Option-Implied Measures of Equity Risk

Chang, Bo Young; Christoffersen, Peter; Jacobs, Kris; Vainberg, Gregory

doi:10.2139/ssrn.1416753

Cited by 68 publications

(86 citation statements)

References 68 publications

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“…Using the forward-looking information embedded in option prices, we extended the work of Chang et al (2012) to develop an option-implied beta estimate that takes into account idiosyncratic skewness in stock prices. Our forward-looking approach uses risk-neutral moments obtained from traded equity option prices to facilitate the identification of systematic risk in the presence of idiosyncratic risk.…”

Section: Resultsmentioning

confidence: 99%

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

Chen

Chung

Tsai

2016

Financial Analysts Journal

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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...

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Section: Resultsmentioning

confidence: 99%

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

Chen

Chung

Tsai

2016

Financial Analysts Journal

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“…Higher-order risk-neutral moments are expressed in terms of the prices of payoffs that depend on future stock prices, namely a quadratic, a cubic, and a quartic contract. This method has gained significant recognition (e.g., Dennis and Mayhew (2002); Han (2008);Chang et al (2012); Neumann and Skiadopoulos (2013)) since it allows one to extract the implied risk-neutral moments without the need to impose any specific assumptions on the underlying asset's stochastic process. The resulting formulas for extracting the riskneutral moments are given in Appendix C.…”

Section: Market Default Likelihood Index (Mdli)mentioning

confidence: 99%

“…Estimation of the risk-neutral moments follows previous literature, particularly the approach in Chang et al (2012). Risk-neutral moments are computed by integrating over…”

Section: Market Default Likelihood Index (Mdli)mentioning

confidence: 99%

Effects of market default risk on index option risk-neutral moments

Andreou

2015

Quantitative Finance

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“…Regarding volatility forecasts, Blair, Poon, and Taylor (2001); Jiang and Tian (2005); Giot and Laurent (2007); and Busch, Christensen, and Nielsen (2011) all state that option forecasts are more informative and accurate than historical forecasts of index volatility even when the historical information set includes intraday, high-frequency returns. 1 Chang, Christoffersen, Jacobs, and Vainberg (2012) show option-implied betas have significant predictive power compared with historical betas, while Kempf, Korn, and Sassning (2015) show that option prices can be used to enhance portfolio optimization. Liu et al (2007) provide the first evidence that option prices provide density forecasts that are superior to forecasts which rely solely on historical prices.…”

Section: Introductionmentioning

confidence: 99%

Density forecast comparisons for stock prices, obtained from high‐frequency returns and daily option prices

Fan¹,

Taylor

Sandri

2017

Journal of Futures Markets

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This paper presents the first comparison of the accuracy of density forecasts for stock prices. Six sets of forecasts are evaluated for DJIA stocks, across four forecast horizons. Two forecasts are risk-neutral densities implied by the Black-Scholes and Heston models. The third set are historical lognormal densities with dispersion determined by forecasts of realized variances obtained from 5-min returns. Three further sets are defined by transforming risk-neutral and historical densities into realworld densities. The most accurate method applies the risk transformation to the Black-Scholes densities. This method outperforms all others for 87% of the comparisons made using the likelihood criterion.

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Option-Implied Measures of Equity Risk

Cited by 68 publications

References 68 publications

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

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

Effects of market default risk on index option risk-neutral moments

Density forecast comparisons for stock prices, obtained from high‐frequency returns and daily option prices

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