The Economic Value of Timing Higher Order (Co-)Moments in Bull and Bear Markets

Abstract

We examine 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 forecast shifts between bull and bear markets, predictability involves the risk premium, volatility and correlations, and may extend to third and fourth moments. We analyze three different equity portfolios data sets, each covering more than eight indexes, including commonly used US Industry and International Book-to-Market portfolios. Allowing for regimes improves portfolio performance for at least a subset of investment horizons and in all data sets. Despite substantial non-normalities in both the Industry and the book-to-market data sets, gains from predicting higher order moments obtain only in the latter. However, tracking and forecasting bull and bear markets turns out to improve realized portfolio performance more generally. The equally weighted strategy leads to lower ex-post performance measures than optimizing ones.