AlphaAssayThe Probabilistic Sharpe Ratio, explained — with a calculator
The Probabilistic Sharpe Ratio (PSR) answers a sharper question than the Sharpe ratio alone: given how long your track record is, and how skewed and fat-tailed its returns are, what is the probability that your true Sharpe ratio exceeds a chosen benchmark (usually zero)? A raw Sharpe of 1.0 means one thing over twenty years and almost nothing over three months — PSR prices that difference. It takes your observed Sharpe, the number of returns, and the shape of the distribution (negative skew and fat tails make a Sharpe less trustworthy), and returns a probability. Bailey and López de Prado introduced it in 2012. The calculator below runs entirely in your browser; nothing is uploaded. Rule of thumb: PSR ≥ 0.95 means the edge over the benchmark is unlikely to be sampling noise.
The calculator
Annualised Sharpes are de-annualised internally (SR ÷ √periods-per-year). The default inputs (Sharpe 1.0 over 756 daily observations, benchmark 0) reproduce the 0.958 row in the table below — same formula, same defaults.
What does the PSR tell you that the Sharpe ratio doesn't?
| observed Sharpe | history | benchmark SR* | PSR | reading |
|---|---|---|---|---|
| 1.0 | 1y daily (252) | 0 | 0.841 | suggestive — one year is not enough to be sure |
| 1.0 | 3y daily (756) | 0 | 0.958 | clears 0.95 — the edge over zero is real |
| 2.0 | 1y daily (252) | 0 | 0.977 | a high Sharpe buys confidence faster |
| 0.5 | 3y daily (756) | 0 | 0.807 | not proven — a weak edge needs long history |
| 1.5 | 2y daily (504) | 1.0 | 0.760 | beating a 1.0 hurdle is not yet established |
Same Sharpe, different verdicts — because history length, distribution shape and the benchmark all move the probability. Run your own numbers above.
The formula, step by step
Step 1 — de-annualise. Work in per-period units: ŜR = SR / √(periods per year),
and the same for the benchmark SR*.
Step 2 — penalise the distribution. The denominator
√(1 − γ₃·ŜR + ((γ₄−1)/4)·ŜR²) inflates when returns are negatively skewed (γ₃) or fat-tailed
(γ₄): the same Sharpe from ugly returns is less trustworthy.
Step 3 — read it as a probability.
PSR = Φ( (ŜR − SR*)·√(n−1) / √(1 − γ₃·ŜR + ((γ₄−1)/4)·ŜR²) ),
where Φ is the standard-normal CDF and n is the number of returns. PSR ≥ 0.95: the edge over the benchmark
is unlikely to be sampling noise.
How is the PSR different from the Deflated Sharpe Ratio?
The PSR asks whether your Sharpe beats one fixed benchmark. The Deflated Sharpe Ratio is the PSR with the benchmark set to the expected maximum Sharpe you would see after N no-skill trials — so it also charges you for the search you ran. Use PSR when you ran a single pre-registered test; use DSR the moment you tried more than one variant. The honest track-record question — how long until PSR clears a bar — is the Minimum Track Record Length. All of this is gate 2 of every AlphaAssay verdict.