The annualised Sharpe ratio is the most widely cited performance metric in quantitative trading, but it has two critical blind spots. First, it assumes Gaussian returns: the standard SR -test is biased when returns are skewed or fat-tailed, as they typically are in stat-arb strategies. Second, it ignores how many strategies were tried to produce the reported number: a SR of 1.5 from one careful test means something very different from SR = 1.5 from the best of 50 tries.
The Probabilistic Sharpe Ratio (PSR) corrects the first problem by adjusting for non-Gaussian return characteristics. The Deflated Sharpe Ratio (DSR) corrects both by incorporating the multiple-testing adjustment. Together, they replace the raw SR as the honest metric for strategy evaluation.
Learning objectives. By the end of this note you should be able to:
- annualise a Sharpe ratio from a series of period returns;
- compute the PSR from the sample SR, skewness, kurtosis, and sample length;
- compute the DSR benchmark SR* from the number of trials and trial SR variance;
- state when the PSR and DSR exceed 0.95 (the 5% false discovery threshold);
- explain why a PSR < 0.95 does not mean the strategy is wrong, only that the evidence is insufficient.
In this lesson
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- The annualised Sharpe ratio
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- The Probabilistic Sharpe Ratio
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- The Deflated Sharpe Ratio
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- The third law of backtesting
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
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