Statistical Inference for Risk-Adjusted Performance Measure

This paper examines the statistical properties of and significance tests for a popular risk-adjusted performance measure, the M-squared measure. Test statistics along with asymptotic moments and probability distributions developed by prior studies are reviewed and their applications to the M-squared measure are discussed. This paper demonstrates through an example that calculation of the analytic test statistic and the corresponding p-value can be performed easily using a spreadsheet or mathematical software. Results of significance tests using bootstrapping are similar to those based on the analytic solutions, suggesting that the analytic solution approach is a useful method for conducting statistical inference. The results appear relatively robust even in small samples