Causal Separation in Portfolio Choice: Screening-Off Information and Conditional Risk

Abstract

Conditional portfolio choice depends on the information used to define conditional moments, yet that information is typically taken as given. We introduce causal separation for portfolio choice: a portfolio-information principle in which horizon-closed conditioning screens asset returns into mutually conditionally independent components, with a common-cause structural model providing its causal interpretation. Exact separation yields a decision-time decomposition of risk into diagonal residual risk and uncertainty in horizon-closed conditional means. Projecting systematic risk onto finite-dimensional driver innovations produces a low-rank represented component, becoming exactly diagonal-plus-low-rank under affine response. The selected information also induces state-sensitivity constraints in a classical equality-constrained Markowitz problem. We derive exact finite covariance-perturbation identities and non-asymptotic bounds linking representation error to portfolio weights and the efficient frontier. Controlled experiments recover the theoretical decomposition, perturbation identities, and intervention behavior. Empirical applications to U.S. equities show substantial reductions in residual cross-sectional covariance and competitive out-of-sample structured covariance estimates in shorter training windows. Causal separation therefore makes the conditioning representation an explicit, testable component of portfolio construction.

29 Pages, 7 Figures, 8 Tables. Under peer-revision in a quantitative finance journal