Stats Backtesting and evidence Backtest overfitting

Ten backtests on pure noise produce a Sharpe of 1.57

5: 1.19+1.1957: 1.39+1.39710: 1.58+1.581020: 1.9+1.92045: 2.24+2.2445100: 2.53+2.53100200: 2.77+2.77200500: 3.05+3.055001,000: 3.26+3.261,000

Computed from Proposition 1 (equation 2.4) of Bailey, Borwein, Lopez de Prado and Zhu. My calculation returns 1.575 at N = 10 against the 1.57 the paper states, and 2.616 at N = 128 against the "above 2.6" the paper states, so the equation is transcribed correctly. All figures assume a one year backtest.

Every configuration tried in a backtest is another draw, and the best is kept. On a strategy with no edge, ten tries on one year of data produce an expected Sharpe of 1.57. Five years of data supports forty five tries, and no more.

1.5710 trials, one year
above 2.6128 trials, one year
45Trials 5 years supports
7Trials 2 years supports

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