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.

TOPICS: Performance measurement, wealth management, manager selection, ESG investing

Key Findings

• • Even highly correlated investments can produce meaningful diversification; conversely, low correlations can produce small return gaps and, therefore, minimal diversification.

• • Normal return gaps between investments are often the same magnitude as the expected returns of the underlying assets.

• • Investors unaware of normal return gaps risk terminating worthy managers; establishing competitive “horse races” between managers is particularly unwise.