# Omega ratio

~~The ~~**Omega ratio** is a risk-return performance measure of an investment asset, portfolio, or strategy. It was devised by Keating & Shadwick in 2002 and is defined as the probability weighted ratio of gains versus losses for some
threshold return target.^{[1]} 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:

- ,

where F is the cumulative distribution function of the returns and r 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 r and so would be preferred by an investor. When r is set to zero the Gain-Loss-Ratio by Bernardo and Ledoit arises as a special case.^{[2]}

Comparisons can be made with the commonly used Sharpe ratio which considers the ratio of return versus volatility.^{[3]} The Sharpe ratio considers only the first two moments of the return distribution whereas the Omega ratio, by construction, considers all moments.

## See also

## References

- ↑ Keating & Shadwick. "A Universal Performance Measure" (PDF).
*The Finance Development Centre Limited*. UK. - ↑ Bernardo, Antonio E.; Ledoit, Olivier (2000-02-01). "Gain, Loss, and Asset Pricing".
*Journal of Political Economy*.**108**(1): 144–172. CiteSeerX 10.1.1.39.2638. doi:10.1086/262114. ISSN 0022-3808. - ↑ "Assessing CTA Quality with the Omega Performance Measure" (PDF).
*Winton Capital Management*. UK.