Profiting with Synthetic Annuities
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Profiting with Synthetic Annuities Option Strategies to Increase Yield and Control Portfolio Risk Michael Lovelady
Vice President, Publisher: Tim Moore Associate Publisher and Director of Marketing: Amy Neidlinger Executive Editor: Jim Boyd Editorial Assistant: Pamela Boland Operations Specialist: Jodi Kemper Marketing Manager: Megan Graue Cover Designer: Alan Clements Managing Editor: Kristy Hart Senior Project Editor: Lori Lyons Copy Editor: Krista Hansing Editorial Services Proofreader: Sheri Cain Indexer: Brad Herriman Compositor: Nonie Ratcliff Graphics: Laura Robbins, Tammy Graham Manufacturing Buyer: Dan Uhrig © 2012 by Michael Lovelady Pearson Education, Inc. Publishing as FT Press Upper Saddle River, New Jersey 07458 This book is sold with the understanding that neither the author nor the publisher is engaged in rendering legal, accounting, or other professional services or advice by publishing this book. Each individual situation is unique. Thus, if legal or financial advice or other expert assistance is required in a specific situation, the services of a competent professional should be sought to ensure that the situation has been evaluated carefully and appropriately. The author and the publisher disclaim any liability, loss, or risk resulting directly or indirectly, from the use or application of any of the contents of this book. FT Press offers excellent discounts on this book when ordered in quantity for bulk purchases or special sales. For more information, please contact U.S. Corporate and Government Sales, 1-800-382-3419,
[email protected]. For sales outside the U.S., please contact International Sales at
[email protected]. Company and product names mentioned herein are the trademarks or registered trademarks of their respective owners. Certain screenshots, including Options Analysis Workspace and Theoretical Positions, were created with TradeStation. ©TradeStation Technologies, Inc. All rights reserved. All rights reserved. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Printed in the United States of America First Printing June 2012 ISBN-10: 0-13-292911-2 ISBN-13: 978-0-13-292911-0 Pearson Education LTD. Pearson Education Australia PTY, Limited. Pearson Education Singapore, Pte. Ltd. Pearson Education Asia, Ltd. Pearson Education Canada, Ltd. Pearson Educatión de Mexico, S.A. de C.V. Pearson Education—Japan Pearson Education Malaysia, Pte. Ltd. Library of Congress Cataloging-in-Publication Data Lovelady, Michael Lynn, 1957Profiting with synthetic annuities : option strategies to increase yield and control portfolio risk / Michael Lynn Lovelady. -- 1st ed. p. cm. ISBN 978-0-13-292911-0 (hardcover : alk. paper) 1. Options (Finance) 2. Annuities. 3. Risk management. I. Title. HG6024.A3L68 2012 368.3’7--dc23 2012009307
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Chapter 1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Chapter 2
Synthetic Annuity Design . . . . . . . . . . . . . . . . . . . . . . . . . 25
Chapter 3
Tracking Performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
Chapter 4
Covered Synthetic Annuities . . . . . . . . . . . . . . . . . . . . . . . 69
Chapter 5
Managing a Covered Synthetic Annuity . . . . . . . . . . . . . . 99
Chapter 6
Generalized Synthetic Annuities . . . . . . . . . . . . . . . . . . . 127
Chapter 7
Managing a Generalized SynA . . . . . . . . . . . . . . . . . . . . 151
Chapter 8
Synthetic Annuities for High-Yielding Stocks . . . . . . . . 169
Chapter 9
Synthetic Annuities for the Bond Market . . . . . . . . . . . . 183
Chapter 10 Synthetic Annuities for the Volatility Market . . . . . . . . . 207 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 225
Acknowledgments I would like to express my sincere gratitude to several people who made this book possible. At Pearson/FT Press, my editor Jim Boyd, who believed in the material and understood better than me what the scope of the book should be; Michael Thomsett, who gave the project invaluable guidance and direction from beginning to end; Lori Lyons, for her dedicated and patient production management; Krista Hansing, for copyedits; and all those who helped with marketing, illustration, and production. I would also like to thank Don DePamphilis at Loyola Marymount University for giving me the idea to write the book and being a mentor; Cooper Stinson, a gifted writer who reviewed early manuscripts and asked all the right questions; Leslie Soo Hoo, for much needed help in reading and revising drafts; and Abbie Reaves, for editing. Also, my friends and family who gave me encouragement and inspiration, and forgave me for missing tee times: my parents, Abigail, Alice, Billie, Brennan, Colby, Connor, Ethan, Eva, Frank, Hannah, Joanna, Lindsey, Matty, Noah, Nolan, Petra, Sally, Steve-O, and Tony. Above all, for life itself, the Triune God of Creation—I always remember.
About the Author Michael Lovelady, CFA, ASA, EA, is the investment strategist and portfolio manager for Oceans 4 Capital Group LLC. Michael designs and implements reduced-volatility and theta-generating hedge fund investment strategies. He developed the “synthetic annuity” (SynA) and uses it extensively in portfolio management. Prior to founding Oceans 4, Michael worked as a consulting actuary for Towers Watson and PricewaterhouseCoopers. Much of his work was related to design issues at a time when many employers were moving away from traditional defined benefit plans. Michael worked with clients to consider and implement alternatives ranging from defined contribution to hybrid DB/DC plans. His experience with retirement income strategies, from both the liability and asset sides, has given him a unique perspective. Michael has also been involved in teaching and creating new methods for making quantitative investing more accessible to students, trustees, and others without math or finance backgrounds. He developed the investment profile—a graphical representation of investments and the basis of a simplified option pricing model, and visually intuitive presentations of structured securities. Michael has served various organizations, including Hughes Aircraft, Boeing, Global Santa Fe, Dresser Industries, the Screen Actors Guild, The Walt Disney Company, Hilton Hotels, CSC, and the Depository Trust Company. He is a CFA charterholder, an Associate of the Society of Actuaries, and an ERISA Enrolled Actuary. He currently lives in Los Angeles.
Preface Profiting with Synthetic Annuities is about the use of options in investing and portfolio management. This book is written for experienced investors who are considering option strategies, for experienced option traders, and for institutional investors interested in alternative strategies. Synthetic annuities are structured securities that use options and management rules to customize the risk/return profile of investments. Options are used to create a synthetic risk-smoothing mechanism and annuity-like cash flows. The management rules are designed to mitigate risk and maximize income over the long term. Together, the options structure and management rules address several emerging issues in investment management:
• The explicit use of hedging, insurance, and risk allocations in risk management instead of reliance on traditional portfolio models
• The desire for greater yields not related to market direction
• A recognition of behavioral influences on investor performance
• The growing importance of volatility-reducing quantitative methods, particularly those related to stock options
• The desire of many investors for annuity-like income streams.
Unlike many books on options and options strategies that deal mainly with tactical trading, Profiting with Synthetic Annuities is about the strategic use of options as integral components of investment portfolios. Synthetic annuities treat options as permanent components of an investment position. The goal is to create a hybrid architecture that balances the long-term investor perspective of mean-variance portfolios and the risk discipline of quantitative-based strategies.
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In terms of presentation, Profiting with Synthetic Annuities uses a unique visual representation of structured securities. As a result, few formulas appear in the book; instead, graphical interpretations communicate the ideas and compare alternative investments.
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1 Introduction If you Google the term synthetic annuity, you won’t find much. There is a reference to an obscure tax issue, as well as an article about design projects by several investment firms and insurers who believe the next Holy Grail is an annuity-like product for 401(k) plans that allows participants to convert highly volatile assets into defined benefit type payments. According to the article, the product rollouts are moving slowly, despite the names behind them: Alliance Berstein, AXA, Barclays Global Investors, John Hancock, MetLife, and Prudential. The products, called hybrid 401(k)s, combine investment portfolios with annuity contracts. The annuities are purchased gradually over time. As plan participants get closer to retirement, the annuities become a larger portion of the total portfolio, providing more stability in later years. The idea behind the product is great, especially considering the massive shift from defined benefit (DB) plans (traditional pension plans) to defined contribution (DC) plans. The problem is, few people are interested. Because interest rates are currently so low, annuity prices, which move in the opposite direction from interest rates, are some of the highest in two generations. And the hybrids won’t protect investors against market crashes, at least for the portfolio assets.1 DC plans such as 401(k)s and IRAs already have about $3½ trillion in assets and are growing fast. Retirement experts believe the growing DC asset base and lack of protection against market risk is a 1
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critical problem. The model of retirement income for the last generation involved three primary legs: defined benefit pension plans and Social Security for the two stable core elements, and 401(k) plans as a savings supplement. But with companies shutting down DB plans that leaves DC plans as the primary source of private retirement income, a role they were never really intended to play. It is estimated that in less than ten years, DC plans will have three times the assets of corporate pension plans. And the market risk of those assets will belong to the individual rather than being backstopped by corporate sponsorship. The transfer of market risk is happening at a bad time. Low interest rates are limiting what can be done in new product design, 70 million Baby Boomers are getting ready to retire and there is no obvious successor to modern portfolio theory (MPT) for building riskcontrolled portfolios. Current low interest rates are also causing managers to rethink asset allocations. In most portfolios, reducing risk means allocating more of the portfolio to bonds, a traditionally less volatile asset class. But in today’s market, with interest rates at 50- to 60-year lows, high allocations to bonds might be the most risky thing an investor can do. At the short end of the yield curve the risk is created by near-zero yields, causing investors to fall behind accumulation goals. At the long end of the curve, the risk is that interest rates might start to go up, causing the value of the bonds to go down. Bond markets can experience the same kind of extended bear markets as equities. From the 1940s until the 1980s, Treasury bonds lost about two-thirds of their value as rates increased, making this one of the worst bear markets in any asset class. Warren Buffett said recently that bonds should come with a warning label. In terms of building risk-controlled portfolios, MPT has failed repeatedly to protect investors during market crashes, which we saw again during the 2008-2009 financial crisis. Diversification, the main risk-management mechanism of MPT, breaks down during extreme events. With MPT behind both institutional portfolios and today’s
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most popular retail products such as balanced mutual funds, target date and life-cycle plans, corporations and individuals are facing the same challenges. How to generate yield in a low interest rate environment? How to control volatility in the equity markets? And how to construct portfolios with limited downside? These are industry-wide issues. The need to focus not only on accumulating wealth, but also on products that offer yield and protection against market risks has been identified as a major trend. In a 2010 report, The Research Foundation of the CFA Institute said “As the world moves from DB to DC plans, the financial services industry will have to meet two big challenges: to engineer products that offer some sort of downside protection and to reduce the overall cost to the beneficiary.”2 Working within the constraints of low bond yields and traditional design tools is unlikely to produce anything investors will get excited about. That is why these are described as big challenges. They require moving outside the current design sets. The challenge of providing downside protection is not simple. There are theoretical and practical obstacles that have become engrained in investment practice. Reducing the overall cost to the beneficiary means finding higher yields than are currently available in the bond markets. This book presents an approach to meeting these challenges by adding options to the design set—not as trading devices, but as structural long-term components of securities and portfolios. Optionsbased strategies are exciting today for many reasons. For active traders, options create incredible flexibility for taking advantage of tactical opportunities. For investors and portfolio managers, options create new yield and risk management capabilities. For asset managers and insurance companies designing products, options offer new ways of translating design principles into product offerings. The next section looks at the design principles used for a fairly conservative, long-term investor form of synthetic annuity. The remainder of this chapter puts the two big challenges in historical and
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theoretical context in order to understand why these problems have persisted for so long and why it is difficult to find solutions.
What a Synthetic Annuity Is—and Is Not Normally in finance, the term synthetic describes a look-alike security. For instance, if you want to create a stock position without holding stock, you buy a call option, sell a put option, and hold a specific bond. Because the payoff of this combination is the same as that of the stock, it is referred to as a synthetic stock. The synthetic annuity described in this book, the SynA, is not a true synthetic in that sense. It is not designed to replicate the guaranteed cash flows of a simple annuity, although it does have features similar to those of an equity-indexed annuity, and it attempts to accomplish some of the same objectives as the hybrid 401(k). Instead of looking at the SynA as, well, a synthetic annuity, I view it more as a style of investing that reflects the following beliefs:
• Market volatility is damaging to investment results; having a mechanism other than diversification alone for managing it is important.
• Dividends have played a critical role in total returns; there are effective ways to increase them for dividend-paying stocks and manufacture them for non-dividend-paying stocks.
• Current methods of measuring risk, such as backward-looking volatility of returns, are limited. Real-time and forward-looking measures are needed to dynamically manage risk.
• Risk allocations and risk budgeting offer new ways to limit losses by including elements of hedging and insurance
• Behavioral finance is useful in recognizing behavioral influences on decision-making and the value we place on investment outcomes.
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By using options in combination with underlying securities, you can emphasize any or all of these objectives to create SynAs ranging from conservative to aggressive. And you will be able to quantify exactly how much volatility is in the position, how much current income is being generated, and how stable the position is. In its most simple form, a SynA translates beliefs and objectives into investable securities. In its generalized form, it can be used to encompass almost any options strategy and simplify them into basic metrics. Rather than having to think about many different strategies, SynAs use a common language of payback periods, market exposure and stability, the properties that are common to all structured securities.
Background In 1987, I went to work as a pension actuary for consulting firm Towers Perrin (now Towers Watson). While I was still finding my way to the office coffee machine, my newly assigned client lost $1 billion in pension assets in one day. It was October 19, 1987, Black Monday. After Black Monday, everyone began talking about risk management. On the institutional side, portfolios were hard hit just when new accounting standards required that pension plans be reflected in corporate earnings. Some of the discussion was on practical ways to immunize corporate earnings from the negative impacts of pension asset declines. But a lot of the discussion was about MPT and the most common portfolio structures, mean-variance-optimized (MVO) portfolios. In an investigation into the causes of the 1987 crash, much of the blame was aimed at Leland O’Brien and Rubinstein (LOR), the inventors of portfolio insurance, a product designed to reduce the risk in pension and other institutional funds. LOR was accused of contributing to the crash with program trading that reduced exposure
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to assets as those assets declined in value. The idea was good, but in execution, it created a cycle of selling that couldn’t be stopped once it got started. Because the bull market that began in 1982 was still intact and the issues were more technical than structural, the market recovered quickly. Portfolio insurance was part of a growing trend toward hedging market risk. There also seemed to be a growing division between those who thought MVO was still the best way to structure portfolios and those who saw a fatal flaw in the application of the theory. Proponents of MPT thought it could be fixed. They recommended some changes to improve the model, such as expanding the portfolio universe to include more asset types and geographies and improvements in the way correlation coefficients were calculated. The critics disagreed. They pointed to past market crashes and said there was a clear history of correlation coefficients converging. They said that the diversification model breaks down under stress and, in market crashes, that “correlations go to one,” eliminating the benefits of diversification.
The 1997 Echo Crash and 1998 Asian Currency Crisis Ten years after the 1987 crash, I started a hedge fund just before what was called the “echo crash.” On October 27, 1997, the Dow Jones Industrial Average fell 554 points, the largest point drop in the history of the index at the time. This time, the macro economic story was more complicated. The market was already nervous about global issues such as the developing currency crisis in Asia and debt levels in Russia. In the United States, the beginning signs of structural issues were showing and nervousness about a possible inflection point in one of the longest-running bull markets in history. (The bull market started in 1982 with the Dow Jones Industrial Average at just over 800 and ran through January 2000, when it reached almost 12,000.)
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The following year, 1998, Asia did in fact experience a currency crisis and Russia defaulted on its debt. The extent to which the U.S. markets were affected proved how interconnected the global economy had become. Also in 1998, a group of Nobel Prize winners and quantitative investors at Long Term Capital Management (LTCM) almost collapsed the U.S. financial system. I had been through the savings and loan crisis as a consultant, but LTCM was my first experience with a systemic crisis as an asset manager. The Federal Reserve eventually stepped in to coordinate a bailout that avoided a larger banking contagion. The arguments over MPT and portfolio construction continued. In fund management, there were incremental changes. The methods used to optimize allocations and define efficient frontiers were evolving, and hedge funds were making their way into more institutional portfolios and gaining popularity as an asset class.
The 2000–2002 Internet Bubble Crash The turbulence in 1997 and 1998 turned out to be just warm-ups to the real show that began in early 2000. From March 2000 until the third quarter of 2002, the S&P 500 fell 49%. That was good compared to the NASDAQ. It fell 78%. In 1999, before the problems started, I had already begun using a volatility-reducing strategy. The 1998 market had convinced me to start experimenting with hedging and various sell disciplines. The problem I was having, along with a lot of other people, was not letting investment-oriented risk management transform into pure trading. Especially since my fund was heavily weighted in emerging technology companies. In late 1999 and early 2000, I started getting defensive and announced to my clients that our portfolios were prepared for as much as a 30% decline. I underestimated. During the brutal months ahead, many of our investments lost 50%—some much more.
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In the asset management industry, this period seemed to me to represent a turning point. The severity of the broad market decline, combined with what was going on in Japan where equity markets were entering a second decade of decline, would, I thought, cause a serious reevaluation of risk management practices. For me personally, it certainly did. With regard to portfolio theory, the evolution continued with new innovations—global tactical asset allocation (GTAA) , global dynamic asset allocation (GDAA), further expansion of the asset universe, newer ways of optimizing allocations and core-satellite separation. The same ideas were filtering down to the retail investor and 401(k) plans in the form of target date and life-cycle plans. The critics repeated what they had been saying all along: The structure was broken, and no amount of “tortured re-optimization” and other fine-tuning would do anything to solve the problem. What happened in 2008 proved they were right.
The 2008-2009 Global Financial Crisis From its peak in 2008 to March 2009, the S&P 500 index fell by 57%. After this event, the climate of critical review seemed to change. The damage from the crisis was so deep and so widespread, people were determined to look at the event more realistically. Lawrence Siegel wrote a guest editorial for the Financial Analysts Journal in 2010 called “Black Turkeys”: Nassim Nicholas Taleb has an elegant explanation for the global financial crisis of 2007–2009. It was a black swan. A black swan is a very bad event that is not easily foreseeable— because prior examples of it are not in the historical data record—but that happens anyway. My explanation is more prosaic: the crisis was a black turkey, an event that is everywhere in the data—it happens all the time—but to which one is willfully blind.3
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Siegel gave several examples of major asset classes that experienced severe bear markets. The Dow Jones Industrial Average dropped 89 percent from 1929 to 1932, Japanese stocks dropped 82 percent from 1990 through 2009, the NASDAQ dropped 78 percent from 2000 to 2002, UK equities dropped 74 percent from 1972 to 1974, and others. The one that surprised me most was the 67 percent decline in long US Treasury bonds between 1941 and 1981. Looking at the S&P 500 index decline of 57% in historical context, Siegel said, “There is no mystery to be explained. Markets fluctuate, often violently, and sometimes assets are worth a fraction of what you paid for them.” Earlier, before the crisis, Reinhart and Rogoff (2008) had released their report on major financial crises in 66 countries over a period of 800 years and found an average equity market decline of 55%.4 As a fund manager, I knew part of the problem I was facing was the severity of asset declines, but another part involved psychological reactions to market ups-and-downs. I knew volatility was having a dramatic effect on fund performance. What I did not realize was the magnitude of what volatility was doing to individual investor returns.
The Effects of Volatility on Investor Returns The mutual fund research group at Morningstar measures the impact of volatility on investor returns. They compare the performance of various funds to the performance of investors in those funds. The difference captures the cost to investors of volatility-related market timing. Table 1.1 shows the average cost for midcap growth and midcap value sectors, the CGM Focus Fund (highly volatile), and the T. Rowe Price Equity Income Fund (highly stable).
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Table 1.1
Cost of Volatility
Annualized returns for the funds for the ten-year period ending July 2009 were compared to the actual returns of the average investor. Except for the Equity Income Fund, the average investor gave up most of the gains. In the case of the most volatile fund, the CGM Focus Fund, investors actually lost 16.8%, compared to a gain of 17.8% for the fund itself.5 The conclusion, consistent with behavioral finance, is that investors stay in less volatile funds, pocketing most of what the managers produce. The opposite is true for volatile funds: people jump into the funds during good times and bail out during bad times. The same tendencies apply to investors managing individual securities and for anyone trying to impose risk controls such as drawdown limits on positions or portfolios. The more volatile the market, the more often defensive emotions and sell disciplines are triggered. TrimTabs and others who keep track of money flows say that the real money is now going straight under the mattress. From January to November 2011, $889 billion went into savings and checking, with only $109 going into stock and bond funds. Many investors look at day-to-day volatility and decide they are just not interested.
Revisiting Modern Portfolio Theory Modern portfolio theory is the dominant force in investing. It extends from simple statistical relationships to statements about the pricing of assets in the form of the Capital Asset Pricing Model (CAPM)
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to methods for building portfolios. For institutions seeking to maximize gains for a given level of risk, mean-variance optimized (MVO) portfolios are the standard. In retail products, the same principles have filtered down into balanced mutual funds, life cycle and target date plans. It is hard to overstate the influence of MPT or its connection to deeply held beliefs about market behavior and prudent ways to invest. But time after time, it fails to provide any real protection. After each new market crisis, no matter how disappointed we get, we always come back to it. Maybe because it is beautiful, it is everywhere and there is no obvious better choice. In his book Capital Ideas Evolving (2007), Peter Bernstein talks about reliance on the CAPM as a paradox. He thinks the CAPM has turned into the most fascinating and influential of all the theoretical developments in investing today: “Yet repeated empirical tests of the CAPM, dating all the way back to the 1960s, have failed to demonstrate that the theoretical model works in practice.” In researching the book, Bernstein interviewed Markowitz to get an update on what he was working on. Markowitz told him, “You will be completely surprised if I tell you about my latest research.” Bernstein said, “He is no longer the same Harry Markowitz whose view [of securities] put Bill Sharpe to work on the [CAPM]. Markowitz has lost faith in what he terms the traditional neoclassical ‘equilibrium models.’”6 A lot of people have lost faith. Richard Ennis, in his article “Parsimonious Asset Allocation,” wrote: Over the past 25 years, institutional investors have become increasingly reliant on asset allocation models that use a complex set of assumptions about the future. … As a result, institutional investors of all types experienced losses far greater than the “worst-case” outcomes predicted by their asset allocation models. It is important to realize that, over time, asset-class return correlations are unstable—really unstable. … What good is a system of risk control that fails when you need it most?7
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Psychologically, it is hard to accept that a system that works so well 90% of the time is not going to help the other 10% of the time. Even if you accept that markets crash, that the declines are severe, and risk control fails, there is still the possibility that something was missed in execution or that next time will be different. To make progress, it is helpful to understand why the system breaks down. Otherwise, it is hard to know if and how to work with it. At this point, there is a great deal of research that fills in the details. It is widely known that severe markets events can cause all asset classes to decline at the same time, a form of contagion that eliminates any positive effect of diversification. Looking closer at this behavior, there are two related issues, implicit beta exposure and optimistic correlation matrix construction. Martin Leibowitz, in his work with institutional investors, identified what he calls implicit beta exposure. He noticed that as endowments and others began to add alternative investments, the portfolios looked dramatically different from each other, but performed about the same. In trying to understand why these portfolios act like each other, and much like a traditional 60% equity/40% bond portfolio, he realized it is because so many assets are linked, either directly or indirectly, to the U.S. equity markets. Because of the linkage, many of the changes were having no real effect on the overall returns or risk measures. Optimistic correlation matrix construction refers to the use of “average” correlations between asset classes to estimate future losses rather than using the “stress” correlations that existed during prior market crashes. Average correlations may work well across market cycles, but it doesn’t make sense to use these same correlations to estimate the magnitude of losses in market crashes. Continuing to set risk policy using average correlations is something like building a house in an earthquake zone and assuming there will be no earthquakes. But, regardless of the mechanics of the failure, the ability to accept that failure occurs is important to making a commitment to change. Sometimes, it is best just to see a flat statement. In the
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monograph from The Research Foundation of the CFA Institute, Investment Management after the Global Financial Crisis, the limitations of MPT are stated bluntly. “MPT does not offer the promise of eliminating losses—even large losses—even under the most favorable assumptions.”8
Moving Forward It would seem that knowledge of the limitations and the empirical facts of the last decade would have forced change by now. But it hasn’t. An industry survey published in 2011 says that despite the renewed focus on risk management, a wide gap still exists between mean-variance and quantitative strategies. Investment managers at financial institutions know, in principle, that basic mean-variance portfolio theory has it limits, but our findings clearly show that, in practice, mean-variance analysis is still the industry workhorse. Possibly to blame for this state of affairs is an absence of consensus on the most appropriate model.9 If we cannot rely on current practice and there is no consensus on how to move forward, what is the next step? How do you frame the possibilities? In the end, maybe it is a matter of taking a step back and asking the fundamental questions. The most basic question is: as investors what do we want and what tradeoffs are we willing to make? One of the answers that I think frames the issue as well as any I have seen is from the Ennis article mentioned above. Investors want three things. They want some downside protection. They want to capture the equity risk premium to the maximum extent consistent with their preference for downside protection. And most would also like to garner excess return (alpha), although we know that, by definition, only about half do so over any particular span of time.10
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I think he is exactly right. Downside protection will always be in demand. Equity risk premiums have historically been 2% to 3% over bond returns. Over long periods of time, this risk premium has been responsible for incredible wealth creation. And with research and other techniques, investors will always look for investments that will outperform market averages. Of course, different investors will put more or less weight on each objective. For example, institutional strategists may play more heavily in risk premiums. Aggressive traders will emphasize alpha and quantitative risk control, but the basic elements are there to describe a wide range of investor goals. Taken together, the three objectives seem very reasonable. But in practice, it is hard to get them—at least, with any sizeable exposure to equities (and bonds too at this point). Why is this? For one, there is a natural tradeoff between the goals of providing downside protection and capturing risk premiums. When I first started looking at this issue, I didn’t understand why it is so difficult to add a risk budget or drawdown limit to a diversification framework. At some point, the incompatibility began to dawn on me. If you try to impose a drawdown limit, it interferes with equilibrium. If you rely on equilibrium, it is never obvious how much downside there is. A gap seems to exist between modern portfolio theory and related mean-variance portfolios—which are great at capturing risk premiums over the long term but lack a risk discipline—and quantitative strategies that have great risk disciplines but are not so good at capturing risk premiums. The question is whether it is possible to bridge the gap and at what cost? And if you try to find a middle ground between premium capture and risk control, how do you do it? Imagine you are a trustee of an endowment, and the fund is down 10% for the year. You were hoping for a return of 8%, so now you’re off almost 20% from where you expected to be. You may have to start looking at spending cuts. You know that if the fund drops another
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10%, it will threaten core functions. If the fund drops another 20%, it is difficult to think about what will happen. What do you do? Do you sell assets now to slow the rate of decline? Or do you hold on and hope for a rebound? Institutions normally have a policy statement to guide trustees through this decision. The policy statement is a strategic plan written in anticipation of market ups and downs. Most encourage riding out the rough times. As part of maintaining the strategic allocations between asset classes, most recommend adding to underperforming assets during a downturn. The plan realizes that rebalancing involves doing the opposite of what most people will feel like doing. For instance, if the equity market is declining, instead of selling equities into market weakness, the plan tells you to maintain the proportion of equities to fixed income. That means buying more equities. However, buying more equities actually accelerates the losses if the market continues to go down. According to equilibrium models, this makes sense because it is the best way to capture risk premiums. When the market recovers, or restores equilibrium between asset class valuations, you make more by having bought the cheaper asset. But it is not the best way to provide downside protection. Objective 1. Some Downside Protection The Harvard experience during the financial crisis is particularly important, as described in this press release: Harvard Endowment Hires New Chief Investment Officer, January 14, 2010 Boston – Harvard University named a new CIO after the school’s endowment dropped $26 billion last year. Long admired for its investment savvy, Harvard was forced into heavy cost cuts and interrupted its high-profile campus expansion.
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I think what happened at Harvard happened to a lot of institutions and people. At some point, losses get too heavy and there is nothing you can do other than start hoping for a turnaround. Once you are down 20%, it seems too late to start managing risk. Instead, you start reminding yourself of deeply held beliefs such as “don’t time the market,” “buy on the dips,” and “think long-term.” Harvard has been at the center of academic theory and practical implementation. It has taken modern portfolio theory to its limits, and most of the time it has paid off. However, sometimes the only way to avoid a 30% loss is to start doing something about it when you are only down 5% or 10%. Objective 2. Capture Risk Premiums in Line with Risk Tolerance In trying to explain why many portfolios lost more than the worstcase outcomes predicted by asset allocation models, one researcher looked at how much risk is really in a mean-variance portfolio. He modeled portfolios under stress using a typical correlation matrix. Then he compared the predicted performance to the actual performance of these portfolios in market crashes. The two weren’t even close. So he tried it again, this time using a correlation matrix built from information about asset behavior during prior market crashes. This time, the results matched almost perfectly. The problem was the way the correlation matrix was estimated, using average rather than stress relationships. Why doesn’t everybody use a correctly constructed matrix? Because it can mean cutting equity allocations by as much as 75%, and few funds are willing to do this. Especially now. Giving up the opportunity for equity risk premiums at a time when bonds are so highly priced might be more risky than doing nothing. If equity allocations are reduced, current low yields on fixed income will not support the promises of pension plans and other institutional sponsors that have assumed annual returns of 7% to 9% or the retirement income needs of many individuals.
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Objective 3. Some Alpha Opportunities Going after alpha opportunities is almost irresistible. The history of Wall Street is the history of story telling—whether it is an undervalued stock, a reversal in a trend, or a chart pattern—and nothing has changed. I love a good story too. It is part of being an investor and an optimist. There are two interesting issues related to alpha. One, the Efficient Market Hypothesis (EMH), has been debated for decades. The other, idiosyncratic risk, seems to be fairly well accepted. EMH addresses the effectiveness of active management such as stock picking, compared to broad asset class exposure. In other words alpha versus beta. Probably more research has been done and material written on this topic than any other in investing. Tests of the EMH going back over 30 years have consistently shown that beating the market with either technical or fundamental analysis is tough. And if current hiring trends are any indication, then EMH is winning. Stock pickers are out; asset allocators are in. As Ennis says, it only works about half the time for most of us. Idiosyncratic risk is non-diversified risk. The issue is whether or not you can expect to be compensated for taking this kind of risk. It is generally thought that the market only provides an extra return for taking an extra risk if that particular risk cannot be diversified away. If you want a credit risk premium, the market should reward you if you buy a diversified portfolio of bonds. However, it is not obligated to reward you if you buy one bond that turns out to be bad, such as Enron, Worldcom, or Greece. If you want an equity risk premium, the market should reward you if you have broad exposure to equities, not if you buy an individual company stock. In other words, theoretically compensated risk is diversified risk or beta risk, not alpha. Traders and quantitative investors understand this and therefore don’t rely on equilibrium or mean-reversion to protect them from losses. Because the nature of the risk is different, it makes sense to manage it differently as well.
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The first step in moving forward for any investor is to find the right balance between seeking downside protection, capturing risk premiums and finding alpha opportunities. After finding a balance, strategy implementation is really an engineering problem. That is, the decisions about the kinds of investments most likely to meet the objectives and the trading rules to manage them. And to realize that in practice, the objectives often compete with each other. For instance, if you want downside protection, you could interfere with the capture of risk premiums. If you want alpha, you shouldn’t expect to capture risk premiums or find any protection from equilibrium. If you want to capture risk premiums, how much downside protection can you really expect? In terms of existing portfolio construction, I am not suggesting diversification models don’t add value—just to recognize what they can and cannot do. The most important decision is when and how to begin managing losses or mitigating volatility. If you don’t want to accept the possibility of large losses, then the strategy needs to manage risk actively so that losses are addressed earlier rather than later. There are two ways of doing this. The first is to stay within the MPT/MVO framework by adding risk management features other than diversification (such as hedging and insurance) and to find securities that add real diversification when you need it most—during market crashes. The second is to go outside the diversification framework to add more dynamic quantitative elements.
