Elements · Proposition III of VI

Every edge has a half-life.

IIIWhy it holds

No strategy is validated once. Market structure, participants and costs drift; the conditions that produced an edge change, and the edge decays with them.

So every live strategy carries its own expiry test: it is re-evaluated on each new window, and retired when the evidence that admitted it no longer holds.

∎Proof

\alpha_t = \alpha_0\, e^{-\lambda t}, \qquad t_{1/2} = \frac{\ln 2}{\lambda}

Proof · every edge has a half-lifeIllustrative · seed 4

A simulated edge that decays exponentially, buried in daily noise. The curve keeps looking fine for months after the edge is mostly gone; the rolling 6-month Sharpe ratio crosses the re-test line first. Nothing is validated once — everything is re-tested on every new window.

Q.E.D.