

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5.2.5. Regressions with Three Explanatory Variables: SMB, HML, and RM–RF Table 9 shows the SUR estimates of the intercepts and coefficients on SMB, HML, and RM for the 16 size – book-to-market portfolios. With the exception of three portfolios, the Small-High, Small-Low, and ME2-Low portfolios, the intercepts for the remaining 13 size – book-to-market portfolios are indistinguishable from zero and have statistically insignificant t-statistics ranging from −1.40 (ME3–BM2) to 1.10 (Small–BM3). Nearly all the slope coefficients on SMB are significant and wit only one exception have t-statistics that lie outside the [−1.98, 1.98] interval. The one exception is the ME2-BM3 portfolio, which returns a t-statistic of −1.84. This quantity, nevertheless, is very close to −1.98. More interestingly, the slope on SMB appears related to size. In three of the four book-to-market quartiles (the exception is the second highest book-to-market quartile (BM2)) the slope on SMB increases monotonically from bigger- to smaller-size quartiles. The explanatory power of HML in stock returns is somewhat weaker than that of SMB. Six out of the 16 size – book-to-market portfolios return t-statistics are within the [−1.98, 1.98] interval. The weak explanatory power, which is in contrast with a strong relationship between stock returns and HML where HML is the only explanatory variable, is due to the interaction between SMB, HML, and RM–RF. Table 4 reports that the correlation coefficients between HML and SMB, and HML and RM–RF are 0.34 and −0.13, respectively. Therefore, the apparently weak power of HML in the three-factor model does not invalidate itself as a significant variable that captures stock returns. This is evidenced in the one-factor model where HML is the only explanatory variable. As further evidence for the role of HML in mimicking book-to-market ratio, the slope on HML tends to decrease from higher- to smaller- BM portfolios. The two portfolios that do not follow this tendency are ME2-BM2 and ME3-BM3. The slope on RM–RF (or the market factor) are all more than six standard errors from zero. The market factor, either in combination with the size and book-to-market factors or standing alone, strongly captures variation in portfolio returns. The adjusted R2 for the three-factor model scores an impressive 0.83, much higher than those reported for the one-factor models (0.16 for HML, 0.30 for SMB, and 0.56 for RM–RF, Table 9). This is a strong indication that the three-factor model is a good model that describes the relationship between size, book-to-market ratio, beta, and stock returns well. 5.2.6. Does the Use of the 3-Month Treasury Bill Rate Matter? In Section 4.2., it was argued that the use of the 3-month Treasury bill rate (USTBL3M) instead of the 1-month Treasury bill rate (USTBL1M) would lead to the same inference as if the 1-month rate was used. This section empirically improves that statement. As the data for the 1-month Treasury bill rate on

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Table 9. Seemingly Unrelated Regressions of Portfolios’ Excess Returns on SMB, HML, and RM–RF in the Three-Factor Model: July 1990–June 2001. Book-to-Market Quartiles

Seemingly Unrelated Regressions (SUR) Results Size Quartiles Big

ME 2

ME 3

−0.44 (−0.88) 0.22 (0.80) 0.18 (0.90) −0.01 (−0.05)

0.18 (0.50) 0.10 (0.38) 0.14 (0.48) −0.65 (−2.20)

−0.34 (−0.95) −1.50 (−1.40) −0.03 (−0.06) −0.14 (−0.37)

1.72 (2.91) 0.98 (1.75) 0.93 (1.10) 2.49 (2.36)

SMB coefficients High (t-statistic) BM 2 (t-statistic) BM 3 (t-statistic) Low (t-statistic)

−0.51 (−7.32) −0.38 (−9.91) −0.45 (−15.66) −0.44 (−12.03)

−0.11 (−2.09) −0.30 (−7.67) −0.08 (−1.84) 0.09 (2.07)

0.18 (3.60) 1.59 (10.53) 0.39 (6.82) 0.72 (13.57)

0.46 (5.54) 0.65 (8.20) 0.74 (6.13) 1.44 (9.71)

HML coefficients High (t-statistic) BM 2 (t-statistic) BM 3 (t-statistic) Low (t-statistic)

0.22 (3.09) 0.03 (0.72) 0.00 (0.02) −0.10 (−2.64)

−0.03 (−0.50) 0.00 (0.03) −0.20 (−4.65) −0.43 (−9.98)

−0.08 (−1.56) 2.57 (16.43) −0.45 (−7.51) −0.80 (−14.45)

−0.08 (−0.96) −0.37 (−4.49) −0.48 (−3.88) −0.91 (−5.89)

RM–RF coefficients High (t-statistic) BM 2 (t-statistic) BM 3 (t-statistic) Low (t-statistic)

0.89 (17.39) 0.88 (31.85) 0.97 (46.26) 1.02 (38.28)

0.99 (26.72) 0.96 (34.15) 1.04 (33.87) 1.13 (37.30)

0.84 (22.86) 1.48 (13.43) 1.07 (25.76) 1.05 (27.14)

0.80 (13.14) 0.90 (15.82) 0.81 (9.26) 0.70 (6.53)

Intercepts High (t-statistic) BM 2 (t-statistic) BM 3 (t-statistic) Low (t-statistic)

Adjusted R2

0.83

Small

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Table 9. (Continued ) The table reports the Seemingly Unrelated Regressions (SUR) results for the three-factor model: R(t) − RF(t) = a + b[RM(t) − RF(t)] + sSMB(t) + hHML(t) + e(t) At the end of June of each year t, all Information Technology stocks on the NYSE, AMEX, and NASDAQ are grouped into 16 portfolios based on their market capitalization (ln(ME)) and book-tomarket ratio (ln(BM)). ME is common equity, which is denominated in millions of U.S. dollars and is measured at the end of June of year t. BM is the ratio of book equity to market equity, with book equity measured at fiscal yearend falling in year t − 1, and market equity measured at the end of December of year t − 1. ln(ME) and ln(BM) are the natural logarithms of ME and BM, respectively. The ME breakpoints are the first, second, and third quartiles of the stocks’ ln(ME). Similarly, the BM breakpoints are the first, second, and third quartiles of the stocks’ ln(BM). Big, ME2, ME3, and Small represent the biggest size quartile, second largest size quartile, third largest size quartile and smallest size quartile, respectively. High, BM2, BM3, and Low represent the highest book-to-market quartile, second highest book-to-market quartile, third highest book-to-market quartile, and the lowest high book-to-market quartile, respectively. SMB (small minus big) is the difference between the returns on small-stock and big-stock portfolios with about the same weighted average book-to-market equity. HML (high minus low) is the difference between the returns on high and low book-to-market equity portfolios with about the same weighted average size. RM is the value-weighted monthly% return on the stocks in the 16 size-BM portfolios. RF is the three-month Treasury bill rate, observed at the beginning of each month.

DataStream is not available after May 1996, the sample period used for the comparison between the effects of these two rates is from July 1990 to May 1996. Employing the SUR procedure, two time-series regressions of the size – bookto-market portfolios’ excess returns on the size (SMB), book-to-market (HML), and market factor (RM–RF) are undertaken. The size factor, SMB, and the book-tomarket factor (HML) are the same in these two regressions. Only the excess returns on the size – book-to-market portfolios and the market portfolio are different: in one regression, the 1-month rate is used; in the other, the 3-month rate is used. Table 10 reports the results of the two regressions. It is clear that the coefficients on SMB, HML, and RM–RF produced by the use of the 1-month rate are nearly identical to those produced by the use of the 3-month rate. If there is any difference, the difference is only 0.01%. The t-test for the mean difference between the 1-month rate SMB coefficients and the 3-month rate SMB coefficients returns a t-statistic of 0.42, which is not significant at the 5% level to reject the null hypothesis of no difference. Similarly, the results of the t-tests for the mean difference between the 1-month rate HML coefficients and the 3-month rate HML coefficients, and between the 1-month rate RM–RF coefficients and the 3-month rate RM–RF coefficients show no sign of difference (in a statistical sense). Thus, the use of the 3-month Treasury bill rate in the preceding sections would not invalidate the conclusion that the three-factor model is well specified for information technology stocks on the NYSE, AMEX, and NASDAQ.

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Table 10. SUR Results Using 1-Month and 3-Month Treasury Bill Rates: July 1990–May 1996. Portfolios

SMB Coefficients

HML Coefficients

RM–RF Coefficients

USTBL1M USTBL3M USTBL1M USTBL3M USTBL1M USTBL3M −0.39 −0.49 −0.37 −0.32 −0.30 −0.33 −0.03 0.05 0.06 2.25 0.12 0.80 0.16 0.47 0.06 1.49

Big-High Big-BM2 Big-BM3 Big-Low ME2-High ME2-BM2 ME2-BM3 ME2-Low ME3-High ME3-BM2 ME3-BM3 ME3-Low Small-High Small-BM2 Small-BM3 Small-Low t-Statistics* t-Critical two-tail**

−0.39 −0.49 −0.37 −0.32 −0.30 −0.33 −0.03 0.05 0.06 2.25 0.12 0.80 0.16 0.46 0.06 1.48 0.42 2.13

−0.05 0.15 −0.06 −0.14 0.03 −0.05 −0.30 −0.38 −0.13 2.52 −0.26 −0.91 −0.05 −0.31 −0.01 −0.96

−0.05 0.15 −0.06 −0.14 0.03 −0.05 −0.30 −0.38 −0.13 2.52 −0.26 −0.91 −0.05 −0.31 −0.02 −0.96

1.21 0.80 0.99 1.01 0.97 1.03 1.12 1.10 0.98 1.26 1.03 1.08 0.90 0.89 0.73 0.57

−0.50 2.13

1.21 0.81 0.99 1.01 0.97 1.03 1.11 1.09 0.98 1.25 1.03 1.08 0.90 0.90 0.74 0.56 0.10 2.13

The table reports the results for the Seemingly Unrelated Regressions of the size – book-to-market portfolios’ excess returns on SMB, HML, and RM–RF, with the excess returns are measured in one of the two ways: (1) using the 1-month treasury bill rate (USTBL1M), and (2) using the 3-month treasury bill rate (USTBL3M). R(t) − RF(t) = a + b[RM(t) − RF(t)] + sSMB(t) + hHML(t) + e(t) SMB (small minus big) is the difference between the returns on small-stock and big-stock portfolios with about the same weighted average book-to-market equity. HML (high minus low) is the difference between the returns on high and low book-to-market equity portfolios with about the same weighted average size. RM is the value-weighted monthly% return on the stocks in the 16 size-BM portfolios. RF is the three-month Treasury bill rate or the one-month Treasury bill rate, depending on each of the approach. The portfolios are formed as follows. At the end of June of each year t, all Information Technology stocks on the NYSE, AMEX, and NASDAQ are grouped into 16 portfolios based on their market capitalization (ln(ME)) and book-to-market ratio (ln(BM)). ME is common equity, which is denominated in millions of U.S. dollars and is measured at the end of June of year t. BM is the ratio of book equity to market equity, with book equity measured at fiscal yearend falling in year t − 1, and market equity measured at the end of December of year t − 1.The ME breakpoints are the first (25%), second (50%), and third (75%) quartiles of the stocks’ ln(ME). Similarly, the BM breakpoints are the first, second, and third quartiles of the stocks’ ln(BM). Stocks with negative BM are excluded so that ln(BM) is calculable. ∗ Tests for mean difference between two-matched samples. ∗∗ At the 5% level of significance.

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Table 11. Pre-Crash and Post-Crash Returns. Portfolios

Panel A. The explanatory variables SMB (t-statistic) HML (t-statistic) RM–RF (t-statistic) Panel B. The dependent variables Big-High (t-statistic) Big-BM2 (t-statistic) Big-BM3 (t-statistic) Big-Low (t-statistic) ME2-High (t-statistic) ME2-BM2 (t-statistic) ME2-BM3 (t-statistic) ME2-Low (t-statistic) ME3-High (t-statistic) ME3-BM2 (t-statistic) ME3-BM3 (t-statistic) ME3-Low (t-statistic) Small-High (t-statistic) Small-BM2 (t-statistic) Small-BM3 (t-statistic) Small-Low (t-statistic)

Mean Pre-Crash

Post-Crash

1.31 (1.88) 1.25 (1.92) −1.90 (−2.44)

0.57 (0.21) 2.92 (1.31) −8.09 (−1.59)

−2.62 (−3.06** ) −1.94 (2.78** ) −2.32 (−3.12** ) −2.41 (−3.09** ) −2.19 (−2.54* ) −2.15 (−2.66** ) −2.23 (−2.66** ) −3.27 (−3.57** ) −1.82 (−2.24* ) 1.09 (0.35) −2.31 (−2.37* ) −2.51 (−2.25* ) 0.96 (0.95) −0.35 (−0.34) −0.16 (−0.12) 2.26 (1.39)

−6.81 (−1.89) −7.28 (−1.70) −7.52 (−1.60) −10.67 (−2.10* ) −5.32 (1.09) −7.26 (−1.80) −8.55 (−1.47) −10.26 (−1.45) −6.87 (−1.59) −6.24 (−1.11) −8.01 (−1.06) −8.02 (0.97) −6.65 (−1.55) −7.14 (−1.04) −7.35 (−1.46) −8.09 (−1.07)

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Table 11. (Continued ) The table compares the mean values of SMB, HML, RM–RF (Panel A), and excess returns on the size – book-to-market portfolios (Panel B) before and after the technology crash in April 2000. Pre-crash values are for the July 1990 – March 2000 period. Post-crash values are for the May 2000–June 2001 period. The month when the crash occurred (April 2000) is excluded. SMB (small minus big) is the difference between the returns on small-stock and big-stock portfolios with about the same weighted average book-to-market equity. HML (high minus low) is the difference between the returns on high and low book-to-market equity portfolios with about the same weighted average size. RM is the value-weighted monthly% return on the stocks in the 16 size-BM portfolios. RF is the three-month Treasury bill rate, observed at the beginning of each month. Portfolios’ excess returns are spreads of portfolios’ monthly returns over the three-month Treasury bill rates. The size – book-to-market portfolios are formed as follows. At the end of June of each year t, all Information Technology stocks on the NYSE, AMEX, and NASDAQ are grouped into 16 portfolios based on their market capitalization (ln(ME)) and book-to-market ratio (ln(BM)). ME is common equity, which is denominated in millions of U.S. dollars and is measured at the end of June of year t. BM is the ratio of book equity to market equity, with book equity measured at fiscal yearend falling in year t − 1, and market equity measured at the end of December of year t − 1.The ME breakpoints are the first (25%), second (50%), and third (75%) quartiles of the stocks’ ln(ME). Similarly, the BM breakpoints are the first, second, and third quartiles of the stocks’ ln(BM). Stocks with negative BM are excluded so that ln(BM) is calculable. The reported means (in percentage) are the time-series averages of the monthly values of the corresponding variables. ∗ Significant at the 0.05 level. ∗∗ Significant at the 0.01 level.

5.3. Information Technology Stock Behavior Before and After the Technology Crash in April 2000 This section investigates how well the three-factor model describes the size and book-to-market effects in two sub-periods, the period before the technology stock crash in April 2000 (the pre-crash period), and the period after the crash (the post-crash period). Section 5.3.1. reports the descriptive statistics for the pre-crash and after-crash variables. Section 5.3.2. presents the regressions results for each of the period. 5.3.1. Inputs for the Three-Factor Model in the Periods Before (July 1990–March 2000) and After the Technology Crash (May 2000–June 2001) Table 11 presents the descriptive statistics for the SMB, HML, and RM–RF variables (Panel A) as well as for the size – book-to-market portfolios’ excess returns (Panel B) for the July 1990–March 2000 period (pre-crash period) and the May 2000–June 2001 period (post-crash period). The month when the crash occurs, April, is excluded to separate the immediate effect of the crash.

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Table 11 reports that most of the (dependent and independent) variables have the post-crash means (i.e. the means for the May 2000–June 2001 period) that are indistinguishable from zero. The post-crash means for SMB, HML, and RM–RF are 0.57%, 2.92%, and –8.09%, with t-statistics of 0.21, 1.31, and –1.59, respectively (Panel A). The post-crash means of the excess returns on the size – book-to-market portfolios also have t-statistics that are less than 2 standard errors from 0, except for the Big-Low portfolio (Panel B). In contrast, (in Panel B) 11 out of the 16 size – book-to-market portfolios have pre-crash mean excess returns (i.e. the mean excess returns for the July 1990–March 2000) that are statistically different from zero. The five portfolios whose pre-crash mean excess returns are indistinguishable from zero are the ME3-BM2 portfolio and those from the smallest – size quartile (the bottom four portfolios). The pre-crash mean for the market excess returns (RM–RF) is also different from zero (t-statistic of −2.44) (Panel A). Although SMB and HML have the pre-crash means that are not different from zero at the 5% level of significance, they are on average significant at the 10% level. The t-statistics for the pre-crash means of these two variables, SMB and HML, are 1.88 and 1.92, respectively. 5.3.2. Regression Results (Using the Three-Factor Model) The regressions results for the pre-crash and post-crash periods are reported in Table 12. In the post-crash period from May 2000 to June 2001, there are 16 crosssectional observations (16 portfolios) and 14 time-series observations (14 months). Because the SUR regression is not applicable in circumstances where there are more cross-sectional observations than time-series observations, the Ordinary Least Squares (OLS) regression is used instead. For comparison purpose, the OLS regression is also applied to the pre-crash period.6 The estimated pre-crash and post-crash coefficients are then compared with each other to determine whether there is any change in the size and book-to-market effects after the technology crash. Three t-tests (for matched sample) for the mean difference between the precrash and post-crash SMB coefficients, between the pre-crash and post-crash HML coefficients, and between the pre-crash and post-crash RM–RF coefficients are conducted. The values of the t-statistics for these tests are reported in Table 12. The mean difference tests indicate that on average the pre-crash coefficients and their post-crash counterparts are the same. All the three t-statistics are well below the t-critical value in magnitude. The highest (in magnitude) is the t-statistic for the difference between the pre-crash HML coefficients and post-crash HML coefficients, is just −0.47, while the critical value at the 5% level of significance for a two-tail test is 2.13.

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Table 12. Ordinary Least Squares (OLS) Regression Results on the Three-Factor Model with Pre-Crash (July 1990–March 2000) and Post-Crash Data (May 2000–June 2001). Portfolios

SMB Coefficients

Big-High Big-BM2 Big-BM3 Big-Low ME2-High ME2-BM2 ME2-BM3 ME2-Low ME3-High ME3-BM2 ME3-BM3 ME3-Low Small-High Small-BM2 Small-BM3 Small-Low t-Statistics* t-Critical two-tail**

HML Coefficients

RM–RF Coefficients

Pre-Crash

Post-Crash

Pre-Crash

Post-Crash

Pre-Crash

Post-Crash

−0.48 −0.39 −0.42 −0.38 −0.14 −0.28 −0.13 0.02 0.14 1.70 0.29 0.75 0.48 0.54 0.86 1.52

−0.68 −0.33 −0.61 −0.71 0.29 −0.19 0.19 0.22 0.52 0.67 0.67 0.68 0.58 1.13 0.71 1.29

0.19 0.04 −0.01 −0.13 −0.06 −0.06 −0.17 −0.37 −0.11 2.65 −0.35 −0.82 −0.15 −0.30 −0.67 −0.99

−0.78 −0.15 −0.40 −0.39 1.13 0.57 0.40 −0.43 0.64 0.56 −0.45 −0.52 0.45 0.17 0.40 −0.99

0.93 0.87 0.97 0.99 1.06 1.02 1.04 1.11 0.91 1.30 1.06 1.06 0.85 0.92 0.93 0.74

0.46 0.83 0.85 0.95 1.31 1.05 1.25 1.15 0.95 1.12 1.09 1.21 0.84 1.03 0.92 0.58

−0.22 2.13

−0.47 2.13

−0.20 2.13

The table reports the results for the Cross-Section Weighting regressions of the size – book-to-market portfolios’ excess returns on SMB, HML, and RM–RF, using pre-crash data and post-crash data. Precrash data are the data for the July 1990–March 2000 period. Post-crash data are the data for the May 2000–June 2001 period. The term “crash” implies the technology crash, which occurred in April 2000. The model for the regressions is: R(t) − RF(t) = a + b[RM(t) − RF(t)] + sSMB(t) + hHML(t) + e(t) SMB (small minus big) is the difference between the returns on small-stock and big-stock portfolios with about the same weighted average book-to-market equity. HML (high minus low) is the difference between the returns on high and low book-to-market equity portfolios with about the same weighted average size. RM is the value-weighted monthly% return on the stocks in the 16 size-BM portfolios. RF is the three-month Treasury bill rate, observed at the beginning of each month. The portfolios are formed as follows. At the end of June of each year t, all Information Technology stocks on the NYSE, AMEX, and NASDAQ are grouped into 16 portfolios based on their market capitalization (ln(ME)) and book-to-market ratio (ln(BM)). ME is common equity, which is denominated in millions of U.S. dollars and is measured at the end of June of year t. BM is the ratio of book equity to market equity, with book equity measured at fiscal yearend falling in year t − 1, and market equity measured at the end of December of year t − 1.The ME breakpoints are the first (25%), second (50%), and third (75%) quartiles of the stocks’ ln(ME). Similarly, the BM breakpoints are the first, second, and third quartiles of the stocks’ ln(BM). Stocks with negative BM are excluded so that ln(BM) is calculable. ∗ Tests for mean difference between two-matched samples. ∗∗ At the 5% level of significance.

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6. CONCLUSION This paper explores the relationship between size, book-to-market, beta, and expected stock returns in the Information Technology sector. In particular, the paper uses two models to test this relationship. The first model assumes stock returns are related to the direct measure of size, book-to-market, and beta (the multivariate model). The second model assumes stock returns are related to returns on the three portfolios that are designed to mimic the size, book-to-market, and beta factors (the three-factor model). The risk-return tests using the multivariate model indicate that the book-tomarket effect is present in stock returns. However, this effect only exists at the 10% level of significance in contrast to the more significant relationship documented by Fama and French (1992) for all non-financial stocks on the NYSE, AMEX, and NASDAQ over the 1963–1990 period. Thus, the book-to-market effect for IT stocks, though present, is not robust over the period 1997–2001. Except for discovering a weak book-to-market effect, the risk-return tests using the multivariate model find no relationship between size, beta and stock returns. Although Fama and French (1992) also document a weak explanatory power of beta, they find that size is significant and that size and book-to-market ratio in combination absorb variation in stock returns. The different results documented in Fama and French’s (1992) paper and this paper might be due to different research designs employed by the two papers. However, research design seems to be playing a trivial part since the results from the FM regressions on individual stocks and on portfolios (in this paper) both lead to similar conclusions. Thus, the relationship between size, book-to-market, beta and stock returns in IT stocks appears to be different from that previously observed in non-financial stocks. The risk-return tests using the three-factor model show that expected returns are strongly related to the size, book-to-market, and market factors. Unlike the multivariate model where size and book-to-market factors are directly measured from the market capitalization and book-equity to market-equity ratio of a stock, the size and book-to-market factors in the three-factor model are represented by the returns on the portfolios that are designed to mimic stocks’ market capitalisation and book-equity to market-equity ratio. The results show that the three-factor model works very well for IT stocks over the July 1990–June 2001 period as well as the sub-periods before (July 1990–March 2000) and after the technology crash (May 2001–June 2001) in April 2000. Why do the multivariate model and the three-factor model produce different results? One possible explanation is that the multivariate model uses annual data while the three-factor model uses monthly data. We argue that the use of monthly data instead of annual data in the three-factor model is not a serious problem that could lead to any spurious conclusions. Examining whether the

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three-factor model produces different results due to the alternative uses of annual data and monthly data could provide a basis for future research. Another possible reason for the differing results produced by the two models is that they are simply not comparable. SMB, HML, and RM–RF might not be good proxies for direct measurements of size (ln(ME)), book-to-market ratio (ln(BM)), and beta respectively. In other words, the mimicking returns for the size (SMB), book-tomarket (HML), and market factors (RM–RF), might not be good indicators of movements in the characteristics (ln(ME), ln(BM), and beta) of stocks. The sub-period results (the periods before and after the technology crash in April 2000) show that the nature of the relationship between stock returns, size, book-to-market, and market factors, or the magnitude of the size, book-to-market, and market premiums, is on average unchanged for both of the sub-periods. The coefficients on SMB, HML, and RM–RF for the July 1990–March 2000 (the precrash coefficients) are not statistically different from those for the May 2000–June 2001 period. This is particularly interesting since this finding is inconsistent with the view that the technology stock crash in April 2000 was a correction of stock prices. As it has been known, the factors in the three-factor model are the “returns” on some specially designed portfolios. It is possible that the behavior of a return on a particular portfolio has been changed after the technology crash (in fact it has as the statistics for SMB, HML, RM–RF, and the size – book-to-market portfolios’ excess returns have changed from the pre-crash period to post-crash period, Table 12); but because all the returns have changed by the same magnitude, the relationship between these returns is unchanged. This conjecture, if true, would offer great support for the three-factor model, since it could work over any time frame and be used for tests of structural change (i.e. relationship change) after an event. This paper makes three important contributions to theory as well as practice. First, it provides more evidence on the risk-return relationship in the information technology sector. The evidence in this paper brings a step towards finding a satisfactory explanation for the deviation from the CAPM. Second, the paper documents in detail the behavior of IT stock prices before and after the technology stock crash in April 2000. This information could be used as a reference for investment decisions. And finally, the paper opens a new direction for future research in the asset-pricing field: looking for (the risk-return) evidence in individual sectors rather than in markets as a whole.

NOTES 1. “Old Economy” stocks are those other than IT stocks. 2. Note that a firm might not have beta for a certain period but might have it at a different time. We account for this by including the firm when its beta is available and excluding it

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when its beta is unavailable. This is done subject to whether the firm fits into our portfolio selection procedure (to be described in the methodology section). 3. A testing year is from July of year t to June of year t + 1. 4. It makes more sense to establish a relationship between SMB, HML, and systematic risk than to find a relationship between size, book-to-market equity, and systematic risk. This is due to the fact that size and book-to-market equity are company-specific factors. 5. Data on the 1-month Treasury bill rate in DataStream is not available after May 1996. 6. Note that the SUR and OLS techniques produce identical estimators but different t-statistics for these estimators. As this section is only concerned with the differences in the pre-crash and after-crash coefficients, the use of OLS is as significant as the use of SUR.

REFERENCES Aldous, D. (1989). Probability approximations via the Poisson clumping heuristic. New York: Springer. Alford, A. W., Jones, J. J., & Zmijewski, M. E. (1994). Extension and violation of the statutory SEC form 10-K filing requirements. Journal of Accounting and Economics, 17, 229–254. Banz, R. W. (1981). The relationship between return and market value of common stocks. Journal of Financial Economics, 9, 3–18. Barber, B. M., & Lyon, J. D. (1997a). Detecting long-run abnormal stock returns: The empirical power and specification of test statistics. Journal of Financial Economics, 43, 341–372. Barber, B. M., & Lyon, J. D. (1997b). Firm size, book-to-market ratio, and security returns: A holdout sample of financial firms. Journal of Finance, 52, 875–883. Black, F. (1993). Beta and return. Journal of Portfolio Management, 20, 8–18. Black, F., Jensen, M. C., & Scholes, M. (1972). The capital asset pricing model: Some empirical tests. In: M. Jensen (Ed.), Studies in the Theory of Capital Market. New York: Praeger. Capaul, C., Rowley, I., & Sharpe, W. F. (1993). International value and growth stock returns. Financial Analysts Journal, 49, 27–36. Chan, K. C., & Chen, N. F. (1988). An unconditional asset-pricing test and the role of firm size as an instrumental variable for risk. Journal of Finance, 43, 309–325. Chan, L. K. C., Hamao, Y., & Lakonishok, J. (1991). Fundamentals and stock returns in Japan. Journal of Finance, 46, 1739–1789. Chui, A. C. W., & Wei, K. C. J. (1998). Book-to-market, firm size, and the turn-of-the-year effect: Evidence from Pacific-Basin emerging markets. Paciﬁc-Basin Finance Journal, 6, 275–293. Daniel, K., & Titman, S. (1997). Evidence on the characteristics of cross sectional variation in stock returns. Journal of Finance, 52, 1–33. Davis, J. (1994). The cross-section of realized stock returns: The pre-COMPUSTAT evidence. Journal of Finance, 49, 1579–1593. Davis, J. L., Fama, E. F., & French, K. R. (2000). Characteristics, covariances, and average returns: 1929 to 1997. Journal of Finance, 55, 389–406. DeBondt, W. F. M., & Thaler, R. H. (1987). Further evidence on investor overreaction and stock market seasonality. Journal of Finance, 42, 557–581. Dimson, E. (1979). Risk measurement when shares are subject to infrequent trading. Journal of Financial Economics, 7, 197–216. Fama, E. F., & French, K. R. (1992). The cross-section of expected stock returns. Journal of Finance, 47, 427–465.

Size and Book-to-Market Effects in the Returns on Information Technology Stocks

91

Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3–56. Fama, E. F., & French, K. R. (1995). Size and book-to-market factors in earnings and returns. Journal of Finance, 50, 131–155. 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. Fama, E. F., & MacBeth, J. D. (1973). Risk, return, and equilibrium: Empirical tests. The Journal of Political Economy, 81, 607–636. Franklin, C. (2000, September). Incubating real options: Can option pricing theory help investors make sense of the business models and valuations of internet incubators? Working Paper, University of Stirling. Haugen, R. (1995). The new ﬁnance: The case against efﬁcient markets. Englewood Cliffs, NJ: PrenticeHall. Jegadeesh, N. (1992). Does market risk really explain the size effect. Journal of Financial and Quantitative Analysis, 27, 337–351. Keim, D. B. (1983). Size-related anomalies and stock return seasonality: Further empirical evidence. Journal of Financial Economics, 12, 13–32. Kothari, S. P., Shanken, J., & Sloan, R. (1995). Another look at the cross-section of expected stock returns. Journal of Finance, 50, 185–224. Lakonishok, J., Shleifer, A., & Vishny, R. W. (1994). Contrarian investment, extrapolation, and risk. Journal of Finance, 49, 1541–1578. Lintner, J. (1965). The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47, 13–37. Lo, A. W., & MacKinlay, A. C. (1990a). When are contrarian profits due to stock market overreaction? Review of Financial Studies, 3, 175–205. Lo, A. W., & MacKinlay, A. C. (1990b). Data-snooping biases in tests of financial asset pricing models. Review of Financial Studies, 3, 431–467. MacKinlay, A. C. (1995). Multifactor models do not explain deviations from the CAPM. Journal of Financial Economics, 38, 3–28. Mech, T. (1993). Portfolio return autocorrelation. Journal of Financial Economics, 34, 307–344. Newey, W., & West, K. (1987). A simple, heteroskedastic and autocorrelation consistent covariance matrix. Econometrica, 55, 703–708. Rajgopal, S., Kotha, S., & Venkatachalam, M. (2000, January). The relevance of web traffic for internet stock prices. Research Paper, Stanford University. Rosenberg, B., Reid, K., & Lanstein, R. (1985). Persuasive evidence of market inefficiency. Journal of Portfolio Management, 11, 9–17. Sadorsky, P. (2003). The macroeconomic determinants of technology stock price volatility. Review of Financial Economics, 12, 191–205. Scholes, M., & Williams, J. (1977). Estimating betas from nonsynchronous data. Journal of Financial Economics, 5, 309–327. Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk. Journal of Finance, 19, 425–442. Trueman, B., Wong, F., & Zhang, X. (2001). Back to basics: Forecasting the revenues of internet firms. Review of Accounting Studies, 6, 305–329.

IMPLIED VOLATILITIES AND AUDITOR REPUTATION: THE ANDERSEN CASE Jonathan M. Godbey and James W. Mahar ABSTRACT Audits are a means of reducing the information asymmetry between managers and investors. If the quality of the audit is in question, outside investors may face a larger informational disadvantage. We test the hypothesis that this informational disadvantage is manifested in the implied volatilities associated with the equity options of the audited ﬁrms. We ﬁnd that volatilities increased for Andersen audited ﬁrms relative to ﬁrms audited by other Big Five accounting ﬁrms. This ﬁnding is consistent with the view that auditors help lessen the information asymmetry problem and that some of this reduction is accomplished by auditor reputation.

1. INTRODUCTION The reputation of a firm’s auditor is widely seen as an important determinant in signaling audit quality to investors. In literature, the importance of auditors and their reputation is shown by Watts and Zimmerman (1983). This importance has subsequently been examined and discussed in both finance and accounting literature. In the financial literature, much of the research into auditor reputation has focused on IPO underpricing and the prestige of the firms’ auditor. The accounting Research in Finance Research in Finance, Volume 21, 93–111 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21004-8

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literature shows a consistent view, but from a different perspective, focusing on the relationship between audit pricing and reputation as well as event-studies showing market reaction as a function of auditor reputation. A common explanation for much of this literature is that auditor reputation serves as a means of reducing information asymmetries between investors and the firm’s management. The Enron-related troubles that befell Arthur Andersen (Andersen) provide a unique opportunity to test the importance of auditor reputation. Over the course of approximately six months, Andersen went from being a highly respected firm to being a symbol of corporate malfeasance. The importance of the decline of Andersen on client stock prices has been examined previously by Chaney and Philipich (C&P, 2002) who report that firms audited by Andersen experienced statistically significant price declines “surrounding dates on which Andersen’s audit procedures and independence were under severe scrutiny.” (p. 1221) There are two possible explanations for the market-adjusted price decline: (1) a decrease in expected cash flow of Andersen audited clients, that is, a change in the mean of the cash flow distribution; and (2) an increase in risk stemming from either higher information asymmetries due to poor audit quality that would allow mangers to hide important information from investors, or an increased likelihood of incurring the costs of changing auditors. One way to gauge whether investors believe that the risk of Andersen audited firms had increased is to examine the volatility implied by the pricing of equity options. Merton (1973), Latane and Rendlemand (1976), and Hull and White (1987) document that the implied volatility of a particular option represents the anticipated risk over the life of the option. Information asymmetries have also been shown to play an important role in the option pricing. For example Patell and Wolfson (1981) show that the implied volatility on equity options drops following firm’s earnings releases. As pointed out by Merton (1987) and later discussed by Bellalah and Aboura (2002), as the amount of, or quality of, available information decreases, the implied volatility, or risk, increases, which in turn increases the required rate of return and decreases the stock price, raising the cost of capital. In this paper, we extend the findings of C&P (2002) by examining how option market participants use auditor reputation in their pricing of equity options. If auditor reputation affects the informational asymmetry between investors and the firm, then the events that undermined Andersen’s reputation should be associated with an increase in the implied volatility of the options of Andersen audited clients. If auditor reputation is unimportant, then there should be no change in the implied volatilities relative to that of firms audited by other Big Five accounting firms. For both the short and long time periods, our results demonstrate that the implied volatility at S&P 500 firms audited by Andersen increased significantly relative to firms audited by other Big Five accounting firms during the time period in

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which Enron and Andersen actions became publicly known. Specific events where the average implied volatility increased include: (1) the restatement of Enron’s financial statements and the announcement that the SEC was investigating the case (November 8, 2001); (2) the Congressional testimony of Andersen CEO Joseph Berardino (December 12, 2001); (3) Andersen’s admission to the shredding of documents while under SEC investigation (January 10, 2002); (4) the dual events of the release of the Powers Report and Andersen’s hiring of former Federal Reserve Chairman Paul Volcker (February 2 and 3, 2002); and (5) the admission by David Duncan that he had ordered Enron documents to be destroyed. These findings are consistent with a view that the quality of auditor reputation is an important factor in reducing the information asymmetry problem. The remainder of the paper is organized as follows: Section 2 provides a review of existing research and an introduction to implied volatilities, Section 3 provides a description of our data and methodology, Section 4 examines the results of the tests, and Section 5 gives a summary and conclusion.

2. LITERATURE REVIEW Auditor reputation is an important means of signaling the quality of a client’s financial reporting and thereby reducing the information asymmetry problem. This area of research was established by Watts and Zimmerman (1983), but has been examined extensively in both financial and accounting literature. The common thread through this auditor reputation literature is that investors use auditor reputation as a signal of quality that reduces informational asymmetry. In financial literature, much of the auditor reputation work has been done within an IPO framework. Titman and Trueman (1986) find that audit quality can help explain IPO underpricing. Similarly, Balvers, McDonald and Miller (1988), and Beatty (1989) find less IPO underpricing when a Big 8 auditor is used. More recent work by Clarkson and Simunic (1994) find that there is less underpricing of Canadian IPOs when a high quality auditor is used. The importance of auditor reputation has also been shown by looking at the pricing of audits. A partial list of those who have examined the relationship between auditor quality and their pricing includes Francis and Simon (1987), Beatty (1993), Dye (1993), and Craswell, Francis and Taylor (1995) who all find that audit firms with higher perceived reputation, price their audits higher than those with lower perceived quality. This pricing may be partially due to the fact that larger (and more highly perceived) auditors have more assets (deeper pockets) and can therefore better withstand potential liabilities in the event of a lawsuit. However, Datar and Alles (1999) show that audit firms understand the importance of their reputation

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and strive to maintain their reputational capital even when legal liability is reduced by their financial assets. Auditor reputation has also been investigated with event-study type tests that measure the market reaction for clients audited by the same auditor. Teoh and Wong (1993) find that the perceived audit quality influences the market’s response to earnings announcements. Franz and Crawford (1998) document that audit clients that are not involved with auditor related litigation lose market value as a result of litigation brought against their auditor which is seen as damaging the auditor’s reputation. Moreover, C&P (2002) report that firms audited by Arthur Andersen experienced market-adjusted stock price declines as the reputation of Andersen fell. Our paper extends the work of C&P (2002) by investigating the cause of the stock price decline that they find for Andersen audited firms following the Enronrelated events. There are two possible explanations for any abnormal decline in stock price: (1) an unexpected change in expected future cash flows available to shareholders; or (2) an increase in risk. Since the stock price represents the present value of the future cash flows, both the expected future cash flows (the mean) as well as the risk of the cash flows are important. Moreover, by focusing on stock price alone, it is impossible to determine which of these factors is present. The implied volatility on the other hand, is not directly influenced by the mean of the expected cash flows, but rather is the option market’s consensus forecast of expected volatility of the underlying stock over the life of the option. The significance of this distinction can be demonstrated by examining the distribution of expected cash flows. Even if operational cash flows are held constant, a decline in audit quality may reduce the expected cash flows available to shareholders due to an increased probability of over-reported earnings or under-reported liabilities. Both possibilities would lower the expected cash flows available to shareholders. In addition, sufficient damage to the auditor’s reputation would necessitate a costly change in auditors. This change reduces the cash flow available to shareholders. Therefore, it is possible that shareholders face a reduction in expected cash flows as well as an increase in the risk of cash flows. This differentiation, which can only be theorized by using stock price data, can be documented with implied volatility data. Thus, two important distinctions exist between our analysis and that of C&P (2002). First, we examine the implied volatility associated with equity option contracts rather than stock returns. This allows us to determine if option traders use auditor reputation in their pricing decisions. Second, and more importantly, we are able to partially disentangle risk from the expected cash flow consequences of Andersen’s loss of prestige, which gives us a better representation of the impact of the auditor’s reputation on informational asymmetries.

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The expected volatility of a given asset cannot be directly observed in the market. However, given the price of an option and the price of the underlying asset, one may use an iterative process to calculate the expected volatility implied by a particular option-pricing model. This implied volatility is thus the market’s expectation of the future volatility of the underlying asset, in this case the stock price. In this paper, the implied volatility for each stock is calculated from at-the-money options with at least 30 days to expiration using the Black-Scholes Option Pricing Model (BSOPM) (Black & Scholes, 1973) adjusted for dividends (Merton, 1973). This model is as follows. C = (e−DT )S 0 N(d 1 ) − Xe−rT N(d 2 ) [ln((e−DT )S

(1)

␴2 /2)T]/(␴

where: d1 = sqrt(T)); d2 = d1 − (␴ sqrt(T)); 0 /X) + (r + S0 = stock price at time zero; X = strike price; T = time to expiration; r = riskfree rate; ␴ = volatility of the underlying asset; D = Annualized dividend yield; N(x) = the cumulative probability distribution function for a variable that is normally distributed with a mean of zero and a standard deviation of 1.0. Merton (1973), Latane and Rendlemand (1976), and Hull and White (1987) show that the implied volatility of a particular option represents the mean anticipated daily volatility, that is the anticipated risk, over the life of the option. Canina and Figlewski (1993) summarize much of the research on the informational content of implied volatilities and document the “volatility-smile” whereby the implied volatility increases as the time to maturity gets small. Dumas, Fleming and Whaley (1998) confirm this finding and show that volatilities are not constant across time. The impact of events, both scheduled and unscheduled, on implied volatilities has been the topic of much research. Patell and Wolfson (1981) as well as Isakov and Perignon (2001) examine changes in implied volatility around scheduled earnings announcements and find that implied volatility drops once uncertainty is resolved. French and Dubofsky (1986) study the effect of unexpected stock splits on the implied volatility. Finally, Levy and Yoder (1993) examine the impact of mergers and acquisitions on implied volatilities. Each of these finds that the option market quickly incorporates the new information and the implied volatilities change accordingly.

3. DATA AND METHODOLOGY In order to examine the effect of changes in auditor reputation on the risk of a firm, implied volatility data was collected for the eighteen months ending August 31, 2002 from ivolatility.com for firms in the S&P 500 as of October 16, 2001. Implied volatility calculations are based on at-the-money put and call

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options with at least 30 days to expiration. The 30-day constraint limits the effect of a “volatility-smile” influencing the findings. At-the-money options are used because they are the most liquid and therefore less likely to be influenced by stale data problems brought about by infrequent trading. This infrequent trading could introduce a bias if the stock, which is more frequently traded than the option, falls in value after the last recorded trade of the option contract. This would be a problem since the implied volatility would be computed with an option trade that occurred before the stock fell in value. As C&P (2002) provide evidence that Andersen audited clients fell in value, this systematic price drop could lead to higher implied volatilities. However, by using liquid at-the-money options, the stale trading problem is reduced. Additionally, the implied volatility is calculated with using the average of the bid and ask quotes which further reduces any stale pricing problem. Each firm’s auditor information was drawn from the firms’ websites as of October 16, 2002 when the news of Enron’s problems became known. The breakdown of firms by auditors and sectors is provided in Table 1. For consistency purposes, only firms audited by one of the Big Five accounting firms (Andersen, Ernst and Young, Deloitte and Touche, KPMG, and PriceWaterhouseCoopers) were studied. This resulted in a final sample size of 495 firms audited by a Big Five accounting firm. If auditor reputation is important in reducing the information asymmetry problem, then the Enron-Andersen-related events of late 2001 and early 2002 Table 1. S&P 500 Breakdown by Auditor and by Sector. Sector

Auditor AA

DT

EY

KPMG

PWC

Other

Totals

Consumer Discretionary Consumer Staples Energy Financials Health Care Industrials Information Technology Materials Telecommunications Utilities

12 5 5 9 5 13 6 10 3 14

14 7 2 13 5 13 11 4 1 11

24 5 5 24 13 17 24 5 3 1

9 7 4 10 5 8 13 3 2 0

26 10 8 18 16 16 26 15 4 11

2 0 0 1 1 1 0 0 0 0

87 34 24 75 45 68 80 37 13 37

Total

82

81

121

61

150

5

500

Note: AA = Arthur Andersen; DT = Deloitte & Touche; EY = Ernst & Young; PWC = Price Waterhouse Coopers. Sectors are from Standard and Poors website. Auditor information is from firms’ websites.

