Confidence and Power of the Sharpe Ratio under Multiple Testing

Abstract

Articles in the financial literature typically estimate the p-value associated with an investment strategy’s performance, without reporting the power of the test used to make that discovery. In this paper I provide analytic estimates to Type I and Type II errors for the Sharpe ratios of investments, and derive their familywise counterparts. These estimates allow researchers to carefully design experiments and select investments with high confidence and power.

Keywords: True positive, false positive, power, significance, recall, multiple testing, non-Normal returns, clustering, machine learning

JEL Classification: G0, G1, G2, G15, G24, E44