Deviation from Normality and Sharpe Ratio Behavior : A Brief Simulation Study

Sharpe ratio has been widely used in the portfolio management industry as well as fund industry (Robertson, 2001; Scholz and Wilkens, 2005). Users often forget the main core assumption describing the appropriateness of such risk-adjusted performance measure, namely asset return normality. This concern is of huge significance insofar as performance indicators drive the asset allocation policy, performance forecasts and cost of capital assessment among others (Farinelli et al., 2008; Lien, 2002; Christensen and Platen, 2007). We employ a brief simulation study to assess the impact of deviations from normality on the performance measures and rankings inferred from Sharpe ratio's estimates. Our analysis allows for assessing the possible bias in both performance measurement and ranking, which results from the existence and the magnitude of skewness and kurtosis patterns in asset returns. We propose a method to extract an unbiased performance measure (i.e. unbiased Sharpe ratios) from observed classic Sharpe ratios after accounting for the returns' skewness bias