Stats › Backtesting and evidence › Deflated Sharpe
After 200 tests, a Sharpe of 0.75 is worth 0.32
| What was measured | Tests assumed | What it becomes | Source |
|---|---|---|---|
| Annual Sharpe 0.75, 20 years of monthly returns, single test p value 0.0008 | 200 | p value 0.15, adjusted annual Sharpe 0.32, haircut about 60% | Harvey and Liu |
| The least profitable of three well known strategies, earnings to price | 50 | Haircut almost 50% | Harvey and Liu |
| The most profitable of the three, betting against beta | 50 | Haircut 7.9% | Harvey and Liu |
| Any observed annual Sharpe ratio below 0.4 | their baseline | Haircut usually more than 50% | Harvey and Liu |
| Any observed annual Sharpe ratio above 1.0 | their baseline | Haircut at most about 25% | Harvey and Liu |
| Annualised Sharpe 2.5, 1,250 daily returns, skewness -3, kurtosis 10, trial Sharpe variance 0.5 | 100 | Noise threshold 0.1132 daily, deflated Sharpe 0.90, fails the 0.95 bar | Bailey and Lopez de Prado |
| Exactly the same backtest, fewer trials behind it | 46 | Deflated Sharpe 0.9505, clears the 0.95 bar | Bailey and Lopez de Prado |
Sources: Harvey and Liu, Backtesting, Journal of Portfolio Management, Fall 2015; Bailey and Lopez de Prado, The Deflated Sharpe Ratio, Journal of Portfolio Management 40(5), 2014. The 0.1132 daily threshold is about 1.79 annualised at 250 trading days a year.
A Sharpe ratio from the best of many backtests is not the same measurement as one from a single test. On twenty years of monthly returns, two hundred tests cut a Sharpe of 0.75 to 0.32. The discount depends on a number almost nobody records.
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