Normal return gaps: Dispersion illuminates diversification

Abstract

Despite ever more sophisticated risk management and measurement, investment professionals have generally overlooked a simple but powerful measure of relative performance and portfolio diversification-the normal return gap. The authors develop a generalized specification of the expected difference in returns between two investments based on the folded normal distribution. Even highly correlated investments can have quite large expected return gaps. They then demonstrate the applicability of this dispersion to capital market forecasts, manager selection, performance evaluation, style tilts, sector bets, socially responsible investing, manager combinations, wash sale taxation, and rebalancing.