Robust performance hypothesis testing with the Sharpe ratio

Olivier Ledoit and Michael Wolf


Applied researchers often test for the difference of the Sharpe ratios of two investment strategies. A very popular tool to this end is the test of Jobson and Korkie [Jobson, J.D. and Korkie, B.M. (1981), Performance hypothesis testing with the Sharpe and Treynor measures, Journal of Finance, 36:889908], which has been corrected by Memmel [Memmel, C. (2003), Performance hypothesis testing with the Sharpe ratio, Finance Letters, 1:2123]. Unfortunately, this test is not valid when returns have tails heavier than the normal distribution or are of time series nature. Instead, we propose the use of robust inference methods. In particular, we suggest to construct a studentized time series bootstrap confidence interval for the difference of the Sharpe ratios and to declare the two ratios different if zero is not contained in the obtained interval. This approach has the advantage that one can simply resample from the observed data as opposed to some null-restricted data. A simulation study demonstrates the improved finite sample performance compared to existing methods. In addition, two applications to real data are provided.

The code in Matlab and in R for the estimator proposed in the paper can be downloaded for free from the website of my co-author Michael Wolf in the Department of Economics of the University of Zurich.

Journal of Empirical Finance, Volume 15, Issue 5, December 2008, pages 850-859

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