Performance & Risk Metrics

Deflated Sharpe ratio (DSR)

A corrected Sharpe ratio that discounts the inflation caused by testing many strategy variants, non-normal returns, and a short track record.

If you backtest a hundred variants of a strategy and keep the best, its Sharpe ratio is biased upward simply by selection. The Deflated Sharpe ratio, introduced by Bailey and Lopez de Prado in 2014, expresses the probability that the observed Sharpe exceeds a benchmark Sharpe inflated by the number of trials, while also adjusting for skewness, kurtosis and sample length. A DSR near 0 means the result is likely a fluke; a DSR near 1 means it is statistically robust.

Formula

D S R = Φ \frac{( S ^ - S _{0} ) T - 1}{1 - γ ^ _{3} S ^ + \frac{γ ^ _{4} - 1}{4} S ^ ^{2}}

Ŝ: observed (non-annualised) Sharpe ratio
S₀: benchmark Sharpe inflated by the number of trials
T: number of return observations
γ̂₃,\ γ̂₄: sample skewness and kurtosis of returns

Related terms

See it in the data