Caught up in the (higher) moments: Essays on the cross-sectional pricing of implied systematic variance, skewness, and kurtosis

This dissertation examines if information extracted from the options markets is priced in the cross-section of equity returns and whether or not this information is a systematic risk factor. Several versions of the Intertemporal Capital Asset Pricing Model predict that changes in aggregate volatility are priced into the cross-section of stock returns. Literature confirms that changes in expected future market volatility are priced into the cross-section of stock returns. Several of these studies use the VIX Index as proxy for future market volatility, and suggest that it is a risk factor. However, prior studies do not test whether asymmetric volatility affects if firm sensitivity to changes in VIX is related to risk, or is just a characteristic uniformly affecting all firms. The first chapter of my dissertation examines the asymmetric relation of stock returns and changes in VIX. The study finds that sensitivity to VIX innovations affects returns when volatility is rising, but not when it is falling. When VIX rises this sensitivity is a priced risk factor, but when it falls there is a positive impact on all stocks irrespective of VIX loadings. The second essay of my dissertation uses the second, third, and fourth moments of the risk-neutral density extracted from options on the S&P 500 as the proxy for changes in the expected future market return distribution rather than just the VIX index. The VIX index, while easily obtained, contains limited information due to its construction. The risk-neutral moments map one-to-one to the real-world volatility smile from market options, and contain all the information in the cross-section of market option moneyness and provide a richer proxy for changes in expected future market return distribution. The analyses find that positive change in risk-neutral skewness is a risk-factor and that change in risk-neutral kurtosis is not. The evidence for change in risk-neutral volatility being a risk factor, however, is ambiguous.