A Unified Theory of Ownership Concentration, Overlap, and Dependence: Margins, Cells, Spectral Structure, and Linear Transmission

Battle Count: 50

The paper provides a rigorous measurement framework for ownership concentration and overlap that is directly relevant to quantitative trading in several ways: (1) rho(A) gives a sharp bound on fire-sale vulnerability, useful for risk management in concentrated positions; (2) X(A) quantifies benchmark-relative active variance capacity, relevant for alpha generation and tracking error; (3) the dashboard (H_I, H_S, M, Psi, X, rho) provides actionable diagnostics for crowding and fragility. However, the paper is primarily a measurement/theory paper rather than a trading strategy paper. It informs risk management and portfolio construction decisions but does not directly generate trading signals. Most relevant for institutional quant traders managing large portfolios, fund-of-funds analysis, and systemic risk monitoring.

Core metrics (H_I, H_S, M, X) are O(nm) and trivially implementable. The SVD of the whitened matrix K for rho(A) is O(nm*min(n,m)) but truncated methods work for sparse panels. The fixed-marginal minimization of M is a strictly convex QP with nm variables and n+m constraints (solvable with standard solvers). The fixed-marginal maximization requires extreme-point search over the transportation polytope, which is more complex. Overall, the basic dashboard is straightforward; the full framework including Psi requires optimization expertise.

The paper is purely theoretical with all proofs provided. A complete worked example (Section 10) with explicit numerical values enables verification. Computational procedures are clearly specified (O(nm) for basic metrics, SVD for spectral quantities, convex QP for fixed-marginal optimization). No proprietary data or code is needed. However, no code repository is provided.