Forty chart indicators tested at a loose 10% bar

Question

A discretionary trader backtests 40 technical indicators, each at a loose 10% significance level. Assume that in reality none of the indicators has any predictive power.

On average, how many of these 40 worthless indicators will appear to "work" in the backtest?

Accepted Answer

The per-test chance. A 10% significance level is generous: even an indicator with zero edge has a 10% chance of looking predictive by accident. The looser the bar, the more often noise sneaks through. Across all forty. Expected false positives equal the number of tests times the per-test false-alarm rate: 	ext{expected false positives} = m 	imes \alpha = 40 	imes 0.10 = 4. So about four indicators will seem to work even though all are useless. The trap. A loose bar plus many tries is the perfect recipe for self-deception. Four indicators that "backtest well" feel like a system, but they ar…

Forty chart indicators tested at a loose 10% bar

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