Free tool · Deflated Sharpe calculator
Is my backtest luck?
Try enough variants of a strategy and the best one will look good by chance alone. Enter your best backtest’s Sharpe ratio and how many variants you tried. The Deflated Sharpe Ratio estimates how much of that result the search itself could explain.
Calculator
Evidence of skill
95.9% deflated Sharpe probability
After allowing for the 50 variants tried, the probability that the true Sharpe ratio is above zero is 95.9%. That clears the 95% bar our audits use.
Statistics, not investment advice.
Worked examples
Same Sharpe, different stories
The number of variants tried matters as much as the Sharpe ratio itself. Load any row into the calculator.
| Case | Sharpe | N | Data | Noise best | DSR | Verdict | |
|---|---|---|---|---|---|---|---|
| One pre-registered idea | 1.20 | 1 | 3 yrs daily | 0.00 | 98.1% | Evidence of skill | |
| The same Sharpe after a 200-setting grid search | 1.20 | 200 | 3 yrs daily | 1.60 | 24.6% | Mostly luck | |
| Indicator sweep, longer sample | 1.80 | 50 | 5 yrs daily | 1.02 | 95.9% | Evidence of skill | |
| Bailey & López de Prado’s example: skew −3, kurtosis 10, trial variance 0.5 | 2.50 | 100 | 5 yrs daily | 1.79 | 90.1% | Inconclusive | |
| Monthly strategy with a fat left tail (skew −1, kurtosis 6, trial variance 0.1) | 1.00 | 20 | 10 yrs monthly | 0.60 | 85.6% | Inconclusive |
The paper’s own example uses 1,250 daily returns and reports a deflated Sharpe of 0.9004; this page uses 252 trading days a year (1,260 returns) and gets 0.9006. Its per-day noise benchmark, 0.1132, is reproduced exactly with 250 days a year.
How this works
Three steps, all published
1. How good does the best of N noise strategies look?
Take N strategies with no skill at all. Their backtested Sharpe ratios still scatter around zero, with variance V. The best of them is expected to reach roughly
SR0 = √V · [ (1 − γ) · Φ−1(1 − 1/N) + γ · Φ−1(1 − 1/(N·e)) ]
where γ ≈ 0.5772 is the Euler–Mascheroni constant, Φ−1 is the inverse standard normal distribution and e is Euler’s number. This is the “expected best Sharpe from noise” above. By default V = 1/years, the sampling variance of an annualised Sharpe estimate when the true Sharpe is zero. That is what our audits assume when the returns of every variant are not supplied. Variants that are near-copies of each other behave like fewer independent trials, so if yours are highly correlated the effective N is lower than the count; if you tried things you have forgotten, it is higher.
2. Is your Sharpe clearly above that bar?
The Deflated Sharpe Ratio is the Probabilistic Sharpe Ratio measured against SR0, using per-period Sharpe ratios (annual ÷ √periods per year) and T returns:
DSR = Φ( (SR − SR0) · √(T − 1) / √(1 − γ3·SR + (γ4 − 1)/4 · SR2) )
γ3 is skewness and γ4 raw kurtosis of the returns. Read DSR as the probability that the strategy’s true Sharpe ratio is above zero once the search over N variants is accounted for. The verdict bands follow the thresholds in our audit rubric: 95% or more is evidence of skill (an audit PASS), 80–95% is inconclusive (CAUTION), 50–80% is probably luck and below 50% is mostly luck (both FAIL).
3. How much history would settle it?
The minimum track record length is the number of returns needed for the observed Sharpe to be significant at 95%:
MinTRL = 1 + (1 − γ3·SR + (γ4 − 1)/4 · SR2) · ( z0.95 / (SR − SR*) )2
We show it twice: against SR* = 0 (a single strategy tested once) and against SR* = SR0 (the noise bar for N variants). If the Sharpe is below the noise bar, no amount of history at that Sharpe will clear it.
The chart shows the exact distribution of the best of N independent noise Sharpe ratios, whose density is N · φ(x/σ) · Φ(x/σ)N−1 / σ with σ = √V. The dashed line is the closed-form SR0, which slightly overstates that distribution’s mean (by about 1% at N = 50).
What this calculator does not check
It takes the Sharpe ratio as given. It cannot see look-ahead bias, survivorship, unrealistic fills or costs, a holdout that was peeked at, or a strategy that only worked in one regime. It assumes returns are independent from period to period. Those are what a full audit tests, on your actual returns.
Sources
Bailey, D. H. & López de Prado, M. (2014). The Deflated Sharpe Ratio: Correcting for Selection Bias, Backtest Overfitting and Non-Normality. Journal of Portfolio Management 40(5), 94–107. SSRN 2460551
Bailey, D. H. & López de Prado, M. (2012). The Sharpe Ratio Efficient Frontier. Journal of Risk 15(2), 3–44. (Probabilistic Sharpe Ratio, minimum track record length.) SSRN 1821643
Harvey, C. R. & Liu, Y. (2015). Backtesting. Journal of Portfolio Management 42(1), 13–28. SSRN 2345489
Harvey, C. R., Liu, Y. & Zhu, H. (2016). …and the Cross-Section of Expected Returns. Review of Financial Studies 29(1), 5–68.
Mertens, E. (2002). Comments on variance of the IID estimator in Lo (2002). Working paper. Lo, A. W. (2002). The Statistics of Sharpe Ratios. Financial Analysts Journal 58(4), 36–52.
The page uses the same formulas as our audit engine (open source on GitHub); a test checks that both give the same numbers to within one part in a million.
Want the full test?
This calculator works from a few summary numbers. A Quick Audit works from your rules and data: a reproduction of your backtest, a holdout and walk-forward check, the deflated Sharpe ratio with your real number of variants, parameter-plateau and cost sensitivity, year-by-year and regime stability, and an A–F fragility grade against a printed rubric.
Statistics, not investment advice.