What Sharpe would the best of 50 junk backtests show?

Question

A researcher backtests 50 parameter configurations over 4 years of data, then reports the single best one, which has an annualized Sharpe of 1.6. Suppose, for the sake of argument, that none of the 50 has any genuine edge.

What Sharpe would you expect the best of 50 zero-edge configurations to show by luck alone, and what does that say about the reported 1.6?

Accepted Answer

Each backtest is a noisy zero. Even a strategy with no real edge produces a nonzero sample Sharpe by chance. For a zero-edge strategy over T years, the sample Sharpe behaves like random noise with a standard deviation (standard error) of about \operatorname{SE}0 \approx \sqrt{\frac{1}{T}}. This is the earlier Sharpe standard-error formula with the Sharpe set to zero. In words, each junk backtest lands a bit above or below zero, with a typical spread of 1/\sqrt{T}. Keeping the best of many is cherry-picking noise. When you run N independent junk trials and keep the maximum, you are sampling th…

What Sharpe would the best of 50 junk backtests show?

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