Portfolio Performance Measurement: Monotonicity with Respect to the Sharpe Ratio and Multivariate Tests of Correlation

This paper shows that there is a broad class of probability distributions for fund returns under which many well-known performance measures are monotonically increasing functions of the Sharpe ratio. It also reports results showing conditions under which monotonicity can fail. The paper shows that under regularity conditions the asymptotic correlation between pairs of performance measures is equal to unity. This result is used to derive unconditional and conditional multivariate tests of unit correlation between an arbitrary number of performance measures. A study of UK investment trusts supports the results.