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Essays on the Forecasting Power of Implied Volatility Prithviraj Shyamal Banerjee Florida State University Libraries Electronic Theses, Treatises and Dissertations The Graduate School 2008 Essays on the Forecasting Power of Implied Volatility Prithviraj Shyamal Banerjee Follow this and additional works at the FSU Digital Library. For more information, please contact [email protected] FLORIDA STATE UNIVERSITY COLLEGE OF BUSINESS ESSAYS ON THE FORECASTING POWER OF IMPLIED VOLATILITY By PRITHVIRAJ SHYAMAL BANERJEE A Dissertation submitted to the Department of finance in partial fulfillment of the requirements for the degree of Doctor of Philosophy Degree Awarded: Spring Semester, 2008 The members of the Committee approve the Dissertation of Prithviraj Shyamal Banerjee defended on March 18, 2008. Dr. David R. Peterson Professor Directing Dissertation Dr. Thomas Zuehlke Outside Committee Member Dr. William Christiansen Committee Member Dr. James S. Doran Committee Member Dr. Danling Jiang Committee Member Approved: Caryn Beck-Dudley, Dean, College of Business The Office of Graduate Studies has verified and approved the above named committee members. ii I dedicate this work to my parents iii ACKNOWLEDGEMENTS I gratefully acknowledge the immense help and guidance of my Chair, Dr. David R. Peterson, from whom I have learnt to do research. I also gratefully acknowledge the help of my other committee members, especially Dr. James Doran and Dr. Danling Jiang, and my uncle Dr. Tarun K Mukherjee, who has helped me more times than I can thank him for. iv TABLE OF CONTENTS List of Tables ............................................................................................vii List of Figures ............................................................................................xi Abstract .................................................................................................xii 1. Introduction ............................................................................................1 2. Implied Volatility and Future Portfolio Returns...........................................11 3. The Forecasting Power of the Risk and Sentiment Components of Implied Volatility ....................................................................47 4. Forecasting Future Portfolio Volatility: The Role of Risk and Sentiment Components of Implied Volatility and other Forecast ......................................112 v REFERENCES ............................................................................................ 164 BIOGRAPHICAL SKETCH ........................................................................... 170 vi LIST OF TABLES Table 1: Estimates from 22-Day and 44-Day Future Market Returns Regressed on VIX ...............................................................................35 Table 2: Regression Estimates for the Fama-French 25 Portfolios Sorted on Book-to-Market Equity and Size .................................35 Table 3: Regression Estimates for the Fama-French 25 Portfolios Sorted on Book-to-Market Equityand Size, Including Four Factors as Independent Variables .............................................................37 Table 4: Descriptive Statistics ..........................................................................38 Table 5: Return Regression Estimates for the Twelve Portfolios Sorted on Book-to-Market Equity, Size, and Beta ............................................39 Table 6: 22-Day Regression Estimates for the Twelve Portfolios Sorted on Book-to-Market Equity, Size, and Beta ............................................41 Table 7: 44-Day Regression Estimates for the Twelve Portfolios Sorted on Book-to-Market Equity, Size, and Beta ...........................................42 Table 8: Return Regression Estimates using High VIX Level Observations ..........................................................................................44 Table 9: 22-Day and 44-Day Regression Estimates of the Four Factors on VIX ..............................................................................45 Table 10: Descriptive Statistics .......................................................................66 Table 11: Regression Estimates of the Raw Sentiment Proxies on Risk Factors ................................................................................70 Table 12: Regression Estimates of VIX on the Orthogonal Sentiment Proxies ............................................................................................73 Table 13: Regression Estimates of 22-day and 44-day Future Returns of Portfolios on VIX............................................................................73 vii Table 14: Regression Estimates of 22-day Future Returns of Portfolios on VIXRISK....................................................................................79 Table 15: Regression Estimates of VIX on the Risk Measures..........................86 Table 16: Regression Estimates of 22-day Future Returns of Portfolios on VIXSENT ............................................................................................87 Table 17: Regression Estimates of 22-day Future Returns of Portfolios on VIXRISK and VIXSENT ............................................................................93 Table 18: Regression Estimates of 22-day and 44-day Future Returns of Portfolios on VIXRISK and the Orthogonal Sentiment Measures.................100 Table 19: Tabulation of Significant Variables with Signs in Table 9.................111 Table 20: Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIX.........................................................................................127 Table 21: Regression Estimates of 22-day Realized Standard Deviation of Portfolios on Lagged Market Standard Deviation.........................................130 Table 22: Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIX and Lagged Market Standard Deviation...........................133 Table 23: Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXRISK, Lagged Portfolio Standard Deviation, and Lagged Market Standard Deviation............................................................136 Table 24: Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXRISK, GARCH Forecast, and Lagged Market Standard Deviation............................................................140 Table 25: Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXSENT, Lagged Portfolio Standard Deviation, and Lagged Market Standard Deviation............................145 Table 26: Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXSENT, GARCH Forecast, and Lagged Market Standard Deviation ..............................148 viii Table 27: Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXRISK, VIXSENT, Lagged Portfolio Standard Deviation, and Lagged Market Standard Deviation .............153 Table 28: Regression Estimates of 22-day Realized Standard Deviation of Portfolios on VIXRISK, VIXSENT, GARCH Forecast, and Lagged Market Standard Deviation ............................................158 ix LIST OF FIGURES Figure 1: Mean Returns for the 12 B/M, Size and Beta Portfolios.....................34 x ABSTRACT In this dissertation, I look at the forecasting power of implied volatility. I decompose implied volatility into a risk component and a sentiment component, and examine the forecasting power of these components for future returns and volatilities of portfolios sorted by important firm characteristics. I find that the forecasting power of implied volatility for returns is higher for higher beta portfolios and for longer horizon holding periods. I also find that the sentiment component of implied volatility has more (less) forecasting power for future returns (volatility) than the risk component. xi CHAPTER 1 INTRODUCTION The Black and Scholes (1973) model implies a one-to-one correspondence between the price of the option and the volatility of the underlying asset. By inverting the option price and using an algorithmic procedure we can back out the volatility, which is called the implied volatility for the asset1. If markets are efficient, the implied volatility of the asset is the market’s best guess of the underlying asset’s volatility over the remaining life of the option. Past studies involving implied volatility have focused on things like its properties and its reaction to events. Especially important is that prior studies analyze implied volatility’s forecasting power for future realized volatility and to a lesser extent, for future realized returns. Poterba and Summers (1986) and Diz and Finucane (1993) find that implied volatility has a mean reverting component. Stein (1989) finds that long-term options “overreact” to changes in the implied volatility of short-term options. Poteshman (2001) finds evidence of under reaction to changes in contemporaneous instantaneous variance and overreaction to increasing or decreasing variance over the prior few days. Event studies of implied volatility examine the reaction of implied volatility to corporate events. Patell and Wolfson (1981) find that implied volatility falls after earnings announcements. French and Dubofsky (1986) find that implied volatility increases with stock splits, whereas Klein and Peterson (1988) find no response of implied volatility to stock splits2. Implied volatility functions have also been used to obtain the risk neutral densities of the underlying asset (Campa, Chang and Reider (1998),
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