Probabilistic Sharpe Ratio Calculator
Enter an observed Sharpe ratio, same-frequency benchmark, observation count, skewness and raw kurtosis to estimate the Probabilistic Sharpe Ratio. The result is an asymptotic probability conditional on those summary statistics—not a probability of future profit, proof of skill or strategy-validation verdict.
Enter one Sharpe comparison
Use summary statistics calculated from the same return series, sampling frequency, benchmark and cost convention.
Non-annualized Sharpe in the original observation frequency.
Same-frequency Sharpe threshold used for this comparison.
Whole number of observations used to estimate the sample Sharpe and moments.
Entered skewness from the same observation sample.
Pearson/raw kurtosis; the normal-distribution reference is 3.
Conditional PSR 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 Probabilistic Sharpe Ratio is calculated
Estimated standard error = √[A ÷ (n − 1)]
PSR = Φ[(SR − Benchmark SR) ÷ Estimated standard error]
Version 1.0.0 implements equation 11 from Bailey and López de Prado. It starts with an observed sample Sharpe and asks how the benchmark comparison changes after accounting for finite sample length and the entered skewness and raw kurtosis.
Every Sharpe input remains in the original observation frequency. A daily sample Sharpe must be compared with a daily benchmark Sharpe; the engine does not multiply by a square-root annualization factor because the paper explicitly frames PSR in the original frequency.
The uncertainty factor A widens or narrows the estimated standard error relative to a normal-moment shortcut. Raw kurtosis uses the Pearson convention in which a normal distribution has kurtosis 3, not excess kurtosis 0.
The difference between observed and benchmark Sharpe is divided by that estimated standard error to form a z value. The standard normal cumulative distribution Φ then maps the z value to the reported PSR.
The calculation is conditional on the entered statistics being correctly estimated from one coherent sample. It does not independently inspect returns, serial correlation, changing regimes, costs, backtest construction or whether the benchmark was chosen before seeing the result.
Worked example from the audited fixture
The audited paper example enters observed Sharpe 0.458, benchmark 0, 24 observations, skewness −2.448 and raw kurtosis 10.164.
- The non-normality factor is 2.601753324 and the estimated standard error is 0.336332737. Dividing the 0.458 Sharpe difference by that standard error gives z = 1.361746717.
- Applying the standard normal cumulative distribution gives PSR = 0.913361084, or 91.3361% after interface rounding. This reproduces the paper result rounded to 0.913 without turning it into a future-performance claim.
Reproduce it: select “Load audited example” above. The governed engine retains full precision and rounds only the visible interface.
How to interpret the result
- The probability is the asymptotic PSR estimator for the entered benchmark comparison. It is not the chance that the next trade, month or year will be profitable.
- Changing the benchmark changes the question. A benchmark of zero asks about exceeding zero Sharpe, while a higher entered benchmark asks a stricter but still conditional comparison.
- A longer sample reduces the formula standard error when the entered Sharpe and moments stay unchanged. In practice those statistics can change as observations are added.
- More adverse entered skewness or heavier raw kurtosis can increase the uncertainty factor for a positive Sharpe. The exact effect depends on all entered terms.
- PSR does not correct for choosing the best backtest from many trials. Use the separate Deflated Sharpe Ratio page only when independent-trial count and across-trial dispersion are defensible inputs.
- Do not convert the percentage into pass/fail language. Strategy review still requires data lineage, out-of-sample evidence, costs, execution and robustness checks outside this calculator.
Assumptions and limits
- The model does not calculate Sharpe, skewness or kurtosis from raw returns and cannot detect entry or transcription errors.
- The published approximation is asymptotic; very small, dependent, overlapping or unstable samples can make the numerical precision look more certain than the evidence.
- Serial correlation, autocorrelation corrections, heteroskedasticity and regime changes are not modeled.
- The benchmark must use the same observation frequency and return convention. Mixing annualized and non-annualized Sharpe values invalidates the comparison.
- Raw kurtosis must use the normal-reference-3 convention. Entering excess kurtosis changes the formula input and produces a different result.
- Multiple-testing selection, data mining and omitted trials are outside PSR and require separate evidence and assumptions.
- No p-value label, confidence band, verified edge, future-performance probability, grade, signal 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
- PSR is the standard normal cumulative probability of an entered observed Sharpe exceeding an entered benchmark after the published sample-length, skewness and raw-kurtosis adjustment.
- No. It is an asymptotic estimator conditional on the entered summary statistics and is not a probability of future profit, persistence or trading skill.
- No. Version 1.0.0 requires observed and benchmark Sharpe in the same original observation frequency and performs no annualization.
- No. Enter Pearson or raw kurtosis, where the normal-distribution reference is 3; excess kurtosis uses a different zero reference.
- It is the same-frequency Sharpe threshold used for this one comparison; the calculator does not choose a benchmark for you.
- No. PSR evaluates one selected comparison. The separate Deflated Sharpe Ratio accepts independent-trial and across-trial dispersion assumptions.
- Skewness and raw kurtosis enter the non-normality factor used in the estimated standard error, so they alter the z comparison when other inputs stay fixed.
- No. The page issues no significance label, edge verdict, robustness grade, forecast, signal or recommendation.
Sources and methodology
- Bailey and López de Prado — The Sharpe Ratio Efficient Frontier — Primary paper containing the PSR and Minimum Track Record Length equations and original-frequency convention.
- NIST — Normal distribution — Authority reference for the standard 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 Sharpe evidence review
Verify the return and cost evidence
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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