Constraint Geometry of Institutional Synchronization

Abstract

Market synchronization can emerge independent of contemporaneous information arrival, driven instead by the common component of institutional optimization under shared constraints. This paper develops the constraint geometry of that mechanism, introducing three theoretical objects. First, the ISTadmissible constraint class — institutional constraint functions that admit a Common-Idiosyncratic Decomposition, delineating the scope of Institutional Synchronization Theory (IST) as a definitional rather than assumptional restriction. Second, Synchronization Pressure — a vector-valued theoretical primitive derived from constraint shadow prices and common gradients, invariant to how the econometrician projects returns. Third, the Synchronization Law — a monotonic relationship between the equilibrium pressure-aligned covariance shift and the capacity-adjusted Synchronization Pressure normalized by market capacity, derived from a minimal Kyle-style linear price-impact assumption. A single Dominance Principle unifies the four established transmission channels of institutional finance — benchmarktracking, VaR, ETF creation/redemption, and short-sale constraints — as regime-specific corollaries. The Law's linearization recovers the empirical Scaling Law documented in Yang (2026b), building on the theoretical framework of Yang (2026a); preliminary cross-market calibration is consistent with universality.

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