Interval Estimation for the Sortino Ratio and the Omega Ratio

In this paper asymptotic confidence intervals for the Sortino and Omega Ratio are proposed and analyzed. First the confidence intervals are derived under the strong assumption of temporal independence and identical distribution of the returns. Later they are obtained assuming that the process followed by returns is strictly stationary and α-mixing of a certain size. In order to evaluate the minimum sample size for a good coverage accuracy of the asymptotic confidence intervals, a simulation study is performed. It is obtained that the minimum sample sizes are very high, especially under the more realistic assumption of not-i.i.d. returns. keywords: financial performance ratio, dependent central limit theorem, strong mixing condition, coverage probability, GARCH model.