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Deflated Sharpe Ratio (DSR)

A Sharpe Ratio adjusted for multiple testing, non-normality, and the number of trials; produces a probability that the true SR is positive.

The Deflated Sharpe Ratio (DSR) was introduced by Bailey and López de Prado (2014) to address the problem that a high backtested Sharpe Ratio may reflect data-mining rather than genuine alpha, particularly when many strategies have been evaluated and the best selected.

DSR computes the probability that the strategy's true (population) Sharpe Ratio is greater than zero, given:

  • The observed in-sample Sharpe Ratio
  • The number of trials (strategy variants) evaluated
  • The skewness and kurtosis of returns (non-normality further penalizes the SR)
  • The length of the track record

A DSR close to 1 means it is very likely the strategy has positive expected alpha. A DSR of 0.5 means the evidence is no better than a coin flip — selection from a large trial set could explain the result entirely.

DSR is directly related to the Probability of Backtest Overfitting; both address the inflation from multiple testing, from complementary angles. The Minimum Track Record Length is a related concept addressing how much data is needed to confidently declare alpha.

Related terms

Sharpe RatioAnnualized excess return divided by annualized standard deviation; the most widely used risk-adjusted performance metric.Backtest OverfittingWhen in-sample optimization causes historical performance to overstate expected live performance.Multiple TestingWhen many strategy variants are evaluated and the best selected, the probability of false discovery rises sharply, inflating backtested Sharpe Ratios.Probability of Backtest Overfitting (PBO)The estimated probability that the best in-sample strategy will underperform the median out-of-sample, using combinatorial cross-validation.Minimum Track Record LengthThe minimum number of return observations needed to conclude, with statistical confidence, that a strategy's true Sharpe Ratio is positive.

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