Probabilistic Sharpe Ratio calculator
This calculator returns the Probabilistic Sharpe Ratio: the probability that a strategy's true Sharpe ratio exceeds a chosen benchmark, given the observed Sharpe, the track-record length, and the skewness and kurtosis of the returns. It runs entirely in your browser — nothing is uploaded or stored.
A Sharpe ratio is an estimate from a sample. PSR asks the question that actually matters to an allocator: given this much data and this return shape, how confident can I be that the true Sharpe beats my benchmark? A PSR of 0.95 is the conventional bar — below it, the record does not support the claim at 95% confidence.
Calculator
Frequency consistency matters. SR̂, SR* and n must describe the same sampling frequency. If you enter an annualised Sharpe, n is still the number of observations (24 monthly returns = 24, not 2). Mixing them is the most common error with this formula.
Formula
Negative skew makes -g1*SR_hat positive, enlarging the
denominator and lowering PSR. Excess kurtosis does the same. Both encode the
fact that fat-tailed, negatively skewed returns make a Sharpe estimate less
trustworthy — which is precisely the profile of strategies that look
best on headline numbers.
Example calculation
The values the calculator loads by default, so you can verify it against an independent implementation before trusting it on your own numbers:
| Input | Value |
|---|---|
| Observed Sharpe SR̂ | 1.50 |
| Benchmark SR* | 0.00 |
| Observations n | 24 |
| Skewness γ₁ | −1.20 |
| Kurtosis γ₂ | 7.00 |
Change the benchmark to 1.00 and the same track record gives z = 0.965 and PSR = 0.8327, which fails the 0.95 bar. Same strategy, different question.
Assumptions
- Returns are independent and identically distributed. Serial correlation — common in illiquid or smoothed portfolios — inflates the apparent Sharpe and is not corrected here.
- Skewness and kurtosis are known. In practice they are estimated from the same short sample, so they carry their own error.
- The test evaluates one track record. If it is the best of many strategies you tested, use the Deflated Sharpe Ratio instead, which adjusts for the number of trials.
- Nothing here accounts for costs, capacity or backtest overfitting.