Existing literature on performance evaluation has used wide variety of performance measures to estimate the risk-return benefits of a portfolio. This has raised questions about the reliability and accuracy of the performance measures. Investors are also concerned whether the choice of a performance measure has an impact on their investment decisions. This paper attempts to resolve this issue by comparing eight risk-adjusted and downside risk-adjusted performance measures using a sample of open-ended equity mutual funds of India, Singapore and Taiwan. We estimate the performance measures by creating a moving window of time and perform Spearman's rank correlation on them. Results show that performance measures that fall in the same category, for example Value-at-Risk (VaR) based measures, are highly correlated to each other, but as we go further and use performance measures that are different from each other, rank correlations decrease. In our study, rank correlations for Sortino ratio are significantly lower for Singapore and Taiwan markets. Therefore, we conclude that the choice of performance measure is significant as it affects the rankings of mutual funds.