Is your Sharpe ratio real — or just the luckiest of N tries? This computes the Probabilistic Sharpe Ratio and the Deflated Sharpe Ratio from the Bailey–López de Prado framework, correcting your backtest for track length, non-normal returns, and the size of the search that produced it — plus the approximate minimum backtest length your trial count demands.
Annualized Sharpe required for DSR = 0.95 as the number of trials grows, at your track length, skew and kurtosis. The dot is you.
Every number above is only as honest as N — and N is self-reported, here and everywhere. Run a thousand backtests, publish the best, type N=10, and the correction for luck quietly evaporates. A thousand honest backtests with only the winner published is a lie that contains no lie.
MIZAN closes that door: every trial is committed to a Merkle tree before evaluation, N becomes the tree's leaf count — not a number anyone types — and the deflation is recomputed inside a zero-knowledge proof, without revealing the strategies. The engine's first published verdict was against its own maker's flagship: DSR 0.68, not significant, published as-is.
Read the paper → How it works → Prove yours →PSR (Bailey & López de Prado, 2012): the probability that the true Sharpe exceeds a benchmark SR*, using the per-period Sharpe, n observations, and the skewness γ₃ and kurtosis γ₄ of returns: PSR = Φ[ (SR − SR*)·√(n−1) / √(1 − γ₃·SR + ((γ₄−1)/4)·SR²) ].
DSR (Bailey & López de Prado, 2014): the PSR evaluated at SR* = the expected maximum Sharpe of N independent unskilled trials, E[max] ≈ σ(SR)·[ (1−γ)·Φ⁻¹(1−1/N) + γ·Φ⁻¹(1−1/(N·e)) ], with γ ≈ 0.5772 (Euler–Mascheroni) and σ(SR) the standard deviation of Sharpe across the trials.
Minimum backtest length (Bailey, Borwein, López de Prado & Zhu, 2014): the approximate track length in years below which the expected maximum Sharpe of N unskilled trials exceeds your annualized Sharpe — reported here from the same E[max] expression; the paper's simple upper bound is 2·ln(N)/SR².
Bailey, D.H. & López de Prado, M., "The Sharpe Ratio Efficient Frontier," Journal of Risk 15:2 (2012) · Bailey, D.H. & López de Prado, M., "The Deflated Sharpe Ratio," Journal of Portfolio Management 40:5 (2014) · Bailey, Borwein, López de Prado & Zhu, "Pseudo-Mathematics and Financial Charlatanism," Notices of the AMS 61:5 (2014). Full lineage: the twenty authors.
Attribution, not endorsement: the cited authors have not reviewed or endorsed this tool. Educational use; not investment advice.
The uncomfortable truth: there is no threshold that means anything by itself. A Sharpe of 2.0 from one pre-registered trial on ten years of data can be highly significant; the same 2.0 selected from a thousand tries on three years may be pure luck. The only honest answer is the deflated one — which is why this page exists.
Because the expected maximum of N random strategies grows with ln(N). Try enough things and one of them will clear any bar by chance. The deflation subtracts exactly that expected luck.
Only as far as you trust their N — which is the open wound in the entire framework, and the thing that can be made structurally impossible to misreport. That is the engine's job, not a calculator's.