Essays on Information in Options Markets A

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Essays on Information in Options Markets A ESSAYS ON INFORMATION IN OPTIONS MARKETS A DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL OF BUSINESS AND THE COMMITTEE ON GRADUATE STUDIES OF STANFORD UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY Travis L. Johnson May 2012 © 2012 by Travis Lake Johnson. All Rights Reserved. Re-distributed by Stanford University under license with the author. This work is licensed under a Creative Commons Attribution- Noncommercial 3.0 United States License. http://creativecommons.org/licenses/by-nc/3.0/us/ This dissertation is online at: http://purl.stanford.edu/hf166pb0337 ii I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Anat Admati, Primary Adviser I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Ian Martin I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Stefan Nagel I certify that I have read this dissertation and that, in my opinion, it is fully adequate in scope and quality as a dissertation for the degree of Doctor of Philosophy. Paul Pfleiderer Approved for the Stanford University Committee on Graduate Studies. Patricia J. Gumport, Vice Provost Graduate Education This signature page was generated electronically upon submission of this dissertation in electronic format. An original signed hard copy of the signature page is on file in University Archives. iii Abstract In the first chapter, my coauthor and I examine the information content of option and equity volumes when trade direction is unobserved. In a multimarket asymmet- ric information model, equity short-sale costs result in a negative relation between relative option volume and future firm value. In our empirical tests, firms in the lowest decile of the option to stock volume ratio (O/S) outperform the highest decile by 0.34% per week (19.3% annualized). Our model and empirics both indicate that O/S is a stronger signal when short-sale costs are high or option leverage is low. O/S also predicts future firm-specific earnings news, consistent with O/S reflecting private information. In the second chapter, I show that in many asset pricing models, the equity mar- ket's expected return is a time-invariant linear function of its conditional variance, which can be estimated from options markets. However, I show that when the relation between conditional means and variances is state-dependent, an observer requires the combined information in multiple variance horizons to distinguish among the states and thereby reveal the equity risk premium. Empirically, I show that while the VIX by itself has little predictive power for future S&P 500 returns, the VIX term structure predicts next-quarter S&P 500 returns with a 5.2% adjusted R2. iv Acknowledgements The first chapter of this dissertation is co-authored with Eric C. So. Thanks to my advisor Anat Admati, and my reading committee Ian Martin, Stefan Nagel, and Paul Pfleiderer, for their comments and guidance. Thanks to an anonymous referee, Mary Barth, Darrell Duffie, Jeff Harris, Sebas- tian Infante, Charles Lee, Arthur Korteweg, Kristoffer Laursen, Ian Martin, Stefan Nagel, Paul Pfleiderer, Monika Piazzesi, Ken Singleton, and seminar participants at Boston College, Dartmouth College, Rice University, SAC Capital Advisors, Stan- ford University, University of California-Berkeley, University of Houston, University of Maryland, University of Notre Dame, University of Pennsylvania, University of Rochester, University of Texas-Austin, University of Wisconsin-Madison, and the Western Finance Association meetings, for their helpful comments and suggestions. Thanks to Data Explorers for graciously providing us institutional lending data. v Contents Abstract iv Acknowledgements v 1 Introduction 1 2 The Option to Stock Volume Ratio and Future Returns 3 2.1 Introduction . 3 2.2 Relation to prior research . 6 2.3 The model . 10 A Equilibrium . 12 B Results and empirical predictions . 14 2.4 Empirical tests . 17 2.5 Additional analyses . 34 2.6 Conclusion . 37 2.7 Tables and Figures . 40 3 Equity Risk Premia and the VIX Term Structure 54 3.1 Introduction . 54 3.2 Relation to prior research . 56 3.3 Model . 61 A A three-factor model of variance and risk premia . 65 3.4 Empirical results . 71 3.5 Conclusion . 77 3.6 Figures and Tables . 78 vi A Appendices for Chapter 2 91 A.1 Simultaneous equations . 91 A.2 Measure of leverage . 93 A.3 Proofs . 93 B Appendices for Chapter 3 102 B.1 Conditional means and variances in prior models . 102 A Bansal and Yaron (2004) . 102 B Campbell and Cochrane (1999) . 103 B.2 Details of Proofs . 103 B.3 Continuous version of the model . 106 A Risk and Return in the Model . 108 B Matching Moments . 