A microscopic p-value on a microscopic edge

Question

Using ten million trades, a firm finds an average edge of $0.2$ basis points per trade with $p = 10^{-8}$ . Management is thrilled: "The p-value is essentially zero, this is a slam-dunk signal."

Explain why an extremely small p-value here does not imply a valuable edge, and what actually determines whether it is worth trading.

Accepted Answer

Why the p-value is tiny. With ten million observations, the noise in the estimated mean shrinks enormously (it scales as 1/\sqrt{n}). So even a microscopic true edge of 0.2 bp produces a gigantic z-statistic and a vanishingly small p-value. The p-value is tiny because of the sample size, not because the edge is large. Why it may be worthless. The edge is 0.2 bp per trade. Realistic trading costs (spread, fees, slippage, market impact) are often several basis points per trade. If costs are, say, 1 bp, this "extremely significant" edge is deeply unprofitable after costs. Statistical significanc…

A microscopic p-value on a microscopic edge

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