Admissible Portfolio Optimization: Information Constraints, Conditional Efficient Frontiers and the Price of Causal Identification

Abstract

Mean--variance portfolio choice takes the conditioning information as given, so that two errors about it, using variables not available at the decision time and treating common variation as idiosyncratic, pass into the portfolio unseen. This paper turns what that practice assumes into a condition declared before estimation, certified from data and priced when it fails. The conditioning information becomes a decision variable subject to admissibility constraints on availability, arbitrage, statistical separation and, for interventional claims, invariance across regimes; an order in which no risk--return quantity enters selects an information class, and the classical problem is solved inside it. We prove that solutions exist, that the value of information is monotone only under an embedding that portfolio constraints can break, so that selection by decision loss admits look-ahead information whenever offered, that the two-stage solution and the joint envelope are minimal elements of two orders on one set, that the diversifiable part of risk is a property of the admissible class, and that causal identification has an explicit price. Allocation performance is downstream of the framework, since the information decision enters the decision regret at second order and the reported risk at first order, while the weights themselves move at first order. On market data the condition holds on small sets of individual securities and fails on pre-diversified portfolios and on books of realistic size, where a factor model with diagonal residual understates its portfolio's variance by a factor that the consequence statistic announces in advance; selecting the same information by decision loss yields portfolios that promise a fraction of the risk they realize.