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should result in higher implied volatilities for Andersen audited firms. If auditor reputation is not important in reducing information asymmetries, then the implied volatility ratios should be the same in the pre and post period. This leads to the null hypothesis: H0 . The implied volatility of Andersen audited firms increases as events likely damaging to Andersen’s reputation occur. Unlike traditional event studies, the information release effecting Enron and Andersen was not completed at one time. From August 14, 2001 (when CEO Jeffrey Skilling resigned) to June 15, 2002 (when Andersen was found guilty of obstruction of justice and ordered to exit the audit business), news that could be seen as damaging was released at irregular intervals. The news that was most directly tied to Andersen was concentrated after November 8, 2001, when Enron announced it would have to restate earnings. Within the aforementioned time period, other specific dates that could be judged as being detrimental to Andersen’s reputation include the dates investigated by C&P as well as other dates after C&P’s February 4, 2002 cutoff. These include November 8, 2001 when the SEC began the investigation into Enron, November 29, 2001 when the SEC expanded its investigation to include Andersen, December 12, 2001 when Andersen CEO Joe Berardino testified in front of Congress, January 10, 2002 when Andersen admitted to shredding documents, January 24, 2002 when Andersen partner David Duncan refused to testify in front of Congressional hearings, and the early February release of the Powers Report as well as Andersen’s hiring of former Federal Reserve Chairman Paul Volcker in an attempt to improve the auditor’s tarnished reputation. Additionally we investigated several dates that were not examined by C&P 2002. These events include March 14, 2002 when the U.S. Justice Department charged Andersen with obstruction of justice, March 27, 2002 when Andersen’s CEO Joseph Berardino resigned, and April 9 when David Duncan admitted that he ordered the shredding of documents (Table 2). As time progressed and the seriousness of the problems became known, many Andersen clients dropped Andersen as their auditor. The magnitude of these departures introduces further problems in the investigation of event dates. The extreme case of this is shown at the end of the event period (the August 30th court mandated end of Andersen’s audit practices) when there were no firms still being audited by Andersen. However prior to this definitive end point, departures from Andersen were so pronounced that any analysis is prone to capture firm specific risk factors. For instance, on June 15, 2002 a Houston jury found Andersen guilty of obstruction of justice. This event was not examined because only 2 of the original sample of 82 firms were still with Andersen. To avoid these sample

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Table 2. Andersen-Enron Timeline. Date

Event Description

August 14, 2001 October 12, 2001

Enron CEO Jeffrey Skilling resigns citing personal reasons Arthur Andersen’s in-house lawyer emails Houston office regarding document destruction policy Enron reports $638 million loss and a $1.2 billion reduction in shareholder equity SEC requests information from Enron regarding losses SEC begins official inquiry into Enron Enron announces the SEC inquiry has been upgraded to a formal investigation Enron revises its last five years of financial statements, admitting net losses of $586 million Andersen receives a federal subpoena for Enron documents Dynegy announces takeover of Enron for $8 billion Enron again restates third quarter earnings and warns on debt repayments Dynegy pulls out of takeover deal and Enron’s credit rating downgraded to junk status SEC investigation expanded to include Andersen Enron files for Chapter 11 bankruptcy protection Andersen CEO, Joseph Berardino, testifies before Congress and admits the auditing firm may have violated securities laws Justice department begins criminal investigation of Enron Andersen acknowledges that it had destroyed documents Andersen Partner, David Duncan, fired Enron employee claims shredding Kenneth Lay resigns as Enron’s CEO FBI begins investigation into shredding David Duncan refuses to testify in front of Congressional hearings regarding shredding of “Enron-related documents” Clifford Baxter, who had reportedly “clashed” with Jeff Skilling over “accounting practices,” is found dead of an apparent suicide Powers report released Andersen hires former Fed Chairman, Paul Volcker U.S. Justice Department charges Andersen with obstruction of justice for allegedly shredding vital Enron documents Andersen pleads not guilty to obstruction of justice charges CEO Joseph Berardino announces his resignation Andersen reports it will lay off 7,000 employees Former Andersen auditor David Duncan enters a plea bargain with prosecutors, admitting he ordered the shredding of incriminating Enron documents Andersen trial begins in a federal courtroom in Houston Jurors find Andersen guilty of obstruction of justice charges and the firm agrees to cease auditing public companies by August 31, 2002 as ordered by the SEC

October 16, 2001 October 17, 2001 October 22, 2001 October 31, 2001 November 8, 2001a

November 9, 2001 November 19, 2001 November 28, 2001 November 29, 2001 December 2, 2001 December 12, 2001a January 9, 2002 January 10, 2002a January 15, 2002 January 22, 2002 January 23, 2002 January 24, 2002 January 25, 2002 February 2, 2002a February 3, 2002a March 14, 2002 March 20, 2002 March 27, 2002 April 8, 2002 April 9, 2002

May 6, 2002 June 15, 2002

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Table 2. (Continued ) Date

Event Description

June 27, 2002

SEC issues restraining order to prevent Andersen from destroying any documents relating to its telecommunication client WorldCom Andersen has its Texas accounting license revoked Andersen Worldwide agrees to pay a $60 million settlement to the plaintiffs in the Enron class-action suit and to creditors of the bankrupt Energy firm Andersen “closes its books,” as its public auditing business is terminated Andersen receives maximum sentence of five years probation and a fine of $500,000 for obstruction of justice relating to Enron scandal

August 16, 2002 August 27, 2002 August 30, 2002 October 16, 2002

Sources: BBC, CBS News, Houston Chronicle, and Washington Post. a Indicates that the event was also investigated by Chaney and Philipich (2002).

size problems we report individual events only up to April 9, 2002 when former Andersen partner David Duncan admitted that he had ordered the destruction of Enron related documents. The rationale for halting the analysis at this point was this was the last major event where at least 50% of the original sample was still with Andersen (Table 3). Table 3. When Firms Dropped Andersen. Date

Event Description

February 3, 2002 March 14, 2002 March 20, 2002 March 27, 2002 April 8, 2002 April 9, 2002 May 6, 2002 June 15, 2002

Andersen hires former Fed Chairman, Paul Volcker Andersen charged with obstruction of justice Andersen enters a not guilty plea CEO Joseph Berardino resigns Andersen reports 7,000 layoffs Former Andersen Auditor David Duncan enters plea bargain Trial begins in Houston Andersen found guilty, ordered to cease public auditing by August 31, 2002 SEC issues restraining order to prevent destruction of WorldCom documents Andersen’s Texas accounting license revoked Andersen agrees to $60 million settlement in Enron class-action suit Andersen terminates its public accounting business Andersen sentenced to five years probation and $500,000 fine

June 27, 2002 August 16, 2002 August 27, 2002 August 30, 2002 October 16, 2002

Number of Andersen Audited Firms 82 73 68 57 51 49 32 3 2 0 0 0 0

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As a consequence of these multiple event dates, a single-event date methodology may not capture the impact of the information. In addition, with so many events in succession, it is possible that the impact of any one event may have been predicted by market participants and already was incorporated into the price of the option. Finally, since the events occur in close proximity to one another, there may be important spillover effects that would prevent the impact of single events being known with certainty. The most extreme example of this contamination is the Saturday February 2, 2002 release of the Powers Report and the Sunday February 3, 2002 hiring of former Federal Reserve Chairman Paul Volcker. Since both events occurred on the weekend, the market reaction to each event cannot be individually measured, as the first day of trading for each was Monday, February 4, 2002. To avoid these multi-news event contamination problems, we use a strategy previously used to evaluate the market reaction to deregulation legislation. Since deregulation legislation is not a single event, but rather a series of committee meetings, press releases, and votes, the outcome could be forecasted, causing no significant market reaction at the time of actual passage of the deregulation bill. Schwert (1981) and Binder (1985) suggest looking before any of the coverage began and then after all of it was over to assure that the total change was captured. Thus, we begin our investigation by determining whether the combination of all the events in sum, had a significant effect on the relative implied volatility of Andersen clients as compared to other Big Five audited firms. To control for market-wide fluctuations in implied volatilities, we begin the analysis by using the VIX. The VIX is the most widely actively traded volatility index. During the 2001–2002 time-period the VIX tracked the implied volatility of at-the-money options for S&P 100 firms.1 Thus, using the VIX introduces a possible bias as our sample is composed of S&P 500 firms. More importantly however, is the problem that 14 of the firms in the sample (17%) are also in the S&P 100 thus causing potential contamination problems. To avoid these contamination problems, for the majority of our analysis we use the ratio of implied volatilities at Andersen audited firms to the implied volatility of the other S&P 500 firms audited by a Big Five accounting firm. This implied volatility ratio, which will be henceforth called the IV ratio, is calculated on a daily basis for each trading day from June 1, 2001 to August 30, 2002 when Andersen officially ceased its audit operations. If all audit firms were identical in audit quality and client make-up, then the implied volatility ratio should be equal to one. However, since there are differences in makeup of clientele (see Table 1), then the ratio may be different than one. By analyzing changes in this ratio, rather than absolute levels, the impact of auditor reputation can be examined. Thus, rather than examining the makeup of the individual firms’ implied volatility, this paper studies the changes of the IV

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ratio to determine whether the events surrounding the Enron-Andersen case had differential effects on the implied volatilities of Andersen’s clients versus clients of other auditors. This methodology also accounts for differences in the audit firms’ initial reputation and changes in market-wide volatility. Copeland, Poon and Stapleton (2000) model implied volatility as a function of firm specific factors. To control for these firm specific factors, which include the “duration of the firm’s profits” and the firm’s leverage, we examine the changes in the IV ratio for the portfolio of Andersen audited S&P 500 firms. Additionally we end our individual event analysis on April 9, 2002 when the size of the sample drops to 39 firms (approximately 50% of the original sample). The August 14, 2001 resignation of Jeffery Skilling has frequently been cited as the beginning of the end for Enron. It would therefore be theoretically possible that the markets could have inferred the troubles with Andersen from this initial announcement. As a result, we create a baseline IV ratio to compare Andersen audited S&P 500 firms to other Big Five audited S&P 500 firms. This ratio is computed on a daily basis by dividing the average implied volatility for Andersen audited firms by the average implied volatility for firms audited by other Big Five firms. The resulting ratio is found for the 20 trading days preceding August 14. This baseline is then compared to the daily IV ratio for the 20 trading days following the release of the Powers report on February 2, 2002. To insure that any changes in implied volatility were not directly caused by the events of September 11, 2001, the procedure is repeated using the ten trading day period immediately prior to the October 16, 2001 announcement by Enron where they first publicly acknowledged large amounts of off balance sheet financing and a major loss. These dates were chosen because by October 1, 2001, market-wide volatility, as measured by the VIX index, had returned to September 10th levels. Once the daily implied volatility ratios were computed, the next step in the investigation was to check the IV ratio data for normalcy. This was accomplished with the Jarque-Bera test, which showed that the data was likely normally distributed (p-value of 0.41). The actual investigation is performed in two ways. First t-tests are used to examine the average implied volatility ratio before and after the event windows. Following the t-tests, a regression analysis was performed with a dummy independent variable to capture the marginal impact of the events. Black (1976) shows that implied volatilities are inversely related to stock price. As C&P (2002) report that Andersen audit clients experienced negative abnormal returns following the reputation damaging events associated with Andersen and their role in the Enron collapse. Consequently, a stock price variable is used to control for any potentially confounding results stemming from the negative

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relationship between the underlying stock price and implied volatility. We regress the change in the implied volatility ratio from before each event to after each event. That is we regress the model: IV ratio = c + b1(Stock Price Ratio) + b2(Time Dummy)

(2)

where: IV Ratio = Average Implied Volatility for Andersen audited firms divided by Average Implied Volatility for firms audited by other Big Five audit firms; Price Ratio = Average stock price for Andersen audited firms divided by average stock price for firms audited by other Big Five audit firms; Time Dummy = 1 in the post event time period. Once the overall (both the 6 and 8 month event windows) impact of the events has been determined, the same methodology is used to examine the impact of the individual events that would be likely to have been interpreted as damaging to Andersen’s reputation. Post event changes in the relative implied volatility are examined for the days 0, +1 and days 0, +4 event windows. T-tests are performed by comparing the daily implied volatility ratio to the average ratio of the 20 days preceding the event. As with the longer event-window tests, we inspect the Table 4. Change in IV Ratio Over Long-Event Windows. Panel A: 8-Month Window Before August 14, 2001

After April 9 2002

Difference

p-Value

0.9007 0.9050

0.9439 0.9473

0.0432 0.0423

0.0000 0.0000

Before October 16

After February 4

Difference

0.8955 0.9000

0.9335 0.9361

0.0380 0.0361

IV ratio Call data Put data Panel B: 6-Month Window

IV ratio Call data Put data

p-Value

0.0000 0.0000

Note: Changes in daily implied volatility ratio: The daily implied volatility ratio is computed by dividing the average implied volatility of Andersen audited firms in the S&P 500 by the average implied volatility of S&P 500 firms audited by other “Big Five” firms. The “Before” trading dates in Panel A are based on the 30-day event window prior to Jeffrey Skilling’s August 14th, 2001 resignation. The “Before” dates in Panel B were selected to minimize the effects of the September 11, 2001 attacks. The average implied volatility on S&P 500 stocks had returned to its pre-attack levels by October 1, 2001. Therefore, the “Before” period in Panel B has only 11 trading days prior to the October 16, 2001 disclosure by Enron of a significant equity write-off and net loss. The “After” trading dates in each Panel are composed of the 30-days following the February release of the Powers report, which was critical of Andersen’s practices.

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individual announcement effects by performing regression analysis using the same equation as in longer (6 or 8 month) event window.

4. RESULTS AND DISCUSSION Tests of both long event windows (the six and eight month) give strong evidence that overall there was a significant increase in the implied volatilities of Andersen audited clients relative to those of firms audited by other Big Five firms (p value 0.0000). This is shown in Table 5. This is consistent with the hypothesis that auditor reputation helps to mitigate the information asymmetry problem. Table 5. Long Event Window Regression Results. Panel A: Calls 8-Month IV Ratio = constant + time dummy Constant Time dummy

0.9007 (212.95) 0.0432 (8.14)

IV Ratio = constant + price ratio + time dummy Constant 1.7472 (3.86) Price ratio −0.8320 (−1.88) Time dummy 0.0398 (7.50)

6-Month

0.8955 (488.38) 0.0380 (14.64) 0.8460 (2.63) 0.0470(0.15) 0.0401 (2.87)

Panel B: Puts IV Ratio = constant + time dummy Constant Time dummy

0.9050 (188.07) 0.0423 (7.01)

IV Ratio = constant + price ratio + time dummy Constant 1.8506 (3.61) Price ratio −0.9295 (−1.84) Time dummy 0.0385 (6.36)

0.9000 (537.56) 0.0361 (15.24) 0.8536 (2.91) 0.0440 (0.16) 0.0381 (2.98)

Note: The IV Ratio is the average implied volatility of Andersen audited firms divided the average volatility of firms audited by other Big Five firms. The average price ratio is the average price of Andersen audited firms divided the price of firms audited by other Big Five firms. The results shown here are for all firms audited by Andersen as of October 16, 2001. The 8-month window regression uses the twenty trading days before the August 14, 2001 resignation of Jeffrey Skilling and the twenty trading days following the April 9, 2002 admission by David Duncan that he had ordered documents to be destroyed. The 6-month window regression uses the ten trading days before the October 16, 2001 Enron earnings announcement, and ten trading days following the April 9, 2002 admission by David Duncan that he had ordered documents to be destroyed. (t-Statistics are in parenthesis.)

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Table 6. Changes in Auditor Implied Volatility Ratio Around Key Dates. Date/Event

August 14, 2001: Enron CEO Jeffrey Skilling resigns

October 16, 2001: Enron reports loss

November 8, 2001: Andersen receives federal subpoena and Enron restates earnings

November 29, 2001: SEC investigation is expanded to include Arthur Andersen

December 12, 2001: Joseph Berardino appears in front of Congress

January 10, 2002: Enron admits to shredding

January 22, 2002: Enron employee claims shredding (January 23) FBI begins investigation into shredding

Before (Days (−20, −1)

(Days 0, 1) Difference (p-Value)

Call data

0.8949

Put data

0.8908

Call data

0.8662

Put data

0.8676

Call data

0.8615

Put data

0.8620

Call data

0.8687

Put data

0.8683

Call data

0.8691

Put data

0.8683

Call data

0.8864

Put data

0.8861

Call data

0.8833

Put data

0.8839

0.8959 0.0010 (0.4612) 0.8964 0.0056 0.3011 0.8589 −0.0073 (0.2483) 0.8656 −0.0020 0.3776 0.8754 0.0139 (0.0260) 0.8762 0.0142 (0.0204) 0.8561 −0.0126 (0.0425) 0.8531 −0.0152 0.0429 0.8926 0.0235 (0.0049) 0.8927 0.0244 0.0053 0.8889 0.0035 (0.4224) 0.8889 0.0028 0.4072 0.8854 0.0021 (0.4269) 0.8873 0.0034 0.3663

Days (0, 4) Difference (p-Value) 0.8887 −0.0062 (0.1700) 0.8878 −0.0030 (0.3904) 0.8628 −0.0034 (0.3102) 0.8644 −0.0032 0.3784 0.8710 0.0097 (0.0221) 0.8697 0.0077 (0.0450) 0.8616 −0.0071 (0.0961) 0.8574 −0.0109 0.0226 0.9040 0.0349 (0.0000) 0.9027 0.0344 0.0000 0.8862 −0.0002 (0.4879) 0.8866 0.0005 0.4757 0.8929 0.0065 (0000) 0.8928 0.0089 0.0817

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Table 6. (Continued ) Date/Event

January 24, 2002: David Duncan refuses to testify

February 4, 2002: Release of Powers Report and Paul Volcker hired

March 14, 2002: Andersen charged with obstruction of justice

March 27 2002: Andersen CEO Joseph Berardino resigns

April 9, 2002: Former Andersen auditor Duncan enters plea bargain

Before (Days (−20, −1)

(Days 0, 1) Difference (p-Value)

Call data

0.8831

Put data

0.8851

Call data

0.9031

Put data

0.9000

Call data

0.9236

Put data

0.9264

Call data

0.9113

Put data

0.9156

Call data

0.8940

Put data

0.8996

0.8932 0.0101 (0.1020) 0.8932 0.0081 (0.1718) 0.9532 0.0501 (0.0068) 0.9527 0.0527 0.0018 0.9105 −0.0131 (0.1134) 0.9160 −0.0104 (0.1752) 0.8862 −0.0251 (0.0452) 0.8930 −0.0226 (0.0539) 0.9033 0.0093 (0.1473) 0.9152 0.0156 (0.0399)

Days (0, 4) Difference (p-Value) 0.9159 0.0328 (0.0002) 0.9169 0.0318 (0.0003) 0.9470 0.0439 (0.0022) 0.9443 0.0443 0.0001 0.9025 −0.0211 (0.0027) 0.9096 −0.0064 (0.0124) 0.8840 −0.0273 (0.0027) 0.8907 −0.0249 (0.0037) 0.9099 0.0159 (0.0048) 0.9162 0.0166 (0.0024)

Note: Implied Volatility Ratio = (Average Implied Volatility of Andersen-audited firms)/(Average Implied Volatility of firms audited by other Big Five auditing firms).

While the long-event window results provide evidence that there was an increase in implied volatilities at Andersen audited clients, they do not say specifically when this increase occurred. As a result, we used the same methodology to examine shorter event windows around the events that were hypothesized as being damaging to Andersen’s reputation. The findings in this area, with both the t-tests as well as the regression analysis, reaffirm that Andersen’s audit clients did experience

108

Table 7. Regressions Around Key Dates. Panel A: Call Data Nov 8

Dec 12

Jan 10

Feb 4

Mar 14

Mar 27

Apr 9

0.9139 (264.19) 0.0373 (7.63)

0.9382 (184.60) 0.0169 (2.35)

0.9411 (277.33) −0.0134 (−2.79)

0.9514 (348.31) −0.0026 (−0.66)

0.8853 (268.05) 0.0339 (7.26)

Avg IV Anderson/Avg IV other = constant + B1 (Avg. Anderson price/Avg. other price) + B2 (Time dummy) Constant 1.7751 2.9387 1.0684 1.4362 2.111 (8.91) (9.97) (3.74) (1.44) (1.48) Avg price ratio −0.8454 −1.9983 −0.1539 −0.5200 −1.1620 (−4.40) (−6.89) (−0.54) (−0.52) (−0.82) Time dummy −0.0016 0.0039 0.0014 0.0403 0.0167 (−0.53) (1.11) (0.47) (5.37) (2.29)

1.7032 (3.77) −0.7924 (−1.69) −0.0125 (−2.72)

2.4735 (3.21) −1.5512 (−1.97) 0.0004 (0.11)

−0.1791 (−0.14) 1.0487 (0.081) 0.0315 (5.69)

0.9394 (190.91) 0.0154 (2.21)

0.9446 (284.03) −0.0117 (−2.48)

0.9548 (362.06) −0.0002 (−0.06)

0.8905 (289.40) 0.0348 (8.00)

Avg IV Anderson/Avg IV other = constant + B1 (Avg. Anderson price/Avg. other price) + B2 (Time dummy) Constant 1.7605 2.8065 0.8413 1.4218 1.9199 (8.32) (9.08) (3.17) (1.37) (1.38) Avg price ratio −0.8291 −1.8667 0.0728 −0.5034 −0.9714 (−4.06) (−6.14) (0.27) (−0.49) (−0.70) Time dummy −0.0037 0.0055 0.0029 0.0380 0.0152 (−1.34) (1.49) (1.07) (4.85) (2.15)

1.5411 (3.38) −0.6204 (−1.31) −0.0110 (−2.37)

1.8856 (2.37) −0.9486 (−1.17) 0.0016 (0.39)

0.1921 (0.15) 0.6881 (0.56) 0.333 (6.38)

Avg IV Anderson/Avg IV other = constant + B2 (Time dummy) Constant 0.8985 0.9077 0.9129 (333.34) (230.81) (549.84) Time dummy 0.0050 0.0172 0.0022 (1.32) (3.09) (0.94)

Panel B: Put Data Avg IV Anderson/Avg IV other = constant + B2 (Time dummy) Constant 0.9008 0.9092 0.9148 (327.81) (239.42) (584.64) Time dummy 0.0028 0.0179 0.0025 (0.73) (3.33) (1.13)

0.9161 (253.90) 0.0352 (6.89)

Note: The IV Ratio is the average implied volatility of Andersen audited firms divided the average volatility of firms audited by other Big Five firms. The average price ratio is the average price of Andersen audited firms divided the price of firms audited by other Big Five firms. Ten trading days before and after each event are used to calculate IV Ratio and Price Ratio. (t-Statistics are in parenthesis.)

JONATHAN M. GODBEY AND JAMES W. MAHAR

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statistically significant increases in their implied volatilities as a result of the damage to Andersen’s reputation. Additionally, the results show which events were particularly damaging to Andersen’s reputation. These findings support the hypothesis that auditor reputation is used by market participants as a means of inferring the quality of a firm’s financial reports and thus helps to lessen the information asymmetry problem (Tables 4, 5, 6 and 7). Specific events where the implied volatility ratio increases relative to the control groups in at least one of the tests include the November 8, 2001 restatement of Enron’s financial statements, the December 12, 2001 Congressional testimony of Andersen CEO Joseph Berardino, the January 10, 2002 admission of shredding documents, the January 24, 2002 refusal of David Duncan to testify, the dual events of the weekend of February 2 and 3, 2002 with the release of the Powers Report and the Andersen hiring of former Federal Reserve Chairman Paul Volcker, and the April 9, 2002 plea bargain by David Duncan. All but the November 8, 2001 and December 12, 2001 events were statistically significant at the 5% level, for both the t-tests as well as the regression analysis that controlled for changes in the underlying stock price.

5. CONCLUSION This paper was motivated by the opportunity to use the Enron and Andersen related troubles to study the impact of auditor reputation on the information asymmetry problem. Consistent with the findings of C&P (2002), who found that stock prices of Andersen audited firms decreased over this time period, we studied how auditor reputation impacts implied volatility at firms audited by Andersen. Both long-term and short-term event-studies were used to examine the effects on implied volatility, of events that were deemed as damaging to Andersen’s reputation. The results of all of the tests yield strong evidence that the implied volatilities at Andersen audited firms increased relative to the firms audited by other Big Five accounting firms over the time period surrounding the events that led to collapse of Andersen. Thus, the results of both tests are consistent with the hypothesis that auditor reputation plays an important role in reducing information asymmetries between investors and the audited firm. By looking at the implied volatility of Andersen audited firms, rather than the stock price, we are able to show that the stock price declines documented by C&P (2002), are due, at least in part, to an increase in the risk of the cash flows. This is a significant contribution because by looking at stock price alone, the decline could be caused by any combination of a reduction of expected cash flows or an increase in risk. While the implied volatility does not allow us to say anything about the

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level of cash flows, we can say definitively that the market expected the risk to increase.

NOTE 1. In September 2003, the VIX was changed to track the implied volatility of S&P 500 firms.

ACKNOWLEDGMENTS We would like to thank David Becher, Joseph Coate, Carol Fischer, Stephan Horan, Lance Nail, Rodney Paul, Jeffrey Peterson, Kenneth Small, and participants at the Southern Finance Association meetings in Charleston SC. Additionally we are indebted to the able research assistance of Patricia Dean, Jill Simme, and Christopher Zimmer. All errors are our own.

REFERENCES Balvers, R., McDonald, B., & Miller, R. (1988). Underpricing of new issues and the choice of auditor as a signal of investment banker reputation. The Accounting Review, 63, 605–622. BBC News (2002, June 17). Andersen’s fall from grace. URL: http://news.bbc.co.uk/1/hi/business/ 2049237.stm. BBC News (2002, February 4). Timeline: Enron’s rise and fall. URL: http://news.bbc.co.uk/ 2/hi/business/1759599.stm. Beatty, R. (1989). Auditor reputation and the pricing of initial public offerings. The Accounting Review, 64, 693–709. Beatty, R. (1993). The economic determinants of auditor compensation in the initial public offerings market. Journal of Accounting Research, 31, 294–302. Bellalah, M., & Aboura, S. (2002). Pricing options on leveraged equity under asymmetric information (Working Paper). Binder, J. J. (1985). Measuring the effects of regulation with stock price data. Rand Journal of Economics, 16, 167–183. Black, F. (1976). Studies of stock price volatility changes. Proceedings of the American Statistical Association, 177–181. Black, F., & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–654. Canina, L., & Figlewski, S. (1993). The informational content of implied volatility. Review of Financial Studies, 6, 659–681. Chaney, P., & Philipich, K. (2002). Shredded reputation: The cost of audit failure. Journal of Accounting Research, 40, 1221–1244.

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Clarkson, P., & Simunic, D. (1994). The association between audit quality, retained ownership, and firm risk in U.S. vs. Canadian IPO markets. Journal of Accounting and Economics, 17, 207–228. Copeland, L., Poon, S., & Stapleton, R. (2000). The implied volatility of options: A test using UK data. Journal of Business Finance and Accounting, 27, 859–885. Craswell, A. T., Francis, J. R., & Taylor, S. L. (1995). Auditor brand name reputation and industry specialization. Journal of Accounting and Economics, 20, 297–322. Datar, S., & Alles, M. (1999). The formation and role of reputation and litigation in the auditor-manager relationship. Journal of Accounting, Auditing and Finance, 14, 401–428. Dumas, B., Fleming, J., & Whaley, R. E. (1998). Implied volatility functions: Empirical test. Journal of Finance, 53, 2059–2106. Dye, R. (1993). Auditor status, legal liability, and auditor wealth. Journal of Political Economy, 887–914. Francis, J., & Simon, D. (1987). A test of audit pricing in the small-client segment of the U.S. audit market. The Accounting Review, 62, 145–157. Franz, D. R., & Crawford, D. (1998). The impact of litigation against an audit firm on the market value of nonlitigating clients. Journal of Accounting, Auditing and Finance, 13, 117–134. French, D., & Dubofsky, D. (1986). Stock splits and implied stock price volatility. Journal of Portfolio Management, 12, 55–59. Houston Chronicle (2002, October 22). Timeline of Andersen events. URL: http://www.chron.com/cs/ CDA/story.hts/special/enron/1452911. Hull, J., & White, A. (1987). Pricing of option assets with stochastic volatilities. Journal of Finance, 42, 281–300. Isakov, D., & Perignon, C. (2001). Evolution of market uncertainty around earnings announcements. Journal of Banking and Finance, 25, 1769–1789. Latane, H. A., & Rendlemand, R. J., Jr. (1976). Standard deviations of stock price ratios implied in option prices. The Journal of Finance, 31, 369–381. Levy, H., & Yoder, J. (1993). The behavior of option implied standard deviations around merger and acquisition announcements. Financial Review, 28, 261–272. Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science, 4, 141–183. Merton, R. (1987). A simple model of capital market equilibrium with incomplete information. Journal of Finance, 42, 483–510. Patell, J. M., & Wolfson, M. A. (1981). The ex ante and ex post price effects of quarterly earnings announcements reflected in option and stock prices. Journal of Accounting Research, 19, 434–458. Schwert, G. W. (1981). Using financial data to measure the effects of regulation. Journal of Law and Economics, 121–158. Teoh, S., & Wong, T. (1993). Perceived auditor quality and the earnings response coefficient. The Accounting Review, 68, 346–366. Titman, S., & Trueman, B. (1986). Information quality and the valuation of new issues. Journal of Accounting and Economics, 8, 159–172. Washington Post (2002, November 14). Timeline of Enron’s collapse. URL: http://www. washintonpost.com/ac2/wp-dyn/A25624–2002Jan10?language=printer. Watts, R., & Zimmerman, J. (1983). Agency problems, auditing, and the theory of the firm: Some evidence. Journal of Law and Economics, 26, 613–633.

SECONDARY EQUITY OFFERINGS: THE CASE OF INSTALLMENTS RECEIPTS Narat Charupat and C. Sherman Cheung ABSTRACT This paper examines secondary equity offerings that were done in the Canadian markets through “installment receipts” (IRs). Previous studies on seasoned equity offerings tend to focus on the price reaction around the announcement date. We extend the analysis to cover a longer period so that the issues of liquidity effect and information asymmetry can be adequately addressed. We also offer evidence to indicate that the use of IRs in secondary offerings can reduce the liquidity impact in markets where market depth is not as substantial as in the U.S.

1. INTRODUCTION Past studies on block trading and secondary equity offerings have documented the discounts that the sellers have to concede in order to execute the transactions.1 (See, for example, Holthausen et al. (1990) in the context of block trading, and Hudson et al. (1993) in the context of secondary offerings.) While the two types of transactions appear to belong to two distinct literatures (i.e. block trading belongs to the microstructure literature whereas secondary issues are in the domain of seasoned security offerings), there are, however, two common dominant themes – information asymmetry and liquidity effect. Information asymmetry arises because Research in Finance Research in Finance, Volume 21, 113–133 © 2004 Published by Elsevier Ltd. ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21005-X

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block sellers (in the case of block trades) and major shareholders (in the case of secondary offerings) are traders with possibly superior information about the shares that they sell. Liquidity effect arises if the demand for a security is not perfectly elastic. Both factors can explain a decline in price as a result of the two types of transactions. The major difference between the two factors is that the price impact of the liquidity effect is temporary, whereas the price effect of information asymmetry is permanent (Scholes, 1972). In this paper, we study secondary equity offerings that were done through “installment receipts” (IRs) in the Canadian markets. An IR is a security that evidences the purchase of an underlying security on an installment basis. Typically, buyers are allowed to pay for the underlying securities in two or three installment payments. The payments are spread over a period of one to two years (more on this in Section 2). Large secondary equity offerings in Canada are commonly done through this method, instead of on a fully-paid basis. We are interested in several issues in this paper. First, we would like to know the role of an IR arrangement in secondary equity offerings. While IRs generally cannot be issued on a public-market basis in the U.S. due to Securities & Exchange Commission’s margin rules, they are quite common in Commonwealth countries such as England, Australia, New Zealand and Canada.2 Yet there has been very little theoretical and empirical research on this instrument. Second, to explain the role of IRs, we trace the price behavior of stocks and, whenever possible, IRs from the period before the announcements of the secondary offering through the announcement dates and the issue dates, to the period after the issue dates. Previous studies on seasoned equity offerings tend to focus on the pricing behavior around the announcement dates and ignore the short-term pricing behavior around the issue dates.3 As a result, the liquidity effect around the issue dates has not been adequately addressed in the literature. We therefore offer a more comprehensive empirical analysis of secondary offerings. Third, we will try to explain the crosssectional behavior around three critical dates – the announcement date, the issue date and the post-issue period. In particular, we are interested in the pricing of the issues and the short-term excess return from buying them. The paper is organized as follows. In the next section, we discuss the institutional features of IRs and the rationale for using them. Section 3 provides details of our sample. Section 4 documents the price pattern of the stocks from the period prior to the announcements of the offerings to post-issue period. It also reports the magnitude of the underpricing of IRs and the short-term excess return from buying them. Cross-section results are reported in Section 5. Section 6 examines the post-issue performance again to address the liquidity effect. Section 7 provides supporting evidence for the benefits of using IRs in secondary offerings. Finally, Section 8 concludes the paper.

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2. INSTITUTIONAL FEATURES OF AND RATIONALE FOR INSTALLMENT RECEIPTS In Canada, IRs cannot be used for initial or seasoned equity offerings involving new shares as the laws prohibit companies from issuing new shares that are not fully paid for. As a result, all of our discussions here concern secondary offerings involving no new shares. In a typical IR arrangement, investors are allowed to pay for the underlying shares in two or three installments. The first payment is required at the closing of the offering, after which the buyers will receive IR certificates. Then, after the final payment is made, the receipt-holders will exchange the IR certificates for common shares of the underlying stock. In the meantime, IRs entitle the holders to the same rights and benefits (e.g. same dividends, voting right, etc.) as if they were holding the underlying stock. This is possible because the issuer (i.e. the seller of the shares) has to place the underlying shares with a custodian who will then pass on the rights and benefits from the shares to the IR buyers. The initial sale of IRs to the public is handled by underwriters who are responsible for issuing a prospectus and filing it with the appropriate regulatory body. The prospectus specifies, among other things, the number of installment payments, and the timing and the dollar value of each payment.4 Generally, the underwriters underwrite only the first installment payment. Therefore, they will no longer be involved once the deal is closed. If the buyers fail to make future installment payments, the issuer bears the default risk. If a buyer defaults, the issuer will arrange to sell the underlying shares which have been set aside for that buyer. The proceeds will be offset against the buyer’s obligation. Any shortfall remains the buyer’s responsibility. Since the most likely scenario for default to occur is when the price of the underlying share substantially declines, the magnitude of the default risks depends on the stock’s volatility and the terms of the installment payments set by the issuers. Hence, the issuers have some control over the magnitude of the risks.5 Some issuers may choose to sell their IR receivables to financial institutions, in which case the default risks should be reflected in the sale prices. After the closing of the offering, IRs are listed on stock exchanges and thus can be easily traded by their holders. By selling their IRs in the market, the holders pass to the buyers the obligation to make future installment payments. As described, IRs are in effect an opportunity for investors to buy the underlying shares on borrowed funds, where the issuers assume the role of lenders. The fact that the issuers choose to do so and bear the associated default risks suggest that there are offsetting benefits from using IRs. One commonly-cited benefit is that their use allows the issuers to enlarge the set of potential buyers to include

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those who want to participate in the offers but cannot do so due to borrowing constraints. These potential buyers include mutual funds and pension funds, which commonly are prohibited from borrowing by their charters, and small investors, who generally find it costly or impossible to obtain leverage. Under this rationale, IRs are not redundant securities as their use will increase the demand for the offers.6 The higher the embedded leverage, the more are the potential buyers IRs will attract. The increase in demand can help reduce the underpricing of seasoned/secondary offerings caused by liquidity effects when securities are not perfectly substitutes for one another. If securities’ demand is not perfectly elastic, investors will require extra compensation in the form of underpricing for having to hold more of a particular security than initially desired.7 The increase in demand helps to reduce the underpricing by raising the markets’ aggregate risk-bearing ability (which is an increasing function of the number of traders in the markets).8 A closely parallel literature on liquidity-induced underpricing is that of block trades. A block trader performs similar functions to those of an underwriter in a public offering; i.e. to facilitate the trade by locating counterparties. It has been observed that seller-initiated block trades are generally transacted at prices below both pre- and post-block prices. This suggests that the sellers have to make price concessions to the buyers. More importantly, the fact that post-issue prices are higher than transacted prices suggests that these concessions arise due to liquidity reasons (e.g. to compensate for search cost).9

3. DATA AND METHODOLOGY Our sample contains all secondary offerings of common shares that were done through installment receipts on the Toronto Stock Exchange (TSE) or the Montreal Exchange (ME) between 1990 and 1999. In total, there are 30 issues involving shares of 29 companies.10 Table 1 provides summary statistics for our sample. Total issue values range from C$ 125 million to C$ 1.8 billion, with a mean of C$ 667 million and a median of C$ 606 million.11 In terms of the percentage of the outstanding shares, these offerings account for between 6.67 and 83.26%, with a mean of 38.91% and a median of 37.32%. These numbers suggest that the issuers in our sample are major shareholders of their companies. The ratios between the number of shares offered and the average daily trading volume are also reported. They range from 22 to 9,939, with a mean of 1,031 and a median of 610. Therefore, the offerings in our sample represent a substantial supply of equity, both in terms of dollar values and trading impact that the markets have to absorb.

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Table 1. Sample’s Summary Statistics.

Total issue value (in C$ million)a 1st installment values (in C$ million)b No. of shares offered as % of no. of shares outstandingc No. of shares offered as multiples of average daily trading volumesd Leverage Offerede

Lowest

Highest

125

1,800

667

606

64

759

297

280

6.67%

83.26%

38.91%

37.32%

9,939

1,031

66.64%

51.82%

22

37.41%

Mean

Median

610

48.92%

a Issue

values are calculated by multiplying the number of underlying shares offered by the sum of the required installment amounts, without taking into account the payments’ present values. Also, the figures are based on dollars at the time of issues. b 1st installment values are calculated by multiplying the number of the underlying shares offered by the amounts of the 1st installments. The figures are based on dollars at the time of issues. c The issue values and the number of offered shares do not include shares subsequently issued (if any) through overallotment options. d The average daily trading volumes are calculated as the average of daily volumes during a 50-day period (from day −150 to day −101) prior to the announcement dates. e Leverage offered is calculated by dividing the present value of future installment payments by the sum of: (i) the initial payment; and (ii) the present value of future installment payments.

Table 1 also reports the issue values based only on their first installment payments, which measures the immediate impact of the offerings in dollar value’s terms. By using IRs, the issuers are able to reduce the immediate dollar impact by an average of over 50%. In addition, the last row of Table 1 reports the degree of leverage offered by the issuers. The degree of leverage for each issue is the ratio between: (i) the present value of the issue’s future installment payments; and (ii) the sum of that present value and the issue’s initial payment. In other words, it is the percentage of the “full” price that investors do not have to pay up front. In terms of issuers, six of the issues in our sample (20%) were sold by individual shareholders, twenty one (70%) by corporate shareholders, and four (10%) by either the provincial or federal governments in the privatization process. The breakdown of the issues according to the years in which they were done is given in Table 2. Details of each secondary issue such as its size, its issuer(s), the number of shares offered, the number of shares outstanding and the terms of the installment payments, were obtained from the TSE Monthly Review and, when available, the

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Table 2. A Breakdown of IR Issues by Year. Year

No. of Issues

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999

0 1 6 6 2 4 2 7 2 0

Total

30

issues’ prospectuses. Closing prices of IRs and their underlying shares, together with market returns, as proxied by the TSE 300 value-weighted index, were collected from the TSE Summary Information Database, Canada Stockwatch and TCE Research Services. We used the Canadian Business and Current Affairs Database to identify the announcement dates (AD) of the offerings. Since some announcements may have occurred before the opening or after the end of the trading on the announcement day, our announcement period consists of AD and AD + 1. The listing dates (LD), on which IRs started aftermarket trading, were readily available from the TSE Monthly Review. The first step in our analysis is to document the price behavior of IRs and their underlying stocks. Our analysis covers the period from 150 days before the announcements to 10 days after issue dates. Previous studies tend to focus on the pricing behavior around the announcement and ignore the behavior around the issue date. If the liquidity effect is present, its effect will be temporary and price recovery will occur after issue date. It is therefore important to examine the price pattern around the issue date. To examine the price pattern of the underlying shares, we calculate the shares’ raw and excess holding-period returns using closing prices for the following seven periods. The first three periods are AD − 150 to AD − 101, AD − 100 to AD − 51; and AD − 50 to AD − 1. These three periods show the stock price movements prior to the announcements. The fourth period is the announcement period (AD and AD + 1). The fifth period is the “interim” period, which is from AD + 2 to LD − 1. The sixth period is the listing dates of the receipts, LD, while the last period is the “post-issuance” period, consisting of 10 trading days after LD. Returns for these periods are then used to determine whether offering announcements are likely to be

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made after share prices have substantially risen, whether the announcements create excess returns on the stocks, and whether the price movements reverse themselves afterwards. Excess holding-period returns on security i over any interval j, XRij , are computed using the “market-adjusted” procedure (see Brown & Warner, 1985), whereby excess returns are the difference between raw returns and market returns. That is, XRij = R ij − M j , where Rij is security i’s raw returns over interval j and Mj is market returns over the same interval. To measure the magnitude of underpricing of the offerings, we compare IRs’ offer prices to their closing prices on the first trading days. This “offer-to-close” measure represents the return that one would get if one buys an IR at its offer price and sells it at the closing price of the first day on which it is listed. This measure has been used in studies of seasoned/secondary offerings such as Smith (1977) and Loderer et al. (1991), and particularly in studies of initial public offerings (IPO). Our reason for using this measure is that each issue of IRs is an offering of a new security since the issue has not been traded before. Hence, there is no prior closing price to which to compare. Note that because IRs are leveraged instruments, our measure of underpricing will also reflect the embedded leverage effect. Therefore, this measure is appropriate if one does not plan to hold the IRs until the next installment payment date. An alternative measure is one that adjusts for the leverage effect. This measure – which we term “adjusted offer-to-close return” – represents the return that one would get if, in addition to acquiring an IR, one also makes a risk-free investment in an amount equal to the present value of its future installment payments. In other words, adjusted returns approximate returns in case the offerings were done on a fully-paid basis. In addition to offer-to-close returns, we also calculate unadjusted and adjusted raw and excess holding-period returns from holding IRs during the period from LD + 1 to LD + 10.

4. TIME SERIES PRICE BEHAVIOR 4.1. Underlying Stocks’ Returns Table 3 presents raw and excess returns on the underlying shares and their associated p-values. In the three 50-day periods prior to the announcements,

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Table 3. Raw and Excess Returns (in Percentages) on the Underlying Shares around the Announcements. Interval of Trading Days

AD − 150 to AD − 101 AD − 101 to AD − 51 AD − 50 to AD − 1 AD to AD + 1 AD + 2 to LD − 1 LD LD + 1 to LD + 10

Raw Returns

Excess Returns

Average (%)

p-Value

% Negative

Average (%)

p-Value

% Negative

4.53 7.62 10.12 −2.49 0.84 −0.71 2.57

0.0268 0.0349 0.0003 0.0092 0.2838 0.3864 0.0032

33 30 23 73 33 67 37

3.48 4.78 7.46 −2.67 0.36 −0.71 2.18

0.0778 0.1462 0.0031 0.0054 0.6486 0.3803 0.0126

43 43 30 77 47 67 33

Note: AD is the announcement date. LD is the installment receipt’s listing date.

the average raw and excess returns are all positive. As we get closer to the announcement dates, both the magnitude of average returns and the proportion of sample with positive returns increase. Note that the all pre-announcement positive raw returns are significant at least at the 5% level and there is a clear pattern that offering announcements are made after sustained substantial run-ups in prices. The announcements have a significant negative impact on prices. The average raw and excess returns during the announcement period (AD and AD + 1) are −2.49 and −2.67% respectively, both of which are statistically significant at the 1% level. More than three quarters of the sample have negative excess returns. In the interim period (AD + 2 to LD − 1), the average excess return is small and positive, but not significantly different from zero. Note that this result can be affected by a selection bias since issuers that experience a substantial decline in their stock prices during this period may delay or cancel their offerings. (See, for example, Mikkelson & Partch, 1986.) On the listing dates of the receipts, the underlying stocks have insignificant negative excess returns. On the other hand, during the 10-day period after the issuance, we find strong evidence of price recovery, the magnitude of which closely matches that of the average price drop on the announcement dates. Altogether, from the announcement period up to the post-issuance periods (i.e. AD to LD + 10), the average excess return (not shown) is −0.75% and not significantly different from zero. The observed pattern of positive returns prior to the announcement dates followed by negative returns at the announcements is consistent with the findings of previous studies of secondary offerings. For example, Korajczyk et al. report a 10.63% cumulative excess return over a period of 100 days prior to

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the announcements, and a negative excess return of −2.49% for the two-day announcement period. Other studies with similar findings include Asquith and Mullins (1986) and Hudson et al. (1993).12 Secondary share sales after significant price increases are commonly explained by information asymmetry. As argued by Myers and Majluf (1984), existing shareholders know more about their firms’ true values than new investors do. If they recognize that the shares are overvalued, they will attempt to take advantage of it. Therefore, their decisions to sell their holdings are construed as a signal that the stocks are overvalued, which implies that the observed price drops is caused by a change in the market’s perception of the shares’ value. Nevertheless, the observed price decline at announcements does not necessarily imply a change in the market’ valuation of the shares. It is possible that at announcements, investors anticipate that the offered shares will have to be underpriced when issued to accommodate the liquidity shock. Therefore, these investors will sell their holdings of the shares at the announcements in the hope that they can buy them back at a lower price from the offering. This kind of liquidity effect is well documented in Scholes’ (1972) study. As a result, we cannot say for certain what causes the observed price behavior around the announcement period. In actuality, it is likely that both the information asymmetry and the anticipation of a liquidity shock contribute to the results. The price behavior after the announcements provides a clue as to the relative importance of the two factors. If the price drops at announcement are due to information, then the drops should be permanent and not reverse themselves since the market’s valuation of the shares has changed (Scholes, 1972). On the other hand, if the drops are due to anticipation of a liquidity shock, then they will be temporary. Our findings of the post-issue date recovery suggest that the majority of the announcement effect in our sample is caused by the liquidity effect. 4.2. Underpricing of IRs Table 4 reports the raw offer-to-close returns on IRs, both unadjusted and adjusted for the leverage effect. The average unadjusted offer-to-close return is 6.08% and Table 4. Raw Unadjusted and Adjusted Offer-to-Close Returns from IRs. Types of Return Unadjusted Adjusted

Mean (%)

Median (%)

Lowest (%)

Highest (%)

% Negative

6.08 (0.001) 2.79 (0.002)

4.98 2.67

−16.25 −8.40

22.69 10.79

27 27

Note: p-Values are in parentheses.

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is significant at the 1% level. Although the returns range from −16.25 to 22.69%, only slightly over a quarter of our sample are negative and 13% of the sample are zero. These figures suggest that, on average, investors will make a sizable profit if they buy IRs at the offering and sell them at the end of the IRs’ first trading day. However, that high return is achieved partly with the added risk from leverage. Adjusted for the leverage effect, the average return reduces to 2.79%, which is also statistically significant. To put our results in perspective, we compare them to the findings of previous studies. We are aware of only two studies that document offer-to-close returns from seasoned and/or secondary offerings, both of which are conducted on fullypaid issues in the U.S. markets. First, Smith (1977) reports a small but significant average offer-to-close return of 0.82%, based on a sample of seasoned offerings of firms listed on the New York Stock Exchange (NYSE) and the American Stock Exchange (Amex) during the period from 1971 to 1975. Secondly, Loderer et al. (1991) find significant average returns of 0.80% for Amex stocks and 1.94% for NASDAQ stocks for the period from 1980 to 1984. However, they do not find significant returns for NYSE stocks. In comparison to these two studies, our sample exhibits higher offer-to-close returns, both adjusted and unadjusted.13 It appears, therefore, that the offerings in our sample are more deeply underpriced than in these previous studies. If, as our results in the previous subsection suggests, the observed underpricing is due to liquidity shocks, then the deeper discounts may be the result of the lack of depth in the Canadian markets compared to the U.S. markets.

5. CROSS-SECTIONAL RESULTS 5.1. Announcement Effects We investigate the possible factors that can help explain the observed price decline at announcements. We do so by regressing the (excess) announcement returns of all issues in our sample on: (i) issue size; (ii) the risk of the offered shares; (iii) stock (excess) returns prior to the announcements, and a liquidity measure. Specifically, the regression equation is Ranni = a 0 + a 1 ISSUE SIZEi + a 2 VOLi + a 3 PRERETi + a 4 MULTIPLEi + e i .

