Deflated Sharpe Ratio Calculator
Enter a selected Sharpe ratio, observation count, skewness, raw kurtosis, independent-trial count and across-trial Sharpe dispersion to estimate the Deflated Sharpe Ratio. It compares the selected result with a paper-derived expected-maximum threshold; it does not verify trial independence, discover omitted tests or prove robustness.
Enter the selected result and trial evidence
Use original-frequency Sharpe statistics. Independent trials and across-trial dispersion must be documented outside this calculator.
Non-annualized Sharpe for the selected result.
Whole observation count behind the selected Sharpe and moments.
Entered skewness from the selected result sample.
Pearson/raw kurtosis; the normal-distribution reference is 3.
Effective independent trials under the paper approximation, not raw parameter rows.
Dispersion of same-frequency Sharpe ratios across the entered independent trials.
Conditional DSR estimate
Entered Sharpe Uncertainty 1.0.0.
On smaller screens, scroll horizontally to inspect the complete calculation table.
| Quantity | Value | Role in this calculation |
|---|
How the Deflated Sharpe Ratio is calculated
Selection benchmark SR₀ = Across-trial Sharpe SD × Expected maximum z
DSR = Φ[(Selected SR − SR₀) × √(n − 1) ÷ √A]
Version 1.0.0 implements equation 2 from Bailey and López de Prado. The method first estimates an expected maximum standard-normal result for the entered number of independent trials, then scales it by the entered across-trial Sharpe dispersion.
The resulting selection-adjusted benchmark replaces the zero or user-chosen benchmark used by ordinary PSR. The selected Sharpe is compared with that threshold using the same sample-length, skewness and raw-kurtosis uncertainty factor.
The Euler–Mascheroni constant γ weights two normal percent-point terms in the paper approximation. When there is only one trial, or across-trial Sharpe dispersion is zero, the governed threshold is exactly zero and DSR reduces to PSR against zero.
Independent trials are an effective evidence input, not automatically the number of parameter combinations, files, runs or strategies reviewed. Correlated trials can contain less independent information than their raw count suggests.
The engine does not add a trial-mean term, estimate a correlation haircut or default the number of trials. Those changes would define a different model and are deliberately outside version 1.0.0.
Worked example from the audited fixture
The audited fixture enters selected Sharpe 0.5, 25 observations, skewness −0.5, raw kurtosis 4.5, ten independent trials and across-trial Sharpe standard deviation 0.2.
- The expected-maximum z value is 1.574598301 and the selection-adjusted benchmark is 0.314919660. The selected-sample uncertainty factor is 1.46875.
- The selection-adjusted comparison gives z = 0.748155666 and DSR = 0.772816865, displayed as 77.2817%. This is a conditional selection-adjusted statistic, not a robustness certificate.
Reproduce it: select “Load audited example” above. The governed engine retains full precision and rounds only the visible interface.
How to interpret the result
- DSR reports the paper-defined asymptotic comparison against the entered selection threshold. It is not the chance the selected strategy will remain profitable.
- More independent trials or greater across-trial Sharpe dispersion can raise the expected-maximum benchmark, making the comparison more demanding when other inputs stay fixed.
- A raw trial count should not be used automatically when trials share data, logic, parameters or research decisions. The calculator cannot estimate effective independence.
- A one-trial or zero-dispersion threshold of zero is a mathematical boundary. It does not prove that no selection occurred or that the research process was complete.
- DSR addresses only the represented multiple-testing effect. Look-ahead bias, survivorship bias, data leakage, cost omissions and researcher discretion can remain.
- Keep a trial ledger and pre-declared evaluation process. Without defensible inputs, a precisely computed DSR can still be an unreliable description of the research.
Assumptions and limits
- The model does not inspect trial results, estimate their dependence or verify that the selected result and trial dispersion use matching Sharpe conventions.
- Omitted, undocumented or selectively discarded trials are invisible to the calculator.
- The expected-maximum approximation relies on the independent-trial framework described in the paper and is not a universal backtest correction.
- The selected Sharpe, skewness and raw kurtosis remain subject to serial dependence, non-stationarity, sampling error and cost assumptions.
- Trial dispersion must be entered in the same original frequency as the selected Sharpe; annualized and non-annualized inputs cannot be mixed.
- The calculation does not replace walk-forward testing, untouched holdout data, execution review or independent replication.
- No robustness grade, significance verdict, verified edge, forecast, signal, position instruction or recommendation is generated.
Observed vs probabilistic vs minimum-length vs deflated Sharpe
These measures share a Sharpe vocabulary but answer different questions. The descriptive ratio summarizes an entered return sample; PSR evaluates one benchmark comparison; MinTRL expresses that comparison as observations; and DSR changes the benchmark for represented independent trials. None alone establishes future performance or suitability.
| Measure | Evidence entered | Question answered | Main boundary |
|---|---|---|---|
| Observed Sharpe | Equal-frequency returns and benchmark returns | Descriptive excess return per sample deviation | No uncertainty or selection adjustment. |
| Probabilistic Sharpe | Entered Sharpe, benchmark, n, skewness and raw kurtosis | Asymptotic probability of exceeding one benchmark | No multiple-trial adjustment or future probability. |
| Minimum Track Record | PSR inputs plus confidence | Formula-implied whole observation count | No calendar forecast or validation verdict. |
| Deflated Sharpe | Selected-sample moments plus independent trials and dispersion | PSR against an expected-maximum threshold | Trial independence and completeness are not verified. |
Frequently asked questions
- DSR is PSR evaluated against a paper-derived expected-maximum Sharpe threshold based on entered independent trials and across-trial Sharpe dispersion.
- It is the effective number of independent trials under the published approximation, not automatically the raw count of parameter rows, files or backtests.
- No. Trial count and dispersion are entered assumptions; the engine does not inspect trial results, estimate dependence or discover omitted research.
- It is the expected-maximum standard-normal value for the entered trial count multiplied by the entered same-frequency Sharpe standard deviation across trials.
- Version 1.0.0 sets the selection threshold to zero, so DSR reduces to PSR against zero under the selected sample moments.
- The selection threshold is zero because the expected-maximum z value is multiplied by zero entered dispersion.
- No. They must use the same original observation frequency and the page performs no annualization or frequency conversion.
- No. It cannot remove data leakage, omitted trials, cost errors or regime change and issues no robustness grade, forecast, signal or recommendation.
Sources and methodology
- Bailey and López de Prado — The Deflated Sharpe Ratio — Primary paper defining the expected-maximum benchmark and DSR calculation.
- Bailey and López de Prado — The Sharpe Ratio Efficient Frontier — Primary source for the underlying PSR non-normality adjustment.
- NIST — Normal distribution — Authority reference for the normal cumulative distribution and percent-point functions.
The primary equations were visually verified in the source PDFs before version 1.0.0 was locked. Independent fixtures separately recompute normal probabilities, percent points, observation rounding and the expected-maximum selection threshold.
Continue the selection-bias review
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Before calculating sample statistics, reconcile the exact statement period, realized results, spread, commission, financing, conversion and symbol terms for the broker entity and account involved. These browser calculations cannot certify that an entered Sharpe, moment estimate or trial ledger is complete.
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