How Do SynAs Fit into the Picture? As structured securities, SynAs start by creating a flexible framework. As part of the framework, options create new design possibilities and help to bridge the gap between mean-variance portfolios and quantitatively managed portfolios. The options, together with management rules, act by:
• Increasing yield
• Adding hedging
• Adding insurance
• Adding a mechanism for risk budgeting
• Allowing for separate alpha and beta applications
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Increasing Yield With stocks, bonds, and cash, there are three sources of investment returns: interest, dividends, and capital gains. Adding options to a security structure creates a fourth source: theta. Compared to interest and dividends, theta, the time decay of options, is by far the most powerful source of yield. It is perhaps the most promising building block of new products. Adding Hedging to Risk Management A SynA adds hedging through an options wrapper on individual securities, normally short call options and long put options. The options create a market or delta hedge, making the security less volatile. This means that, in addition to the normal portfolio diversification (accomplished by asset allocation and security selection), the security itself has a new element of diversification. The long underlying position has an almost perfect negative correlation with the options. So regardless of how the security behaves with regard to the other securities in the portfolio, the security is diversified against itself. Even under extreme conditions, this element of diversification will not break down. The idea is to strengthen the diversification features of MVO without interfering with the equilibrium features responsible for risk premiums unless it is necessary. At the portfolio level (described in Chapter 10), a volatility asset class SynA adds another effective diversifier, again within the framework of MVO.
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Hedging can be used as a strategic (long-term) element of the position or for tactical (short-term) trading opportunities. When hedging is used strategically, it lowers the volatility of the position— and low-volatility investing is more efficient, often generating 40 to 60 basis points of improved return without a corresponding increase in risk.11 Adding Insurance to Risk Management A typical SynA reinvests a portion of call option proceeds to purchase puts. Puts are a simple and effective way to add insurance protection to an investment position. The initial setup of a SynA specifies a minimum number of puts. Going forward, the long-term management rules encourage opportunistic financing of additional put protection so that, over time, net principle is fully protected. Adding Risk Budgeting or Risk Allocations Risk budgeting, or risk allocations, is an extra layer of risk control. A risk budget might be set at 5% to 20% of the amount invested. In traditional portfolios in which the only decisions are buy, sell, or hold, if the risk budget is exceeded, it means that the position is sold to prevent further loss. In the case of SynAs, risk budgets are used to trigger a reduction in the net cost basis rather than a sell of the position itself. This softer form of risk budgeting adds a stronger risk-management mechanism than available with MVO, but also helps to preserve longterm holdings and cut down on portfolio turnover. Allowing for Separate Alpha and Beta Applications Many institutional portfolios are separated into alpha and beta. Individuals often do the same, treating retirement accounts (beta) and trading accounts (alpha) differently. The beta portion of the portfolio usually contains broad asset class exposures, intended to produce income and capture risk premiums. The alpha portion represents
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more targeted investments to take advantage of perceived market inefficiency, or trades based by fundamental or technical analysis. SynAs can be used in the alpha portion or the beta portion of a portfolio, or both. And they can be customized for each position depending on your views of mean-reversion or minimum values. In the beta portion of the portfolio, you have the choice of when and by how much to apply risk budgets. Hopefully, the additional diversifiers within the MVO framework make it unnecessary to apply absolute risk controls to the beta portion of the portfolio in most market conditions. In the alpha portion, all the risk-control elements, including risk budgeting, are appropriate. As mentioned earlier, in the pursuit for alpha, there is no theoretical reason to expect risk premiums, so it is important to have the ability to dynamically adjust market exposure. Risk budgeting controls single-security idiosyncratic risk more tightly. In summary, a SynA works across all three dimensions of risk management: diversification, hedging and insurance. It starts by creating a level of delta hedging on an investment position that makes it less volatile. It also uses a minimum level of insurance to slow down losses during price declines. Then, if necessary, management rules call for adjustments to invested capital to maintain risk budgets. The idea is to let the SynA operate within the Markowitz diversification framework as much as possible by adding diversification features that stand up under stress, and when necessary, beyond it, by adding dynamic hedging.
Reducing Risk, Seeking Returns, or Both? Because I have talked so much about risk, I might have given the impression that a SynA is a defensive tool. It is, but my objective has always been offense, finding ways to increase returns. I have always thought that the better the risk control, the more opportunities you have to be aggressive.
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In “A Qualified Commitment to DB Plans,” (2009) CFO Research Services surveyed plan sponsors of defined benefit plans on a number of topics related to risk management during the 2008–2009 financial crisis. The sponsors were asked, “Going forward, are you more focused on increasing investment returns or decreasing investment risks?” More than three-quarters answered: reducing risk. An interesting aspect of the survey was that the companies that were more interested in increasing returns also had the most sophisticated approach to risk management: The deep economic recession has battered most defined benefit (DB) pension plans, and many sponsors have been scrambling to address risk. … Consistent with past studies, more than three-quarters of survey respondents say they will focus more on reducing risk than on seeking additional returns. However, those companies that are focused on seeking additional returns are far more likely—by a three-to-one ratio—to already use synthetic hedges than those companies focused more on reducing risk. One conclusion is that those seeking additional returns have already addressed important components of pension risk. To put it another way, reducing risk and seeking returns are not mutually exclusive.12 That is exactly the objective of a SynA: to be aggressive in seeking returns, and do it within a disciplined risk-management framework. To do that, a SynA creates a hybrid architecture that balances the long-term investor perspective of mean-variance portfolios and the risk discipline of quantitative-based strategies.
References 1. Feldman, Amy. “Can a Hybrid 401(k) Save Retirement?” http://www.businessweek.com/magazine/content/09_07/ b4119061756100.htm.
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2. Fabozzi, Frank J., CFA, Focardi, Sergio M., and Jonas, Caroline. Investment Management after the Global Financial Crisis. 2010. The Research Foundation of CFA Institute. 3. Siegel, Lawrence. Guest Editorial. “Black Swan or Black Turkey? The State of Economic Knowledge and the Crash of 2007–2009,” Financial Analyst Journal, Vol. 67, No. 5, July/ August 2010. 4. Reinhart, Carmen M., and Kenneth S. Rogoff. 2008. “This Time Is Different: A Panoramic View of Eight Centuries of Financial Crises.” NBER Working Paper No. 13882 (March). 5. Kinnel, Russell. 2009 “Why Your Results Stink,” Kiplinger. http://www.kiplinger.com/magazine/archives/2009/11/kinnel. html. 6. Bernstein, Peter. Capital Ideas Evolving. 2007: John Wiley & Sons, Inc., Hoboken, New Jersey. 7. Ennis, Richard. “Parsimonius Asset Allocation.” Financial Analysts Journal. CFA Institute. 8. Fabozzi, Frank J., CFA, Focardi, Sergio M., and Jonas, Caroline. Investment Management after the Global Financial Crisis. 2010. 9. Amenc, Noel, Felix Goltz, and Abraham Lioui. “Practitioner Portfolio Construction and Performance Measurement: Evidence from Europe,” Financial Analyst Journal, Vol. 67, No. 3, 2011. http://papers.ssrn.com/sol3/papers. cfm?abstract_id=1861373 10. Ennis, Richard. “Parsimonius Asset Allocation.” Financial Analysts Journal. CFA Institute. 11. Clarke, Roger. “Squeeze Play,” Roger Clarke interviewed by Jonathan Barnes, CFA Institute Magazine, November/December 2010.
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12. CFO Research Services, “A Qualified Commitment to DB Plans,” (2009). https://secure.cfo.com/research/index.cfm/displ ayresearch/13982794?action=download.
2 Synthetic Annuity Design This chapter provides an overview of the synthetic annuity (SynA) and how options are used to achieve the design objectives outlined in the preface, including:
• The explicit use of hedging, insurance, and risk allocations in risk management instead of reliance on traditional portfolio models
• The desire for greater yields not related to market direction
• A recognition of behavioral influences on investor performance
• The growing importance of volatility-reducing quantitative methods, particularly those related to stock options
• The desire of many investors for annuity-like income streams
The presentation is somewhat unique in that there are no formulas. Structured securities, such as a SynA, become very complex and difficult to communicate with formulas, but the same structures are fairly easy to understand when translated into pictures. The device used to translate the SynA into graphs is the investment profile, which is simply an enhanced standard payoff curve. The only difference between a payoff curve and the investment profile is that the investment profile also includes the probability that each payoff will occur. Adding probabilities turns the payoff curves into “random variables,” the basis of stochastic math and option pricing. In a sense, the investment profile is the “fractal” version of quantitative finance. 25
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The information contained in the investment profile also makes it possible to quantify the value of various payoff curves to answer questions about the tradeoffs involved. For instance, how do the gains and losses of a SynA compare to the gains and losses of the underlying security? How much current income does it generate? Is it efficient in providing a shock-absorbing effect to volatility? From a behavioral finance point of view, does it increase the value of the holding to the investor? And, is it effective at managing the risk of an investment position? The first example in this chapter is the investment profile of a stock. Then options are added to the stock to show how the payoff curve is reshaped to achieve the design objectives. Next, a case study for an investor with a concentrated stock position illustrates a real-life context. The case study also talks about behavioral issues, including the difference between actual gains/losses and the perceived value of those gains/losses. This chapter ends by extending the single-period investment profile to a multiple period example. The example looks at the actual performance of a SynA on Apple Inc. during the 2008 calendar year, including the financial crisis. The example documents how the Apple SynA operated in calmer periods to generate income and reduce cost basis, and in turbulent periods to protect principal.
What Is a Synthetic Annuity, and How Does It Work?
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used for defensive purposes in some instances; at other times they can help with offense. They can be used in a standard setup as a default security structure, or they can be used contingently as conditions change. At setup, a typical SynA looks similar to a covered call position, with two differences. The first difference is the use of staggered strikes. The second is that some of the cash received from selling the call options is used to purchase put options. The net effect is to transform the stock position into a related security that is less volatile—and produces higher levels of current income. Of course, nothing is free— the tradeoff is some upside. The steps to create a typical SynA are: 1. Buy the underlying security. 2. Sell in-the-money covered call options on a portion of the position. 3. Sell at-the-money covered call options on a portion of the position. 4. Sell out-of-the-money covered call options on a portion of the position. 5. Buy out-of-the-money put options, using part of the money from the call options. Normally, all options are for the near-month contract. For example, for Apple, Inc., the SynA might look like this: 1. Buy 1,000 shares of AAPL. (For the example, assume a current price of $550.) 2. Sell 300 shares (three contracts) of the near-month call option, with a strike of $530. 3. Sell 400 shares of the near-month call option, with a strike of $550.
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The Investment Profile
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Note Mathematically, whenever you specify each possible outcome of an unknown event and the probability of that outcome, you have defined a random variable. Random variables are the basis of stochastic math and the Black-Scholes option pricing formula. In these terms, the investment profile is a graph of the investment gain-loss random variable.
Figure 2.1 is an example of an investment profile for a stock investment. In this example, an investor has bought 10,000 shares of XYZ at $45 a share. The graph shows the gain (loss) as the straight line labeled “stock utility” and the probabilities of each gain (loss) as the imposed lognormal distribution. The investment profile contains a great deal of information. Using just the information in this picture, it is possible to calculate many riskrelated metrics, such as value-at-risk, conditional value-at-risk, and expected gain and expected loss. It is also possible to use an investment profile to compare the value of various investment alternatives.
Assigning Probabilities Using Implied Volatility Probabilities can be assigned to the investment profile in different ways, but one method has both practical and theoretical advantages: using the Black–Scholes option pricing model and implied volatility (IV) from the options market. In pricing options, several input items are used, such as the stock price, the strike price of the option, the term of the option, and the risk-free interest rate. All these items are known at the time the option is priced.
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Figure 2.1 Investment profile of stock-only position
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Only one variable is not known: volatility. Volatility must be estimated in some way. Given an estimate of volatility, you can price the option. Volatility and option price have a one-to-one relationship. For a given level of volatility, you get a certain option price. You can also look at this relationship in reverse. For a given option price (knowing all the other pricing variables), you can “back into” the volatility that corresponds to the option price. When volatility is calculated in this way, it is called implied volatility (IV). Most trading platforms calculate IV; but if not, you can use the option price on the exchange and back into the volatility that corresponds to the observed price. When you know the IV, you can use it to assign the probabilities to the investment profile. A theoretical advantage of using IV is that it is consistent with currently traded options. A practical advantage is that the future stock prices predicted in the model are consistent with the options and futures instruments that can be used to hedge the stock price risk. In addition, because of higher leverage available by using options, knowledgeable investors often use the options markets first rather than the cash equity markets to make directional bets; thus, it can be argued that the options markets contain useful information about future stock prices. To create an investment profile, you have to make one more assumption about the exact definition of volatility that relates to how the volatility is translated into the shape of the probability curve. A convenient and commonly used definition is that of normally distributed stock returns used in the Black–Scholes option pricing formula. Figure 2.1 was based on an implied volatility of 32% and the Black– Scholes definition of volatility.
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Using Options to Reshape the Investment Profile What if you are interested in changing the profile—for example, if you want to decrease the chances of large loses? If you are willing to give up some upside, you can change the payoff curve to accomplish that by using options. Figure 2.2 shows a typical SynA profile as the white line. Notice that the gain–loss of the stock has been reshaped so that losses are smaller. Consider another positive benefit for prices around the current share price of $45: The line has moved up, and the breakeven point has decreased, or moved to the left. On the other hand, you give up possible large gains. The crossover point of the two lines occurs close to $47. Below that price, the SynA is better. Above that amount, the stock is better. Because the gain–loss values and the probabilities of both the stock and the SynA are known, it is possible to compare them. One way to do this is to calculate the expected values (or weighted outcomes) of the gain–loss profiles, as shown in the table in Figure 2.2. The ratio of the SynA to the stock is 1.24. That means, based on expected or weighted values, on average, the SynA is 1.24 times, or 24%, more effective in meeting the risk/reward objectives. Intuitively, you can see how this might be true. By focusing on the most likely outcomes—for example, the range –1 and +1 standard deviations, which occurs about 68% of the time—of the 21 possible stock prices, all but 4 are actually more favorable under the SynA. Because the more favorable outcomes are concentrated in the most likely areas of the distribution, the SynA performs better. This example assumes that investors value $1 of gain and $1 of loss equally. According to behavioral finance research, however, most investors don’t think that way. They tend to dislike large loses more than they like large gains. It is possible to reflect attitudes about gains and losses through the use of utility functions.
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Figure 2.2 Investment profile of stock only position and SynA 33
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Adjusting the Profile for Behavioral Finance The purpose of a utility function is to express how investors feel about various levels of gain and loss. According to generally accepted patterns based on research, people’s perception of the value of large gains tends to decrease as the gain becomes larger. Also, people tend to dislike losses at a relatively fast pace as the losses pile up. In fact, as losses become worse, it is not unusual for an investor to feel the loss two or three times as bad as the actual dollar amount. Figure 2.3 shows a typical pattern for a utility function. The darker area of the payoff line is the same as in previous figures; it is just the dollar amount of the gain-loss. The lighter curved line represents the investor’s perceived value of the gain-loss. Notice that the utility function curve lies under the gain-loss line at all points. On the ride side of the chart, as gains become larger, the line is slightly lower than the actual gain-loss because according to behavior finance, most investors do not appreciate increasingly larger gains on a dollar-for-dollar basis as much as smaller gains. Here, the discount at the far right is around 15%. On the left side of the chart, the deviation is much more exaggerated. As losses approach –2 standard deviations, the utility curve is about 2[1/2] times the gain-loss. By using utility functions, you have a choice of two ways to look at gain-loss profiles. The first is to view the gain-loss as the actual dollar amount. The second is to view the gain-loss in terms of emotional impact. Combining the information in Figure 2.2 with the utility function in Figure 2.3 produces the revised, utility-based random variables shown in Figure 2.4.
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Investor utility curve Figure 2.3
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Figure 2.4 Comparison of utility curve for stock-only position and SynA
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The right side of this chart, where the maximum discount is 15%, is not that different from the actual dollar version. However, the left side is noticeably different, as losses are measured on the much stricter utility scale. Because loss reduction is more important on this scale, it is not surprising to see that the SynA is relatively more attractive also, as shown in the revised table on the preceding page. Using the utility curve—that is, perceived gain-loss rather than actual gain-loss—the SynA has a weighted average score of 1.64 compared to the stock-only position. In other words, the SynA is 64% more effective at balancing this particular risk/reward preference.
Concentrated Stock Example My friend Steve’s company was recently purchased. Under the terms of the deal, he will receive stock in the acquiring company. He called me to talk about alternatives to selling the stock. He mentioned selling call options to generate income. He also wants some downside protection. He told me, “When it drops a half-point, I think about how much I lost.” This situation is common among investors who have concentrated stock positions. It provides a good place to start in terms of describing synthetic annuities. The acquiring company was the model for XYZ earlier—that is, the stock is currently trading for $45, the number of shares is 10,000, and the annualized implied volatility is 32%. A typical SynA is constructed by selling options at various strike prices, with relatively more sold at-the-money. A portion of the money received is used to buy put options. Here are the number of options purchased (long) or sold (short) and the strike prices:
• 3,000 short call options with strike price = 42.50
• 4,000 short call options with strike price = 45.00
• 3,000 short call options with strike price = 47.50
• 4,000 long put options with strike price = 40.00
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The following table is a summary of the cash flow from the option transactions.
The net proceeds from setting up the SynA were $18,530. These proceeds may be viewed as a type of dividend. In the context of the SynA, I sometimes refer to it as a virtual dividend. One important effect of the virtual dividend is to reduce the cost basis in the position. Of course, by selling the call options, some of the potential upside is given up, at least over the single period. Over multiple periods, the management rules discussed later in the book are designed so that it is not necessary over longer periods of time to give up large upside potential. Above a certain price level (strike plus premium earned), it would have been better to hold the stock rather than the SynA. In terms of downside protection, the gain/loss profile at lower price levels changes because of the 4,000 put options. If the stock price drops below $40, the SynA is better for two reasons. First, the cost basis is reduced by $18,530. Second, purchasing the put options provides downside protection on 4,000 shares for prices below $40. The net effect of the SynA setup can be seen in Figure 2.5 (also shown earlier in Figure 2.2). Notice that although the stock crosses the x-axis at $45.00, the SynA crosses the x-axis at $43.15. The breakeven point for the SynA has shifted to the left because the cost basis was reduced. The shift is equal to $1.85, the per-share virtual dividend ($18,530 ÷ 10,000 shares).
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Figure 2.5 Investment profile of stock-only position and SynA
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Behavioral Finance Adjustments I wanted to get an idea of how Steve would react to different levels of gain and loss. We just talked about a few points on the curve, and Steve told me how he would feel about those outcomes. Using these points of reference, I adjusted a general risk-averse pattern to construct the full utility curve. Usually, investors can simply look at the curve and have confidence that they have communicated accurately how they feel about various possible outcomes. For purposes of utility curve, I have extended the option period to one year so Steve can see a wider range of outcomes. Steve’s utility curve is the one presented earlier and is shown again in Figure 2.6. The lighter area extending down the left side of the graph represents Steve’s utility. At the far left, the stock price was $23. At a price of $23, the actual loss per share was $22 ($45 – $23). Steve told me that an actual loss of $23 would feel to him like a loss of $60, so I extended the actual loss line to the perceived loss of $60. On the far right side of the graph, the new line fell below the old line also, but on a percentage basis, it was not as dramatic as losses. The curve is consistent with a risk-averse profile in which each additional dollar of gain is appreciated at a declining rate. In Steve’s case, he appreciated large gains for another reason, but not as much as the actual dollar amount: because of the correlation between the stock price and the health of the industry in which he works. If the stock price is up, both the economy and Steve’s job security are likely better than if the stock price were down. This correlation also helps to explain the steepness of the dashed line curve on the left side of the graph. Steve said that a large loss, like that depicted on the left side, would feel almost three times as bad as it really was. Losses of this magnitude could threaten his retirement goals.
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Figure 2.6 Investor utility curve
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SynA profile? Should you use the actual gain (loss) or the perceived gain (loss)? This question has no single correct answer. The conservative answer is to use the perceived gain (loss). In terms of protecting against loss of capital, perceived gains (losses) both understate the gains and overstate the losses, creating a bias toward less risky investments. Steve asked that trading decisions be based on the utility curve (perceived), not the actual gain (loss). As you can see from Figure 2.7, the utility function causes exaggerations of the left side of the graph, reflecting greater aversion to loss. As before, the probability that the stock price will close within the two orange markers (–1 to +1 standard deviation) is 68.3%. The probability that the stock price will close within the two blue markers (–2.1 to +2.1 standard deviations) is about 96%. Corresponding to the new graph is the new summary table shown in Figure 2.7. In this version, both the stock only value and the SynA expected value are lower than before. Because losses are considered to be far worse than corresponding gains, the expected value of the stock and SynA is negative, with the stock-only position having an expected value of –$17,169 and the SynA having an expected value of –$2,663. On a relative basis, however, the SynA has become even more attractive. When measured on actual gains and losses, the SynA is 24% more valuable. On a utility-adjusted basis, the SynA is 64% more valuable.
A Multiple-Period Perspective The previous analysis compared a SynA to a stock investment over a single period. Over longer periods of time, the management rules of a SynA describe how to adjust the options positions. The details of the management rules will be presented later, but I wanted to point out how the SynA is intended to work over time in calm and turbulent markets by looking at an actual example.
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Figure 2.7 Utility curve for stock only position and SynA
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In calmer markets, the only adjustments to the options positions are often the rollouts of the options that occur at expiration. In more turbulent markets, tactical adjustments may be required between expiration dates. In other words, if the stock price remains within certain bounds, the setup could remain unchanged for the entire month, with the first change happening at the options expiration date when you roll out the options on the SynA for the next month. If the stock price moves outside a predetermined price boundary during the month, you make adjustments to keep the effective market exposure within target ranges. The intra-month adjustments and inter-month rollouts are part on the overall SynA design, which is long-term in nature. The following section illustrates how a SynA works over multiple periods to generate income and control risk.
The Synthetic Annuity in Turbulent Markets
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to some extent, control cost basis. The advantage of a SynA is that you can reduce your cost basis without having to sell the underlying security. A SynA has two components that smooth volatility in an effort to avoid having to make cost basis adjustments. The first is a form of delta hedging (through the short options) that reduces volatility. The second is partial insurance protection provided by the put options. If these are not enough and the position loss exceeds an explicit risk budget, then the adjustment rules kick in. Even then, the risk budget does not force the sell of the security; it acts as a signal that it is time to adjust the cost basis. In Apple’s case, during 2008 there was a risk budget of approximately 10% of the cost basis. Depending on the macroeconomic outlook and fundamental health of a particular company, some flexibility exists in how to apply the risk-management tools. However, when the loss on a position exceeds a predefined amount, the adjustment rules require a reduction in cost basis. Figure 2.8 shows how the cost basis compared to the price of Apple stock through 2008. As the year began, the cost basis was close to the stock price, both around $200. During the year leading up to September, the cost basis fell significantly below the price, which was needed by the end of the year, as the price dropped to about $90. As the stock price moved down with the overall market in reaction to the Lehman bankruptcy, the cost basis continued to be reduced, to keep it close to the position value. Because the real risk of the position is the difference between value and cost basis, at no time during 2008 was there exposure to a large unrealized loss. The derivatives created a shock-absorbing effect and the management rules enforced discipline. By contrast, if the position had been managed as buy-and-hold, the potential loss (unrealized loss) at the end of the year would have exceeded $100 per share.
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Figure 2.8 Cost basis compared to Apple stock price 2008
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During stressful market periods, the focus of the synthetic annuity is risk control. This was true during the second half of 2008 and the first quarter of 2009. At other times, when the market is more stable, either trending or oscillating, the focus shifts to income generation, which also steadily reduces the cost basis. For Apple, an example is the second quarter of 2008, a relatively stable price environment. Figure 2.9 zooms in the period from April 1, 2008, to June 30, 2008, and again compares stock price to cost basis. On April 1, the difference between Apple’s stock price ($150) and the cost basis ($127) was $23. By the end of the quarter, the difference had widened to $55. An important aspect of the strategy is the ability to increase this spread, even when the stock price is not increasing. The basic idea behind this part of the strategy, during relatively stable times, is to be paid for waiting. Option time decay means the position is increasing in value just by the passage of time. The reduction in cost basis over time contributes to overall risk control. For example, if you buy a stock for $100 and you get a $5 dividend during the first year, your “real” principle exposure is $95, versus a non- dividend-paying stock for which your exposure stays at $100. A SynA uses the same logic; it just provides the opportunity to reduce principle exposure at a much faster rate. When a stock has a period of stability or a moderate uptrend, it is possible to recapture the entire cost basis in three to seven years.
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Figure 2.9 Cost basis compared to Apple stock price, 2nd quarter 2008
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In addition to reducing the cost basis, the put option component acts as partial insurance protection. Put options are a simple and effective way to insure against large losses, but they are also expensive. The cost of complete protection on most portfolios can average more than the investment returns. For insurance to work and be affordable, either you have to time the market to have it only when you need it, or you need to finance it in some way that doesn’t put too much of a drain on investment returns. A SynA is set up so that it has partial put protection. As cost basis is reduced and put options become less expensive at lower strikes, the sell of call options finances larger amounts of put protection, with the intent of establishing full principal protection over time.
3 Tracking Performance This chapter introduces the administrative tools and graphic displays used in the book to illustrate SynAs. The material also presents the basic metrics for describing and tracking performance. If you trade options and use cost basis or net principle in your trading decisions, you are probably already familiar with the ideas behind most of this material. If you are new to structured securities, please keep in mind this chapter provides only a brief overview of option Greeks. The examples in the chapters on setup and management of SynAs (Chapters 4, “Covered Synthetic Annuities,” and 5, “Managing a Covered Synthetic Annuity”) should provide a more meaningful context and interpretation of the Greeks and the rationale behind trading decisions. The first section presents a sample template that I use to track cost basis, position gain/loss, and payback periods. The template simply offers an example of how to summarize the information to set up and monitor performance. For example, it shows the current cost basis and how to roll it forward to the next period. Because a SynA is adjusted periodically based on its relationship to cost basis, it is necessary to track cost basis—at least during the first few months. The template also shows the calculation of position gain/loss and the projected payback period. The position gain/loss is compared to maximum loss to indicate when a trade needs to be made, and the projected payback period measures the rate at which the SynA is creating virtual dividends. 53
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The second section covers a feature of the TradeStation® platform, called a theoretical position. The theoretical position helps to describe a SynA by combining information for a security and options on the security. Using this feature, you can follow SynA metrics such as delta, gamma, and theta to structure and manage positions.
Note The term cost basis as used in this book refers to net principle or net capital invested. It is used for trading decisions and is not intended to be a tax definition of cost basis.
Tracking Template The tracking template consolidates the information needed to make trading decisions. The most important decision is when and how to adjust cost basis. It is not necessary to use this particular template—in fact, many times I don’t use any template. As long as you know when you have reached your maximum loss, any method works. If the underlying security is not volatile, you could keep a running total of options transactions on a notepad next to the computer. I generally have an idea of the price at which I should start looking more closely at gain/loss. If the price is comfortably above that amount, I just download transaction records periodically to update the cost basis. For example, if you buy at $25 and don’t reach your maximum loss unless the price drops below $22, then you don’t need real-time cost basis information unless the price gets close to $22. The template format in Figure 3.1 attempts to standardize the process, probably at the cost of making it seem overcomplicated. The important point about whatever method you use is that you have easy access to the information you need to make trading decisions. When the market becomes volatile, having an easy-to-read display showing current cost basis and how close the position is to a trading trigger is helpful.
Deere & Company tracking template
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Figure 3.1
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Cost Basis Cost basis is the net amount invested in a security. For a stock that doesn’t pay a dividend, cost basis is simply the amount paid for the stock. For a stock or equity index that does pay a dividend, cost basis is reduced each time you receive a dividend. Similarly, for a fixed-income security, cost basis is reduced by interest or coupon payments as they are received. For a SynA, the calculation also involves tracking cash flows from options transactions. The cost basis of the underlying security is adjusted down by the amount received from selling options; the cost basis is adjusted up by the amount paid for options. The terms net options credit or net options premium is the difference between the amount received from selling options and the amount paid for options. I also refer to the net options credit as a virtual dividend. Cost basis is rolled forward from the beginning of a period to the end of the period, as follows: Beginning-of-period cost basis Minus actual dividends Minus virtual dividends (net options credit) Equals end-of-period cost basis
Trade Trigger The first rule of SynA management is to not lose more than you are comfortable losing without doing something about it. The gain or loss on the position is the difference between the current value of the position and the cost basis. Comparing the loss, if it exists, to the maximum loss indicates when you need to make a trade. For example, if your maximum loss is $2,000, the current value of the position is $20,000, and the cost basis is $22,500, the template would indicate that you are $500 over the maximum loss. Therefore, you need to make a trade to reduce the cost basis by at least $500.
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Projected Payback Period The payback period is the time it takes to recover invested capital, or cost basis, through interest payments, dividends, or optionsrelated cash flows. For example, an average S&P 500 stock paying a 2.5% percent dividend has a payback period of 40 years. One of the objectives of the SynA is to steadily reduce cost basis over time. With a SynA, the payback period can often be reduced significantly. The ability to accelerate the payback period has important implications for yield and for financing insurance protection. The payback period in the template is shown in months for both the underlying security and the corresponding SynA.
Example of Tracking Template The template in Figure 3.1 for Deere & Company (DE) has entries for cost basis, the current gain/loss, the trade trigger, and projected payback months.
• Cost Basis: The four columns under Cost Basis show the roll forward from the beginning of the period (BOP) to the end of the period (EOP), based on actual dividends and the net credit from options transactions. In this case, the stock has just been purchased for $21,300. The net credit from setting up the DE SynA ($292.92) is subtracted from the cost basis to calculate the EOP cost basis, or $21,007. The row labeled Stock tracks the performance of the stock position without regard to options transactions. It is a pro-forma view of how a buy-and-hold position would have performed, and therefore is updated only with actual dividends.
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• Trade Trigger: The display should make it clear when you have reached a trigger point. In this case, the cost basis is $21,007 and the position value is $21,300, resulting in a current gain of $293. Because there is a gain, nothing needs to be done. If there were a loss, it would be compared to the max loss of $2,000 and the excess, if any, would be displayed in the Sell Call $ column.
• Payback Months: For the pro-forma Stock row, payback months are estimated as the cost basis divided by the monthly dividend, where the monthly dividend is the latest declared quarterly dividend divided by three. For the SynA, payback months are calculated by dividing the cost basis by the sum of the monthly dividend and the estimated monthly theta. (See the section “Calculation of Payback Period” in Chapter 4 for more information.)
TradeStation Platform The examples in this book use a particular screen view from the TradeStation® platform.1 As in most trading platforms, various display screens give you access to standard and customized ways of organizing information. In TradeStation, these screens are referred to as workspaces. One of these workspaces, the Options Analysis Workspace, is useful in building and tracking synthetic annuities.
