Asset Pricing When Returns are Nonnormal: Fama-French Factors vs. Higher-Order Systematic Co-Moments

Abstract

A number of papers (notably Fama and French (1993, 1995)) find that non-market risk factors, such as size and the book-to-market ratio, are priced by investors. We test whether these other risk factors are merely proxies for omitted higher-order market-risk factors. Using size-sorted portfolio returns at daily, weekly, monthly, quarterly, and semi-annual intervals, we find in every case that the distribution of returns differs significantly from normality. Since returns are not normal, we expect higher-order co-moments to matter to investors. We show that adding systematic co-moments (but not standard moments) of order 3 through 10 reduces the explanatory power of the Fama-French factors to insignificance in almost every case.

JEL Classification: G12