A Correction for Classic Performance Measures

Abstract

Non-normality in asset returns is now a common feature of financial markets. However, many practitioners as well as investors do still refer to classic risk adjusted performance measures to assess their investment. For example, Sharpe and Treynor ratios are designed for a Gaussian world. Then, employing them for a performance assessment prospect relative to the risk borne is a biased approach. If we look for consistency in risk assessment and in asset performance valuation, we need to look for robust methods or tools. Moreover, the well-known mathematical consistency and numerical tractability concerns drive our preference for simple methods. Under this setting, we propose to account in a simple way and to some extent for the skewness and kurtosis patterns describing the deviations from normality. We adjust therefore the classic Sharpe and Treynor ratios to asymmetries in the downside and upside deviations from the mean values of asset returns. Specifically, the adjusted Sharpe and Treynor ratios are weighted by the upside and downside deviation risks. Accounting for skewness and kurtosis changes generally the ranking of hedge fund performance. Moreover, the obtained adjusted performance measures capture well the skewness and/or kurtosis patterns in hedge fund returns depending on the targeted investment strategy.