Options Analysis Workspace Figure 3.2 is an example of a TradeStation Options Analysis Workspace for Deere & Company (DE). The workspace is divided into three sections. The top section shows the current price of DE, 1
Certain screenshots, including Options Analysis Workspace and Theoretical Positions, were created with TradeStation. ©TradeStation Technologies, Inc. All rights reserved.
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Source: TradeStation Technologies, Inc.
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Figure 3.2 TradeStation options analysis for DE on October 12, 2011
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along with other real-time information such as price and marketimplied volatility. The large middle section contains call and put option quotes, market-implied volatilities, and selected Greeks—in this case, delta, gamma, and theta. The bottom section combines a user-defined set of stock and options. In TradeStation, this section is referred to as a theoretical position.
Theoretical Position A theoretical position is simply a consolidated view of a SynA; that is, it shows the underlying security and the options on the security that make up a SynA. The theoretical position is used in two ways. First, in setting up a SynA, it enables you to quickly see if the position meets your design criteria before executing the trades. Second, after you execute the trades to establish a SynA, the theoretical position helps you track and manage it. The theoretical position updates automatically in the platform, so it is a real-time representation of the SynA going forward. Figure 3.3 is a closer look at the information in the theoretical position. Most of the SynA examples presented in the book use this display format. This particular example is a representation of the Deere & Company SynA, where each of the five rows describes a particular component of the SynA. For example, the bottom row is the stock component. Reading across the bottom row is the stock symbol (DE), the number of shares (or Qty, which is 300 here), the price ($71.00), the profit and loss (Gross P&L of $21.00), the Spread Quote (or bid and ask), the Maximum Gain (unlimited), and the maximum loss ($21,300 or the amount invested). The position delta is $300, or simply the number of shares. Gamma and theta are both zero (by definition).
Figure 3.3 Deere & Company theoretical position on October 12, 2011
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Source: TradeStation Technologies, Inc.
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The row immediately above the stock component describes one of the options, labeled DE 111022C70. The symbol format is read as follows:
• DE is the stock symbol.
• 111022 is the option expiration date, with year first (2011, Oct 22).
• C means this is a call option, and 70 is the strike price.
Reading across, Quantity (Qty) is –1, meaning short 1 contract, or 100 shares. Also shown is Price ($2.50), Max Gain (Loss) ($250 = $2.50 × 100 shares), and the option Greeks: Delta$ (–$61.02), Gamma$ (–$8.13), and Theta$ ($10.08). Continuing to read up in the theoretical position, the next two rows show the details of a $72.5 strike call and a $67.5 strike put. The top line adds the individual component rows. This consolidated row describes the SynA, including the three Greeks on the right side of the screen view, as follows:
• Position Delta$: The SynA has a delta of $178.46. This means that, for each $1 change in the stock price, the value of the SynA changes by $178.46.68, creating a damping effect on volatility, compared to a stock position with a delta of $300.
• Position Gamma$: Gamma is –$10.33. Gamma is a measure of how much position delta changes as the stock price increases by $1. In this case, if Deere goes up to $1 from $71.00 to $72.00, Delta$ will decrease by approximately $10.33, from $178.46 to $168.13. In general, the smaller the gamma, the more stable the position. The SynA’s covered in the next chapter—the covered SynA’s—are fairly stable by nature, so gamma tends to be small and plays a minor role. For the generalized SynA’s in later chapters, gamma plays a much more important role.
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• Position Theta$: Theta is $12.82, meaning that the options are decaying in value by $12.82 per day. Because the options are a net short position, this time decay adds to the position value. Multiplying daily theta by 30 gives an estimate of monthly theta. $12.82 × 30 is $384.60, or the monthly “virtual dividend.”
Note You might see delta, gamma, and theta presented in any one of three ways: as a number, a percentage, or a dollar amount. The context usually determines which is used. When speaking in general terms, referring to a number or percentage is easier. For example, saying that delta is 0.40 (or, equivalently, 40%) means that the position moves by 40¢ for each dollar move in the underlying security. Without knowing how many shares are in the position, stating the Greeks in dollar amounts is not possible. However, when speaking specifically about a position such as the preceding one, in which you know the number of shares, referring to a dollar amount is usually more descriptive. In the examples that describe a specific SynA, the number of shares is known, so the Greeks are shown in dollar amounts. When talking about delta ranges or delta adjustments without referencing a specific SynA, either decimal numbers (for example, a delta target range of 0.30 to 0.70) or their equivalent percentages (as with a delta target range of 30% to 70%) are used.
Although I do not use other trading platforms, I understand that many are capable of providing the same basic information as TradeStation. You might want to verify that you can create theoretical positions in a format similar to the one shown, or at least have an idea of what would be required to view it easily. If your platform does not allow you to summarize Greeks easily, you can use another method, based on specific dollar moves in the underlying security, as an alternative to delta-based adjustments.
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Transaction Records After setting up a SynA, I download the transactions to keep a record of the net premium received. Normally, any trading platform enables you to download transaction information directly into an Excel spreadsheet or an Access database. Figure 3.4 shows the Excel file for the Deere options transactions: The net credit from the options transactions is – $70.03
Paid for the long $67.5 strike put
+ $113.97
Received for the short $72.5 strike call
+ $248.98
Received for the short $70 strike call
= $292.92
Net credit
Note The column labeled Amount is the option price × quantity – commission, where the commission is per contract. For example, the premium received for the $70 strike call is $250 and the commission on the trade is $1.02, for a net credit of $248.98.
In addition to the downloaded information, I add two more columns—intrinsic and time value—where intrinsic value measures how much the option is in-the-money (or ITM). Time value is the remainder of the premium. How often you download and update information depends on how volatile the stock price is. If a particular position has not been close to the maximum loss, I usually wait until the end of the month or quarter, download the transaction information, and update the cost basis at that point.
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Figure 3.4 Deere & Company options transactions
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I also want to point out that cost basis tracking is usually not required over the long term. Hopefully within a reasonable period after setting up a SynA, the cost basis will be reduced enough so that full protection of the cost basis can be financed through the normal process of rolling out options over time. The idea here is that as the cost basis of the position is steadily reduced over time, the normal amount spent on put options will be enough to cover the reduced cost basis in total. At that point, it is not necessary to continue to track cost basis.
Putting It All Together: Synthetic Annuity Overview Combining all the information into a single view provides an easyto-use overview of a synthetic annuity. Figure 3.5 shows the combination of the theoretical position, the tracking summary, and the transaction records. In this figure, you can see the complete picture. The top section, the theoretical position, shows the individual pieces and the consolidated view of the SynA. You can see, for example, how much smoothing is being accomplished and the rate at which virtual dividends are being generated. Delta measures smoothing. With a position delta of $178.46, the SynA moves up or down about 59% ($178.46 ÷ $300.00) of the stock move. Theta, or the rate of virtual dividends, is $12.82 per day. The middle section, or tracking template, updates cost basis information from period to period and highlights the need to trade when the maximum loss is exceeded. The bottom section documents the actual trades and shows how information flows into the tracking template. Again, it is not necessary to use this or any particular method. The only critical element in management knowing when you have reached your risk budget and knowing the general level of delta so that the SynA does not become too detached from the underlying security.
Figure 3.5 Deere & Company SynA Overview
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Source of screenshot: TradeStation Technologies, Inc.
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4 Covered Synthetic Annuities A covered synthetic annuity (CSynA) is a synthetic annuity that uses only covered call options and protective put options. A CSynA is a more conservative investment than its underlying security because covered calls and protective puts work to make the potential losses from a CSynA less than those of the underlying security. To illustrate how a CSynA functions, the chapter begins by comparing a CSynA to a covered call strategy and addressing the main objections to using covered calls. Then, a CSynA is constructed using Deere & Company stock as the underlying security. The CSynA transforms the Deere stock position into a related security that is less volatile and produces higher levels of current income. Of course, nothing is free in investing; the tradeoff here is that you give up some upside. The performance metric section presents a more detailed explanation of risk and return expectations, based on the number of short options, ranging from a contingent position (zero options) to a fully covered position. This chapter ends with a description of an algorithmic CSynA, or standardized version of a CSynA, that you can implement and manage using a simple set of rules.
Note For new options traders, most brokers include covered calls and protective puts as part of Level 1 options approval, which is normally available even to those without options experience.
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Covered Synthetic Annuity (CSynA) A CSynA is a form of “managed” covered call strategy. Covered call strategies are popular tools for enhancing returns and providing limited amounts of risk protection. Still, many investors don’t like to use covered calls because you give up the upside but still have the downside. That’s true, to a large degree. Imagine that you buy a stock for $100 and sell an at-the-money (ATM) call for $3. If the stock goes to $150, you get $3. If it drops to $50, you suffer the loss—except for $3. The problem is that options can quickly become “disconnected” from the security price as the security price declines, and can quickly become “too connected” as the security price rises. Figure 4.1 shows a one-year call option with a strike price of $45 on a stock trading at $45. The ATM option, in the center column, has a delta of 0.5727, or about 57%, meaning that the option moves about 57¢ for each dollar move in the stock price. The other columns illustrate the effect on delta of a quick price change in the underlying security. In the first column, where the security price has dropped to $30, delta falls to 0.1212, or 12%. At that point, the option price changes by only 12¢ for each dollar of change in the stock price. In general, the lower the delta, the more “disconnected” the option is and the less the option protects against further declines for a covered call position. On the other end of the table, where the stock price has risen to $60, the option delta rises to 87%, meaning that the option is very connected to the stock price, moving 87¢ for each dollar of stock price change. For a covered call position, the short option eliminates most of the gains from any further increases in stock price. With shorter-term options, the effect of volatility and time is much stronger. Option deltas can approach 0 on the downside or 1 on the upside after only a few points of price movement for one-month options.
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Figure 4.1 Call option deltas at various stock prices
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How do option deltas translate into covered call position deltas? The delta of a covered call position is the delta of the stock (or underlying security) minus the delta of the option. By definition, stock delta is 1.0, so as the stock price declines and the option delta approaches zero, the covered call delta approaches 1.0. Conversely, as the stock price increases, the option delta approaches 1.0 and the covered call delta approaches zero. In other words, during price declines, the option fades away and the covered call begins to act like the stock by itself, with a delta of 1.0. During price increases, the option delta approaches 1.0, so the covered call delta approaches zero. This is just a restatement of the common objection to covered calls: You give up the upside and still have the downside. Theta is affected as well. In general, theta is highest when the stock price is close to the strike price of the option. That is, ATM options produce the highest levels of theta. As the stock price moves away from the strike price, theta goes down regardless of the direction the price moves. As the covered call delta moves below about 0.2 or above about 0.8, the rate of theta is relatively low and, therefore, time decay is minimal. Because of delta and theta effects, a covered call strategy is much more effective as long as the underlying security price stays close to the option strike price, where the balance between delta and theta works to your advantage. The balance between delta (the market exposure) and theta (the rate of time decay or virtual dividend payments) is fundamental to options-based strategies. To address balance, a CSynA differs in three ways from a covered call position. The first difference is that the call option strike prices are normally staggered. Staggering the strike prices of the short call options makes delta more stable across a wider range of prices. The second difference is that part of the cash received from selling the call options is used to purchase put options. Reinvesting part of the call option premium in long put options creates stronger downside protection.
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Third, the CSynA includes management rules (discussed in the next chapter) that help to maintain and balance the relationship between delta and theta over the longer term.
Example: Deere & Company I have been looking at Deere recently and wondering whether it is a good time to buy. As I write this in October 2011, the right answer in this case (as with everything else) probably depends on Europe. But with a P/E below 12 (a discount to its historical multiple) and a yield higher than the 10-year Treasury, and considering that Deere is a beneficiary of the long-term agricultural secular trend, buying doesn’t sound like a bad idea. After all, with the world’s population expanding and farmers needing to increase production to satisfy an appetite for more and better food, Deere seems to be in the right place for the long term.
Building a CSynA: The Steps Setting up a CSynA involves these steps: 1. Select the underlying security, normally a stock or other security that you would like to own long term. 2. If you don’t expect the price to go up right away, sell one or more covered call options on the security. 3. Buy out-of-the-money put options, using part of the money from the call options. After reviewing Deere, everything looks reasonable. Here are the steps I went through to build the DE CSynA.
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Figure 4.2 Deere & Co option quotes
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Step 1: Buy the Underlying Security I bought 300 shares of DE at $71, for a total position value of $21,300. Of course, the number of shares is determined by your portfolio size and how diversified you want to be. For this example, I am assuming a total portfolio size of around $300,000, so that this position represents about 7% of the total. The results can be scaled for larger portfolios. Step 2: Unless You Expect the Price to Go Up Right Away, Sell One or More Covered Call Options Deere has already reported earnings, and the results of the crop report are out. Of course, I hope it goes up from here, but I don’t know of any short-term catalysts. As with most other stocks, it will probably move with the macro picture. If I did have a view of direction, I would probably give it some room to run. Instead of selling calls immediately, I could either put in limit sell orders for options at higher strike prices or simply wait to see how far momentum might take it. In setting up a covered SynA, no requirement states that you must begin to extract theta right away. To give you an idea of the option prices available as I began to set up the CSynA, Figure 4.2 shows near-the-money options prices at the market close on October 12, 2011. In this case, I sold two option contracts, a $70 strike call for $248.98 and a $72.5 strike call for $113.97, for a total of $362.95. Because a CSynA can use only covered calls, the limit is three option contracts for this position. Because I think Deere is slightly undervalued, I will wait to sell the third option. Normally at setup and at monthly roll-forwards, if I have no opinion about stock price direction, I sell the maximum number of call options.
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Step 3: Use 20% to 30% of the “Time Value” of the Call Option Premiums to Purchase One or More Put Options The call premiums totaled $362.95, but some of that is intrinsic value. The $70 strike call option is ITM (in-the-money), so it needs to be split between intrinsic value and time value. Of the $248.98 premium received, $100 is intrinsic value ($71 current price – $70 strike price). Therefore, the time value of the $70 strike option is $148.98. Because the $72.5 strike call is OTM (out-of-the-money), the entire premium, $113.97, is time value. The total time value is $262.95. I bought a put option with a strike of $67.5 for $70.03, or about 27% of the time value. Subtracting the price of the put from the proceeds from the two calls leaves $292.92 as a net credit. That’s it—finished. Figure 4.3 shows the overview. This is the same overview from Chapter 2, indicating the following:
• Delta of $178 (or 59% of the stock-only delta)
• Daily theta of $12.82 (or payback rate of 49 months)
• $292.92 net transaction credit (reflected as a reduction in cost basis) The observations on the CSynA Greeks are repeated here:
• Position Delta$: The CSynA has a delta of $178.46. This means that, for each $1 change in the stock price, the value of the CSynA will change by $178.46. This creates a damping effect on volatility, compared to a stock position with a delta of $300.
Figure 4.3 Deere & Company CSynA at setup on October 12, 2011
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Source of screenshot: TradeStation Technologies, Inc.
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• Position Gamma$: Gamma is –$10.33. Gamma tells you how quickly delta changes. Specifically, gamma is a measure of how much position delta changes if the stock price increases by $1. For example, if Deere stock price goes up by $1 from $71 to $72, Delta will decrease by $10.33, from $178.46 to $168.13. In other words, instead of capturing about $178 gain as the stock price moved from $71 to $72, gamma tells you that you will capture only about $168 if the stock price goes up by another dollar. This is consistent with the earlier result of diminishing returns during stock price increases for covered positions. The opposite is true for declining stock prices. If Deere stock moves from $71 to $70, gamma tells you that the position delta will increase by $10.33, from $178.46 to $188.79. That is not as bad as the stock itself, which would fall by $300, but the cushioning effect of the position begins to deteriorate as the price of the stock drops. Again, you get the same result as the covered position. In general, the closer gamma is to zero, the more stable the position delta is. Most CSynA’s are fairly stable by nature, so gamma tends to be small and plays a minor role. In Chapter 7, “Managing a Generalized Synthetic Annuity,” gamma plays a much more important role.
Note Keep in mind that delta and gamma are not exact. They are instaneaous approximations and generally apply within fairly narrow price ranges. It is not correct to think that they will describe the downside risk if the stock price falls by $10 or $15. The further the price is from the current value, the worse the approximation.
• Position Theta$: Theta is $12.82, meaning that the options are decaying in value by $12.82 per day. Because you are short the options here, time decay is a credit; that is, it adds to the
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position value. Multiplying daily theta by 30 gives an estimate of monthly theta. $12.82 × 30 is $384.60, or the monthly “virtual dividend,” shown in the column labeled Monthly Theta.
Calculation of Payback Period Deere pays a quarterly dividend of 41¢ per share. How long will it take to pay off an investment in Deere from the dividend alone? The amount invested in the position is $21,300, and the annual dividend rate is $1.64 per share. On 300 shares, the annual dividend is $492, or $41 per month. Payback months on the stock-only position is calculated by dividing the current cost basis of $21,300 by the monthly dividend of $41, which equals 520. That is the number of months it will take to recover the cost basis from the dividend alone. Now look at what happens to the payback period for the CSynA. With the CSynA, there are two sources of cash flow. First, because the CSynA includes the stock position, there is the actual dividend of $41 per month. Second, selling two call options and buying one put option produced a net credit of $296 (of which $196 is time value). This is not a large reduction in cost basis immediately, but when the rate of cost basis reduction (as measured by theta) is projected into the future, the number of months required to pay back the investment is cut by a factor of 10. Let’s walk through the calculation. From the theoretical position, Position Theta$ is $12.82 per day. Multiplying the daily rate by 30 gives an estimate for monthly theta of $384.60. Adding the monthly dividend of $41 produces a total monthly “dividend” of $425.60 for the CSynA. Dividing the current cost basis of $21,004 ($21,300 reduced by the net option credit) by $425.60 gives a payback period of 49 months. Am I really saying that by making a couple of options transactions, you can cut the payback period by a factor of 10? Yes, potentially.
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But you have to be careful when interpreting these numbers. To get a little more comfortable, take a look at an alternative calculation of theta and payback period.
A Different Calculation of Payback Period The longer-term power of theta is evident in the payback period. But what does this mean? Is it reasonable to think that you can recover your entire cost basis in 49 months (or in 13 months, as you will see in the leveraged version in Chapter 6)? Maybe something about the calculation of theta is confusing the issue. To get an intuitive feel for the payback period, let’s approach the calculation of theta in a simpler way. Let’s look at the options and what the CSynA will be worth at option expiration. Figure 4.4 breaks the option premium into intrinsic value and time value, and shows how the CSynA will look at expiration.
Figure 4.4 Time value and payback period
Both the put option and the $72.5 strike call option are OTM, so they are composed of only time value, as shown in the table. The $70 strike call option is ITM. The ITM, or intrinsic value, is $1, based on the current stock price of $71. At any time before expiration, the options have both intrinsic value and time value. But just before options expiration, the options have no time left, thus there is no time value. The price of the call options at expiration is simply the amount by which the stock price exceeds the strike price. The column labeled Expiration Date Value
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shows the value the options will have at expiration if the stock price is the same as it is today. The assumption that the stock price remains the same at expiration is the best way to isolate the effects of the passage of time on option prices. Of course, in reality, the stock price will be whatever it is. But say that the stock price is $72 at expiration. The $70 strike call will be worth $2. But we could say that $1 of it was because of stock price movement and $1 was due to the passage of time. So you would get to the same place anyway. Assuming that price stays constant is the easiest way to measure the time decay or theta. The options transactions took place on October 12, 2011. The options expire on October 22, 2011, or ten days later. That means the time value of the options will go to zero over the next ten days. At that point, the options will have the value shown in the column labeled Expiration Date Value. Under the strategy, the options are used to modify the behavior of the combined stock option position. The underlying security shares are long-term investments, so you do not want to let any of the options be exercised. Before the market close on the 22nd, the options that are ITM are to be repurchased and rolled over to the next month. If the stock price is $71 at expiration, the options will be repurchased at their current intrinsic value of $100. The net gain over the next ten days, in this scenario, will be $196, equal to the time value. That is, the gain will be equal to the premium received for the options minus the amount to repurchase the ITM options. So, you will make $196 over the next ten days due to the passage of time. If you make $196 over ten days, the monthly amount is about three times that, or $588 a month. Dividing the cost basis of $21,004 by $588 is 36 months, even better than the 49 months using the platform (or more exact) definition of theta. It seems that the back-ofthe-envelope calculation of payback period confirms the speed at which theta is working.
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Still, can this be right? To get paid back this quickly on an investment, there must be more to the story. There is. The assumptions themselves are almost contradictory. You are getting paid high premiums for the call options because the market is assuming a certain level of volatilty. At the same time, the assumption is that the stock price will not move. Actually, the assumption was that the stock price at expiration would be the same as today. (Technically, that is not an assumption that it doesn’t move in the meantime—just that it finishes at the same place.) The chance also exists that you will need to adjust the options positions prior to expiration. Realistically, the more a stock price moves around, the more likely, under the strategy, that an adjustment will be made. If adjustments are made to keep delta within a target range, for instance, those adjustments, depending on how they are made, could reduce the returns and lengthen the payback period. Volatility is the most important driver of options pricing. Right now, volatility is relatively high. At lower levels of volatility, the call option premiums would be less, which would lengthen the payback period. However, if the stock remains within a certain range and the pricing of options stays at elevated levels so that you could roll out the options month after month at current pricing, it would take only about four years to fully recover the cost basis. This is maybe not likely, but it’s possible. To avoid too much optimism, I normally think of the payback period as a reminder of what is possible, not an assumption about returns. It is simply an indication of the power of theta.
Note It can be argued that I reduced the cost basis too much by including both the intrinsic value and the time value of net options credit. I agree, but the projection is dominated by the rate of theta rather than an extra $100 in cost basis reduction, especially because
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the $100 is not projected into the future—only the time value is projected. I think the extra complexity of an exact calculation of cost basis reduction for one month is not worth the effort and does not significantly distort the overall result. However, for multiperiod projections, it is important to include only the time value of options in cost basis reduction. In other words, including total net credit does not anticipate the repurchase of option intrinsic value before expiration.
The Number of Options and the Strike Prices Notice that I didn’t sell three short call options. Selling the maximum number of call options is not necessary. In fact, this example offers a choice to sell zero, one, two, or three short calls. The strike prices are also flexible. Deciding how many options to sell and the strike prices of those options depends on what you want to achieve in terms of market exposure (delta) and income generation (theta) and the tradeoffs between them. In general, the more options you sell, the lower the delta and the higher the theta. If you sell less than the maximum number of options to set up the CSynA, you can always sell the others later, if you want to. For example, you might decide to make future option sales contingent on a higher or lower stock price. Or if the stock trends upward and you think it might keep going, you are not required to sell the other options. To get a feel for the level of tradeoffs for Deere, consider Figure 4.5. The exhibit makes it clear that delta and theta work together to simultaneously decrease market exposure and increase current income. To maximize theta, sell the maximum number of options. To maximize delta, don’t sell any options.
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Figure 4.5 Delta and theta by number of short options
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Stock-Only or Contingent SynA Of course, if you don’t sell any options, you just have 300 shares of stock. You might wonder how a stock position can be a CSynA. This scenario points out that selling options is not necessary to create a CSynA. The only rule required for a CSynA is that you must establish a maximum loss amount and then, when you reach that amount, you must do something about it. Because the important aspect of the CSynA is an intent to do something if it becomes necessary, I think of this form of CSynA as a “contingent” CSynA. (Of course, if you never sell any options, you will also not create any theta, so it is assumed that you will sell options at some point in the future.) Sometimes, you might enter a position because you think there is a near-term catalyst. In such a case, you might not want to sell any call options or buy any put options at the time you enter the trade. If you are right about the catalyst, you can get better pricing on the options after a moveup. You do nothing unless the price falls enough to exceed the max loss.
One to Three Short Options: The Tradeoff Between Delta and Theta When you sell even one call option, you begin to reduce delta and create theta. By looking at the individual options available and the theoretical position before you execute the trades, you can balance, within ranges, the level of delta you prefer and how much theta you want to generate. This balance between delta (the market exposure) and theta (the rate of time decay or virtual dividend payments) is fundamental to options-based strategies. In selling call options, you give up potential upside, but you get theta in return. Sometimes, you might prefer to sell only OTM options to maintain most of the upside, with the understanding that OTM options have smaller deltas and, therefore, less protection on the downside.
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The more theta you decide to generate, the more upside you will be giving up, but as a positive, the smaller the volatility will be. Earlier, Figure 4.3 showed the stock-only delta as $300 (by definition, the delta of a stock position is the number of shares). By selling options, you can decrease market exposure and the related volatility of the CSynA. Selling one option reduced delta to $223, selling two short options reduced it to $176, and selling three short options reduced it to $150, cutting delta in half. Theta moves in the opposite direction—that is, as you sell more options, delta goes down and theta goes up. In any particular situation, you might be more interested in reducing volatility or increasing yield. Think of stocks such as Southern Company, Verizon, or Kinder Morgan, all of which pay high dividends. They have also been remarkably stable, even in historically volatile periods. If you are not concerned about volatility and are satisfied with the yield, you can look at options as simply a yield-enhancement mechanism. For instance, you could sell one or more OTM or farOTM options to boost the yield. In low-interest-rate environments, certain high-yielding stocks have “natural” put protection because, as the price falls, the yield rises. This is especially true for companies that have disciplined cash-management practices such as Master Limited Partnerships or those that are regulated by public commissions such as utilities. The only drawbacks to pursuing yield enhancement CSynA’s is that the option premiums are very low due to the stable nature of prices. The possibility also exists that, in a recovering economy, prices on relatively defensive securities can decline simply due to an outflow of funds as the “risk on” trade returns. For securities with higher volatility, you might want to sell more call options as a volatility-reduction mechanism. Even though improving yield might not be your main objective, you get that as well. No one right answer exists. Each situation presents its own opportunities, depending on your outlook on risk, your belief in the long-term
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prospects of the company, and the degree to which you want to emphasize volatility reduction and yield over capital gains. You can also reflect your view of the importance of dividends, both actual and virtual, to investment returns.
How Important Are Dividends to Total Return? Over the past 80 years, dividends have contributed an almost equal share of total returns as capital gains to the S&P 500. One factor in CSynA design was to recognize the importance of the role dividends have played in total portfolio returns. As Figure 4.3 pointed out, CSynA’s let you adjust the yield source. The more options you sell, the more the expectation moves away from capital gains and toward theta (dividends). Whether a CSynA works in a particular situation depends not only on how the underlying security acts, but also on your expectations about where return will come from and how patient you are in waiting for it. For this reason, the more you think that the return of a security will come from capital gains (that is, the more you think the price will move up), the fewer options you should sell. The more you want to emphasize dividends over capital gains, the more options you should sell. Of course, the balance can change as events unfold, but in the CSynA structure, you have the flexibility to make adjustments.
Longer-Term Delta Targets One of the objectives of the CSynA is to dampen the effect of market volatility. By selecting the number and strike prices of the call options you sell, you can achieve a higher or lower delta. As a general rule, the more options you sell, the lower the delta and the lower the volatiity. Also, the delta reduction depends not only on the number of options sold, but also on the strike prices of those options. As a
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general rule, for any particular option, the more ITM, the higher the option delta and, therefore, the lower the CSynA delta. For instance, in Figure 4.1, the delta of an ATM option was 57%. As the stock price increased, making the option more ITM, delta increased to 70% for a $5 ITM option, 80% for a $10 ITM option, and 87% for a $15 ITM option. In most market conditions, I usually like the delta target percentage to be between 0.4 and 0.6—that is, I like to have about 40% to 60% of the stock price movement flow through to the CSynA. I think of this range as a strategic target that applies in average conditions to average securities. In turbulent market conditions, or when tactical trading opportunities exist, I adjust delta down or up to fit my outlook. The average longer-term strategic target can be described in terms of a standardized CSynA.
The Standard CSynA In practice, I normally set up CSynA’s in a straightforward way. If I have 300 shares of the underlying, I simply sell an ITM call, an ATM call, and an OTM call. I use about 25% of the time value of the proceeds to purchase an OTM put option. On options expiration day, I repurchase any ITM options and sell the next month’s options in the same formation: one ITM, one ATM, and one OTM. If the underlying is not that volatile, I look at it once a week or about every 500 Dow points (whichever comes first) and make tactical adjustments if delta is below 0.25 or above 0.75. That’s it. This middle-of-the-road management style is consistent with a belief in the EMH (efficient market hypothesis—in other words, it is hard to beat a liquid market in heavily traded securities). It generally has a delta of about 0.50 and theta of around 20% to 30% annually, depending on the level of implied volatility.
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In general, the CSynA is flexible—it can be used in different ways in different situations. But what if you are more interested in a simple application of the basic principles of a CSynA? In that case, you can use a simplified form of the strategy, called a standard CSynA. The standard CSynA is easy to set up and manage. It can be applied in an almost algorithmic fashion. After you select the underlying security and setting a risk tolerance, you have little to think about. As with the typical setup discussed previously, it uses a full covered position, has a delta target of around 50%, and makes delta adjustments at 25% and 75%. It is easy because it narrows the set of possibilities. Sometimes, to narrow a set of possibilities, you first need to understand what the possibilities are. That way, in deciding to exclude a decision point, at least you know what you are excluding—and why. If you think about simply selling a call option, you need to specify a few parameters, such as the underlying security, the strike price, and the expiration date. For more complicated strategies, such as iron condors, the number of parameters goes up because you must specify information for all four legs. And that is just for the setup. Trying to parameterize the management rules would become unmanageable as you attempted to articulate where and how to make adjustments, terminate the trade, or initiate the next setup. Still, simplicity is important, if it exists. I admit that I was a little relieved when I went through the exercise of imagining how someone might enter a CSynA trade into a drop-down menu on a trading platform. In fact, only three inputs are required: the risk allocation or budget and the high and low delta adjustment points. And if you are willing to accept “average” values for those inputs, the process is as simple as clicking a CSynA box. To illustrate what I mean, it is helpful to start with a more generalized parameter set and narrow it so that the assumptions and investment “beliefs” built into a standard CSynA are obvious. The following is a list of some of the general parameters that might apply to a standard CSynA. A discussion of each follows.
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Standard SynA Parameters —
Fundamental/technical valuation high
—
Fundamental/technical valuation low
—
Minimum value
E
Momentum (M), reverting (R), or micro-efficient (E)
—
Price-related delta (custom SynA)
7%
Max drawdown % (risk budget)
100% Covered % (100% = full covered position) Yes
Spread evenly
—
Exclude ITM
—
Exclude ATM
—
Exclude OTM
75%
Upper delta adjustment (0.75 for reverting; 0.65 for momentum) Lower delta adjustment (0.25 for reverting; 0.40 for momentum)
25%
Fundamental/Technical Valuation High and Low If you have views on valuation levels, you can express them in the way you set strike prices and time the options trades. For example, you might buy a security for $50 because you think it is really worth $60. In that case, it makes sense to use the contingent CSynA setup and wait until the price gets close to your view of the real value. The first two parameters refer to the buy and sell points for securities based on perceived value. The standard version of a CSynA bucks convention and does not use predefined valuation ranges. It does not have opinions about the real value of securities. It assumes that the market price is the correct value, at least in the sense that fundamental or technical analysis is not helpful in determining a better value. More on this is discussed shortly when covering the microefficient parameter.
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As with all the parameters, these assumptions apply only to the standard version. Nothing prevents you from using these parameters as guidelines for setting up trades for other CSynA’s.
