How much history to halve the detectable edge

Question

With 900 days of data, a backtest can reliably detect a mean edge of 6 bps (its minimum detectable effect). You want to be able to detect an edge of just 3 bps, keeping the same \alpha and power. How many days of data would you need?

Accepted Answer

The scaling law. The minimum detectable effect shrinks like 1/\sqrt{n}, so to detect a smaller edge you need more data, with n \propto 1/(	ext{edge})^2. Apply it. Halving the detectable edge (6 	o 3 bps) requires multiplying the sample by (6/3)^2 = 4: n{	ext{new}} = 4 	imes 900 = 3{,}600 	ext{ days}. That is roughly fourteen years of daily data instead of about three and a half, just to sharpen the resolution by a factor of two. Takeaway. Resolving an edge half as large needs four times the history: 900 days becomes 3,600. Small edges are expensive to pin down.

How much history to halve the detectable edge

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