with Raymond Kan and Xiaolu Wang, 2020, working paper. [pdf coming soon].Sharpe ratios and squared Sharpe ratios are often used to compare the performance of different investment strategies or different asset pricing models. Typically, inference on the difference in sample Sharpe ratios or squared Sharpe ratios of two investment strategies is based on asymptotic analysis, while a finite-sample analysis of differences in sample Sharpe ratios and squared sample Sharpe ratios has been largely missing in the literature. In this paper, we provide an exact finite-sample analysis of these sample quantities under multivariate normality. In addition, we identify situations where the asymptotic tests do not provide accurate inferences in finite samples. Finally, we show how our finite-sample inference tools can be used in practice and illustrate the advantages of the proposed finite-sample tests over the existing asymptotic tests using Monte Carlo simulations and an empirical illustration.