Market Skewness Risk, Risk Aversion and the Cross-Section of Stock Returns

Previous research suggests that the cross section of stock returns has substantial exposure to risks captured by higher moments of market returns, implied by S&P500 index option prices. However, assuming that risk aversion is time-varying, a risk-based explanation would suggest that the exposure is priced in periods of high risk aversion, while it is not necessarily priced/weaker in periods of low risk aversion. We find that for market skewness and kurtosis, this hypothesis is not supported by the data. We find that each of the higher moment prices of risk is time-varying and has significantly different patterns under different market conditions, proxied by a measure of investors’ relative risk aversion. In particular, in line with our reasoning, our results suggest that only in down-markets (high risk aversion periods), the exposure to the market volatility innovations is priced significantly negative in the cross-section of stocks, while it is not priced in up-markets (low risk aversion periods). In contrast, we find that in down-markets, market skewness and kurtosis are not priced risk factors, while the price of market skewness risk is significantly negative and the price of kurtosis risk is positive in up-markets. However, the previously reported results for skewness and kurtosis are counterintuitive, strictly violate the risk compensation principles and, therefore, do not support a risk-based explanation. The results persist even after controlling for the Fama-French and Carhart factors