The term structure of equity option implied volatility Christopher S. Jones Tong Wang Marshall School of Business Marshall School of Business University of Southern California University of Southern California Los Angeles, CA 90089 Los Angeles, CA 90089 [email protected] [email protected] 213-740-9485 213-740-9663 VERY PRELIMINARY { PLEASE DO NOT QUOTE October 2012 Abstract This paper investigates the relationship between the slope of the implied volatility (IV) term structure and future option returns. In Fama-Macbeth regressions we demonstrate that im- plied volatility slopes are positively correlated with future returns on short-term at-the-month straddles. A strategy that buys straddles with high IV slopes and short sells straddles with low IV slopes returns seven percent per month, with an annualized Sharpe ratio just less than two. Risk-adjustment using Fama-French, Carhart, and S&P 500 Index straddle factors only increases the return spread. Surprisingly, we find no relation between IV slopes and the re- turns on longer-term straddles, even though the correlation between the returns on portfolios of short-term and long-term straddles generally exceeds 0.9. Furthermore, we find no time-series predictability in average straddle returns or in the returns on the long-short strategy identified above. We interpret these results as evidence that the return predictability we document is un- related to systematic risk premia. We believe that our results point to two possible explanations. One is that temporary hedging pressure pushes option prices away from efficient levels. The other is that short-term options are more likely to be mispriced by noise traders than long-term options. JEL classification: G12, G13 Keywords: options, implied volatility, return predictability 1 Introduction Option-implied volatilities reflect risk-neutral expectations of the future future volatility of the un- derlying asset. Because these expectations are computed under an equivalent martingale measure, they embody expectations under the true probability measure as well as premia on risk factors such as jumps or stochastic volatility. One might therefore suppose that implied volatilities have some predictive ability to forecast the future returns on options and their underlying assets. This prediction has been confirmed directly in several recent papers and indirectly in a number of others. Bollerslev et al. (2009) show that the spread between implied and realized volatility forecasts stock market returns. Specifically, when implied volatility is high relative to realized volatility, then future stock returns tend to be higher. Goyal (2009) find that a similar variable has strong predictive power in the cross section of at-the-money straddle returns, with high volatilities forecasting negative straddle returns. Other papers, such as Jones (2003), that estimate stochastic volatility and/or jump models using both stock and implied volatility series generally find that nonzero premia on volatility and/or jump risk are necessary to fit both series, which implies that option expected returns will vary with the level of actual or implied volatility. In the fixed income literature, it is well known that the slope of the term structure has significant predictive power for future bond returns, with positive slopes associated with high excess returns on intermediate and long-term bonds. Work in this area goes back to seminal papers such as Fama and Bliss (1987) and Campbell and Shiller (1991). The importance of the term structure slope can be attributed to the fact that risk premia have relatively minor effects on the discounting of short- maturity cash flows and much larger effects for long maturities. Subtracting the short maturity 1 yield from the long maturity yield seems to isolate the component of yields that is driven by risk premia rather than expected future interest rates. In this paper we ask whether the slope of the implied volatility term structure is a predictor of future stock and option returns. When predicting option returns, we focus on the returns on at-the-money (ATM) straddle, which is a portfolio of one ATM call and one ATM put, both with the same maturity. The straddle portfolio is naturally close to zero-delta, which means that it primarily represents a bet on volatility (or time varying jump risk) rather than being a directional bet on the underlying asset. We examine predictability both in the time series and in the cross section, and we examine both indexes and individual equities. Our primary finding is that the slope of the implied volatility term structure has strong and highly significant predictive power for future short-term straddle returns. For straddles with one month remaining until expiration, a one percentage point increase in the difference between long and short IV results in a 0.5 to one percent decrease in expected straddle returns. in expected return per year. This effect remains significant after controlling for the volatility difference measure of Goyal (2009), which is the difference between implied and historical volatility, as well as numerous other controls. A long-short strategy that buys straddles with high IV slope and sells straddles with low IV slope results in an average monthly return of 7.0%, which is accompanied by a t-statistic of 7.7. Risk adjustment with a multifactor model increases both numbers. The strength of these results makes it surprising, therefore, that we find almost no predictability in longer-term straddle returns. When we examine the one-month returns on straddles with as few as two months until expiration, the predictive ability of the IV slope vanishes almost completely. 2 Furthermore, the return on a long-short strategy that buys high IV slope straddles and shorts low IV slope straddles generates essentially zero returns when implemented with longer maturity straddles. This is even more puzzling given that the large correlations between portfolios of short-term and long-term straddles, which range from 0.91 to 0.94. We find no predictability in the pure time-series component of straddle returns. The average IV slope across all equity options does not predict the average return on equity straddles. In addition, the implied volatility slope constructed from S&P 500 index options has no predictive power for future index straddle returns. For two reasons, we believe that it is unlikely that the predictability of short-term straddle returns is the result of cross-sectional variation in risk. Primarily, this is because of the extremely high correlations between the returns on portfolios of long and short straddles and the fact that long- term straddles show little predictability. A risk-based reconciliation of these findings would require an extremely large Sharpe ratio on the component of short straddle returns that is orthogonal to long straddle returns. This Sharpe ratio is too large to be consistent either with common sense or the \good deal" bounds of Cochrane and Saa-Requejo (2000). The second reason is the lack of time series predictability. The finance literature has been relatively conclusive in showing that factor risk premia in equity, fixed income, and option markets all vary significantly through time. If the return on short-term straddles represents some systematic factor, then its lack of predictability would make it somewhat unique among risk factors. We proceed in Section 2 by describing our data sources. Section 3 reports the results of cross- sectional regressions of straddle returns on the IV slope and various controls. We analyze trading 3 strategies and time-series predictability in Section 4. In Section 5 we attempt to refine the slope measure by decomposing slope into expectation and risk premium components. Section 6 concludes. 2 Data Our study's primary focus is on option prices, which we obtain from the IvyDB database of Option- metrics. This database contains end-of-day quotes on equity, index, and ETF options in addition to option-level contractual characteristics (strike price, expiration date), trading data (volume and open interest), implied volatilities, and \Greeks" (delta, vega, etc.). Our primary sample is re- stricted to options on common equity and not ETFs or indexes, though we analyze index options separately. Our sample period starts in January of 1996, which is the start of the Optionmetrics dataset, and ends in December of 2010. Although we use daily data to construct many explanatory variables, the straddle returns we analyze are monthly. Our short-term straddle is an investment that is initiated on the Monday following expiration week, which is either the third or fourth Monday of the month. On that day (or the first day after it if that Monday is a holiday), one call and one put on each underlying are purchased. The contracts chosen are those with one month remaining until expiration, with a strike price that is closest to the current spot price. The cost of each option is assumed to be the midpoint of each option's bid-ask spread. The short-term straddle is held until expiration, so the terminal value is determined based solely on the difference between stock and strike prices. We do not allow for early exercise. Long-term straddle returns are computed similarly, except that they are not held until expira- 4 tion. The long-term straddle is defined as the straddle with the longest maturity available subject to being no longer than four months and considering only those options that are part of the traditional monthly expiration calenday. (I.e., we do not consider \weeklys.") Regardless of the maturity, the straddle is held for one month and sold at a price determined by option bid-ask midpoints. The schedule on which new options are introduced ensures that in any given month the cross-section of long-term straddles will be approximately equally divided between two-month, three-month, and four-month maturities.