Threshold gains divided by shortfalls
For returns r₁ through rN and target τ, calculate G = Σ max(rᵢ − τ, 0) and S = Σ max(τ − rᵢ, 0). Omega equals G/S when S is positive. Returns exactly on the target contribute to neither sum. The calculation does not annualize either the observations or the ratio. Enter a 1% target as 1 when the return entries are percentages; using 0.01 would ask a different question.
How changing the target changes the answer
Consider returns of −2%, 1%, and 4%. With a zero target, gains total five percentage points and shortfalls total two, producing Omega of 2.5. With a 1% target, gains total three points and shortfalls also total three, producing 1.0. The same returns can therefore have very different ratios under different objectives. Neither target changes what actually happened to the sample; it changes how the outcomes are evaluated.
Read the denominator before ranking strategies
With no observations below target, there is no finite gain-to-shortfall ratio; a missing denominator should never be presented as proven safety. A sample sitting entirely on target has neither gains nor shortfalls. Omega ignores the order of returns, so it cannot distinguish a clustered loss sequence from scattered losses of identical size. Match sample periods, fee treatment, and targets when comparing strategies, and examine drawdowns separately if the path of capital matters.