(1)

Ranni is the excess return on stock i during the announcement period. Proxies for ISSUE SIZEi include FRACTIONi , which is the number of shares offered

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divided by the number of shares outstanding for stock i; and VALUEi , which is the dollar value of issue i, as calculated in Table 1. However, as will be discussed later in Section 6, the two proxies are correlated. Therefore, they will not appear in the same regression. We use VOLi , which is the standard deviation of stock i’s returns during the period from AD − 100 to AD − 51, as our proxy for the shares’ risk. PRERETi is the excess return on stock i over a period of 100 trading days prior to the announcement.14 MULTIPLEi , is the ratio between the number of shares offered and the average daily trading volume over the period from AD − 150 to AD − 101. Strictly speaking, MULTIPLEi is a proxy for issue size. However, since it is not correlated with the other two proxies, we treat it as an independent liquidity measure. Table 5 presents the results of our regressions. Each column represents the resulting coefficients of the above regression equation. Each of the above independent variables was individually run first and then all independent variables were run together. None of the variables has significant explaining power. The lack of a significant relationship between PRERETi and announcement period’s returns is consistent with several previous studies of secondary offerings.15 It also suggests that the offerings in our sample were, on average, not informationrelated. To see this, note that according to information reasons, large price runups before the offerings suggest that the issuers are attempting to sell overvalued stocks. Hence, the higher the price run-ups, the more negative the impact of the offering announcements will be. On the other hand, if the sales are not informationrelated, no significant relationship should be observed, which is what our results show. Note also that what we find here is consistent with the argument that we make in Section 4.1 that the observed post-issue price recovery suggests that the announcement effect is mainly due to liquidity reasons. The coefficients for both proxies for issue size – FRACTIONi and VALUEi− are insignificant, which is consistent with previous studies of seasoned/secondary offerings.16 The coefficient of VOLi is negative, as predicted by both the information and the liquidity reasons.17 The lack of significance is similar to the results in Masulis and Korwar (1986), who calculate variances based on the 60day period prior to the announcements, but is in contrast to the results in Hudson et al. (1993), who calculate variances based on the 250-day period (from day −500 to day −251) prior to the announcements. To make sure that our results are not influenced by the choice of periods over which return deviation is measured, we also ran the same regressions with deviation over AD − 150 to AD − 101. All of the results are not significant. Hence, the lack of significance does not depend on the choice of periods. In sum, our regressions of the announcement effect on various independent variables provide some support for the liquidity explanation, but none for the

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Table 5. Regression Estimates of Announcement Period’s Excess Returns on Various Independent Variables. Variablea

(2)

(3)

(4)

(5)

(6)

(7)

−0.043 (0.024) 0.042 (0.345)

−0.049 (0.017)

−0.029 (0.008)

−0.019 (0.227)

−0.027 (0.006)

−0.027 (0.444) 0.036 (0.621)

−0.041 (0.095)

0.000 (0.196) 0.000 (0.202) −0.405 (0.609) 0.004 (0.923)

0.000 (0.793) −1.011 (0.393) 0.013 (0.817)

0.000 (0.250) 0.000 (0.314) −0.633 (0.495) 0.008 (0.880)

Note: p-Values are in parentheses. They are calculated based on standard errors that are computed using the heteroskedasticty consistent estimator of White (1980). a VOL is the standard deviation of stock returns during the period from AD − 100 to AD − 51. PRERET is the shares’ excess returns during the i i 100-day period prior to the announcements. FRACTIONi is the number of shares offered divided by the number of shares outstanding. MULTIPLEi is the ratio between the number of shares offered and the average daily trading volume over the period from AD − 150 to AD − 101. VALUEi is the dollar value of issue i.

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Intercept FRACTIONi VALUEi MULTIPLEi VOLI PRERETi

(1)

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information reason. We also run the above regressions using raw Ranni and PRERETi . The results lead to the same conclusion and therefore are not produced here. 5.2. Underpricing of IRs Next, we use a regression analysis to ascertain the liquidity effect by testing for the relationship between the offer-to-close returns on IRs and the proxies for issue size, liquidity and the risk of the offered shares (i.e. FRACTIONi , VALUEi , MULTIPLEi , and VOLi ). As mentioned in Section 2, underpricing is a form of compensation to investors who have to hold more of a certain security than initially desired. The larger the size of the offer and/or the riskier the offer, the greater is the required compensation. As a result, the magnitude of underpricing should be positively related to the proxies for issue size and risk. Table 6 reports the results of the regressions. In Panel A, the dependent variable is unadjusted returns. Again, each of the above independent variables was individually run first and then all independent variables were run together. First, we examine the regression results with each independent variable individually run. Of the two proxies for issue size, VALUEi is significant at the 10% level. The proxy for liquidity, MULTIPLEi , is significant at the 1% level. However, the two coefficients have opposite signs to each other. The proxy for risk, VOLi , is significant at the 10% level, but its negative sign contradicts the predictions of the liquidity hypothesis (see Note 17). The general regression involving all variables indicates that none of the variables is statistically significant. To make sure that the above results are not caused by the leverage effect, we also report in Panel B the results of the same regressions but with adjusted returns as the dependent variable. While MULTIPLEi and VOLi continue to be significant at the 1 and 10% levels respectively, VALUE no longer has explanation power when regressions were run with only one independent variable. Again, the general regression involving all variables indicates that none of the variables is statistically significant.

6. IRS’ RETURNS FOLLOWING THE LISTING DATES The previous section shows that investors can earn a sizable return if they subscribe to IRs and sell them on the listing dates. In this section, we look at returns from holdings IRs during the first 10 days of their trading. That is, we want to know the additional return that the investors will get if they do not sell their holdings on the listing dates but instead sell them 10 trading days later.

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Table 6. Regression Estimates of Offer-to-Close Returns on Various Independent Variables. Variablea

Panel B Intercept FRACTIONi VALUEi MULTIPLEi VOLi

0.046 (0.202) 0.023 (0.773)

(2)

0.013 (0.710)

(3)

0.063 (0.001)

(4)

0.113 (0.003)

(5)

0.085 (0.190) 0.071 (0.519)

0.000 (0.098) −0.000 (0.010)

0.028 (0.149) −0.000 (0.997)

0.018 (0.338)

0.032 (0.001)

−3.320 (0.079) 0.057 (0.003)

−0.000 (0.712) −3.040 (0.302) 0.049 (0.141) 0.020 (0.721)

0.000 (0.435) −0.000 (0.011)

−1.680 (0.091)

−0.000 (0.811) −1.575 (0.307)

(6)

0.072 (0.254) 0.000 (0.231) −0.000 (0.924) −2.667 (0.353) 0.053 (0.122) 0.000 (0.798) −0.000 (0.963) −1.592 (0.320)

Note: p-Values are in parentheses. They are calculated based on standard errors that are computed using the heteroskedasticty consistent estimator of White (1980). a VOL is the standard deviation of stock returns during the period from AD − 100 to AD − 51. FRACTION is the number of shares offered divided i i by the number of shares outstanding. MULTIPLEi is the ratio between the number of shares offered and the average daily trading volume over the period from AD − 150 to AD − 101. VALUEi is the dollar value of issue i.

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Panel A Intercept FRACTIONi VALUEi MULTIPLEi VOLI

(1)

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Table 7. Raw and Excess Returns from IRs and Underlying Stocks for the 10-Day Holding Period. Types of Return

Mean (%)

Median (%)

Lowest (%)

Highest (%)

% Negative

Raw returns Unadjusted IR return Adjusted IR return Underlying stock return

5.25 (0.008) 2.51 (0.006) 2.57 (0.003)

2.38 0.85 0.28

−12.50 −4.17 −3.42

28.57 14.16 13.08

33 33 37

Excess returns Unadjusted IR return Adjusted IR return Underlying stock return

4.86 (0.010) 2.12 (0.023) 2.18 (0.013)

3.07 2.00 1.88

−8.51 −5.57 −4.07

28.81 15.07 13.98

40 37 33

Note: p-Values are in parentheses.

Table 7 report raw and excess returns on IRs, on both unadjusted and adjusted bases, for the 10-day holding period (not annualized). The raw unadjusted returns have a mean of 5.25%, which is significant at the 1% level. This number is slightly lower than the average offer-to-close return reported in Table 4, while the percentage of the sample that have negative returns is slightly higher. Combining the two periods, investors can, on average, earn over 10% (unadjusted) if they buy an IR from the offering and sell it 10 days after it is listed. Adjusted for the leverage effect, the average excess adjusted return on IRs over the 10-day holding period is 2.12%, which is significant at the 5% level. This figure is approximately the same as the average excess return on the underlying shares over the same period, which, as reported in Table 3, is 2.18%. This should come as no surprise since the adjusted return on an IR is derived from removing the leverage effect and this should result in obtaining the underlying stock. Also, arbitrage between the two instruments should ensure that the adjusted return on an IR and the return on the underlying stock are the same. Hence, both of these two positive excess returns can be regarded as an evidence of price recovery. This evidence provides strong support for the liquidity effect. To provide further support for the liquidity effect, we also test for the relationship between the 10-day excess returns on the two instruments and proxies for issue size and liquidity as follows: (IR)RLD10i = b 0 + b 1 ISSUE SIZEi + b 2 MULTIPLEi + e i .

(2)

(IR)RLD10i denotes the 10-day excess (IR) stock return on (IR) stock i. Adjusted IR returns are not used here because they are equivalent to stock returns as explained earlier. The results are reported in Tables 8 and 9. The coefficient of MULTIPLEi

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Table 8. Regression Estimates of 10-day Excess Unadjusted IR Returns on Proxies for Issue Size. Variablea Intercept FRACTIONI VALUEI MULTIPLEI

(1)

(2)

(3)

(4)

(5)

−0.026 (0.477) 0.191 (0.055)

0.055 (0.121)

−0.300 (0.129)

0.033 (0.381)

−0.015 (0.683) 0.135 (0.213)

0.000 (0.033)

0.000 (0.912) 0.000 (0.037)

0.000 (0.816)

0.000 (0.381)

Note: p-Values are in parentheses. They are calculated based on standard errors that are computed using the heteroskedasticty consistent estimator of White (1980). a FRACTION is the number of shares offered divided by the number of shares outstanding. i MULTIPLEi is the ratio between the number of shares offered and the average daily trading volume over the period from AD − 150 to AD − 101. VALUEi is the dollar value of issue i.

Table 9. Regression Estimates of 10-day Excess Stock Returns on Proxies for Issue Size. Variablea Intercept FRACTIONI VALUEI MULTIPLEI

(1)

(2)

(3)

(4)

(5)

−0.125 (0.539) 0.088 (0.077)

0.251 (0.114)

0.012 (0.207)

0.013 (0.441)

−0.005 (0.810) 0.050 (0.336)

0.000 (0.004)

0.000 (0.906) 0.000 (0.004)

0.000 (0.777)

0.000 (0.123)

Note: p-Values are in parentheses. They are calculated based on standard errors that are computed using the heteroskedasticty consistent estimator of White (1980). a FRACTION is the number of shares offered divided by the number of shares outstanding. i MULTIPLEi is the ratio between the number of shares offered and the average daily trading volume over the period from AD − 150 to AD − 101. VALUEi is the dollar value of issue i.

is positive and significant. It appears that large issues produce stronger recovery. In other words, not only do we have price recovery, but those that potentially have largest liquidity impact also produce the greatest recovery.

7. THE BENEFITS OF USING IRS In this section, we test for the benefits of using IRs to facilitate the offerings. As mentioned in Section 2, the rationale for using IRs is that their use will increase the demand for the offers and, as a result, reduce the magnitude of the price concessions that the issuers have to make. The larger the issue size, the more demand IRs need to help attract. The attractiveness of IRs depends primarily on the degree of leverage they offer.18 Therefore, if the conjectured benefits exist, we should observe a positive

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Table 10. Regression Estimates of Leverage Offered on Proxies for Issue Size and Liquidity. Variablea Intercept FRACTIONI VALUEI MULTIPLEI

(1)

(2)

0.443 (0.000) 0.193 (0.023)

0.460 (0.000)

(3) 0.525 (0.000)

0.000 (0.010) −0.000 (0.273)

Notes: p-Values are in parentheses. They are calculated based on standard errors that are computed using the heteroskedasticty consistent estimator of White (1980). a FRACTION is the number of shares offered divided by the number of shares outstanding. i MULTIPLEi is the ratio between the number of shares offered and the average daily trading volume over the period from AD − 150 to AD − 101. VALUEi is the dollar value of issue i.

relationship between the degree of offered leverage and proxies for issue size and liquidity. The regression estimates of leverage offerred on proxies for issue size and liquidity are reported in Table 10. Both proxies for issue size – VALUEi and FRACTIONi – are positively related to the levels of leverage offered to the levels of leverage offered and are significant at the 1% or the 5% levels respectively.19 In other words, firms with large issues tend to offer more leverage by having a small first installment payment. This supports our conjecture that issuers use IRs to reduce the price concessions that they have to make.

8. CONCLUSIONS This paper offers a comprehensive review of secondary offerings using IR’s. Despite the common usage of IRs in Commonwealth countries, there has been very little theoretical and empirical research on this instrument. While we not only confirm empirical findings in other studies on regular seasoned equity offerings such as abnormal price increases prior to the issue and then price declines upon announcements, but also provide additional details on the underpricing of IRs and their subsequent price recovery. This points to the similarity of secondary offerings and block trades. The price decline tends to be temporary due to a less than perfectly elastic demand function for stocks. The evidence is also consistent with price reactions associated with the inclusion of new stocks into the S&P 500.20 We also examine the rationale for using IRs. The evidence here indicates that firms with large issues tend to reduce the amount of the first installment, This will increase demand and reduce the immediate liquidity impact in dollar terms when

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the issues hit the market. The IR arrangement can therefore be a very useful device to minimize the liquidity impact for markets that lack the same depth as the U.S. markets.

NOTES 1. In this paper, the general term “seasoned equity offerings” refers to the sale of either new or existing shares to the public, while the term “secondary equity offerings” refers to the sale of existing shares to the public by major shareholders. Hence, in our context, “secondary equity offerings” share the same characteristics as block trades since they involve trades in large amounts of shares without changing the number of shares outstanding. 2. For example, in the 1980s, the British government heavily used IRs to facilitate their privatization of state-owned enterprises. More recently, in 1998, Ameritech Corp. sold its (substantial) holding in Telecom New Zealand through an IR plan in the New Zealand market. In Canada, while IRs have been around for decades, it was not until the 1990s that they became popular among Canadian investors. 3. The exception is the paper by Hudson et al. (1993). 4. Usually, the investors can choose to pay future installments early and receive the underlying shares right away. However, that would be irrational as long as interest rate is greater than zero and IRs can be traded in the market. An exception to this is when the buyers buy IRs as a part of an arbitrage transaction (i.e. together with a short position in the underling shares), in which case early payments may be made if the cost of maintaining the short-sale position is greater than interest that can be earned on future installment payments. 5. To the best of our knowledge, there have been two cases of default in the Canadian market. To avoid default, some issuers chose instead to reduce the amount of future installment payments. 6. While IRs are riskier than the underlying shares due to the leverage effect, investors can, as mentioned earlier, in most cases choose to pay the remaining installment payments immediately and obtain the underlying shares. Alternatively, investors can easily unlever their IRs by holding long risk-free assets. Therefore, the additional risk from leverage should not discourage buyers. Note also that the attractiveness of IRs will depend on the implicit leverage cost, which, in turn, depends on the terms of the installment payments and the (unobservable) offer price if the issue were sold on a fully-paid basis. 7. Examples of this type of explanation include the price-pressure hypothesis discussed in Scholes (1972), and the “price-of-immediacy” model proposed by Grossman and Miller (1988). 8. Underpricing of secondary offerings can also result from information asymmetry among the issuers, underwriters and different types of traders provided that the prices observed in the pre-issue markets are not perfectly revealing. However, as we report in Section 4, our results do not support this hypothesis. 9. See, for example, Holthausen et al. (1990) and Keim and Madhavan (1996). 10. One company in our sample, Hudson Bay Co., had two offerings in the sample period. 11. These figures were calculated by multiplying the number of underlying shares offered by the sum of the required installment amounts, without taking into account the payments’

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present values. This method is the same as that used in the prospectuses. Note that the figures are based on dollars at the time of issues. That is, no adjustment for inflation was made to them. 12. Asquith and Mullins (1986) find a 9.60% excess return during the period from 160 days to 10 days prior to the announcement dates, followed by a –2.0% excess return during the announcement period. Hudson et al. (1993) report a 4.28% cumulative abnormal return during the 60-day period before the announcements, and a −2.65% excess return during the announcement period. 13. As there has not been a study of offer-to-close returns from seasoned/secondary offerings in the Canadian markets, we compare our results to the findings from the Canadian initial public offerings (IPO) markets. Jog and Srivastava (1995) report an average offerto-close return of 5.40% between 1971 and 1992. Using a shorter data period (from 1984 to 1987), Clarkson and Merkley (1994) find an average return of 6.44%. These two results are similar in magnitude to our unadjusted returns, but are higher than our adjusted returns. 14. The alternative period of 150 trading days before the announcements was also used, and yielded similar results. 15. Hudson et al. (1993) find no significant relationship between price drops and preannouncement returns, while Asquith and Mullins (1986) and Korajczyk et al. (1990) find a very weak relationship. The choices of periods over which the pre-announcement returns are measured appear to influence their results. 16. Scholes (1972), Asquith and Mullins (1986) and Korajczyk et al. (1990) find no significant relationship between issue size and announcement period’s return. Hess and Bhagat (1986), Masulis and Korwar (1986) and Barclay and Litzenberger (1988) report similar findings for a sample of industrial issues. 17. If the negative returns on the announcement days are due to anticipation of a liquidity shock, a mean-variance analysis such as that in Grossman and Miller (1988) can be used to show that the magnitude of underpricing is positively related to the variance of the stock. A similar positive relation exists if underpricing is due to information asymmetry. This is because return volatility can reflect the degree of information asymmetry between existing and potential shareholders. 18. A somewhat analogous example is the amount of required margins on futures contracts. It has been shown that the level of margins is inversely related to the demand for futures contracts (See, for example, Hartzmark (1986), Fishe and Goldberg (1986) and Addrangi and Chatrath (1999)). One explanation for it is that margins are committed funds which reduce traders’ flexibility in case profitable investment opportunities subsequently exist. Unless the traders unwind their futures position and get back the margin deposits, they will have to borrow to take advantage of the profitable opportunities. Hence, the flexibility cost depends on the leverage cost and constraint that the traders face. To apply this logic to our context, IRs can be thought of as futures contracts where the first installment payment is the initial margin, while fully-paid offers are contracts where the full price is the initial margin. Therefore, investing in IRs involves lower flexibility cost. 19. Different versions of leverage such as the ratio of future payments (without adjustment for the present value factor) to the sum of all payments and the ratio of future payments over the initial payment. The conclusions are the same. 20. See, for example, Shleifer (1986).

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ACKNOWLEDGMENTS Both authors gratefully acknowledge the financial support from the Social Sciences and Humanities Research Council of Canada. Please address all correspondence to C. Sherman Cheung at [email protected].

REFERENCES Addrangi, B., & Chatrath, A. (1999). Margin requirements and futures activity: Evidence from the soybean and corn markets. Journal of Futures Markets, 19, 433–455. Asquith, P., & Mullins, D. (1986). Equity issues and offering dilution. Journal of Financial Economics, 15, 61–89. Barclay, M., & Litzenberger, R. (1988). Announcement effects of new equity issues and the use of intraday price data. Journal of Financial Economics, 21, 71–99. Clarkson, P. M., & Merkley, J. (1994). Ex ante uncertainty and the underpricing of initial public offerings: Further Canadian evidence. Canadian Journal of Administrative Sciences, 11, 54–67. Fishe, R. P. H., & Goldberg, L. G. (1986). The effects of margins on trading in futures markets. Journal of Futures Markets, 6, 261–271. Grossman, S., & Miller, M. (1988). Liquidity and market structure. Journal of Finance, 43, 617–633. Hartzmark, M. L. (1986). The effects of changing margin levels on futures market activity, the composition of traders in the market, and price performance. Journal of Business, 59, S147–S181. Hess, A. C., & Bhagat, S. (1986). Size effects of seasoned stock issues: Empirical evidence. Journal of Business, 59, 567–584. Holthausen, R., Leftwich, R., & Mayers, D. (1990). Large-block transactions, the speed of response, and temporary and permanent stock-price effects. Journal of Financial Economics, 26, 71–95. Hudson, C. D., Jensen, M. R. H., & Pugh, W. N. (1993). Information versus price-pressure effects: Evidence from secondary offerings. Journal of Financial Research, 16, 193–207. Jog, V., & Srivastava, A. (1995). Underpricing in Canadian IPOs 1971–1992 – an update. Fineco, 4, 81–89. Keim, D. B., & Madhavan, A. (1996). The upstairs market for large-block transactions: Analysis and measurement of price effects. Review of Financial Studies, 9, 1–36. Korajczyk, R. A., Lucas, D., & McDonald, R. L. (1990). Understanding stock price behavior around the time of equity issues. In: R. G. Hubbard (Ed.), Asymmetric Information, Corporate Finance, and Investment (pp. 257–277). Chicago: University of Chicago Press. Loderer, C., Sheehan, D. P., & Kadlec, G. P. (1991). The pricing of equity offerings. Journal of Financial Economics, 29, 35–57. Masulis, R., & Korwar, A. (1986). Seasoned equity offerings: An empirical investigation. Journal of Financial Economics, 15, 91–118. Mikkelson, W., & Partch, M. (1986). Valuation effects of security offerings and the issuance process. Journal of Financial Economics, 15, 31–60. Myers, S., & Majluf, N. (1984). Corporate financing and investment decisions when firms have information that investors do not have. Journal of Financial Economics, 13, 187–221.

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Scholes, M. (1972). The market for securities: Substitution versus price pressure and the effects of information on share prices. Journal of Business, 45, 179–211. Shleifer, A. (1986). Do demand curves for stocks slope down. Journal of Finance, 41, 579–590. Smith, C. (1977). Alternative methods for raising capital: Rights versus underwritten offerings. Journal of Financial Economics, 5, 273–307. White, H. (1980). A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica, 48, 817–838.

A NEW APPROACH TO TESTING PPP: EVIDENCE FROM THE YEN T. J. Brailsford, J. H. W. Penm and R. D. Terrell ABSTRACT Conventional methods to test for long-term PPP based on the theory of cointegration are typically undertaken in the framework of vector error correction models (VECM). The standard approach in the use of VECMs is to employ a model of full-order, which assumes nonzero entries in all the coefﬁcient matrices. But, the use of full-order VECM models may lead to incorrect inferences if zero entries are required in the coefﬁcient matrices. Speciﬁcally, if we wish to test for indirect causality, instantaneous causality, or Granger non-causality, and employ “overparameterised” full-order VECM models that ignore entries assigned a priori to be zero, then the power of statistical inference is weakened and the resultant speciﬁcations can produce different conclusions concerning the cointegrating relationships among the variables. In this paper, an approach is presented that incorporates zero entries in the VECM analysis. This approach is a more straightforward and effective means of testing for causality and cointegrating relations. The paper extends prior work on PPP through an investigation of causality between the U.S. Dollar and the Japanese Yen. The results demonstrate the inconsistencies that can arise in the area and show that bi-directional feedback exists between prices, interest rates and the exchange rate such that adjustment mechanisms are complete within the context of PPP.

Research in Finance Research in Finance, Volume 21, 135–154 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21006-1

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1. INTRODUCTION The purchasing power parity (PPP) hypothesis implies that, over the long-run, changes in the exchange rate between the currencies of two countries reflect changes in the ratio of those countries’ price levels. PPP has important implications for an explanation of exchange rate movements and for exchange rate forecasting in the long-term. In general, most studies tend to reject PPP in the short-run while in the long-run there is both evidence supporting and rejecting PPP.1 One factor contributing to these mixed results relates to the procedure used in testing. In recent years the theory of cointegration has been widely applied to tests of PPP. If the individual variables involved in the PPP relationship, namely the nominal exchange rate and the ratio of domestic to foreign prices, are nonstationary, but a specific linear combination of them is stationary, then PPP is claimed to hold. A major criticism of the classical residual-based tests for nonstationarity, such as the augmented Dickey and Fuller test, is that they lack power to distinguish between unit root and near unit root stationary processes, and therefore they have a tendency to accept the null hypothesis of non-stationarity (DeJong et al., 1989; Hakkio, 1984). This has prompted the use of tests that employ the null hypothesis of stationarity (Fisher & Park, 1991; Kwiatkowski et al., 1992). However tests for PPP are sensitive to the null hypothesis employed. That is, PPP could be rejected under a null hypothesis embodying the presence of a unit root, but accepted in a test with a null hypothesis of stationarity. In the context of a vector time-series framework, which indicates the dynamic relationships among the relevant financial variables, conventional methods to test for PPP are undertaken in full-order vector error correction modelling (VECM). However standard full-order VECM models are based on nonzero elements in all their coefficient matrices. As the number of elements to be estimated in these possibly over-parameterised models grows with the square of the number of variables, the degrees of freedom will be heavily reduced. In addition, in applications of VECM models to financial market data, a priori assumptions of zero entries may be required. Therefore the use of full-order VECM models may lead to incorrect inferences. Specifically, if we wish to test for indirect causality, or Granger non-causality which crucially depends on the positions of zero entries in the coefficient matrices, and we ignore the entries assigned a priori to be zero and employ “overparameterised” full-order VECM models, the power of our statistical inferences is weakened. Further, if the underlying true VECM and the associated cointegrating and loading vectors contain zero entries, the resultant specifications can produce conclusions concerning the cointegrating relationships among the variables which would be different to the conclusions arising where the a priori zeros are ignored, and give rise to potentially different conclusions concerning PPP.

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If the structure is patterned then an approach that uses a zero-non-zero (ZNZ) VECM is a more straightforward and effective means of testing for Granger causality, Granger non-causality, indirect causality and instantaneous causality. Further, one deficiency encountered in empirical research using cointegration theory is to provide satisfactory financial and economic interpretation for estimated cointegrating vectors. As demonstrated by Wickens (1996) it is important to introduce a priori information, perhaps to produce ZNZ patterns. To explicitly address this issue Penm et al. (1997) present a search algorithm in conjunction with model selection criteria to identify the optimal specification of a ZNZ patterned VECM for an I(1) system. However that paper did not fully discuss the existence of zero entries in causality and cointegration theory. This paper demonstrates an approach that incorporates zero entries in the VECM. The study re-examines PPP in the context of a three-variable system that includes prices, interest rates and the exchange rate. The model is tested using a variety of data relating to the Japanese Yen. The contribution of the paper is three-fold. First, the approach used in the study demonstrates how a ZNZ patterned VECM can be used in the context of PPP and cointegration. Second, the paper demonstrates that instantaneous causality should not be ignored in tests of PPP (e.g. as in Cheng, 1999), particularly with low frequency data. Third, the paper shows that PPP does hold within the context of the Yen in a model that incorporates interest rate effects, but this is only over the period of an open Japanese economy. The paper is structured as follows. Section 2 reviews VECM modelling for an I(1) system and discusses overall causality detection. Section 3 revisits PPP and briefly reviews prior evidence. The issue of instantaneous causality is examined in Section 4. Section 5 presents a re-examination of the relationship between the U.S. Dollar and Japanese Yen. Concluding remarks are presented in Section 6.

2. VECM MODELLING FOR AN I(1) SYSTEM Begin by considering the general vector autoregressive (VAR) model of the form: y(t) +

q

B ␶ y(t − ␶) = ␧(t),

(1)

τ=1

where ␧(t) is an s × 1 independently and identically distributed vector random process with E{␧(t)} = 0 and: E{␧(t)␧ (t − ␶)} = V,

␶ = 0,

E{␧(t)␧ (t

␶ > 0.

− ␶)} = 0,

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V is the residual variance-covariance matrix, and B␶ , ␶ = 1, 2 . . ., q are s × s parameter matrices, B q (L) = I +

q

B␶L␶,

␶=1

where L denotes the lag operator, and Ly(t) = y(t − 1). It is assumed that the roots of |B q (L)| = 0 lie outside or on the unit circle to ensure that y(t) can contain I(1) variables. Of note, y(t) is integrated of order d, I(d), if it contains at least one element which must be differenced d times before it becomes I(0). Further, y(t) is cointegrated with the cointegrating vector, ␤, of order g, if ␤ y(t) is integrated of order (d − g), where y(t) has to contain at least two I(d) variables.2 Under this I(1) assumption: B q (L) = B q (1)L + (I − L)B q−1 (L) Following Engle and Yoo (1991), the equivalent VECM for (1) can be expressed as: B q (1)y(t − 1) + B q−1 (L) y(t) = ␧(t),

(2)

where y(t) contains variables of two types, namely I(0) and I(1) and = (I − L). Eq. (2) can be rewritten as: B ∗ y(t − 1) + B q−1 (L) y(t) = ␧(t),

(3)

where B ∗ = B q (1) and B ∗ y(t − 1) is stationary and the first term in (3) is the error correction term. The term B q−1 (L) y(t) is the vector autoregressive part of the VECM. Because y(t) is cointegrated of order 1, the long-term impact matrix, B∗ , must be singular. As a result, B ∗ = ␣␤ and ␤ y(t − 1) is stationary, where the rank of B∗ is r, and ␣ and ␤ are matrices of dimensions s × r and r × 2s respectively. The columns of ␤ are the cointegrating vectors and the rows of ␣ are the loading vectors. Model development is more convenient using VECMs, rather than the equivalent VARs, if the systems under study include integrated time series. Engle and Granger (1987) note that, for I(1) systems, the VARs in first difference will be mis-specified and the VARs in levels will ignore important constraints on the coefficient matrices. Although these constraints may be satisfied asymptotically, efficiency gains and improvements in forecasts are likely to result by imposing them. The analogous conclusion applies to I(1) systems, such as those typically encountered in tests of PPP. Comparisons of forecasting performance of the VECMs versus VARs for

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cointegrated systems have been reported in studies such as Engle and Yoo (1987) and LeSage (1990). The results of these studies indicate that, while in the short-run there may be gains in using unrestricted VAR models, the VECMs produce longrun forecasts with smaller errors when the variables used in the models satisfy the test for cointegration. Further to these developments, we consider a hypothesis where every (i, j)th element, for specified i and j, is zero in all coefficient matrices in a VAR. If this hypothesis is framed in the VAR expressed by (1), these zero entries will also hold in the error-correction terms and in the vector autoregressive part of the equivalent VECM, say (2). A discussion of this property is provided in Appendix 1. Analogously we can achieve a result that if all (i, j)-th coefficient elements in the error-correction terms and all (i, j)-th coefficient elements in the vector autoregressive part of the VECM are zeros, then every (i, j)-th entry is zero for all coefficient matrices in a VAR. The implications of the above outcome are straightforward. If yj does not Granger-cause yi , then any (i, j)-th entry must be zero for all coefficient matrices in the VAR. Also all (i, j)-th coefficient elements in the equivalent VECM are zeros. In a similar way, we can demonstrate that if yj does Granger-cause yi, then the (i, j)-th element of Bq (L) in (1) is nonzero. Also, at least a single (i, j)-the coefficient element is nonzero in Bq (1) or Bq-1 (L) in the equivalent VECM. Of note, an indirect causality from yj to yi through ym indicates yj causing yi but only through ym . Hence, yj Granger-causes ym , ym Granger-causes yi , and yj does not Granger-cause yi directly. We can easily demonstrate that the VAR in (1) has nonzero (m, j)-th and (i, m)-th elements and a zero (i, j)-th element in Bq (L). This indirect causality can also be shown in the equivalent VECM, which has at least a single nonzero (m, j)-th element and a single nonzero (i, m)-th elements in Bq (1) and Bq-1 (L). Also all the (i, j)-the elements in the equivalent VECM are zeros. The above discussion indicates that Granger causality, Granger non-causality and indirect causality detected from both the ZNZ patterned VECM and its equivalent ZNZ patterned VAR are identical. Since the use of the VECM is more convenient, it is obvious the ZNZ patterned VECM is a more straightforward and effective means of testing for the Granger causal relations. The same benefits will be present if the ZNZ patterned VECM is used to analyse cointegrating relations.

3. PURCHASING POWER PARITY TESTING The PPP theory states that exchange rates between currencies are in equilibrium when their purchasing power is the same in each of the two countries. Formally

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the PPP condition can be expressed as follows: Pt = Et , P ∗t where Pt denotes domestic price level, P ∗t denotes foreign price level, and Et denotes units of domestic currency per unit of foreign currency. The classical way of testing for PPP is to regress the nominal exchange rate, ln(E t ), against the ratio of domestic to foreign prices, ln(P t /P ∗t ). Standard Wald statistics are then calculated to test whether the coefficient estimates are consistent with the restrictions embodied in the PPP hypothesis. This approach usually yields results that do not accept the PPP hypothesis (e.g. Cumby & Obstfeld, 1984; Frenkel, 1981; Roll, 1979). A major problem with this approach is that the timeseries properties of nominal exchange rate and prices are not specifically taken into consideration. If nominal exchange rates and the ratio of domestic to foreign prices are integrated series, and they usually are, then this test could be biased toward rejecting the null hypothesis of PPP. To overcome this problem, cointegration has been widely utilised to test for PPP. Following Engle and Granger (1987), if ln(E t ), and ln(P t /P ∗t ) are characterised as integrated of order 1 and if there is a long-term cointegrating relationship between them, where ␤ denotes the cointegrating vector and ␤ X t = ␤ (ln(E t ), ln(P t /P ∗t )) = ␧t with ␧t a variable which is stationary, then PPP is claimed to hold.3 Various studies have used the methods of unit root tests and cointegration tests for PPP by examining the bilateral exchange rates for a number of countries. A general outcome of these studies is that long-term PPP appears not to hold, when tests based on short- or medium-length time-series are used (e.g. Mishkin, 1984; Piggot & Sweeney, 1985; Roll, 1979). However, when longer time samples are used, PPP generally holds (e.g. Abauf & Jorion, 1990; Froot & Rogoff, 1994; Lothian & Taylor, 1996). The inconsistency in results can be attributed to the fact that statistical tests become less powerful in small samples. Another result is that high-frequency data (e.g. monthly data) does not generally lead to support of PPP in the long-term (e.g. Corbae & Ouliaris, 1988; McNown & Wallace, 1989; Taylor, 1988). However when researchers shift to low-frequency data and use cointegration techniques to test PPP, the evidence usually supports the long-term convergence of real exchange rates toward PPP (e.g. Edison, 1987; Kim, 1990). Recently Cheng (1999) has included the interest ratio variable to conduct PPP testing and causality detection. If the foreign interest rate falls below the domestic interest rate as a result of an increase in the domestic rate, the domestic currency may appreciate against the foreign currency.4 Cheng’s analysis concerns PPP

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between the USA and Japan using annual data over the period 1951–1994 and he finds evidence supporting PPP in the long run. Cheng (1999) uses a VECM to examine the relationship between the U.S. Dollar and the Japanese Yen and the following one-sided Granger causality test: (1 − L)y t = ␣0 +

M

␣m (1 − L)y t−m +

m=1

+

Q

N

␤n (1 − L)x t−n

n=1

␩k (1 − L)z t−k + ␯t

(4)

k=1

Note that neither ␤0 nor ␩0 is included in the specification (4). Since a VECM is equivalent to a VAR model with unit roots, and (4) is valid only when no instantaneous causality exists among the variables (Geweke, 1982; Hatanaka, 1982), instantaneous causality is implicitly neglected in (4). Moreover, when using low frequency data, such as annual time-series as in Cheng (1999), the impact of time aggregation suggests that instantaneous relations should not be ignored.

4. INSTANTANEOUS CAUSALITY INVESTIGATION The use of VECM models in financial time-series is versatile. The models can be employed as a means of detecting Granger causality, Granger non-causality and indirect causality. In this section, the focus is on instantaneous causality. Specifically, the section demonstrates that the one-sided Granger causality test proposed in Cheng (1999) is valid only when no instantaneous causality exists among the variables. To begin with, consider a bivariate VECM of (2) and define q−1 11 y1 (t) Bi12 i Bi q−1 y(t) = L, , B (L) = y2 (t) Bi21 Bi22 i=1 ␣1 ␧1 (t) , ,␣= ␧(t) = ␧2 (t) ␣2 and ␤ y(t − 1) = e(t − 1). Thus we have q−1 B11 B12 y1 (t − i) ␧1 (t) y1 (t) ␣1 i i e(t − 1) = + + , y2 (t) y2 (t − i) ␧2 (t) ␣2 Bi21 Bi22 i=1 (5)

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where

   v11 c E{␧(t)␧ (t − ␶)} =   0,

c , v22

␶ = 0, ␶ > 0.

v11 0 and v22 0. Both y 1 (t) and y 2 (t) are mutually instantaneously caused if and only if c = 0. Also both y 1 (t) and y 2 (t) are not instantaneously caused if and only if c = 0 (Penm & Terrell, 1984).5 1 −cv−1 22 Premultiply (5) by the matrix , then we have 0 1

q−1 B11 − cv−1 B21 y1 (t) i 22 i + 21 y2 (t) 0 1 B i i=1 ␧a (t) ␦ y1 (t − i) e(t − 1) = + , y2 (t − i) ␧2 (t) ␣2 1

−cv−1 22

22 Bi12 − cv−1 22 Bi

Bi22

−1 where ␦ = ␣1 − cv−1 22 ␣2 and ␧a = ␧1 − cv22 ␧2 . Now the first equation of this new system becomes

y 1 (t) +

q−1 i=1

␥i y 1 (t − i) +

q−1

␩j y 2 (t − j) + ␦e(t − 1) = ␧a (t),

(6)

j=0

−1 21 11 where ␩0 = −cv−1 22 . Thus ␩0 = 0, if and only if c = 0. Also ␥i = B i − cv22 B i −1 22 and ␩j = B 12 j − cv22 B j . If ␩0 = 0, (6) is different from the one-sided Granger causality test. Only if ␩0 = 0, is (6) equivalent to the one-sided Granger causality test proposed in Cheng (1999). Thus this one-sided test is valid only when no instantaneous causality exists between y 1 (t) and y 2 (t). The same result is obtained in a trivariate system. In Appendix B we summarise the method of instantaneous causality detection with all cases for a trivariate system.

5. EMPIRICAL RESULTS In this section, the PPP hypothesis is re-examined using the ZNZ patterned VECM modelling proposed earlier. The data are drawn from the U.S.-Japan relation

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and replicate Cheng’s (1999) test. Following Cheng (1999), the following three variables are studied contemporaneously in a stochastic vector system. (i) Japanese Yen to U.S. Dollar: exchange rate (E) per U.S. Dollar. (ii) Japanese CPI to U.S. CPI: ratio of price levels (P). (iii) (1 + U.S. discount rate)/(1 + Japanese discount rate): interest rate ratio (IR).6 While our interest is in assessing the presence or absence of the instantaneous causality in the proposed E-P-IR system, using the ZNZ patterned VECM modelling, we also use the cointegrating vectors detected to assist with the answer to other questions, such as whether the PPP hypothesis in the long-term is supported by the system selected. For comparison purposes the following three data sets relating to the above three variables are obtained (from DataStream™ ). (i) Annual data over the period 1951–1994. (ii) Semi-annual data over the period 1974–2000. (iii) Quarterly data over the period 1974–2000. The first data set is identical to that of Cheng (1999). For both the second and the third data sets, the samples begin in 1974. This point is often chosen as a cut-off as it coincides with the end of the Bretton Woods system and the first world oil shock.7 For the post-Bretton Woods era, the number of annual observations for the E-P-IR system is insufficient to conduct the analysis. Moreover, given the earlier evidence that shows that tests of PPP are sensitive to the sampling interval, semiannual and quarterly data are employed. These samples allow an assessment of long-term PPP and short-term responses. The variables are log transformed such that y 1 (t) = log(E), y 2 (t) = log(P), and y 3 (t) = log(IR). Unit root tests indicate that all transformed series are I(1). We then conduct the search procedures proposed in Penm et al. (1997) to obtain the optimal ZNZ patterned VAR models. In the course of selecting the optimal lag order (p) for the autoregressive part of the VECM system, the principle used by Chen and Wu (2000) to enhance the procedure is adopted. That is, we examine whiteness for the residual vectors from the VECM chosen by the Akaike Information Criterion (AIC). If the residual vector process proves to be non-white, we sequentially increase p to p + 1, and check the resultant residual vector process until the process is a vector white noise process. The optimal ZNZ patterned VECM and the optimal ␣ and ␤ are then selected by using the Schwarz criterion (SC). The search results for each data set are presented in Tables 1–3 respectively. The estimated residual variance-covariance matrices and the selected patterns of the cointegrating vector produce some interesting results. For the annual

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Table 1. Annual Sampling – The VECM for the Relationship, Linking Exchange Rates, Consumer Price Indices and Interest Rates between Japan and the USA Selected by SC Using the GLS Procedure. Non-zero (i, j)-th Entries in Estimated Coefficient Matrices, B(␶) and B ∗ ␶

i, j

Entry [Standard Error (S.E.)]

i, j

Entry (S.E.)

1

2,2

3,3

−0.3998 (0.111)

3

3,3

4

1,2

−0.7635 (0.110) −0.5714 (0.123) 0.3064 (0.154) 0.2159 (0.111) −0.3000 (0.150) −0.2665 (0.104) −0.1812 (0.128) −0.1417 (0.101) 0.1439 (0.043) 0.4439 (0.073)

1,3

−0.2313 (0.106) −0.8082 (0.164) −0.3792 (0.156)

2,2 5

1,1

6

3,3

7

2,1

8

2,2

B∗

3,1 3,3  The type of Vˆ selected: 

6.0042E-03 0 −1.9727E-04

Residual Analysisa

1,2

3,2

−0.1333 (0.031)  −1.9727E-04  0 4.8548E-05

0 5.0680E-04 0

Existing Lags 0

Normalised value of SC

3,1

1

1 1.014

2 1.033

3 1.048

4

5

1.065

1.082

Long-term Cointegrating Relationship Identified: log(E) = 0.9256 log(P) − 3.0841 log(IR)

Granger Causal Patternb Recognised:

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Table 1. (Continued ) Note: Variables: y 1 (t) = log(E), y 2 (t) = log(P), y 3 (t) = log(IR). Sample Period: 1951–1994 q−1 VECM: B ∗ y(t − 1) + y(t) + ␶=1 B(␶) y(t − ␶) = ␧(t). a The residual analysis confirms the residuals have white noise characteristics. For simplicity, the values of SC for q > 5 are not presented, but can be supplied to readers upon request. b x Granger-causes y only and not instantaneously: (Notation: x y). feedback, not instantaneously: (Notation: x y). instantaneous causality only: (Notation: x y).

data set, the non-diagonal Vˆ shown in Table 1 indicates the existence of the instantaneous causality in the system. This outcome could result from the effect of time aggregation on instantaneous causality in low frequency data. The presence of causality in the system is prima facie consistent with PPP and the results of Cheng (1999). Further, the positive relation between log(E) and log(P) is consistent with PPP in that an increase in relative price levels in Japan is associated with a depreciation of the Yen. However, a closer inspection of the cointegrating vector reveals an opposite sign between log(E) and log(IR) indicating that, ceteris paribus, an increase in IR leads to an appreciation in the Yen. This latter result is inconsistent with theory which asserts an opposite relation.8 This result could be due to a number of factors. First, since the number of the observation vectors is only 44, the poor parameter estimates in the cointegrating vector may be caused by the small sample size. Second, over the time period studied, the Japanese economy has undergone major change. In the early part of the sample, the Japanese economy was subject to considerable controls. For instance, heavy regulation and macroeconomic controls were prevalent during the 1950s and 1960s which included a fixed foreign exchange rate, restrictions on foreign investment, subsidized central lending and a targeted industrial policy. It was not until 1964, when Japan joined the OECD, that there was a relaxation of foreign investment controls. In contrast, the latter part of the sample represents a period when the Japanese economy developed into a major and open global economy.9 The results may simply reflect the outcome of combining data from different economic frameworks. Further disaggregation is not possible due to the small number of observations. Hence, while there is some evidence from the annual data that PPP holds, such a conclusion must be interpreted with caution given the findings in relation to the interest rate effect. For the semi-annual data set, the non-existence of instantaneous causality is detected from the diagonal Vˆ . This outcome indicates that the possible effect on instantaneous causality through time aggregation does not arise in the semi-annual data. In relation to PPP, there is evidence of causality in the system. Further, the positive relation between log(E) and log(P), and the positive relation between log(E) and log(IR) shown in Table 2 indicates that an increase in IR or an increase

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Table 2. Semi-Annual Sampling – The VECM for the Relationship, Linking Exchange Rates, Consumer Price Indices and Interest Rates between Japan and the USA Selected by SC Using the GLS Procedure. Non-zero (i, j)-th Entries in Estimated Coefficient Matrices, B(␶) and B ∗ : ␶

i, j

Entry (S.E.)

I, j

Entry (S.E.)

i, j

1

1,1

0.2935 (0.131) −1.5557 (0.216) −0.2143 (0.097) −1.4196 (0.215) −0.2344 (0.096) −1.2674 (0.213) 0.7376 (0.277) 0.7659 (0.267) 0.2710 (0.124) −0.7863 (0.205) −0.2610 (0.093) −0.1101 (0.054) 0.1225 (0.050) −0.8395 (0.220) 0.5438 (0.237) −0.3607 (0.149) 0.1854 (0.109) 0.2804 (0.113) 0.3242 (0.104) 0.3628 (0.111)

2,1

1.5094 (0.321) 0.6581 (0.137) 1.2662 (0.323) 0.4816 (0.167) 1.0817 (0.312) −0.1358 (0.054) −1.2130 (0.222) −1.0656 (0.219) −0.2069 (0.095)

2,2

2,1

0.7484 (0.258)

2,3

−0.7076 (0.209)

2,1

0.9418 (0.254) −0.2828 (0.134) 0.1673 (0.098)

2,2

0.1266 (0.091)

2,3

−0.5905 (0.203)

3,1

−0.4603 (0.150) −0.3685 (0.148)

2,3 2

1,3 2,3

3

1,3 2,3

4

2,1

5

2,1

6

1,1 2,3

7

1,3 3,2

8

1,2 2,3

9

2,1 3,1

10

2,2

11

2,2 3,3

12

3,3

3,1 2,1 3,1 2,1 3,2 2,3 2,3 1,3

3,1 2,2

2,3 2,3

−0.5359 (0.183) −0.4266 (0.167)

3,3 2,2

Entry (S.E.) 0.2641 (0.101) 0.5017 (0.131) 0.1452 (0.091)

2,2

0.1918 (0.087)

3,1

−0.2304 (0.151) 0.6782 (0.260)

2,1

3,1

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Table 2. (Continued ) 14 B∗

−0.3252 (0.062) 2,1 −2.0284 2,2 0.2774 2,3 (0.263) (0.039)   6.3903E-03 0 0  The type of Vˆ selected:  0 2.7613E-05 0 0 0 4.5149E-05 3,2

Residual Analysis

Existing Lags 0

Normalised value of SC

1.8547 (0.175)

1.