Minimum Value Particularly for hard assets such as commodities and real estate, many people like to set minimum values, or prices at which they want to own more of the asset. Or they might think that certain companies are so good at managing invested capital that there are predefined entry points. If you think that oil is a bargain at $65, or that you should buy gold at $1,000, or that Berkshire Hathaway stock is a must-buy at $55, you can modify the normal CSynA operation to change the profile at these minimum levels. The idea of intrinsic value of an asset might be compelling, but the standard CSynA doesn’t recognize this, either.
Momentum, Reverting, or Micro-Efficient Specifying this parameter helps to determine how and when to make adjustments. A momentum investor looks for price strength and might increase exposure as the price increases. A mean-reverting investor might interpret price strength differently if he or she believes that price strength means the exposure should be decreased. As you might have guessed, the standard CSynA doesn’t use this information. The standard CSynA is consistent with a micro-efficient view of security prices. In other words, it makes the assumption that the market price is hard to beat—not necessarily that the market price is right or correct, just that beating the market is hard with either fundamental or technical analysis. In fact, this is probably one of the most researched areas of investment theory. Paul Samuelson, among others put forth an interesting corollary to this. Samuelson believes that although the market exhibits incredible micro-efficiency (meaning,
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at the individual security level), it often exhibits macro-inefficiency (meaning, at the asset class level). The standard version assumes micro-efficiency—that is, it agrees with the efficient market hypothesis in its weak (technical analysis cannot give you an advantage) and semistrong (fundamental analysis cannot give you an advantage) forms. Given all the publicly known information, the standard version doesn’t try to make predictions about where the price is going because it believes the market price is where it should be.
Price-Related Delta In some cases (one of which is discussed in Chapter 9, “Synthetic Annuities for the Bond Market”), you might want to customize delta exposures based on the security price level. Within bounds, it is consistent with the automatic delta adjustments built into the SynA structure. If you prefer to exaggerate the effect, you can easily do so. From a theoretical standpoint, it is a customized blend of views on the previous parameters. The standard version doesn’t use this parameter.
Maximum Drawdown (Setting a Risk Tolerance) The maximum drawdown or risk tolerance is the amount you are willing to lose before taking some kind of action. Risk tolerance is also sometimes referred to as risk allocation or risk budget. When the loss on the position reaches this amount, the strategy dictates that you sell enough call options to lower cost basis so that the loss is back within the 7% limit. The standard SynA, and all versions of any SynA, uses this parameter. It is required for the quantitative risk-management discipline. Chapter 5, “Managing a Covered Synthetic Annuity,” covers applying the risk budget in detail.
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Covered Percentage This parameter and the next four parameters describe how many options are sold and which ones to exclude, if any. The standard version is 100%, meaning that it sells the maximum number of covered options. If there are 300 shares of the underlying security, it sells 300 short options. If you have 1,000 shares, it sells 1,000 options. In nonstandard setups, this parameter enables you to specify that you want to sell only 50% of the maximum covered options. For example, someone who simply wants to enhance the return from a high-yielding stock could decide to sell only 200 options on a 400share position and to sell only OTM options. In that case, this person would exclude the sale of ITM and ATM options. This type of setup and management produces less theta but maintains more upside and decreases the chances that the stock could be called away prior to expiration.
Upper and Lower Delta Adjustments These parameters determine when a delta adjustment is made. The wider the range, the less frequently the adjustments are made. The purpose of the adjustments is to not lose contact with the underlying. The chapters that follow present examples of delta adjustments. The standard version uses a lower bound of 25% and an upper bound or 75%, although you can change this parameter.
Summary of the Standarized CSynA The standardized CSynA simplifies the setup and management of a CSynA. It requires only three parameters: 1. Maximum drawdown on cost basis 2. Upper delta adjustment level 3. Lower delta adjustment level
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If average values for these parameters (for example, 7% on drawdown, 75% on upper, and 25% on lower) are used, nothing else is required.
The BuyWrite Index By specifying a particular set of parameter values, a standard CSynA can be evaluated in the same way as the CBOE BuyWrite Index (BXM). The BXM is a simple covered call index on the S&P 500, where it is assumed that each month the index is purchased and an ATM option or slightly OTM option is sold against the index. Even though it is simple, it has outperformed the S&P 500 in terms of both the return achieved and the risk taken to get that return. The CBOE website includes a summary of the risk and return metrics of the BXM and reports from Callan and Ibbotson. See www.cboe.com/micro/bxm/ for a complete description of the BXM. Although I haven’t done it yet, I think it would be interesting to run parallel models of the S&P 500, the BXM, and the standard CSynA at various settings of the parameters to see how they stack up. With regard to investment theory, the standard CSynA assumes micro efficiency—that is, it eliminates the need to make directional price bets. Chapter 1, “Introduction,” discussed a typical CSynA. Generally, when I am deciding which call options to sell and how many of them, I don’t have a view on the direction of the security price. I typically sell the maximum number in a level pattern of ITM, ATM, and OTM options. For example, if I buy 100 shares of the underlying security, I sell one ATM call option. If I buy 200 shares, I sell the closest ITM call option and the closest OTM call option. For 300 shares: 1 ITM, 1 ATM, and 1 OTM; for 400 shares: 1 ITM, 2 ATM, 1 OTM, and so on, up to 1,000 shares with 3 ITM, 4 ATM, and 3 OTM. This practice is consistent with a view that the market is efficient on a micro basis and that the price of a security reflects available
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information. At times, I think I know more than the market, but when I don’t, I focus more on theta than on trying to pick a price direction. In Deere’s case, I did have a slight belief that the stock was undervalued, so I sold two options instead of three. In terms of performance, the standardized CSynA at setup has the following characteristics:
• Volatility, or delta, of about 50% of the underlying
• A payback period that is five to ten times less than the average dividend-paying stock
• Significantly lower drawdown expectations
Payback periods and yield are influenced by the implied volatility of the options. For the S&P 500 Index, a rule of thumb is to divide the VIX by 10 to get an estimate of monthly yield. For individual securities, volatilities are normally higher than the index, with some of the highest implied volatilities on volatility itself. The higher the implied volatility of the option, the more potential there is to accelerate payback periods. The next chapter covers some of the advantages and disadvantages of high volatility.
Supplemental Material The CBOE S&P 500 BuyWrite Index The CBOE S&P 500 BuyWrite Index (BXM) is a benchmark index designed to track the performance of a hypothetical buy–write strategy on the S&P 500 Index. Announced in April 2002, the BXM Index was developed by the CBOE in cooperation with Standard & Poor’s. To help in the development of the BXM Index, the CBOE commissioned Professor Robert Whaley to compile and analyze relevant data from June 1988 through December 2001. Data on daily BXM prices now is available from June 30, 1986, to the present time (see the next section). The BXM is a passive total return index based
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on (1) buying an S&P 500 stock index portfolio and (2) “writing” (or selling) the near-term S&P 500 Index (SPXSM) “covered” call option, generally on the third Friday of each month. The SPX call written has about one month remaining to expiration, with an exercise price just above the prevailing index level (that is, it is slightly out of the money). The SPX call is held until expiration and cash settled, at which time, a new one-month, near-the-money call is written. Visit the BXM FAQ for more information about the construction of the index.
BXM Study by Callan Associates In 2006, Callan Associates, an investment services consulting firm, published a new study on the CBOE S&P 500 BuyWrite Index, with an analysis of performance from June 1988 through August 2006. The study builds upon the earlier studies done by Professor Robert Whaley (now at Vanderbilt University) and by Ibbotson Associates. The new Callan Associates study had several key findings, including these: 1. BXM generated superior risk-adjusted returns over the last 18 years, generating a return comparable to that of the S&P 500 with approximately two-thirds of the risk. (The compound annual return of the BXM was 11.77%, compared to 11.67% for the S&P 500, and BXM returns were generated with a standard deviation of 9.29%, two-thirds of the 13.89% volatility of the S&P 500.) 2. The risk-adjusted performance, as measured by the monthly Stutzer Index over the 18-year period, was 0.20 for the BXM versus 0.15 for the S&P 500. A comparison using the monthly Sharpe Ratio yielded similar results (0.22 versus 0.16, respectively), confirming the relative efficiency of the BXM over the 219-month study period.
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3. The BXM underperformed the S&P 500 during most rising equity markets and consistently outperformed the S&P 500 in all periods of declining equity markets, demonstrating the return cushion provided by income from writing the calls. 4. The BXM generates a return pattern different from that of the S&P 500, offering a source of potential diversification. The addition of the BXM to a diversified investor portfolio would have generated significant improvement in risk-adjusted performance over the past 18 years.
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5 Managing a Covered Synthetic Annuity The performance of a CSynA over time depends on how volatile the underlying security is and how it is adjusted. The goal is to maintain a reasonable level of exposure to the underlying security so that theta remains high and the level of price exposure remains consistent with your views on security valuation. The first section in this chapter talks about the automatic exposure adjustments that happen as a natural consequence of the options components of the CSynA. Later sections cover cost basis adjustments that might be required as part of the risk discipline, tactical adjustments, and the monthly roll forward. The discussion ends with an example using the Deere & Company CSynA setup in the last chapter.
Automatic Adjustments Assume that you have 1,000 shares of XYZ stock currently trading at $50 and that you set up the CSynA as follows:
• 1,000 shares of XYZ
• 300 short calls with a $45 strike price
• 400 short calls with a $50 strike price
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• 300 short calls with a $55 strike price
• 300 long puts with a $40 strike price
If XYZ’s price moves up, the short call options will be more “connected” to the stock price and the SynA will be less connected to the stock price. If XYZ’s price moves down, the short call options become less connected and, therefore, the SynA is more connected. This is true of any strategy that uses covered calls. With a stock-only position, each share moves by $1 for each $1 move in the stock. This is not true for the CSynA. How much you gain or lose for each $1 move in the underlying stock price depends on what the stock price is. The number and strike prices of the options determine how the CSynA interacts with the underlying security price. So how can you visualize what this price-dependent exposure looks like?
Automatic Adjustments: How the CSynA Interacts with Security Prices A natural adjustment process takes place with a CSynA. It is an automatic change in the level of exposure to the underlying security as the price of the security moves up and down. In markets where volatility is fairly low and the market is not trending too fast in either direction, the adjustment does naturally what an average value investor would want to do anyway. For the previous example (1,000 shares of stock that is currently trading for $50), assume that you believe $50 represents a fair price. If you simply buy the stock, your “exposure” will be 1000 shares, regardless of the stock price. In other words, you will gain or lose $1,000 for every $1 move in the stock price, regardless of whether the stock price is $40 or $60. In contrast, a CSynA, with short call options and long put options, will change the overall position exposure as the stock price changes.
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Delta, as a measure of connectedness, takes into account both time and the strike prices of options. For this part of the discussion, let’s look at a simpler relationship. Let’s ignore time value for now and just count the number of shares of XYZ that are not being limited by the option strike prices—that is, how many shares are “in play,” or the number of OTM options. Figure 5.1 shows how the options affect the number of shares that are in play at various stock prices. For instance, the put option shown in column three (“Long Put 40”) does not affect the position until the stock price reaches $40. At that point, if the stock price continues to fall, the put option kicks in to take out 300 shares of exposure. In the next column (Short Call 45), you can see how the $45 strike price call option affects exposure. If the stock price is below $45, the call option is not in play. Above $45, the option reduces exposure by 300 shares. Above $50, the option shown in the next column reduces exposure by another 400 shares. The column on the far right adds the exposures of the stock and the options to give the total exposure by stock price.
Trending versus Reverting The automatic adjustments might be exactly what you want if you think XYZ is a mean-reverting stock that is worth $50. The CSynA adjusts the exposure automatically for you. It effectively “sells” some of the position when the price goes up and “buys” more of the position when the price goes down. It doesn’t do this in the sense of actually making a transaction; it does it in the sense of how much you are exposed to the price action of the stock. The exception is the operation of the put option to reduce exposure if the price drops too much. This is to protect you in case the market crashes or something unexpected happens that could affect your opinion of the company.
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Figure 5.1 Effective number of shares (OTM shares)
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For stock prices slightly lower than the purchase price ($40 to $45), none of the call options is ITM, so the effective number of shares owned is 1,000. For prices slightly above the purchase price ($45 to $50), the effective number of shares is 700. If the price goes above $50, the exposure drops to 300; at prices above $55, it is as though you had sold the position. At this point, all options are ITM. Because of the automatic adjustment in the CSynA, you have effectively already sold most of it and you don’t need to do anything. If you wanted to at that point because of the price increase and the cost basis reduction, you could even purchase more put options to completely protect the cost basis at reasonable prices. If you do nothing, your gain is being extracted through the net premiums you received on the options and the gain on the effective shares as it went up. If something happened in the meantime and you changed your opinion about the fundamental value of the security, you can adjust the delta exposure, but that is a conscious decision. Otherwise, you continue to roll out the options at the current strike price levels to extract more income; when the stock price falls back into the range, you will have effectively bought back your position. The CSynA in the previous example is not intended for playing a trend. It is best suited for a reverting stock when you are satisfied with the price and believe that, at lower prices, the security represents better value and, at higher prices, it represents less value. The next section presents the three rules of CSynA management, in the context of cost basis and delta adjustments: 1. Protect principal. 2. Manage delta. 3. Finance insurance.
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Cost Basis Adjustments By far the most important CSynA management rule is to protect principal. If you have to choose between protecting principal and making potential profits, choose principal protection. I’m not saying you should risk nothing, but set a risk budget and make adjustments when you reach it. Rule 1: Protect principal. Sell call options to adjust your cost basis if the loss on a position exceeds your risk tolerance. Because the SynA is a risk-first strategy, the first rule is designed to enforce risk control. It is not guaranteed to avoid large losses, but it is intended to make you “do something” in an effort to avoid large losses. The mechanics of the trade are fairly simple, and there is flexibility in how many options you choose to sell and at what strike prices. Usually, you can satisfy this rule by selling OTM call options. Emotionally, those are the least painful trades because the possibility still exists that the position will recover, and you haven’t given up too much upside. But if you have to sell ATM or even ITM options, please do it. If you let yourself get too far behind, you might reach a point at which you find it almost impossible to react to further price drops. For example, if you set a risk tolerance of $2,000 and your current position loss is $3,000, you should sell enough call options to “get back” at least $1,000. If you decide to sell the minimum amount ($1,000), you might have to sell more the next day if the stock price falls again. Selling more than the minimum gives you some cushion that could help you avoid having to trade again. I normally sell 20% more than the minimum. In this example, I would sell $1,200 of call options, to provide a $200 cushion.
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Choosing Which Options to Sell The rule itself helps you decide which options to sell. Let’s say you have a small loss in excess of your risk budget. You can satisfy the rule with the options that are easiest (from an emotional standpoint) to sell. Those are near-term OTM options. They are easy to sell because you get the premium and you keep some upside capital gain potential. For a stock that drops from $100 to $95, selling a $105 strike call option is not too hard, especially if it expires in less than a month. How bad can it be to get the option premium and keep a $10 capital gain opportunity (assuming that the stock moves from $95 to $105)? But if the stock drops to $90, you might need to sell ATM options to satisfy the rule. A drop to $80 would probably make you sell ITM options. In other words, the greater the drop in security price, the lower the option strike price must be to lower the cost basis enough. Selling lower-priced strike options also lowers the delta exposure, more than selling ATM or OTM options. This is intentional in the design. Think about Netflix or Green Mountain. When high-beta stocks or momentum growth stocks turn down, it is not a good idea to try to pick the bottom or make a stand on valuation beliefs. The put options you bought at setup plus the effect of this rule will hopefully help you maintain emotional indifference if the security price takes a dive.
Mean-Reverting or Trending The cost basis rule doesn’t make a distinction between whether the underlying security is mean-reverting or trending. I realize that this is somewhat contradictory to the mean-reverting nature of the SynA structure. And in situations when you want to stick with the position as it falls, you have strategy overrides. Chapters 8, “Synthetic Annuities for High-Yielding Stocks,” and 9, “Synthetic Annuities for the Bond Market,” discuss two possibilities. You can identify
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positions in which you do not want to enforce the cost basis rule, but it is assumed that you would make that decision in advance of the trade. Of course, if you want to give a particular position more room to fluctuate, you can also set a higher risk budget in advance. The decision to override the strategy can have a large impact on performance, either good or bad. When I decide to exclude a position from the cost basis rule, I usually break out the performance of the position and report it separately. Figure 5.2 shows an example of performance attribution in which the mean-reversion exclusion produces extra volatility. I just want to point out here that it is possible to be flexible about the rules (although in reporting, I think it adds another high-level source of return that should be broken out from theta generation and market-related sources).
How Often Should You Remeasure? In normal situations, I recommend looking at a CSynA at least once a week to see if it requires a cost basis adjustment. If the market or the underlying security is volatile, you might want to set price triggers to alert you when you need to pay closer attention. However, when a cost basis adjustment is required, it is usually because something has gone wrong. At that point, you might want to track gain–loss daily until the price stabilizes.
Delta Adjustments The target delta defines how closely you want your position to move with the underlying stock. If delta is too low, you will not have enough exposure; if the actual delta gets too high, you might have too much exposure. For example, if your target delta is 0.50 and your range is 0.35 to 0.60, then when the delta is below 0.35 or above 0.60, you need to make an adjustment.
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Figure 5.2 Sources of return
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If the delta is too low, you should buy to close enough of the lower strike call options to get delta back in the target range. If the delta is too high, you can sell call options to reduce it. By selling call options, you also increase theta. If you have already sold all the options you can, buy to close some of the higher strike options (which you should make a profit on because the underlying price has gone down) and sell enough ATM or ITM options to get delta back into the range. Rule 2: Manage delta. Set a delta target range and adjust the SynA to keep it in the range. As mentioned before, the challenge of any quantitative mechanism is to keep you out of the big losers and keep you in the big winners. On a portfolio level, it is to help you participate in bull markets and reduce your exposure in bear markets. From a design standpoint, the challenge is to balance the time-decay characteristics of options with their directional characteristics, which tend to work in the opposite direction. For instance, if you want to participate in a strongly up-trending market, long calls work best. If you want to avoid market crashes, long puts work best. But both long calls and long puts require you to pay for time decay or theta. Strategies that require you to pay for theta can be very profitable—if you can time the market. However, on average and over longer periods, timing the market is hard. A typical CSynA is theta generating. Any theta-generating strategy generally does not perform well if the market moves quickly in the wrong direction. Because it prefers mean-reverting markets, trending markets can cause problems. When a stock or other security moves quickly—either up or down—you might need to adjust the CSynA to account for the new price level. Let’s look at two of these adjustments, first for a quick price move down and then for a quick price move up.
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Defensive Adjustments The Deere CSynA had 300 shares with two short options. The delta was around $180, or 60% of the stock delta of $300. What would happen if Deere fell the next day by $5, from $71 to $66? The loss would not be high enough to trigger a cost basis adjustment, but the dampening effect of the call options would be less (at $66) than at $71. Say that delta fell to 0.25. At that point, delta is telling you that the options will cushion a further price fall by only 25¢ for every dollar of decline. When delta becomes too low, it is because the stock price has dropped and the options have less influence on the SynA because they have become too far OTM. Sometimes when this happens, it triggers a cost basis adjustment. But other times, you might have reduced cost basis to the point that drawdown is not a problem, but you might want to limit delta anyway. If you have not sold the maximum number of options, you can simply sell an ATM or ITM option to bring delta into your desired range. If you have sold the maximum number of covered options, you can buy back the most OTM option first (which, at this point, should be very cheap) and sell an ATM or ITM option as before.
Offensive Adjustments What happens if the price moves up quickly—say, from $71 to $76? Then both options would be ITM with higher deltas. Only 100 shares would be “in play.” If the price increase happened because of good news that you think affected the company’s fundamental valuation, you might be optimistic about short-term prospects. If you revised your target price to $100, you would not want to let the options take you out of future price movements. But the options have done just that, so you need to make an adjustment.
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You have a couple choices. You know that you want to increase delta, so you should buy back at least one of the options. The option creating the least amount of theta is always the one that is most ITM. So buy back the lower strike option. That option probably has a delta of 0.80 to 0.90, so buying it back is almost equivalent to putting a third of the stock position back in play. At this point, you have only one short option. Your short-term view determines what you do next. If you think that the price will continue to go up strongly, buy back the last outstanding option and wait for the stock to hit your price target before selling any new short calls. If you think that the price will base or fluctuate in the short term, you can roll up or roll out, or both.
Offensive Adjustments: Rolling Up, Out, or Up and Out Rolling up means that you buy ITM options and sell new ATM or OTM options at the same expiration date to replace them. Rolling out means buying to close options and selling the same strike price options at a later expiration date. Rolling up and out means buying back options and selling new options with higher strikes and longer durations. In all these situations, you are attempting to not lose connection to the underlying security, to maintain the balance between theta generation and delta price cushioning. Remember the criticism of covered call options? “You cut off the upside but continue to have the downside.” Hopefully, Rule 1 helps you deal with the downside problem. But what about cutting off the upside? I need to address that because it is a good point. A particularly irritating situation happens with covered calls. Imagine that you have done your homework, and you’ve picked a great company that you think has terrific upside and a near-term catalyst. You wait for it to go up, but it doesn’t. You decide that you were wrong about the catalyst and decide to sell call options. Once in a
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is flexibility in the number and strike prices of the put options. The lower the strike you choose, the more options you will be able to buy. Emotionally for me, Rule 3 is the hard part. Personally, I don’t like this step. In fact, I expect that, most of the time, this will be a losing trade. I like being an optimist; I don’t like buying insurance.
Look for Opportunities to Finance Put Protection You can insure against a loss in different ways. The simplest and most straightforward way of insuring against losses is to buy put options. A frequent question I get is, “Why don’t you just purchase the put options and not sell the call options? That way, you don’t have to give up the upside.” The answer is, I would love to do that—if it weren’t so expensive. It is a matter of tradeoffs. How expensive is it? Well, if you purchase a one-year ATM put option on a stock with 30% volatility, it will cost you about 12% of the stock price. Most people assume that stocks will return an average of 8% to 10% a year, so to get complete protection, you might be paying more than you expect to make. For a longer-term solution, it is important to find a more efficient way to finance protection. This gets back to the goal of accelerating the rate at which you reduce cost basis. Consider Figure 5.3. It prices the put options, assuming that you need to purchase the protection on only your cost-basis, not the current price of the stock. The figure shows the price, as a percentage of cost basis, to buy a put option if the cost basis were reduced by 2% a month. This is an aggressive assumption, but it illustrates the point.
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Figure 5.3 Black-Scholes put option pricing
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By steadily reducing the cost basis, the strike price of the put options that is necessary to protect principal goes down. As the strike price goes down, the put options become cheaper to buy. The goal is to be able to buy more put options for the same 20% to 40% of the call option proceeds that is allocated to buy puts. Over a few months, it is possible that the money you have available to spend on puts will be enough to buy complete protection—that is, protection on all shares in the position, not just a portion of them. Hopefully, you will be able to purchase full protection on principal, or invested capital, at a reasonable price, financed by the call option premiums.
Sell Time “Retail,” Buy Time “Wholesale”: The Square Root Rule As you look for opportunities to finance put options, consider buying longer-term options, especially during periods of low market volatility. The mathematics of option pricing make it possible to buy “more time” on options with a “volume discount.” If you are not familiar with stochastic projections and option pricing, consider an interesting feature of how random movements “spread out” over time. Random price movements do not spread out on a one-for-one basis with time; they spread out at a rate proportional to the square root of time. This means that an option with a term of four months is not four times as expensive as a one-month option; because of the square root relationship between volatility and time, a four-month option is only twice as expensive as a one-month option. Similarly, a nine-month option is three times as expensive as a one-month option, and an option that expires in one year is priced at about 3.5 (the square root of 12) times a one-month option. As you can see in Figure 5.4, the price of a four-month option is $6.90, only two times the price of the one-month option of $3.45. The nine-month option is equal to three times the one-month option. Similarly, an option that expires in one year is priced at about 3.5 (the square root of 12) times.
Figure 5.4 Black-Scholes option pricing at one to nine months
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Assumptions: $100 Stock Price, $100 Strike Price, 30% Volatility, 0% Risk-free Rate
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To take advantage of the time volume discount, when making dynamic adjustments to a SynA, you might want to sell options with a short time to expiration and buy options with a longer time to expiration. When comparing the effective price per day, long-dated options are often a better choice than more near-dated options. The disadvantage of this approach for highly volatile stocks is the possibility that you buy put protection at a certain level—say, a strike price of $50—and then the stock quickly moves up in price to $70. At that point, you will probably be more interested in protecting profits closer to the current price than those $20 below the current price.
The Monthly Roll Forward Periodically, you will need to roll forward any options that may be ITM at options expiration, to prevent exercise. You can use options of any term you want in setting up and managing a CSynA. I think that using near-month options and adjusting delta more often, as opposed to using two-month or longer terms, offer advantages. The same time volume discounts that apply to put options also apply to call options, but in this case, you want to sell the more expensive near-dated options instead of the less expensive longer-dated options. If you use near-month options, you will need to repurchase any ITM options before expiration each month and sell the new options. The remainder of this section walks through the actual October expiration date rollout of the Deere SynA. Figure 5.5 is the same as Figure 4.2, which shows the initial setup as of October 12.
Figure 5.5 SynA as of October 12, 2011 at market close
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Source of screenshot: TradeStation Technologies, Inc.
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In the nine days following the setup, no adjustments were made. The options expiration date was Saturday, October 22. On Friday, October 21, the last trading session before expiration, about 10 minutes before the market closed, the SynA looked like Figure 5.6. At that point, Deere was trading at $71.79, so the $70 strike call was ITM. I repurchased this option for $1.80 to prevent exercise. The other two options were OTM, so I didn’t need to do anything; they expired worthless. Immediately after I bought the $70 strike call option to close the position, the CSynA became just a stock position again. Without any outstanding options, there was nothing other than 300 shares of stock. At that moment, the delta became $300—or, in percentage terms, 1.0, or 100%. Without options, theta went to zero, so the payback period is projected forward using only the actual dividend. Because the October options transactions reduced the cost basis slightly, the payback period is 517 months instead of 520 months for the stockonly position. Normally, I would have sold the new November options at the same time I closed out the October options, but there were some positive developments in the macro picture, so I decided to wait a few days to sell the November options. I also wanted to emphasize that it is not necessary to have short options on the position at all times. If you want to play a directional move, it is perfectly okay to do so. After the market close, I updated the cost basis with the closing transaction for the $70 strike call, as in Figure 5.7. You can see that there is a slight reduction in cost basis and that the current gain is a little higher for the CSynA than stock.
Figure 5.6 SynA as of October 21—options expiration
Figure 5.7
Updated DE tracking template
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Source: TradeStation Technologies, Inc.
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Other than that, nothing much has happened. But only ten days have elapsed since I purchased Deere. Let’s skip ahead a few days. I sold two November calls and bought one November put. On October 28, 2011, the SynA options transactions and tracking summary looked like Figure 5.8. The stock price moved up to $78.65. The options trades produced net cash of $388 ($300 + $162 – $74), which is shown as a reduction to cost basis in the CSynA row of the tracking summary. Delta dropped from $300 to $183, and theta went from zero to $8.38 per day. At a rate of $8.38 per day, the payback period went from 517 to 71. This is a little longer payback period than the initial 49 months when setting up the CSynA, but it is common for the payback period to fluctuate. I could lower the period by selling another call option, but the price action has been good, so I am not concerned about the difference. You can choose how you want to structure the CSynA. Selling more calls swaps current income for potential capital gains and reduces volatility. After the options transactions, instead of the CSynA moving dollar for dollar with the underlying stock, it moves only $183 for each $300 move in the stock, or 0.61 or 61% as much. With no options outstanding, the expectation is that all returns would come in the form of capital gains and a small dividend. By selling options, you choose to emphasize current income and less volatility over capital gains.
Example of Tactical Adjustment In the next couple weeks, European uncertainty had again begun to push the market lower. By November 9, Deere stock was below $73. Taking a look at the CSynA in Figure 5.9, I noticed that delta was $225 and theta was only $1.22.
Figure 5.8 DE SynA as of October 28
Figure 5.9 DE SynA as of November 9
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Source of screenshot: TradeStation Technologies, Inc.
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Source of screenshot: TradeStation Technologies, Inc.
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Look at the effect on each option component of the CSynA. The $72.5 strike put option is performing well. It was purchased for $74 and is now worth about $200. You can see this from the spread quote columns. Open is the ask, and Close is the bid. Open is shown as $2.03, and Close is $1.97. So at the time I took the screenshot, the put option was trading at a bid of $1.97 and an ask of $2.03. The Gross P&L column shows the difference between what I paid and the current bid, or $123. More important than the current price is the protection the put option offers if the price continues to fall. In terms of effective shares, it eliminates 100 of the 300 below a stock price of $72.5, the strike on the option. In other words, if things start to get really bad, you have to manage only a 200-share position, not a 300-share position. The next option, the $80 strike price call option, is now deep OTM—that is, it is no longer close to the stock price. I sold it for $162, and now it is worth about $10 (it is shown as $0.08 to $0.12, or an average $0.10—that is $0.10 per share, or $10 for the 100 share contract). As with the put option, it is a gain. Likewise, for the $77.5 strike call, I sold it for $300 and it is now worth about $40. Delta has changed for the call options because, as they move farther away from the stock price, they are less connected and, therefore, less of a cushion on price movements. This is no required cost basis adjustment, but I decided to make a small tactical adjustment. I thought it might be a good idea to lower delta and raise theta a little. To do that, I sold a call option. As discussed previously, the general effect of selling call options is to lower delta and raise theta. And the lower the delta you want, the lower the strike price needs to be. Theta is maximum when the option is about ATM. In this case, I wanted a slight adjustment, so I chose an OTM option with a strike price of $75. It doesn’t have a drastic effect: It simply lowers the cost basis a little, reduces delta a little, and raises theta a little. Figure 5.10 shows the transaction and the effect on the CSynA. Again, it’s nothing drastic, but it does pull delta below $200 and raises theta. Now that I have been in the trade for about a month, you
Figure 5.10 Updated DE overview
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Source of screenshot: TradeStation Technologies, Inc.
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can start to see the effect. Cost basis is lower by around $600, and I have generally been running a less volatile position. The put option strike price is actually above the cost basis now, and I will start to take advantage of the spread between position value and cost basis more as I move forward. The larger the spread, the cheaper it is to finance total protection on the cost basis. A psychological benefit emerges when you reach the point at which you know you will not lose money on principal; the goal is to reach that point as soon as possible.
The December Roll Forward and Summary of Results On Wednesday, December 14, I made a tactical adjustment by selling a January 2012 $75 strike call option for $2.36. Then on Friday, December 16 (options expiration day), I checked the December options to see if any were ITM. None were, so I just let them expire worthless. Before the market closed, I sold the options listed in the following transactions. Figure 5.11 shows the resulting CSynA and the tracking metrics. Notice that the Greeks are blank because this screenshot was taken after the market close. I calculated a daily theta of $17 and entered it in the tracking summary. Three months into the trade, cost basis has been reduced to $19,958, or $66.53 per share, almost a $4.50 per share decrease. That is on track for a three- to five-year payback period, which is what I was hoping for. So far, so good.
How Does volatility Affect the Payback Period? Quick price moves and reversals can extend payback periods. Specifically, the payback period is affected by the number of times you adjust the SynA in the wrong direction. Consider an example. For Deere, a spike up in price, to $79.25, occurred on Wednesday, November 30.
Figure 5.11 DE overview as of December 16—options expiration
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Source of screenshot: TradeStation Technologies, Inc.
