Accurate Inference on Sharpe Ratios and Testing Their Homogeneity via Bartlett-Type Correction

The Sharpe ratio is a prominent risk-adjusted performance measure used in investment analysis. In this paper, we assume that a random sample is available from a normal distribution and propose a simple and accurate method for inference on the Sharpe ratio. Moreover, the rate of convergence of the proposed method is derived. The method relies on a Bartlett-type correction to the likelihood ratio statistic, yielding improved finite-sample accuracy. The methodology is further extended to the problem of testing the homogeneity of Sharpe ratios across multiple populations or investment strategies, an issue that remains relatively underexplored in the literature. Real-life mutual funds data are used to illustrate the differences in interval estimates obtained by the proposed method and existing approaches, as well as to demonstrate the application of the homogeneity test. Extensive simulation studies confirm the extreme accuracy of the proposed method and the reliability of the testing procedure even when the sample size is small.