with Raymond Kan and Xiaolu Wang, 2020, working paper. [pdf coming soon].In this paper, we contrast finite-sample, asymptotic, and bootstrap tests of equality of Sharpe ratios and squared Sharpe ratios for the two-asset and two-tangency portfolio cases. We show that there are realistic scenarios where the asymptotic and bootstrap tests are unreliable. Moreover, we propose improved bootstrap tests and document their excellent performance using Monte Carlo simulations. Finally, we argue that the resampling method of Fama and French (2018) leads to biased estimates of the out-of-sample Sharpe ratios, and we show how unbiasedness can be achieved in their setting. Several empirical applications are considered to illustrate the relevance of our new results.