Long-Horizon Stock Returns Are Positively Skewed

At long horizons, multiplicative compounding induces strong-to-extreme positive skewness into stock returns; the magnitude of the effect is primarily determined by single-period volatility. Consequently, at horizons greater than five years, returns --individual or portfolio-- will be positively skewed under reasonable parametrizations. From an investor perspective, the strong positive skewness implies that the mean compound return will serve as a poor guide for typical long-horizon outcomes. Moreover, the large effects of compounding on higher-order moments are shown to affect the validity of Taylor expansions used to approximate preferences for skewness, when applied to returns of annual or longer horizons.