Dealing with the Limitations of the Sharpe Ratio for Portfolio Evaluation

Abstract

Portfolio performance evaluation is an important criterion for selecting investment instruments. Traditionally Sharpe, Treynor, and Jensen’s Ratios are used to measure the performance of various portfolios, and for comparisons and ranking, Sharpe ratio being the most prominent performance measure. Owing to the limitation of the unrealistic assumption of Sharpe ratio that returns are normally distributed, many exponents have criticized its use as a performance measure. So a need arose to develop alternatives to Sharpe ratio or to put it in other words, overcoming the limitations of Sharpe ratio. More than 100 alternative risk-adjusted performance measures can be identified in literature, most of them attempting to remedy the shortcomings of the Sharpe ratio which relies on normally distributed returns. However, there is a fervent discussion in literature whether the choice of risk-adjusted performance measure actually matters or not. This paper focuses on the risk-adjusted performance measures which are applied to the return distribution of a portfolio of 6 mutual funds. The funds were first evaluated as per the Sharpe ratio and after it was found that the returns are not normally distributed, the portfolios were evaluated using the Adjusted Sharpe ratio and the Modified Sharpe ratio. It was found from the analysis that in many cases, the adjusted Sharpe ratio and the modified Sharpe ratio provided ranking results which were different from the traditional Sharpe ratio. In certain instances, the rankings were highly correlated to the Sharpe ratio as well as to each other.

Keywords: Sharpe Ratio, Normal Distribution, Adjusted Sharpe Ratio, Modified Sharpe Ratio, Ranks, Skewness, Kurtosis

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