The skew risk premium in the equity index market. Working paper

We develop a new method for measuring moment risk premiums. We find that the skew premium accounts for over 40 % of the slope in the implied volatility curve in the S&P 500 market. Skew risk is tightly related to variance risk, in the sense that strategies designed to capture the one and hedge out exposure to the other earn an insignificant risk premium. This provides a new testable restriction for asset pricing models trying to capture, in particular, disaster risk premiums. We base our results on a general trading strategy by replicating contracts that swap implied for realized conditional asset moments. (JEL G01, G11, G12, G13) We provide strong empirical evidence for the coexistence of both skew and variance risk premiums in the equity index market. We show that the two premiums are driven by common factors. Strategies to exploit the variance risk premium—writing options at all strikes–and strategies to exploit the skew risk premium–writing low strike options and buying high strike options—are both profitable. But the skew strategy is highly exposed to variance risk, and once that is hedged away, the remaining risk premium is insignificantly differen