The Sensitivity of the Asymptotic Variance of Performance Measures with Respect to Skewness and Kurtosis

Performance measures such as the Sharpe ratio and the information ratio are estimation subject to estimation error. Lo (2002) derives the explicit expressions for the statistical distribution of the Sharpe ratio. Bertrand and Protopopescu (2007) have extended his work to the bivariate case which corresponds to the Information ratio. In the present paper, we analyze the effects of skewness and kurtosis of portfolio and benchmark returns on the precision of the estimation of the Sharpe ratio and of the information ratio. We show that these effects are in line with what decision theory suggests about preferences of investors about skewness and kurtosis. Moreover, these effects are significant and can disturb the performance evaluation process if they are neglected.