Inference on the Sharpe ratio via the upsilon distribution

TL;DR

This paper introduces the upsilon distribution and demonstrates its application in frequentist and Bayesian inference on the Sharpe ratio, including hypothesis testing and interval estimation, even in factor models.

Contribution

It presents the upsilon distribution as a new statistical tool for inference on the Sharpe ratio, extending its use to factor models of returns.

Findings

The upsilon distribution encompasses Lecoutre's lambda-prime distribution.

It enables hypothesis testing and confidence interval construction for the Sharpe ratio.

Applications include both independent samples and factor models.

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.