Certified Alpha Capacity: Statistical Evidence, Economic Lifetime, and Arbitrage under Decay

Abstract: In this paper we study whether a trading signal can accumulate enough statistical evidence for reliable deployment before its economic value decays. We solve the problem by measuring statistical evidence and remaining opportunity on a common Kullback-Leibler information scale, obtaining an exact feasibility threshold in a canonical Gaussian model and general information lower bounds beyond it. We show that finite information budgets generate survival frontiers, search penalties, and a market equilibrium in which arbitrage activity shortens the lifetime of certifiable opportunities; a retrospective funding-rate study illustrates the role of persistence.