From distribution areas to a calculation you can audit
Keating and Shadwick define Omega using the cumulative return distribution F: the area under 1 - F above L divided by the area under F below L. For an empirical sample of n equally weighted returns, those areas equal sum(max(R - L, 0)) / n and sum(max(L - R, 0)) / n. The common n cancels in the ratio. This uses the sizes of threshold exceedances, not just how often returns beat the target.
- Use simple returns from consecutive, non-overlapping periods. With no external cash flows, a period return is ending account equity / starting account equity - 1. Include open-position valuations and the stated trading costs.
- L has the same units and period as R. A 1% monthly target is 0.01 alongside decimal monthly returns. An assumed 12% effective annual target corresponds to (1.12)^(1/12) - 1 = 0.948879% monthly, under a constant compound-rate convention.
- A return equal to L contributes zero to both sides. A positive return below L still counts as a shortfall: +1% is 1 percentage point below a +2% target.
- With unequal observation probabilities, use the same probability weights in both sums. Do not mix a weighted upside average with an unweighted downside average.