Lucio De Capitani

We study the estimators of three financial performance measures: the Sharpe Ratio, the Mean Difference Ratio and the Mean Absolute Deviation Ratio. The analysis is performed under two sets of assumptions. First, the case of i.i.d. Normal returns is considered. After that, relaxing the normality assumption, the case of i.i.d. returns is investigated. In both situations, we study the bias of the estimators and we propose their bias-corrected version. The exact and asymptotic distribution of the three estimators is derived under the assumption of i.i.d. Normal returns. Concerning the case of i.i.d. returns, the asymptotic distribution of the estimators is provided. The latter distributions are used to define exact or asymptotic confidence intervals for the three indices. Finally, we perform a simulation study in order to assess the efficiency of the bias corrected estimators, the coverage accuracy and the length of the asymptotic confidence intervals. Keywords: Financial Performance Measure, Sharpe Ratio, Mean Difference Ratio, Mean Absolute Deviation Ratio, Concentration Measures, Statistical Analysis of Financial Data.