The Skewness of the Stock Market over Long Horizons

Higher moments of long-horizon returns are important for asset pricing but are hard to measure accurately using standard techniques. We provide theory showing that short-horizon (e.g., daily) returns can be used to construct precise estimates of long-horizon (e.g., annual) moments without making strong assumptions about the data-generating process. Skewness comprises two components: skewness of short-horizon returns and a leverage effect, that is, covariance between variance and lagged returns. We provide similar results for kurtosis. An application to U.S. stock index returns shows that skew is large and negative and attenuates only slowly as one moves from monthly to multiyear horizons.