1 1.008

2 1.020

3 1.033

4 1.042

5 1.043

Long-term Cointegrating Relationship Identified: log(E) = 0.1367log(P) + 0.9144log(IR)

Granger Causal Pattern Recognised: Note: Variables: y 1 (t) = log(E), y 2 (t) = log(P), y 3 (t) = log(IR) q−1 Sample Period: 1974 to 2000; VECM: B ∗ y(t − 1) + y(t) + ␶=1 B(␶) y(t − ␶) = ␧(t).

in P leads to a depreciation of the Yen. This result is now consistent with theory. For instance, when the price level in Japan is increasing, the Yen depreciates in order to retain PPP. Further, when the relative interest rate in Japan increases, there is an associated appreciation of the Yen. In reference to the Granger causal relations among the variables, feedback relations exist between the pair of log(E) and log(P), the pair of log(P) and log(IR), and the pair of log(E) and log(IR). Hence, the feedback within the system is complete and shocks to any one of the variables will be processed through the system. In addition, Fig. 1 shows that all roots detected lie outside the unit circle (> 1). This latter finding shows that the ZNZ patterned VECM can increase the modelling power. To check the adequacy of the model fit, the results in Table 2 support the hypothesis that the residual vector is a white noise process. We now turn to the quarterly data set. The non-existence of instantaneous causality is also detected from the diagonal Vˆ in Table 3. Thus the effect of the time aggregation on instantaneous causality can be ignored in high(er) frequency data. The presence of causality and the positive relations between log(E) and log(P), and log(E) and log(IR) shown in Table 3 are again consistent with theory. Hence, we conclude that both the semi-annual and quarterly data analyses support the PPP

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Table 3. Quarterly Sampling – The VECM for the Relationship, Linking Exchange Rates, Consumer Price Indices and Interest Rates between Japan and the USA Selected by SC Using the GLS Procedure. Non-zero (i, j)-th Entries in Estimated Coefficient Matrices, B(␶) and B ∗ : ␶ 1 2 3 4 5

7 8 9 10 11 13 14 B∗

i, j

Entry (S.E.)

i, j

Entry (S.E.)

i, j

0.2561 3,3 −0.2394 (0.102) (0.091) 2,3 −0.5383 3,1 0.3439 (0.115) (0.102) 2,2 0.1812 (0.084) 2,2 −0.1886 (0.082) 1,1 0.2297 1,3 −0.2214 2,3 (0.098) (0.085) 3,2 −0.1028 (0.054) 2,3 −0.2054 (0.108) 2,2 −0.2566 (0.086) 2,1 0.2740 2,3 −0.2867 (0.122) (0.110) 1,3 −0.2356 2,2 −0.2069 2,3 (0.087) (0.082) 2,2 0.2486 (0.074) 2,1 0.2807 2,3 −0.3183 3,3 (0.116) (0.099) 2,2 0.1921 (0.086) 2,1 −0.3913 2,2 0.0607 2,3 (0.057) (0.010)   3.2208E-03 0 0  The type of Vˆ selected:  0 1.9538E-05 0 0 0 3.1288E-05 3,1

Residual Analysis

−0.3539 (0.111)

−0.3198 (0.107)

−0.1692 (0.086)

0.3515 (0.046)

Existing Lags 0

Normalised value of SC

Entry (S.E.)

1.

1

2

3

1.007

1.014

1.021

4 1.028

5 1.036

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Table 3. (Continued ) Long-term Cointegrating Relationship Identified: log(E) = 0.1551 log(P) + 0.8983 log(IR)

Granger Causal Pattern Recognised: Note: Variables: y 1 (t) = log(E), y 2 (t) = log(P), y 3 (t) = log(IR) q−1 Sample Period: 1974–2000; VECM: B ∗ y(t − 1) + y(t) + ␶=1 B(␶) y(t − ␶) = ␧(t).

Fig. 1. Histogram of Roots for Semi-Annual Sample. Note: Minimum: 1.002 Median: 1.078 Maximum: 1.895.

Fig. 2. Histogram of Roots for Quarterly Sample. Note: Minimum: 1.015 Median: 1.148 Maximum:1.555.

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hypothesis in the long run. In examining the Granger causal relations, although there is no direct Granger causation from log(P) to log(E), there is however indirect causation from log(P) to log(E) via log(IR). In addition direct Granger causation exists from log(E) to log(P), and feedback relations exist between the pair of log(P) and log(IR), and the pair of log(E) and log(IR). We therefore conclude that Granger causal relation (directly or indirectly) exists between log(E) and log(P) in both semi-annual and quarterly data samples. Since all detected roots shown in Fig. 2 lie outside the unit circle, the results give no support to the hypothesis of instability. The possibility of a structural shift, which is reflected in unstable roots, is not a problem. Again, to check the adequacy of the model fit, the results in Table 3 support the hypothesis that the residual vector is a white noise process.

6. CONCLUSION In this paper we have demonstrated a new approach that involves ZNZ patterned VECM modelling to examine PPP, and associated causality and cointegration. Three contributions have been made. First, the paper demonstrates an approach that allows for zero entries in the VECM and shows how it can be applied to a three variable system that includes prices, interest rates and the exchange rate. Second, the paper shows that the one-sided Granger causality test proposed in Cheng (1999) is valid only when no instantaneous causality exists among the variables. Since time aggregation can contribute to instantaneous causality in low frequency data (such as annual data), instantaneous causality cannot be ignored. Indeed, in a test using annual data between Japan and the USA, evidence is found of instantaneous causality. Hence, caution is required when interpreting prior evidence. Third, prior studies have reported inconsistent results in relation to tests of PPP. In this paper, the sampling interval and the sample period is varied. Support for PPP is strongest when semi-annual data are employed. The results indicate that bi-directional feedback exists between prices, interest rates and the exchange rate and hence sheds light on the adjustment mechanisms through which PPP is achieved.

NOTES 1. A good survey of the literature can be found in MacDonald (1995). 2. In this paper, we consider only the case d = 1, although the procedure can be generally applied to models where d > 1. 3. For this case, McFarland et al. (1994) propose that the necessary condition for PPP exists in the long-term. The necessary and sufficient condition means that these two variables are cointegrated and the cointegrating vector is ␤ = (1, −1).

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4. Cheng (1999) found no evidence of causality between productivity and the terms of trade against the exchange rate, and thus excluded these variables from the model. 5. Since the VECM of (2) is equivalent to the VAR of (1), thus instantaneous causality exists between y 1 (t) and y 2 (t) if and only if c = 0. Also both y 1 (t) and y 2 (t) are not instantaneously caused if and only if c = 0. 6. Consistent with the Fisher equation, the interest rate ratio is expressed in this form and is numerically closer than the simple ratio of percentage rates. 7. In time series analysis economic and financial systems are evolving, and although episodic structural shifts may occur in the test period, model evolution in vector systems can be handled through time update and order update methods to investigate the structure changes. These methods utilise each incoming observation to update the model structure and the model parameters. 8. Cheng (1999) does not report the signs on the coefficients. 9. For a history of the Japanese post-war economy, see Komiya et al. (1988).

REFERENCES Abauf, N., & Jorion, P. (1990). Purchasing power parity in the long run. Journal of Finance, 45, 157–174. Chen, S. L., & Wu, J. L. (2000). A re-examination of purchasing power parity in Japan and Taiwan. Journal of Macroeconomics, 22(2), 271–284. Cheng, B. S. (1999). Beyond the purchasing power parity: Testing for cointegration and causality between exchange rates, prices, and interest rates. Journal of International Money and Finance, 18, 911–924. Corbae, D., & Ouliaris, S. (1988). Cointegration and tests of purchasing power parity. The Review of Economics and Statistics, 70, 508–511. Cumby, R., & Obstfeld, M. (1984). International interest rate and price level linkages under flexible exchange rates, a review of recent evidence. In: Bilson & R. Marston (Eds), Exchange Rate Theory and Practice. Chicago: University of Chicago Press. DeJong, D. N., Nankervis, J. C., Savin, N. E., & Whiteman, C. H. (1989). Integration versus trend stationarity in macroeconomic time-series. Working paper 89–99, University of Iowa. Edison, H. J. (1987). Purchasing power parity in the long-term: A test of the dollar/pound exchange rate (1890–1978). Journal of Money, Credit and Banking, 19, 376–387. Engle, R. F., & Granger, C. W. J. (1987). Cointegration and error correction representation, estimation and testing. Econometrica, 55, 251–276. Engle, R. F., & Yoo, B. S. (1987). Forecasting and testing in co-integrated system. Journal of Econometrics, 35, 143–159. Fisher, E. O. N., & Park, J. Y. (1991). Testing purchasing power parity under the null hypothesis of cointegration. The Economic Journal, 101, 1476–1484. Frenkel, J. A. (1981). The collapse of purchasing power parities during the 1970s. European Economic Review, 16, 145–166. Froot, K. A., & Rogoff, K. (1994). Perspectives on PPP and long-run real exchange rates. NBER working paper 4952. Geweke, J. (1982). Measurement of linear dependence and feedback between multiple time-series. Journal of the American Statistical Association, 77, 304–313.

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Hakkio, C. (1984). A re-examination of purchasing power parity. Journal of International Economics, 17, 265–277. Hatanaka, M. (1982). The causality and the exogeneity tests in the simultaneous equations. Osaka University: Mimeo. Kim, Y. (1990). Purchasing power parity in the long run: A cointegration approach. Journal of Money, Credit and Banking, 22(4), 491–503. Komiya, R., Okuno, M., & Suzumura, K. (Eds) (1988). Industrial policy of Japan. Tokyo: Academic Press Japan. Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54, 159–178. LeSage, J. P. (1990). A comparison of the forecasting ability of ECM and VAR models. Review of Economics and Statistics, 72, 664–671. Lothian, J. R., & Taylor, M. P. (1996). Real exchange rate behavior: The recent float from the perspective of the past two centuries. Journal of Political Economy, 104(3), 488–509. MacDonald, R. (1995). Long-run exchange rate modeling: A survey of the recent evidence. Staff Papers, International Monetary Fund, 42, 437–489. McFarland, J. W., McMahon, P. C., & Ngama, Y. (1994). Forward exchange rates and expectations during the 1920s: A re-examination of the evidence. Journal of International Money and Finance, 13(6), 627–636. McNown, R., & Wallace, M. S. (1989). National price levels, purchasing power parity, and cointegration: A test for four high inflation economies. Journal of International Money and Finance, 8, 533–545. Mishkin, F. (1984). Are real interest rates equal across countries? An empirical investigation of international parity conditions. Journal of Finance, 39, 1345–1358. Penm, J. H., Penm, J. H. W., & Terrell, R. D. (1997). The selection of zero-non-zero patterned cointegrating vectors in error-correcting modelling. Econometric Reviews, 16, 281–304. Penm, J. H. W., & Terrell, R. D. (1984). Multivariate subset autoregressive modelling with zero constraints for detecting causality. Journal of Econometrics, 3, 311–330. Piggot, C., & Sweeney, R. (1985). In: S. Arndt, R. Sweeney & T. Willett (Eds), Exchange Rates, Trade and the U.S. Economy. Washington, DC: American Enterprise Institute. Roll, R. (1979). Violations of purchasing power parity and their implications for efficient international commodity market. In: M. Marshall & S. Giorgio (Eds), International Finance and Trade. Cambridge, MA: Ballinger. Taylor, M. P. (1988). An empirical examination of long-term purchasing power parity using cointegration techniques. Applied Economics, 20, 1369–1381. Wickens, M. R. (1996). Interpreting cointegrating vectors and common stochastic trends. Journal of Econometrics, 74, 255–271.

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APPENDIX A ZERO ENTRIES IN A VAR AND ITS EQUIVALENT VECM FOR AN I(1) SYSTEM. In an I(1) system, the VECM of (2) can be expressed as: B q (1)y(t − 1) + B q−1 (L) y(t) = ␧(t). Further, we have the following relations: B k (L) = B k (1)L + B k−1 (L)(I − L),

k = q and q − 1.

(A.1)

If the (i, j)-th entries of B k (L), B k (1),and B k−1 (L)are b ij (L), b ij (1), and c ij (L) respectively, we have b ij (L) = b ij (1)L + c ij (L)(1 − L).

(A.2)

Now we define c ij (L)by c ij (L) = c 0 + c 1 L + · · · + c k−1 L k−1 , thus c ij (L)(1 − L) = c 0 + (c 1 − c 0 )L + · · · + (c k−1 − c k−2 )L k−1 − c k−1 L k (A.3) If b ij (L) = 0, then b ij (1) will also be zero. From (A.2), we have that c ij (L)(1 − L) = 0. (A.3) produces c 0 = 0, (c 1 − c 0 ) = 0, . . ., c k−1 − c k−2 = 0, c k−1 = 0 which leads to c i = 0, i = 0, 1, . . . , k − 1, and therefore c ij (L) = 0. At this point, if the (i, j)-th entry of B q (L)is zero, then the (i, j)-th elements of both B q (1) and B q−1 (L) are zeros. Therefore it can be concluded that if yj does not Granger-cause yi , then any (i, j)-th element must be zero for all coefficient matrices in the VAR. Also all (i, j)-th coefficient elements in the error-correction terms and in the vector autoregressive part of the equivalent VECM, will also be zeros. Further, from (A.1) if the (i, j)-th element of B q (L) is nonzero, then at least the (i, j)-th element is nonzero in B q (1) or B q−1 (L). Thus, we have just demonstrated that if yj does Granger-cause yi , then the (i, j)-th element of B q (L) in the VAR is nonzero. In addition at least a single (i, j)-th coefficient element is nonzero in B q (1) or B q−1 (L) of the equivalent VECM.

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APPENDIX B DETECTING INSTANTANEOUS CAUSALITY IN A TRIVARIATE SYSTEM 

v11 e  v22 In a trivariate system of (2), with V =  e f h eight different patterns of instantaneous causality.

f



 h , we have the following v33

(1) y 1 (t), y 2 (t)and y 3 (t) are mutually instantaneous directly caused if and only if e = 0, f = 0 and h = 0. (2) y 1 (t) and y 2 (t) are instantaneously indirectly caused via y 3 (t) if and only if e = 0, f = 0 and h = 0. (3) y 1 (t) and y 3 (t) are instantaneously indirectly caused via y 2 (t) if and only if f = 0, h = 0 and e = 0. (4) y 2 (t) and y 3 (t) are instantaneously indirectly caused via y 1 (t) if and only if h = 0, e = 0 and f = 0. (5) y 1 (t) does not cause instantaneously y 2 (t) and y 3 (t) if and only if e = f = 0, and h = 0. (6) y 2 (t) does not cause instantaneously y 1 (t) and y 3 (t) if and only if h = e = 0, and f = 0. (7) y 3 (t) does not cause instantaneously y 1 (t) and y 2 (t) if and only if f = h = 0, and e = 0. (8) No instantaneous causality exists among y 1 (t), y 2 (t) and y 3 (t) if and only if e = f = h = 0. The pattern of instantaneous causal relations can be detected by selecting the case that minimises the model selection criterion.

CORRELATION AMONG STOCK MARKETS UNDER DIFFERENT EXCHANGE RATE SYSTEMS Paul Sarmas ABSTRACT This study investigates the linkage between the Hong Kong stock market and Singapore stock market and the U.S. stock market during the preand post-East Asia Financial Crisis in 1997 and 1998. It uses multivariate regression models to study the impact of Hong Kong’s ﬁxed exchange rate system and Singapore’s free-ﬂoating exchange rate system on their respective stock markets. The results indicate that the exchange rate is not a signiﬁcant determinant of linkage between the U.S. and the two Asian stock markets, but the evidence suggests that stronger post-crisis relationships between the U.S. and the two Asian stock markets. The evidence also supports a stronger shortrun relationship between the U.S. and Hong Kong stock markets relative to that between the U.S. and Singapore stock markets.

1. INTRODUCTION Since the collapse of the Bretton Woods fixed exchange rate system in the early 1970s, most countries have switched from a fixed exchange rate system to a floating exchange rate system. However, some countries insist on keeping their fixed exchange rate systems in order to achieve economic stability and development. Research in Finance Research in Finance, Volume 21, 155–173 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21007-3

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Hong Kong and Singapore are dubbed “twin cities” and share many similar economic features. For example, both emerged under British governance, and both are small and open metropolitan economies with well-functioning domestic private sectors and highly rated public services. The two governments had enjoyed healthy budget surpluses and accumulated large official foreign reserves before the Asian economic crisis in 1997–1998. Both economies successfully pursued an export-oriented strategy and upgraded their industrial structures toward higher value-added activities. Each of them has become a regional financial center and the operational headquarters of many multinational corporations in the Pacific Asia region. Remarkable contrasts, however, exist between the two economies’ monetary systems and exchange rate regimes.1 Hong Kong has had a currency board regime since 1983, with the HK dollar pegged to the U.S. dollar at a fixed rate. For more than a half century up to the 1970s, Singapore had a classical sterling-based currency board system. Since then, it has evolved a managed floating system that maintains the value of the Singapore dollar against a trade-weighted basket of currencies within an undisclosed band. This study investigates the relationships between daily returns of two Asian countries’ stock markets and the U.S. stock market under fixed and flexible exchange rate systems. The motivation for this study has come about as a result of developing a strategic plan for a diversified portfolio investment in the prosperous Asian financial markets. The study proposes to analyze the effect of daily changes of exchange rates and the U.S. stock market on the daily returns of Hong Kong and Singapore stock markets, and it also tries to assess the movement of the Asian stock markets under the two different exchange rate systems. Although other traditional economic factors are also important, it is the perception of many financial analysts that exchange rate systems would serve as vital links between the U.S. stock market and the two Asian countries.

2. FOREIGN EXCHANGE RATE SYSTEMS AND ASIAN STOCK MARKETS The rules of the fixed exchange rate regime were set under the Bretton Woods system and were enforced by the International Monetary Fund (IMF) from 1945 (the end of the Second World War) until 1971. The main features of the Bretton Woods system are the relatively fixed exchange rates of individual currencies in terms of the U.S. dollar and the convertibility of the dollar into gold for foreign official institutions.2 However, as time passed, each country’s fiscal and monetary policies become more complex, and different unexpected economic

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shocks finally made it impossible to have all the currencies pegged to each other (Award, 1998). Some countries, including Hong Kong, adopted the a rather rigid currency board principle, maintaining a fixed exchange regime, while still maintaining the fixed exchange rate policy either pegged to the U.S. dollar or to other major currencies (Tornell, 2000). Under this system, the local monetary authority guaranteed the complete and free convertibility of the local currency against the pound sterling at a fixed exchange rate. The local note issue had 100% backing by sterling deposits in London. Continuous speculative attacks could smash market confidence, resulting in a breakdown of the peg. However, even under such adverse circumstances, the Hong Kong Monetary Authority (HKMA) has been committed to maintaining the fixed exchange rate system adopted in October 1983, and this has proven to be effective in maintaining the confidence during the transition of Hong Kong to Chinese control in 1997 (Yam, 1999). Amid the international monetary uncertainty in 1973, as with many other nations, the Singapore government adopted a managed floating system. Meanwhile, the authorities continued to relax their foreign exchange controls gradually, and finally liberalized controls by 1978.3 Under the free-floating exchange rate system, Singapore successfully withstood the test of time, even during the Asian Crisis in 1987, and achieved stable money policy and prosperous business development (Wu, 2000).

3. RELATIONSHIPS OF THE EXCHANGE RATES AND THE STOCK MARKETS The correlation among financial markets has been studied extensively, and the overall results are at best mixed and inconclusive. For instance, Bala Arshanapalli and John Doukas (1995) studied the presence of a common stochastic trend between U.S. and the Asian stock market movements during the post-October 1987 period. The evidence suggests that the “cointegrating structure” that ties these stock markets together has substantially increased since October 1987. The results indicated that the Asian equity markets are less integrated with Japan’s equity market than they are with the U.S. market. In another study, Wong (1995) investigated whether a U.S.-type intra-monthly seasonal behavior in daily stock index returns also exists in the major Asian markets. The study revealed that, although similar day-of-the-week effects have been documented in the U.S. and in the major Asian markets, the U.S.-type intra-month effect on stock returns is weak and unstable over time in Singapore, Hong Kong, Malaysia, Taiwan and Thailand. Instead, returns generated in these

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markets are fairly independent of the U.S. market. The weak linkage between the financial markets across nations would suggest that there are potential benefits in international diversification. Al Awad and Goodwin (1998) examined short-run and long-run dynamic linkages among weekly real interest rates for G-10 countries using a variety of time-series tests. The authors focused on the time-series properties of nominal interest rates, ex-ante expected rates of inflation, and real interest rates. In-sample and out-of-sample Granger causality tests were also conducted to evaluate lead/lag relationships among real interest rates. The results provided strong support for wellintegrated markets, particularly in the long run. Their study indicated that the U.S. financial markets might have a certain impact on Hong Kong’s and Singapore’s money markets. Numerous empirical studies have focused on the relationship between foreign exchange rates and stock markets. However, the validity of their findings seems to be sensitive to underlying exchange rate regime and economic conditions. For instance, Bahmani-Oskooee and Sohrabian (1992) found that there was a two-way relationship between the changes in levels of exchange rate and the fluctuation of a stock market. Their empirical results show that there is a dual causal relationship between stock price and the effective exchange rate of the dollar in the short run. However, the long-run relationship between the two variables failed to show statistical significance. Yet another study by Mok (1993) used an ARIMA approach and the Granger causality test to explore the causality of daily interest rates, exchange rates and stock prices in Hong Kong for period 1986 to 1991. The result of that study concluded that the interest rate and exchange rate information was efficiently incorporated in the stock market prices, both at the daily market close and at the opening. The author also pointed out that there is a weak bi-directional causality between stock prices and the exchange rate. Following the same premise, Ying Wu (2000) used an error correction model to explore the asymmetric effects of four different exchange rates on Singapore stock prices, and the effects’ sensitivity to economic instability. Both the Singapore currency appreciation against the U.S. dollar and Malaysian ringgit and the depreciation against the Japanese yen and Indonesian rupiah led to a long-run increase in stock prices for most selected periods of the 1990s. However, the effect associated with the U.S. dollar exchange rate has a sign reversal between the 1997–1998 crisis periods and the 1999–2000 recovery periods. Ying Wu’s study indicated that the influence of exchange rates on stock prices increased in chronological order in the 1990s. So the positive relationship between the stock market and the exchange rate tends to receive more attention in recent years. In a more recent study, Phylaktis and Ravazzolo (2001) studied the long run and short-run dynamics between stock price and exchange rate, and channels

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through which great shocks impacted on these markets. They used cointegration methodology and multivariate Granger causality tests, and applied the model to a group of Pacific Basin countries over the period from 1980 to 1998. The evidence suggested that stock and foreign exchange markets are positively related, and the U.S. stock market acts as a conduit for these links, where these links seemed not to be affected by foreign exchange restrictions. Thus, it showed once again that an inconsistent relationship exists between stock markets and exchange rates, no matter whether the exchange rate system is fixed or flexible.

4. RESEARCH DESIGN AND METHODOLOGY Despite the recommendation by Hung and Cheung (1995) to use weekly instead of daily data to avoid the interference of synchronous trading, this study uses daily data to capture the effects of market shocks. Also, the results don’t show any significant improvement when weekly data rather than daily data is used in the test procedure. This research studies and compares the effect of the daily returns on the U.S. stock market on Hong Kong and Singapore stock markets under the different exchange rates system before and after the Asian Financial Crisis in 1997–1998. It was the intent of this study to provide a more recent and specific picture by contrasting the interrelationship between the Hong Kong stock market and the U.S. stock market and between the Singapore stock market and the U.S. stock market from the perspective of different exchange rate systems. This empirical study was structured to address a number of specific issues. First, the stationarity of all the time series variables is tested, because only the stationary data can be employed in a regression test. The second task performed was to examine collinearity of the explanatory variables: Hong Kong, Singapore, and the U.S.4 A collinearity test will show the correlation among the independent variables of three countries’ data in the regression model. Only the variables with no collinearity were selected for regression analysis. Third, multiple regression tests were used to determine the relationship between the dependent variable (daily return of Hong Kong or Singapore stock market) and independent variables (U.S. stock market return and the exchange rate changes before 1997 and after 1998). Finally, application of the Granger causality tests was expected to determine the pair-wise short-run relationship between those variables. The structural design of this article can be characterized as an inferential study. It uses multivariate analysis to assess the statistical significance of various predictors about a single dependent variable (Zikmund, 2000). The independent variables are: (1) the daily return of the U.S. stock market; and (2) the daily changes of the exchange rate for the Hong Kong dollar against the U.S. dollar or the daily

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changes of the exchange rate for the Singapore dollar against the U.S. dollar. The dependent variables are: the daily return of the Hong Kong stock market or the daily return of the Singapore stock market. Many time series analyses have been based on the assumption that the underlying data series are stationary. The test of stationarity is often referred to as a unit root test. The Dickey-Fuller test is known as one of the early approaches to test unit roots and the degree of integration. If time series data has no unit root, then it is said to be “integrated of order zero” or I(0). If data has one or more than one unit roots, that means it is not stationary. It has to be differenced5 once or more to become stationary, expressed by I(1) and I(t) (Watsham & Parramore, 1997). The unit root tests will be applied to HSI (the daily change of the Hang Seng Index of Hong Kong), HGX (the daily change of the exchange rate for Hong Kong dollar against the U.S. dollar), SP500 (the daily change of the Standard and Poors 500 Index of the U.S.), STI (the daily change of the Straits Times Index of Singapore), SGX (the daily change of the exchange rate for the Singapore dollar against the U.S. dollar). For a time series, it is appropriate to formulate the following regression equation for the Augmented Dickey-Fuller (ADF) test. The test will be conducted separately for each time series data and for pre- and post-Asia Financial Crisis periods. (1 − L)Y t = ␣0 + ␤Y t−1 +

n

Y i (1 − L)Y t−i + e

(1)

i=1

where: Y is the series of daily variables being tested, L is the lag operator, ␣0 is an estimated constant, ␤ is regression coefficients, n is the number of lags differences for E in approximately white noise,6 and e is the errors or residuals. The null hypothesis to be tested for unit roots is that the series are non-stationary in the data levels. For the Dickety-Fuller (ADF) test, if the absolute value of calculated t-statistic is larger than the critical value provided by the ADF test, the null hypothesis of unit roots (not stationary) is rejected, and the time series variables are stationary. Next, the natural log of the variables will be used to express relations that deal with proportional changes in the variables for the Multiple Regression Analysis. In this format, the coefficient of the independent variables will be the percentage changes in the dependent variables per 1% change in each independent variable. In addition, the variance inflationary factor (VIF) test will be conducted to test the collinearity of the independent variables in order to set up better regression models. If a set of explanatory variables is uncorrelated, then optimal VIF will be equal to 1.7

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161

The following multiple regression model will be tested separately for each country’s historical data and for the pre- and post-Asia Financial Crisis period. Y = ␣0 + ␤0 X + ␤1 SP500 + e i

(2)

where: Y is the percentage change in the daily stock index in Hong Kong or Singapore, ␣0 = an estimated constant, ␤0 and ␤1 are regression coefficients, X is the percentage change of daily exchange rate, SP500 is the percentage change in the daily S&P 500 index, and ei is the errors or residuals. Based on the observed U.S., Hong Kong and Singapore daily stock indices and foreign exchange rates, the regression models are as follows: lnHSI = ␣1 + ␤1 HKX + ␤2 lnSP500 + e lnSTI = ␣2 + ␤3 SGX + ␤4 lnSP500 + e

(3)

where: lnHSI is the logarithm of daily Hang Seng Index measured by the percentage changes in the daily closed Hong Kong Stock Market Index, lnSTI is the logarithm of daily Straits Times Index measured by the percentage changes in the daily closed Singapore Stock Market Index, ␣1 , ␣2 are intercept, an estimated constant, ␤1 , ␤4 are the coefficients of the percentage change in the Hong Kong dollar or Singapore dollar’s exchange rates and the daily return of the S&P 500, HKX is the percentage change in HK$ daily exchange rate against US$, SGX is the percentage change in SG$ daily exchange rate against US$, lnSP500 is the logarithm of S&P 500 index proxied for percentage change in the daily closed U.S. stock market, and e is the error or residual term. In addition to examining the correlation of variables for the exchange rate and the stock market, this study investigates the short-run dynamics by Granger causality tests. Because correlation does not necessarily imply causation in any meaningful sense of that world, Granger causality tests have been used frequently to investigate short run relationships among two or more variables. A high degree of causality from one variable to another indicates that the two variables are integrated and that changes in one variable will tend to cause changes in the other. Thus, the Granger approach to the question of whether X causes Y is to see how much of the current Y can be explained by the past value of Y and then to see whether adding lagged values of X can improve the explanation. Y is said to be Granger-caused by X if X helps to predict Y, or equivalently if the coefficients on the lagged Xs are statistically significant. The causality issue between stock markets and the exchange rate is determined with the following equation, Y t = ␣ + ␤i Y t−1 + . . . + ␤j Y t−n + e t

(4)

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where ␣ is a 3 by 1 vector of parameters representing intercept terms; ␤i are 3 by 3 coefficient matrices of parameters with polynomials in the lag operator L; and et are a 3 by 1 series of independent random vectors, white noise vector with zero mean and finite covariance matrix. The above method will have the expanded version of the Vector Autoregressive (VAR)8 for Hong Kong or Singapore as follows:     HSI A10   A11 (L)      HKX A   =  20  +  A21 (L)   SP A30 A31 (L)   eHSI   +  eHKX  eSP      STI A10   A11 (L)       SGX =  A20  +  A21 (L)   SP A31 (L) A30   eSTI   +  eSGX  eSP 

 HSIt−1      A22 (L) A23 (L) ×  HKXt−1    A32 (L) A33 (L) SPt−1 A12 (L)



A13 (L)



(5)  STIt−1      A22 (L) A23 (L) ×  SGXt−1    A32 (L) A33 (L) SPt−1 A12 (L)



A13 (L)



(6)

where Aio are the parameters representing intercept terms and Aij are the polynomials in the lag operator L. The lag structure will be arbitrarily tested from 2 to12 lags. The following six simple hypotheses will be tested to find the pair-wise short-run relationship (Granger Causality) between the variables for Hong Kong, H0 : HKX does not cause HSI,

H1 : HKX does cause HSI.

(7)

H0 : HSI does not cause HKX,

H1 : HSI does cause HKX.

(8)

H0 : SP does not cause HSI, H1 : SP does cause HSI.

(9)

H0 : HSI does not cause SP, H1 : HSI does cause SP.

(10)

H0 : SP does not cause HKX,

H1 : SP does cause HKX.

(11)

H0 : HKX does not cause SP,

H1 : HKX does cause SP.

(12)

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The following six simple hypotheses will be tested to find the pair-wise short-run relationship (Granger Causality) between the variables for Singapore, H0 : SGX does not cause STI,

H1 : SGX does cause STI. (13)

H0 : STI does not cause SGX,

H1 : STI does cause SGX. (14)

H0 : SP does not cause STI, H1 : SP does cause STI.

(15)

H0 : STI does not cause SP, H1 : STI does cause SP.

(16)

H0 : SP does not cause SGX, H1 : SP does cause SGX.

(17)

H0 : SGX does not cause SP, H1 : SGX does cause SP.

(18)

The null hypotheses will be rejected if the calculated F-statistics are significant. It is normal to say that there exists a causation that one variable Granger causes the other.

5. THE DATA SOURCES This research primarily involves analyzing and interpreting historical daily data without considering other factors such as interest rate, inflation rate, money supply, GDP, and the unemployment rate. The reason for this limitation is that most of those other data are available on a monthly basis rather than a daily basis, and they are of exposed to collinearity problems as independent variables. The daily returns of each stock market consist of the Hang Seng Index (HSI) for the Hong Kong stock market, the Straits Times Index (STI) for the Singapore stock market, and the S&P 500 index for the U.S. stock market. The daily foreign exchange rates include the fixed-linked exchange rate for the Hong Kong dollar against the U.S. dollar (HKX) and the free-floating exchange rate for the Singapore dollar against the U.S. dollar (SGX). Due to the 1997–1998 Asian Financial Crisis, the movement of the stock markets in Hong Kong and Singapore was considered as very erratic during that period. In order to avoid the potential influence of the 1997–1998 crises, the data are divided into two sets: the Pre-Asian Financial Crisis Period from January 1995 to December 1996 and the Post-Asian Financial Crisis Period from January 1999 to December 2000. The data are gathered from the Hong Kong Monetary Authority (HKMA), Monetary Authority of Singapore (MAS), and U.S. Federal Reserve Bank in St. Louis. The daily data size is 456 for the pre-crisis period from January 1995 to December 1996. The daily data size is 464 for the post-crisis period from January 1999 to December 2000.

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Table 1. Unit Root Test. HGX

HSI

SGX

STI

SP

Pre-crisis unit root test ADF Test statistic 1% Critical value 5% Critical value 10% Critical value

−9.075 −3.457 −2.868 −2.571

−10.025 −3.457 −2.868 −2.571

−9.247 −3.457 −2.868 −2.571

−10.464 −3.457 −2.868 −2.571

−9.768 −3.457 −2.868 −2.571

Post-crisis unit root test ADF Test statistic 1% Critical value 5% Critical value 10% Critical value

−11.576 −3.457 −2.878 −2.571

−10.073 −3.457 −2.878 −2.571

−8.953 −3.457 −2.878 −2.571

−9.475 −3.457 −2.878 −2.571

−10.848 −3.457 −2.878 −2.571

6. EMPIRICAL RESULTS The unit root test was performed to check the stationarity of all the variables. The unit root test results, as shown in Table 1, indicate that all the absolute values of the calculated ADF test statistics are larger than the absolute value of the MacKinnon critical values at the 1, 5 and 10% significance level, and thus, the null hypothesis of a unit root will be rejected. This suggests that all the time series variables for the regression model are stationary. The variance inflationary factor (VIF) was used to measure collinearity of the variable data. The VIF statistics and variance analysis as shown in Tables 2–5 are in the acceptable range from 1.00 to 1.80 for the pre- and post-crisis period. Therefore, there is no reason to suspect any colliearity for the set of explanatory variables, and the appropriate regression analysis can be performed. The multiple regression estimates, as show in Tables 2 and 3, provide the following relationship between Hang Seng Index (HSI) and daily changes in exchange rate (HKX) and the U.S. stock market (SP500 ). The multiple regression analysis of the data, shown in Tables 4 and 5, indicate the strength of the linear relationship between Singapore’s STI Index and the foreign exchange rate (SGX) and the U.S. stock market index (S&P500 ). The results can be summarized as shown below: lnHSIpre = 36.23 − 16.62 HKX + 1.09SP500 lnHSIpost = −52.84 + 23.65 HKX + 1.92SP500 lnSTIPre = 6.44 + 0.084 ln SGX + 0.191 ln SP500 lnSTIpost = −4.03 − 3.19 ln SGX + 1.85 ln SP500

(19)

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Table 2. Regression and Variance Analysis. lnHSI = ␣1 + ␤1 HKX + ␤2 SP500 + e Section A – Regression Estimation Predictor Constant HGX S&P S = 0.03169 R2 = 0.96 Adjusted R2 = 0.96

Coef.

S.E. Coef.

T

P

VIF

36.236 −16.617 1.09124

5.371 2.624 0.01139

6.751 −6.343 95.772

0.000 0.000 0.000

1.000 1.000

Section B – Variance Analysis Source

DF

SS

MS

F

P

Regression Residual error

2 454

9.0897 0.4276

4.5449 0.0009

4826.94

0.0000

Total

456

9.5173

Note: Pre-Crisis: January 1995 to December 1996.

Table 3. Regression and Variance Analysis. lnHSI = ␣1 + ␤1 HKX + ␤2 SP500 + e Section A – Regression Estimation Predictor Constant HKX S&P S = 0.07317 R2 = 0.81 Adjusted R2 = 0.81

Coef.

S.E. Coef.

T

P

VIF

−52.837 23.651 1.923

3.542 1.916 0.0844

−14.912 12.351 22.783

0.000 0.000 0.000

1.800 1.800

Section B – Variance Analysis Source

DF

SS

MS

F

P

Regression Residual error

2 462

10.3872 2.4732

5.1946 0.0054

970.53

0.0000

Total

464

12.8604

Note: Post-Crisis: January 1999 to December 2000.

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Table 4. Regression and Variance Analysis. lnSTI = ␣2 + ␤3 SGX + ␤4 S&P500 + e Section A – Regression Estimation Predictor Constant SGX S&P S = 0.04913 R2 = 0.79 Adjusted R2 = 0.79

Coef.

S.E. Coef.

6.4372 0.0844 0.19129

0.1731 0.233 0.01958

T 37.18 3.6 9.77

P

VIF

0 0.717 0

1.2 1.2

Section B – Variance Analysis Source

DF

SS

MS

F

P

Regression Residual error

2 454

0.2651 1.1038

0.13249 0.00243

54.49

0.0000

Total

456

1.3689

Note: Pre-Crisis: January 1995 to December 1996.

Table 5. Regression and Variance Analysis. lnSTI = ␣2 + ␤3 SGX + ␤4 SP500 + e Section A – Regression Estimation Predictor Constant SGX S&P S = 0.08920 R2 = 0.56 Adjusted R2 = 0.56

Coef.

S.E. Coef.

T

P

VIF

−4.0330 −3.1913 1.8455

0.5487 0.2814 0.07797

−7.361 −11.382 23.671

0.000 0.000 0.000

1.100 1.100

Section B – Variance Analysis Source

DF

SS

MS

F

P

Regression Residual error

2 462

4.7421 3.6764

2.3706 0.008

297.91

0.0000

Total

464

8.4185

Note: Post-Crisis: January 1999 to December 2000.

Correlation Among Stock Markets

167

In the case of Hong Kong, the estimated coefficients of the foreign exchange rate (−16.62) for the pre-crisis period, and in the case of Singapore, the estimate coefficient of the foreign exchange rate (−3.19) for the post crisis period may appear somewhat controversial. The inverse relationship between changes in HSI and changes in exchange rate in the pre-crisis period, and between changes in STI and changes in exchange rate during the post-crisis period, can be explained by the inflation factor. A higher rate of inflation in the home country forces the domestic currency to lose its value, and hence, investors will demand a higher risk premium and a higher rate of return, which causes stock prices to fall. Therefore, depreciating the Hong Kong dollar (or the Singapore dollar) represents higher inflationary pressure in Hong Kong (or Singapore), which could explain each country’s sluggish economy and depressed stock market. However, in the pre-crisis period of the Singapore case and the post-crisis period of the Hong Kong case, there exists a positive correlation, and this agrees with the previous findings of positive relationship. In the macro economic view, depreciating the Hong Kong (or Singapore) dollar will increase exports of the corresponding country, which usually stimulates their export-oriented economy, and results in a booming Singapore (or Hong Kong) stock market. In this scenario, lack of statistical significance is consistent with findings in similar studies involving different currencies and stock markets. The correlation coefficients for the U.S. S&P stock index are quite different from the coefficients of the exchange rate. These two variables resulted in a significant positive correlation between the Asian Stock markets and the U.S. stock market. In addition, the movements of the U.S., Hong Kong, and Singapore stock markets grew stronger during post-crisis period. The standard errors of the regression, which describes the dispersion of data points above and below the regression line, indicate that there would little variance between the predicted values and the actual values. The residual analysis reveals that the errors are normally distributed, as they are linearly related to HSI and STI, and the linear assumption holds for this model. The R2 and adjusted R2 are high enough to conclude that a large portion of changes in Hang Seng Index can be explained by the Hong Kong dollar’s exchange rate movements and the S&P 500 daily return during both sub-periods. However, both statistics indicate a somewhat weaker relationship between the explanatory variable and the Straits Times Index (Singapore’s stock market index). The F-statistic is used to determine the significance or existence of the regression line. At a 5% level of significance, the output F-statistics for both of the Hang Seng Index (HSI) and the Straits Times Index (STI) exceed the critical value on the F distribution (with 2 and 453 degree of freedom) which is 3.07. In addition, the P-value of the F-test for both regression estimates during the pre- and post-crisis

168

Table 6. Granger Causality Test for Hong Kong. Null Hypothesis

Lags: 2 F-Stat.

Lags: 4

Lags: 6

Lags: 8

Lags: 10

Lags: 12

Prob.

F-Stat.

Prob.

F-Stat.

Prob.

F-Stat.

Prob.

F-Stat.

Prob.

F-Stat.

Prob.

Pre-crisis for HSI, HKX and SP500 HIS not cause HKX 0.038 HKX not cause HIS 0.028 SP not cause HKX 0.282 HKX not cause SP 0.638 SP not cause HIS 66.926 HSI not cause SP 0.024

0.963 0.972 0.754 0.529 0.000 0.977

0.731 1.289 0.649 0.452 34.117 0.902

0.571 0.273 0.628 0.771 0.000 0.463

1.704 1.523 0.873 0.627 22.961 1.298

0.118 0.169 0.515 0.708 0.000 0.257

1.210 1.105 0.559 0.412 16.952 0.812

0.291 0.359 0.811 0.914 0.000 0.592

1.006 1.291 1.182 0.442 13.605 0.844

0.437 0.233 0.301 0.925 0.000 0.587

1.058 1.119 1.057 0.620 12.161 0.821

0.395 0.343 0.395 0.825 0.000 0.629

Post-crisis for HSI, HKX and SP500 HSI not cause HKX 1.604 HKX not cause HIS 0.927 SP not cause HKE 70.261 HKX not cause SP 0.918 SP not cause HIS 0.020 HSI not cause SP 0.944

0.202 0.397 0.000 0.400 0.981 0.390

2.279 0.730 38.083 1.716 0.212 0.741

0.060 0.572 0.000 0.145 0.932 0.564

0.500 3.052 0.336 0.596 24.171 1.069

0.808 0.006 0.918 0.734 0.000 0.380

0.721 2.297 0.253 0.754 19.320 0.895

0.673 0.020 0.980 0.643 0.000 0.520

0.526 2.097 0.328 0.659 15.673 1.072

0.872 0.024 0.973 0.763 0.000 0.382

0.683 2.313 0.365 0.796 13.175 1.031

0.768 0.007 0.975 0.655 0.000 0.419

PAUL SARMAS

Null Hypothesis

Lags: 2 F-Stat.

Lags: 4

Lags: 6

Lags: 8

Lags: 10

Lags: 12

Prob.

F-Stat.

Prob.

F-Stat.

Prob.

F-Stat.

Prob.

F-Stat.

Prob.

F-Stat.

Prob.

Pre-crisis for STI, SGX and SP500 SP not cause SGX 0.697 SGX not cause SP 0.999 STI not cause SGX 1.566 SGX not cause STI 1.861 STI not cause SP 0.552 SP not cause STI 20.779

0.499 0.369 0.210 0.157 0.576 0.000

0.443 0.824 1.039 1.248 1.005 10.422

0.777 0.510 0.386 0.290 0.404 0.000

0.691 0.885 1.308 2.193 1.486 7.116

0.657 0.506 0.252 0.043 0.181 0.000

0.789 1.174 1.639 1.718 1.288 5.218

0.613 0.313 0.112 0.092 0.248 0.000

0.671 1.091 2.318 0.638 1.033 4.476

0.752 0.368 0.012 0.782 0.415 0.000

1.663 1.624 2.743 0.513 0.843 3.860

0.073 0.082 0.001 0.907 0.606 0.000

Post-crisis for STI, SGX and SP500 SP not cause SGX 0.966 SGX not cause SP 0.738 STI not cause SGX 0.260 SGX not cause STI 2.510 STI not cause SP 1.615 SP not cause STI 34.470

0.381 0.479 0.771 0.082 0.200 0.000

1.106 0.558 0.765 1.777 0.896 18.789

0.353 0.693 0.548 0.132 0.466 0.000

0.998 0.807 1.399 1.536 1.448 12.574

0.426 0.565 0.213 0.165 0.195 0.000

1.444 0.641 0.957 1.558 0.858 9.906

0.176 0.743 0.469 0.135 0.552 0.000

1.381 0.678 1.143 1.286 1.222 8.389

0.186 0.745 0.329 0.236 0.274 0.000

1.834 0.571 1.025 1.093 1.360 6.809

0.041 0.866 0.424 0.364 0.182 0.000

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Table 7. Granger Causality Test for Singapore.

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periods are 0.000 and less than critical value at 5% level. This indicates that at least one of the explanatory variables is related to daily changes in HSI or STI, and the regression lines are significant for the regression model to predict the movements in these indices. The results of the Granger causality test for the Hang Seng Index are illustrated in Table 6. During the pre-crisis period, given the arbitrary 2, 4, 6, 8, 10 and 12 lags, the calculated larger F-statistics and zero probabilities reject the null hypothesis that the daily return of the S&P 500 index does not Granger-cause the daily return of the Hang Seng Index. This depicts a unidirectional causality from the daily return of the U.S. equity market to the daily return of the Hong Kong equity market. In the post-crisis period, the unidirectional causality starts to appear in the lag interval of 6, 8, 10 and 12, which reveal the postponed but stronger influence of the daily change of the U.S. stock market on that of the Hong Kong stock market after the crisis. Lack of unidirectional or bi-directional causality is evident between the exchange rate changes and the two equities markets. However, there exists a unidirectional causality from the S&P 500 daily return to the exchange rate daily return given 2 and 4 lags period. The results of the Granger causality test for the Straight Times Index are summarized in Table 7, which shows no unidirectional or bi-directional causality between the daily changes of the exchange rate and the two equity markets, either pre-crisis or post-crisis given the arbitrary 2, 4, 6, 8, 10 and 12 lags. As Hong Kong, the calculated larger F-statistics and zero probabilities reject the null hypothesis that the daily return of the S&P 500 index does not Granger cause the daily return of the Straits Times Index. This indicates a unidirectional causality from the daily return of the U.S. equity market to the daily return of the Singapore equity market, either before or after the crisis. In the post-crisis period, there is a stronger unidirectional causality from the U.S. equity market to the Singapore equity market, given the same lag interval of 2, 4, 6, 8, 10 and 12. This supports the multiple regression test result.

