The Sharpe ratio is a commonly used measure of portfolio performance. But because it is based on mean-variance theory, this measure can only
be used in some restrictive cases, for example, when return distributions are normal. When return distributions are non-normal, the Sharpe ration can lead to misleading conclusions and unsatisfactory paradoxes, see Bernardo and Ledoit and Hodges . There have been proposed numerous universal performance measures that, in one way or the other, are alternatives to the Sharpe ratio and try to take into account non-normality of return distributions. For some examples, see Sortino and Price, Dowd , Stutzer, Keating and Shadwick , Gregoriou and Gueyie , Kaplan and Knowles , and Ziemba. The main drawback of many of these alternative performance measures is that they lack a solid theoretical underpinning. In this article we review the latest results on portfolio performance measures based on either expected utility theory or non-expected utility theory (the latter is opposed to the von Neumann and Morgenstern expected utility theory). The main purpose of this article is to show that unless we know exactly the investor’s preferences, and unless all investors share the same preferences, a single performance measure that is suitable for all investors cannot exist.
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