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Elements · Proposition I of VI

Every edge starts at zero.

IWhy it holds

Every idea begins at the origin. Before a strategy is allowed to mean anything, we assume it means nothing: the expected excess return is zero, and every pattern is noise until the data forces us to think otherwise.

The burden of proof sits with the hypothesis, never with the sceptic. A result that cannot beat its own null is not a weak result — it is no result.

∎Proof

H0: α=0,t=αˉs/nH_0:\ \alpha = 0, \qquad t = \frac{\bar{\alpha}}{s/\sqrt{n}}
Proof · luck under the nullIllustrative · seed 1000
050100−3−2−10123annualised Sharpe ratio · true edge = 0best of 1,000 · 2.85
1,000 simulated strategies whose true edge is exactly zero: one year of daily returns each, mean 0. 183 of them still show a Sharpe ratio above 1.0, and the best reaches 2.85. Without a null hypothesis, luck looks like skill.

Q.E.D.