7. SUMMARY AND CONCLUSION Previous studies hypothesized that there exists a certain kind of relationship between exchange rate and stock markets, but the relationship between exchange rate fluctuations and the changes of the stock market indices is inconsistent. The literature also notes that there exists a positive relationship among the international stock markets. This study focused on the relationships between daily returns of the two selected Asian markets plus the U.S. stock market and their respective exchange rates. The main objective was to examine whether these links are different

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under the different foreign exchange rate systems pre- and post-Asian Financial Crisis in the mid 1997 and 1998. The initial step involved examining this relationship by applying a Multiple Regression analysis, which tests for the correlation between these countries’ stock markets and their exchange rates. Then, the Granger Causality test was performed to study the further interactions between the various markets under the different exchange rate systems. The empirical results show that different exchange rates systems have no significant role in determining the linkage between the two Asian countries stock markets and the U.S. stock market. The multiple regression analysis indicates that the relationship between the stock markets and the exchange rate were inconsistent and conflicting both before and after the crisis. The exchange rate had a positive effect on the Hong Kong stock market in the pre-crisis period, but a negative effect in the post-crisis period. The exchange rate had a small inverse effect on the Singapore stock market in the pre-crisis period, but positive effect in the post-crisis period. The further investigation by the Granger Causality test indicates no short-run relationship for the Hong Kong and Singapore exchange rates and their equity market or the U.S. stock market before the crisis. Nevertheless, after the crisis, there existed a short-run linkage for the daily changes of the Hong Kong exchange rate and the daily return of S&P 500. This also supports the inconsistent relationship between the exchange rates and the equity markets. Both positive and negative effects may be explained with the inflationary disturbance and the macro economic view. The complex relationship between stock prices and foreign exchanges can be supplemented by the Fisher effect and financial theories. However, the impact of change in the fixed exchange rate on the stock market was too great when interpreted from the regression output. It is impractical to see the dramatic effect on the stock market after the change of the exchange rate because consequent dynamic market adjustments eliminate the results as predicted by the efficient markets theory and the equilibrium theory. Additionally, Hong Kong’s fixed-linked exchange rate system limits such change. Therefore, the inference of the exchange rate effect on the equity market is invalid because the system is shown to be incomplete without considering other important factors. The empirical investigation also implies that both of the Hong Kong and Singapore stock markets were stable and positively correlated with the U.S. stock market in the periods of pre- and post-crisis. This reflects the strong effect of the U.S. stock market on the movements of the Asian stock markets. The two tests also reveal that the movements of the Hong Kong and Singapore stock markets were closer to those of the U.S. before and after East Asia Financial Crisis. The causality test reveals only the short-run unidirectional causality from the U.S. equity market to the two Asian equity markets. In Singapore, there were

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consistent effects of the daily U.S. stock market fluctuations on the daily changes of the Singapore market, either pre-crisis or post-crisis. In contrast, in Hong Kong, the daily S&P 500 return had an immediate effect on the daily Hang Seng return before the crisis. However, after the crisis, this effect was delayed until the influence of the daily exchange rate changes given more lag periods. All these effects support the previous findings that the linkage was increasing in a chronological order between the Asian equity markets and the U.S. equity market in the 1990s. The study further reveals that there were different degrees of the linkage between the two Asian countries and the U.S. stock markets, and the East Asian Crisis appears to differ in the degree of that linkage.

NOTES 1. For a detailed discussion refer to Zheng (2001). 2. For further study, please refer to Eiteman (1997) and Shapiro (2003). 3. Please refer to Monetary Authority of Singapore web site (www.mas.gov.sg). 4. There are evidence that both the Hong Kong and the Singapore financial markets are influenced by the stock market movements in the U.S., the UK and Japan. For further examination refer to the article by Chan, Cup and Pan (1992). However, this study focuses on the correlation between the U.S. stock market and those of Hong Kong and Singapore, in order to account for the effects of the two exchange rate systems: Hong Kong Dollar’s fixed rate system versus Singapore Dollar’s floating rate system. 5. Differencing is the process of calculating the change in the value of a variable in successive time periods. Integration refers to the degree of differencing that a datum requires for it to be transformed into a stationary series (Solnik, Bourcelle & Le Fur, 1996). 6. The equation assumes that a time series is “white noise”, which means the variables have zero mean, a constant variance, and zero correlation between successive observations (Leady & Ormrod, 2003). 7. A more conservative criterion would employ alternatives to least-square regression if the maximum VIF exceeds 5 (Levine, Berenson & Stephan, 1999). 8. Vestor Autoregressive (VAR) is a system in which every equation has the same right hand variables, and those variables include lagged values of all the endogenous variables. (Levine, Berenson & Stephan, 1999).

REFERENCES Arshanapalli, B., & Doukas, J. (1995). Pre and post-October 1987 stock market linkages between U.S. & Asian markets. Paciﬁc-Basin Finance Journal, 3, 1–14. Awad, M. A., & Goodwin, B. K. (1998). Dynamic linkages among real interest rates in international capital markets. Journal of International Money and Finance, 453–519. Bahmani-Oskooee, M., & Sohrabian, A. (1992). Stock prices and the effective exchange rate of the Dollar. Applied Economics, 459–464.

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Chan, K. C., Cup, B. E., & Pan, M. S. (1992). An empirical analysis of stock prices in major Asian markets and the United States. The Financial Review, 27, 289–308. Eiteman, D. K. (1997). Multinational business ﬁnance (8th ed.). Reading, MA: Addison-Wesley. Federal Reserve Bank of St. Louis (FRBS). Internet address at URL: www.stls.frb.org/fred/data/ exchange.html. Hong Kong Monetary Authority Monthly Bulletin. Internet address at URL: www.info.gov.hk/ hkma/eng/statistics. Hung, B., & Cheung, Y. L. (1995). Interdependence of Asian emerging equity markets. Journal of Economic Dynamics and Control, 4, 243–259. Levine, D. M., Berenson, M. L., & Stephan, D. (1999). Statistics for managers, using Microsoft Excel, Phstat Excel ‘98 Add-In (2nd ed.). New York: Prentice Hall. Leady, P. D., & Ormrod, J. E. (2003). Practical research, planning and design (8th ed.). Upper Saddle River, NJ: Prentice Hall PTR. Mok, H. M. K. (1993). Causality of interest rate, exchange rate and stock prices at stock market open and close in Hong Kong. Asia Paciﬁc Journal of Management, 123–143. Monetary Authority of Singapore. Internet address at URL: www.mas.gov.sg. Phylaktis, K., & Ravazzolo, F. (2001). Stock price and exchange rate dynamics. Department of Banking and Finance Working Papers. City University Business School, 321–244. Shapiro, A. C. (2003). Foundations of multinational ﬁnancial management (4th ed.). New York: John Wiley and Sons, Inc. Solnik, B., Bourcelle, C., & Le Fur, Y. (1996). International market correlation and volatility. Financial Analysts Journal, 1734–1745. Wong, K. A. (1995). Is there an intra-month effect on stock returns in developing stock markets? Applied Financial Economics, 5, 285–289. Wu, Y. (2000). Stock prices and exchange rates in a VEC model – the case of Singapore in the 1990s. Journal of Economics and Finance, 36–48. Zheng, W. Y. S. (2001). Hong Kong and Singapore equity market’s U.S. correlation under the different exchange rate system. MBA Thesis. Pomona, CA: California State Polytechnic University. Zikmund, W. G. (2000). Business research methods (6th ed.). New York: Dryden Press, Harcourt College.

MULTIPLE BANKING AS A COMMITMENT NOT TO RESCUE Paul Povel ABSTRACT We show why investors may prefer not to be a ﬁrm’s unique lender, even if they are in a strong bargaining position. Some ﬁrms need additional funds after a ﬁrst investment: providing additional funds is rational after the ﬁrst investment is sunk, but together the two investments are unproﬁtable. A unique lender will always provide additional funds and make losses. Two creditors can commit not always to provide funds: inefﬁcient negotiations over debt forgiveness may end with a project’s liquidation, which is harmful ex post, but helpful ex ante, if it keeps entrepreneurs with nonpromising projects from initially requesting funds.

1. INTRODUCTION This paper analyzes a bank’s incentives to forgive debt and refinance a distressed firm. We compare the decision of a unique lender with that of two banks, which have jointly provided a loan to the firm. We show that banks may prefer such cofinancing, even if they enjoy a strong bargaining position relative to the firm. The main difference between single and multiple banking lies in the negotiations that are necessary, if the firm cannot repay its debt but it could profitably be refinanced. Suppose that refinancing is profitable, once an initial investment is sunk, but that ex ante it is not. Some firms will need refinancing, others not, and the Research in Finance Research in Finance, Volume 21, 175–199 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21008-5

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creditors would like to finance the latter, only. The entrepreneurs of the respective firms, however, who are informed about their prospective financial needs, are only interested in receiving a loan, irrespective of whether it will be performing well or badly. If the creditors could commit not to refinance a firm, the entrepreneurs with ex ante unprofitable firms would prefer to be inactive, instead of being forced to liquidate their firm prematurely. A single lender cannot credibly commit to being tough, as it is always sequentially rational to refinance a distressed firm, once the initial loan is sunk. We argue that introducing multiplicity on the side of the lenders can make such a commitment possible. Even if they agree on the need to rescue the firm, two lenders will have to bargain about the distribution of the overall loss. Asymmetric information between the banks is the cause of inefficiencies in the rescue decision: with positive probability the firm is not refinanced, and it is liquidated, instead. There is a large literature now, which analyzes the effects of single or multiple lending on the decisions of a firm. One strand of the literature analyzes the effects that the structure of the creditors’ claims has on the possibilities to reorganize a distressed firm. Gertner and Scharfstein (1991) and Detragiache (1994) for instance assume that bonds are held by atomistic investors and therefore cannot be renegotiated. They analyze the effects of different bankruptcy regimes on the possibilities to reorganize a distressed firm. These effects can be used strategically by a firm, i.e. different financial structures can be used to achieve different goals. Several papers have asked the question why a firm may prefer to have one or many creditors. The difference between the market-based financial system in the U.S. and the bank-based system in Germany and Japan are striking, and an analysis of the relative advantages of the two systems is an important research program. A frequently stated advantage of the “main bank” financial system in Germany and Japan is that distressed firms are rescued more frequently (see e.g. Hoshi et al., 1990, for the case of Japan, and Edwards & Fischer, 1994, for the case of Germany). Some theoretical papers have analyzed the conditions under which “main bank” finance is more efficient than a system with multiple lenders (see e.g. Dewatripont & Maskin, 1995; Fischer, 1990; von Thadden, 1995). As Edwards and Fischer (1990) conclude, however, these models are not compatible with the empirical evidence for the German case. While in the models at most one “main bank” can emerge, in reality a German firm has more than one “Hausbank.” The question to analyze is thus why we may observe more than one nonatomistic lender. Several answers are possible. First, one could argue that banks are risk averse and want to spread out their risk exposure by sharing risks with their competitors. This is certainly true, but not a very satisfying explanation from a theoretical point of view. Banks are usually

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thought of as “large,” compared with the size of the average firm. They should therefore be able to diversify away most of their risks, as was modeled in Diamond (1984). This makes them de facto risk neutral, and they should not suffer from risk exposure. After all, it is the banks’ business to deal with risks and to allocate them optimally, and not to avoid risks. Additionally, it would be interesting to know whether there is more behind multiple banking than mere risk-sharing. Second, a bank may lack the funds to finance a project. Dewatripont and Maskin (1995) suggested that such smallness could be a solution to the soft budget constraint problem in centralized economies. Inability to finance a project exclusively may be a real problem when firms are very large. However, even in cases when the firms are very small, compared with their banks, we find multiplicity. As before, there is a need for additional explanations. Third, firms may want to have many banks because this protects them from being exploited by too strong a partner, as was suggested in von Thadden (1992). This third rationale for multiple banking implies that neither the banks nor the firms enjoy exceptionally strong bargaining positions in their relationship. This contrasts with the general perception that in bank-dominated financial systems, banks are in a stronger position. Many situations can occur in which a firm has to rely on its bank or banks and in which the bank can cheaply “punish” earlier unfriendly behaviour. Finally, some authors analyze the use of multiple claimants, holding different types of securities, in solving agency problems: the investors may have poor incentives either to really monitor their debtor, or to make proper use of their information (e.g. to liquidate a firm). See e.g. Diamond (1993), Bergl¨of and von Thadden (1995), Dewatripont and Tirole (1994), Rajan and Winton (1995), and Repullo and Suarez (1995). The present paper offers a rationale for multiplicity, which complements the explanations above. We argue that multiplicity is requested by the banks, who use it as a commitment device for eventual renegotiations of the lending contracts. The inefficiencies that arise in rescue negotiations (the banks have to determine their respective degrees of debt forgiveness) are a threat for entrepreneurs with bad projects. If the inefficiencies are sufficiently strong, this allows the banks to deter nonprofitable projects, and to finance high quality ones, only. The idea that multiplicity can serve as a commitment device was first stated in Hellwig (1991). Dewatripont and Maskin (1995) analyze the role of “multiple lending” in hardening the “soft budget constraint” of a firm. In their model, however, multiplicity is a credible commitment not to rescue only because of the assumption that lenders are “small,” and cannot provide both an initial and a refinancing loan. Bolton and Scharfstein (1996) analyze a renegotiation problem that is similar in spirit to ours. In their model, too, multiplicity is used as a

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commitment to be inefficient in renegotiations, with the result that high quality firms borrow from two creditors, while low quality firms prefer to borrow from a single creditor. Our model differs from theirs in several aspects. First, we work in a complete contracting environment. There is no variable in this model, which is “observable but not verifiable.” In Bolton and Scharfstein (1996), the entrepreneur can hide the returns of the project, and claim that the returns had been low. An optimal contract “punishes” him by threatening to liquidate the assets that are still valuable to him. In our model, the banks want to keep away nonprofitable projects, i.e. projects with a low probability of being successful. Second, we model the renegotiation process explicitly, and base it on observations from a financial system with “main banks.” Bolton and Scharfstein (1996) use the Nash Bargaining Solution and the Shapley Value, instead, to model bargaining outcomes. Other related work includes Yosha (1995) and Bhattacharya and Chiesa (1995), who analyze the strategic use of single or multiple lending as a commitment device with respect to nonfinancial decisions. More precisely, they study the relative advantages of public or bank lending, if the two regimes have different effects on how sensitive information can leak to a firm’s competitors. They thus provide more and richer explanations for multilateral lending, which add new aspects to the purely financial models. A second contribution of this paper is the development of a new model of inefficient bargaining, which has realistic features. We model the negotiations between the banks as a war of attrition. As soon as the banks have been informed that the firm must be refinanced, negotiations start. In these negotiations, each of the two banks tries to convince its opponent to write down the larger fraction of its claims. A rescue is only possible if one of the banks gives in: it frees the way to a rescue of the firm by accepting its opponent’s rescue plan. The reason why the banks eventually give in is that a rescue may become impossible, and the firm has to be liquidated. Each bank has a privately known valuation for the business relationship with the firm, which it loses if the latter is liquidated. The impossibility to rescue can arise at any time, as soon as the parties have started to bargain, and the longer the rescue is delayed, the more likely it becomes that the banks are forced to liquidate the firm. If a bank has a high valuation at risk, it has strong incentives to accept its opponent’s plan, only to ensure that the firm is rescued. As the opponent could have an even higher valuation, however, it also has an incentive to hold out for a while. This tradeoff determines the banks’ strategies in the war of attrition. Admati and Perry (1991), Fernandez and Glazer (1991), and Abreu and Gul (2000) are other papers, in which two parties must come to an agreement in time consuming negotiations. We could have used variants of these models, instead of the war of attrition, to capture the inefficiencies of the renegotiation process.

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The models in the three papers, however, are somewhat technical, too, and do not generate more elegant results than our model. We believe, therefore, that the war of attrition is a good compromise between the requirements for the analysis and the tractability of the results. The rest of the paper is structured as follows: In Section 2, the projects and the entrepreneurs are introduced, and the difficulties of a single bank are discussed. The model is extended in Section 3, where two banks finance a firm, and renegotiate if it must be refinanced. These renegotiations are modeled as a war of attrition. Section 4 solves this model to find the equilibrium of the renegotiation stage, as well as that of the whole game. Section 5 presents some empirical evidence, and discusses implications and extensions of the model. Section 6 concludes. Proofs are in the Appendix A.

2. THE MODEL WITH ONE BANK There is a large number of entrepreneurs who can start one project each. Each entrepreneur privately knows the type of project that he can start, either “good” or “bad.” The proportion of entrepreneurs with “good” projects, ␥, is common knowledge. The timing of a project is the following. In the first period, an investment I must be sunk. In period 2 the project types become publicly observable. Payoffs are earned in the third (the last) period. A “good” project earns R > I, while a “bad” project earns zero. Both project types can be liquidated, which earns r, where 0 ≤ r < R. A “bad” project can be “rescued” in period 2: if an additional amount ¯ is earned, instead of zero. J is invested, a payoff R Assumption 1. It is profitable to rescue a “bad” project in period 2, as ¯ − J > r. However, it is not profitable to finance a “bad” project ex ante: R ¯ − J − I < 0. Neither should a random sample of projects be financed: R ¯ − J − I) < 0. ␥(R − I) + (1 − ␥)(R The entrepreneurs’ payoffs depend on whether their projects were started and completed. If a project was not started, the entrepreneur earns zero utility. If the project was started, and either completed successfully (if “good”) or rescued (if “bad”), his utility is M > 0. If a project was started and then liquidated, this causes harm to the entrepreneur, and his payoff is −m (where m > 0). The entrepreneurs have no wealth of their own, and need outside finance to start their projects. We assume that a project cannot be separated from its entrepreneur. “Good” projects cannot be continued without him, and “bad” projects cannot be rescued – both types would have to be liquidated. The entrepreneurs are

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protected by limited liability. No punishment can be used legally to influence the entrepreneurs’ decisions, except for the liquidation of the project, which gives them negative utility. As we assume that it is not profitable to finance a cross section of projects, an investor must find a way to separate the “good” from the “bad” projects. Ideally, only the former would be financed. A bank could propose a contract which specifies that “bad” projects are liquidated in period 2. It would like to commit never to refinance, as this would prevent the entrepreneurs with “bad” projects from applying for initial loans I. Unfortunately, as one can easily verify, such a threat is not credible. Entrepreneurs with both “good” and “bad” projects will apply for I, as those with “good” projects have nothing to fear, and those with “bad” projects know that there will be a rescue. As a result, the single bank faces a random sample of projects, and it has to reject all loan requests. Due to a lack of commitment no project is undertaken, even though there would be valuable investment opportunities.

3. THE MODEL WITH TWO BANKS The lack of a commitment possibility in the case of a single bank can be overcome (at least partially) by having more than one creditor for each project. If each of two banks provides, say, half of the initial loan, both have some rights over the returns of the firm at t = 3. If the entrepreneur asks for the additional loan J, a part of the total investment will have to be written off. The banks will bargain over how much each should forgive. If this bargaining is sufficiently inefficient, and the consequences of this inefficiency cause harm to the entrepreneur, the underinvestment problem can be solved. It will be shown below, that two banks can commit to rescue with a probability which is strictly smaller than one. There is a critical value for this probability, which we denote by q¯ . It is determined by the entrepreneurs’ utility functions: q¯ M − (1 − q¯ )m = 0.

(1)

If an entrepreneur’s “bad” project is rescued with probability q¯ and liquidated with probability (1 − q¯ ), his expected payoff is exactly zero. He is thus indifferent between applying for a loan, and being inactive (which earns a sure payoff zero). If the rescue probability is strictly below q¯ , he prefers not to apply for the loan. In this case, only the entrepreneurs with “good” projects apply for funding. Therefore, if the banks can credibly commit not to refinance with a probability larger than (1 − q¯ ), multiple banking strictly dominates bilateral lending relationships.

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The model with two banks incorporates some observations about private workouts and bankruptcy negotiations that are reported in the business press, in empirical and descriptive papers (e.g. Edwards & Fischer, 1994; Fischer, 1990), in studies on the banking system and insolvency procedures in Germany, and in the large literature on the reform of the bankruptcy laws in Germany. These observations, or “stylized facts,” are: (1) (2) (3) (4)

Banks seem to have a strong bargaining position. The parties involved try to keep the negotiations secret. The banks want to terminate the negotiations quickly. It is likely that customers and suppliers are lost if they hear that there are rescue negotiations. (5) Whether to rescue or not is rarely subject to dispute. (6) The parties rather bargain about who is to sacrifice how much. We have used these observations to construct a model of debt renegotiations, such that it captures important elements of an existing financial system, and it generates results which can again be compared with reality. To do so, we must expand the model with a single bank, by adding some assumptions. Two comments will be helpful before this is done. First, all additional assumptions could have been added to the model with a single bank, without changing any of the results. This has not been done, as it would have complicated the exposition unnecessarily. Second, we will make assumptions that are much more restrictive than is necessary to generate the results. Again, this is done to simplify the notation. Where assumptions are “extreme,” we mention this fact, and discuss weaker alternatives. We model the renegotiation process between the two banks of a firm as a war of attrition. Each of the two banks tries to convince its opponent to carry the burden of refinancing. An outside observer of the negotiations will find that no progress is being made for a while: the banks fail to come to an agreement on how to split ¯ − I − J, if there should be a rescue. The negotiations can end in the overall loss R two different ways. Either one of the banks gives in, i.e. it accepts the rescue plan of its opponent. Or fate turns against the firm: a rescue becomes impossible for exogenous reasons, and it must be liquidated. In the latter case, each bank incurs a loss (additional to the financial loss). The size of this loss is privately known by the respective bank. In equilibrium, the higher it is, the more a bank fears liquidation, and the less it is willing to reject its opponent’s rescue plan. We now introduce the extensions of the single banking model, incorporating the observations listed above. The equilibrium of the war of attrition will be analyzed in Section 4. The first observation above states that banks are the main players in rescue negotiations. This is captured by assuming that they are the only bargaining parties,

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and by assuming that the courts strictly enforce Absolute Priority Rules. These rules specify that no party may receive any of the returns of the firm, if the banks have neither been repaid in full, nor have agreed to such a payment. Observation 2 describes how the banks want to keep the negotiations secret. It is helpful in achieving this goal to conclude an agreement as quickly as possible (see Observation 3). The reason for this wish for secrecy lies in the bankruptcy laws, which in most countries favour the banks (France is a notable exception). The assets of the firm usually are used as collateral for the loans from the banks, and absolute priority rules enforce the need to repay these claims first. The customers and suppliers are the parties who typically do badly in bankruptcy. Similar to a bank run, they have every incentive to request what they are owed, as soon as they discover the firm’s problems, and not to engage in any new trades (except possibly on a cash-only basis). We model this sensitivity of a rescue to the cooperation of these parties as a heavily reduced form of Observation 4. Assumption 2. At any time during the rescue negotiations, the public can discover that there are such negotiations going on. This happens by the time t with probability F(t). If the negotiations have been discovered, a rescue becomes immediately impossible, and the project must be liquidated. Assumption 2 is stronger than is necessary for the results. Nevertheless, it is not unrealistic. Firms whose assets consist almost exclusively of human capital are an example. If the competitors of an advertising company find out that it is in difficulties, they will try to hire its best employees on the spot. Robbed of its most valuable “assets,” the distressed company is not worth rescuing anymore, and must be liquidated. For this reason, a formal insolvency in this industry can end after a couple of hours. Furthermore, there is anecdotal evidence from the U.K., which indicates that secrecy may be a crucial requirement for a successful rescue. The Bank of England assists in the rescue of distressed large companies, by coordinating the parties’ efforts as soon as possible. It is not uncommon that in the negotiation meetings the parties have to use coded names to identify the distressed firms, even if everybody is informed about the real ones. Secrecy may also be relevant if without it potential customers are lost; for example, airlines may not able to get any more advance bookings if their customers fear being stranded abroad in case of the airline’s bankruptcy filing. We have to make some technical assumptions, in order to make the model tractable: Assumption 3. The “discovery technology” F of the public has a mass point with measure ␲ > 0 at t = 2, and a density f with support (2, ␶], where ␶ < ∞.

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The mass point at t = 2 is necessary for the uniqueness of the equilibrium strategies.1 These are determined by two differential equations, the solution of which is not unique without a socalled boundary condition. The mass point leads to a static lottery over rescue and liquidation at t = 2, which gives us such a boundary condition. This lottery is a logic extension of the dynamic war of attrition game to a discrete pre-stage, and is therefore used in the model: as will be shown below, the dynamic war of attrition is the limiting case of a discrete time game, if the length of a time unit becomes infinitesimal. Assumption 3 further restricts the support of f to a finite interval. The reason for this is that the results would be difficult to interpret if ␶ = ∞ (it would be possible that the banks bargain endlessly). It is by no means a necessary assumption. Furthermore, one can easily imagine why the firm’s distress should be discovered in finite time. For example, there may be legal obligations to make the distress publicly known if certain contingencies arise. Observation 5 states that the negotiating parties normally agree that the firm should be rescued (if they start to negotiate). This is captured by the complete information about the costs and returns of a rescue, and by the assumption that a rescue is profitable (Assumption 1). Not everything is common knowledge between the negotiating parties, however. Assumption 4. After signing the initial loan contract, each bank B i develops a privately known valuation i for the business relations with the firm. The bank loses i if the firm is liquidated. The valuations are independently and identically distributed, with a common probability density function g (g is strictly positive on its support + , continuous and differentiable; denote the cumulative distribution function by G). There are many possible interpretations for the loss of i if the firm is liquidated. For instance, it may be an estimate of future profits from dealing with the firm. Alternatively, the bank may incur costs or lose profits because the liquidation of its debtor damages its public image or leads to tighter supervision by the banking regulator. Finally, i may parametrize agency problems within the bank. A bank manager’s career prospects may be worsened, if “his” firm must be liquidated. Similarly, the bank manager and the entrepreneur may have become good friends. In both cases, the decision making unit in the bank would lose something if the firm is liquidated, and would prefer to rescue it. The banks’ willingness to assist a distressed debtor is frequently underlined in studies of the German financial system (see e.g. Schneider-Lenn´e, 1992). It is questioned in Fischer (1990). His evidence, however, is based on interviews with insolvency practitioners, and can therefore be assumed to be biased to the banks’ disadvantage. In their analysis of private workouts in the U.S., Gilson et al. (1990)

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conclude that restructuring is the more likely, the more debt is owed to banks. This may be caused by the banks’ superior skills and capabilities in attempting to rescue a firm, but it may also signal that banks are more willing to rescue a firm than other creditors. In the model this willingness to rescue is captured by the valuation i . Assumption 4 and the next assumption jointly capture Observation 6, that the banks bargain about who has to bear how much of the loss. The set of outcomes that the banks can achieve is restricted to simplify the analysis, that is how the net ¯ minus the cost J and the opportunity cost r) from rescuing surplus s (the returns R can be split (it is positive because of Assumption 1). ¯ − r − J). No Assumption 5. The banks fight for the whole surplus s := (R offer to share the surplus is made or accepted. If one bank gives in it receives its share r i in the liquidation value r of the firm from the other bank, where r 1 and r 2 are specified in the initial contract. The winning bank is committed to rescue the firm immediately, but may keep the returns for itself. As before (in Assumption 2), the formulation of Assumption 5 is much stronger ¯ − J can only be than necessary. A sharing rule saying that the gross surplus R shared in proportions ␣ and (1 − ␣), where ␣ = (1/2), would be sufficient. This would lead to significant complications of the analysis, however, which are not rewarded by the additional insight that one gets. This completes the introduction of the model with two banks. As one can easily see, the assumptions that have been added in this section could also have been introduced in the single bank model, without changing anything. The loss of a valuation i if the firm is liquidated would make a single lender even more willing to refinance a “bad” project. This rescue happens already without the valuation, however. In the model with one bank, a strategy for the bank consisted of a financing and a refinancing decision. In the case with two banks it is slightly more complicated. We first consider the part of the strategy which is used in the rescue negotiations. If a firm needs refinancing, the sequence of events is the following. First, the banks decide whether they want to give in immediately. If none of the banks has given in, the negotiations are discovered with probability ␲, and the firm must be liquidated. With probability (1 − ␲) the continuous time war of attrition starts. We assume that if both banks give in simultaneously, each “wins” with probability 1/2. A strategy is a function T i : + → [2, ␶], which determines for each moment of time whether a bank B i with valuation i should give in or not. It will be shown in Section 4, that if the equilibrium strategy tells this bank to stop at time T i (i ), it will stop at every later time, as well. Thus, we will define T i as determining the first time at which a bank plans to stop. This includes the static lottery which is played because of the mass point in F at t = 2.

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One may wonder why the banks cannot renegotiate the lending contract, after it has been signed. Both are fully aware of the inefficiency that will arise, if the contract is renegotiated using the war of attrition. Why cannot one bank (or a third bank) take over all debt for a flat price? Suppose B 1 would make such an offer to B 2 . B 2 would claim to have a valuation 2 = 0 and not to fear the war of attrition, in order to increase the takeover price. B 1 would claim to have the same valuation, to decrease the price. None of the two has any incentive to admit having a positive valuation, until a rescue is really needed. In this case, however, the war of attrition will start. The time that passes by is the only credible information about one’s valuation, as talk is “cheap,” and neither before nor during the war of attrition the parties can renegotiate more efficiently. Even a bank with valuation i = ∞ would wait until a rescue is necessary, as it might be that the opponent gives in. Nothing is lost by waiting until t = 2, at which time both banks can prevent a liquidation with probability one by giving in.

4. EQUILIBRIUM STRATEGIES The first step in solving the renegotiation game is to determine which types would want to start the war of attrition, and which types would prefer to give in immediately, in order to secure the rescue of the firm. If no bank gives in immediately, the negotiations are discovered with probability ␲ (the mass point in F), and the firm is liquidated. With probability (1 − ␲) the continuous time war of attrition starts. A bank with a very high valuation at stake will not want to gamble for the surplus s, and stop immediately. We must determine which is the lowest valuation, for which this is still true. Denote this cut-off value of bank B i with ␭i . If its valuation is i > ␭i , it should strictly prefer to give in immediately, while if it is i < ␭i , it should want to start the war of attrition, and plan to stop later than t = 2. We define ␭i as the valuation with which a bank B i is indifferent between giving in immediately, and starting the war of attrition, if it is sure that the opponent will either give in immediately (with probability 1 − G(␭2 )), or will start the war of attrition without giving in (with probability G(␭2 )). Consider the bank with valuation i = ␭i − ␧, where ␧ > 0. Given the definition of ␭i , there must be a ␦ > 0, such that it will strictly prefer to start the negotiations, if the probability that the opponent gives in immediately, as soon as the negotiations have started, is ␦. Thus, a bank with a valuation below ␭i has an incentive to hold out for a strictly positive amount of time. A bank with a valuation higher than ␭i , however, strictly prefers to give in immediately.

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Lemma 1. The cut-off values ␭1 and ␭2 are defined implicitly by s 1 − G(␭2 ) s 1 − G(␭1 ) ␭1 = and ␭2 = . 2␲ G(␭2 ) 2␲ G(␭1 )

(2)

Since ␭i is continuous and monotonic in ␭j , a symmetric solution exists. It can happen that there are multiple solutions, since the two equations in Lemma 1 must be solved simultaneously. We assume that the banks play the symmetric solution in this case, and denote the common cut-off value with ␭.2 As was mentioned before, the war of attrition is only one of many possible ways to model negotiations with inefficient delays. The model could have been slightly simplified by assuming that the support of G is bounded (see Assumption 4). Suppose it was common knowledge that the highest value i that a bank can attribute to its business relationship with a firm is A < ∞, because a bank’s line manager cannot “bet the ranch.” The results would be qualitatively the same, except that we would have ␭ = A. Our formulation allows for banks that give in immediately with a certain probability, depending on the parameters of the model. If both banks decided to stay in the game, the war of attrition starts. A strategy T i in this war of attrition specifies the earliest instant at which a bank wishes to stop, given the realisation of its potential loss, i . Lemma 2 derives some characteristics that equilibrium strategies must have. In Proposition 1 we will show that these necessary conditions are also sufficient conditions for the existence of a unique equilibrium, together with the boundary conditions that are determined in Lemma 1. Lemma 2. Let T 1 and T 2 be equilibrium strategies of the game defined above. Then the strategy T i is (i) strictly decreasing in the liquidation loss i , (ii) continuous, (iii) differentiable, and (iv) bank B i stops at ␶ if and only if i = 0. In equilibrium it will never be the case that the bank with the higher loss level will decide to stay in longer than its opponent. The threat of the public’s discovery must have strictly more weight in a bank’s reasoning the higher i is, while the gain from winning, the surplus s, is constant. Only a bank with zero liquidation loss will wait until ␶, and it will not want to stop earlier than ␶. A bank with strictly positive loss level will either stop immediately at t = 2 (if it has costs i ≥ ␭) or at some moment after t = 2 but earlier than ␶. At every moment, both players update their beliefs about the opponent’s valuation. Since T i is continuous and strictly decreasing, each i is mapped one-to-one with a stopping time T i (i ). T i can be inverted to yield a function L i : [2, ␶] → + . At each instant t i there is a valuation L i (t i ) with which a bank would plan to stop. As time passes by, a player’s expectation about the maximal valuation that his opponent could possibly have decreases. Bygones are

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not “bygones” in this game: every second that passes by signals information about a bank’s valuation, and is relevant for the present and future decisions of the opponent. As was mentioned above, the finiteness of ␶ is not a necessary condition for the tractability of the model. If the function f had an infinite support, then Lemma 2.(iv) would state that banks with zero liquidation loss never stop, and banks with strictly positive loss levels plan to stop at some finite time. L i , the inverse of the strategy function T i , is the lowest cost level that would make bank B i want to stop at time t. It will be helpful for characterising the equilibrium strategies in the following. These are determined by finding for each moment t 1 a valuation L 1 (t 1 ), such that B 1 is exactly indifferent between stopping at t 1 , and waiting for a small amount of time , and giving in then (the derivation is similar to that of the cut-off values ␭i ). If the bank gives in at time t 1 , its payoff is r 1 for sure. We require this payoff to be equal to the expected payoff, if it decides to wait until t 1 + : G(L 2 (t 1 + )) (F(t 1 + ) − F(t 1 )) (1 − F(t 1 + )) (r 1 − L 1 (t 1 )) + r1 r1 = G(L 2 (t 1 )) 1 − F(t 1 ) 1 − F(t 1 ) G(L 2 (t 1 )) − G(L 2 (t 1 + )) F(t 1 + ) − F(t 1 ) + (r 1 − L 1 (t 1 )) G(L 2 (t 1 )) 1 − F(t 1 ) 1 − F(t 1 + ) ¯ + (3) (R − r 2 − J) . 1 − F(t 1 ) The second expected payoff (on the right-hand side of Eq. (3)) has four components. The opponent may have a low valuation, and plan to give in later than t 1 + . By this time, the negotiations may have been discovered, and the firm must be liquidated. The bank receives its share r 1 of the liquidation value r, but loses L 1 (t 1 ). If the negotiations are not discovered, it will give in at time t 1 + , which earns r 1 . On the other hand, the opponent may plan to give in between t 1 and t 1 + . As before, the negotiations may be discovered, or they may not. In the ¯ − J, and pays r 2 latter case, the firm is rescued. The bank pockets the surplus R to the opponent. We abstract from the possibility that both may give in at t 1 + simultaneously, as the probability that this happens is negligible. Equation (3) can be simplified by rearranging, subtracting r 1 on both sides, and ¯ − r 1 − r 2 − J). A division of both sides by leads to by substituting s for (R G(L 2 (t 1 )) − G(L 2 (t 1 + )) 1 − F(t 1 + ) s G(L 2 (t 1 )) 1 − F(t 1 ) F(t 1 + ) − F(t 1 ) =− (4) L 1 (t 1 ). (1 − F(t 1 ))

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Since the strategies are differentiable everywhere it is possible to take the limit as goes to zero. The same procedure can be repeated for the second bank, and we get a system of two differential equations: G(L 2 (t 1 )) f(t 1 ) L 1 (t 1 ) , (5) L 2 (t 1 ) = − g(L 2 (t 1 )) 1 − F(t 1 ) s f(t 2 ) L 2 (t 2 ) G(L 1 (t 2 )) L 1 (t 1 ) = − . (6) g(L 1 (t 2 )) 1 − F(t 2 ) s Given the strategy of the opponent, Eq. (5) determines the optimal response of bank B 1 , if it has loss level L 1 (t 1 ) = 1 (the two are equivalent, if the equilibrium strategy tells bank B i with cost level i to stop at time t i ) and bank B 2 plays strategy L 2 (·). If Eq. (5) were an inequality, B 1 would either want to wait longer than t 1 (if <), or it would want to have stopped earlier (if >). Since by Assumption 2 the probability density function g is strictly positive on −1 : [0, 1] → + , G has an inverse function G + . Equations (5) and (6) can be integrated, and this leads to the following reaction function for bank B i : ti f(t) L i (t) L j (t i ) = G −1 G(␭)exp − dt . (7) 1 − F(t) s 2 Equation (7) implicitly describes the strategy of bank B j that makes bank B i exactly indifferent between stopping at t i and stopping at t i + (where is a small amount of time), given its cost level L i (t i ). The analogous can be done to derive the strategy of the other bank. The solution to these two equations will give us the equilibrium strategies for the banks. We will continue with the differential equations (5) and (6), and show that there is a unique equilibrium. The reaction functions will be helpful in Section 5, where we present some comparative statics. With the help of the differential equations and the boundary conditions it is now possible to describe the equilibrium strategies of the players for the whole renegotiation game. Proposition 1. The renegotiation game has a unique symmetric Bayesian equilibrium, which is implicitly described by the system of differential equations (5) and (6), and the boundary conditions T 1 (␭) = T 2 (␭) = 0. The equilibrium strategy for bank B i is to stop at time t if and only if i ≥ L i (t), where L i (t) is determined in Eq. (7). We can now find the equilibrium strategies for the whole game with two banks, including the financing decision. Whether an entrepreneur with a bad project applies for a loan in the first period depends on the probability with which his

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project is rescued in the second period. In Eq. (1) we determined an upper bound q¯ to this probability, such that “bad” projects are not financed. Proposition 2. If the probability of non-rescue due to bargaining delays is high enough, ␭ M 2 F(T 1 (1 ))G(1 )g(1 ) d1 ≥ , (8) M+m 0 the entrepreneurs will apply for the initial loan if and only if the project is of the “good” type. Proposition 2 is the main result of the paper. There are cases in which a financial system with multiple banking performs strictly better than one with single bank lending. If the condition in Eq. (8) is met, the banks prefer to require co-financing by a second bank to being a single lender.

5. EMPIRICAL IMPLICATIONS The main result of the paper is that banks might want to syndicate a loan to a firm, if they fear to find themselves in a harmfully weak bargaining position if the firm has to be refinanced. The loan is shared for strategic reasons, and the banks propose to share even if they have all bargaining power. There can be other reasons for why loans are syndicated, however, like (see Section 1) risk aversion, the sheer size of the loan, or because the strong competition on the lenders’ side. These reasons complement each other, and it is not clear which one was the most important if a loan has been shared. There is some empirical work on this question for the U.S. and for Germany. For the U.S., Gilson et al. (1990) have analyzed the performance of private workouts. One of their results is that debt restructurings are more likely if the number of lenders is small, which could support the result above. For the case of Germany, Fischer (1990) and Edwards and Fischer (1994) report that all but the very small firms have several “main banks,” which could be interpreted as supporting the conclusions in this paper. Interesting evidence is reported in Armendariz (1999). She analyzes the performance of several development banks, i.e. the default rates of their loans. Some of these banks require that projects are co-financed by commercial banks, while others usually are the unique providers of capital. The former enjoy considerably less arrears in the repayment of their loans. Her interpretation of these facts is that the requirement of co-financing hardens the Soft Budget Constraint of development projects, exactly what the results above suggest.

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A similar observation can be made if firms grow: suppose that for a small firm ¯ s − J s > I s , while for a larger firm R ¯ l − J l < I l . Then a “main bank” could R require that a growing firm finds a second main lender, for instance by committing to finance only a fraction of a major investment. Similarly, a bank could require co-financing if fixed costs of rescuing a firm are higher than the net surplus s for small firms, but lower for larger firms. We now analyze other implications of the model. The equilibrium strategies of all parties are unique, and therefore we can analyze the effects of varying some of the parameters of the model. ¯ a lower liquidation value Proposition 3. A higher expected value of the firm R, r and a lower additional loan J lead to later concessions. This in turn implies that the liquidation of a “bad” firm becomes more likely. The intuition behind Proposition 3 is clear: if the prize is increased, and the expected costs of fighting remain unchanged, the banks have an incentive to fight longer. The implications for rescue negotiations are surprising, however. Of two otherwise identical candidates for a rescue, the one with a higher post-rescue ¯ i.e. the more profitable, is more likely to be liquidated. Similarly, the one return R, with a lower liquidation value is more likely to be liquidated. This seems to be counterintuitive, as usually we would expect a valuable rescue to be undertaken. The result follows from two modeling assumptions. First, the negotiations are inefficient, as the “cake” that is to be split can disappear at any time. Second, the banks’ valuations for the surplus from a rescue and for the rescue itself are independent. Suppose that s depends on the number of employees of the firm, and that the banks’ public relations suffer if they cause unemployment by not assisting a distressed debtor (they lose i ). In this case we would expect a bank to be more willing to rescue if the firm is larger. A “valuable” firm could therefore be rescued for different reasons, either because a rescue is profitable (large s), or because failing to rescue would cause indirect costs (large i ). The second reason is an incentive problem that is similar to the one underlying our assumption: once a project has been financed, its investors have too strong incentives to refinance it (see Mitchell, 1993, or Aghion et al., 1999, on the problems that this can cause for banking regulation). The result should hold, however, in situations in which the valuations i are small, compared with the surplus from a rescue, s. One could analyze the refinancing decisions of foreign banks, that care less about their public image outside their home country. Similarly, one could analyze these decisions in sectors, regions, or during time periods, in which unemployment and bankruptcies are not considered as being major problems.

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A further implication of Proposition 3 concerns the allocation of the assets of a distressed firm. Many bankruptcy procedures are court-led, and contain rules that are meant to protect the interests of all parties. This may make it difficult to use the assets in the most efficient way, as for instance their quick sale to the highest bidder. The liquidation value of a firm is therefore lower than necessary if a formal procedure is started, with the consequence that a rescue becomes less likely. The variables R and I (the return of a “good” project and the initial investment) have no effect on the strategies, because of the simplified structure of the model. As was suggested above, we could allow a bank’s valuation i to depend on the size of its stake in the firm. The larger the loan, the more the bank is exposed to public scrutiny, and the more it will therefore be willing to cover up “mistakes” by rescuing the firm. Similarly, the relative shares r i in the liquidation value r play no role. The reason for this is that the bank receives a payment of at least r i whatever the outcome of the negotiations. We could easily change the sharing rule such that r i plays a role in the banks’ renegotiation strategies. For instance, a sharing rule could require that the bank that gives in receives a share ␣ < 1/2 of the surplus. Next, consider a variation in the public discovery technology, the density function f. Suppose that ␲ remains constant, and that f is changed to f 1 such that the hazard rate is higher (the term f/(1 − F) on the RHS of Eq. (7)). Assume that this makes the second discovery technology is superior, i.e. it becomes more skewed to the left. The RHS of Eq. (7) becomes more negative, and in order to restore the equilibrium L 2 must become steeper and L 1 must decrease. Proposition 4. Assume that early discovery becomes more likely, such that the hazard rate of the discovery technology f/(1 − F) increases. Then the banks tend to give in earlier. Rescue negotiations can become more difficult to hide, if the disclosure requirements for banks or firms are tightened. The introduction of a new business paper in a region can have a similar effect. The effect of a change in the discovery technology by varying ␲ is similar: an increase in ␲ leads to a reduced stopping time for all types (see Lemma 1). Unfortunately the effect on the likelihood of liquidation is not easy to specify for the general case, as two effects are opposed: the banks stop earlier but discovery becomes more likely. This would be interesting, as one could derive implications for disclosure rules of stock markets, or for the benefits of having a more transparent economy. Consider the following change, however: Proposition 5. Suppose that the support of f is rescheduled such that f 1 (t) = f(␣ · t), where ␣ < 1. Then the banks tend to stop earlier, but the probability of liquidation is unchanged.

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Suppose that the speed of all information channels is increased symmetrically. In this case the moment of sure discovery ␶ has an effect on the stopping time of a bank with cost i = 0, but not on the relative stopping times of the other types (as it does not appear in the derivations). In this case, the improvement of the discovery technology had no material effect. Thus, stricter disclosure requirements can be neutral, and therefore (depending on the parameters) welfare reducing or improving. Similarly, we can analyze changes in the distribution of types. Here the “hazard rate” is somewhat complicated, as the types are revealed “backwards,” i.e. the first types that reveal themselves by stopping are those with high costs i . The “reversed” hazard rate is thus g()/G(). We encounter the same difficulties as in Proposition 4, as we can determine (using the equilibrium conditions (5) and (6)) the effect on the banks’ strategies, but not the effect on the probability of liquidation. Proposition 6. Assume that the probability of being low is higher, such that the “reverse” hazard rate of the type distribution g/G increases. Then the banks tend to give in earlier. This seems to be a surprising result, as one would expect “tougher” banks to hold out longer. However, the result states that a bank with type will stop earlier. This is intuitive, as it must be more pessimistic about its strength relative to other types. The overall effect cannot be determined without making assumptions on the functional forms of f and g. Negotiation costs can easily be introduced to the model. They have been omitted for simplicity, but can be expected to have an effect on rescue negotiations. Examples for such costs are the need to set up a management team which analyzes the firm’s state and the rescue plans (i.e. the opportunity costs of sending bank managers to attend negotiations), legal costs (the costs of hiring lawyers), or the material costs of planning and negotiating (expenses for business consultants and industry experts, travel expenses). Proposition 7. Assume that each bank incurs a continuous cost c per unit of time dt, while the negotiations take place. Then the banks tend to stop earlier than in the case of no costs, and rescues are more likely. Even though this type of bargaining costs reduces the net surplus from a rescue, this material loss has no effect on the banks’ decisions. At each instant, the past costs are sunk, and “bygones are bygones.” However, c has an effect on the decision whether to wait another infinitesimal amount of time. It decreases the expected payoff from waiting, and therefore the banks stop earlier with higher costs. Thus, while the already incurred costs have no effect, the costs

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that have to be incurred if the negotiations continue are relevant for the decision to stop. Finally, the entrepreneurs’ utility functions are relevant. As m, the utility loss that an entrepreneur incurs if his project is liquidated, increases, funds become available for more parameter settings. Thus, there is a use in this model for the stigma that is attached to a business failure. While we do not want to suggest that this is a good way of solving incentive problems, we can conclude from the model that the financing patterns of two regions or industries should be different if bankruptcy is “not a big deal” in one of them, while it has strong negative connotations in the other.

6. CONCLUSIONS This paper studies the difference between single and multiple banking. It concentrates on renegotiation problems, which are shown to be solved better in the case of multiple banking. We assume that entrepreneurs ask banks for loans, such that they can start projects. These may be of a “good” or “bad” type, where the type of a project can be observed by the respective entrepreneur, only. “Bad” projects need refinancing at an intermediate stage, which makes them nonprofitable from an ex ante perspective. However, once the initial loan is lost, refinancing is better than the only alternative, liquidation. A single bank cannot commit not to refinance a bad project, which would keep entrepreneurs with “bad” projects from applying for a loan. Two banks, however, can commit not to refinance with some probability. The reason for this are inefficiencies in the negotiations between the banks, when they have to agree on their respective degree of debt forgiveness. If the probability of liquidation is sufficiently high, entrepreneurs with “bad” projects do not ask for a loan at all. We model the negotiations as a war of attrition. Each of the two banks incurs a privately known loss, if the firm is liquidated, and therefore would like to have it refinanced. Additionally, refinancing is profitable, once the initial loan is sunk. The banks have to agree on how to split the costs and revenues, if they refinance the firm. These negotiations take time, and the longer they last, the more likely it becomes that a rescue becomes impossible (for exogenous reasons). In order to prevent this, the banks plan to “give in” after a while, i.e. to let the opponent pocket the gain from rescuing, only to make sure that the firm is refinanced. There is a unique equilibrium in this game: the higher the potential loss, the earlier a bank decides to give in. The negotiations can last for a while, if both banks’ potential losses are low, and therefore the firm is liquidated with positive probability.