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When the price spiked up, delta dropped below my target of 30%. The adjustment was to buy back a $72.5 call (for $680) and sell an $80 call (for $115). The net “roll-up” cost was $500, resulting in an increase in cost basis. Because the stock dropped again, I would have been better off not making the adjustment. Results without the tactical adjustment would have improved. The current cost basis would be $65.22 instead of $66.52. No big deal, right? Probably, but the $65 put cost 68¢. Spending 20% of the time value of the new calls would have financed two $65 strike put options instead of one $67.50 strike put options. That would have been total put protection on two-thirds of the position. That means that, within three months, the cost basis reduction was sufficient to allow financing of put protection on invested capital. In other words, there is no way to lose money—at least, on most of the position. As it is, one more month should allow the same protection, assuming no crash in the meantime. The point is that spikes up, then down or else down, then up can affect results. You can take a couple steps to avoid some of the fluctuations. Under the standard management rules for this stock, I would have looked at it each Friday, which would have avoided this trade. The other idea is to smooth the results using moving averages rather than point-in-time prices. That would have worked as well in this case. Regardless, the CSynA performed well. It was less volatile than the underlying stock, cost basis has been reduced from $71 to $66.52, it has produced a larger gain ($2,125 for the CSynA versus $780 for the stock), and there is a reasonable chance that cost basis can be reduced at a rate that will pay back invested capital in less than five years. On top of that, hopefully within a month or two, put option financing or most (or all) of the principal amount will be self-sustaining (from a portion of the call premiums). No cost basis adjustments were required during the period because the maximum drawdown was not reached.
6 Generalized Synthetic Annuities The covered SynA rules are more restrictive than necessary for an experienced options trader. Within the SynA framework, you have a great deal of flexibility in setting performance targets. If you have higher option approval trading levels, you can set up and manage SynA’s in many ways. This chapter addresses SynA design flexibility. With a CSynA, you are restricted in the amount of theta you can generate. The only theta-generating options you have available are short calls, and you are limited in how many you can sell. With the generalized SynA, you can create additional theta by overselling calls and selling puts. A revised investment profile and a Deere example illustrate theta leverage in this chapter.
Note Brokers might differ on definitions, but here are typical options trades by approval level: Level 1: Covered call writing, protective puts Level 2: Put/call buys, collars, covered puts Level 3: Put/call spreads Level 4: Put writing, cash-covered puts Level 5: Uncovered call writing
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Some trades discussed in this chapter require Level 5 option approval, but for most situations, Level 3 is adequate to create leverage and, in general, using spreads helps to control risk better than using uncovered options.
Reshaping the Investment Profile Figure 6.1 is the investment profile from Chapter 2, Figure 2.4. As before, it assumes 10,000 shares of a stock trading at $45 with implied volatility of 32%. The net credit was $18,530, from the following transactions:
• 3,000 short call options with strike price = 42.50
• 4,000 short call options with strike price = 45.00
• 3,000 short call options with strike price = 47.50
• 4,000 long put options with strike price = 40.00
As discussed in Chapter 2, the net effect of the transactions on the CSynA was to shift the payoff curve (white line) up and to the left for the most likely outcomes and reduce the losses at lower stock prices. In exchange, at higher stock prices, some of the upside potential was given up. For the generalized SynA, if you choose, you can go further in reshaping the curve. By removing the restrictions on the number and type of options, you can create larger credits—and widen the range at which the SynA produces gains.
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Figure 6.1 Investment profile of stock-only position and SynA
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Consider an example of a SynA produced by these options transactions:
• 3,000 short call options with strike price = 42.50 (same as before)
• 4,000 short call options with strike price = 44.00 (new)
• 12,000 short call options with strike price = 45.00 (was 4,000)
• 3,000 short call options with strike price = 47.50 (same as before)
• 3,000 short put options with strike price = 46.00 (new)
• 4,000 long put options with strike price = 40.00 (same as before) Figure 6.2 shows the new investment profile:
The net credit from this SynA is $50,510, compared to $18,530 for the covered version. Also, the payoff curve has been significantly reshaped. The profit region of the curve has been extended on the down side to almost one standard deviation. On the right side of the investment profile, notice that overwriting call options results in increasing losses for stock prices above $50. Instead of giving up some upside, the new profile indicates the possibility of large losses at higher stock prices. By leveraging theta, the structure also becomes less stable. Being less stable means that you might have to adjust the position more often in response to price changes. Whenever an aggressive stance is taken, it is important to respond quickly to any adverse price moves.
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Figure 6.2 Investment profile of leveraged SynA
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Notice the shape of the curve: It resembles a rounded version of a short straddle or strangle. However, the underlying long position makes it more stable than either of these and enables you to extend the wings so that the upside and downside crossovers occur at one standard deviation. In general, the more leverage you use, the higher the center of the curve will be. You can think of the height of the curve as being proportional to theta. Because the majority of the options were sold ATM or close, theta decay is rapid. In terms of probabilities, if you look at the crossover point for the SynA compared to the stock (approximately $47.5), there is almost an 80% chance that the stock price will be below the crossover at expiration. The net effect is much faster theta generation, at the cost of stability. In the setup and management sections that follow, I recommend that you consider selling call spreads and put spreads instead of using naked options in this illustration. The spreads will better protect you against large losses in the event of big price moves. If you use spreads, the shape of the curve flattens slightly at the center and cuts off the downward trajectory at the ends. The shape begins to resemble an iron condor. From a risk management perspective, using spreads in a SynA has the same advantages and tradeoffs as moving from a short straddle to a condor.
Theta Targets and the Investor Perspective Theta adds another dimension to return sources. It is capable of producing much larger yields than dividends or interest payments. Theta can be so tempting that I have to sometimes remind myself of my objective. I know someone who runs an iron condor strategy, and we compare notes. In a condor strategy, the objective is to not be an investor. (By the way, I highly recommend Michael Benklifa’s book Profiting
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with Iron Condors, to get a condor trader’s perspective.) For the most part, I use SynA’s for the opposite reason: to help me be an investor. The perspectives are different. Condor traders don’t want to own the underlying security; they just want theta. And they get it by selling options on the underlying security. A condor trader hopes for a stable price and steady time decay. Any price move, even up, can upset the trade. If you look at the way a SynA is structured, theta has the most “force” or the highest point on the curve at the current stock price. And this particular trade is profitable as long as the price stays within one standard deviation of the current price. In fact, I am tempted to focus more on theta than on the underlying security when the rate of return is high enough. How high are we talking about? It is possible to set up a SynA with 100% annualized returns—or more. I don’t recommend it, though. Even though perspectives of the SynA investor and condor trader are completely opposed, they share a belief in the power and usefulness of theta. The goal is to figure out how to harness it. Before looking at an example, let me talk about broad design objectives, to put some of the conversation in context. Figure 6.3 is a sample product design description that might help.
Figure 6.3 Theta target products
The “products” are labeled SynA 10, SynA 20, and so on, where each specifies an annualized yield target. For example, SynA 10 has
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a theta target of 10% annualized returns from theta. This is not an aggressive target; it can be reached usually by selling OTM options and, depending on the level of implied volatility probably, maybe not even a full covered position. So you might be able to get 10% by selling 500 options with a strike price of 10% OTM on a 1,000 share position. Delta levels are determined by how many options you sell and at what strike prices. Selling OTM options only on a portion of the underlying position reduces delta by a fairly moderate amount. It will probably stay above 70%. As more options are sold to increase theta, delta will be reduced as usual—as long as only calls are being sold. When puts are sold as well, you can do something with a generalized SynA that you could not do with a CSynA. You can increase theta and keep delta at higher levels as well (more on this in the next chapter). In the product description is a column labeled Probability of Blow Up. You have to consider the probability of a blow up with many options strategies such as condors, but most conservative SynA’s will not blow up—at least compared to owning the underlying security. In other words, if you were happy owning the underlying security and the market crashes, you cannot be “more unhappy” with most conservative SynA’s because the outcomes are at least as good. For more aggressive structures such as the SynA 50, designed to produce 50% annualized returns, a higher probability of unexpected results exists. The higher the theta expectations, the lower the stability. At some point, targeting high levels of theta overwhelms the “investor perspective” advantages of the strategy. For day traders, anything less than 100% annual return possibilities might not be exciting. But for a pension plan that needs 8% to meet funding requirements, increasing yield by 2% a year can be exciting. For an individual investor who is investing for retirement, increasing yield from the rate on the long bond to 10% could increase eventual retirement income by three times or more. The important point to keep in mind is that the higher the level of theta you attempt, the less stable the instrument becomes.
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Before getting into more aggressive applications, let’s look at one advantage of being able to using option spreads (Level 3). It is a simple variation of a standard CSynA, but it illustrates how you can modify exposures using put spreads instead of being restricted to protective puts.
A Variation of the Standard CSynA By making a slight change to a CSynA, you can use the flexibility of higher options levels in a less aggressive way. The variation is to use long put spreads instead of long puts to get more “first dollar” protection, especially when you have a view on minimum value or don’t mind increasing exposure at lower prices. From a theoretical point of view, some argue that puts are too expensive and that OTM puts are relatively the most expensive. The SynA compensates for this by using call options to finance put options. Under put-call parity, the pricing remains balanced to prevent arbitrage opportunities. By using this variation, you can also take advantage of put overpricing by selling the more relatively overpriced OTM puts. (For more on the overpricing of put options, see Bondarenko, Oleg. “Why Are Put Options So Expensive?” April 2003. AFA 2004 San Diego Meetings; University of Illinois at Chicago Working Paper. Available at ssrn.com/abstract=375784.) Figure 6.4 is a variation of the Figure 5.1 in Chapter 5, showing the effective number of shares. Compared to Figure 5.1, the effective number of shares distribution is changed so that 700 shares is maintained down to the strike price of the short put. For securities for which you want more exposure at lower levels, this variation uses the put protection more effectively. Of course, you could choose to buy further OTM puts to cut off the downside at some point. If you have a particular pattern of price-based exposure you want, you can structure it in various ways.
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Figure 6.4 Effective number of shares (OTM shares)
Deere & Company SynA When I set up the Deere covered SynA, I also set up a Deere generalized SynA, to illustrate the flexibility you have in the generalized SynA that is not available in the covered version. Figure 6.5 shows the covered version from Chapter 3, “Tracking Performance,” along with the tracking template and the transactions that created the CSynA. As discussed in Chapter 3, there is an initial positive cash flow of $292 (reduction in the cost basis), the SynA is less volatile than the stock position (delta is $178 versus the stock delta of $300), and, at the current rate of theta, it is projected to take 49 months to pay back the investment. In terms of management, the structure is fairly stable, so other than the monthly rollout, the position will be monitored for gain–loss about once a week; you can make delta adjustments if delta gets too high or too low.
Figure 6.5 Deere & Company SynA overview
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Source of screenshot: TradeStation Technologies, Inc.
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Figure 6.6 is a more aggressive generalized setup. This Deere SynA has approximately the same delta as the Deere CSynA, but with a higher theta. The difference in the setup is that I oversold calls. That caused a drop in delta that I offset by selling puts. When you oversell call options, you might reduce delta below your target level. To move delta back up to your target, you can sell put options. Selling a put option increases delta. Both short calls and short puts increase theta. As a quick reminder, the following are the directional effects on delta and theta of the four option trades: 1. Buying call options increases delta and decreases theta. 2. Buying put options decreases delta and decreases theta. 3. Selling call options decreases delta and increases theta 4. Selling put options increases delta and increases theta. Overselling calls and then selling puts to achieve a target delta is what I refer to as leveraging theta. The more leverage you use, the less stable the position will be going forward.
SynA Stability (Gamma) and Yield (Theta) The stability of the position can be measured as a first approximation by gamma. The CSynA had a gamma of –$10.33. This generalized SynA has a gamma of –$40.36. Because gamma is a measure of how quickly delta changes as the stock price changes, the SynA’s delta changes at four times the rate of the CSynA. Another way to think of stability is by comparing Figure 6.1 to Figure 6.2. In Figure 6.1, the CSynA levels off on the right side of the graph, but it never goes negative. That is, no matter how high the stock price goes, the CSynA will always have a gain, even if it is capped. However, for higher stock prices, the SynA can result in a loss. You can think of the slope of the payoff curve as the stability of the structure. High gammas mean that the slope of the curve is more downward pointing.
Figure 6.6 Generalized SynA overview
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Source of screenshot: TradeStation Technologies, Inc.
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On the other hand, by selling more options, the net credit is higher: $1140.86, compared to $292.92. This is also the amount by which the cost basis is reduced, so the gain–loss crossover on the downside is lower, improving the loss profile on that side of the distribution. And look at theta: It goes up to $49.11 per day. At this rate, it would take only 13 months to recover the cost basis. Is this really achievable? I don’t know. I know what the numbers tell me. I know that if I go through the calculation of time decay, it is possible. But I also know that frequent delta adjustments eat into profits. So volatility would need to stay high (for options pricing) and the actual stock price movements would need to be nonvolatile (so that frequent adjustments would not eat into potential profits). This is somewhat contradictory, but it could happen. Based on experience, I have had investments that are well behaved in terms of not needing frequent adjustments, and I have reduced cost basis to zero in less than three years. I have never accomplished it in less than a year without high leverage or high delta. By “high delta,” I mean guessing right about price direction. I view those results more as luck in trading than as discipline in structuring securities, so don’t count on a payback period of 13 months. As mentioned before, it is simply an indication of what is possible; the instability of the SynA will probably not make it easy.
Investor or Market Maker One of the attractive features of a SynA is that investors may prefer its risk profiles. They make it easier to sleep at night. When you decide to leverage theta, you might be moving away from investing into theta trading. For market makers and prop desks, this is their bread and butter. They have the systems to monitor exposures and make adjustments as frequently as they need to. Market makers especially have the tools to keep delta within ranges, usually at zero. At the extreme, SynA’s could be set up as delta-neutral hedges around
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an underlying security, but the time and effort involved is substantial. And there is no guarantee that the results will be better in the end. I just wanted to point out the basic difference in intent and operation between a moderately leveraged SynA and a trading strategy.
More on Design Flexibility In the previous examples, the CSynA natural curve—that is, a curve that cuts off a portion of both the upside and downside and shifts the center of the curve up and to the left—was modified by more aggressive options positions. The specific curve was a modified short straddle. But no restriction governs the curve shape. In the most general case, you can think of any stock or option strategy fitting into the SynA framework. The model simply indicates the characteristics of the strategy in terms of delta, theta, gamma, and use of risk (through the probability distribution). If you wanted to put a pure options strategy into the model—say, a ratio backspread—you could easily do so. The stock component is zero, and the options components are the normal backspread options. The point is, you can overlay almost any option strategy payoff curve you want onto an underlying security, or you can leave out the underlying and create options-only strategies. In the next chapter, the options structure that gets the most attention is the iron condor overlay. One advantage of the visual approach to design and management of SynA’s is that it is not necessary to restrict the design to any standard option strategy. By using the basic levers of the SynA, you can manage the structure by selling different numbers of options at different times to meet the overall target curve instead of trying to stay within any particular “named” strategy. Understanding the four basic options trades is all you need to know. If theta is too low relative to
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your goal, you know that you can raise it by selling options. If delta is too low, either buy back call options or sell put options. If delta is too high, sell call options or buy back put options. If you want to add downside protection, buy put options (more effective in crashes) or sell call options (less effective in crashes). By combining the underlying security and the four options trades, you will be able to create your own customized payoff curve and manage it over time to stay within your design targets. By watching the Greeks and your cost basis, you will be able to manage risk and model how your security will act in different market conditions.
Other Forms of SynA’s Synthetic annuities come in four basic forms:
• A positive delta form (discussed already)
• A negative delta form (or what I call a reverse SynA)
• An alternative positive delta form
• An alternative negative delta form
The negative delta form has applications for short positions, and the two alternative forms can be derived from the first two forms by the put–call parity relationship.
Reverse Synthetic Annuities Until now, SynA’s have all been structured with positive delta. Positive delta means that bets are still being placed on the side of increasing security prices. But it doesn’t have to be that way: You can build SynA’s to profit from decreasing security prices, too. To do this, you just think in reverse. A typical SynA has the following components:
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• A long position in stock or other underlying security
• One or more short calls (to generate theta)
• One or more long puts or put spreads (to provide downside protection)
But what if you want to short a stock (or other security) and you want to apply the same SynA principles to the short position? In other words, instead of profiting from a combination of theta and increasing prices, what if you want to profit from theta and decreasing prices? To build a reverse SynA, just take the opposite side of each component so that it looks like this:
• A short position in stock or other underlying security
• One or more long calls (to provide upside protection)
• One or more short puts (to generate theta)
How does this new SynA behave? Before answering that, let’s recap the thinking behind the typical SynA. Compared to a stock position, the typical SynA has less volatility, generates more income, and, in exchange for that, gives up some of the potential upside. The reason for the put options is to protect the value of the position, in case the stock goes down too much. You can look at the objectives in terms of the components:
• Long stock contributes positive delta and profits if the price goes up.
• Short calls do three things: contribute cash flow (yield), dampen volatility (delta), and potentially give up some of the profit if the stock goes up significantly.
• Long puts cost a little but protect against steep declines.
In the case of the reverse SynA, the pieces serve the opposite function, but the objectives of (1) trading off large profits for current income, (2) achieving less volatility, and (3) securing more loss
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protection are the same. Only the direction is different. Here is how each component works to accomplish the overall objective:
• Short stock contributes negative delta and profits if the price goes down.
• Short puts do three things: contribute cash flow (yield), dampen volatility (delta), and potentially give up some of the profit if the stock goes down significantly.
• Long calls cost a little cash flow but protect against steep increases.
The philosophy is the same, but you can use the reverse design to take advantage of decreasing prices. This is especially useful if you have a long/short portfolio structure. Having a reverse, or short, SynA can be valuable because you can generate theta on both long and short positions. And a SynA can help manage one of the most frustrating aspects of short positions. A common problem of long/short funds is that the companies’ prospects are dim, but at the same time, their cheapness makes them susceptible to takeovers or other news that can cause price spikes. The SynA enables you to build in protection against spikes with long calls.
Alternative Forms If you look at the investment profile of a covered call position and a short put, you will see that they are identical, as in Figure 6.7. This particular example is for a stock that is currently trading at $45. The options have a strike price of $45, the period is one year, implied volatility is 30%, the risk-free rate of return is 1%, and there are no dividends. Using the Black-Scholes formula, the option price is $5.12.
Investment profile of short put option or covered call position
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Figure 6.7
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This relationship—that is, that a covered call and a short put (plus a bond) can be established using payoff illustrations or by applying the put–call parity relationship. So any time you set up a covered call position, you could have set up a short put position (plus a bond) and gotten the same investment results. Even though, mathematically, it doesn’t matter which you do, from a portfolio management standpoint, it can feel different. Actually buying the underlying security can feel more “committed” to long-term holding as opposed to contingent holding, which is more easily managed with a short put approach. For example, when I bought Deere, my intent was to hold it long term. In Chapter 8, “Synthetic Annuities for High-Yielding Stocks,” I talk about a position in International Paper Company in which I use short puts instead of the covered call portion of the SynA. With International Paper, I am more interested in having it during risk-off periods and less interested during risk-on periods. Not actually holding the underlying security helps me move in and out of the position without the “intent” of tying up capital long term. To the extent that it helps psychologically in establishing long-term versus semi-trading positions, the following section presents the alternative forms of the long underlying security (usually positive delta) and the reverse, or short underlying security (usually negative delta) SynA’s.
Put–Call Parity Put–call parity refers to a relationship between an underlying security, a call option on the security, a put option on the security, and a bond. The parity relationship is often used to create synthetic positions in any one of the four components using the other three. The put–call parity relationship is normally expressed as follows: Call + Bond = Put + Underlying Asset Rearranging terms, it can be rewritten as follows: Underlying Asset – Call = Bond – Put
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In other words, a covered call (left side of the equation) is equal to a certain bond plus a short put. This relationship can be simplified by assuming that the interest rate is zero, which it currently is for short durations. By assuming that interest rates are zero, the bond term simply becomes cash equal to the strike price of the options. If the underlying asset is a stock, the parity relationship can be written as follows: A long stock position plus a short call option with strike K = A short put option with strike K plus cash equal to K The first line is just a covered call position. The equivalency means that you can either (1) buy stock and sell a call option or (2) sell a put option and hold cash. To see that this is true, you can compare the two positions. Assume that you have two accounts, both with $10,000. In account 1, you purchase 100 shares of XYZ at $100 and also sell 100 call options expiring in one month for $3 per share. In account 2, you sell one naked short put contract for the same $3 and hold $10,000 in cash. The strike price on both options is $100 = K. The following table shows how both accounts will appear at option expiration (time 1) at three different stock prices ($90, $100, and $110): Time 0
$90
$100
$110
Account 1 Cash Stock value Option value Total account 1
$300
$300
$300
$300
$10,000
$9,000
$10,000
$11,000
–$300
$0
$0
–$1,000
$10,000
$9,300
$10,300
$10,300
$10,300
$10,300
$10,300
$10,300
Option value Total account 2
$0
$0
$0
$0
–$300
–$1,000
$0
$0
$10,000
$9,300
$10,300
$10,300
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Both account 1 and account 2 have the same value at each of the three stock prices in the example. In fact, this statement is generally true. These two accounts will have the same value at all stock prices. Because they act the same, they are, by definition, equivalent.
Alternative Form: Positive Delta Put–call parity gives you a choice when structuring a SynA. In previous examples, positive delta SynA’s were set up by buying stock and selling call options, as in account 1. You can accomplish the same outcome by selling puts and holding cash, as in account 2. Also at times, you might want to sell puts to establish new positions. One example is buying a partial position in a security and completing a full position purchase only if the security falls to a lower level. In Chapter 8, the put–call parity relationship is the rationale for selling puts to begin a position in International Paper Company. In that case, a partial naked put position is used, hoping for a further decline in price to buy the rest of the position at lower prices, meaning at higher yields. When the full position is in place, I think it is a good idea to add long puts at a lower strike price. This part of completing the SynA is the same as before. That is, a complete SynA is a combination of covered calls and long puts at lower strike prices. The alternative form is therefore a combination of short puts and long puts at lower strike prices. Even with a partial naked put position, it is a good idea to at least enter a limit order for the long puts on the partial position. For the short put version of the SynA, because there are both short puts and long puts on a portion of the SynA, the short/long combination is a put spread. Because you receive more for the short put than you pay for the long put, it is a credit put spread. This produces the following relationship: A SynA with covered calls and long puts = A SynA with short puts and long puts (or a short put credit spread)
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Alternative Form: Negative Delta You can also use the put–call parity relationship on the reverse SynA. Instead of short stock/short puts, you can substitute a short call. In the reverse SynA, the loss protection is needed in case of a spike upward in price, so long calls serve the same purpose as long puts in the positive delta SynA. That leads to a similar relationship as before: A reverse SynA with a covered short position (short underlying plus short put) and long calls = A reverse SynA with short calls and long calls (or a short call credit spread)
Strategic Versus Tactical Positions As mentioned, one distinction I make in deciding what form of SynA to use is to determine whether I am establishing a long-term strategic position or establishing a potentially shorter-term tactical position. Deere is a long-term position, so I don’t mind being more “committed” by buying the underlying security. On the other hand, International Paper is more tactical, in that I want more exposure when the market is under stress and less exposure as the market recovers. Deere’s appeal is a strong secular growth thesis. International Paper’s appeal is somewhat growth related, but it is also partly a feature of stocks that pay dividends in the range of 3% to 5%. As the price falls, the dividend yield increases, hopefully offering price support that acts as a natural put option. The fact that I want more exposure to IP during risk off and less during risk on means that I might want to use short puts instead of covered calls; from an ownership perspective, those positions are easier to adjust in terms of capital commitments. I also make a distinction between establishing a position for the first time and maintaining a position for the long term in deciding between these two alternatives.
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The same reasoning applies to my choice of the reverse SynA, compared to the alternative reverse SynA. I tend to use the reverse SynA for long-term short positions. For example, I am short the euro in dollar terms. That is, I have short position in FXE, the euro/dollar ETF. Because this is a long-term position where I think the price movement is down, I use a reverse SynA. It is strategic. For the volatility index, on the other hand, I want negative delta or a short position only when the VIX is trading above certain price levels. At lower levels of the VIX, I want less exposure. A certain amount of gravity pulls the VIX and related securities such as the VXX down, but more bad news out of Europe could cause a spike well above where I am now. Because I do not want a long-term position, I use the alternative—that is, I sell call options to establish a partial position, with the intent of selling more if the spike occurs to fill out more of the position. This is exactly a mirror image of what I did with International Paper. In that case, I think that the price cannot stay too low because higher yields will attract buyers. I did, however, buy long puts, in case a bigger problem develops. For the volatility index, I don’t think the current high levels are sustainable over any significant period of time. At these levels, the VIX is signaling almost 30-point daily moves in the S&P 500 Index. But, in case the VIX goes to 60 or 70, I want to buy some long calls to protect against unlimited upside. The trade is to sell call options at various strike prices and buy long call options at higher strike prices for protection. Hopefully, the examples in the high-yield stock (Chapter 8) and volatility chapters (Chapter 10) will help to make this material clear and illustrate that you might prefer one “equivalent method” to another.
7 Managing a Generalized SynA Managing a generalized SynA often requires more attention and more frequent adjustments. The management rules are similar to those of the CSynA, except that, when leveraging theta, using spreads instead of naked options is usually a good idea. This chapter also includes some comments on combining risk exposures to stabilize certain hedged SynA’s.
Cost Basis Adjustments and Financing Insurance Protecting cost basis is again the most important aspect of SynA management. If you are trading Level 3 options and above, you probably have your own views about risk management. Instead of talking about rules beyond that related to cost basis, I present guidelines that have been useful to me. I also walk through some scenarios that seem to come up frequently in SynA management. Cost basis rule: Sell call options to adjust your cost basis if the loss on a position exceeds your risk tolerance. This is the same as with the CSynA, except when you have a dedicated combined position. Exception for combined positions: If you have a hedged position that is the combination of two or more individual positions, you can apply the rule to the combined position. For example, if you are hedging interest rates against European 151
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banking headline risk with a short euro currency position, it might be more effective to combine the position gains/losses when applying the cost basis rule. The mechanics of the trade are the same as with the CSynA. That is, you have flexibility in how many options you choose to sell and at what strike prices. The difference with the generalized SynA is the speed at which adjustments might be required. Because you can set up more aggressive positions, SynA gamma will normally be higher, and therefore more sensitive to underlying security price moves. As before, you should follow the cost basis rule even if you have to sell ATM or ITM options. After selling call options, you might have a negative delta position, which is okay if it is necessary. In the case of a volatile stock such as Netflix or Sears Holding, being delta negative after the first price shock can be an advantage. Getting to a less risky stance or using delta hedging lets you live to fight this battle again or move on to a better opportunity. Guideline: Invest between 20% and 40% of the time value received from the sell of call options to purchase put options. As with the CSynA, if the call options you sell are ATM or OTM, the premium is all time value. If you had to sell ITM options, look at only the time value portion of the premium for this guideline. Again, you have flexibility in the number and strike prices of the put options. The lower the strike you choose, the more options you will be able to buy. One advantage of steadily reducing cost basis is that, within a few months of a stock that is not too volatile, you should be able to purchase put protection on most of all the shares using a strike price close to your cost basis.
Delta Adjustments Delta adjustments for a generalized SynA follow the same basic guidelines as those for a covered SynA, except that the generalized
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structure is often more leveraged and more sensitive to changes in the underlying security price. Because of the greater instability, you might want to consider narrowing the delta target range, to trigger adjustments earlier. Guideline: Set a delta target range and adjust the SynA to keep it in the range. This is the same as for the covered SynA. Again, how you apply the guideline defines how closely you want your position to move with the underlying stock. If the actual delta gets too low, you will not have exposure; if the actual delta gets too high, you might have too much exposure. For example, if your target delta is 0.50 and your range is from 0.35 to 0.60, then when the delta is below 0.35 or above 0.60, you need to make an adjustment. If the delta is too low, you should either buy back call options (for Level 1 investors) or sell put options. If the delta is too high, you can sell call options to reduce it (by selling call options, you also increase theta). The difference for the generalized SynA is that you often will be working with much higher gammas, so the triggers will be activated more frequently.
Be Careful with Adjustment Leverage Imagine that you have set up a SynA on an underlying stock trading at $50 and that the maximum payoff occurs at $53. A day or two later, the stock goes up to $55 on some good fundamental news. Say that delta has now dropped from 50% to 30%. You don’t want to miss out on the ride if it keeps going up. What do you do? If the case of a CSynA, the only thing to do is adjust delta by buying back one or more call positions. You could leave the stock position naked, or you could roll the options up or out or both, depending on how far you think the price might run. Later, if the price falls again, you can make the defensive adjustments, again with calls.
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With the generalized SynA, you have more choices. When the price reaches $55, you could buy back a call. But buying back the call means you are repurchasing the time value that you just sold. You will also be lowering theta. As an alternative to buying back a call (or more accurately stated, “buying-to-close”), you can sell a put. By selling a put you increase delta and theta at the same time. You also capture some of the price increase you missed out on during the increase from $50 to $55. As the price increased from $50 to $51, you got about 50¢ of the increase because delta was 50%. From $51 to $52, you might have gotten 45¢ because delta goes down as the price goes up. You get less with each dollar increase. Knowing this creates a preference that the stock price go up slowly. If the price increase happens slowly, you are making a combination of delta return and theta return. Selling puts into price strength helps restore the balance. The short put causes the maximum payoff to move up to a higher price point. It increases both theta and delta, as long as the price stays up. If it reverses, a downward movement in stock price might actually feel good if the price drop is small. If it is more than a couple of points, you will have more leverage not only in theta, but also in delta. The cushioning effect of the call options is somewhat countered by the fact that you now have a short put also. If the price drops to a certain point, you need to start selling calls against the position to stabilize it. Gamma is now working against you. As the price drops, the put delta gets larger and you have essentially increased your effective shares potentially above your actual number of shares. Now, if the price reverses again to the upside, you face the same problem on the call side. This process of trying to counter the price movement by selling puts as the price increases and selling calls as the price decreases might turn out well, but it creates a natural leverage in the position that tends to get more unstable as you approach option expiration.
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You can visualize what is happening by thinking of the payoff curve. It starts out fairly flat, as with the CSynA. When the price goes up too fast and you sell a put, you are reshaping the curve. You are pushing the maximum payoff, or the high point on the curve to the right, so that it will be closer to the actual stock price. You are also raising the curve to create more theta force. At the same time, however, you have caused the left side of the curve to bend down. That means that when the price goes below a certain amount, the loss will be larger than if you had not sold the put. The same thing applies when you sell the call option to counter any future price drop. You reshape the curve again, pulling it to the left and up in the middle, but with more slope on the right side now. The SynA chart in Figure 6.2 (Chapter 6) shows an example of what happens. Theta is powerful, but the wings drop off steeply at the ends. Continuing the leverage is tempting because you believe that you are in control of that leverage. And that might be true most of the time—but when the price is moving enough to create the situation in the first place, it could be the beginning tremors of something bigger. If you get hit with serious volatility at that point, it will be difficult to manage. I went through this scenario because with high leverage, you should consider using spreads instead of naked options to make these adjustments. The spread will help taper the wings of the payoff curve so that you have a chance to reposition in extreme volatility. The rationale is exactly that of a spread or straddle trader who decides to use a condor instead. Guideline: When adjusting delta down into the range by selling call options, if the adjustments result in overwriting call options (that is, uncovered call options), you should generally write call spreads instead of naked calls. This guideline depends on how often you are comfortable adjusting the position and how much margin buying power you are
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comfortable giving up. It also depends of the nature of the security. Very high beta stocks—stocks that are likely takeover candidates— and volatility indicators that can spike easily are some cases in which you might prefer the spread. In writing the call spreads, it is okay to write calendar spreads instead of vertical spreads, to take advantage of the pricing discount for longer terms. The purpose is to protect you from rapid snap-backs in price. A day trader who wants to leverage theta could attempt to compensate for naked calls by selling puts or put spreads, but for an investor who wants to keep the adjustments to weekly or monthly, this rule is important to protect against naked call exposures.
