New Tests of Correlation and the Choice of Measures of Portfolio Performance

We show that subject to regularity conditions, for a given location-scale distribution all performance measures which are increasing functions of reward and decreasing functions of risk are monotonically increasing functions of the Sharpe ratio. For large sample sizes, the correlation between pairs of performance measures is asymptotically equal to unity. Therefore, a new specification for tests of correlation between pairs of performance measures, as well as a new multivariate test, is proposed. An empirical application is performed using UK Investment Trusts. We demonstrate that some performance measures have low correlations. Possible justifications are presented and discussed