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The model is designed to isolate the advantage of multiplicity for the lenders. We thus abstract from many aspects which are relevant for the choice between bilateral and multilateral finance, as well as for reorganisation procedures. One of these is the tradeoff between single and multiple banking. Bolton and Scharfstein (1996) analyze a case where either single or multiple lending may be optimal, and also derive results for voting rules, as well as for the optimal use of assets as collateral. Similarly, the effects of different bankruptcy laws need further analysis. In the model the two banks decide to share the highest priority rank. It would be interesting to analyze a model in which their claims have different ranks. A further topic for future analysis is whether and how a distressed firm is rescued, if the banks do not enjoy the highest priority rank.

NOTES 1. A simple alternative to the mass point assumption will be discussed below, see Lemma 1. 2. A sufficient condition for uniqueness can be found by inverting ␭2 (␭1 ), and requiring that the slope of this inverse is never equal to the slope of ␭1 (␭2 ). It is, however, difficult to interpret: 2 g(G −1 [s/(2␲ + s)]) 2␲ g() = ∀ ∈ + . [G()]2 [G(G −1 [s/(2␲ + s)])]2 s

REFERENCES Abreu, D., & Gul, F. (2000). Bargaining and reputation. Econometrica, 68, 85–117. Admati, A., & Perry, M. (1991). Joint projects without commitment. Review of Economic Studies, 58, 259–276. Aghion, P., Bolton, P., & Fries, S. (1999). Optimal design of bank bailouts: The case of transition economies. Journal of Institutional and Theoretical Economics, 155, 51–70. Armendariz, B. (1999). Development banking. Journal of Development Economics, 58, 83–100. Bergl¨of, E., & von Thadden, E.-L. (1995). Short-term versus long-term interests: Capital structure with multiple investors. Quarterly Journal of Economics, 109, 1055–1084. Bhattacharya, S., & Chiesa, G. (1995). Proprietary information, financial intermediation, and research incentives. Journal of Financial Intermediation, 4, 328–357. Birckhoff, G., & Rota, G.-C. (1978). Ordinary differential equations. New York: Wiley. Bolton, P., & Scharfstein, D. (1996). Optimal debt structure with multiple creditors. Journal of Political Economy, 104, 1–25. Dewatripont, M., & Maskin, E. (1995). Credit and efficiency in centralized and decentralized economies. Review of Economic Studies, 62, 541–555. Dewatripont, M., & Tirole, J. (1994). A theory of debt and equity: Diversity of securities and manager–shareholder congruence. Quarterly Journal of Economics, 109, 1028–1054.

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Diamond, D. (1984). Financial intermediation and delegated monitoring. Review of Economic Studies, 51, 393–414. Diamond, D. (1993). Seniority and maturity of debt contracts. Journal of Financial Economics, 33, 341–368. Edwards, J., & Fischer, K. (1994). Banks, ﬁnance and investments in Germany. Cambridge: Cambridge University Press. Fernandez, R., & Glazer, J. (1991). Striking for a bargain between two completely informed agents. American Economic Review, 81, 240–252. Fischer, K. (1990). Hausbankbeziehungen als Instrument der Bindung zwischen Banken und Unternehmen. Unpublished doctoral dissertation, University of Bonn. Gertner, R., & Scharfstein, D. (1991). A theory of workouts and the effects of reorganization law. Journal of Finance, 46, 1189–1222. Gilson, S., John, K., & Lang, L. (1990). Troubled debt restructurings. An empirical study of private reorganization of firms in default. Journal of Financial Economics, 27, 315–353. Hellwig, M. (1991). Banking, financial intermediation and corporate finance. In: A. Giovannini & C. Mayer (Eds), European Financial Integration (pp. 35–63). Cambridge: Cambridge University Press. Hoshi, T., Kashyap, A., & Scharfstein, D. (1990). The role of banks in reducing the costs of financial distress in Japan. Journal of Financial Economics, 27, 67–88. Mitchell, J. (1993). Creditor passivity and bankruptcy: Implications for economic reform. In: C. Mayer & X. Vives (Eds), Capital Markets and Financial Intermediation (pp. 197–224). Cambridge: Cambridge University Press. Rajan, R., & Winton, A. (1995). Covenants and collateral as incentives to monitor. Journal of Finance, 50, 1113–1146. Repullo, R., & Suarez, J. (1995). Monitoring, liquidation, and security design. Review of Financial Studies, 11, 163–187. Schneider-Lenn´e, E. (1992). Corporate control in Germany. Oxford Review of Economic Policy, 8, 11–23. von Thadden, E.-L. (1992). The commitment of finance, duplicated monitoring, and the investment horizon. Working Paper, University of Basel. von Thadden, E.-L. (1995). Long-term contracts, short-term investment and monitoring. Review of Economic Studies, 62, 557–575. Yosha, O. (1995). Information disclosure costs and the choice of financing source. Journal of Financial Intermediation, 4, 3–20.

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APPENDIX A: PROOFS Proof of Lemma 1 (A.1) compares the respective payoffs for bank B 1 with valuation ␭1 , given ␭2 : ¯ −J−r R G(␭2 )r 1 + (1 − G(␭2 )) + r1 2 ¯ − r 2 − J) + G(␭2 ) (1 − ␲)(R ¯ − r 2 − J) + ␲(r 1 − ␭1 ) . = (1 − G(␭2 ))(R

(A.1) The left-hand side of Eq. (A.1) is the expected payoff if bank B 1 gives in immediately. With probability G(␭2 ) the opponent has a low valuation and does not give in. The firm is rescued, and the bank receives r 1 . With probability 1 − G(␭2 ) the opponent gives in, as well, and the net surplus is shared (in expected terms). The right-hand side of (A.1) is the payoff if the bank gives in as soon as the war of attrition has started. With probability 1 − G(␭2 ) the opponent has a high valuation ¯ − J, and and will give in immediately. The bank rescues, pockets the surplus R pays r 2 to the opponent. With probability G(␭2 ) the war of attrition starts. It is discovered with probability ␲, and the firm is liquidated. With probability (1 − ␲), the game could continue, but by definition the bank plans to stop, which earns r 1 . Some simplifications of (A.1) and of an analogous equation for bank B 2 lead to the two equations in Lemma 1. There is always an interior solution for the cut-off levels: If ␭i goes to zero, then ␭j (␭i ) goes to infinity, while if ␭i goes to infinity it goes to zero.

Proof of Lemma 2 (i) We first show that T i is nonincreasing, and then that it is strictly decreasing. By utility-maximisation it must be the case that V1 (t 1 , T 2 (·), 1 ) ≥ V1 (t 1 , T 2 (·), 1 )

∀t 1 ,

∀t 1 = T 1 (1 )

(A.2)

V1 (t 1 , T 2 (·), 1 ) ≥ V1 (t 1 , T 2 (·), 1 )

∀t 1 ,

∀t 1 = T 1 ( 1 ),

(A.3)

and

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where Vi (t i , T j (·), i ) is the expected payoff of bank B i with cost level i , if it stops at t i , and bank B j plays strategy T j (·): Vi (t i , T j (·), i ) = Pr{T j (j ) ≥ t i } (F(t i )(r i − i ) + (1 − F(t i ))r i )

¯ − r j − J) + F(T j (j )) r i − i − (R {j |T j (j )
¯ − r j − J) g(j ) dj . + (R

(A.4)

The payoff of a bank depends on the chosen stopping time t i , the opponent’s strategy T j and the (privately known) loss i of losing the firm. With probability Pr{T j (j ) ≥ t i } the opponent plans to stop later than t i . If the public discovered the negotiations (this happens with probability F(t i )), the payoff is (r i − i ). If the secret was kept well, the bank receives r i from bank B j who rescues the firm. The second term of Eq. (A.4)is the equivalent if the opponent plans to stop earlier. Here ¯ − J) if the firm can be rescued and pays r j to the opponent. the bank receives (R We can rewrite the two inequalities Eqs (A.2) and (A.3) using Eq. (A.4). Subtracting the RHS of Eq. (A.3) from the LHS of Eq. (A.2), and the LHS of Eq. (A.3) from the RHS of Eq. (A.2), we get F(T 2 (2 ))( 1 − 1 )g(2 ) d2 Pr{T 2 (2 ) ≥ t 1 }F(t 1 )( 1 − 1 ) + {2 |T 2 (2 )
≥ Pr{T 2 (2 ) ≥ t 1 }F(t 1 )( 1 − 1 ) +

{2 |T 2 (2 )
F(T 2 (2 ))( 1 − 1 )g(2 ) d2

or, rearranging, [(1 − Pr{T 2 (2 ) < t 1 })(F(t 1 ) − F(t 1 ))]( 1 − 1 ) ≥ F(t 1 )g(2 ) d2 − {2 |t 1
{2 |t 1
F(T 2 (2 ))g(2 ) d2

× ( 1 − 1 ). If t 1 > t 1 , the following holds: (1 − Pr{T 2 (2 ) < t 1 })(F(t 1 ) − F(t 1 )) ≥0≥ [F(t 1 ) − F(T 2 (2 ))]g(2 ) d2 , {2 |t 1
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and it must be the case that 1 ≥ 1 . On the other hand, if t 1 > t 1 : (1 − Pr{T 2 (2 ) < t 1 })(F(t 1 ) − F(t 1 )) ≥ Pr{t 1 < T 2 (2 ) < t 1 }(F(t 1 ) − F(t 1 )) ≥ [F(t 1 ) − F(T 2 (2 ))]g(2 ) d2 , {2 |t 1
and it must be the case that 1 ≥ 1 . Thus for all t 1 , t 1 , in equilibrium ( 1 − 1 ) · (t 1 − t 1 ) ≤ 0, i.e. the strategies are nonincreasing in the liquidation loss. Assume that T 1 is not strictly decreasing, i.e. there are a , b > a , such that for all ∈ [a , b ], T 1 () = ␪. Then there is an ␧ > 0 such that all types 2 with T 2 (2 ) ∈ (␪ − ␧, ␪] prefer to wait until ␪ and stop then, if the opponent did not stop. Then the types ∈ [a , b ] could gain by stopping at ␪ − ␧ instead of ␪: The probability of winning is not affected, but the risk of losing is diminished. (ii) Assume that T 1 is discontinuous at . Then there are t a , t b > t a such that a type never stops at any t ∈ (t 1 , t 2 ). A type 2 with T 2 (2 ) ∈ [t a , t b ) would thus wait only until t a , and stop if the opponent did not stop. This implies that no one stops at any t ∈ (t a , t b ). But then there are types ˆ 1 and an ␧ > 0 such that T 1 (ˆ 1 ) ∈ [t b , t b + ␧], who prefer stopping at some t ∈ (t a , t b ). (iii) Assume that T i is not differentiable at . (a) Let the left-hand derivative be higher than the right-hand derivative (T i is flatter to the left of ). Then there is an ␧ > 0 such that no type j stops at any t ∈ (T i () − ␧, T i ()]. It pays to wait longer since after the point of discontinuity it becomes relatively likely that the opponent stops. This holds since both f and g are continuous and differentiable. (b) Let the right-hand derivative be higher. Then there is an ␧ > 0 such that no type j stops at t ∈ [T i (), T i () + ␧). It pays to stop earlier since it becomes more likely that B i stops immediately after T i (). In both cases T j is not continuous, contradicting (ii) above. (iv) If type 1 = 0 stops at ␪ < ␶, all types with higher loss level stop earlier because of Lemma 2(i). Then in equilibrium no type of the other bank should stop later than ␪. There is an ␧ > 0 such that types 1 ∈ (0, ␧] find it profitable to wait until ␪ and wait for the opponent to stop. Proof of Proposition 1 The differential equations are Lipschitz-continuous on [2, ␶] which implies that a solution exists and is unique (see e.g. Birckhoff & Rota, 1978, Chap. 6). At each

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t ∈ [2, ␶], the (expected) payoffs from stopping or non-stopping can be compared, as was done in deriving Eq. (5). Since the strategies are strictly decreasing, at t < T 1 (1 ), i.e. if L 1 (t) > 1 , the payoff to bank B i with loss level 1 will be higher if it waits. The opposite holds for L 1 (t) < 1 . For all t ≥ t 1 , type L 1 (t 1 ) can only decrease his payoff by waiting, and will stop whenever possible. The players constantly update their beliefs using Bayes’ Rule. If a player stops at the wrong time (this is the only deviation that is possible) the opponent will have no difficulties in updating his beliefs: If a player stops too early, the game is over and beliefs are not relevant anymore. If a player waits too long, the strategy tells him to stop immediately: Type i stops at any time t if t > T i (i ). Again, the opponent can update his beliefs without problems.

Proof of Proposition 2 Follows directly from the Assumptions and Proposition 1.

Proof of Proposition 3 The reaction curves L i (see Eq. (7)) are shifted outward, if s is increased. The indirect effect via the cut-off value ␭ goes in the same direction: ␭i (␭j ) is shifted outward, as well (see Lemma 1).

Proof of Propositions 4, 5 and 6 As Proposition 3: analyze the equilibrium conditions Eqs (5) and (6), and the indirect effect via the cutoff value ␭ in Lemma 1.

Proof of Proposition 7 Equation (7) is changed to −1 L 2 (t 1 ) = G G(␭)exp − 2

t1

f(t) 1 − F(t)

L 1 (t) c + dt . s s

(A.5)

A comparison of Eqs (A.5) with (7) shows that all types will want to stop earlier, including zero-cost types.

OPPORTUNITY COST AND PRUDENTIALITY: AN ANALYSIS OF COLLATERAL DECISIONS IN BILATERAL AND MULTILATERAL SETTINGS Herbert L. Baer, Virginia G. France and James T. Moser ABSTRACT This paper develops a model that explains how the creation of a futures clearinghouse allows traders to reduce default and economize on margin. We contrast the collateral necessary between bilateral partners with that required when multilateral netting occurs. Optimal margin levels balance the deadweight costs of default against the opportunity costs of holding additional margin. Once created, it may be optimal for the clearinghouse to monitor the ﬁnancial condition of its members. If undertaken, monitoring will reduce the amount of margin required but need not affect the probability of default. Once created, it becomes optimal for the clearinghouse membership to expel defaulting members. This reduces the probability of default. Our empirical tests suggest that the opportunity cost of margin plays an important role in clearinghouse behavior particularly their determination of margin amounts. The relationship between volatility and margins suggests that participants face an upward-sloping opportunity cost of margin. This appears to dominate the effects that monitoring and expulsion might have on margin setting.

Research in Finance Research in Finance, Volume 21, 201–227 © 2004 Published by Elsevier Ltd. ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21009-7

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The field of competition . . . consists of all the individuals who are willing and able to recontract about the articles under consideration. F. Y. Edgeworth

1. INTRODUCTION AND LITERATURE REVIEW Contract terms that specify posting of collateral effect a limit on the exposure to loss from counterparty nonperformance. This outcome is obtained in two ways. First, seizure of deposited collateral inherently reduces losses resulting from contract nonperformance. Second, posting of collateral encourages contract performance.1 This paper studies decision making for instances where collateral requirements are costly. We show that cost-avoidance within a competitive market reliably predicts certain outcomes.

1.1. Introduction Brennan (1986) employs the Theory of Efficient Contract Design to model the price limits employed by futures exchanges. The theory explicitly recognizes the influence of cost-minimization incentives for the contract terms developed by exchanges. In that setting, he shows that price limits lessen contract nonperformance. Improvements in contract performance enable reductions in required collateral. Those reductions, in turn, lower contracting costs. This paper applies the Theory of Efficient Contract Design first to model the determination of collateral required from contracting counterparties. We then extend this result to highlight how reducing credit risk affects contract terms. Futures exchanges specialize in providing facilities for designing and exchanging contracts. Their interest in successful trading of contracts makes these organizations a logical source for empirical examination of the hypotheses suggested by our model. Our empirical analysis discriminates among competing representations of an exchange’s margin decision by examining margin coverage ratios – required margin divided by a forward-looking measure of volatility. In the first, the marginal opportunity cost of margin requirements is constant. The second allows for increasing costs for margin funds. Both time series and cross section evidence is developed. Our model predicts margin adjustments when margin coverage is too high (and too expensive) or too

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low (and too risky).2 Time series evidence concludes that coverage ratios increase (decrease) when coverage ratios are lower (higher) than their unconditional means. Examining a cross section of margin-coverage ratios, we find that the opportunity cost of margin deposits significantly influences the level of magin required from exchange members. Our regressions suggest a negative relationship between economy-wide shifts in the opportunity cost of margin deposits and levels of margin coverage. In addition, we find a negative relationship between margin coverage and participant-specific shifts in participants’ borrowing needs as proxied by levels of implied standard deviation. These suggest that opportunity costs are important and that market participants face upward-sloping schedules of opportunity costs for their margin deposits.

1.2. Literature Review We advance the theory of margins by explicitly incorporating the cost of margin deposits into the margin-setting decision. This establishes a tradeoff between these costs and prudential concerns. Further examination of this tradeoff gives insight into the effect of clearinghouse activities on its margin-setting decisions. Craine (1997) models the clearinghouse as a profit-maximizing entity and describes margin in terms of options to default. He contends that, since the clearinghouse charges no default premia, it must keep premium values at or close to zero. Our model, by contrast, argues that the values of default premia and counterparty risk offset across agents. Fenn and Kupiec (1993) also implicitly assume that the clearinghouse is an independent cost-minimizing entity. Their clearinghouse minimizes the sum of margin costs, settlement costs, and costs incurred when deficits arise in clearinghouse accounts. The clearinghouse sets the probability of a deficit equal to the ratio of opportunity costs per settlement period to the marginal cost of an account deficit. As volatility increases, increasing settlement frequency lowers this sum, and the margin-to-volatility ratio declines. We model the clearinghouse as a club that minimizes the joint costs of its members. In our formulation, the clearinghouse need not make a profit, nor even recoup any deadweight losses incurred by its membership because members willingly subsidize the clearinghouse to avoid the greater cost of a bilateral arrangement.3 Neither Craine nor Fenn and Kupiec provide motivation for clearinghouse development. Our model results for expulsion and the value added by clearing activities match those of Bhasin and Brown (1997). They model the value of exchange seats as stemming from trading activity. Their model analyzes intra day default incentives.

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They show that the values of exchange seats secure under-margined positions held during the day. Their model complements ours by explaining the dynamics of collateralizing against default during the trading day. We develop the monitoring activities of exchanges as part of their intermediating role. In this respect, the model resembles the delegated monitoring described by Diamond (1984), and the modeling of risk management and financial guarantees by Merton and Bodie (1992) and Hsieh (1993). We extend the earlier work by explicitly incorporating certain institutional features of clearinghouses. These features include expulsion from the clearinghouse, clearinghouse monitoring of members’ financial condition and the possibility that members face increasing costs for external funds. These have very different effects on optimal margin setting and the probability of default. Our model also parallels Gorton’s (1985) modeling of bank clearinghouses, particularly concerning expulsion and risk mutualization.

2. DETERMINING COLLATERAL FOR BILATERAL CONTRACTS We first model the setting of collateral requirements in a bilateral marketplace. Two parties j and h negotiate contracts for their own accounts but are unable to compel contract performance. Contract nonperformance, that is, failure to fulfill contractual terms always entails deadweight loss.4 These deadweight losses include costs of recontracting, higher borrowing costs that arise from liquidity problems, and costs arising from financial distress. Recovery against losses is limited to collateral deposited by the defaulting counterparty. We assume that a default-free trustee holds collateral deposits. Counterparties posting collateral with the trustee bond their contract performance. There are two periods. In the opening period, the two parties enter a contract with each other. The motivation for trading is exogenous to our model; however, our model does imply that cost reductions increase whatever benefits trading provides. Let N(j, h) denote the number of contracts outstanding between j and h. If N(j, h) is positive, j holds a long position in the contract. If N(j, h) is negative, then j’s position in the contract is short. Contra-positions are held by h, so that N(h, j) = −N(j, h). The contract settles at the contract’s next-period price or, at contract expiration at the value of the underlying good. The distribution of this price has a zero mean and finite standard deviation of ␴.5 Collateral posted by j with h is denoted M(j, h), and that posted by h with j is denoted M(h, j). Collateral are cash deposits held in interest-bearing accounts. Interest on deposits is paid to its respective depositor.6 At the end of period

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two, the contract is settled. If x is positive and less than M(h, j), x is transferred from the account of the short to the account of the long. Thus the short now has M(h, j) – x; the long now has M(j, h) + x. If x is negative and |x| is less than M(j, h) then x is transferred from the long to the short. After contracts are settled, traders immediately restore their collateral-account balances to M(j, h) and M(h, j), by either depositing cash when they are on the losing side or withdrawing excess balances on gains. These account adjustments restore equal values for the default options and counterparty risk of both counterparties. Figlewski (1984) shows that contract counterparties implicitly give each other options to default. In the simplest case, contract default occurs whenever losses exceed margin-account balances. Thus, if x is positive and greater than M(h, j), the short rationally defaults on the contract and the long takes possession of the margin assets M(h, j). Similarly, if x is negative and |x| is greater than M(j, h), the long rationally defaults and the short takes possession of the margin assets M(j, h). Remaining losses include recontracting costs, higher borrowing costs arising from liquidity problems, and costs of financial distress. These are deadweight losses. Agent j’s expectation of these losses is: D(j, h) = ␣N

∞ M(h,j)

(x − M(h, j)f(x, ␴) dx)

(1)

where N is the net number of contracts j has open with h; i.e. the absolute value after summing across N(j, h). Agents jointly minimize the cost of contracting as would be obtained in a perfectly competitive market. This is realistic provided agents freely choose among a large number of counterparties each willing to minimize joint contracting costs. Post-trade bargaining problems are included in the cost-recovery factor subsumed in ␣. Proposition I. Collateral amounts are optimal when the default probability equals the ratio of the opportunity cost for posting additional collateral to the deadweight loss rate. Contracting entails three costs: the total opportunity cost of margin deposits I(j); counterparty risk, that is, the expected difference between the promised and the actual payment when h defaults on j, L(j, h); and expected deadweight losses incurred when h defaults on j, D(j, h). Offsetting these costs, each party also receives an option to default O(j, h). The two parties jointly minimize the

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following costs: I(j) + I(h)

Opportunity Costs

D(j, h) + D(h, j) Deadweight Losses L(j, h) + L(h, j) Counterparty Risk O(j, h) + O(h, j) Default Options

(2)

Default involves both a loss to one party and a corresponding gain to the other. Alternately stated, one party’s default option is another party’s counterparty risk, that is, that L(j, h) = O(h, j). In our representative-agent framework, the expression for joint contracting costs reduces to: I(j) + I(h) + D(j, h) + D(h, j)

(3)

The first order conditions for minimization of (3) with respect to M(j, h) and M(h, j) are: i i [1 − F(M ∗ (j, h), ␴)] = and F(M ∗ (j, h), ␴) = (4) ␣ ␣ where i is the opportunity cost for an additional dollar of margin. Equation (4) implies that counterparties optimally collateralize when their default probabilities equal their ratios of opportunity cost of additional margin to their deadweight loss rate. The higher this ratio, the lower is the optimal collateral level. Nonzero collateral requirements are optimal when i/␣ < 1. Should i/␣ exceed unity, counterparties set margin at zero, the losing trader always defaults, and contracts are unenforceable. Since the objective function is linear in the number of contracts, the opportunity cost of additional margin is constant. This implies that the collateral per unit of exposure is independent of the aggregate level of exposure, and that collateral amounts can be set on a per-contract basis. Further, if the distribution of price changes is symmetric, equal collateral amounts are required for both long and short positions. Proposition II. when the distribution of price changes is uniquely invertible and the opportunity cost of collateral deposits is constant, optimal coverage ratios do not vary with volatility. When a unique inverse exists for the price-change distribution depicted in Eq. (4), the coverage ratio giving the level of collateral to exposure to price changes is: M∗ i −1 =F ,1 (5) ␴ ␣ Inspection of (5) confirms that margin increases proportionately with ␴.

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This implies that optimal coverage ratios do not vary with volatility. For instance, Proposition II holds if the distribution of price changes is normal.

3. DETERMINING COLLATERAL FOR A MULTILATERAL CLEARINGHOUSE This section models a clearinghouse acting solely as a netting facility.7 We establish the benefits from clearinghouse arrangements within a framework that regards the clearinghouse as a club of its members, not as a separate, for-profit agency. We then model the margin-level choices made by clearinghouses as balancing the deadweight losses from counterparty defaults against opportunity costs incurred by posting margin. Although depositing interest-bearing assets can fulfill margin requirements, we argue that opportunity costs are nonzero when the firm’s marginal borrowing cost exceeds the return on its marginable assets.8

3.1. The Intermediary Role of a Clearinghouse Clearinghouses intermediate by substituting themselves as contract counterparties. This achieves certain economies by reducing both deadweight default costs and the opportunity costs of holding assets in margin accounts. We represent the clearinghouse acts as a club, that is, a voluntary organization that furthers the joint interests of its members by internalizing certain shared costs. This approach is more general than the standard profit-maximizing framework in that the model can be modified to represent the heterogeneous interests generally found within exchange organizations. Clearinghouse members minimize their joint contracting costs by committing to rules that allocate contract-default losses among themselves. Many loss-sharing rules are consistent with this objective function. Importantly, the model is consistent with the industry practice of paying for losses from a clearinghouse guarantee fund, in effect sharing losses pro rata among clearing members.9 Proposition III. If members have the same i and ␣, the clearinghouse sets margin at the same level as though contracts were cleared and settled bilaterally. Let party j’s open interest nh=1 N(j, h) be denoted by N(j). If we assume that f, the distribution of price changes, is symmetric then the clearinghouse chooses

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M(j, h) to minimize joint contracting costs of: ∞ n |N(j)| iM(j) + ␣ (x − M(j))f(x, ␴) dx j=1

M(j)

(6)

In our representative framework, i and ␣ are the same for all members and the solution to this problem is given by Eq. (4). Thus, per contract, margin will be the same whether contracts are cleared and settled bilaterally by counterparty pairs or multilaterally through a clearinghouse. We argue this representative-agent framework serves as a useful starting point in the following sense. Exchanges screen members for their financial ability to fulfill contracts. That effort tends to reduce member heterogeneity in their credit risk dimensions. Later sections of the paper consider the monitoring efforts undertaken by exchanges as they attempt to retain low levels of heterogeneity. Because a clearinghouse will set the same margin rate that these agents willingly negotiate between themselves, analyzing the benefits derived from forming a clearinghouse is straightforward. The essential benefit of the clearinghouse is that it permits its members to economize on margin while also reducing expected deadweight losses. Clearinghouses economize on margins and deadweight loss because, for the same set of contracts, participants’ net positions are less risky. Consequently, total margin deposits required by the clearinghouse are smaller than totals required for a comparable set of bilateral transactions. In addition, pro rata expected deadweight losses are also smaller. Proposition IV. Total margin deposits posted by each member will be the same or lower under a clearinghouse system than under a system of bilateral collateral deposits. Under a clearinghouse system, j posts margin against the net of his position with the rest of the market, that is M |N(j)|. In effect, a multilateral clearinghouse secures the losing positions of a potential defaulter with its winning positions. That is, members are prevented from “cherry picking” among their contracts realizing gains while defaulting on those contracts where losses have been realized. The margin posted by each member will be the same or lower under a clearinghouse system. Proposition V. Under an appropriate loss-sharing arrangement, total expected deadweight losses are lower under a clearinghouse system than under a system of bilateral collateral deposits. Similarly, no counterparty’s expected deadweight loss is greater under a clearinghouse system and for some expected deadweight losses will be smaller.10

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In a bilateral system, j’s expected loss from counterparty default is proportional to the number of their open contracts; that is nh=1 |N(j, h)|. Member j benefits by joining a multilateral clearinghouse that keeps default-loss exposure proportional to net open contracts; that is, proportional to |N(j)|. Other loss-sharing arrangements can also achieve this result.

3.2. Increasing Opportunity Cost of Funds The cost of funds function may be increasing as the amount of required margin increases. Thus, an increase in margins drives up the marginal cost of funds. Proposition VI. Where the marginal cost of funds is increasing, the optimal coverage ratios decrease with volatility when prices are normally distributed and the opportunity cost of margin assets is increasing. If marginal costs of margin are increasing in M then: i = ␳(M); ␳ (M) > 0

(7)

and the clearinghouse sets margin to meet the condition: ␳ (M) = [1 − F(M, ␴)] ␣

(8)

An increase in ␴ now causes the clearinghouse to increase margin less than proportionately with ␴. As the standard deviation increases, the clearinghouse increases margin levels to keep the probability of default constant. However, doing so drives up the members’ marginal financing costs. The members of the clearinghouse therefore choose to bear greater deadweight losses to economize on their financing costs. Thus, coverage ratios should decrease with volatility. Note that, even if their cost functions are identical, individuals holding different numbers of contracts may have different marginal costs of funds. In addition, unlike the agents of the previous section, the slope and level of member cost functions may differ. This will result in disagreement among members as to appropriate margin levels, though each will have only one preferred margin level. The club literature suggests that in decisions made by diverse interests, majority rule reflects median voter preferences provided individuals have single-peaked preferences.11 For such preference structures, relevant marginal costs are those of median voting members. Severe disagreement about appropriate margin levels will lead some traders to avoid becoming a member of the clearinghouse, of these some may seek economies through other arrangements.

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4. TESTS OF THE MODEL The modeling of the previous sections suggests three hypotheses for clearinghouse determination of required margin. The first of these is a positive relationship between margin levels and risks stemming from the contracts. Baer, France and Moser (1995b) provide supporting evidence for this result. The second is that clearinghouses incorporate the cost of maintaining margin balances into their margin-level decisions. Thus, we can expect a negative correlation between margin levels and the opportunity costs of clearinghouse members. Our remaining hypothesis relates to coverage ratios, predicting that coverage ratios are invariant to risk levels when members have constant costs while increasing costs imply a negative correlation between coverage ratio and risk level.

4.1. Description of the Sample Data Set Margin data are from the clearing organizations for eighteen contracts trading on the following futures exchanges: the Chicago Board of Trade, the Chicago Mercantile Exchange, the Coffee, Sugar and Cocoa Exchange, the Commodity Exchange, and the New York Mercantile Exchange. These eighteen contracts are the most heavily traded contracts having options on the underlying futures contract. During the sample period, with the exception of contracts listed by the New York Mercantile Exchange, exchange affiliation was the basis for determining margin requirements. The speculative positions of non-clearing members are assessed the highest levels of margin.12 The initial margin requirement for clearing members is usually the same as the initial margin amount for the hedge positions of non-clearing members. Finally, the maintenance margin requirements of clearing members are the same as their initial requirements. Thus, our assumption that periodic settlement restores the account to the level M gives a lower bound for a clearing member’s margin account. Members must always have at least the amount of the current initial margin, and may choose to allow excess balances to remain in the account. Table 1 summarizes our sample. Listed under each exchange are the contracts trading on that exchange. The start date is the first date used in the sample; generally, this is the beginning of options trading on the respective futures contracts. In each case, the sample extends through June 1991. Sample dates are the last Thursday of every contract month. The number of available observations ranges from 29 for the Treasury bond and Deutschemark contracts to 15 for the Heating Oil contract. We report mean margin levels for positions classed as initial nonmember speculative

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Table 1. Margins and Implied Volatilities. Contract

Sample Start Date

Number Observations

ISD

Sample Means Speculative Margin

Member Margin

Margin

Coverage

Margin

Coverage

Chicago board of trade Corn 3/85 Soybeans 12/84 Treasury bond 3/84 Wheat 3/87

26 26 29 16

0.21 0.16 0.11 0.21

520.58 1396.38 2618.97 725.31

5.10 5.61 5.32 4.38

353.85 1067.31 2120.69 543.75

3.38 4.20 4.27 3.24

Chicago mercantile exchange British Pound 3/85 Deutschemark 3/84 Eurodollar 3/85 Japanese Yen 6/86 Live Cattle 12/84 Swiss Franc 3/85 S&P 500 3/84

26 29 17 21 23 26 26

0.12 0.12 0.01 0.10 0.14 0.12 0.17

2197.23 1864.17 925.00 2069.67 756.78 2111.38 11134.62

5.44 5.45 7.06 4.90 4.02 4.81 10.17

1938.46 1689.66 823.53 1788.10 619.57 1875.00 4865.38

5.02 5.01 6.07 4.24 3.29 4.25 4.56

Coffee, sugar and cocoa exchange Coffee 12/87 15 Sugar 3/85 26

0.30 0.53

2733.33 1209.62

5.25 5.46

1366.67 604.81

2.62 2.73

Commodity exchange Copper 6/86 Gold 3/84 Silver 12/84

20 28 27

0.30 0.16 0.24

1734.50 1692.46 2004.52

4.81 5.34 5.55

1355.00 1253.57 1585.00

3.66 3.95 4.10

New York mercantile exchange Crude oil 12/86 Heating oil 9/87

19 15

0.36 0.37

2284.21 2293.33

7.53 6.79

2284.21 2293.33

7.53 6.79

Note: Table reports summary statistics for a sample of futures contracts. Start date is the first sample date. Mean margin is the average of initial speculative or initial member margin required on the sample dates. Mean ISD is the average implied standard deviation for options trading on the sample dates. Margin coverage is respective mean level of margin divided by the dollar volatility of the contract.

and for clearing members (or nonmember hedgers) on the above-indicated sample dates. For each sample date, we impute volatilities for the respective contracts. The needed data are from various issues of the Wall Street Journal. These data are: prices for call options expiring in the next delivery month at each strike price traded on that date, futures settlement prices for corresponding delivery months, and Treasury bill rates with maturities most closely matching the time until expiration of the option contracts. The Barone-Adesi and Whaley (1987) model was used to impute

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volatilities for each of the option contracts. For each contract, we calculate a time series of representative implied standard deviations (ISDs) on each sample date using a Taylor-series approximation based on iterated regressions as described by Whaley (1982). The table reports mean ISDs. These range from a low of 0.01 for the Eurodollar contract to 0.53 for the sugar contract.13 Margin coverage ratios divide the respective margin amounts by dollar-price volatility. Dollar-price volatility is the product of the ISD and the notional value of the contract – futures prices times number of deliverable units – after adjusting the annualized volatility for the length of the holding period. This gives a marketbased forecast of holding period volatility. Dividing initial speculative and member margin requirements by their respective dollar volatilities gives coverage ratios. Columns 6 and 8 list mean coverage ratios for the member and nonmember categories. The peak of the frequency distribution for mean nonmember speculative margin coverage ratios is about five. This implies that margin levels most often cover five times the expected single-day price deviation. Comparison of the means of nonmember speculative and member margin requirements reveals that clearing members’ margin is about 80% of that for speculative positions. The exception is the New York Mercantile Exchange where they are equal. Notably, the coverage ratio for the S&P 500 contract well exceeds the typical level obtained for nonmember speculative positions, averaging 10.17 during the sample period. In contrast to the coverage obtained by nonmember margin levels, the S&P 500 members’ margin, generally around four, is within the range obtained for other contracts. The difference between coverage ratios for the S&P and other nonmember speculative margins probably reflects considerations unique to the sample period. Market breaks in 1987 and 1989 increased debate over the need for regulatory intervention in the determination of stock-index margin requirements may have resulted in higher margins than the clearinghouse would have set for purely prudential reasons. The contrast between margin for the S&P contract and the others is more noticeable on recognizing that during part of this period, the S&P 500 contract settled twice per day. Other contracts settled only once per day throughout the period. Since we calculate coverage ratios with daily standard deviations, the coverage ratio for the S&P 500 should be smaller, not larger. Other things equal Fenn and Kupiec’s (1993) analysis suggests coverage ratios should be approximately half as large. Assuming price changes are normally distributed, the coverage ratios for clearing members imply that the probability of a price change exceeding required margin from one settlement period to the next is much less than 1%. The “excess” of coverage suggests that actual distributions are kurtotic, a result that is consistent with the findings of Kofman (1993).

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4.2. Time-Series Evidence We use daily data for four of the eighteen contracts to gain further insight into the margin-setting process. These contracts are: Deutschemark, S&P 500, Soybean and Treasury Bond. Daily implied volatilities, computed as previously described, were matched with required margin levels on these dates and margin coverage ratios computed. We examine the time series of these quantities. The first test considers whether the coverage ratio for a contract tends to revert to its long-run, unconditional mean. Denoting coverage ratios CRt , our model implies that shocks to these ratios initiate intervention that restores them to desired levels. Specifically, prudential concerns dictate that coverage ratios regarded as too small should lead to increasing margin coverage and opportunity cost concerns dictate that excessively large ratios lead to reducing margin coverage. Our model equilibrates these pressures, and predicts a mean-reverting time series of coverage ratios. We employ the augmented Dickey-Fuller (ADF) procedure to consider this hypothesis. Changes in coverage ratios are regressed on the first lag of their levels and lags of changes in the coverage ratio. The specification is: CRi,t = ␣i,0 + ␣i,1 CRi,t−1 +

K

␣i,1+j CRi,t−j + u i,t

(9)

j=1

The number of lags – K – is determined by comparing Akaike’s Information Criterion (AIC) at various lag lengths, choosing the lag length that obtains the largest AIC value. The test examines the coefficient on the lag level, employing Fuller’s (1976) critical values: −1.95 at the 5% level and −2.58 at the 1% level. Table 2 reports the results of these tests. Coefficient t statistics below these critical values suggest mean reversion in the series. We find evidence of mean reversion at the 1% level or better in every case. Evidence of mean reversion in coverage ratios can be the result of mean reversion in volatilities. Although substantial research finds evidence that the volatility of returns on financial assets is nonstationary,14 in our sample volatility appears to be stationary. We examine the possibility that the mean reversion in coverage ratios is caused by mean reversion in volatility by comparing the mean half lives from coverage-ratio shocks to the half lives for volatility shocks. From Eq. (9), the mean half-life from a coverage-ratio shock is given by 1 − log(2)/log(␣i,1 ). Substituting for the CR variables in (9) with the respective volatilities – these are the denominators of the coverage ratios – gives the half-life for a shock to volatility. Halflives are computed for two standard errors above and below the

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Table 2. Estimates of Margin Coverage Adjustment. CRt = ␣0 + ␣1 CRt –1 +

K

i=1 ␣1+i CRt –i

+ ut

Initial Member Margin Contract

␣1

t(␣1 )

−0.004579 −3.52 −0.004704 −2.88 −0.012160 −4.04 −0.017178 −6.84 CRt = ␣0 + 4l=1 ␣l1 Q l CRt –1 + K i=1 ␣4+i CRt –i + u t Deutschemark S&P 500 Soybean Treasury Bond

Quartile Rankings of Margin Coverage at Time t − 1 Contract

Deutschemark S&P 500 Soybean Treasury Bond

Lowest Quartile

Second Quartile

Third Quartile

Highest Quartile

␣1

t(␣1 )

␣1

t(␣1 )

␣1

t(␣1 )

␣1

t(␣1 )

−0.0135 −0.0438 −0.0277 −0.0408

−3.18 −4.47 −2.12 −5.96

−0.0084 −0.0417 −0.0265 −0.0389

−2.58 −5.25 −2.88 −6.48

−0.0097 −0.0239 −0.0200 −0.0356

−3.43 −4.44 −2.91 −6.55

−0.0090 −0.0233 −0.0180 −0.0321

−3.78 −5.35 −3.49 −6.83

Note: Table reports results for the two time series specifications listed below. CRt is the time-t ratio of initial member margin to the option-implied volatility stated in dollars. Ql is the coverage quartile for margin coverage during the sample period. K, the number of lagged changes in coverage ratio included in the specification, is determined by AIC. Critical values are from Fuller (1976): −1.95 at the 5% level and −2.58 at the 1% level. Lower values of t are indicative of reversion to the mean; i.e. rejects the null of no mean reversion.

coefficient estimates from the volatility specification and for the coverage-ratio specification. In no case do these ranges overlap. Hence, we reject the alternative hypothesis that adjustments to coverage ratios stem from volatility reverting to its long-run mean rather than from exchange action.15 We can be confident at the 5% level that exchanges actively adjust margin levels in response to coverage-ratio shocks. We extend these tests to detect if reversion to the mean is more rapid when coverage ratios are above or below their long-run averages. The prudential hypothesis of previous authors such as Gay, Hunter and Kolb (1986) predicts that clearinghouses respond to low coverage ratios by raising margin requirements. Previous models of prudentiality do not predict clearinghouse response to shocks resulting in excess margin coverage. In contrast, the model of this paper predicts that a high cost of margin coverage induces clearinghouses to lower margin coverage with the provision that they meet prudentiality objectives. The ADF test

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is modified to test for differential slopes on the lagged level of the coverage ratio. Quartiles are determined for the sample of coverage ratios and indicator variables, denoted Ql , used to classify observations into quartiles. Lagged coverage ratios are interacted with quartile-indicator variables to measure differential responses by the clearinghouses. This specification is: CRt = ␣0 +

4 l=1

␣l1 Q l CRt−1 +

K

␣i CRt –i + u t

(10)

j=1

We report these results in the lower panel of Table 2. Most coefficients differ reliably from zero. The exception is the speculative margin requirement of the soybean contract where response to low coverage ratios has the correct sign but is not statistically significant. However, in every case, coefficients on the highest quartile classification differ reliably from zero. This is consistent with clearinghouse policies that lower margin requirements when margin coverage ratios exceed their long-run averages and implies an internalization of the costs of high margins born by the exchange membership. Fenn and Kupiec (1993) predict a similar cost internalization. Comparing the coefficients on the low and high coverage quartiles adds evidence for the presence of tradeoffs between prudentiality and margin costs. Coefficients that are larger (in absolute value) imply quicker responses to shocks to the coverage ratio. In every case, the coefficients on the low-coverage quartiles are larger in absolute value than those on the high-coverage quartiles. This implies that these clearinghouses respond more quickly to surety lost when coverage ratios decline than to the increase in costs borne by clearinghouse members when coverage ratios rise.16

4.3. Pooled Cross-Section Time Series Analysis The opportunity cost of margin is the difference between the cost of financing an additional dollar of margin assets and the return on those assets. If margin deposits were non-interest-bearing cash, movements in firms’ short-term borrowing costs would suitably measure changes in the opportunity cost of margin. However, members most often fulfill margin requirements with securities or standby letters of credit. For securities, the appropriate measure of opportunity cost is the riskadjusted difference between the yield on the margin assets and an additional dollar of credit. During our sample period, the sampled exchanges accepted government and agency-debt securities as margin, Treasury bills being the most widely posted form of margin.17

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Ideally, we need a time series on the spread between the risk-adjusted borrowing costs of market participants and rates on Treasury bills. Lacking this, we adopt a proxy for the cost of borrowing. The proxy should capture economy-wide shifts in the borrowing costs. In addition, borrowing-cost changes should be correlated across borrowers even though members may be at different points on their respective credit supply curves. Commercial banks are a significant source of credit to futures market participants. Consequently, the prime rate measures credit costs. When the prime rate rises, firms with prime-based loan agreements experience a change in borrowing costs. To isolate credit premia we use differences between the prime rate and the Treasury bill rate to represent changes in the opportunity cost of margin. Our model implies a negative correlation between coverage ratios and volatility levels when members face inelastic supplies of external finance. Holding constant the coverage ratio, open interest, and the other assets of clearing members, a volatility increase implies higher margin deposits and greater reliance on external finance. With an upward-sloping supply of external funds, a higher margin requirement raises the opportunity cost for margin deposits. A clearinghouse which is optimizing as our model suggests will respond to this higher opportunity cost by reducing its coverage ratios. Thus, a constant cost for borrowing implies a positive correlation between volatility and individual member borrowing costs. Hence, our model implies a negative correlation between volatility and coverage ratio. This discussion suggests the following test specification: CRit = ␣0i + ␣1 R t + ␣i2 ISDit + ␮it

(11)

where i denotes the ith contract, Rt is a proxy variable capturing variation in the opportunity cost of borrowing from economy-wide changes in bank financing, and ISDit is the implied standard deviation for the particular contract. Including these implied standard deviations incorporates both intertemporal and crosssectional differences in market participants’ opportunity cost that might result from differences in the demand for credit to finance margin positions. The increasing opportunity cost model implies the following coefficient restrictions: ␣1 ≤ 0 and ␣i2 ≤ 0. Table 3 presents estimation results for Eq. (11). The first three columns of data in Table 3 present the results from OLS estimation of Eq. (11) for the eighteen contracts included in our sample. With the exception of the British pound, gold and silver, the coefficients on ISD are negative and differ reliably from zero. The coefficient on the interest-rate-spread variable differs significantly from zero only for the contracts on the British pound and wheat. From these results we conclude that after controlling for the opportunity costs imposed by margin deposits, the

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Table 3. Estimates for the Opportunity Cost Specifications. Unrestricted Coefficients

Intercept

Opportunity Cost

ISD

Within-Exchange ␣ij1 = ␣ij1 Coefficient Restrictions: ␣ij2 = ␣ij2 ∃j Intercept

Opportunity Cost

ISD

−0.91 (0.08)

−27.71 (0.77)

−0.19 (0.16)

−3.47 (0.34)

−0.88 (0.42)

−6.01 (0.39)

−1.02 (0.42)

−4.62 (0.44)

−0.50 (0.28)

−5.70 (0.86)

14.35 (1.89) 7.47 (0.91)

−3.57 (0.76) −0.32 (0.28)

3.36 (10.32) −17.33 (2.41)

11.23 (0.38) 10.50 (0.27)

Deutschemark

8.83 (2.33)

0.18 (0.82)

−32.72 (8.70)

11.06 (0.40)

Eurodollar

13.56 (4.78)

1.07 (1.64)

−2807.12 (291.75)

10.62 (0.84)

Japanese Yen

10.77 (0.62)

−0.38 (0.24)

−51.34 (5.20)

9.89 (0.24)

Swiss Franc

9.65 (1.86)

−0.00 (0.61)

−40.41 (8.79)

10.54 (0.32)

S&P 500

7.86 (7.14)

4.25 (2.41)

−51.23 (18.45)

17.38 (1.00)

Corn

9.26 (2.56)

−0.80 (0.93)

−9.66 (2.52)

9.35 (0.47)

Soy Bean

10.57 (2.47)

−0.20 (0.96)

−27.38 (6.99)

6.50 (0.57)

Treasury Bond

7.60 (0.80)

0.21 (0.28)

−25.22 (4.28)

6.25 (0.44)

Wheat

12.18 (1.77)

−2.18 (0.65)

−9.12 (2.82)

5.86 (0.49)

Heating Oil

8.60 (2.51)

−0.19 (0.92)

−3.81 (0.85)

11.25 (1.18)

Crude Oil

9.89 (1.84)

−0.41 (0.74)

−3.35 (0.79)

8.71 (1.14)

Coffee

10.47 (2.46)

−1.22 (0.83)

−6.71 (1.56)

9.31 (1.20)

Sugar

8.05 (2.32)

−0.40 (0.86)

−3.01 (0.71)

10.51 (1.19)

Gold

7.90 (1.56)

−0.65 (0.52)

−6.14 (5.97)

7.45 (0.74)

British Pound Cattle

∃j

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Table 3. (Continued ) Unrestricted Coefficients

Intercept

Opportunity Cost

ISD

Within-Exchange ␣ij1 = ␣ij1 Coefficient Restrictions: ␣ij2 = ␣ij2 ∃j Intercept

Silver

8.80 (2.39)

−1.15 (1.05)

−1.30 (6.87)

8.15 (0.80)

Copper

7.95 (1.63)

−0.57 (0.67)

−5.32 (1.81)

7.89 (0.77)

Opportunity Cost

∃j

ISD

Note: Standard errors in parentheses. Table reports results for two methods of estimating the following time-series and cross-sectional specification: CRijt = ␣ij0 + ␣ij1 Rt + ␣ij2 ISDit + ␮ijt . Variable definitions are: CRijt is the coverage ratio for contract i traded at exchange j on date t, Rt is the excess of the prime rate over the 3-month treasury bill rate, and ISDit is the implied standard deviation for options trading on contract i at date t. Unrestricted coefficients are from separate OLS regressions for each contract. The within-exchange restricted coefficients are from estimating those equations as a system of seemingly unrelated regressions. Regressions include equality restrictions on the two right-hand side variables. Within the five exchanges, the coefficients on R are restricted to equality and the coefficients on ISD are restricted to equality. See Table 1 for contracts traded on the five exchanges.

coefficients on ISD generally (17 of 18 contracts) support the hypothesis of increasing cost. Thus, volatility increases lead to lower coverage; that is, margin coverage increases but by a smaller percentage than the accompanying volatility increase. We also estimate Eq. (11) as a system of 18 equations using the method of iterated seemingly unrelated regressions. To represent better the fact that exchange decisions on margin requirements reflect the opportunity costs and risk tolerances of their memberships irrespective of their preferred trading venues, we impose coefficient restrictions. Specifically, we require equal coefficients on the opportunity costs for all contracts trading within a single exchange. Likewise, we impose the restriction that the ISD coefficients on contracts trading within an exchange also be equal. The effect of these restrictions is to represent exchange members as, at the margin, indifferent as to the margin requirements for the various contracts they may trade on the exchange. Columns 4 through 7 of Table 3 report the SUR results. With the exception of the opportunity cost at COMEX, all coefficients are negative and differ significantly from zero at usual confidence levels. This result concurs with the increasing-cost conclusion obtained from the OLS coefficients on ISD. The significantly negative coefficients on opportunity cost bolster this conclusion. This implies that with

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risk exposure held constant, an increase in the opportunity cost of margin deposits prompts exchanges to choose lower margin and, therefore, less risk coverage. We also compare the margin coverages for gross- and net-margin exchanges. The two gross-margin exchanges – the CME and the NYMEX – require clearing members to post with their respective clearinghouses, the full amount of margin due on all the positions carried by each clearing member. In contrast, the net-margin exchanges – the CBOT, the CSCE and the COMEX – allow clearing members to post margin on the net of their long and short positions. The ability to net contracts can substantially lessen aggregate margins deposited with the exchange. Hence, increasing costs implies that the coefficients on opportunity cost and on ISD for gross-margin exchanges should be larger in absolute value than those for net-margin exchanges. Four F tests generally support this view. Comparing ISD results, the coefficient for the CME is substantially larger in absolute value than for the CBOT. Likewise, the equal-weighted average of ISD coefficients for the CME and the NYMEX is larger than the equal-weighted average of ISD coefficients for the CBOT, CSCE and the COMEX. The F tests for these comparisons conclude that the differences are significant. Comparing opportunity cost results, the coefficient for the CME is substantially larger in absolute value than that for the CBOT. This difference is statistically significant. Comparing the weighted-average coefficients for the CME and NYMEX with those for the CBOT, CSCE and COMEX also obtains a larger effect, but the comparison is not statistically significant at the usual levels.

