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López de Prado's Sharpe-with-error-bars. Tells you how much your sample actually proves.
Probabilistic Sharpe Ratio (PSR) is Marcos López de Prado's extension of Sharpe ratio that returns the probability that the true population Sharpe exceeds a benchmark, given the observed sample. It accounts for sample size, skew, and kurtosis. PSR = 95% means there is a 95% chance the strategy's true Sharpe exceeds your chosen threshold.
PSR(SR*) = Φ((SR_obs − SR*) · sqrt(n−1) / sqrt(1 − γ₃·SR_obs + ((γ₄−1)/4)·SR_obs²))PSR(SR*) = Φ((SRobs − SR*) · sqrt(n−1) / sqrt(1 − γ3·SRobs + ((γ4−1)/4)·SRobs2))A z-score for whether your observed Sharpe is statistically distinguishable from your chosen benchmark Sharpe, run through the normal CDF to produce a probability. Fat tails and negative skew make the denominator larger, lowering PSR.
Sharpe ratios are noisy at small sample sizes. A 1-year backtest showing Sharpe of 2.0 may have PSR(>0) of only 80% — meaning there is a 20% chance the strategy is actually unprofitable in the long run. PSR forces you to confront how much your data actually proves.
This is the metric that catches lucky-streak strategies. A strategy with extremely high Sharpe over a short window often has PSR much lower than its raw Sharpe would suggest, because the sample is too small to be statistically meaningful.
You observe Sharpe of 1.2 over 36 monthly returns. Skewness is −0.5, excess kurtosis is 2.0. Benchmark Sharpe (SR*): 0.
Without the skew/kurtosis adjustment, t-stat ≈ 1.2 · sqrt(35) = 7.1 → PSR ~99.99%
With negative skew and fat tails, the denominator inflates and PSR drops — to roughly 97%, still significant but less certain than naive analysis suggests.
PSR(>0) above 95% means your Sharpe is statistically distinguishable from zero. PSR(>benchmark) above 75% means you have a real edge above your chosen benchmark. PSR is a probability, so it sits in [0, 1].
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Open the Sharpe Ratio Calculator →When PSR(>benchmark) is above 90%. Otherwise treat it as a lucky streak.
At least 60 observations is typical (5 years of monthly data). With daily data, 1 year is usually sufficient.
Zero (Sharpe > 0 means the strategy is profitable) or 0.5 (above-typical equity Sharpe) are common choices.
Yes — alongside standard Sharpe, Lo-adjusted Sharpe, and benchmark Sharpe for direct comparison.
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