Deflated Sharpe Ratio Calculator
What is the Deflated Sharpe Ratio?
The deflated Sharpe ratio (DSR), developed by Bailey & López de Prado, adjusts your observed Sharpe ratio for multiple testing. If you tested 100 strategies and picked the one with the highest Sharpe, that Sharpe is inflated by selection bias. DSR tells you the "true" Sharpe after accounting for how many strategies you tested.
Why It Matters
Most published Sharpe ratios are inflated. If a quant tests 50 parameter combinations and reports the best Sharpe, they're reporting the maximum of 50 random draws — not the true edge. The deflated Sharpe corrects for this by subtracting the expected maximum Sharpe from the observed Sharpe.
The Formula
The deflated Sharpe uses three corrections:
- Multiple trials: E[max] ≈ (1-γ)·Φ⁻¹(1 - 1/N) + γ·Φ⁻¹(1 - 1/(N·e)), where N is the number of trials and γ is Euler's constant
- Non-normality: variance_factor = 1 - skew·SR + ((kurt-1)/4)·SR²
- Effective Sharpe: SR_effective = SR_observed / sqrt(variance_factor)
DSR = SR_effective - E[max]
If DSR > 0, your strategy likely has real edge even after accounting for multiple testing.
How dMoERA Uses This
dMoERA's 7-stage validation pipeline computes the deflated Sharpe ratio for every uploaded strategy. A strategy must pass the DSR check (among others) before it's allowed into the live router. This prevents lucky backtests from getting real capital.
Frequently Asked Questions
- What is a good deflated Sharpe ratio?
- A deflated Sharpe ratio above 0 indicates your strategy likely has real edge after accounting for multiple testing. Values above 0.5 are strong; values above 1.0 are exceptional.
- How many trials should I enter?
- Enter the number of strategy variations, parameter combinations, or backtests you ran before selecting this strategy. If you tested 20 parameter sets, enter 20. If you only tested one, enter 1.
- Why does skewness and kurtosis matter?
- The standard Sharpe ratio assumes returns are normally distributed. Strategies with negative skew (fat left tail) or high kurtosis (fat tails both sides) are riskier than Sharpe suggests. The deflated Sharpe penalizes these.
- How is this different from the regular Sharpe ratio?
- The regular Sharpe ratio doesn't account for how many strategies you tested or the shape of your return distribution. The deflated Sharpe corrects for both, giving a more honest measure of edge.
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