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Nematrian Reference Library

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Introduction (partial) "In a recent paper, Shadwick and Keating (2002b) present a new measure of performance called Omega. According to the authors, Omega was developed to overcome the inadequacy of many traditional performance measures when applied to investments that do not have normally distributed return distributions. Unlike other measures of performance, Omega was developed with the intention to take the entire return distribution into account. In this paper we show that Omega is essentially the ratio of a call price to a put price. The result has several implications as far as this measure of performance is concerned. First, it provides a very intuitive explanation for what Omega is and what its limitations are. Second, it communicates to investment professionals what Omega is not a “significantly new” measure of risk since its building blocks (i.e., call and put options) have long been used to measure potential risk and return of investments. In a sense, Omega takes these well known building blocks and arranges them in a manner that provides an intuitive measure of risk/return. Third, one could use the vast body of research in the area of option pricing to obtain accurate estimates of Omega and to gain a better understanding of its properties. In particular, since most investments do not satisfy the basic assumptions of Black-Scholes option pricing model, non=parametric as well as approximate option pricing models (e.g., see Jarrow and Rudd (1982), Rubenstein (1998), Stutzer (1996)) can be used to obtain estimates of Omega. Finally, this paper presents a new version of Omega called Sharpe-Omega. This measure provides exactly the same information that Omega provides, but the formulation is very similar to the well known Sharpe ratio."

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