Omega Ratio

The Omega Ratio (Keating & Shadwick, 2002) is a non-parametric performance measure that uses the entire return distribution rather than its first two moments. For a threshold τ (typically zero or the risk-free rate), Omega is the ratio of the probability-weighted gains above τ to the probability-weighted losses below it.

Formula

Ω(τ) = ∫_τ^∞ (1 − F(x)) dx   /   ∫_-∞^τ F(x) dx

where F(x) is the cumulative return distribution. The numerator is the expected gain above τ, the denominator the expected loss below it. By construction Ω(τ) = 1 at τ = mean return.

Why Omega improves on Sharpe

• ·Captures skewness and kurtosis: two strategies with identical Sharpe but different tail behaviour have different Omegas.
• ·Threshold-aware: a pension fund with a 4% liability target evaluates Omega at τ = 4%; a hedge fund at τ = 0.
• ·Non-parametric: no Gaussian assumption — Omega works on empirical distributions or Monte Carlo samples directly.

Reading Omega

Ω > 1 means probability-weighted gains exceed probability-weighted losses at the threshold. Ω = 2 means gains above τ are twice the magnitude of losses below τ — a strong asymmetric profile. Strategies with positive skew (trend-following, long convexity) typically show Omega much higher than their Sharpe would predict.

How MEDGE Capital uses Omega

Max Omega is one of the 12 optimization objectives. The user-selected threshold parameter τ defaults to 0 (gains vs losses) but can be set to a custom target return — useful for funds with liability matching requirements.