Performance measurement is one of the most studied subjects in financial literature. Since the introduction of the Sharpe ratio in 1966, a large variety of newmeasures has appeared constantly in scientific journals as well as in practitioners’ publications. The most complete and significant studies
of performance measures, so far, have been written by Aftalion and Poncet, Le Sourd, Bacon, and Cogneau and Hubner. A review of the most recent literature led us to collect several dozen measures that we classify into four families. We first present the class of relative measures, starting with the
Sharpe ratio. Secondly, we analyse absolute measures, beginning with the most famous one - the Jensen alpha. Thirdly, we study general measures based on specific features of the return distribution, where the pioneering contributions are those of Bernardo and Ledoit, and Keating and Shadwick. Finally, the fourth set concerns a few measures that explicitly take into account the investor’s utility functions
Several recent finance articles use the Omega measure (Keating and Shadwick, 2002), defined as a ratio of potential gains out of possible losses, for gauging the performance of funds or active strategies, in substitution of the traditional Sharpe ratio, with the arguments that return distributions are not Gaussian and volatility is not always the relevant risk metric. Other authors also use Omega for optimizing (non-linear) portfolios with important downside risk. However, we question in this article the relevance of such approaches. First, we show through a basic illustration that the Omega ratio is inconsistent with the Second-order Stochastic Dominance criterion. Furthermore, we observe that the trade-off between return and risk corresponding to the Omega measure, may be essentially influenced by the mean return. Next, we illustrate in static and dynamic frameworks that Omega-based optimal portfolios can be closely associated with classical optimization paradigms depending on the chosen threshold used in Omega. Finally, we present robustness checks on long-only asset and hedge fund databases, that confirm our results.
Following the recent crisis and the revealed weakness of risk management practices, regulators of developed markets have recommended that financial institutions assess model risk. Standard risk measures, such as the value-at-risk (VaR), emerged during the 1990s as the industry standard for risk management and become today a key tool for asset allocation. This paper illustrates and estimates model risk, and focuses on the evaluation of its impact on optimal portfolios at various time horizons. Based on a long sample of US data, the paper finds a non-linear relation between VaR model errors and the horizon that impacts optimal asset allocations.
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