On Testing the Equality of the 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 design to develop the Multiple Sharpe ratio test statistic to test the hypothesis of the equality of the 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 pair-wise Sharpe ratio test, we illustrate our approach by testing the equality of Sharpe ratios for the eighteen iShares. Whereas the pair-wise Sharpe ratio test show that the performance of all the 18 iShares are 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 test in our paper provides investors with a tool to evaluate their portfolio performances and enables them to make wiser decisions in their investments.

Keywords: MANOVA, Asymptotic distribution, delta-method, iShares

JEL Classification: C0, D81, G10