Admissible Information Sets for Mean-Variance Portfolio Optimization
Summary
This paper makes the information used in mean-variance portfolio choice part of the optimization problem. It argues that standard portfolio analysis can be distorted by including variables unavailable at decision time or by mistaking shared variation for idiosyncratic risk. The authors define admissible information classes using advance constraints on availability, no-arbitrage, statistical separation, and—in claims about interventions—invariance across specified regimes. They select an information class without using risk-return outcomes, then solve the classical portfolio problem within it.
The theoretical results cover existence, invariance to recoding, and the value of admissible information; they also identify when choosing information by decision loss can admit look-ahead data. An estimator is reported as consistent with second-order regret. In market data with 127 candidate drivers, the condition is attainable for individual equities but nearly unchanged by a larger search for pre-diversified portfolios. When exact separation fails, minimum-variance portfolios can match shrinkage with lower turnover while leaving some risk unexplained. These findings depend on the stated admissibility assumptions and do not establish that causal identification is always worth its search cost.
Key ideas
- Information availability and statistical separation are treated as constraints on portfolio choice.
- The admissibility order selects an information class without relying on risk-return outcomes.
- Causal claims require invariance across declared regimes, with identification carrying a search cost.
- The empirical condition behaves differently for individual equities and pre-diversified portfolios.
- When exact separation fails, minimum-variance portfolios can reduce turnover while retaining unexplained risk.
Tags
Full text
# 2610.00147 # Admissible Portfolio Optimization: Information Constraints, Conditional Efficient Frontiers, and the Price of Causal Identification Mean--variance portfolio choice takes the conditioning information as given and optimizes over weights, so two errors about that information pass into the portfolio unseen: using variables unavailable at the decision time and treating common variation as idiosyncratic. We make the conditioning information a decision variable subject to hard admissibility constraints declared in advance: availability, a no-arbitrage-preserving enlargement of the decision filtration, statistical separation and, for interventional claims, invariance across declared regimes. A lexicographic admissibility order in which no risk--return quantity enters selects an optimal information class, and the classical problem is solved inside it. We prove existence, invariance under recodings, and a value-of-admissible-information theorem whose failure conditions show that selection by decision loss admits look-ahead information whenever present; the two-stage solution and the joint envelope are the minimal elements of two orders on one set. Under exact separation the diversifiable part of risk is a property of the admissible class and is interventionally stable only under interventional admissibility; requiring causal identification carries an explicit oracle price traded against search complexity. The estimator is consistent with second-order regret. On market data with 127 candidate drivers the condition is attainable on individual equities, where enlarging the search reduces the defect at a measurable rate, and not on pre-diversified portfolios, where it is nearly invariant to the search because the residual dependence is the common factor itself. Where it fails, the covariance still yields minimum-variance portfolios that match shrinkage at markedly lower turnover while discarding a measurable part of their risk, which an exact decomposition attributes to the residual share, breadth and average residual correlation.
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