Comparing Sharpe ratios: So where are the p-values?

Until recently, since Jobson and Korkie (1981), derivations of the asymptotic distribution of the Sharpe ratio that are practically useable for generating confidence intervals or for conducting one- and two-sample hypothesis tests have relied on the restrictive, and now widely refuted, assumption of normally distributed returns. This paper presents an easily implemented formula for the asymptotic distribution that is valid under very general conditions — stationary and ergodic returns — thus permitting time-varying conditional volatilities, serial correlation, and other non-iid returns behaviour. It is consistent with that of Christie (2005), but it is more mathematically tractable and intuitive, and simple enough to be used in a spreadsheet. Also generalised beyond the normality assumption is the small sample bias adjustment presented in Christie (2005). A thorough simulation study examines the finite sample behaviour of the derived one- and two-sample estimators under the realistic returns conditions of concurrent leptokurtosis, asymmetry, and importantly (for the two-sample estimator), strong positive correlation between funds, the effects of which have been overlooked in previous studies. The two-sample statistic exhibits reasonable level control and good power under these real-world conditions. This makes its application to the ubiquitous Sharpe ratio rankings of mutual funds and hedge funds very useful, since the implicit pairwise comparisons in these orderings have little inferential value on their own. Using actual returns data from 20 mutual funds, the statistic yields statistically significant results for many such pairwise comparisons of the ranked funds. It should be useful for other purposes as well, wherever Sharpe ratios are used in performance assessment.