Selling Call/Put Pairs I use a certain technique when I think that a security is approaching levels at which I want to own more of it. For example, if I am following delta adjustment rules and have sold a call option or a call spread where the lower call strike is approaching a minimum value, I might choose to sell a put spread at the same time. For example, let’s say I bought a security for $50 and followed the price down using the cost basis rule until it hit $35, where I was convinced that it had price support. I would still follow the rule, but at $35, I might choose to sell both a call and an ATM or OTM put spread at the same time. Selling the put spread leverages theta and provides more of a cushion before I need to adjust delta in the other direction if the price does snap back. This technique is good only if you also don’t mind owning more of the stock at lower levels and, importantly, don’t mind making more fine-tuned adjustments to cost basis, if necessary. By selling both calls and puts, you reduce the existing cost basis faster, but the position also becomes less stable. You might want to reserve the technique for cases in which you have given the position an exemption from the cost basis rules, as discussed with minimum
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value positions. In those situations, the natural increase in exposure as the price drops will be consistent with your objective. Guideline: When adjusting delta up into the range by selling put options, consider using put spreads instead of naked puts. Again, I say “consider” because there’s always the possibility that a black-swan event could cause sudden moves in the security price. Some types of securities might be less prone to these events; examples are utility or high-quality, high-dividend stocks with great balance sheets, and volatility-related securities such as the VXX that are more likely to experience large increases than large decreases (when the VIX is less than 20). When a black-swan event occurs, two things happen. First, if you have anything other than ice water flowing through your veins, you will be psychologically stunned. In my case, sometimes the size of the event makes me question whether it is real. I tend to defend the value of my investments, in an effort to not realize the pain of an unrealized loss. Second, volatility blows out. That is, volatility spikes to high levels, making put options that could have been purchased cheaply the moment before the event happened almost prohibitively expensive the moment after. If you sold a put spread instead of a naked put, the long leg of the spread gives you price support at some level. Of course, you don’t want to spend too much on the long leg, because it will be a losing trade most of the time. Even if you spend only a few cents on the long leg, it will give you a worst-case scenario (other than zero) to begin to trade against. You can also finance part of the long leg by selling a further OTM put option when you are willing to set a minimum value. I recommend doing that only with high-quality stocks with strong balance sheets. For example, when I adjust the Berkshire Hathaway position using puts, I don’t mind selling a slightly ITM put, buying a fairly OTM put, and then selling the put with the next strike price down.
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The protection isn’t as strong, but hopefully the gap protection will be enough to give me time to reevaluate the situation. If it is worse than I expected, I can go back in with short calls or short calls/long put collars.
Emotional Indifference and Price Preferences I mentioned the concept of emotional indifference in the introduction. It means that you don’t care that much about price movements, at least within normal ranges. What is different about most SynA’s is that you will probably prefer to not see the price go up too fast. If it does, you will feel like you made a mistake by selling the call options. (You will feel better if you used call spreads.) By looking at the modified payoff curve, you can see where the maximum profit occurs. Or if your SynA is not too complicated, you can probably get a feel for where the maximum profit occurs by looking at the strike prices of the short calls. If you have a full covered position, it happens at the high strike price. Beyond that, you don’t get any more upside, so it creates a preference that the price stays lower than that. If your SynA is complicated—that is, leveraged with several overwritten spreads—the point at which the maximum profit occurs might not be obvious. If you are using complicated option structures, you probably will also be using platform charting that tracks the payoff curve in real time for you. Figure 7.1 shows a Chesapeake Energy SynA payoff curve. The current price of CHK at the time the chart was created was $25.81. The chart indicates that the maximum payoff occurs at about $27.
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Figure 7.1 CHK payoff chart
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Knowing where the maximum profit occurs naturally creates a price preference. If you are like me, you will normally feel better when you capture most or all the profit. That means you were right to sell the call options. However, if the outcomes are reasonably good over a range of prices and theta is being generated at high rates, you might not care that much about where the price actually is on the expiration date, as long as it stays fairly close to the maximum. In this example, if the price stays between about $25 and $30, the profit will be above $2,500. If the price begins to move outside that range, my tendency is to “push” the curve to where the price is. Pushing the curve is the process described by the previous delta adjustments; it is just another way to think of the adjustments. For instance, if the price drops to $24, delta will go up, probably above the delta range. Whether you are watching price or delta, the adjustment is the same: Sell call options or call option spreads to increase delta and reshape the payoff curve so that it moves up and to the left. You cannot control where the security price is, but you can “move” the curve so that the price is more centered. By making the adjustments, you create more theta and move the maximum point in the curve closer to the current price of $24. As an alternative to using delta as the trade trigger, it is also possible to set up decision trees based on price. Because price is more straightforward than deltas, price is easier to use, especially if your platform does not provide consolidated SynA deltas. In practice, I often use price as a signal to look at delta. With a good platform, you are just a click away from either. For the CHK SynA, I might decide to make a delta adjustment if delta rises above 80%. I have an idea that will happen if the price drops to $24. In reality, it also depends on time until expiration and implied volatility, but $24 is a good starting point. If the price hits $24, I flip over to the SynA theoretical position to see what the delta really is. If it is 75%, I do nothing. If it is 80% or more, I adjust by selling one or more call spreads until the delta is below 70%.
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For an algorithmic trader, using prices to trigger delta adjustments is close enough and might be easier to implement. Just be aware that if the price hits a trigger early in the period, the delta might be quite a bit different than if the trigger is reached late in the period. Also be aware that the number of adjustments will be affected by how often you look at the prices.
Price-Based Delta Targets Chapter 9, “Synthetic Annuities for the Bond Market,” includes an example of a security for which the price level is the starting point for setting delta targets. The idea is that there is a minimum value for interest rates. At the time of this writing, interest rates on Treasury bonds are some of the lowest in 60 years. An argument can be made for interest rates staying level or even declining in the next few years, but if the economy shows any signs of life, the bond market could be vulnerable as an asset class. By intentionally making delta targets higher at lower interest rates, the position is customized to reflect a specific exposure pattern. This kind of customization can be done on any security. When the exposure pattern follows the natural automatic exposure pattern of a typical SynA, you don’t need to make other adjustments. If you want to exaggerate the pattern or create another payoff profile, you can use your target price–based delta to guide your adjustments. When the pattern is specific or you need to follow it closely, make sure gamma is low enough that the structure is stable, or you might find that you need to make frequent or daily adjustments. In the special case of price-based targeting, you can push the payoff curve to approach that of a particular option strategy payoff. By following the guidelines in this chapter, something resembling a modified condor often evolves naturally.
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The Iron Condor (Almost) Overlay Which generates the most favorable profile for those interested in maximum theta generation within risk tolerances: a SynA or an iron condor? For an iron condor trader, delta is intentionally kept low. Most condor traders don’t like seeing delta exceed 20%. They want to trade a large number of contracts with a small probability of exercise. The large number of contracts makes adjustments to the position difficult if it gets too close to a strike price. An old adage talks about the condor strategy being like picking up change in front of a steamroller: As long as you don’t fall down and get run over, it’s easy. While the condor avoids high-delta sections of the payoff curve— that is, at the center—the SynA goes straight for them. This is because theta is highest for ATM options. Because theta is high for each option, a SynA uses much smaller numbers of options to generate the same absolute theta. With a condor, if a sudden price move puts you close to the short strike price, it becomes unstable. In fact, the speed at which it becomes unstable increases as it gets closer to the strike. That makes it harder to perform delta adjustments. The SynA, on the other hand, becomes unstable at a slower rate. If the natural leverage process described earlier is managed by making contingent trades on the opposite wing, you can hopefully finance stability at a lower cost. Let me explain what I mean by contingent trades. You can think of the SynA as having a core consisting of a security and four option legs:
• Short call options, usually centered on the current stock price
• Long call options, usually at higher prices
• Long put options, usually at safety net levels
• Short put options, used either to finance the long put options or to customize the payoff curve
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Whenever a delta adjustment is made, it pushes the curve in a particular direction because the price (or delta) has moved outside a preset range. Imagine that the price has increased from $50 to $55 and that the adjustment is to sell a $55 put into the price strength to get delta up into the range. At the same time, one of the legs on the opposite side of the structure will necessarily be cheaper. In this case, it is the long put option at the safety net price level. So at the same time you sell the short put, you buy the opposite-wing long put. The long put is much cheaper at this point than if you had purchased it at the trade setup. If the safety net level is around $45; the long put is $10 OTM and should cost only a few dollars. If you want to go further, sell a $40 short put to finance part of it. The position is not as protected, but that $5 gap insurance could be enough, depending on the quality of the security. The same logic holds for the other wing. If you need to sell a call to lower delta because the price dropped, at the same time, buy the long call on the opposite wing. With a condor, because of the instability, you probably want to establish the four-part trade at setup. Owning the underlying security makes a SynA more stable at setup, so you can execute the contingent trades along the way as you add leverage through the delta adjustments.
Intrinsic Value and Mean Reversion This is one of the most interesting aspects of any strategy, but it has increased significance for a SynA. By its nature, a SynA increases the exposure to a position as the price decreases, and decreases the exposure to a position as the price increases. This is great if a stock is simply fluctuating around its “true” value due to typical market influences and noise traders. In that case, it is effectively selling some of the position at higher prices and buying it back at lower prices.
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The problem is trying to distinguish between normal market fluctuations and what could be the start of a broad market decline or a fundamental problem with the company. In these cases, you don’t want to let the stock drop too far before making adjustments to the cost basis. The default assumption is that you can’t really tell the difference between normal drops and the beginnings of a real problem. The adjustments are meant to be conservative. A different situation arises when you have some valid reason to believe that mean reversion is going to happen, preferably in the not-too-distant future. If this were really the case, you would not have to make the conservative adjustments. In fact, you could actually increase the power of the strategy by ramping up the effect. So instead of taking cost basis out as the price drops, you could actually increase exposure by adding even more to the position as it dropped. You could do this by selling puts at lower levels. That would increase both delta and theta. The same applies to the price moves up. Instead of having to sell puts to increase delta and theta, you could do the reverse: sell calls in anticipation of a price decline back to the mean value. The effect on profits is extremely powerful. You just need to be correct about mean reversion. I tend to recognize mean reversion under two conditions. One is a trading tactic. It happens during merger and acquisition activity when a recent price paid establishes a near-term floor on the stock price. An example of this is when Exxon purchased XTO; shortly afterward, Total made an investment in Chesapeake. Based on proven reserves, this gave Chesapeake a period during which investors were unlikely to bid down the price below the implied transaction price. This is a temporary situation, however, because fundamentals can change quickly and the industry as a whole could decline in value. The second situation is related to long-term Treasury rates. The ETF with symbol TBT moves with 20+-year Treasury bond rates. As
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rates go up, TBT goes up. We maintain a position in the TBT by selling puts in increasing amounts as rates continue to decline. There is the risk that rates could go very low and stay there for an extended period of time. Over the longer term, the trade will work as you get more heavily invested and theta becomes high enough to offset any further decline. But that doesn’t mean there won’t be a period of adjustment if the fall in rates is fast. So where does mean reversion come in? Well, rates on the long bond cannot go below 0%. In addition, it is unlikely that rates will go below 2.5% on a historical basis. But if there were a prolonged period of deflation, this could happen. For this reason, I use put options instead of the actual TBT—at least I will get paid for option time decay. The search for situations in which there is price support, even in the short term, can be profitable. Mean reversion is an active part of the strategy, and I am constantly looking for these opportunities as they arise.
Earnings Reports When you are using an options-based strategy, changing the investment profile for specific events is easy. The flexibility to change the profile at any time is a key benefit of a SynA. With regard to the earnings reports specifically, much of the annual volatility of a stock comes from the four quarterly reporting days. It is up to you whether you want to accept the volatility. If you have a view on price, you can make tactical bets. If you don’t have a view and would prefer not to take a chance, you can convert the options positions to collars before the earnings announcement and then reestablish your normal SynA option profile the day after the report. You can give the collars some room to move, or you can set the short call strike equal to the long put strike, to take out all the risk. Of course, implied volatility is higher before the earnings announcement, but many times it is not enough higher to justify the risk, especially in a concentrated position.
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Ex-Dividend Dates The possibility exists that ITM options will be exercised anytime, but as a practical matter, it usually occurs only on the ex-dividend date. This is due to a trading strategy that exploits timing elements, as opposed to the underlying investment strategy of the SynA. In taxexempt accounts, usually no harm is done, other than a commission to buy back the position if it gets called. In taxable accounts, you can also buy to close the position, but check with your tax advisor on the consequences of the exercise/buyback. You can avoid the situation by buying ITM options before the ex-date, selling extra OTM options to keep delta in range, and then reversing the trade after the ex-date. You will pay the commissions on the trades, but this might be worthwhile if you are sensitive to the tax effects.
Mean Reverting and Trending Triggers If you believe that the security has mean-reverting tendencies, you might want to consider pairs trading whenever the price reaches your upper or lower trigger points. For instance, if you think the security has a low valuation level of $50 and a high valuation level of $60, you might want to do this:
• If the price reaches $60, sell call options and buy far-OTM put options to complete the put spread.
• If the price reaches $50, sell put options and buy far-OTM call options to complete the call spread.
If you believe the security is trending, you might want to consider the following pairs trades:
• If the price reaches $60, this is confirmation of the trend, so sell OTM put options and buy OTM call options.
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• If the price reaches $50, the trend is broken, so sell ATM or ITM options to protect cost basis and reduce delta.
Theta-to-Delta Ratios Certainly, it is preferable to generate high levels of theta and, at the same time, provide high levels of risk control. But that would mean getting high yield on a safe instrument. Everyone would do that if possible. But there’s always a tradeoff between safety and yield. Once I tried selling deep ITM call options on a high-yielding stock, to see what would happen. I bought Verizon stock that paid a nice dividend. Then I sold a $10 strike call option to get most of my money back. There was almost no possibility of VZ falling below $10, and my invested capital was only $10 after selling the call option. I waited to see what would happen. If I got the dividend on the stock and my “safe” cost basis was $10, return on capital would be huge and the investment would be almost riskless. It didn’t work. My VZ stock was called away on the ex-dividend date. Evidently, some people out there don’t want other people to make high returns with no risk. But making delta adjustments does involve a tradeoff that can be managed and quantified. Take a look at Figure 7.2, which measures an aspect of the risk/reward tradeoff by the ratio of theta to delta. The five columns show call and put option pricing under the BSM formula, with the same assumptions, but using five different option strike prices, from $90 to $110. The stock price is $100, the assumed volatility is 30%, and the term of the option is one month. Starting in the first column, with an option strike price of $90, the call option premium, or price, is $10.45. This is $10 of intrinsic value and 45¢ of time value. For deep ITM call options, delta is high. In this case, it is 89.61%. So the option moves almost 90¢ for every dollar move in the underlying security. But deep ITM options tend to
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have very little theta. In this case, it is only 45¢ over a period of one month—or, rounded, about 1¢ a day. If you look at the ratio of theta to delta, it is only 5.96%, meaning that delta is much larger, relatively, than theta.
Figure 7.2 Theta-to-delta ratios
The center column has a strike price of $100, or an ATM option. The same calculation shows that the ratio is 80.13%. Moving to the far right, the option strike price is $110, or a far OTM option. The price, 62¢, is close to the time value of the $90 strike option, but notice that the ratio of theta to delta is much higher, at 51.42%. On a relative basis, this option gives you more theta per unit of delta. These relationships might be helpful when you want to adjust delta or theta to fit your outlook, particularly when you are deciding which options to repurchase or which to sell to modify the payoff curve.
8 Synthetic Annuities for High-Yielding Stocks If you are a CNBC Mad Money home gamer, you are probably familiar with some of Jim Cramer’s expressions:’ “Wait for a pullback,” “Schnitzel a little,” “Get paid to wait,” and “Take advantage of accidental high yielders.” With a SynA, you can do all of these at once.
Getting Paid to Wait: International Paper Monday September 19, 2011. Today on Mad Money, Jim Cramer recommended International Paper (IP). He said that buying a little now is a good idea. The company pays a dividend, and at the current price of $27.22, the yield is 3.8%. International Paper is a paper and packaging company that has performed well in spite of its cyclical business. If the stock price does fall, the yield goes up, and you can pick up more shares with a higher yield. I like Jim Cramer. To me, he is a throwback to Peter Lynch, who picked stocks the old-fashioned way. If he had to wait in line to buy the product, or his kids were talking about it, or his wife wanted to go there, Lynch would research it. He ran the Fidelity Magellan Fund before the market got so efficient that a stock picker had trouble making money. Cramer and Lynch both love growth stocks, but they recognize that, in turbulent markets, there’s nothing like good dividend yields to protect investors. 169
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Source: TradeStation Technologies, Inc.
Figure 8.1 International Paper SynA
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In this volatile market, some of the best performers have been high-yielding stocks with good balance sheets. In my portfolio, I have Verizon and Kinder Morgan, both high yielders. I’m amazed by how well they have held up (and held down volatility) during the recent ups and downs. When you look at the yield and the price action, the relative performance of these stocks—utilities, telecom, and pipelines with high dividends—has been impressive. Here’s a look at IP on September 20, 2011, at the market close: Last trade: $27.22 52-week range: $20.77–$33.01 Price/earnings (ttm): 9.31 EPS (ttm): 2.93 Dividend and yield: $1.05 (3.80%) I have followed IP for a few years. I believe that high-yield stocks should perform well short term, so I decided to follow Cramer’s advice and buy. The question for me was how to structure the trade. Cramer’s recommendation came in two parts: buy a little now and hope the stock drops to around $26. Based on the current dividend, if the price drops to $26.25, the yield will go from 3.8%, where it is now, up to 4.0%, a number that Cramer described as the magic yield that will begin to attract more investors. The higher the yield, the more demand there is, adding support to the stock price. And if the stock stays down for a while, at least we get paid to wait. As Cramer points out, the stock is not a buy just because of dividend yield. It is a great company with great management that also has a high dividend. Sounds good to me. The decision I need to make is whether to buy the stock or build a SynA around it. So I compared the two approaches and decided on the SynA. I set up the SynA by selling one in-the-money (ITM), two at-themoney (ATM), and one out-of-the-money (OTM) options. In total, I got $519 for the options. The TradeStation window in Figure 8.1
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shows each option separately and the position totals, including a delta of $179.29 and a theta of $9.87 per day. So how does this compare to simply buying the stock?
Allocated Capital This example uses allocated capital of around $10,000, or about 400 shares of stock. The stock trade would be to buy 200 shares now at $27.21 and place a limit buy order at $26.25 for the other 200 shares. In round numbers, there is about $5,000 of allocated capital per half-trade. Of course, the numbers can be scaled from there to any position size, but for comparison, this works. Because the SynA has a delta of $179, it is equivalent to 179 shares of stock—close to 200 shares. So to begin, allocated capital is roughly the same for 200 shares of stock and the SynA.
Completing the Position: Buying the Other 200 Shares If you had decided on the stock trade, you would need to wait until the price dropped to $26 and complete the trade by buying the other 200 shares. With the SynA, you don’t need to do anything because, as the stock price changes, the delta also changes, making the number of equivalent shares approach the full 400 shares at lower stock prices and fade to zero at higher stock prices (see Figure 8.2).
Figure 8.2 International Paper effective shares
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Yield The stock pays a dividend of $1.05 a share annually. If you had bought 200 shares, that equates to $210 a year, or about $18 per month. In comparison, how much does the SynA pay? Let’s look at both the instantaneous theta from TradeStation and the “average theta.” From the TradeStation screen, instantaneous theta is $9.87 per day, or about $300 per month. Average theta, which is simple and at times a better estimate, is calculated by assuming that the stock remains at the current price of $27 until the options expire in 31 days. At that time, the options could be bought to close if they were ITM. Assuming that the price at expiration is equal to the current price of $27, the options you sold with strike prices of $26 and $27 would be worthless and there would be no need to do anything. To buy to close the $28 strike option would cost $100 because they would be $1 ITM. That means you get to keep $419 ($519 premium – $100 buy to close). You have 31 days until expiration, so the average theta is around $14 ($419 ÷ 31). If you use average theta, the SynA pays you almost as much in one day as you get from the dividend yield in one month. If you annualize average theta, the yield grows to more than $4,900, or almost 100% annualized return on $5,000 of invested capital. The situation is actually a little better than this because you would have used $5,000 as allocated capital, thus higher for the stock trade ($27 × 200) and lower for the SynA ($27 × 179). This assumes that the stock price stays at $27 and you continue to get current pricing. That is not going to happen. The stock price will move around, and the option prices could go down. Still, there is really no comparison between the magnitude of yield possible with theta and the dividend yield. Theta is many times more powerful—that is, if it can be captured correctly. Yield was the main reason I chose the SynA over the stock trade.
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But, two more reasons are valid. First, if the stock price goes down, the plan was to buy some or add to a position anyway. The put options accomplish this for you automatically. The more the stock price goes down, the more delta goes up, so the more shares of stock you effectively own. With the stock trade, you have to actually buy and sell stock at different price levels to keep the yield at 4%. In other words, you would need to do manually what the SynA does for you automatically. You would need to sell some of the shares you own as the stock price moved above $27 and buy more as the price dropped below $26. The third reason is that, with the SynA, the stock price can go down by the amount you got for the options, and you can still break even. With the stock, any decline in price will result in a loss on the first 200 shares.
Managing the SynA Longer Term How would I manage this position? A simple rule is to just roll out the options at the same strike prices each month. By doing this, I have essentially set a fundamental valuation range of $26 to $28, where I am more “invested” at lower prices and less so at higher prices, for a classic value investor approach. The dividend yield helps to stabilize the stock price. As the price moves lower, the dividend yield increases. At 3.8%, it is already quite a bit higher than the 30-year Treasury rate. Stocks that have “accidental high yields” are in tremendous demand and performed extremely well during the last market correction. If you believe that IP has intrinsic value, either because of the underlying assets or because of the yield, you could put in place a plan to buy more at lower prices. You could do this by putting in limit orders to sell additional puts, or you could buy the stock outright. Later, if you want to add this stock to your core holdings, you can allow the short put options to exercise. That would result in long stock
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positions. Then you could sell out of the money calls to increase the effective dividend yield and buy protective puts. At this point, the position is a standard form positive delta SynA. What can go wrong? Two things. First, the stock price could spike up, and you would miss out on the ride except for the $519 you got by selling options. Normally, a spike up is associated with a good market, so your portfolio would be doing okay and you would make a profit. Accepting that is not hard. And if you wanted to, you could sell some higher strike puts to reestablish your delta target—that is, you could mix trend following with a value perspective that might be consistent with higher valuation ranges, based on the overall demand for equities. Or you could simply stick to your original 26 to 28 strikes and play higher beta stocks if you believe the market is rallying. Either way, this is not a bad situation. The second thing that can go wrong is for the stock price to spike downward. The reason is important, but don’t let that interfere with risk management. The most common reason for a spike down in stocks is a sell-off in the broad market. If that happens and the price performs well on a relative basis, it could mean that the dividend yield support is working properly. In that case, you can take your time, reevaluate, and decide whether the new macro environment is too harsh. But if the stock underperforms on a relative basis, you need to take immediate action. That could be to sell ATM or ITM calls to reduce delta, to buy put spreads, or to short the stock against the naked puts. Shorting against the naked puts creates a covered position much like a covered call position using long stock and short calls. At that point, the position is a negative delta SynA. Sharp price declines with naked puts is always a problem. If you want to sleep better at night, use put spreads instead of naked puts. In this case, selling 26 to 28 strikes and buying a 23 or 24 strike creates a safer position. Even buying a 20 strike, which costs only around 10¢, will help you because you’ll know that it can get only so bad. With a 20 strike as the worst outcome, you can start selling calls to stop
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the bleeding without worrying about an accounting scandal or fraud. Keep in mind that preparing for the downside is something you need to do anyway if you bought the stock instead of selling puts.
Update: September 30, 2011 You can’t say this market isn’t interesting. Today is Friday, September 30, 2011—I wrote this chapter just ten days ago, but this kind of action deserves an update. September 30 is the end of the third quarter—the worst quarter for equity investors since the financial crisis. As usual, many commentators are predicting the worst, downgrading the outlook from a recession to a full-blown depression and maybe “a complete economic collapse.” It does look bad. Gross domestic profit (GDP) was revised from 1.9% to 0.4%, the FOMC announced it would keep rates low “through mid-2013,” and the debt ceiling/default debacle led directly to Standard & Poor’s downgrade of U.S. debt. Then, the Fed conceded that the recovery was worse than expected and that 2012 was looking grim as well. Should you take the advice to “sell everything and brace for impact”? Or should you just follow the rules? Getting back to our investment, International Paper is now trading at $23.25. What happened to the price support at $26.25? Is this opportunity or time to be defensive? Last trade: $23.25 52-week range: $21.44–$33.01 Price/earnings (ttm): 7.95 EPS (ttm): 2.93 Dividend and yield: $1.05 (4.30%)
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Figure 8.3 shows how the SynA looks now. Delta increased as the stock price went down, as it was designed to do. Ten days ago, delta was $179. Now it is $326. The SynA is acting like 326 shares at the current price. If the price continues to fall, the maximum delta will be $400, equal to the number of short options. Volatility has spiked. Figure 8.4 is a snapshot of the average implied volatility for puts and calls. Of course, the higher the volatility, the higher the price of puts and calls. For a company with relatively stable earnings and high yield, volatility is unlikely to stay at these higher levels for long. In these situations, stepping back and considering the alternatives is worthwhile. The investment thesis was that a lower stock price and a corresponding higher dividend yield would support the stock price. The reality was that, under high stress, the price support was not as strong as originally thought. The price has already fallen $3 below that 4.0% magic number, reached at $26.25. At the current price of $23.25, the yield is 4.5%. I know that the screen says 4.3%, but as fast as prices were falling today, the calculation just didn’t reflect the latest numbers. What is the right thing to do now? I don’t know. Hope for a recovery? Usually, when hope is what you have left, you are in bad shape already. That being said, if you want to be a little more optimistic, you can be glad that you contained the loss—and you can remember that lower prices could mean better buying opportunities. For the SynA, the first question is always, what do you have to do? If the loss exceeds the trigger amount, the rules say that you have to do something. The current loss is $972. In the previous discussion, the allocated capital was $10,000, or about 400 shares. Those numbers can be scaled to the size of the portfolio. In terms of the tracking portfolio of $300,000, a full position is 5% to 8% of the total value of $300,000, or $15,000 to $24,000.
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Figure 8.3 International Paper SynA as of September 30
Source: TradeStation Technologies, Inc.
Figure 8.4 International Paper implied volatility
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Source: TradeStation Technologies, Inc.
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If IP’s allocation is $20,000 and the loss trigger was set at 7% ($1,400), you aren’t required to do anything yet because the current loss of $972 is below the trigger. In fact, you could fill out the position now, if you want to. However, keep in mind the new stock price that would cause you to have to make an adjustment. The current delta is $326, so a price drop of only a point and a half would push you over the threshold. If you increase delta at this point, you could go through the $1,400 loss limit quickly. And maybe this is not the best time to be loading the portfolio; maybe keeping some powder dry is better. After all, people are talking about a global meltdown. Remember how the first quarter of 2009 felt. People were talking about a meltdown then, too. That is when the market started its rise that eventually took it up 100% off the bottom. The best buying opportunities come when the forecasts are the worst. That doesn’t mean that you can infer the opposite: It is not true that when the forecasts are the worst, you have the best buying opportunity. Sometimes, the forecasts are right. When the macro news is dominating the market as much as it is right now, you could try to hedge some of the risk of completing the position by putting on a macro hedge. I have started doing this by buying 112 strike puts on the S&P and selling the 105 strike puts. For a net cost of less than $2, you can buy $7 of gap protection. The more protection you have on market risk, the more you can allocate to the loss trigger on individual positions.
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Let’s look at a couple alternatives for completing the position. Figure 8.5 shows a straightforward doubling-down approach. As with setting up the half position, this involves simply centering the strikes around the current price in the same 1-2-1 pattern. If you do this, you increase the delta to $536 and increase theta to $20.40. The current loss stays the same, at $972, still below the trigger at $1,400. To reach the trigger, the stock price would need to fall only about $1 from today’s price. That is tight, so you would have to be ready to recover cost basis by selling calls if this did happen. As an alternative, you could use the setup shown in Figure 8.6. It has roughly the same delta, but the number and strike prices of the options are different. Instead of eight short options, there are ten; the strike prices also have been moved closer to the current stock price. The reason for this type of setup is to increase theta. Notice that, by moving the strikes closer to the stock price and increasing the number of options, theta goes up by almost 50%, from $20.40 to $29.94. Concentrating the option strikes also results in an increase in gamma, which moves up from $79.18 to $115.73. This tells you that if there were a quick upward movement in the stock price, the behavior of the alternative setup would be a little different. As the stock price moves up, delta moves down more quickly in this setup. In other words, the effective number of shares you own declines as the stock price rises. When you expect a quick move up, you might want to maintain a higher delta, so the first setup is preferable. Also, if you think the stock is likely to go down, the higher gamma means the effective number of shares will also rise more quickly, mainly because there is a larger number of short options in this setup. This sort of tradeoff between high theta and high gamma is typical. As always, it is important to model your downside risk. In simple terms, think about what happens when the stock price declines by a large amount. For instance, if the price goes down to $15, each of these short option deltas approaches 1.0 on a percentage basis or $100 on a dollar basis. As deltas approach 1.0, the options act like stock.
Figure 8.5 International Paper SynA—Centered
Source: TradeStation Technologies, Inc.
Figure 8.6 International Paper SynA—Linear Increase
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Source: TradeStation Technologies, Inc.
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That means you have losses associated with 1,000 shares of stock or a delta of $1,000. In the first setup, the maximum delta is $800. I have not included any long puts in the discussion so far because the full position is still being accumulated. When the full position is reached, it is a good idea to buy protective puts with a portion of option proceeds, consistent with the rules described earlier.
Leveraging Theta One more setup is worth considering. This scenario requires you to monitor the SynA more closely and possibly make adjustments more often. But it can be more profitable as well. The idea is to take advantage of high volatility by selling more options and, at the same time, keeping delta level or lowering delta for a more conservative stance. Higher volatility means higher pricing on your short puts or calls. In the leverage setup, you sell both: You sell puts to complete the position, and you sell calls to keep delta at current levels or to lower it. Because the possibility of both a spike up or a spike down from this point exists, you should consider selling put and call spreads instead of naked puts and calls.
9 Synthetic Annuities for the Bond Market This chapter looks at how a synthetic annuity can be applied to the bond market. In particular, for investors who are concerned about a rebound in interest rates—and a corresponding decrease in bond prices—this chapter includes an example of a SynA used to enhance yields and to hedge bond prices. This includes a discussion of bond market dynamics and the attractiveness of a particular investment thesis, made even more attractive by how well the thesis fits with the natural adjustments inherent in a bond SynA. This chapter ends with an excerpt from a paper by James Bullard of the St. Louis Federal Reserve Bank. I think he has an interesting perspective on future inflation and bond yields.
