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:

$\Omega (r)={\frac {\int _{{r}}^{\infty }(1-F(x))\,dx}{\int _{{-\infty }}^{r}F(x)dx}}$,

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

• Post-modern portfolio theory
• Upside potential ratio
• Sharpe ratio
• Sortino ratio
• Modern Portfolio Theory

References

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

External links

• How good an investment is property?
• "The Omega Measure: A better approach to measure investment efficacy" (PDF) (Press release). California: Propertini.