The Skewness of the Stock Market at Long Horizons

Abstract

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, i.e. covariance between variance and lagged returns. We provide similar results for kurtosis. An application to US stock-index returns shows that skew is large and negative and attenuates only slowly as one moves from monthly to multi-year horizons.