Option-Implied Equity Risk and the Cross Section of Stock Returns

Abstract

T he classical capital asset pricing model, CAPM (Sharpe 1964;Lintner 1965;Black, Jensen, and Scholes 1972), is the most widely used method in practice for measuring equity risk (e.g., Block 1999; Graham and Harvey 2001;Welch 2008), but several studies have documented its failure to characterize cross-sectional asset prices (e.g., Fama and French 1992, 1993Lewellen and Nagel 2006). Motivated in part by this failure, an abundance of authors have investigated the link between the implied, forwardlooking information in the options market and future stock returns. 1 Recently, Chang, Christoffersen, Jacobs, and Vainberg (2012; hereafter, CCJV) constructed a simple estimate for equity beta from option prices; 2 however, Buss and Vilkov (2012) found a flat relationship between the CCJV beta measure and future stock returns. A potential problem with the approach taken by CCJV is that they made the assumption that idiosyncratic skewness is zero, whereas researchers have found that idiosyncratic skewness affects asset prices (e.g., Boyer, Mitton, and Vorkink 2010; Conrad, Dittmar, and Ghysels 2013).We used forward-looking information from the options market to estimate systematic market risk while controlling for the impact of idiosyncratic skewness. 3 We found that our option-implied beta is a strong predictor of future stock returns and that the associated premium is also a strong predictor of future market returns, providing support for the notion that forward-looking information is embedded in traded equity option prices.More specifically, we used daily option prices to calculate the implied moments of the one-month return distribution for each firm in the sample. Using these option-implied moments, we then estimated the monthly option-implied beta for each firm through nonlinear GMM (generalized method of moments) estimation. We used estimates for 3,484 unique optioned firms over the sample period, January 1996 through December 2012.We found that a long-short portfolio formed on the option-implied beta generated an average monthly risk-adjusted return of 0.96% with a significantly positive t-statistic of 3.47. We further report that the long-short portfolio returns formed on the option-implied beta (e.g., the implied market risk premium) can significantly forecast future market returns with a t-statistic of 3.01. In addition, we found that our option-implied beta is a significant predictor of future realized betas and that the optionimplied market risk premium is positively associated with certain macroeconomic variables, such as the dividend yield and the term spread.We should note that our sample is restricted to firms with equity options outstanding and that our results do not take into account transaction costs or potential short-selling constraints. Firms with options are typically liquid, however, and of large market capitalization.In an attempt to understand why our results differ from those of CCJV (2012), we found that idiosyncratic skewness does correlate with CCJV's implied beta but not with ours, which m...