Ex Post Portfolio Performance with Predictable Skewness and Kurtosis

This paper examines the ex-post performance of optimal portfolios with predictable returns, when the investor horizon ranges from one month to ten years. Due to the investor's ability to anticipate shifts from bull to bear markets, predictability involves the risk premium, volatility and correlations, and may extend to third and fourth moments. We analyze three different equity portfolios datasets, each covering more than eight indexes, including the commonly used US Industry and International Book-to-Market portfolios. Allowing for regimes improves portfolio performance for at least a subset of investment horizons in all datasets. Despite large non-normalities in both the Industry and the BM dataset, gains from predicting higher order moments obtain only in the latter - where third rather than fourth moments matter. The equally weighted strategy usually leads to lower ex-post performance measures than optimizing ones, despite simple econometrics and power utility preferences underlying optimal strategies.