QUANTITATIVE TOOL
Bailey & López de Prado (2014). Corrects the observed Sharpe Ratio for multiple testing, non-normal returns, and short samples. The metric that separates real alpha from backtest overfitting.
— WHY IT MATTERS
When you test 20 strategies and pick the best one, the winner's Sharpe Ratio is biased upward. The more strategies you test, the higher the expected maximum Sharpe — even if all strategies have zero true skill. The Deflated Sharpe Ratio quantifies this bias and tells you the probability that your observed Sharpe is genuinely above what you'd expect by chance.
— CALCULATOR
The annualized Sharpe of the strategy you picked. This is usually your best-performing backtest or live result.
Total trading days in the backtest. E.g. 1 year ≈ 252, 2 years ≈ 504.
Count every strategy, parameter set, or variation you tested before picking this one.
0 = symmetric. Negative = occasional large losses. Most strategies: between −1 and 0.
3 = normal distribution. Above 3 = more extreme days than expected. Most strategies: between 3 and 6.
0 = completely different strategies. 1 = all basically the same. If unsure, 0.2–0.5 is a reasonable guess.
— RESULTS
Probability that the true Sharpe exceeds SR₀ (the expected maximum under null). Above 0.95 = statistically significant.
Verdict
Not significant. The observed Sharpe is likely explained by multiple testing alone.
Threshold SR₀
1.0461
Expected maximum Sharpe across N trials if all strategies have zero true skill.
Effective independent trials
8.2
Number of strategies adjusted for correlation.
Z-score
0.6221
Standard deviations above the threshold.
SR standard error
0.7296
Estimation uncertainty of the Sharpe Ratio.
— METHODOLOGY
Correlated strategies are not independent tests. We compute the effective number of trials: N_eff = N(1 − ρ̄) + ρ̄. Perfectly correlated strategies collapse to a single trial.
Using the Euler-Mascheroni correction, we compute SR₀ — the Sharpe you'd expect from the best of N_eff strategies, assuming all have zero true skill: SR₀ ≈ √(1/(T−1)) × [(1−γ)Φ⁻¹(1−1/N) + γΦ⁻¹(1−1/(Ne))].
The PSR incorporates skewness and kurtosis into the standard error of the SR estimator, then computes the probability of exceeding the threshold: DSR = Φ[(ŜR − SR₀)√(T−1) / √(1 − γ₃ŜR + ((γ₄−1)/4)ŜR²)].
— FORMULAS
DSR = Φ[(ŜR − SR₀)√(T−1) / √(1 − γ₃ŜR + ((γ₄−1)/4)ŜR²)]
Probability that the true SR exceeds the selection-bias threshold SR₀. Values above 0.95 indicate genuine skill at 95% confidence.
SR₀ ≈ √V[ŜR] × [(1−γ)Φ⁻¹(1−1/N) + γΦ⁻¹(1−1/(Ne))]
Expected maximum Sharpe from N independent trials under null. γ = 0.5772 (Euler-Mascheroni). Grows as √(2·ln(N)) for large N.
σ(ŜR) = √[(1 − γ₃ŜR + ((γ₄−1)/4)ŜR²) / (T−1)]
Accounts for non-normality. Negative skewness and fat tails increase estimation uncertainty.
N_eff = N(1 − ρ̄) + ρ̄
Adjusts for correlation between strategies. ρ̄ = 0 gives N independent trials; ρ̄ = 1 collapses to 1 trial.
— REFERENCE
Bailey, D.H. & López de Prado, M. (2014). "The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting, and Non-Normality." The Journal of Portfolio Management, 40(5), 94–107.
— FAQ
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