IntermediateRisk & PerformancePython
Finance, Omega Ratio¶
The Sharpe ratio squeezes a whole return distribution into a mean and a standard deviation, which throws away everything interesting about its shape. The Omega ratio keeps the shape. You pick a threshold return that matters to you, then compare all the gains above it to all the shortfalls below it. The answer uses every moment of the distribution, skew and fat tails included, without ever having to estimate them.
An Omega of one means the gains above your bar exactly balance the losses below it. Above one the strategy earned more than it gave up relative to that bar. Because the threshold is yours to choose, one track record has a whole Omega curve rather than a single score, and that curve is where the insight lives.
The pieces¶
excess_gains_and_losses(returns, threshold)splits the series into the average gain above the bar and the average shortfall below it, both reported as positive numbers.omega_ratio(returns, threshold)divides the first by the second. This is the headline number.omega_curve(returns, thresholds)evaluates the ratio across a range of bars and returns the pairs, so you can see how quickly a strategy fades as you demand more of it.annual_threshold_to_periodic(annual, periods_per_year)converts a yearly bar like five percent into the per period rate the other functions expect.
Reading the number¶
At a threshold of zero the Omega ratio simply asks whether the ups outweigh the downs. As you raise the bar the ratio always falls, because more of the distribution counts as shortfall. Two strategies can rank one way at a low bar and the opposite way at a high one. A fund that grinds out small steady gains beats a lottery ticket for a cautious investor, and the ordering can flip for an aggressive one. The crossing point of two Omega curves is the bar at which your preference should change.
Why keep the whole distribution¶
Standard deviation punishes upside surprises exactly as hard as downside ones, and it says nothing about asymmetry. Two funds with identical means and volatilities can hide very different tail behaviour, one clipping small losses while the other quietly accumulates crash risk. Omega sees the difference because it works directly on the observed returns rather than on two summary numbers. That makes it a natural companion to the Sharpe rather than a replacement, each answers a question the other cannot.
Example¶
from omega_ratio import omega_ratio, omega_curve, annual_threshold_to_periodic
returns = [0.004, -0.01, 0.006, -0.03, 0.012, 0.002, -0.005, 0.02]
print(omega_ratio(returns)) # gains versus losses around zero
bar = annual_threshold_to_periodic(0.05) # a five percent annual bar
print(omega_ratio(returns, bar)) # the same series judged harder
print(omega_curve(returns, [0.0, 0.001])) # how the score fades as the bar rises
A note on the edges¶
A series with no returns below the threshold has no shortfall to divide by, so the ratio is infinite, reported as positive infinity rather than a crash. A series sitting exactly on the threshold everywhere is reported as one, the neutral score. Both are honest answers to degenerate inputs.
Where to go next¶
- For the volatility based cousin see
Sharpe and Sortino Ratio. - For the drawdown based cousin see
Finance - Calmar Ratio. - For the broader toolkit of track record measures see
Quantitative Methods - Performance Analysis.
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