Conditional Sharpe Ratios

•This paper demonstrates the connection between Sharpe ratio and stochastic dominance.•Conditional Sharpe ratios are statistical ordinates of conditional stochastic dominance.•CSR measures lower partial risk-adjusted returns of an asset under market conditions.•Multiple comparisons of CSRs allow us to examine dominance under market conditions.•CSR has predictability for portfolio future performance.

Facing investment choices, investors may care more about potentially excess losses in a downtrend market than excess gains in an upside market. Conditional Sharpe ratios (CSR) are statistical ordinates of conditional stochastic dominance (CSD) that measure lower partial risk-adjusted excess returns of an asset with respect to return distribution on the benchmark. A multiple comparison of serial CSR statistics thus provides an overall view of portfolio performance corresponding to different market scenarios. An example demonstrates that CSR is able to discriminate funds' downside performance which the conventional Sharpe ratio generally fails to do. A large out-of-sample analysis of US mutual fund shows that CSR has predictability for portfolio future performance.