Probabilistic Sharpe Ratio Calculator
Observed backtest statistics
Kurtosis is Pearson kurtosis, where a Normal distribution equals 3. Annualized Sharpe values are converted back to the entered observation frequency before applying the PSR formula.
Evidence behind the Sharpe
Why the same Sharpe can carry different evidence
Sharpe alone does not report estimator uncertainty. A short return history has less evidence than a long one, and negative skew or high kurtosis can increase uncertainty around the estimated Sharpe. The Probabilistic Sharpe Ratio converts that uncertainty into the probability that the estimated Sharpe exceeds a chosen benchmark under the method's assumptions.
The calculation uses the Bailey and López de Prado PSR formulation. If the inputs are annualized, this implementation first divides both observed and benchmark Sharpe by the square root of the entered periods per year so the Sharpe horizon matches the individual return observations.
Minimum track record is a conditional estimate
The minimum-track-record output asks how many observations would be needed to reach the selected one-sided confidence level if the observed Sharpe, skewness, kurtosis, and sampling frequency stayed unchanged. It is not a forecast that more data will preserve the current performance.
If the observed Sharpe does not exceed the entered benchmark, the tool does not report a finite minimum track record. Adding more observations cannot make an unchanged below-benchmark point estimate exceed that benchmark.
What PSR does not fix
PSR does not repair look-ahead bias, survivorship bias, stale or incorrect data, execution assumptions, regime change, serial dependence, or strategy mining. The method uses sample skewness and kurtosis, which are themselves estimates and can be unstable in short or heavy-tailed samples.
Most importantly, PSR by itself does not correct for choosing the best result from many attempted strategies. The multiple-testing tool isolates that search-multiplicity problem. The win-rate confidence tool covers finite-sample uncertainty in a different statistic, while the transaction-cost tool addresses execution friction.
Reusable sensitivity data
The downloadable grid compares annualized Sharpe ratios of 0.5, 1.0, 1.5, and 2.0 across 100, 252, and 1,000 daily observations under zero skew and Pearson kurtosis of 3, using a zero-Sharpe benchmark.
Method sources
- Bailey & López de Prado, The Sharpe Ratio Efficient Frontier, introducing the Probabilistic Sharpe Ratio and minimum track record length.
- Bailey & López de Prado, The Deflated Sharpe Ratio, extending the framework to selection bias and multiple testing.