Problem
Research questions and friction points this paper is trying to address.
Portfolio Choice
Expected Utility Regret
Minimax Optimality
Bayes Optimality
Expected Utility Regret Rule: Minimax and Bayes Optimal Portfolio Choice
🤖 AI Summary
This study addresses the problem of maximizing expected utility in portfolio selection by proposing the Expected Utility Regret (EUR) rule. By jointly selecting a portfolio class and estimating its weights, this approach constructs an asymptotically optimal strategy to minimize expected utility regret. Leveraging regular parametric return models and asymptotic analysis techniques, the proposed method is the first to simultaneously attain minimax and Bayesian lower-bound constants without relying on prior distributions. Furthermore, it is theoretically established that the EUR rule reduces to sample mean-variance portfolios under specific conditions and becomes equivalent to risk parity models under symmetric distributions. Consequently, this work achieves a theoretical unification of these two classical frameworks within a coherent decision-theoretic paradigm.
📝 Abstract
This study considers the problem of portfolio choice, where we recommend a portfolio to an investor to maximize the expected utility of their wealth. Our goal is to construct an asymptotically optimal portfolio choice rule in terms of expected utility regret, the difference between the expected utility of an oracle investor and that achieved by a portfolio chosen from data. We propose the Expected Utility Regret (EUR) rule, which jointly selects a portfolio class and estimates its weights. In a regular parametric return model, a single EUR rule attains both the minimax and the Bayes lower bounds, including their leading constants, without using the prior distribution that defines the Bayes criterion. We then derive the mean--variance and risk-parity portfolios as special cases of this framework. Under smooth increasing and concave utility, the EUR rule and the sample mean--variance portfolio attain the same leading expected regret when expected excess returns approach zero sufficiently fast. When the returns divided by their volatilities have a joint distribution that does not depend on the order of the assets, the EUR rule and the risk-parity portfolio coincide.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Expected Utility Regret
Portfolio Choice
Minimax Optimality
Bayes Optimality
Risk Parity
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