The Risk of Skewness and Kurtosis in Oil Market and the Cross-Section of Stock Returns

We show that exposure to the risk of kurtosis in oil market drives the cross-section of stock returns from 1996 to 2014. The average monthly difference between the return of portfolio of stocks with low exposure and high exposure to the risk of kurtosis is -0.37%, showing that higher exposure to oil’s kurtosis risk will be penalized by lower average returns. We are able to confirm the significance of kurtosis risk within the statistical framework of Carhart 4-factor model. In contrast to the skewness risk, which is only a significant player in some of the sub-periods, kurtosis risk is keeping its significance through all sub-periods, as well as after taking market moments into account and within different maturities. The significance of the risk of skewness gets more evident moving from shorter to longer maturities. The risk of volatility, which has been shown to be a significant-priced risk in the cross-section of stock returns in literature, loses its significance after controlling for the third and fourth moments.