The volatility of the stock market index return is an indicator of market-wide risk, and the CAPM predicts that it is a determinant of the market equity premium. Recent studies by Ang, Hodrick, Xing and Zhang (2006) and Adrian and Rosenberg (2008) also demonstrate that contrary to the CAPM intuition, market-wide volatility risk is priced in the cross-section of stock returns. Given these findings, and given the overwhelming evidence in the literature that market-wide skewness and kurtosis are important indicators of market-wide risk, and that those risks do not co-vary perfectly with volatility risk, an investigation of higher moments of the market return as pricing factors in the cross-section of stock returns seems worthwhile.
We extend the investigation of Ang et al. (2006) and examine how market skewness and kurtosis risks affect the cross-section of stock returns within the context of the Intertemporal Capital Asset Pricing Model (ICAPM) of Merton (1973). Our hypothesis is that the market volatility, skewness, and kurtosis are all state variables reflecting the future investment opportunity set. The ICAPM then predicts that innovations in market volatility, skewness, and kurtosis must be priced risk factors in the cross section of risky asset returns.
We empirically test this hypothesis using moments of the market return implied by S&P 500 index options, extracted using the methodology of Bakshi and Madan (2000), Carr and Madan (2001) and Bakshi, Kapadia, and Madan (2003). These moments are thus forward looking.
The moments are computed every day, so the resulting estimates are also genuinely conditional. This approach avoids the traditional trade-off problem with estimates of higher moments from historical returns data, which need to use long windows to increase precision, but short windows to obtain conditional rather than unconditional estimates.