Tests of the correlation between portfolio performance measures

This paper reports an investigation into measures of portfolio performance. The Sharpe ratio is the natural performance measure when asset returns come from any elliptically symmetric distribution, regardless of the investor utility function and subject only to regularity conditions. Under such distributions, the measures of portfolio performance which are in common use are monotonic functions of the Sharpe ratio. It is shown that for large sample sizes the correlation between measures of performance which are functions of the Sharpe ratio is asymptotically equal to unity. <p> The correct specification for tests of the correlation between portfolio performance measures is therefore the null hypothesis ρ = 1. A multivariate test of the correlations between several measures of performance is presented. This may be used in either a multivariate or bivariate setting. The paper presents a detailed example based on a number of FTSE indices. Performance measures are computed both parametrically using the normal distribution and using sample estimates. The new test does not lead to the rejection of the null hypothesis that all correlations are equal to unity. This suggests that despite the evidence of non-normality in returns there seems to be little gained in abandoning the Sharpe ratio.