5. EXTENSIONS: OTHER CLEARINGHOUSE RISK CONTROL MECHANISMS The preceding sections model a clearinghouse using margin deposits to manage default losses and provide evidence supporting the model. This simple clearinghouse need not monitor the financial condition of its participants, link margin deposits to the riskiness of its participants, expel nonperforming members or otherwise seek to control risk. Yet, these ancillary activities are likely sources for additional economies. Exploring these issues adds to our understanding of presentday institutional arrangements. This section begins by examining clearinghouse policy toward defaulting members. We then model the monitoring activities of the clearinghouse with respect to the value of membership and to the financial condition of its members.

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5.1. The Threat of Expulsion Because clearinghouses reduce deadweight losses from opportunistic default and allow participants to economize on margin costs, membership is valuable. When traders expect to trade in more than one period, the threat of expulsion reduces opportunistic default. Verifiable membership value reduces the amounts of required margin because the expulsion threat induces contract performance beyond that obtainable from margin deposits. A member’s presence may also be beneficial to other members. Such joint benefits raise questions about the credibility of an expulsion threat. This subsection lays out conditions for a credible expulsion policy. Let C denote the capitalized value derived by members from continued membership. This value has two sources: expectations of lower loss rates resulting from contract default and lower margin requirements. We denote gains accruing to member d as C(d, d) and the aggregate of benefits accruing to other members as C(d, CH). A short contract position rationally responds to an expulsion threat by performing if contract-performance costs are less than membership value:

n

N(d, j) |x − M| < C(d, d) (12)

j=1

A similar condition applies to long positions. A clearinghouse rationally expels its defaulting members if default costs, including both the contractual shortfall and the deadweight loss, exceed the value losses other members incur by expelling d, that is, when:

n (13) (1 + ␣)

N(d, j)

|x − M| > C(d, CH)

j=1 Combining these conditions, a credible expulsion threat exists and a potential defaulter rationally performs on the contract when

n

C(d, CH) <

N(d, j)

|x − M| < C(d, d) (14) (1 + ␣)

j=1

As the membership of a clearinghouse increases, the cost to the group as a whole of expelling any one member will decline, but the cost to an individual of losing clearing privileges will, if anything, increase. When members suffer virtually no loss from refusing to trade with d, then C(d, CH) = 0. If C(d, CH) = 0 and C(d, d) > 0, then an expulsion threat is always credible. Moreover, it is Pareto improving for clearinghouse members to pre-commit to expelling any member defaulting on

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a contract because the threat of membership loss reduces opportunistic default without raising margin levels.18 The expulsion threat alters the clearinghouse’s basic maximizing problem in that |x| > M is the optimal default rule only when the value of future clearing privileges is ignored. Equation (14) gives a more general default rule for the short position. This has three implications. First, due to the threat of expulsion, firms default in fewer states of the world. Second, the value of clearing membership C perfectly substitutes for margin deposits M in preventing default but third, the value of membership imperfectly substitutes for margin deposits when default occurs. This is because increases in required margin increase the amount received in default states but the benefits of membership are not transferable.19 Proposition VII. When the clearinghouse can make a credible expulsion threat, the optimal margin coverage ratio increases as volatility increases. When C is identical across individuals, a credible expulsion threat increases the lower limit of integration in Eq. (6) from M to M + C/|N*(j)|, where N* is the median trader’s exposure. The clearinghouse now minimizes:

∞ n

x − M(j) f(x, ␴)dx |N(j)| iM(j) + ␣ (15) j=1

C M(j)+ |N(j)|

The first order condition for minimization of (15) with respect to M(j, h) and M(h, j) is: C C C i 1 − F M ∗∗ + ,␴ + f M ∗∗ + ,␴ = |N(j)| |N(j)| |N(j)| ␣ Whenever clearinghouse membership is valuable, then C > 0 and the final term on the hand side of (16) is strictly positive. This means that a policy of expelling a defaulting member reduces the probability of default F(·) to less than i/␣, the level prevailing absent expulsion. Since a credible expulsion threat acts as a substitute for costly margin, the clearinghouse will choose a higher level of protection than it otherwise would. Differentiating Eq. (16) with respect to M** and C/|N(j)|, implies that when margin is taken dM** /d(C/|N(j)|) < 0. Thus, increasing the value placed on membership decreases the amount of margin required to obtain a given level of safety. Intuitively, as membership and the volume cleared expands over time, the threat of expulsion becomes more serious because clearing privileges are more valuable, and the clearinghouse can place greater reliance on the expulsion threat as a deterrent to default, thus decreasing the optimal level of margin.

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If the threat of expulsion is an important part of the guarantee system, how would coverage rations change when volatility changes? On the one hand, if we hold the value of clearing C constant, then optimal margin coverage ratio M** /␴ increases as volatility increases. Thus, margin must increase more rapidly than volatility to supply the same level of protection. This result contrasts sharply with our analytic results for constant or increasing costs of margin deposits. On the other hand, it may be that the value of clearing C changes systematically with changes in volatility. The most likely conjecture is that the value of clearing increases as volatility increases, because increased volatility is likely to be associated with increased volume of trading. This could reverse the result cited in the previous paragraph: if clearing becomes more valuable in volatile markets, it is possible that optimal margin could drop. The above suggests the benefits of clearinghouse creation can go beyond margin economies and avoiding deadweight default costs. Creation of a clearinghouse assures contract performance at levels beyond that obtained by margin deposits. Further, it can be the case that reliance on membership value is more cost effective than relying simply on margin deposits.

5.2. The Clearinghouse as Monitor Relaxing the assumption that only collateral can be attached in case of default, we allow counterparties to grant senior claims on unencumbered assets k(j).20 Each party knows its own k(j), however we assume counterparties incur an examination cost to learn k(j). This cost is denoted e. Traders choose to be monitored when the savings from these senior claims against k(j) exceed examination costs. Examination, at most, saves the firm the opportunity cost of holding k(j), that is, the maximum savings is ik(j). If the quantity ik(j) is less than e, then inspection does not pay. However, failure of this condition is not sufficient for inspection to occur. If the optimal margin M*|N(j)| without inspection is less than k(j), the opportunity cost savings from granting a senior claim against k(j) is iM*|N(j)|.21 Proposition VIII. When the clearinghouse acts as monitor to verify the existence of unencumbered assets, coverage ratios increase as volatility increases. Inspecting a member firm reveals one of two conditions. Members post no margin when unencumbered assets k(j) exceed M* |N(j)|. Alternately, if k(j) is less than M* |N(j)|, then the clearinghouse’s problem is of the same form as Eq. (6) with M + k(j)/|N(j)| substituted for M.

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If k(j) is less than M* |N(j)|, the optimal margin rule is:

M

∗∗∗

k(j) + = F −1 |N(j )|

i ,s ␣

(16)

Because k(j) is less than M* |N(j)|, parties still post margin. Thus, for a constant opportunity cost of margin, the optimal default probability is identical to the noexamination case because firms substitute claims against unencumbered assets for more costly forms of margin. Unlike the case where expulsion acts as a deterrent to default, if default occurs, the other assets can be seized, making them a perfect substitute for margin deposits. However, when opportunity costs are increasing in total required margin, examination decreases the optimal default rate. When other assets are substituted for margin, the cost of additional margin decreases, and the optimal level of protection can thus be increased. Equation (16) implies that with monitoring, coverage ratios increase as volatility increases, as unencumbered assets k(j) decrease, and as the number of open contracts increases. The result that the optimal coverage ratio declines as firms become less able to substitute unencumbered assets for collateral deposits differs from the predictions of the constant opportunity cost model (Eq. (4)) and the increasing opportunity cost model (Eq. (8)). Since firm asset holdings are dissimilar, reliance on unencumbered assets entails scrutiny of member positions, with margin setting on a member-bymember basis. Instead, margin requirements are uniform across the memberships of organized clearinghouses. This uniformity arises for several reasons. First, payment delays may be the principal cause of deadweight losses for members of the clearinghouse. The presence of unencumbered-but-illiquid assets may not be useful for time-critical settlement requirements. Second, timely verification of the existence of k may significantly raise clearinghouse costs, making is uneconomical to monitor at all. Third, netting may reduce each party’s net exposure to such low levels that intensive monitoring can not be cost-effective. In any event, the uniformity of margins across members suggests that if clearinghouses do engage in extensive monitoring, it must be for purposes other than controlling risk between members. The prediction of a positive correlation between volatility and the coverage ratio also contrasts sharply with the independence of the coverage ratio and volatility. Thus, this result is distinct from the simple netting model of Eq. (5) and the negative correlation generated by the increasing opportunity cost of funds model of Eq. (10).

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6. SUMMARY We incorporate the cost of external funds and the deadweight losses associated with counterparty default into collateral decisions. Given their scale of activities, it is not surprising that clearinghouses internalize these costs into their margin decisions. Thus, clearinghouse pursuit of prudentiality through margin is constrained by the costs that members incur by carrying these balances. When margin is set without regard to additional information about the condition of the clearinghouse members, the coverage ratio is either uncorrelated or negatively correlated with volatility. The time series of coverage ratios supports the conclusion that clearinghouse determination of margin incorporates prudential concerns. Our empirical results demonstrate that clearinghouses respond to high levels of margin by adjusting coverage ratios downward. This behavior is not consistent with prudentiality alone, but is consistent with exchanges optimizing across the costs of placing margin deposits and the costs from incurring deadweight losses. Our pooled-regression results show that futures clearinghouses set margin in a cost-minimizing fashion, balancing the risk of loss against the greater opportunity costs associated with higher margins. Those results suggest that at least part of these opportunity costs arise because market participants have imperfect access to capital markets for their general financing. We extend our model to capture other institutional features. We expect positive correlations between coverage ratios and volatility when clearinghouses actively monitor their members for risk-management purposes. Our emphasis on the foundations of the clearinghouse makes clear that membership is valuable. Because membership is valuable, expelling defaulting members is credible and effective for the clearinghouse. This means that members will perform on their contracts even when price moves exceed the value of margin on deposit.

NOTES 1. The term collateral is used for all instances where a deposit is required to reduce exposure to credit risk. The term “margin” when used here is the special case applying when collateral deposits are uniform within broad categories of counterparties. 2. Baer, France and Moser (1995b) re-examine some previous tests of prudentiality. 3. For-profit exchanges operating in a competitive market can also be expected to cost minimize. Hence, our model also applies to for-profit organizations. 4. For example, courts may be unable to force the transfer of collateral quickly enough to avoid deadweight default costs and will involve significant legal costs.

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5. Generalization to a multi-contract exchange results in a relation between the loss on a portfolio of contracts and the sum of margin deposits. The results depend on the extent of members’ diversification. See Baer, France and Moser (1993). 6. Most margin deposits at U.S. exchanges are in interest-bearing forms though markedto-market gains or losses (variation margin) require cash payments. For example, a U.S. Treasury Bill deposited as margin would be returned to the depositor when the account is closed. This arrangement effectively gives the depositor interest on deposit. The London Clearinghouse pays interest on cash deposits. Our model covers both cases. If cash is deposited, the opportunity cost is driven by the levels of market rates. Clearinghouses also allow limited use of standby letters of credit (SLOCs) for margin. 7. A futures clearinghouse also allows its members to exploit a variety of other scale economies accessible only by acting as a group. Centralization simplifies record keeping since members need only keep track of their positions with the clearinghouse. Credit monitoring and control is simplified, since members’ financial standing need only be assessed once by the clearinghouse, rather than by every counterparty. Economies of scope exist between record keeping and credit control, since knowledge of a member’s net position is needed to assess exposure. Finally, precommiting to binding arbitration lowers cost because disputes are no longer a matter for bilateral bargaining. See Baer, France, and Moser (1995a). 8. Calomiris and Hubbard (1995), Fazzari, Hubbard and Petersen (1988); and Hubbard and Kashyap (1992) provide evidence that nonfinancial firms behave as if financing growth through external financing is relatively expensive. Baer and McElravey (1994) report similar results for U.S. banking corporations. 9. The use of margin as collateral, the netting, and the attendant loss-sharing rules effectively redefine the legal priority of claims. We assume the ability of a clearinghouse to take possession of margin assets in the event of default is not obstructed by law. When we say a “pre-agreed rule,” we assume that the priority of claims in the event of default is clear. Historically, the rise of clearinghouses resulted in a clarification and streamlining of bankruptcy law as it applied to futures claims. 10. Certain loss-sharing rules can undo this result by allocating a disproportionate share of losses to an individual member. Since loss-sharing rules are agreed upon in advance and since clearinghouse membership is voluntary, it can be shown that such rules will not be adopted. Futures exchanges generally use a common fund to pay for defaults. 11. See Laffont (1988, pp. 51–53), or Cornes and Sandler (1986). Exchanges usually set margins, not on the basis of a direct vote, but by a committee designed to be representative of the membership. 12. Margin amounts collected when these accounts are opened are called initial margin. Should deposited amounts fall below a specified maintenance level, the margin balance must be restored to the current initial level. Maintenance margin requirements in U.S. stock markets differ. In stock markets, should a deficiency occur, margin must be restored to the maintenance level. 13. Implied standard deviations for short-term interest rate contracts are generally expressed in terms of yield variation. For consistency with our other contracts, they are reported here in terms of variation of rates of return. 14. See Bollerslev, Chou, Jayaraman and Kroner (1991).

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15. Another possibility not considered here is that the margin responses of exchanges induce subsequent changes in volatility. The evidence does not generally support this claim, however for an alternative view, see Hardouvelis (1988). 16. An F test indicates that the difference between the coefficients on the high and low quartiles of the S&P and Deutschemark contracts is significant at better than the 95% level. 17. Other clearinghouses, for instance the Options Clearing Corporation, have long accepted equity as margin. Futures clearinghouses are increasingly adopting this practice. 18. A minimal number of clearing members may be necessary to insure that none are too valuable to expel. 19. This presumes that the value of an exchange seat reflects trading rather than clearing privileges, as suggested by Bhasin and Brown (1997). If clearing memberships were a separately traded asset, their value would reflect the value of C(d, d) for the marginal member, and that amount could be recouped by the other members in a default. The model would then closely resemble that in the next section, where counterparties grant senior claims on assets. 20. Relaxing this assumption implicitly assumes that courts are effective in seizing collateral and that the speed of payment is not an issue. If payment delay is the principal reason that default imposes a deadweight loss on the membership, then the existence of unencumbered assets may be irrelevant. 21. We assume that the inspection process includes assessing the probable value of k in the default state. Clearinghouses “haircut” non-cash assets by valuing them at less than current market value.

ACKNOWLEDGMENTS Much of this paper was completed while France was visiting at the Chicago Mercantile Exchange and the University of Chicago. Susanne Malek and Jan Napoli provided valuable research assistance. The authors thank John Conley, Ramon DeGennaro, Mark Flannery, Gary Koppenhaver, Todd Petzel, Will Roberds, Jerry Roberts, an anonymous referee, and seminar participants at the University of Illinois at Urbana-Champaign, the Federal Reserve Bank of Chicago, the University of Tennessee, and the Chicago Risk Management Workshop. Opinions expressed are entirely those of the authors and do not reflect concurrence by the Federal Reserve, the Chicago Mercantile Exchange, or the World Bank.

REFERENCES Baer, H. L., France, V. G., & Moser, J. T. (1993). Opportunity cost and prudentiality: A representativeagent model of futures clearinghouse behavior. Faculty Working Paper #93–0142, University of Illinois. Baer, H. L., France, V. G., & Moser, J. T. (1995a, Spring). What does a clearinghouse do? Derivatives Quarterly, 1(3), 39–46.

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Baer, H. L., France, V. G., & Moser, J. T. (1995b). Determination of collateral deposits by bilateral parties and clearinghouses. In: Proceedings of the 31st Annual Conference on Bank Structure and Competition (pp. 525–546). Chicago: Federal Reserve Bank of Chicago. Baer, H. L., & McElravey, J. (1994, January). Capital adequacy and the growth of U.S. banks. In: C. Stone & A. Zissu (Eds), Global Risk Based Capital Regulations: Management and Funding Strategies. Homewood, IL: Dow-Jones-Irwin. Barone-Adesi, G., & Whaley, R. E. (1987). Efficient analytic approximation of American option values. Journal of Finance, 42, 301–320. Bhasin, V., & Brown, D. P. (1997, January). The organization of competitive financial exchanges. Working Paper, Indiana University. Journal of Financial Markets (Forthcoming). Bollerslev, T., Chou, R. Y., Jayaraman, N., & Kroner, K. F. (1991). ARCH modeling in finance: A selective review of the theory and empirical evidence with suggestions for future research. Journal of Econometrics, 52, 5–59. Brennan, M. J. (1986). A theory of price limits in futures markets. Journal of Financial Economics, 16, 49–56. Calomiris, C. W., & Hubbard, R. G. (1995, October). Internal finance and investment: Evidence from the undistributed profits tax of 1936–1937. Journal of Business, 68(4), 443–482. Cornes, R., & Sandler, T. (1986). The theory of externalities, public goods, and club goods. Cambridge: Cambridge University Press. Craine, R. (1997). Valuing the futures market performance guarantee. Macroeconomic Dynamics, 1(4), 701–719. Diamond, D. (1984). Financial intermediation and delegated monitoring. Review of Economic Studies, 51, 393–414. Fazzari, S. M., Hubbard, R. G., & Peterson, B. C. (1988). Financing constraints and corporate investment. Brookings Papers on Economic Activity, 141–195. Fenn, G., & Kupiec, P. (1993). Prudential margin policy in a future-style settlement system. Journal of Futures Markets, 13, 389–408. Figlewski, S. (1984). Margins and market integrity: Margin setting for stock index futures and options. Journal of Futures Markets, 4(Fall), 385–416. Fuller, W. A. (1976). Introduction to statistical time series. New York: Wiley. Gay, G. D., Hunter, W. C., & Kolb, R. W. (1986). A comparative analysis of futures contract margins. Journal of Futures Markets, 6(Summer), 307–324. Gorton, G. (1985). Clearinghouses and the origin of central banking in the U.S. Journal of Economic History, 45(June), 277–283. Hardouvelis, G. A. (1988, Summer). Margin requirements and stock market volatility. Federal Reserve Bank of New York Quarterly Review, 13(2), 80–89. Hsieh, D. A. (1993). Implication of non-linear dynamics for financial risk management. Journal of Financial and Quantitative Analysis, 28(March), 41–64. Hubbard, R. G., & Kashyap, A. K. (1992). Internal net worth and the investment process: An application to U.S. agriculture. Journal of Political Economy, 100(June), 506–534. Kofman, P. (1993). Optimizing futures margins with distribution tails. Advances in Futures and Options Research, 6, 263–278. Laffont, J.-J. (1988). Fundamentals of public economics. Cambridge, MA: MIT Press. Merton, R. C., & Bodie, Z. (1992). On the management of financial guarantees. Financial Management, 21(Winter), 87–109. Whaley, R. E. (1982). Valuation of American call options on dividend-paying stocks: Empirical tests. Journal of Financial Economics, 10, 29–57.

COLLATERALIZATION AND THE NUMBER OF LENDERS IN PRIVATE DEBT CONTRACTS: AN EMPIRICAL ANALYSIS Gordon S. Roberts and Nadeem A. Siddiqi ABSTRACT Using the Dealscan database of large, U.S. corporate loans, we examine the determinants of the number of bank relationships and the presence or absence of collateral. Consistent with prior studies, we ﬁnd that important explanatory variables are ﬁrm quality, desire for ﬁnancial ﬂexibility, the probability of ﬁnancial distress, growth opportunities and ﬁrm size. Higher quality ﬁrms as well as ﬁrms with a stronger desire for ﬁnancial ﬂexibility are less likely to collateralize and borrow from more lenders. Larger ﬁrms as well as those with lower probabilities of ﬁnancial distress and greater growth opportunities prefer multiple lenders.

1. INTRODUCTION Why do some firms choose to borrow from a single bank while others engage in multiple banking relationships? What factors determine whether a firm secures its loans and how do the two decisions interact? A number of recent empirical studies analyze multiple banking relationships in Europe: Detragiache et al. (2000) and Research in Finance Research in Finance, Volume 21, 229–252 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21010-3

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D’Auria et al. (1999) – Italy, Degryse and Ongena (2001) – Norway, Farinha and Santos (2002) – Portugal, and Harhoff and Korting (1998) – Germany. Studies on U.S. banking relationships have focused on small firms (Petersen & Rajan, 1994) and the role of multiple bank relationships in mitigating hold-up problems and creating financing flexibility (Houston & James, 1996, 2001). The present paper examines the determinants of bank relationships and collateral for large U.S. loans in the Loan Pricing Corporation’s DealScan database for the period 1990–1999. Consistent with prior studies, we find that important explanatory variables are firm quality, desire for financial flexibility, the probability of financial distress, growth opportunities and firm size. Higher quality firms as well as firms with a stronger desire for financial flexibility are less likely to collateralize and borrow from more lenders. Larger firms as well as those with lower probabilities of financial distress and greater growth opportunities prefer multiple lenders. Although there is a common set of explanatory variables, tests for interdependence effects suggest that the number of bank relationships and whether to offer collateral are independent decisions. Section 2 reviews relevant literature. Section 3 presents the models and variables used. The data sample is presented in Section 4, which is followed by a discussion of our simultaneous modeling technique analysis in Section 5. Section 6 presents our statistical analysis and Section 7 concludes paper.

2. PRIOR LITERATURE Prior research indicates that firm quality, the probability of financial distress, growth opportunities, the desire for managerial flexibility, and firm size are relevant determinants of both the number of lenders and whether loans are collateralized. We discuss each decision in turn. We can summarize the testable hypotheses from these studies with respect to the collateralization and the number of creditors in private debt contracts as shown in Table 1.

2.1. Number of Lenders We expect firms with greater growth opportunities to borrow from multiple lenders for moral hazard reasons (Repullo & Suarez, 1998) as well as to limit the single lender’s bargaining power and to mitigate any information monopoly (Houston & James, 1996; Rajan, 1992). A similar argument applies to larger firms. Detragiache, Garella and Guiso (2000) present a model in which borrowing from multiple banks can ensure a more stable supply of credit. Avoiding rationing by a single lender

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Table 1. Summary of Hypotheses. Collateralization

Number of Creditors

Growth

− Gilson and Warner (2000)

Probability of distress

+ Gorton and Kahn (1993), Rajan and Winton (1995)

Firm quality

+ Bolton and Scharfstein (1996)

+ Rajan (1992), Houston and James (1996), Repullo and Suarez (1998) − Berlin and Mester (1992), Chemmanur and Fulghieri (1994) + Degryse and Ongena (2001) + Berlin and Loeys (1988), Houston and James (1996), Rajan (1992), Bolton and Scharfstein (1996) − Detragiache et al. (2000), Degryse and Ongena (2001) + Repullo and Suarez (1998), Detragiache et al. (2000) + Gilson and Warner (2000)

− Rajan and Winton (1995) Firm size Loan purpose

+ Gilson and Warner (2000)

Note: The table summarizes the hypotheses and findings of previous studies on collateralization and number of creditors in private debt contracts with respect to the five firm characteristics mentioned. A “+” in front of the study indicates a positive hypothesized relationship between the debt contract and the firm characteristic, and conversely a “–” in front of the study indicates a negative relationship. Collateralization and Number of Creditors are binary variables, with “1” indicating presence of collateral, or multiple creditors, and “0” indicating absence of collateral, or single creditor, respectively.

reduces the risk that a profitable project will have to be prematurely liquidated. If the adverse selection problem is very severe because outside banks have less information than the borrower’s inside bank and suspect the firm to be a bad risk, it may pay for the firm to establish multiple relationships from the beginning. Hence, they theorize that larger and less profitable firms are less likely to have single banking relationships. Degryse and Ongena (2001) examine how the number of bank relationships affects firm performance for a sample of Norwegian firms. Firms with valuable proprietary information may use fewer creditors in order to prevent information leakage. At the same time, financially distressed firms facing credit rationing at their main bank may be forced to seek additional, more costly financing elsewhere. Farhina and Santos (2002) obtain a similar result for Portuguese firms. A positive association between the probability of financial distress and the number of bank relationships is also present in Germany according to Harhoff and Korting (1998). Firms that are looking to increase managerial discretion and flexibility, as indicated by the loan purpose, will also borrow from multiple creditors (Gilson & Warner, 2000). In contrast, firms with greater probability of financial distress, or higher credit risk firms find the option to renegotiate more valuable and hence

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may prefer to borrow from fewer lenders (Berlin & Mester, 1992). Further, Chemmanur and Fulghieri (1994) find that banks are able to use reputation as a commitment device to promise firms credibly that they will devote more resources toward evaluating them and thereby make better renegotiation-versus-liquidation decisions in the event of financial distress.

2.2. Collateralization High growth firms, as well as those specifically looking to increase managerial discretion and flexibility, as indicated by the loan purpose, are expected to put up less collateral. Rajan and Winton (1995) analyze the role of covenants and collateral in private debt contracts as incentives for lenders to monitor. They find that, in order to balance monitoring against efficient liquidation, the private lender should only take collateral in a bad state, signaling the information to the public. Their model also predicts that the collateralization of private debt will be correlated with financial distress possibilities of the firm. Gorton and Kahn (1993) reach a similar conclusion: collateral and seniority are crucial since they allow the bank to threaten the borrower and liquidate inefficient projects. Gilson and Warner (2000) find in their empirical study that bank loans are more often secured than junk bonds. They explain this by noting that security reduces managerial discretion since firms cannot easily sell assets that are pledged as collateral. They theorize that firms looking for the “flexibility to grow” would prefer less collateralization, as well as multiple creditors, to free managers from the immediate obligation of paying off debt, and increase their freedom to set corporate policies. Pozzolo (2002) examines the relationship between secured lending and borrowers’ riskiness. He develops a theoretical model predicting that banks require guarantees on loans to riskier borrowers. Using information on bank loans to a large sample of Italian non-financial firms, he finds empirical support for the predictions of his model. In contrast, John, Lynch and Puri (2002) develop and test a theoretical model based on agency problems between managers and claimholders suggesting that secured debt is not issued by riskier borrowers. Bolton and Scharfstein (1996) also hold that higher quality firms offer more collateral to bond against strategic defaults. They identify lack of liquidity as a cause of default positing that highquality firms borrow from multiple lenders. As a result, their work suggests that firm decisions on the number of lenders and collateral are jointly determined. Summarized in Table 1, our brief review of prior studies identifies growth, probability of financial distress, firm quality, firm size and loan purpose as factors driving choices of collateralization and the number of creditors. As the table

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demonstrates, prior research fails to reach a consensus on the impacts of these variables.

3. VARIABLES AND MODEL The different firm characteristics reviewed in the previous section are proxied as follows. Firm quality

Probability of distress

Growth opportunities Loan purpose

We proxy firm quality by Standard and Poor’s bond rating; the ratings of AAA, AA through C are translated to an ordinal scale ranging from 2 to 21, as recorded by COMPUSTAT. Blume et al. (1998) point out that rating agencies, such as Standard and Poor’s, employ both publicly available information, such as accounting statements, and non-public information, such as confidential interviews with management, to assign quality ratings as a measure of the “creditworthiness” of a corporation with respect to a particular debt security. Their survey of prior studies concludes that quality ratings do have some informational content and that these ratings contain information beyond what is publicly available. Their own empirical study also concludes that bond rating standards have become more stringent over time. This is proxied by the Z score value, calculated using Altman’s (1968) model. The Z score model utilizes multiple discriminant analysis to obtain a linear function of variables that is able to discriminate membership between two populations, bankrupt and non-bankrupt. The Z score indicates how close the firm is to being classified as being in one of the groups, i.e., the score is a measure of the probability of being in financial distress. The standard market to book ratio is used to proxy for growth opportunities. Following Carey et al. (1998) and Dennis et al. (2000), we place into groups the 16 stated uses of the debt by the borrowers, as recorded by the Loan Pricing Corporation, to indicate the purpose of the loan. We utilize Carey et al.’s (1998) four groups and categorize loans as being made for the following purposes: (1) general corporate purposes; (2)

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debt repayment/consolidation; (3) takeover/acquisition; and (4) other. The size of the firm is approximated by the natural logarithm of sales.

Aside from the above firm characteristics, we also control for the effects of leverage in our regressions. The importance of controlling for leverage is demonstrated by Lang, Ofek and Stulz (1996), who find that future growth and investments are negatively related to leverage. Johnson (1998) also found that leverage was statistically and economically significantly higher for firms with bank debt due to the fact that bank debt attenuates negative effects on leverage of potential asset substitution problems. Hence, omitting this variable would cause our model to be misspecified. Leverage is measured by the book value of debt divided by the market value of equity plus the book value of debt. We control for the type of private debt issued since this may directly affect the need for collateral as well as the number of creditors. The facility type is also categorized into one of four groups as follows: (1) short-term revolver; (2) long-term revolver; (3) term loan; and (4) other (including leases, bridge loans, notes, standby letters of credit, etc.). For the collateral regression, we also control for the amount of fixed assets available to put up as collateral, as well as the type of lead lender, whether bank or finance company. Carey et al. (1998) and Houston and James (2001) describe finance companies as “asset-based” lenders and banks as “cash flow” lenders. In making a loan, an asset-based lender emphasizes collateral as a source of ultimate repayment whereas a cash flow lender relies more heavily on projected cash flow from operations. The amount of fixed assets is measured by the ratio of fixed assets to total assets, while the lender type is a binary variable, with 1 for a finance company as lead lender and 0 for a bank as lead lender. A detailed formulation of all the regression variables is in Appendix A. We utilize a simultaneous model capable of assessing the interdependencies between the choice of the number of creditors as well as the amount of collateral offered hypothesized by Bolton and Scharfstein (1996). Building on the framework of Dennis et al. (2000), we model our regressions as follows: Collateral = ␣1 Creditors + ␤ 1 X 1 + e 1 Creditors = ␣2

Collateral + ␤

2X2

+ e2

(1) (2)

where the ␣’s are coefficients of the interdependence effects. This permits a direct test for the significance of interdependence effects. Both Collateral and Creditors are binary variables, with 1 indicating presence of collateral or multiple

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creditors, and 0 the absence of collateral or a single creditor, respectively. X1 and X2 contain the firm characteristic proxies, discussed above, that are expected to influence the decision to issue collateral for the loan and the number of creditors, respectively.

4. DATA We started construction of our sample set from the DealScan 5.6 database compiled by the Loan Pricing Corporation (LPC). In this area of the literature, Shockley and Thakor (1997) were the first to utilize the LPC database to empirically analyze the fee structure of bank loan commitment contracts.1 The LPC database provides detailed market information on commercial loans and private placements made to publicly held U.S. companies that are required to file such information with the Securities and Exchange Commission (SEC). The database also includes deal information obtained directly from banks, which is later confirmed after the deal is recorded with the SEC. The data include details such as the name of the borrower, the names of all lenders party to the loan contract at origination, the type, purpose, maturity, amount, material restrictions and contract date of the loan as well as other details. An illustration of relevant sample data from LPC’s DealScan database is presented in Table 2. Table 2. Sample Data from Loan Pricing Corporation’s DealScan Database. Borrower Name

Amgen Inc.

Beverly Enterprises

Ticker Deal purpose Deal active date Deal size Facility type Facility size Facility active date Facility maturity days Seniority Secured Bid option Materially restricted Lenders and share

AMGN Debt repayment/consolidation 23-Jun-95 $ 223,000,000 Standby LC $ 73,000,000 23-Jun-95 05-Dec-97 Senior No No Yes Swiss Bank Corp (58.9%), ABNAMRO (41.1%)

BEV General corporate purposes 01-Nov-94 $ 375,000,000 Revolver < 1Yr. $ 375,000,000 01-Nov-94 . No No No No J. P. Morgan & Co. (100%)

Note: The database contains over 200 searchable fields. Only some of the relevant fields are illustrated in this sample. Each deal (or package) may consist of one or more facilities, with each facility separately listed.

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In constructing our sample, we eliminated those loan records for which data required to fully characterize the borrower were unavailable on the COMPUSTAT database. We use the previous year’s COMPUSTAT data to avoid a simultaneity bias. Furthermore, we retain only those loan records for which a bond rating was assigned. These criteria result in a total of 218 loans. Hence, all 218 records are complete with respect to all the information needed for the study. There are no records that have any missing information, since they are filtered along the way. A summary of the sample characteristics is presented in Table 3. Since we restrict it to firms with bond ratings only, our sample represents medium to large firms with access to both the public and private debt markets. This bond rating “filter” should not bias our sample too much since the LPC dataset is compiled primarily from firms’ SEC filings, and smaller firms would have been excluded from this process to begin with.2 Furthermore, larger firms would have more bargaining power with lenders and thus would be better able to affect the structure of private debt contracts to suit their needs than smaller sized firms (Rajan, 1992). This structure, chosen by the borrower rather than that dictated by the lender, is precisely what we wish to study. Table 3. Summary Statistics of Sample Set. Variable

Mean***

Median

Std. Dev.

BONDRAT CUMPROF DEBTASST EBITSALE FACMATUR FACSIZE FACTA FACTD FATA FIRMVAL LTDTA MKTBOOK MKTLEV OITA SALES TOTASST ZSCORE

11.10 0.1446 0.3415 0.1562 1405.37 533.25 0.1520 0.6058 0.4424 6801 0.2881 1.5301 0.3333 0.0909 6327 6119 4.3250

11.00 0.1211 0.3249 0.1317 1826.00 250.00 0.0947 0.3372 0.4024 2483 0.2594 1.4127 0.2787 0.0843 2282 2286 3.1884

3.32 0.2265 0.1611 0.1376 707.54 851.97 0.1685 1.2294 0.2262 13016 0.1561 0.4982 0.1920 0.0591 10804 10570 4.5719

Note: All dollar figures are in millions of dollars, except the share price. The complete definition of the variables is found in Appendix A. ∗∗∗ All mean values were found to be statistically significantly different from 0 at the 1% level.

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5. MODEL ESTIMATION Following Dennis et al. (2000), we apply Mallar’s (1977) two-stage estimation procedure for simultaneous equation models with limited dependent variables to our model.3 We note that Eqs (1) and (2) both involve discrete binary choices and hence use a simultaneous probit model. In the first stage, a reduced form model for each of the two endogenous variables is estimated: Collateral = 1 X + ␧1

(3)

Creditors = 2 X + ␧2

(4)

where X is the set of all exogenous variables in X1 and X2 . Since both Collateral and Creditors are dichotomous variables, we can only estimate 1 /␴1 and 2 /␴2 , where ␴21 = Var(␧1 ) and ␴22 = Var(␧2 ). Thus, writing Collateral∗ as Collateral/␴1 and Creditors∗ as Creditors/␴2 we get the estimable structural functions. ␴2 , ␴1

Creditors∗ +

␤ 1 e1 X1 + ␴1 ␴1

(5)

␴1 , ␴2

Collateral∗ +

␤ 2 e2 X2 + ␴2 ␴2

(6)

Collateral∗ = ␣1 Creditors∗ = ␣2

We first estimate the reduced forms by probit maximum likelihood. Then we substitute the predicted values of Collateral∗ and Creditors∗ into Eqs (5) and (6) and estimate the structural equations by the probit maximum likelihood method. The asymptotic covariance matrices are then derived as per Maddala (1983). Define ␴2 ␤1 ␥1 = ␣1 , ␴1 ␴1 ␴2 ␤ 2 ␥ 1 = ␣2 , ␴1 ␴2 and let a1 =

␾1 , 1 (1 − 1 )

A 1 = ␾1 a 1 , N

W1 =

␾2 2 (1 − 2 ) ∗ 2 X A 2 = ␾2 a 2 , Z = X

1 A 1 ZZ N 1

a2 =

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GORDON S. ROBERTS AND NADEEM A. SIDDIQI N

W2 =

1 A 2 XX N 1

N ␴2 1 ZX W3 = A 1 ␣1 N ␴1 1

W4 =

1 N

N

a 1 a 2 E[(y 1 − 1 )(y 2 − 2 )]XZ

1

Then the covariance of N 1/2 (␥ˆ

1

− ␥01 )(where ␥01 is the true value of ␥1 and ␥ˆ 1

is the two-stage estimator) is −1 −1 −1 −1 W −1 1 [W 1 − W 3 W 2 W 4 − W 4 W 2 W 3 + W 3 W 2 W 3 ]W 1

(7)

The covariance of ␥ˆ 2 is similarly derived as follows. a1 =

␾1 , 1 (1 − 1 )

␾2 2 (1 − 2 ) ∗ 1 X A 2 = ␾2 a 2 , Z = X

A 1 = ␾1 a 1 ,

a2 =

N

W5 =

1 A 2 ZZ N 1

W6 =

W7 =

1 N 1 N

N

A 1 XX

1 N 1

␴1 ZX A 2 ␣2 ␴2

N

W8 =

1 a 1 a 2 E[(y 1 − 1 )(y 2 − 2 )]XZ N 1

N 1/2 (␥ˆ

Then the covariance of is the two-stage estimator) is

2

− ␥02 ) (where ␥ˆ 02 is the true value of ␥2 and ␥ˆ 2

−1 −1 −1 −1 W −1 5 [W 5 − W 7 W 6 W 8 − W 8 W 6 W 7 + W 7 W 6 W 7 ]W 5

(8)

Following Carey et al. (1998), the fit of the probit model is estimated by McKelvey and Zavoina’s (1975) pseudo-R2 measure, calculated as in Greene (1999).

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let E[y∗ |y] = yf = ␤ X + ␭ (n − 1)var(yf) pseudo − R2 = n + (n − 1)var(yf)

(9)

where ␭ is the inverse Mill’s ratio, and y is either the Collateral or Creditors binary variable for the two models. This 2-stage simultaneous model approach allows us to jointly analyze the two effects that may be missed by the single-equation approach.4

6. ANALYSIS 6.1. Univariate Analysis To help in making comparisons, we divide the general statistics from Table 3 into two sub-tables. Table 4 compares firms offering collateral against those not offering collateral.5 We note that firms not offering collateral are of better quality (BONDRAT), consistent with Rajan and Winton (1995): in order to provide the private lender with Table 4. Summary Statistics of Sample Set Separated by Collateralization. Collateral (N = 42)

Variable

BONDRAT CUMPROF DEBTASST EBITSALE FACMATUR FACSIZE FACTA FACTD FATA FIRMVAL LTDTA MKTBOOK MKTLEV OITA SALES TOTASST ZSCORE

Mean**

Median

14.74 0.0110 0.4704 0.0700 1582 224.42 0.2160 0.5365 0.4308 1081 0.4215 1.3500 0.4673 0.0534 1770 1167 2.6377

15.00 0.0413 0.4902 0.0913 1676 100.00 0.1580 0.3272 0.4310 732 0.4818 1.2630 0.4783 0.0681 1025 830 2.4402

No Collateral (N = 176)

Std. Dev.

Mean**

Median

Std. Dev.

1.86 0.1596 0.1657 0.2001 682 352.62 0.2524 0.7053 0.2075 1095 0.1732 0.3968 0.1709 0.0627 2530 1530 1.1501

10.23 0.1764 0.3107 0.1768 1364 606.95 0.1367 0.6224 0.4452 8165 0.2563 1.5731 0.3013 0.0999 7415 7300 4.7277

10.00 0.1489 0.2874 0.1387 1826 300.00 0.0880 0.3372 0.3964 4962 0.2344 1.4249 0.2592 0.0937 3551 3863 3.5069

2.99 0.2287 0.1443 0.1090 709 917.92 0.1381 1.3253 0.2309 14144 0.1337 0.5111 0.1831 0.0547 11707 11433 4.9762

Note: All dollar figures are in millions of dollars, except the share price. The complete definition of the variables is found in Appendix A. ∗∗ All mean values were found to be statistically significantly different from 0 at the 5% level, except for RELEPS and CUMPROF, which were not significantly different from 0.

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sufficient incentive to monitor and force liquidation when efficient, higher quality firms decrease collateral. Our finding that lower quality firms are more likely to offer collateral supports Pozzolo (2002) for Italian firms while contradicting both Bolton and Scharfstein (1996) and John, Lynch and Puri (2002). Furthermore, those offering collateral are not as profitable and have higher probabilities of financial distress in the near future (OITA, ZSCORE). This is also in accordance with the hypotheses of Rajan and Winton (1995) and Gorton and Kahn (1993), that firms which expect to face higher probabilities of financial distress provide more collateral to give lenders greater control as well as the ability to threaten liquidation of inefficient projects. Finally, we find that firms borrowing from multiple lenders have greater growth potential (MKTBOOK) than those borrowing from single lenders. This supports the theory of Gilson and Warner (2000) that high growth firms put up less collateral to increase managerial discretion and flexibility. In looking at Table 5, which compares firms using multiple creditors with those using single creditors, we find that firms using a single lender have statistically significantly higher leverage (DEBTASST, MKTLEV) in accordance with the findings of Detraigaiche et al. (2000), Degryse and Ongena (2001), and Harhoff and Table 5. Summary Statistics of Sample Set Separated by Number of Lenders. Variable

BONDRAT CUMPROF DEBTASST EBITTA FACMATUR FACSIZE FACTA FACTD FATA FIRMVAL LTDTA MKTBOOK MKTLEV OITA SALES TOTASST ZSCORE

Multiple Lenders (N = 182)

Single Lenders (N = 36)

Mean***

Median

Std. Dev.

Mean***

Median

Std. Dev.

11.17 0.1425 0.3313 0.1438 1460.38 552.75 0.1609 0.6611 0.4361 6379 0.2819 1.5590 0.3156 0.0929 6213 5753 4.5863

11.00 0.1204 0.3232 0.1401 1826.00 250.00 0.1073 0.3736 0.3904 2483 0.2510 1.4200 0.2676 0.0885 2396 2286 3.3300

3.25 0.2313 0.1584 0.0643 694.92 891.11 0.1713 1.3185 0.2266 11699 0.1546 0.5142 0.1813 0.0619 10192 9681 4.8500

10.75 0.1552 0.3929 0.1344 1110.91 434.65 0.1072 0.3263 0.4742 8933 0.3195 1.3839 0.4228 0.0811 6903 7966 3.0042

11.00 0.1226 0.3786 0.1225 1096.00 137.50 0.0630 0.1586 0.4592 2748 0.2980 1.2985 0.4306 0.0710 2094 2849 2.3063

3.68 0.2026 0.1670 0.0481 711.93 617.93 0.1481 0.5338 0.2245 18357 0.1617 0.3812 0.2206 0.0413 13643 14278 2.4082

Note: All dollar figures are in millions of dollars, except the share price. The complete definition of the variables is found in Appendix A. ∗∗∗ All mean values were found to be statistically significantly different from 0 at the 1% level.

