Inference on the Sharpe ratio via the upsilon distribution

Abstract: The upsilon distribution, the sum of independent chi random variates and a normal, is introduced. As a special case, the upsilon distribution includes Lecoutre's lambda-prime distribution. The upsilon distribution finds application in Frequentist inference on the Sharpe ratio, including hypothesis tests on independent samples, confidence intervals, and prediction intervals, as well as their Bayesian counterparts. These tests are extended to the case of factor models of returns.