Generalized Performance Measures: Optimal Overweighing of Fees Relative to Sample Returns

Abstract

Performance measures such as alpha and the Sharpe ratio are typically based on sample returns net of fees. This implies the same weighing to sample returns and to fees. However, sample return parameters are noisy estimates of true parameters, while fees are known with certainty. Thus, intuition suggests that fees should be given more weight than sample returns. We formalize this intuition, and derive the optimal overweighing of fees. We show that the resulting generalized performance measures are better predictors of future net performance than the standard performance measures, and they better explain future fund flows.