110 Bibliography 113 vii List of Tables 2.1 Descriptive statistics by year. 42 2.2 Factor regression results by deciles of O/S, ∆O/S, and ΩO/S. 43 2.3 Fama-MacBeth multivariate regressions. 47 2.4 Strategy alphas sorted by short-sale costs. 49 2.5 Option volume alphas sorted by leverage. 51 2.6 Future return skewness by deciles of call-put volume ratio. 52 2.7 Earnings surprises and earnings announcement returns. 53 3.1 Data and Calibrated Model Moments . 82 3.2 Descriptive Statistics of Term Structure . 83 3.3 Return Prediction Regressions . 84 3.4 Principal Components (Full Sample) . 87 3.5 Principal Components (No 2008-2009 Financial Crisis) . 89 B.1 Summary of Model Notation . 108 B.2 Data and Calibrated Model Moments . 111 viii List of Figures 2.1 Persistence of O/S-return relation. 40 2.2 Cumulative hedge returns by year. 41 3.1 Model Equity Risk Premia and the VIX Term Structure . 78 2 3.2 Functions integrated to compute VIX12 on January 2nd, 1996. 79 3.3 Time Series of the Term Structure . 80 3.4 Return predictability factors in the VIX term structure . 81 B.1 Risk premia and variances in Campbell and Cochrane (1999). 104 ix Chapter 1 Introduction Classical finance theory assumes derivatives like options are redundant securities that can be perfectly replicated using the underlying asset. Transaction costs, incomplete markets, and asymmetric information are all examples of market imperfections that make accurate replication impossible, implying derivative markets are not redun- dant and may provide an alternative channel for fundamental information to reach investors. My dissertation research explores the non-redundant information about underly- ing assets provided by option markets. Pursuant to this agenda, I have two distinct chapters, each relying on option market data as a source of information about the economics of financial markets. The first chapter, \The Option to Stock Volume Ratio and Future Returns," is co-authored with Eric So, an accounting student here Stanford. Eric and I shared responsibility for all parts of the paper: the theory, the empirics, the writing, and the editing. The paper has been accepted at the Journal of Financial Economics but hasn't yet been published. In the paper, we examine the information content of option and equity volumes when trade direction is unobserved. In a multimarket asymmetric information model, equity short-sale costs result in a negative relation between relative option volume and future firm value. In our empirical tests, firms in the lowest decile of the option to stock volume ratio (O/S) outperform the highest decile by 0.34% per week (19.3% annualized). Our model and empirics both indicate that O/S is a stronger signal when short-sale costs are high or option leverage is low. 1 CHAPTER 1. INTRODUCTION 2 O/S also predicts future firm-specific earnings news, consistent with O/S reflecting private information. The second chapter, \Equity Risk Premia and the VIX Term Structure" is my job market paper. In it, I show that in many asset pricing models, the equity market's expected return is a time-invariant linear function of its conditional variance, which can be estimated from options markets. However, I show that when the relation between conditional means and variances is state-dependent, an observer requires the combined information in multiple variance horizons to distinguish among the states and thereby reveal the equity risk premium. Empirically, I show that while the VIX by itself has little predictive power for future S&P 500 returns, the VIX term structure predicts next-quarter S&P 500 returns with a 5.2% adjusted R2. Chapter 2 The Option to Stock Volume Ratio and Future Returns 2.1 Introduction In recent decades, the availability of derivative securities has rapidly expanded. This expansion is not limited to equity options and now includes a vast array of securities ranging from currency options to credit default swaps. Derivatives contribute to price discovery because they allow traders to better align their strategies with the sign and magnitude of their information. The leverage in derivative securities, combined with this alignment, creates additional incentives to generate private information. In this way, trades in derivative markets may provide more refined and precise signals of the underlying asset's value than trades of the asset itself. Understanding how and why derivatives affect price discovery is therefore vital to understanding how information comes to be in asset prices. This study focuses on the information content of trading volumes. Observed transactions play an important role in price discovery because order flow imbalances can reflect the sign and magnitude of private information.
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