Point and Interval Estimation for some financial performance measures

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. Firstly, the case of independent and identically normally distributed returns is considered. After that, relaxing the normality assumption, the case of independent and identically distributed returns is investigated. In both situations, we study the bias of the estimators and we propose their bias-corrected version. The exact and the 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 distributions of the estimators are provided. The latter distributions are used to define exact or large sample confidence intervals for the three indices. Finally, we perform a simulation study in order to assess the efficiency of the bias corrected estimator, the coverage accuracy and the length of the asymptotic confidence intervals