The Effects of the Sample Size, the Investment Horizon and Market Conditions on the Validity of Composite Performance Measures: A Generalization

In our previous study, the empirical relationship between Sharpe measure and its risk proxy was shown to be dependent on the sample size, the investment horizon and market conditions. This important result is generalized in the present study to include Treynor and Jensen performance measures. Moreover, it is shown that the conventional sample estimate of ex-ante Treynor measure is biased. As a result, the ranking of mutual fund performance based on the biased estimate is not an unbiased ranking as implied by the ex-ante Treynor measure. In addition, a significant relationship between the estimated Jensen measure and its risk proxy may produce a potential bias associated with the cumulative average residual technique which is frequently used for testing the market efficiency hypothesis. Finally, the impact of the dependence between risk and average return in Friend and Blume's findings is also investigated.