An Intersection–Union Test for the Sharpe Ratio

The Sharpe Ratio Efficient Frontier

We evaluate the probability that an estimated Sharpe ratio exceeds a given threshold in presence of non-Normal returns. We show that this new uncertainty-adjusted investment skill metric (called Probabilistic Sharpe ratio, or PSR) has a number of important applications: First, it allows us to establish the track record length needed for rejecting the hypothesis that a measured Sharpe ratio is b...

The mean–variance ratio test—A complement to the coefficient of variation test and the Sharpe ratio test

To circumvent the limitations of the tests for coefficients of variation and Sharpe ratios, we develop the mean-variance-ratio statistic to test the equality of the meanvariance ratios and prove that our proposed statistic is uniformly most powerful unbiased. In addition, we illustrate the applicability of our proposed test to compare the performances of stock indices.

The Sharpe Ratio Indifference Curve

Notes on the Sharpe ratio

Herein is an incomplete collection of facts about the Sharpe ratio, and the Sharpe ratio of the Markowitz portfolio. Connections between the Sharpe ratio and the t-test, and between the Markowitz portfolio and the Hotelling T 2 statistic are explored. Many classical results for testing means can be easily translated into tests on assets and portfolios. A ‘unified’ framework is described which c...

Sharpe Ratio Practice Note