Is This a Cyclical High in Bond Prices? Many investors who hold Treasury securities and other bonds have performed well through the market downturn. In spite of a U.S. debt downgrade and questions about the dollar as the dominant reserve currency going forward, Treasury yields have declined to the lowest levels in 60 years, pushing bond prices up to record levels. Low bond yields present two serious problems for investors. First, the yield itself is too low to meet return requirements, especially for pension plans and other institutional funds that have explicit return expectations. Second, the tremendous gains in bond prices may 183
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begin to reverse. An important question for investors now is whether bonds, particularly U.S. Treasuries, are experiencing a form of macroinefficiency, for a variety of reasons:
• The European sovereign debt crisis, forcing safe-haven dollardenominated investments
• A secular trend among pension plans, especially European, to increase bond exposures
• Proposed pension accounting rule changes that will force equity volatility effects onto the corporate income statement (OCI phase out)
• Strategic allocation distortions, such as those described by Martin Leibowitz in his article “Alpha Orbits” (discussed in the later section “When Strategy Complements an Investment Thesis”).
Even without macro inefficiency, it is possible we have already seen the cyclical lows in yields. If that is true and interest rates begin to stabilize or rise to rates that existed just a year ago, bond prices have a long way to fall—in 2010, the long bond was around 5%, and by early 2012, it was closer to 3%. A growing number of strategists and large institutional managers are predicting an asset class rebalancing. They are saying that the overvaluation of equities that has existed over the past two decades is over and, compared to bonds, equities now offer a better risk/return profile. If the rebalancing starts to gain steam, the selling pressure on bonds could start a new bear cycle. Remembering that one of the most devastating bear markets in any asset class occurred between 1941 and 1981 when long U.S. Treasury bonds lost two-thirds of their value, it is not surprising that many debt investors are asking how to protect their bond portfolios if and when interest rates start back up. If you want to hedge the risk of yield underperformance and bond price erosion, a synthetic annuity structure can help do both.
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The Synthetic Annuity as a Hedging Instrument In the equity examples of earlier chapters, the main idea behind a SynA was to reshape the investment profile while maintaining “ownership” in the underlying company. In that role, a SynA actually encourages long-term participation in individual companies or beta exposure to broad markets. The SynA in this chapter is somewhat different. It is more similar to tactical trading applications such as the International Paper SynA, in which the desired exposure to the underlying security changes based on the price of the underlying. A bond SynA can be used in two ways. One is a directional bet on interest rates. The other, and the main focus of this chapter, is as a natural hedge for an existing bond portfolio. The SynA structure is similar in both situations, even though the total portfolio effect is different. The following discussion starts from the point of view of an investor with an existing bond portfolio and the role of the SynA as a natural hedge.
Bondholder Risk From the perspective of a bondholder, the primary risk is an increase in rates and a drop in bond prices. So a hedge should go up in value as rates go up, to counter the decrease in bond prices. Going back to the choices of SynA types from the section “Other Forms of SynAs” in Chapter 6, you have four ways to build the SynA, two with positive delta and two with negative delta. These are the two positive delta (long bias) forms:
• A covered call position in an underlying that goes up with interest rates
• An equivalent position using short puts instead of covered calls
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These are the two negative delta (short bias) forms:
• A covered put position in an underlying that goes down as rates go up
• An equivalent position using short calls instead of covered puts
A SynA can be constructed on any traded instrument with exchange-traded options. You can choose from several bond market and interest rate–related instruments, including indices/ETFs such as HYG, LQD, AGG, JNK, TIP, PFF, TLT, and TBT. All these instruments have exchange-traded options, so any of them can be the underlying in a SynA. Two ETFs that are directly related to interest rates are the TLT and the TBT. The TLT goes down as rates go up, and the TBT goes up as rates go up. So you could use either a short position in the TLT or a long position in the TBT as the underlying. For illustration, let’s use the TBT as the underlying security. Because it goes up with interest rates, you can use a covered call position (as in the first listed point earlier) or a short put position (as in the second listed point). As discussed earlier, the payoff curve of a short put is the same as the payoff curve of a covered call, so instead of buying the TBT and selling call options, you can sell put options and hold cash. This is the same setup as the International Paper (IP) SynA. With IP, the goal was to get exposure to the security by selling puts. Selling puts creates positive delta and creates theta. It also increases the exposure to the underlying at lower prices and decreases the exposure at higher prices. So far, nothing is different from the IP example, at least in structure. The difference is the intent. This SynA is not a stand-alone investment position; it is operating as a hedge. Both the cost basis and delta adjustments are different for a hedge. The gain or loss of a hedge is normally combined with the gain or loss on the position it is hedging. If the two are perfectly matched, the gain in one offsets the loss in the other, so the net gain/loss is zero. Rarely is the hedge perfect, but the net gain/loss is generally low.
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The primary adjustment for a standalone SynA is the cost basis adjustment when the maximum drawdown is exceeded. To apply the cost basis rule for a SynA used as a hedge, the gain or loss includes the underlying bond portfolio, so the net gain or loss is compared to the drawdown limit. If the SynA hedge is only partial, meaning that the change in the value of the SynA is less than the change in value of the bond portfolio, there is no need to track cost basis or to make cost basis adjustments with regard to the hedge SynA itself. This is true when the increase in the value of the bond portfolio from decreasing rates is larger than the corresponding decrease in value of the SynA. As an example, imagine that you have a bond portfolio with a total value of $1 million at the current interest rate of 3%. If interest rates rise to 4%, assume that your portfolio will have a value of $900,000. You set up a hedge SynA such, that at 4%, the SynA will be worth $50,000 more than it is today. In combination, the bond portfolio and the hedge lose $50,000, half of what the bond portfolio would have lost. Similarly, if rates go down, the bond portfolio will go up in value and the hedge SynA will have an offsetting loss. If you have intended to apply any drawdown limits to the existing bond portfolio, you could now apply the drawdown limit to the combined hedged position, which is less volatile. If you were not using a drawdown limit on the bond portfolio, there would be no need to do it now, either. The question is whether to apply a drawdown limit to the hedge SynA by itself. I don’t think so. In its role of hedge, it is simply making an existing position less volatile. The only time you might want to apply a drawdown limit is when the loss on the hedge is actually larger than the gain on the bond portfolio. An example of this is presented later in Figure 9.2, where an aggressive SynA is used to capture large amounts of theta and at the same time serves as a price hedge. Another difference is the use of long puts. In a normal SynA, part of the call option credit is used to purchase long puts as insurance, in case a severe price decline happens. Because this is a hedge, you
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don’t need to purchase the long puts. A severe price decline would also affect bond values. Any delta adjustments you make depend on the structure of the SynA and whether you want increasing delta exposures at lower rates. Because this is the natural effect of the automatic adjustments, you might not need to make delta adjustments. These are all advantages for a hedge-type SynA. If you set up the SynA properly, it doesn’t need to be adjusted at all. The idea behind the structure is that short puts will increase in value as interest rates go up. This increase in value helps to offset the decline in bond values. In addition, theta generated from the put options acts to enhance the bond yield. Notice that the number of effective put options varies by the level of the TBT, which, in turn, is related to interest rates on the long bond: The lower the yield, the more options are in play. Consider Figure 9.1, which shows a SynA structure of short puts on the TBT. This SynA consists of one short put with a strike of $17, one short put with a strike of $18, and so on, up to one short put with a strike of $23. As I am writing this, the TBT is? around $19 and the 30-year Treasury rate was? approximately 3.0%. This particular setup would be good for someone who thinks interest rates are fairly stable and meanreverting around 3% to 3.5%. If interest rates and the TBT (which move in the same direction) go up, this SynA makes money. It also becomes less exposed to rates at higher levels and more exposed to rates at lower levels, as shown by the SynA Effective Shares column. By scaling the position so that the dollar delta matches the gain in the bond portfolio (that is, dollar duration) of the bond portfolio, you create an effective price hedge. At the same time, by selling options, you also generate theta.
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Figure 9.1 Bond SynA
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Of course, the level of theta generation and the estimates of drawdown and payback periods depend on pricing at the time of strategy execution. The number of options depends on the duration of your bond portfolio and how much you want to hedge. As with all SynA strategies, sudden moves in the underlying require adjustments to maintain a level hedge ratio. The particular structure presented here uses naked puts instead of put spreads. For more stability, you can use spreads instead. This is an example of a minimum value SynA—that is, a SynA in which the exposures are increased as the underlying price decreases. The belief is that the underlying must reach a minimum value at some point. The fixed-income SynA offers the added comfort that SynA losses will be somewhat offset by the increase in the value of the bond portfolio. In other words, if the SynA goes down because of interest rate declines, the value of the bond portfolio will most likely be going up. One other point to keep in mind is that problems can arise with the instrument used (TBT or other interest rate derivative) if the instrument fails to track interest rates properly. Basis risk and slippage are common problems with the TBT in particular.
Note The TBT is related to the yield on 20+-year Treasury securities. It moves in the same direction as interest rates—at least it is designed to do so over daily periods. For periods longer than one day, the TBT is not a perfect hedging instrument. The absolute level of the TBT is not tied to the absolute level of interest rates; it is a cumulative measure of daily returns. Thus, it is possible that, over longer periods, the TBT can actually move in the wrong direction. If you do use it, be sure to read the prospectus, particularly the chart showing how the performance can vary based on volatility. In extreme volatility, it has had days where it even moves in the wrong direction. And as with any ETF that uses futures, it is subject to negative roll yield, depending on the shape of the term structure.
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Adding Yield The same mechanism, selling options, generates yield in the bond SynA the same way it did in the equity SynA. In the equity examples, theta-generated yield was referred to as virtual dividends. Virtual dividends either enhance the dividends that the underlying pays or add a source of dividends when the underlying doesn’t pay one. In the bond market, theta can be thought of in a similar way: an enhancement to the current bond yield. The magnitude of the yield depends on several factors, including how many options are used, the strike prices, and the implied volatility priced into the options. An investor who wants a modest yield enhancement could get that with a relatively small number of OTM options. To get more aggressive yield improvements, you need to sell more options. As in the equity cases, a balance exists between delta and theta. The more stable you want delta to be (that is, the more stable the price hedge), the more ATM and ITM options you need to use. To be more specific, say you have a bond portfolio with a duration of 10 that is currently yielding 4%. You want to enhance the yield to 8% and cut the effective duration to 5. And you are willing to give up some of the increase in portfolio value if rates go down, to finance the hedge. The pattern of options in Figure 9.1 is spread out enough for a stable delta across a medium range of interest rates, and it has enough close-to-the-money options to generate lower to medium levels of theta. Of course, you can get as aggressive as you want. With Level 5 option trading approval, the only restraint is buying power. Say that you want to use the bond portfolio duration as the delta target—that is, you want the SynA to move dollar for dollar with the bond portfolio. In that case, you would be completely hedged against interest rate increases (at least over short time periods and within the limitations of the TBT instrument).
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To match duration with delta, start by selecting the exposure per bond unit that you prefer at different levels of interest rates. This pattern reflects your views on the mean and the strength of mean reversion. Starting with a particular pattern of option strike prices, the level of theta is determined by the number of options it takes to become delta neutral. But as in the generalized examples, you can leverage theta by selling more puts and simultaneously selling calls. By leveraging, you keep delta at your target level while increasing theta. Figure 9.2 gives an example of an aggressive SynA. The SynA in Figure 9.2 is rate based, meaning that delta varies depending on the level of rates. For example, delta has a target value of $2,000 per bond unit at 5.00% and $7,000 at 3.00%. This reflects a directional view of interest rates and a specific amount of price hedge. It is a tailored design. It is also an aggressive design, as you can see from the Average Annual Theta column. If implied volatility remains at current levels and rates remain at 3%, this design will generate almost 50% gains from theta. Because the theta target is so high, this setup is more of a directional bet than a hedge.
Stress Testing The columns on the right side of the exhibit quantify the risk involved in this design. In any aggressive design, stress-testing the model is a good idea. You want to understand the maximum drawdown under extreme conditions, such as short-term rate shocks (as with the one that happened in September 2008 to March 2009 and the one that happened in August 2011). SynA’s with high levels of theta can sometimes recover quickly as long as they are rolled out over time at the same strike prices. The same volatility that created the problem (drop in interest rates) tends to help in the recovery because higher implied volatilities mean higher premiums for the short options.
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Rate-based bond SynA Figure 9.2
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In the note in the last section, I mentioned that the TBT is not a perfect instrument because it does not follow rates in a consistent way. If you use it, be aware of the slippage that occurs. If the TBT is trading at $25 when the long bond rate is 3%, that doesn’t mean that the next time the long bond rate is 3%, the TBT will also be $25; it could be $20. This is a complicated instrument to forecast, so you have to be careful to base your delta target on interest rate levels, not the level of the TBT. To account for slippage, you can counter it in some ways, such as selling a certain number of call spreads in addition to short puts. However, no exact formula exists, and the movement in the TBT is highly dependent on the overall level of volatility.
Inflation and the Future of Bond Prices In 2010, Bill Gross of PIMCO called U.S. Treasury securities the most overvalued asset class in the world. In 2011, he backed up his view by selling Treasury holdings in PIMCO’s flagship bond fund. Then not long afterward, he reversed his position. It was never clear to me whether this was because of benchmark risk or because of a change in his outlook. Regardless, he was correct to reverse his position. Since then, Treasury rates have fallen off a cliff. The fall in yields was especially severe just after the failed debt ceiling negotiations in late July and again after the European Central Bank failed to react more forcefully to banking weakness two weeks later. With continued revelations about how bad the sovereign debt problem was in Europe, the dollar and U.S. debt seemed to be the only remaining safe havens. With rates on the 30-year Treasury bond below 3%, bond owners have to question what will happen if there is any sign of economic recovery. Foreign owners might also question the effect of dollar devaluation on the purchasing power of those securities. Looking ahead, it is possible that rates on the long end of the curve have been pushed about as low as they can go, meaning the likely end of the bond market super-bull phase that started in 1981.
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On the other end of the spectrum is a Japanese-style deflationary spiral that could occur if the U.S. and Europe slip back into recession while also trying to correct fiscal imbalances. If the reality looks like Japan, where equities have fallen by 75% over 20 years and bond yields remain close to zero, there could still be much more strength to come in Treasuries.
When Strategy Complements an Investment Thesis Personally, thinking that rates cannot continue to decline is tempting. Betting on steady or rising interest rates is an almost irresistible investment thesis to me. What makes it worse is that I know that if I can find a situation in which a few things exist together, I can create SynA’s that resonate with price movements instead of needing to be adjusted against them, such as:
• A natural bottom in prices close to the current price
• An ability and desire to increase exposure as prices drop more
• A relatively short payback period (even if I am wrong about prices)
• A negative correlation to the rest of the portfolio
• Logical reasons why macro-inefficiency might exist Right now, here are my thoughts on where we are:
• A natural bottom in prices: The 30-year Treasury is under 3%. I think it would take extreme conditions to push the rate lower than 2.5%.
• An ability and desire to increase exposure as prices drop: It is possible that macro inefficiency drives rates down further; however, absent a worldwide recession, increasing exposure at lower rates makes sense. In other words, if I liked the thesis at 3%, is it possible I would like it more at 2.5%?
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• A relatively short payback period when I am wrong: The SynA generates higher levels of theta as the rate falls. Even at the target theta rate, the estimated recovery period on a 0.5% drop in rates is between 3 and 6 months.
• A negative correlation to the rest of the portfolio: This is questionable and probably should be broken into two scenarios: an orderly decline in interest rates within a relatively stable economy and a turbulent decline in rates as a result of a systemic event. In the first case of an orderly decline, theoretically, falling rates are good for equities for two reasons. First, asset classes compete against each other in attracting capital, so what is bad for bonds is good for equities. Second, the lower the rate, the higher the present value of discounted cash flows, so equity multiples benefit from lower rates. Because the rest of the portfolio has either direct equity exposure or implicit equity exposure, this should translate into negative correlations. In the second case, when the market is under severe pressure, all asset classes might fall together. The strategy works best when the period of stress has already occurred.
• Logical reasons why macro-inefficiency might exist: Other than the reasons I talked about earlier, Martin Leibowitz offered another possibility in his article “Alpha Orbits,” where he outlines how optimization techniques could potentially cause past performance to influence the allocation to bonds going forward. In this scenario, the pressure of motivated bond buyers pushes the price of bonds higher. The bond’s realized returns then attract momentum investors. As asset returns are calculated going forward, the higher returns are reflected in expected return assumptions. This might actually cause new allocation studies and prompt the optimizers used to calculate efficient frontiers to increase bond allocations. “And so the
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price keeps going higher and higher, while the bond yield—the best measure of expected long-term returns—sink lower and lower!” Leibowitz’s article is hypothetical, but it illustrates how asset class allocations can become distorted. In my opinion, this dynamic might have been playing out already. As mentioned, SynA’s are more powerful when they don’t need to be adjusted. This could be because either they are being used as a hedge or the natural changes in exposures are exactly what you want. If you also have conviction about mean reversion or minimum values for prices, you can increase the weighting as prices drop. Figure 9.1 was an example. The share exposure goes up linearly as prices drop. There are 100 shares of exposure at $23, 200 shares of exposure at $22, and so on, up to 700 shares of exposure at $17. Below $17, the exposure stays level at 700 shares. What if you think interest rates are not likely to go lower than they are now? And you are convinced that, if they do, they will not go below 2.5% (on long-duration Treasuries)? You can calculate the amount of cost basis recovery due to theta that occurs in one month. Say that it is 50¢ per month on the linear pattern. If you want to accelerate the payback, you can extend the pattern or change the pattern. Instead of linear, you could start to accelerate the increase in exposure if and when interest rates fall further. To extend the pattern, you can enter limit sell orders on short puts (I normally set a minimum of $1 of premium) for strike prices below $17. To go further and accelerate the pattern, you can execute limit sell orders for increasingly more put options as the price drops— for example:
• A limit order to sell one put at a strike price of $16 for $1
• A limit order to sell two puts at a strike price of $15 for $1
• A limit order to sell three puts at a strike price of $14 for $1
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By extending the limit orders to lower prices, you can take advantage of price spikes down and generate more theta by having more ATM options. But it is more aggressive, so you need to be diligent about stress testing. Make sure that you are comfortable with the results if the following happens: 1. Prices spike down and stay down. 2. Prices decline gradually to levels lower than your worst estimate. 3. The instrument you are using (for example, TBT) does not track interest rates due to basis risk or slippage (very important). By “limit order,” I don’t mean that you should enter GTC orders in your trading platform. Maintaining these yourself as reminders to trade is better. In the case of a catastrophic event, you want to reevaluate before pulling the trigger. Keep in mind one other point, especially if you are using the SynA as a hedge against a bond portfolio. The aggressive structure might work well as interest rates go down, but if interest rates go up, effective exposure decreases and the hedge wears off. If in fact, interest rates are not mean reverting and begin to trend upward, you need to adjust the SynA to keep delta at the desired hedge level. To protect against trending rather than reverting prices, you can use the same method discussed in earlier chapters. That is, you invest a portion of the option credit in long options that will increase in value during a trending market. For example, if and when you execute new short put positions, also buy OTM long call options at the same time. The pricing on the OTM long calls will be cheap because they execute only during price declines. You can choose whatever strike prices you want for the long calls, but I recommend targeting the upper end of the higher put strikes. In this case, that would be around $20 to $22. Hopefully, in spending 15% to 20% of the credit, you can get enough long calls to stabilize delta in the event of a price spike.
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What Could Go Wrong? Some people ask, “Why would you invest in something you don’t have conviction about?” I’m the opposite. Whenever I have conviction, I start looking for why I might be wrong. It doesn’t necessarily stop me from acting, but sometimes I am less surprised in the end. If you are like me and think rates are going up, I want to recommend two articles, one from James Bullard, at the St. Louis Fed (see excerpt later in this chapter), and one from Richard Hokenson, of Hokenson & Company. In his paper “Seven Faces of the Peril,” James Bullard, president and CEO of the Federal Reserve Bank of St. Louis, discusses “the possibility that the U.S. economy may become enmeshed in a Japanese-style, deflationary outcome within the next several years.” It is a sobering analysis, with two main conclusions: “(1) The FOMC’s extended period language may be increasing the probability of a Japanese-style outcome for the U.S., and (2) on balance, the U.S. quantitative easing program offers the best tool to avoid such an outcome.” Bullard presents two possible interest rate paths. A certain amount of inflation is necessary for effective Fed monetary policy. When inflation drops too low, the equilibrium point for interest rates shifts from an inflationary regime to a deflationary regime. As he points out, the U.S. is closer now to the Japanese deflationary equilibrium point than the historical U.S. equilibrium point. To combat disinflation, the Fed started (in mid-August 2010) a new round of quantitative easing. With the Fed printing money to buy Treasury securities, additional pressure affects rates. Whether the Fed is monetizing debt is debatable, but historically, the easiest way out of severe debt problems is to use the printing press and currency devaluation. Hokenson’s viewpoint in an article titled “The Race to Zero” is equally interesting. Hokenson looks at the relationship between shrinking populations and low interest rates. He finds a strong
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relationship among long-term interest rates, nominal GDP growth, and labor force. He argues that labor force is slowing worldwide, which will pull down nominal GDP growth and nominal interest rates. If you throw in government dysfunction, deleveraging among developed economies, and structural financial issues, it is plausible to make an argument for a Japanese scenario unfolding in the U.S. and Europe. For many years I have been interested in what happened to Japan and whether it could happen to us. What caused the Japanese equity market to lose almost 80% of its value over a 20-year period, and why, in spite of almost zero interest rates, have the Japanese not been able to kick-start their economy? Of the plausible answers, one involves demographics over the longer term and the ability to digest debt over the shorter term. In the U.S., the short-term key could be digesting the remains of the housing bubble. If the rate of household generation over the next year or two can turn the tide, we could add a component of the construction industry back to the GDP and start a virtuous cycle of job creation and consumption. But this could also go the other way. Housing bubbles take a long time to correct. We can continue massive stimulus for only a finite period, probably not more than two years. Personally, I think that the U.S. will pull out of the recession, at least somewhat, and interest rates will rise before we start dealing with real problems, such as $60 trillion of unfunded liabilities related to government pensions, Social Security, Medicare, and Medicaid. Kicking the can down the road through another economic cycle or two could happen before reality sets in. But that is just an opinion. I don’t think anyone knows what will happen. That is why a SynA has rules that take some judgment out of the process. Having opinions about where the equity market and interest rates might go is fine. Having an investment thesis and developing conviction is also fine. But if a Japanese scenario does unfold and interest rates go down and stay down, and if the equity market is cut by 80%, those who “buy on
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the dips” or continue to rebalance portfolios based on a policy statement allocation could easily be wiped out. Serious people with serious arguments are discussing those possibilities. An area of academic and practical interest related to volatility is the consistent difference between the level of volatility that is priced into variance swaps and options and the actual realized volatility, or the implied minus the actual volatility spread. This phenomenon has several explanations, but whenever I look at risk projections from firms that estimate the global economic impacts of various future events, I don’t see the disconnect. We simply haven’t experienced any of the major catastrophic events that could have happened. Nuclear conflicts and regional wars, dirty bombs in metropolitan areas, energy supply shocks, global trade wars, and many other disruptive events simply have not happened. But they could. And if they do, this particular interest rate strategy will not help. In the aftermath of one of these events, risk assets of all types will be sold and money will flood into the safest asset in the safest currency. Treasury rates could go below 2% on the long end. This is unlikely, but if it happened, the equity and risky credit portions of most portfolios would be under extreme pressure, margin calls would cause indiscriminate selling, and, to the extent the hedge SynA loses more in value than the bond portfolio gains in value, you would be exposed. I bring this up to point out the value of having far OTM long puts in place as a speed breaker.
Excerpt from St. Louis Fed Paper, “Seven Faces of ‘The Peril’” I have heard several fund managers who use global macro strategies say that the most important single item to get right is the direction of inflation. Inflation drives everything. Get that wrong, and you will probably get the portfolio wrong. The following excerpt is
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from a paper by James Bullard, which highlights a critical problem for bond investors: the instability of inflation expectations in relation to policy initiatives. This paper was fascinating to me from the first sentence: “In this paper I discuss the possibility that the U.S. economy may become enmeshed in a Japanese-style, deflationary outcome within the next several years.” As I said earlier, I think the U.S. will come out of this downturn. A Japanese-style deflationary outcome would be devastating to our economy. It would also be devastating to the majority of portfolios that are heavily weighted toward equities and rebalance to buy more on dips. When I started my fund, the first question I asked was whether the Japanese experience could happen to us. Originally I said no because of the health of our banking system and demographic differences. But today our banking system is not what it was in the late 1990s, housing is not the same driver of wealth-effect consumption, we have a more realistic view of debt levels, and we may have passed the crest of the wave of baby-boom money flows into asset accumulation plans. There is something else, too: our optimism and resolve. Confidence counts for a lot. The point is that even if we get past the current economic stagnation, the issues discussed in the paper will be relevant for some time, and these scenarios should at least be considered in decisions about portfolio construction and risk management.
Seven Faces of “the Peril” By James Bullard. President and CEO, Federal Reserve Bank of St. Louis. This version: 29 July 2010. Any views expressed are my own and do not necessarily reflect the views of other Federal Open Market Committee members. Preprint, Federal Reserve Bank of St. Louis Review September– October Issue
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Abstract In this paper I discuss the possibility that the U.S. economy may become enmeshed in a Japanese-style, deflationary outcome within the next several years. To frame the discussion, I rely on an analysis that emphasizes two possible long-run outcomes (steady states) for the economy, one which is consistent with monetary policy as it has typically been implemented in the U.S. in recent years, and one which is consistent with the low nominal interest rate, deflationary regime observed in Japan during the same period. The data I consider seem to be quite consistent with the two steady state possibilities. I describe and critique seven stories that are told in monetary policy circles regarding this analysis. I emphasize two main conclusions: (1) The FOMC’s extended period language may be increasing the probability of a Japanese-style outcome for the U.S., and (2) on balance, the U.S. quantitative easing program offers the best tool to avoid such an outcome. 1. The Peril In 2001, three academic economists published a paper entitled The Perils of Taylor Rules. The paper has vexed policymakers and academics alike since that time, as it identified an important and very practical problem—a peril—facing monetary policymakers, but provided little in the way of simple resolution. The analysis appears to apply equally well to a wide variety of macroeconomic frameworks, not just to those which are in one particular camp or another, so that the peril result has great generality. And, most worrisomely, current monetary policies in the U.S. (and possibly Europe as well) appear to be poised to head straight toward the problematic outcome described in the paper. The authors of the 2001 paper are Jess Benhabib of New York University, along with Stephanie Schmitt-Grohè and Martìn
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Uribe, both now at Columbia University. They studied abstract economies in which the monetary policymaker follows an active Taylor-type monetary policy rule, that is, the policymaker changes nominal interest rates more than one-for-one when inflation deviates from a given target. Active Taylor-type rules are so commonplace in present day monetary policy discussions that they have ceased to be controversial. Benhabib, et al., also emphasized the zero bound on nominal interest rates. They suggested that the combination of an active Taylor-type rule and a zero bound on nominal interest rates necessarily creates a new long-run outcome for the economy. This new long-run outcome can involve deflation and a very low level of nominal interest rates. Worse, there is presently an important economy that appears to be stuck in exactly this situation: Japan. To see what Benhabib, et al., were up to, consider Figure 1. This is a plot of nominal interest rates and inflation for both the U.S. and Japan during the period from January 2002 through May 2010. The frequency is monthly. The Japanese data are the circles in the Figure, and the U.S. data are the squares. The short-term nominal interest rate is on the vertical axis, and the inflation rate is on the horizontal axis. To maintain international comparability to the extent possible, all data are taken from the OECD main economic indicators. The short-term nominal interest rate is taken to be the policy rate in both countries the overnight call rate in Japan and the federal funds rate in the U.S. Inflation is measured as the core consumer price index inflation rate measured from one year earlier in both countries. The data in the Figure never mix during this time period: The U.S. data always lie to the northeast, and the Japanese data always lie to the southwest. This will be an essential mystery of the story. The full paper is available on the St. Louis Fed website at http:// research.stlouisfed.org/econ/bullard/pdf/SevenFacesFinalJul28.pdf.
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Figure 9.3 Interest rate instability
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10 Synthetic Annuities for the Volatility Market This chapter looks at how a synthetic annuity framework can be applied to the volatility market. Being able to structure volatility positions as long-term components of a portfolio adds a powerful tool in fund management. A number of strategists have even argued that volatility—specifically, selling volatility—should be considered an asset class on its own merits, similar to equities and fixed income. But regardless of whether volatility is an actual asset class, it is interesting because it is strongly negatively correlated to equities and it is capable of producing high levels of risk-adjusted return. These features of volatility add another dimension to risk management at the portfolio level while drawing on one of the most exciting sources of theta, where volatility on volatility (or volatility squared) often runs above 100%. The objective of a volatility-related SynA is to capture this source of diversified returns by creating a structure for converting volatility measures into a risk management tool and helping to counteract some common problems of “holding” volatility.
Portfolio Diversification One of the areas I have become interested in over the past couple years is structuring volatility trades. I think it represents one of the most promising emerging areas of portfolio risk management. The 207
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reason is simple: When the market is going down, volatility is normally going up. Anytime you can add a negatively correlated asset to a portfolio, you increase the potential for achieving the most valuable kind of diversification. In constructing a portfolio, the decision to add a new asset—at least according to practitioner models—should be based on both the expected returns of the new asset and the correlation of the new asset to the existing portfolio. As discussed in the introduction, one problem with asset correlations is the way they are calculated. A common method involves using relationships that exist over long periods of time—periods that include both nonturbulent and turbulent market conditions. By “smoothing” correlations over different time periods, the power of diversification to deliver more return with less risk is overstated. Because these relationships break down during crashes, they do little to limit losses. Diversification sounds great as a principle, but it has failed in important ways as a risk management tool. When correlations are estimated using only relationships between assets that existed during prior market crashes, it becomes clear that risks measured in terms of expected drawdowns are much higher than they appear using average market conditions. Some estimates suggest that equity exposure would need to be cut in half, or more, to get the risk down to the level indicated by using average correlations. This is really nothing more than acknowledging in the mathematics what everyone already knows: Correlations go to 1 in crashes, and most of the diversification benefits disappear. In spite of its limitations in controlling drawdowns, most people agree that diversification in general is important. It is critical to avoiding idiosyncratic risk and extracting risk premiums, and it certainly improves portfolio performance in less extreme markets. I don’t think the debate on diversification is about whether or not it is useful, but rather the recognition of realistic behavior of assets under stress and the search for better sources of diversification. The promise of
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volatility is in its almost perfect diversifying behavior exactly at the time it is needed most.
