On testing the equality of multiple Sharpe ratios, with application on the evaluation of iShares

ABSTRACT Extending the work of Jobson and Korkie (1981), Lo (2002) and Memmel (2003), this paper applies the technique of the repeated measures designed to develop a multivariate Sharpe ratio statistic to test the hypothesis of the equality of multiple Sharpe ratios. We also work out the asymptotic distribution of the statistic and its properties. To demonstrate the superiority of our proposed statistic over the traditional pairwise Sharpe ratio test, we illustrate our approach by testing the equality of the Sharpe ratios for 18 iShares. Whereas the pairwise Sharpe ratio test shows that the performance of all 18 iShares is indistinguishable, our test results reject the equality of the Sharpe ratios in each year as well as in the entire sample, implying that the 18 iShares perform differently in each year as well as in the entire sample, with some outperforming others in the market. The multivariate Sharpe ratio statistic developed in our paper provides investors with a tool to evaluate their portfolios’ performance and enables them to make wiser decisions in their investments.