The Omega ratio is a risk-return performance measure of an investment asset, portfolio, or strategy. It was devised by Con Keating and William F. Shadwick in 2002 and is defined as the probability weighted ratio of gains versus losses for some threshold return target. The ratio is an alternative for the widely used Sharpe ratio and is based on information the Sharpe ratio discards. Omega is calculated by creating a partition in the cumulative return distribution in order to create an area of losses and an area for gains relative to this threshold. The ratio is calculated as:
Ω ( θ ) = ∫ θ ∞ [ 1 − F ( r ) ] d r ∫ − ∞ θ F ( r ) d r , {\displaystyle \Omega (\theta )={\frac {\int _{\theta }^{\infty }[1-F(r)]\,dr}{\int _{-\infty }^{\theta }F(r)\,dr}},}
where F {\displaystyle F} is the cumulative probability distribution function of the returns and θ {\displaystyle \theta } is the target return threshold defining what is considered a gain versus a loss. A larger ratio indicates that the asset provides more gains relative to losses for some threshold θ {\displaystyle \theta } and so would be preferred by an investor. When θ {\displaystyle \theta } is set to zero the gain-loss-ratio by Bernardo and Ledoit arises as a special case. Comparisons can be made with the commonly used Sharpe ratio which considers the ratio of return versus volatility. The Sharpe ratio considers only the first two moments of the return distribution whereas the Omega ratio, by construction, considers all moments.
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