Volatility As a Diversifying Asset Evidence suggests that adding even small amounts of volatilityrelated positions to portfolios can significantly improve both returns and Sharpe ratios. But what is a volatility-related position? Volatility is not normally thought of as an asset. It does not pay interest or dividends. It is not a company that can grow cash flow. Most fund managers don’t like to allocate a significant portion of a portfolio to anything that does not generate long-term returns. In very general terms, assets and asset classes are defined by (1) whether investors have a reasonable expectation of passive returns and (2) the presence of theoretically based risk premiums. For example, buying bonds creates passive returns, a revenue stream that compensates investors for saving. Buying corporate bonds that have some credit risk, as opposed to Treasury bonds, is believed to provide a credit risk premium—why would anyone buy a more risky asset without being compensated for it? Moving out on the risk spectrum, stocks should have an equity risk premium (ERP) to account for the lower claim status of equity investors compared to bond investors. How does volatility fit into this picture? First, although volatility measures themselves don’t necessarily produce passive returns, selling volatility does. Goldman Sachs noted that selling equity index volatility offers significant passively generated returns with Sharpe ratios on some strategies producing four times that of U.S. equities and outperforming 12 of 13 CS/Tremont hedge fund indices on a riskadjusted basis.1 Volatility is translated into returns through the pricing of derivative instruments such as options and swaps. Strategies with net short
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positions in options or swaps are essentially short volatility. These include variance swaps, covered and uncovered calls, short puts, straddles, strangles, and structured securities that are net-short options such as the synthetic annuity (which, at different times and in different configurations, takes on properties of most of these strategies). There is another, related way that volatility fits into the picture. That is by selling volatility on measures of volatility, discussed later in the section “Volatility-Squared SynA.”
Volatility Risk Premium The theoretical foundation of a synthetic annuity is based partly on the evidence that selling volatility has historically produced a volatility risk premium (VRP). The existence of a VRP has been explained in different ways. One explanation of the VRP is related to the supply of hedging instruments. It is derived from a supply/demand imbalance between those seeking risk hedges and those willing to provide them. According to this argument, the suppliers will not step in to provide liquidity in this market unless they are offered a premium. The fact that pricing anomalies occur has been known for a long time. Fisher Black and Myron Scholes made the following statement with regard to option pricing in 1973: “The actual prices at which options are bought and sold deviate in certain systematic ways from the values predicted by the formula. Option buyers pay prices that are consistently higher than those predicted by the formula.” Academic studies since then have supported their observation. If buyers are paying too much, then as sellers, SynA holders are receiving the extra payment or premium.2 Regardless of the source of VRP, returns have been large enough that even modest short volatility allocations in a portfolio have resulted in significant expansion of the efficient frontier.3
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Another aspect of volatility that can be traded is the difference between the volatility priced into options and the actual volatility that unfolds over the life of the option. The difference in implied and historical volatility is measured in instruments such as the CBOE VARB-XTM. The VARB-XTM is an index that tracks the performance of a hypothetical volatility arbitrage trading strategy, where the strategy is designed to capitalize on the historical difference between the implied option volatilities on the S&P 500 index and the realized (historical) volatility of the S&P 500. Even though this strategy can produce high returns and Sharpe ratios over fairly long periods, it can also blow up at the worst times. In August 2011, for example, actual volatility turned out to be much worse than implied, and the strategy produced highly negative returns while volatility itself continued to provide real diversification. (See www.cboe.com/micro/vty/ introduction.aspx for more information.) Because of the potential for high losses during market turbulence, implied versus actual arbitrage strategies should be used carefully.
Portfolio Applications During a crash when volatility spikes, it is acting like a true hedge. So, if volatility acts like a hedge, why not use it as one? Many funds are doing just that. But the strategy has problems, mainly related to the instruments available for tracking volatility. The most commonly used measure of volatility is the CBOE Volatility Index® (VIX®). The VIX reflects market expectations of nearterm volatility priced into S&P 500 stock index option prices. In other words, the VIX is calculated as the implied volatility of short-term options. Currently, there is no effective way to own the VIX, at least the spot VIX. Because the VIX is not an investable index, you have to get exposure through futures and options on the VIX or through VIXrelated instruments, each of which has drawbacks.
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For instance, if you look at a longer-term chart of the VXX, the iPath S&P 500 VIX Short-Term Futures ETN, you will see an obvious downtrend. This has been caused in part by the process of rolling forward the futures contracts, where the next month’s price is higher than the spot price, causing negative roll yield, a downward pressure on price over time. The VIX market generally has an upward sloping term structure or contango. When this is the case, buying and holding the VIX through the VXX is expensive. On average, you would need to make almost 4% a month just to counteract the effects of contango on the roll of VIX futures contracts. (For additional discussion, see Nick Cherney, William Lloyd, and Geremy Kawaller. “Portfolio Applications for VIX-Based Instruments,” Journal of Indexes.4) One advantage of a SynA is its capability to counteract some or all of the effects of negative roll yield.
Volatility-Squared SynA: Creating Yield on Volatility What is a volatility-squared SynA? The term volatility squared refers to the volatility on volatility. A volatility-squared SynA is a SynA that uses short options on an underlying security that is itself a measure of volatility. In other words, this SynA enables you to take a short volatility position on volatility. A SynA built on an underlying volatility index produces yield just as a SynA does on an underlying equity or fixed-income instrument. Because volatility on volatility is normally high, the yield is potentially high as well. For instruments such as the VXX that are related to the level of volatility and have exchange-traded options, there is an implied volatility on VXX options, or volatility on the volatility measure. In terms of absolute levels, the implied volatility on volatility can be off the charts. Figure 10.1 shows a TradeStation screenshot on the VXX from August 22, 2011.
Figure 10.1 Implied volatility on VXX
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Source: TradeStation Technologies, Inc.
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Notice the average implied volatility. The level is greater than 135%. The skew is also high, with the put volatility at 136% and the all volatility at 176%. Of course, volatility levels are not this high when the VIX is lower. When VIX spikes, so does the VXX and the volatility on the VXX. But even at lower levels of the VIX, the IV on the VXX is still sufficient to generate high levels of yield using a SynA.
Building Volatility SynA’s How can you take advantage of this? The answer depends on the range in which the VIX is trading. If it is lower than 20, treat it exactly like interest rates. In other words, if you think there is a natural bottom to volatility, begin to establish a short put position as it approaches the bottom. On the other end of the spectrum, when the VIX is high, another type of opportunity arises when the VIX is above 40. When volatility is trading in the midrange between 20 and 40, it is generally very unstable, so structuring trades is more difficult. Let’s look at what can be done and why at the low and high ranges.
Building a SynA When the VIX is under 20 When the VIX is low, the objective is to build a SynA that will act as a volatility spike hedge. Having a severe market selloff without a spike in volatility (VIX) and volatility-related instruments such as the VXX and the VXY is unusual. A volatility spike hedge can be extremely valuable because the spikes themselves can be large and the volatility priced into options goes up at the same time. Historically, when the VIX is lower than 20, the market is comfortable and probably rising. During these periods, there is an opportunity to accumulate VIX-related positions. The idea is to start accumulating lower-range VXX positions during the market rise, in anticipation of the next period of turbulence. If the VIX continues to drop, these positions can lose money initially; however, it is likely that your portfolio will be doing well in the low stress environment.
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If you simply buy the VXX and hold it, it will serve as a volatility hedge in the event of a market crash. As the VIX increases during periods of turbulence, the VXX will increase as well, helping to offset the losses in the long portion of your portfolio. But as pointed out earlier, the cost of holding this ETN longer term is high. Instead of buying the VXX, you can build a SynA using the VXX as the underlying. You can choose either of the long (positive delta) versions of a SynA. As discussed in Chapter 6, in the section “Other Forms of SynA’s,” the first version uses a long position in the underlying, short calls and long puts. The second version is a credit put spread plus cash. The total exposure, or delta, depends on whether you are in the accumulation phase of the position or at the point where you have the full position. In the accumulation phase, you can leave off the long puts or use far OTM puts instead because, during this phase, you should be emotionally indifferent to further declines. The opportunity to pick up more VXX at lower levels balances losses on the existing position. This is the same logic used in the International Paper and TBT examples, where the target exposure to the underlying goes up as prices go down. The advantage of using the SynA instead of a long VXX position is that it enables you to generate theta during the calm market periods. The target delta exposure at various levels of the VIX depends on how quickly you want payback if the VXX continues to fall and how much portfolio protection you want. Modeling the drawdown on the volatility-related SynA is a good idea, assuming that the VIX continues to fall to a level of 10 to 15. Also, I recommend including a reasonable cost of negative roll yield, somewhere between 2% and 4%. The same graded scale that was used to build the interest rate SynA is appropriate for the volatility SynA. In other words, you are betting on a minimum value of the VIX and increasing exposure as the price drops to the minimum. A graded scale helps you pace the trade and control your exposure. As mentioned, be prepared to watch this position lose some value as you accumulate the full position.
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If the VIX moves below 15, you also might want to start accumulating long OTM calls with a portion of the net option proceeds. You still want to maintain a net credit, but a few long calls in a market crash can be extremely profitable. Because these are relatively expensive (the put–call skew pointed that out earlier), you can use a spread to decrease the cost. You can also use the time volume discount in the spread by buying longer-dated options and selling shorter-dated options. The long call options help flatten delta exposure in difficult markets. With only short puts, delta fairly quickly begins to disappear as the VXX spikes up. Long calls, even if they are far OTM, begin to kick in as the VXX goes up and as the IV on the VXX goes up. Both the absolute price increase and the expanding IV contribute rapidly to the rising long option price. In this configuration, you are using the SynA framework to finance long calls from a portion of the proceeds from selling puts. This makes sense especially if you believe that you are close to a natural bottom in the VIX. As the VIX settles in around a support level of 10 to 15, the cost of the call options goes down doubly because of lower absolute levels of the VXX and lower IV priced into the VXX call options. If the VIX goes below 10, consider even starting to take slightly net negative theta positions in anticipation of a directional move up. Keep in mind that similar to the relationship between bond rates and the TBT/TLT, the ETFs that track volatility suffer from tracking error. The VXX is not an easy instrument to trade because of the large amount of slippage and its sensitivity to intraday and interday volatility. Depending on the shape of the futures curve—particularly in times of high contango—there may be higher levels of negative roll yield as well. Theta on the SynA helps counteract this to some degree, which is one advantage of the SynA, compared to holding long-term positions in VIX-related instruments that use futures. As with the TBT, you can also leverage theta by selling call spreads. With a VIX-related instrument used as a portfolio hedge,
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make sure the spread is fairly tight in case of a spike. You can adjust the theta on the call spreads in addition to the theta on the short puts to counteract even high levels of negative roll yield. If you are using advanced applications, begin to look for put–call arbitrage opportunities as the puts are priced at relatively low IVs. At some points, you might have a directional preference in the movement of the underlying security and can place limit orders to take advantage of arbitrage by placing the first leg of the arbitrage trade in the direction of your preference and placing a limit order in the other direction. For example, if your maximum portfolio gain happens when the underlying goes up without regard to the arb trade, sell the underlying. If the underlying goes up, you will make money. If it goes down, complete the synthetic long side of the arb trade.
Building a SynA When the VIX Is Greater Than 40 By late 2011, the VIX had gone above 50 for the first time since 2008. Betting against a larger spike is difficult, but the VIX cannot sustain these levels without some sort of systemic problem. As systemic problems unfold, the uncertainty about the size of the problem and how widely it will spread causes demand for protection, pushing put prices higher. Although this is an emotionally difficult period for building a SynA, it can be extremely profitable—as long as you are prepared for things to get much worse and you have the dry powder to make it to the other side. You do not want to get caught in a margin squeeze, especially since it will happen at the same time your portfolio is under the most stress. With that said, let’s look at how to structure a SynA when the VIX is high. My approach usually is to begin to sell call option spreads on one of the volatility measures, such as the VXX, and use a portion of the money to buy put options. Do this a little at a time, because the ride
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could get wild before it starts to calm down. In other words, this is the fourth type of SynA covered in Chapter 6, “Generalized Synthetic Annuities.” It is based on a view that prices will fall over the mid- to longer term and that the risk is a price spike. This could also be set up as the third type of SynA, with a short position in the underlying such as the VXX, short puts to generate theta, and long calls to protect against a spike. As pointed out in earlier chapters, the two setups are mathematically equivalent.
Stress Testing Fundamentally, I view the low-range VIX SynA as good rainy-day planning, whereas the high-range VIX SynA is more of a trade, but one that is well priced. If you stress test your portfolio, the low-range SynA will move up in value as the market moves down. The short puts will quickly drop in value, and the long calls will begin to climb in value. So both components of the SynA help offset portfolio losses. The opposite is true for the high-range SynA. If volatility continues to rise, which means that equities are probably falling, the SynA will move in the same direction as the rest of the portfolio: down. So if it provides no diversification, why would you do it? It is simply based on price. The premiums on OTM call options can be tempting, especially if you can ride out the spikes or, better yet, take advantage of further spikes to add to the position. You just have to keep in mind that volatility normally does not reach 40 unless the market sees the potential of something catastrophic. Although the price movement in the high-range SynA is not diversifying, it is indirectly helpful in other ways.
Option Prices and Other Portfolio Effects The effects of volatility on a portfolio are not symmetric. In rising markets, volatility is normally falling. In falling markets, volatility
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is normally rising. This not only makes volatility a great diversifier, it also means that volatility affects hedging and trading decisions. In very stable markets where the VIX is under 15, puts are relatively inexpensive and the premiums from selling call options are relatively low. In other words, it is cheaper time to buy options. During these periods, capital gains are usually strong, so you might want to shift your emphasis from theta-generated income to price gains and low-cost put protection—That is, theta is lower and delta exposure is higher. The opposite is true during periods when the market is under stress. During these periods, it makes sense to emphasize more theta income and lower delta exposures. Put option prices are higher, but offset by the ability to finance them with higher-priced call option premiums. In this case, theta is higher and delta lower. In general, the higher the volatility, the more expensive options are. Because SynA’s are generally net short options, the higher the volatility, the more you will receive from selling options and the more theta the SynA is capable of generating. A rule of thumb is to divide the VIX by 10, and that is the monthly gross income from theta. You can see how this scales from the lowrange SynA to the high-range SynA. When the VIX is 40, the potential exists for 4% monthly income on a SynA built on the S&P 500 Index. SynA’s built on individual securities, in which implied volatilities are higher than on the index, have more income potential. Of course, the price movements predicted by the higher volatility make the potential returns harder to achieve. Still, two things are working in your favor. The first is that if you previously implemented the low-range SynA, the high-range SynA short calls are not risky; they are just the completion of a well-timed call spread. It is well timed because the long call leg of the low-range SynA was purchased during a time of low volatility (and, therefore, low prices), and you sold the short leg at much higher levels during a
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time of high volatility and high prices. The second is that the higher overall levels of volatility work to increase the effectiveness of the other SynA’s in the portfolio as call options are sold at higher prices. I look at the level and direction of volatility as one of a few indicators that affect a broad range of portfolio management decisions, such as the level and direction of inflation and the equity index yield versus Treasury rates. Volatility dictates both the rate at which you can extract virtual dividends and the relative cost of put protection. For instance, in low volatility environments, you may want to consider financing a portion of position-level put protection from the low-range SynA rather than through the normal number of short call options, which may be priced too low to justify the upside limitation. Or you could simply decide to sell fewer options in favor of contingent sales if and when you need to for cost-basis adjustments. The point is that extremely low volatility usually happens during periods when the market is stable or rising and call premiums are depressed as they price in low implied volatility.
Example of a VXX SynA As the European debt crisis evolved through the summer and fall of 2011, the VIX and related volatility measures such as the VXX remained high. Until November, it was unclear as to how far Germany and France were prepared to go to support the southern countries. Also unclear was whether the ECB recognized the full extent of the problem. When Timothy Geithner got involved, there was talk of some creative backstops that might be used to help with rolling over short-term debt. During critical periods, a metric often emerges as the canary in the coal mine. In this one, it was the rate on Italian sovereign debt.
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When the Italian sovereign debt rate peaked and started down, I began to build a high-range volatility SnyA. As the ECB began to put forward potential solutions and later credit facilities, it calmed the markets and I added to the position as the VIX started to fall. There appears to be a lag effect for volatility. Instead of falling quickly, the VIX is a little skeptical and likes to tail off, even when it looks like the crisis has passed. Figure 10.2 shows the SynA in December, a few days before options expiration. The SynA consisted of short calls only. The VXX had already fallen from higher than 50 to around 41, and implied volatility on the VXX had fallen from 150% to around 100%. The position delta was ($183.92), and theta was $191.15. This shows the power of high volatility to produce high theta-to-delta ratios. Because this SynA consisted of short calls only, you might be asking what makes it a SynA and not just a string of short call options. The distinguishing factor of all SynA’s is a commitment to risk control, to do something when the maximum position drawdown is exceeded. The risk control on this SynA was contingent short puts, which turned out not to be necessary because of the gradual decline in the VXX. When the options expired, I did not roll out the SynA because the VIX had settled in the midrange between 20 and 40, a range that can be unstable. In summary, converting a relatively underutilized asset that is perfectly behaved in market crashes into a yield-producing security adds a powerful new tool in portfolio construction. This chapter discussed the opportunities for low-range, negatively correlated SynA’s and high-range, mega-theta SynA’s. The problems with tracking error and slippage in the underlying instruments need to be addressed, but there appear to be exciting opportunities of adding volatility exposures to portfolio architecture.
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Source: TradeStation Technologies, Inc.
Figure 10.2 Volatility SynA on PowerShares ETF VXX as of December 14, 2011
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Endnotes 1. Grant, Maria, CFA, Gregory, Krag, and Lui, Jason. Goldman Sachs United States: Option Research, “Volatility as an Asset Class” 2007. 2. Bernstein, Peter. Capital Ideas Evolving. 2007: John Wiley & Sons, Inc., Hoboken, New Jersey, p. 100 and 165. 3. Grant, Maria, CFA, Gregory, Krag, and Lui, Jason. Goldman Sachs United States: Option Research, “Volatility as an Asset Class” 2007. 4. Cherney, Nick, Lloyd, William, Kawaller, Geremy. “Portfolio Applications for VIX-Based Instruments.” Journal of Indexes. Copyright IndexUniverse.com 2011.
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Index Symbols 401(k) plans, 1 A adjustments automatic, 99 reverting, 101-103 security price interaction, 100-101 trading, 103 CSynA’s automatic, 99-103 cost basis, 104-106 delta, 106-116 tactical, 120-124 generalized SynA’s cost basis, 151-152 delta, 152-153 leverage, 153-158 allocated capital, 171 alpha, 19-21 opportunities, 17-18 “Alpha Orbits,” 184 alternative SynA’s, 144 negative delta, 149 positive delta, 148 Apple, 47, 50 approval level, options, 127 Asian currency crisis (1998), 7 asset allocation models, 16 assets, volatility, 209-210 B behavioral finance, 4 Benklifa, Michael, 132 Bernstein, Peter, 11 beta, 20-21
Black, Fisher, 210 Black Monday (1987), 5 Black-Scholes option pricing formula, 29-31 bonds, 183 adding yield, 191-192 low yields, 183 payback periods, 196 prices, 195 cycles, 183-184 inflation, 194-195 risks, 185-190 stress testing, 192 Buffett, Warren, 2 Bullard, James, 199, 201-204 BuyWrite Index (BXM), 94-97 C calculations, CSynA payback periods, 79-83 Callan Associates, BXM study, 96 call options call/put pairs, selling, 156-158 covered, 27, 72-73 CSynA’s, 83 put-call parity, 146-148 call/put pairs, selling, 156-158 Capital Asset Pricing Model (CAPM), 10-11 Capital Ideas Evolving, 11 CAPM (Capital Asset Pricing Model), 10-11 Cherney, Nick, 212 Chesapeake Energy SynA payoff chart, 158-160 concentrated stocks, 37-47 contango, 212 contingent CSynA’s, 85
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Index
cost basis adjustments, 54 CSynA’s, 104-106 generalized SynA’s, 151-152 tracking template, 56-57 cost basis rule, 151 covered call options, 69-73 versus SynAs, 27 covered percentage parameter (CSynA), 93 covered synthetic annuities (CSynA’s). See CSynA’s (covered synthetic annuities) Cramer, Jim, 169 CSynA’s (covered synthetic annuities), 69, 99, 127 automatic adjustments, 99 reverting, 101-103 security price interaction, 100-101 trading, 103 building, 73-76, 79 call options, 83 contingent, 85 cost basis adjustments, 104-106 covered calls, 70-73 December roll forward, 124-126 Deere & Company, 73-88 delta adjustments, 106-108 defensive, 109 offensive, 109-112 put protection, 112-116 deltas long-term targets, 87-88 versus theta, 85-87 dividends, 87 monthly roll forward, 116-118, 120 natural curve, 141-142 payback period, 79-83 volatility, 124-126 standard, 88-89, 93 BXM (BuyWrite Index), 94-97 covered percentage, 93 fundamental/technical valuation, 90-91 lower delta adjustments, 93 maximum drawdown, 92 micro-efficient parameter, 91-92 minimum value, 91 momentum parameter, 91-92 parameters, 94-95 price-related delta, 92 reverting parameter, 91-92 upper delta adjustments, 93
stock-only, 85 strike prices, 83 tactical adjustments, 120-124 variation, 135 cycles, bond prices, 183-184 D DB (defined benefit) plans, 1-2 DC (defined contribution) plans, 1-2 December roll forward, CSynA’s, 124-126 Deere & Company CSynA example, 73-88 generalized SynA, 136-138 defensive delta adjustments, CSynA’s, 109 defined benefit (DB) plans, 1-2 defined contribution (DC) plans, 1-2 delta, 62-63 call options, 70-72 CSynA’s, 76-78, 85-87, 106-108 defensive, 109 long-term targets, 87-88 offensive, 109-112 put protection, 112-116 generalized SynA’s, 152-153 SynA’s, 171 targets, price-based, 161 diversification, portfolios, 207-212 dividends, 4 CSynA’s, 87 ex-dividend dates, generalized SynA’s, 166 yields, 173-174 dot.com bubble crash (2000-2002), 7-8 downside protection, 14-16 drawdown limits, 14 E–F earnings reports, generalized SynA’s, 165 echo crash (1997), 6 Efficient Market Hypothesis (EMH), 17 Ennis, Richard, 11, 13 Enron, 17 equity risk premiums, 14 ETFs (exchange traded funds), 186 ex-dividend dates, generalized SynA’s, 166
Fidelity Magellan Fund, 169 fundamental/technical valuation high parameter (CSynA), 90-91 fundamental/technical valuation low parameter (CSynA), 90-91 G–H gamma, 62-63 CSynA’s, 78 generalized SynA, 138-140 GDAA (global dynamic asset allocation), 8 generalized SynAs, 127-133, 140-141 Deere & Company, 136-138 gamma, 138-140 managing, 151 adjustment leverage, 153-158 cost basis adjustments, 151-152 delta adjustments, 152-153 earnings reports, 165 ex-dividend dates, 166 intrinsic value, 163-165 iron condor overlay, 162-163 mean reversion, 163-166 price-based delta targets, 161 price preferences, 158-161 theta-to-delta ratios, 167-168 trending triggers, 166 theta, 138-140 targets, 132-135 global dynamic asset allocation (GDAA), 8 global financial crisis (2008-2009), 8 global tactical asset allocation (GTAA), 8 Greeks, 53, 63 Gross, Bill, 194 growth stocks, 169 GTAA (global tactical asset allocation), 8 hedging, 19-20, 185 high-yielding stocks, 170 Hokenson, Richard, 199 hybrid 401(k) plans, 1 I idiosyncratic risk, 17 implied volatility (VXX), 214 implied volatility (IV), investment profiles, 29-31
227
inflation, bond prices, 194-195 International Paper (IP), 169-171, 176-177, 180-182 Internet bubble crash (2000-2002), 7-8 intrinsic value, generalized SynA’s, 163-165 Intuitive Surgical (ISRG), 111 Investment Management after the Global Financial Crisis, 13 investment profiles, 25, 28-29 adjusting for behavioral finance, 34, 37 assigning probabilities, 29-31 options, 32 probability distributions, 25, 29 reshaping, 128-141 stock-only position, 29 versus payoff curves, 25-26 investment thesis, strategy complements, 195-198 IP (International Paper), 169-172, 176-177, 180-182 IRAs (Individual Retirement Accounts), 1 iron condors, 162-163 J–K–L Kawaller, Geremy, 212 Leibowitz, Martin, 12, 184, 196 Leland O’Brien and Rubinstein (LOR), 5 Level 1 options, 69 leverage adjustments, generalized SynA’s, 153-158 theta, 182 Lloyd, William, 212 Long Term Capital Management (LTCM), 7 long-term management, SynA’s, 174-176 LOR (Leland O’Brien and Rubinstein), 5 lower delta adjustments parameter (CSynA), 93 LTCM (Long Term Capital Management), 7 Lynch, Peter, 169
228
Index
M macro-inefficiency, 196 Mad Money, 169 managing CSynA’s, monthly roll forward, 116-120 generalized SynA’s, 151 adjustment leverage, 153-158 cost basis adjustments, 151-152 delta adjustments, 152-153 earnings reports, 165 ex-dividend dates, 166 intrinsic value, 163-165 iron condor overlay, 162-163 mean reversion, 163-166 price-based delta targets, 161 price preferences, 158-161 theta-to-delta ratios, 167-168 trending triggers, 166 SynA’s, long-term, 174-176 managing CSynA’s automatic adjustments, 99 reverting, 101-103 security price interaction, 100-101 trading, 101-103 cost basis adjustments, 104-106 December roll forward, 124-126 delta adjustments, 106-108 defensive, 109 offensive, 109-112 put protection, 112-116 tactical adjustments, 120-124 markets, turbulent, 47-52 market volatility, 4 investor returns, 9-10 Markowitz, Harry, 11 maximum drawdown parameter (CSynA), 92 mean reversion, generalized SynA’s, 163-166 mean-variance-optimized (MVO) portfolios, 5, 11 micro-efficient parameter (CSynA), 91-92 minimum value parameter (CSynA), 91 modern portfolio theory (MPT), 2-7, 10, 13 momentum parameter (CSynA), 91-92 monthly roll forward, CSynA’s, 116-120
MPT (modern portfolio theory), 2-7, 10, 13 MVO (mean-variance-optimized) portfolios, 5, 11 N–O negative delta SynA’s, 142-144 alternative form, 149 net options credit, 56 net options premium, 56 non-diversified risk, 17 offensive delta adjustments, CSynA’s, 109-112 options approval level, 127 call, covered, 72-73 investment profiles, 32 Level 1, 69 prices, volatility, 218-220 security price, 70 selling, 105 Options Analysis Workspace (TradeStation), 58-66 P parameters (CSynA’s), 89, 94-95 covered percentage, 93 fundamental/technical valuation high, 90-91 fundamental/technical valuation low, 90-91 lower delta adjustments, 93 maximum drawdown, 92 micro-efficient, 91-92 minimum value, 91 momentum, 91-92 price-related delta, 92 reverting, 91-92 upper delta adjustments, 93 “Parsimonious Asset Allocation,” 11 payback period bonds, 196 CSynA’s, 79-83 volatility, 124-126 tracking template, 57-58 payoff chart, Chesapeake Energy SynA, 158-160 payoff curves versus investment profiles, 25-26 performance, tracking, 53-54, 66 tracking template, 54-58 TradeStation, 58-66
“Portfolio Applications for VIX-Based Instruments,” 212 portfolios diversification, volatility market, 207-212 global dynamic asset allocation (GDAA), 8 global tactical asset allocation (GTAA), 8 insurance, 5-6 mean-variance-optimized (MVO), 5, 11 modern portfolio theory (MPT), 2-7, 10, 13 volatility effects, 218-220 positions strategic versus tactical, 149-150 theoretical, 54-63 positive delta SynA’s, alternative form, 148 price-related delta parameter (CSynA), 92 prices bonds, 195 cycles, 183-184 inflation, 194-195 options, volatility, 218-220 probability distribution, investment profiles, 25, 29 Profiting with Iron Condors, 133 projected payback period, tracking template, 57-58 protective puts, 69 put/call pairs, selling, 156-158 put-call parity, 146-148 put protection, financing, 112-116 puts call/put pairs, selling, 156-158 put-call parity, 146-148 Q-R “Qualified Commitment to DB Plans, A,” 22 “Race to Zero, The,” 199 random variables, 29 ratios, theta-to-delta, generalized SynA’s, 167-168 records, 64-66 retirement accounts, 20-21 returns, volatility, 9-10 reverse SynA’s, 142-144 reverting parameter (CSynA), 91-92
229
risk allocations, 4, 20 bonds, 185-190 budgeting, 4, 20 idiosyncratic, 17 management, 19-20 measurements, 4 non-diversified, 17 reducing, 21-22 tolerance, CSynA, 92 rolling out/up, 110 S Scholes, Myron, 210 securities prices automatic adjustments, 100-101 options, 70 structured, 25 selling call/put pairs, 156-158 “Seven Faces of the Peril,” 199-204 Sharpe, Bill, 11 Siegel, Lawrence, 8-9 stability, generalized SynA’s, 138-140 standard CSynA’s, 88-89, 93 BXM (BuyWrite Index), 94-97 covered percentage, 93 fundamental/technical valuation, 90-91 lower delta adjustments, 93 maximum drawdown, 92 minimum value, 91 parameters, 91-95 price-related delta, 92 upper delta adjustments, 93 stochastic math, 29 stock-only CSynA’s, 85 stock-only positions versus SynAs, 40-42 stocks concentrated, 37-47 growth, 169 high-yielding, 170 strategic positions, versus tactical, 149-150 strategies, investment thesis, 195-198 stress testing bonds, 192 volatility SynA’s, 218 strike prices, CSynA’s, 83 structured securities, 25
230
Index
synthetic annuities (SynA’s), 4-5, 26-28 aggressive approach, 28 alternative, 144 negative delta, 149 positive delta, 148 as hedging instrument, 185 creating, 27-28 generalized, 127-141 Deere & Company, 136-138 gamma, 138-140 managing, 151-168 theta, 138-140 theta targets, 132-135 managing, long-term, 174-176 reverse, 142-144 turbulent markets, 47-52 utility curve, applying, 44-45 versus covered call positions, 27 versus stock-only positions, 40-42 VIX, 214-218 volatility-squared, 212-214 high VIX, 217-218 low VIX, 214-217 stress testing, 218 VXX, 220-221 T tactical adjustments, CSynA’s, 120-124 tactical positions versus strategic, 149-150 TBT (technical barriers to trade), 186-194 theoretical positions, 54, 60-63 theta, 63, 78, 85-87 generalized SynA, 132-140 leveraging, 182 theta-to-delta ratios, generalized SynA’s, 167-168 tracking performance, 53-54, 66 tracking template, 54 cost basis, 56 example, 58 projected payback period, 57 trade triggers, 56 TradeStation, 58-66 tracking template, 54 cost basis, 56 example, 58 projected payback period, 57 trade triggers, 56 TradeStation, 58-66
trade triggers, tracking template, 56-58 trading accounts, 20-21 transactions, records, 64-66 trending triggers, generalized SynA’s, 166 turbulent markets, 47, 50-52 U–V upper delta adjustments parameter (CSynA), 93 utility curve, 34, 37, 42 SynA, applying to, 44-45 utility functions, 34, 37 variables, random, 29 VIX over 40, building volatility SynA’s, 217-218 under 20, building volatility SynA’s, 214-217 volatility, 4 implied volatility (IV), 29-31 investor returns, 9-10 option prices, 218-220 payback periods, CSynA’s, 124-126 portfolios, 218-220 diversification, 207-212 volatility market, 207 volatility risk premiums (VRPs), 210-211 volatility-squared SynA’s, 212-214 high VIX, 217-218 low VIX, 214-217 stress testing, 218 VRPs (volatility risk premiums), 210-211 VXX SynA’s, 220-221 volatility, 212-218 W–Z Whaley, Robert, 96 “Why Are Put Options So Expensive?,” 135 Worldcom, 17 yields, 173-174 bonds, 183 adding, 191-192 stress testing, 192 generalized SynA’s, 138-140 increasing, 19
