The low return distortion of the Sharpe ratio

Abstract

This article formalizes the undesirable property of the Sharpe ratio that a fund with a certain poor performance can increase its Sharpe ratio in a prospective period by generating a sufficiently negative excess return. Specifically, we set out the conditions that a fund must meet to be exposed to this kind of effect. Furthermore, we provide a formal statement of the excess return value that needs to be deceeded to obtain a higher Sharpe ratio. In an empirical application, we investigate the practical relevance of this kind of distortion. We find that an economically significant number of funds listed in the CISDM hedge fund database have at least once reported a sufficiently negative return, causing an increased Sharpe ratio fund performance.