Pockets of predictability: a stochastic crowding model and finite-sample regime detection for the endogenous decay of trading anomalies

Return predictability in financial markets is self-erasing: once an anomaly is discovered and capital flows toward it, its excess return decays. We develop a parsimonious stochastic model of this feedback in which the alpha of a trading signal is depleted in proportion to the capital deployed against it, while capital responds to a lagged estimate of alpha. The resulting two-dimensional linear diffusion is solved in closed form. We prove that the anomaly’s expected excess return converges not to zero but to the marginal cost of exploitation—a dynamic analogue of the Grossman-Stiglitz equilibrium—and we establish a sharp dichotomy: when capital responds slowly relative to the speed at which market participants update their alpha estimates, predictability decays monotonically, whereas fast-responding capital generates endogenous, quasi-periodic crowding cycles in which windows of predictability recurrently open and close. We obtain explicit formulas for the stationary law, the autocovariance function, the half-life of an anomaly, and the long-run fraction of time a predictability window is open, and we exhibit a saturation phenomenon: beyond a critical competition intensity, the decay rate of an anomaly is governed solely by the speed of alpha estimation. In the second part of the paper we study the statistical problem this dynamics creates for an investor: detecting, from a finite rolling window, whether the current regime is predictive. Rather than impose a Markov regime, we use the threshold indicator generated directly by the sampled crowding diffusion and derive its one-step switching probability in closed form from the Gaussian autocorrelation. For a covariance-based detector in a stationary threshold-regime predictive regression we prove non-asymptotic misclassification bounds in which every constant is explicit, using a corollary of the Laurent-Massart inequality and an exact moment-generating-function bound for Gaussian products. Optimizing the bound yields a principled prescription for the rolling-window length, and we prove a performance-transfer theorem bounding the Sharpe-ratio loss of the detector-conditioned strategy relative to the regime oracle by the misclassification probability. Monte Carlo experiments confirm the closed-form stationary law and autocovariance to within one percent, reproduce the qualitative post-publication decay documented in the empirical literature, and show that the detector-conditioned strategy recovers roughly seventy percent of the oracle’s conditioning gain at the theoretically prescribed window length. A positivity-preserving multiplicative depletion specification is also analyzed: the exact Gaussian law is lost, but positivity and the stationary mean at the exploitation cost remain valid, while the spectral dichotomy and half-life saturation survive under the natural local-impact calibration.