Why Does Skewness Matter? Ask Kurtosis.

Abstract

I investigate the relationship between measures of skewness and expected stock returns. Forcing the data to fit a linear model, past research finds only a negative relationship between these variables. Using a novel methodology that endogenously estimates breakpoints in the relationship between two variables, I find three distinct zone. Expected returns are decreasing in skewness, but only for a region of relatively low absolute values of skewness. For distributions which are highly left- or right-skewed, the relationship is actually positive. Moreover, I find that kurtosis plays a major role in mediating this relationship. Adding measures of the fourth moment to all models tested turns all skewness coefficients negative, and most statistically insignificant. Relying on probability theory, I provide a theoretical framework that supports all empirical findings.