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Korting (1998) that companies maintaining single relationships tend to be more leveraged. However, we find firms using multiple lenders to be more profitable with better future prospects than firms using a single lender (OITA, ZSCORE). This is in contrast to the findings of Degryse and Ongena (2001), Detraigaiche et al. (2000), Farinha and Santos (2002) and Harhoff and Korting (1998), but in accordance with the hypotheses of Berlin and Mester (1992) and Chemmanur and Fulghieri (1994), that firms with greater probability of financial distress, or higher credit risk firms find the option to renegotiate more valuable and hence borrow from fewer lenders. This could perhaps be explained by the differences in the financial systems of the United States and more concentrated markets in Italy, Norway and Portugal. In highly concentrated markets, profitable firms may not be able to maintain multiple banking relationships in a healthy, competitive manner, even if they so desired. In Norway, for example, two banks have 90% of the market, and firms may not feel that establishing multiple relationships will adequately mitigate hold-up problems, especially at the cost of giving up a strong, healthy relationship with a single lender. However, in the U.S., due to the large diffused market, profitable firms are able to shop around and maintain multiple relationships easily. Furthermore, it is the profitable firms that would be most worried about restricting relationships to only one lender, to limit the lender’s bargaining power and mitigate any information monopolies (Houston & James, 1996; Rajan, 1992). We also find that firms using multiple creditors seem to have greater growth potential (MKTBOOK). This is in line with the predictions of Repullo and Suarez (1998) and Rajan (1992) and Houston and James (1996) that such firms borrow from multiple creditors for moral hazard reasons as well as to limit the single lender’s bargaining power and mitigate any information monopoly. Firms with multiple creditors are also borrowing more, whether on an absolute basis or on a relative basis (FACSIZE, FACTA), and are issuing debt with longer maturities.

6.2. Regression Analysis The results of the simultaneous regressions on the collateralization and the number of creditors in private debt are presented in Table 6.6 With pseudo-R2 of 70% and 44% respectively, both of which are significant at the 1% level, the regressions fit reasonably well. We find that the two decisions are not interrelated since the coefficients of the interdependence effects are insignificant. The quality and loan purpose proxies are significant for the collateralization regression in column (1). The positive coefficient on the quality proxy indicates that firms of lower quality put up more

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Table 6. Primary Regression Results. Characteristic

Firm quality Leverage Probability of distress Growth potential Loan purpose Loan type Lead lender Fixed assets Firm size

Proxy

Intercept Interdependence BONDRAT MKTLEV ZSCORE MKTBOOK PURPGRP FACGRP FINCOT FATA LGSALE Pseudo R2 N

Collateralization (1)

Multiple Creditors (2)

Coefficient

p-Value

Coefficient

p-Value

−6.8057 −0.6382 0.4325 −1.5554 0.0091 −0.1365 0.3041 0.4410 −1.2397 0.7705

0.0003*** 0.4380 0.0009*** 0.5327 0.8880 0.8231 0.0489** 0.0665* 0.1881 0.2596

1.5185 0.5809 −0.0102 −3.0098 0.0488 0.0602 −0.1472 −0.1614

0.6083 0.1259 0.9423 0.0094*** 0.5302 0.8833 0.3947 0.5222

0.7031 218

0.0000*** 218

0.2603 0.4375

0.0309** 0.0009***

Note: Results shown are those from the second stage of a 2-stage simultaneous equations model, using corrected asymptotic variances. The variables are as defined in Appendix A. Column 1 is a probit model where 1 = Collateral, and 0 = No Collateral. Column 2 is also a probit model where 1 = Multiple Creditors, and 0 = Single Creditor. ∗ Coefficients significant at the 10% level. ∗∗ Coefficients significant at the 5% level. ∗∗∗ Coefficients significant at the 1% level.

collateral and firms of higher quality put up less collateral for private debt.7 This is in support of Rajan and Winton’s (1995) theory that private lenders only take collateral in the bad state as incentives to monitor and force efficient liquidation. In contrast, our result here does not support the argument by Bolton and Scharfstein (1996) and John, Lynch and Puri (2002) that higher quality borrowers minimize strategic defaults by increasing collateralization. The significant loan purpose proxy is in support of Gilson and Warner’s (1999) finding that firms that are looking for managerial freedom and “flexibility” put up less collateral. The loan purposes labeled “1” and “2” are for general purposes and those labeled “3” and “4” are those for special purposes like takeovers and acquisitions. Hence, managers are looking for flexibility, freedom and discretion in everyday affairs, while offering collateral only in special, risky projects like takeovers. We also find that collateralization depends on the type of debt issued. Collateral is offered for term loans, but not for revolvers. Neither the growth nor the probability of distress proxies are significant in the collateralization regression. In column (2) of the probit regression analyzing multiple creditors, the leverage and size proxies are significant. The positive sign on the size proxy is in accordance

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with the hypothesis of Repullo and Suarez (1998) that larger firms would prefer multiple lenders since single lenders would be unable to enforce a credible threat of liquidation. It is also in support of Detragiache et al.’s (2001) hypothesis that larger firms maintain multiple creditors to avoid liquidity risk due to the lender and to ensure a stable supply of credit. The negative sign on the leverage proxy implies that more highly leveraged firms prefer single creditors to multiple creditors, in support of the findings of Degryse and Ongena (2001). They state that “highly leveraged firms choose a single relationship since firms judged fit to carry a lot of debt do not face credit rationing by their single bank.” Hence this finding is quite robust to regime changes, and validated in both the Norwegian and U.S. samples. This is also in support of Johnson (1998) who found that leverage was statistically and economically significantly higher for firms with bank debt due to the fact that bank debt attenuates negative effects on leverage of potential asset substitution problems. However it is inconsistent with Houston and James’ (1996) finding of a negative relationship between leverage and the proportion of bank financing. They explain their results as consistent with either economies of scale in issuing public claims or the notion that bank monitoring is a public good and firms with more leverage may use the same level of bank debt.

6.3. Alternative Speciﬁcations and Robustness Checks Degryse and Ongena (2001) and Detragiache et al. (2002) find that profitability impacts the number of bank relationships. Since our analysis focuses on incremental decisions that may be based on relationship or transaction lending (Boot & Thakor, 2000), specifically adjusting for profitability should not have any impact on the robustness of our results. To test this, we run a set of simultaneous regressions on collateralization and the number of creditors, but adding a fitted profitability variable (ratio of operating income to total assets) in the second stage of the model to analyze this effect.8 The results are presented in Table 7. As expected, our base results are materially unchanged. We re-ran the regressions using alternative measures for profitability, namely the EBIT to total assets ratio, and Altman’s (1993) cumulative profitability measure, calculated as retained earnings divided by total assets. Again, we did not find any difference in results. We also evaluated alternative specifications of the base model and did not find any major difference in results. Since the correlation matrix (Table B.1 in Appendix B) indicates that some variables are highly and significantly correlated with others (for example market leverage), we drop each one of the variables from the model in turn to test for robustness of the results. Two sample results

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Table 7. Comparative Regression Results. Characteristic

(Fitted) Profitability Firm quality Leverage Probability of distress Growth potential Loan purpose Loan type Lead lender Fixed assets Firm size

Proxy

Collateralization (1)

Intercept Interdependence OITA BONDRAT MKTLEV ZSCORE MKTBOOK PURPGRP FACGRP FINCOT FATA LGSALE Pseudo R2 N

Multiple Creditors (2)

Coefficient

p-Value

Coefficient

p-Value

−6.1223 −0.6229 −3.5702 0.4317 −1.7544 0.0079 −0.1835 0.3011 0.3992 −1.2584 0.5579

0.0249** 0.4368 0.7123 0.0008*** 0.5099 0.9000 0.7709 0.0498** 0.1301 0.1839 0.5140

1.5834 0.5923 0.0970 −0.0140 −3.0195 0.0482 0.0617 −0.1516 −0.1627

0.5957 0.1183 0.9821 0.9206 0.0125** 0.5352 0.8824 0.3837 0.5199

0.7033

0.0000*** 218

0.2607 0.4378

0.0316** 0. 0016*** 218

Note: Results shown are those from the second stage of a 2-stage simultaneous equations model, using corrected asymptotic variances, with a fitted profitability variable inserted in the second stage. The variables are as defined in Appendix A. Column 1 is a probit model where 1 = Collateral, and 0 = No Collateral. Column 2 is also a probit model where 1 = Multiple Creditors, and 0 = Single Creditor. ∗∗ Coefficients significant at the 5% level. ∗∗∗ Coefficients significant at the 1% level.

are included in the appendix (Tables C.1 and C.2, with market leverage and the market to book ratio dropped, respectively) that show that even when these highly correlated variables are dropped, the results do not change materially.

7. CONCLUSIONS This paper empirically assesses theoretical predictions on two aspects of debt contracts, the number of creditors and use of collateral, employing a current database of private U.S. corporate debt transactions. We simultaneously model the two aspects of debt contracts, since there may exist trade-off effects not captured in non-simultaneous models. Further, we focus on these two aspects of debt contracts from the borrower’s strategic perspective, and not from a lender’s pricing perspective. We do not find support for Bolton and Scharfstein’s (1996) theory that the two decisions are made jointly to minimize strategic defaults and the loss of value

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in liquidity defaults. Rather, we find that the two decisions are not interrelated. Firms of lower quality put up more collateral and firms of higher quality put up less collateral possibly because private lenders only take collateral in the bad state as incentives to monitor and force efficient liquidation (Rajan & Winton, 1995). Furthermore, those offering collateral also give lenders greater control as well as the ability to threaten liquidation of inefficient projects (Gorton & Kahn, 1993; Rajan & Winton, 1995). We also find that firms that are looking for managerial freedom and “flexibility” put up less collateral (Gilson & Warner, 2000). Large U.S. firms in our sample with greater probability of financial distress, or higher credit risk firms find the option to renegotiate more valuable and hence borrow from fewer lenders (Berlin & Mester, 1992; Chemmanur & Fulghieri, 1994). Due to moral hazard reasons as well as to limit the single lender’s bargaining power and mitigate any information monopoly, firms with greater growth opportunities borrow from multiple creditors (Rajan, 1992; Repullo & Suarez, 1998). Larger firms prefer multiple creditors for the same moral hazard reasons (Repullo & Suarez, 1998), or to avoid liquidity risk due to the lender and to ensure a stable supply of credit (Detragiache et al., 2001). Finally, we find that more leveraged firms choose a single lender, perhaps due to the fact that they do not face credit rationing from their relationship lender (Degryse & Ongena, 2001), or due to the attenuation of the negative effects on leverage of potential asset substitution problems (Johnson, 1998). Overall, larger, less leveraged firms choose multiple lenders and smaller, more leveraged firms choose a single lender. We also discover differences and similarities in the behavior of U.S. and European firms, perhaps due to the different financial systems in which they operate. More leveraged firms in both environments prefer single lenders to multiple creditors. However, profitable European firms operating in a highly concentrated financial market maintain single relationships, while large, profitable U.S. firms working in a large and diffused financial market, maintain multiple relationships to mitigate lenders’ informational monopolies (Houston & James, 1996; Rajan, 1992). Viewed broadly, our results show that the variables identified in prior studies, firm quality, the probability of financial distress, growth opportunities, the desire for managerial flexibility, and firm size, play major roles in explaining two important features of loan contracts in the U.S.

NOTES 1. Other users of the LPC database include Carey, Post and Sharpe (1998), who use the database to empirically establish the basic difference between bank and non-bank lenders

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and borrowers. Angbazo, Mei and Saunders (1998) use the database to analyze credit spreads on highly leveraged transaction loans. Hubbard et al. (1999) use it in analyzing bank effects in borrower’s cost of funds. Strahan (1999) uses it to analyze the pricing of borrower risk. Dennis et al. (2000) use it to analyze the determinants of contract terms in bank revolving credit agreements. 2. Strahan (1999) compared the DealScan firms with those found in the COMPUSTAT universe and found that the median DealScan firm was not only larger (by a factor of four) but also more profitable (almost double) than the median COMPUSTAT firm. 3. See Chapter 8 of Maddala (1983) for more details on the two-stage estimation procedure. 4. We appreciate the help of William Greene in resolving some econometric issues with the model. 5. Statistical significance for ratio differences were calculated using the non-parametric Wilcoxon sum rank test since ratios are not normally distributed and other tests would not be valid. 6. As suggested by Gujarati (1995) and Greene (1997), since some of the variables are significant in the regression, and the R2 is not very high (less than 75%), we conclude that correlation amongst regressors is not a problem. The full correlation matrix is presented in Appendix B along with some alternate regressions in Appendix C. 7. Recall that COMPUSTAT records S&P bond ratings in an “inverse” fashion: 2 for AAA and 21 for C. 8. Using the method explained in Section 5, the profitability variable is estimated in the first stage as an independent variable. The predicted value is then inserted into the second stage as a fixed value to estimate the rest of the variables.

ACKNOWLEDGMENTS We thank James Darroch, Vasil Mihov, Kamphol Panyagometh, Pauline Shum, John Smithin, and participants at the 2000 FMA Annual Meeting for comments that helped to improve the paper. We would also like to acknowledge the help of William Greene in resolving econometric issues and Sumon Mazumdar and Yuxing Yan in accessing the DealScan database.

REFERENCES Altman, E. I. (1968). Financial ratios. Discriminant analysis and the prediction of corporate bankruptcy. Journal of Finance. Altman, E. I. (1993). Corporate ﬁnancial distress and bankruptcy: A complete guide to predicting and avoiding distress and proﬁting from bankruptcy. New York: Wiley. Angbazo, A., Mei, J., & Saunders, A. (1998). Credit spreads in the market for highly leveraged transaction loans. Journal of Banking and Finance, 22, 1249–1282. Berlin, M., & Mester, L. (1992). Debt covenants and renegotiation. Journal of Financial Intermediation, 2, 95–133.

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Blume, M. E., Lim, F., & Mackinlay, A. C. (1998). The declining credit quality of U.S. corporate debt: Myth or reality? Journal of Finance, 53, 1389–1412. Bolton, M., & Scharfstein, D. (1996). Optimal debt structure and the number of creditors. Journal of Political Economy, 104(1), 1–25. Boot, A. W., & Thakor, A. V. (2000). Can relationship banking survive. Journal of Finance, 55, 679–713. Carey, M., Post, M., & Sharpe, S. A. (1998). Does corporate lending by banks and finance companies differ? Evidence on specialization in private debt contracting. Journal of Finance, 53, 3. Chemmanur, T. J., & Fulghieri, P. (1994). Reputation, renegotiation and the choice between bank loans and publicly traded debt. Review of Financial Studies, 7, 475–506. D’Auria, C., Foglia, A., & Reedtz, P. M. (1999). Bank interest rates and credit relationships in Italy. Journal of Banking and Finance, 23, 1067–1093. Degryse, H., & Ongena, S. (2001). Bank relationships and firm profitability. Financial Management, 30(1), 9–34. Dennis, S., Nandy, D., & Sharpe, I. G. (2000). The determinants of contract terms in bank revolving credit agreements. Journal of Financial and Quantitative Analysis, 35, 87–110. Detragiache, E., Garella, P. G., & Guiso, L. (2000). Multiple versus single banking relationships: Theory and evidence. Journal of Finance, 55, 1133–1161. Farinha, L., & Santos, J. A. C. (2002). Switching from single to multiple bank lending relationships: Determinants and implications. Journal of Financial Intermediation, 11, 124–151. Gilson, S. C., & Warner, J. B. (2000). Private versus public debt: Evidence from firms that replace bank loans with junk bonds. Working Paper. Harvard Business School. Gorton, G., & Kahn, J. (1993). The design of bank loan contracts, collateral, and renegotiation. Working Paper. National Bureau of Economic Research. Greene, W. H. (1999). Econometric analysis. Upper Saddle River, NJ: Prentice-Hall. Gujarati, D. N. (1995). Basic econometrics. McGraw-Hill. Harhoff, D., & Korting, T. (1998). How many creditors does it take to Tango? Berlin: Wissenschaftszentrum. Houston, J., & James, C. (1996). Bank information monopolies and the mix of private and public debt claims. Journal of Finance, 51, 1863–1890. Houston, J., & James, C. (2001). Do relationships have limits? Banking relationships, financial constraints, and investment. Journal of Business, 74, 347–374. Hubbard, R. G., Kuttner, K. N., & Palia, D. N. (1999). Are there “bank effects” in borrowers’ cost of funds?: Evidence from a matched sample of borrowers and banks. Working Paper. Federal Reserve Bank of New York. John, K., Lynch, A. W., & Puri, M. (2002). Credit ratings, collateral and loan characteristics: Implications for yield. Journal of Business. Johnson, S. A. (1998). Effect of bank debt on optimal capital structure. Financial Management, 27(1), 47–56. Lang, L., Ofek, E., & Stulz, R. (1996). Leverage, investment and firm growth. Journal of Financial Economics, 40, 3–29. Maddala, G. S. (1983). Limited dependent and qualitative variables in economics. New York, NY: Cambridge University Press. Mallar, C. D. (1977). The estimation of simultaneous probability models. Econometrica, 45(7), 1717–1722. McKelvey, R., & Zavoina, W. (1975). A statistical model for the analysis of ordinal level dependent variables. Journal of Mathematical Sociology, 4, 103–120.

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Petersen, M., & Rajan, R. (1994). The benefits of lending relationships: Evidence from small business data. Journal of Finance, 49, 3–37. Pozzolo, A. F. (2002). Secured lending and borrowers’ riskiness. Working Paper. Banca d’ Italia. Rajan, R. (1992). Insiders and outsiders: The choice between informed and arm’s-length debt. Journal of Finance, 47, 1367–1400. Rajan, R., & Winton, A. (1995). Covenants and collateral as incentives to monitor. Journal of Finance, 50, 1113–1146. Repullo, R., & Suarez, J. (1998). Monitoring, liquidation, and security design. Review of Financial Studies, 11(1), 163–187. Shockley, R. L., & Thakor, A. V. (1997). Bank loan commitment contracts: Data, theory, and tests. Journal of Money, Credit, and Banking, 29(4), 517–534. Strahan, P. E. (1999). Borrower risk and the price and nonprice terms of bank loans. Working Paper. Federal Reserve Bank of New York.

APPENDIX A DETAILED FORMULATION OF VARIABLES Variable BONDRAT

CUMPROF DEBTASST EBITSALE EBITTA FACMATUR FACSIZE FACTA FACTD

PURPGRP

FACGRP

Definition (and Data Source) Standard and Poor’s bond rating; the ratings of AAA, AA through C are translated to an ordinal scale ranging from 2 to 21 by COMPUSTAT. Cumulative Profitability = Retained Earnings/Total Assets (COMPUSTAT) Total Debt/Total Assets (COMPUSTAT) EBIT/Total Sales (COMPUSTAT) EBIT/Total Assets (COMPUSTAT) Loan Maturity in Days (LPC) Loan Size (LPC) Loan Size/Total Assets (COMPUSTAT; LPC) Loan Size/Total Debt (COMPUSTAT; LPC) Loans are categorized into one of four groups depending on their stated purpose as follows. (1) General corporate purposes. (2) Debt repayment/consolidation. (3) Take over/acquisition. (4) Other. The Loan (or facility) type is also categorized into one of four groups as follows. (1) Short term revolver. (2) Long term revolver.

Collateralization and the Number of Lenders in Private Debt Contracts

FATA FIRMVAL LTDTA MKTBOOK MKTLEV OISALE OITA RELEPS SALES SHAREPR TOTASSET ZSCORE

249

(3) Term loan. (4) Other. Fixed Assets/Total Assets (COMPUSTAT) Firm Value = Market Value of Equity + Total Debt (COMPUSTAT) Long Term Debt/Total Assets (COMPUSTAT) (Market Value of Equity + Total Debt)/(Common Equity + Total Debt) (COMPUSTAT) Market Leverage = Total Debt/(Total Debt + Market Value of Equity) (COMPUSTAT) Operating Income/Total Sales (COMPUSTAT) Operating Income/Total Assets (COMPUSTAT) Earnings Per Share/Total Assets (COMPUSTAT) Total Sales (COMPUSTAT) Share Price (COMPUSTAT) Total Assets COMPUSTAT) Altman’s (1968, 1993) Z-Score = 3.3 × (EBIT/Total Assets) + (Sales/Total Assets) + 1.4 × (Retained Earnings/Total Assets) + 1.2 × (Working Capital/Total Assets) + 0.6 × (Market Value of Equity/Total Debt) (COMPUSTAT)

250

APPENDIX B CORRELATION MATRIX FOR REGRESSION VARIABLES Table B.1. Correlation Amongst Independent Variables.

MKTLEV

ZSCORE FACGRP PURPGRP FATA LGSALE BONDRAT

MKTBOOK

ZSCORE

FACGRP

PURPGRP

FATA

LGSALE

BONDRAT

1.0000

−0.6535 0.0001*** 1.0000

−0.5666 0.0001*** 0.5631 0.0001*** 1.0000

0.0231 0.7346 0.0396 0.5610 0.0501 0.4615 1.0000

0.1265 0.0623* −0.1659 0.0142** −0.0912 0.1798 –0.0234 0.7311 1.0000

0.1830 0.0067*** −0.1612 0.0172*** −0.3397 0.0001*** 0.0665 0.3285 −0.0869 0.2012 1.0000

−0.1648 0.0148** −0.0033 0.9618 0.0957 0.1589 –0.1010 0.1373 −0.2159 0.0013*** −0.0998 0.1417 1.0000

0.5183 0.0001*** −0.3187 0.0001*** −0.2037 0.0025*** 0.1065 0.1169 0.2049 0.0024*** 0.0287 0.6740 −0.6074 0.0001*** 1.0000

−0.6535 0.0001*** −0.5666 0.0001*** 0.0231 0.7346 0.1265 0.0623* 0.1830 0.0067*** −0.1648 0.0148* 0.5183 0.0001***

0.5631 0.0001*** 0.0396 0.5610 −0.1659 0.0142** −0.1612 0.0172** −0.0033 0.9618 −0.3187 0.0001***

0.0501 0.4615 −0.0912 0.1798 −0.3397 0.0001*** 0.0957 0.1589 −0.2037 0.0025***

−0.0234 0.7311 0.0665 0.3285 −0.1010 0.1373 0.1065 0.1169

−0.0869 0.2012 −0.2159 0.0013*** 0.2049 0.0024***

−0.0998 0.1417 0.0287 0.6740

Note: The numbers below the correlation coefficients are p-values indicating significance of the correlation. ∗ Coefficients significant at the 10% level. ∗∗ Coefficients significant at the 5% level. ∗∗∗ Coefficients significant at the 1% level.

−0.6074 0.0001***

GORDON S. ROBERTS AND NADEEM A. SIDDIQI

MKTBOOK

MKTLEV

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APPENDIX C ROBUSTNESS CHECKS FOR REGRESSION RESULTS Table C.1. Alternative Regression Results. Characteristic

Firm quality Leverage Probability of distress Growth potential Loan purpose Loan type Lead lender Fixed assets Firm size

Proxy

Intercept Interdependence BONDRAT MKTLEV ZSCORE MKTBOOK PURPGRP FACGRP FINCOT FATA LGSALE Pseudo R2 N

Collateralization (1)

Multiple Creditors (2)

Coefficient

p-Value

Coefficient

−7.8320 −0.7490 0.4125

0.0001*** 0.4812 0.0002***

0.1346 0.5502 −0.0696

0.9615 0.1277 0.6072

0.0703 0.1519 0.3319 0.4676 −1.2628 0.8216

0.6323 0.7896 0.0455** 0.0785* 0.2317 0.2617

0.1320 0.5475 −0.1046 −0.1161

0.1002 0.1464 0.5200 0.6318

0.7061

0.0000*** 218

0.2206 0.4746

p-Value

0.0492** 0.0118*** 218

Note: Results shown are those from the second stage of a 2-stage simultaneous equations model, using corrected asymptotic variances, with the market leverage variable dropped. The variables are as defined in Appendix A. Column 1 is a probit model where 1 = Collateral, and 0 = No Collateral. Column 2 is also a probit model where 1 = Multiple Creditors, and 0 = Single Creditor. ∗ Coefficients significant at the 10% level. ∗∗ Coefficients significant at the 5% level. ∗∗∗ Coefficients significant at the 1% level.

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Table C.2. Alternative Regression Results. Characteristic

Firm quality Leverage Probability of distress Growth potential Loan purpose Loan type Lead lender Fixed assets Firm size

Proxy

Intercept Interdependence BONDRAT MKTLEV ZSCORE MKTBOOK PURPGRP FACGRP FINCOT FATA LGSALE Pseudo R2 N

Collateralization (1)

Multiple Creditors (2)

Coefficient

p-Value

Coefficient

p-Value

−7.0433 −0.5770 0.4223 −1.2455 0.0033

0.0000*** 0.4383 0.0005*** 0.5413 0.9527

1.7029 0.5857 −0.0122 −3.0691 0.0496

0.5605 0.1292 0.9320 0.0038*** 0.5044

0.3123 0.4315 −1.1818 0.7777

0.0320** 0.0605* 0.1772 0.2408

−0.1526 −0.1612

0.3784 0.5247

0.7001

0.0000*** 218

0.2550 0.4371

0.0318** 0.0004*** 218

Note: Results shown are those from the second stage of a 2-stage simultaneous equations model, using corrected asymptotic variances, with the growth potential variable dropped. The variables are as defined in Appendix A. Column 1 is a probit model where 1 = Collateral, and 0 = No Collateral. Column 2 is also a probit model where 1 = Multiple Creditors, and 0 = Single Creditor. ∗ Coefficients significant at the 10% level. ∗∗ Coefficients significant at the 5% level. ∗∗∗ Coefficients significant at the 1% level.

AN EXAMINATION OF THE EFFICIENCY OF SINGLE VS. MULTIPLE COMMON BOND CREDIT UNIONS James D. Tripp, Peppi M. Kenny and Don T. Johnson ABSTRACT As of 1982, federal credit unions were allowed to add select employee groups and thus create institutions with multiple-group common bonds. We examine the efﬁciency of single bond and multiple bond federal-chartered credit unions by using data envelopment analysis (DEA), a non-parametric, linear programming methodology. Results indicate that multiple bond credit unions have better pure technical efﬁciency than single bond credit unions. However, single bond credit unions appear to be more scale efﬁcient than the multiple bond credit unions. Our results also indicate that members of multiple bond credit unions may derive greater wealth gains than members of single bond credit unions.

1. INTRODUCTION In 1981, approximately 500 federal-chartered credit unions closed their doors due to failure or liquidation. The U.S. economy was suffering through one of its worst recessions since the early 1930s. The number of business failures rose Research in Finance Research in Finance, Volume 21, 253–263 Copyright © 2004 by Elsevier Ltd. All rights of reproduction in any form reserved ISSN: 0196-3821/doi:10.1016/S0196-3821(04)21011-5

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dramatically, particularly in those industries referred to as “smokestack.” Many of the occupational-based credit unions that served these smokestack industries found themselves in critical situations with their futures jeopardized. It was at this point, in April 1982, that the National Credit Union Administration (NCUA) implemented a change in policy to try to reduce the number of failures that was occurring. That change was to allow federal credit unions to add select employee groups (SEGs) to their membership, and thereby create occupational-based credit unions with multiple-group common bonds. Federal credit unions could then expand their existing charters to serve different membership groups as long as each group had its own common bond (Johnson, 1999). This ruling by the NCUA had an immediate impact on the number of credit union failures. In 1982, 272 credit unions failed or were liquidated and that number fell to 90 in 1983. This policy change allowed occupational credit unions to diversify their membership base and no longer be dependent on a single employer. By 1997, over 3,600 federal credit unions had changed their charters and added at least one SEG. The commercial banking industry vigorously opposed this common bond expansion, fighting it all the way to the U.S. Supreme Court and winning (National Credit Union Administration vs. First National Bank and Trust). However, in 1998, Congress passed the Credit Union Membership Access Act that effectively endorsed this looser form of organizational common bond for credit unions. A December 1999 survey by the Credit Union National Association (CUNA) reported that over 40% of all credit unions now served multiple groups (Johnson, 1999). The NCUA’s concern regarding the lack of diversification in the customer base of occupational credit unions mirrored similar concerns that were raised regarding the savings and loan (S&L) industry in the early 1980s. S&L regulators were concerned about the inability of savings institutions to diversify their asset portfolios due to the restrictions on the types of loans that could be made. This created a high degree of concentration risk for the S&L industry. Similarly, the NCUA felt that occupational credit unions serving only a single employer had very high levels of concentration risk. This notion of greater concentration risk is supported by an empirical study done by Kohers (1986) and who reported that occupational credit unions serving sponsors operating in unstable business-cycle environments experienced higher loan delinquency rates and held higher levels of liquidity. A more recent study by Frame, Karels and McClatchey (2002) also found evidence of benefits from diversification in credit union membership. While these studies address the reduction in risk that accrues to credit unions that expand their membership base, little research has been undertaken to evaluate the impact of having a multiple common bond on credit union efficiency.

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255

A study by Emmons and Schmid (1999), reported that similar preferences of members in multiple-group credit unions might allow those credit unions the opportunity to be more efficient. Additionally, they show graphically that average operating costs decrease as the number of members increases. However, regression results indicated a positive relation between multiple membership groups and the ratio of total operating expenses to total assets, indicating inefficiencies may exist. If inefficiencies do exist in multiple bond credit unions, how does this affect credit union members? In the profit-driven banking industry, bank shareholders should be financially rewarded as their banks operate more efficiently. However, in not-for-profit credit unions, members/owners may not be rewarded as efficiency increases. Hinson and Juras (2002) posit that wealth gains may accrue to members of credit unions that have narrower spreads between loan rates and deposit rates. The purpose of our paper is to examine technical efficiency, both pure technical and scale, of single bond and multiple bond credit unions over a five-year period (1998–2002). We utilize data envelopment analysis (DEA) a non-parametric, linear programming methodology to expose any inefficiencies that might exist. In addition, we utilize a method similar to Hinson and Juras (2002) to evaluate whether the type of membership (single or multiple bond) has any impact on wealth gains that accrue to members.

2. RELEVANT LITERATURE Over the past twenty years, many researchers have studied the issue of efficiency in financial institutions. The bulk of this research has focused on the commercial banking industry. Studies focusing on the banking industry generally conclude that inefficiencies found are primarily due to the inefficient utilization of resources (poor management) rather that scale inefficiencies related to inappropriate size (see Aly et al., 1990; Elysasiani & Mehdian, 1990; Ferrier & Lovell, 1990; Grabowski et al., 1994; Miller & Noulas, 1996; Rangan et al., 1988). The efficiency of one type of financial institution, credit unions, has been less frequently considered. In addition to the Emmons and Schmid (1999) research, a general study of credit union efficiency was undertaken by Fried, Lovell and Vanden Eeckaut (1993). They reported an average of 20% productive inefficiency in the U.S. credit unions they examined. Other credit union studies have focused on efficiency issues in the Australian market. Worthington (1999, 2000) reported overall technical inefficiency at 46% in one study and 30% in another. However, it should be noted that there are substantial differences between U.S. and Australian

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credit unions. For example, Australian credit unions pay a federal income tax while U.S. credit unions do not. In order to compete effectively with other credit unions and other financial institutions, it is imperative for credit unions to be as efficient as possible.

3. DATA Data were collected for the years 1998–2002 from the National Credit Union Administration’s on-line database (NCUA, 2003) that contains financial and statistical reports filed by U.S. credit unions. For our study, we chose occupational credit unions, both single bond (Type 13) and multiple bond (Type 43), whose primary sponsors operated in the machine manufacturing industry. As mentioned earlier, credit unions with sponsors operating in the more cyclical business sectors face more concentration risk and therefore would be more likely to diversify by adding SEGs to the existing membership. We restricted our sample to credit unions operating in the machine-manufacturing sector to limit the impact of economic variability across industries on our results. The resulting data set included 36 single bond credit unions and 58 multiple bond. In order to test for efficiency, it must first be determined what specifically do credit unions produce, or what is their output. Two approaches used in previous studies regarding financial institutions were considered: the intermediation approach and the production approach. Under the intermediation approach, financial institutions are considered producers of services that collect deposits and purchase funds that are intermediated into loans and other assets. Additionally, deposits are viewed as inputs, along with labor and capital, while measures of output are defined as the financial institution’s various dollar volumes of earning assets. Finally, under the intermediation approach, total cost is defined as total operating costs and interest expense. Alternatively, under the production approach, financial institutions are viewed as producers of services related to individual deposit and loan accounts. Both capital and labor are used to produce these account services. Output is defined as the number of deposit and loan accounts and total cost is defined as total operating costs and does not include interest expense. Also, according to Humphrey (1985), some control factor for differences in the average sizes of accounts across different-sized financial institutions must be incorporated under this approach. According to Clark (1988), reasonable arguments have been made for both approaches to modeling a financial institution’s behavior. Clark also noted that the empirical results do not appear to be sensitive to the method used in defining costs and outputs.

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Table 1. Descriptive Means of Credit Uniona Variables, 1998–2002.

Total loans Total investments Total assets Total shares and deposits Total interest expense Total non-interest expense Total income

Single Bond

Multiple Bond

$1,442,771 $780,713 $2,311,683 $1,917,534 $64,593 $72,461 $166,766

$18,129,815 $9,335,428 $28,875,096 $24,686,060 $861,687 $842,899 $2,155,058

a The

sample consists of occupational credit unions whose primary sponsors were in the machine manufacturing industry.

For purposes of this paper, the intermediation approach is utilized. Using this method, input and output variables comparable to those used by Miller and Noulas (1996) in their study of bank performance were selected. The input variables (in dollars) are: (1) Total shares and deposits (TSD) (2) Total interest expense (TIE = interest on borrowed money + dividends on shares + interest on deposits) (3) Total non-interest expense (TNIE = total operating expenses less provision for loan losses). The outputs variables (in dollars) are: (1) Total loans (TL = unsecured credit card loans + all other unsecured loans + new vehicle loans + used vehicle loans + total all other loans to members + total first mortgage real estate loans + total other real estate loans) (2) Total investments (TIN) (3) Total income (TI = interest on loans – interest refunded + income from investments + income from trading securities + fee income + other operating income). Sample statistics are displayed in Table 1.

4. METHODOLOGY These input and output variables are utilized in a data envelopment analysis model (DEA) in order to examine efficiency of multiple common bond and single bond credit unions. The use of DEA for purposes such as this was first introduced by Charnes, Cooper and Rhodes (CCR) in 1978. DEA models seek to determine

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which decision making units (DMUs) under consideration are efficient given the use of m inputs for generating s outputs. The efficient DMUs out of the set of n DMUj (where j = 1, . . ., n) will lie on the envelopment surface. Inefficient DMUs do not lie on the surface. In developing the envelopment surface through solving mathematical programming models, each DMUj is examined relative to the other DMUs in the sample. Consequently, the measured efficiency is sample specific. The first model utilized examines an input-oriented data envelopment frontier with variable returns to scale as originally developed by Banker, Charnes, and Cooper (BCC model, 1984). The model uses n DMUj (j = 1, 2, . . ., n) observations with m inputs represented by xij (i = 1, 2, . . ., m) and s outputs represented by yrj (r = 1, 2, . . ., s). With variable returns to scale the model can be formulated as follows (Zhu, 2003): m s s− s+ min␪−␧ r i + i=1

r=1

subject to n

␭j x ij + s − i = ␪x io ,

i = 1, 2, . . . , m;

j=1 n

␭j y rj − s + r = y ro ,

r = 1, 2, . . . , s;

j=1

␭j ≥ 0,

j = 1, 2, . . . , n

and n

␭j = 1

j=1 + with s − i representing the input slack, s r representing the output slack, ??, is a non-archimedean constant, and λj being nonnegative scalars. This BCC model provides a measure of pure technical efficiency. For the constant returns to scale input-oriented data envelopment model as originally developed by Charnes, Cooper and Rhodes (CCR model, 1978), the last condition above, nj=1 ␭j = 1, is dropped. The CCR model provides an overall technical efficiency measure. The desired output from the models is an efficiency score. The efficient target with variable or constant returns to scale is given by (Zhu, 2003): ∗

xˆ io = ␪∗ x io − s − i

i = 1, 2, . . . , m

An Examination of the Efﬁciency of Single vs. Multiple Common Bond ∗

yˆ ro = y ro + s + r

259

r = 1, 2, . . . , s

with efficiency scores represented by ␪∗ . In order to apply the above, a twostage process of calculations is necessary. First optimal ␪∗ is found through the maximization of a reduction in inputs. Second, optimizing the slack variables is considered to move DMUs onto the efficient frontier. In utilizing the model, efficiency scores represented by ␪∗ are generated for each DMU. The DMUs with ␪∗ = 1 are those that fall on the efficient frontier. All other DMUs could improve efficiency by decreasing input levels. Overall technical efficiency, as given by the CCR model, can be separated into two components: pure technical efficiency and scale efficiency. By adding the convexity constraint in the BCC model, variable returns to scale are permitted and consequently a measure of pure technical efficiency is produced from the BCC model (Worthington, 1999). A measure of scale efficiency can then be generated by dividing overall technical efficiency by pure technical efficiency (CCR result/BCC result) (Mosheim, 2004). Graphical depiction of these efficiency components can be found in Miller and Noulas (1996). In order to test for the impact of membership type (single or multiple bond) on wealth gains to credit union members, we used a technique similar to Hinson and Juras (2002). These authors posit that federally tax-exempt credit unions’ profits belong to members/owners and that credit union management should strive to offer lower loan rates and higher deposit rates to their memberships. While Hinson and Juras utilize net interest margin as a proxy for wealth gains, we focus on the yield spread between the share yield (dividends on shares divided by total shares) and loan yield (interest received on loans less rebates divided by total loans) as our measure.

5. RESULTS The causes of inefficiency for a DMU can stem from two sources. The DMU’s inefficiency may be a result of inefficient operations (as measured by pure technical efficiency) or be attributed to disadvantageous conditions (as measured by scale efficiency) related to the environment in which it operates (Cooper et al., 2000). The overall technical efficiency (OTE), pure technical efficiency (PTE), and scale efficiency (SE) scores for the 36 single bond (Type 13) and 52 multiple bond (Type 43) credit unions are displayed in Table 2. The OTE scores for both the single bond and the multiple bond credit unions showed relatively high levels of global efficiency under the assumption of constantreturns-to-scale. The OTE scores for single bond credit unions ranged from a low

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Table 2. DEA Mean Efficiency Scores. Year

Bond

Pure Technical Efficiencya,b

Overall Technical Efficiencya,c

2002

Scale Efficiencya

Multiple Single

0.958335 0.934366*

0.896216 0.899950

0.935713 0.964157**

2001

Multiple Single

0.962876 0.941904

0.952796 0.929627*

0.989622 0.987044

2000

Multiple Single

0.956571 0.921376**

0.924107 0.904476

0.965759 0.981117**

1999

Multiple Single

0.951139 0.944458

0.877354 0.895255

0.923102 0.948185*

1998

Multiple Single

0.968690 0.960163

0.948237 0.950947

0.979117 0.990202**

a Efficiency

scores are sample specific to the credit unions within the sample. A higher score indicates greater efficiency; the credit unions that are most efficient have a score of 1.0. b A measure of operational efficiency. c A measure of global efficiency. ∗ Significant at 10%. ∗∗ Significant at 5%.

of 0.895255 in 1999 to a high of 0.950947 in 1998 and averaged 0.916051 for the five years studied. The multiple bond credit unions’ OTE scores ranged from a low of 0.877354 in 1999 to a high of 0.952796 in 2001 and averaged 0.919742. These results indicate that the inefficiency was approximately 8% for both types and is smaller than reported in other U.S. credit union studies. However, sample and methodological differences when utilizing DEA make it very difficult to compare our results to other credit unions studies. The PTE scores reported in Table 2 provide efficiency measures using a local measure of scale under the assumption of variable returns to scale. The findings show that the multiple bond credit unions were more efficient on a pure technical basis in all five years examined. These differences were significant at the 0.10 level in 2002 and the 0.05 level in 2000. This finding is indicative of greater managerial efficiency in the multiple bond credit unions. However, the scale efficiency (SE) scores displayed in Table 2 highlight an efficiency advantage for the single bond credit unions. As reported earlier in Table 1, the average single bond credit union was substantially smaller than the average multiple bond credit union over the 1998–2002 time period (total assets of $2.3 million vs. $28.9 million). According to Cooper et al. (2000), this

An Examination of the Efﬁciency of Single vs. Multiple Common Bond

261

Table 3. Yield and Yield Spread Means. Loan Yielda (%)

Share Yieldb (%)

Yield Spreadc (%)

Year

Type of Bond

2002

Multiple Single

8.3501 10.0782***

2.3346 2.3968

6.0155 7.6814***

2001

Multiple Single

9.0058 9.9805**

3.3466 3.5817

5.6590 6.3988*

2000

Multiple Single

8.5101 9.3825**

3.6695 4.0961***

4.8406 5.2864

1999

Multiple Single

8.8000 9.9233**

3.5686 3.9639**

5.2314 5.9595

1998

Multiple Single

9.1589 9.9720**

3.6891 3.9270

5.4699 6.0450

a Interest

received on loans, less rebates, divided by total loans. on shares divided by total shares. c Loan Yield minus Share Yield. ∗ Significant at 10%. ∗∗ Significant at 5%. ∗∗∗ Significant at 1%. b Dividends

may indicate that these smaller credit unions are operating under advantageous conditions relative to larger multi-bond credit unions. SE results in Table 2 reveal that single bond credit unions had significantly higher efficiency scores in four of the five years studied. Table 3 presents the results regarding differences in member wealth gains between single bond and multiple bond credit unions over the 1998–2002 timeperiod. The yield spread is lower in all five years for the multiple bond credit unions and significantly so in 2001 (0.10 level) and 2002 (0.01 level). Multiple bond credit unions had significantly lower loan rates in all five years studied while the single bond credit unions provide higher share rates. However, as interest rates in the economy trended lower in 2001 and 2002, there was no significant difference in the share rates of the two types of credit unions. This finding indicates that multiple bond credit unions may be improving their members’ financial welfare by providing better interest rates than single bond credit unions.

6. CONCLUSIONS Prior credit union research has shown that the creation of multiple bond credit unions has reduced the amount of concentration risk in the industry. The results of

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our study reveal additional benefits of this diversification. As measured by the pure technical efficiency scores, multiple bond credit unions appear to offer superior managerial expertise. These larger multiple bond credit unions are quite likely managed by individuals with higher levels of education and greater experience resulting in greater operational efficiency. In addition, these multiple bond credit unions appear to pass along the financial gains of this managerial efficiency to their members by offering superior rates over their single bond counterparts. The only negative finding regarding multiple bond credit unions concerns their scale efficiency. Our results indicate that the larger multi-bond credit unions are less efficient on a size basis than the smaller single bond credit unions. From a regulatory perspective, the results of our study should be encouraging since both single and multiple bond credit unions appear to be operating at relatively high levels of overall efficiency. Additionally, the finding that multiple bond credit unions may offer better managerial efficiency and wealth gains to their members might justify regulators promoting further expansion in this area.

REFERENCES Aly, H. Y., Grabowski, R., Pasurka, C., & Rangan, N. (1990). Technical, scale and allocative efficiencies in U.S. banking: An empirical investigation. Review of Economics and Statistics, 72, 211–218. Banker, R. D., Charnes, A., & Cooper, W. W. (1984). Some models for estimating technical and scale inefficiencies in data envelopment analysis. Management Science, 30(9), 1078–1092. Charnes, A., Cooper, W. W., & Rhodes, E. (1978). Measuring efficiency of decisions making units. European Journal of Operational Research, 2, 429–444. Clark, J. A. (1988). Economies of scale and scope at depository financial institutions: A review of the literature. Economic Review, Federal Reserve Bank of Kansas City, September/October, 16–23. Cooper, W. C., Seiford, L. M., & Tone, K. (2000). Data envelopment analysis: A comprehensive text with models, applications, references and DEA-solver software. Boston: Kluwer. Elysasiani, E., & Mehdian, S. M. (1990). A nonparametric approach to measurement of efficiency and technological change: The case of large U.S. commercial banks. Journal of Financial Services Research, 4, 157–168. Emmons, W. R., & Schmid, F. A. (1999). Credit unions and the common bond. The Federal Reserve Bank of Saint Louis Review, 81(September/October), 41–64. Ferrier, G. D., & Lovell, C. A. K. (1990). Measuring cost efficiency in banking: Econometric and linear programming evidence. Journal of Econometrics, 46(October/November), 229–245. Frame, W. S., Karels, G. V., & McClatchey, C. (2002). The effect of the common bond and membership expansion on credit union risk. Financial Review, 37(November), 613–636. Fried, H. O., Lovell, C. A. K., & Vanden Eeckaut, P. (1993). Evaluating the performance of U.S. credit unions. Journal of Banking & Finance, 17, 251–265. Grabowski, R., Rangan, N., & Rezvanian, R. (1994). The effect of deregulation on the efficiency of U.S. banking firms. Journal of Economics and Business, 46, 39–54. Hinson, Y. L., & Juras, P. E. (2002). Performance evaluation of credit unions: Reaping the benefit of tax status. Journal of Managerial Issues, 14, 145–161.

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Humphrey, D. B. (1985). Cost and scale economies in bank intermediation. In: R. Aspinwall & R. Eisenbeis (Eds), Handbook for Bank Strategy. New York: Wiley. Johnson, E. (1999). Multiple-group memberships, http://www.cuna.org/data/newsnow. Kohers, T. (1986). Parent organization’s activities as a cause for differential credit union operating characteristics. Southwest Journal of Business and Economics, 4(Fall), 11–21. Miller, S. M., & Noulas, A. G. (1996). The technical efficiency of large bank production. Journal of Banking & Finance, 20, 495–509. Mosheim, R. (2004). The efficiency of credit unions in Hawaii and Puerto Rico. http://www.ceterisparibus.uprm.edu/articulos/vol3/articulo6.htm. NCUA (2003). Call report data files under FOIA. http://www.ncua.gov/data/FOIA/foia.html, Alexandria: NCUA. Rangan, N., Grabowski, R., Aly, H. Y., & Pasurka, C. (1988). The technical efficiency of U.S. banks. Economic Letters, 28, 169–175. Worthington, A. C. (1999). Measuring technical efficiency in Australian credit unions. The Manchester School, 67(March), 231–248. Worthington, A. C. (2000). Cost efficiency in Australian non-bank financial institutions: A nonparametric approach. Accounting and Finance, 40, 75–97. Zhu, J. (2003). Quantitative models for performance evaluation and benchmarking: Data envelopment analysis with spreadsheets and DEA Excel solver. Boston: Kluwer.