The Risk of Expected Utility Under Parameter Uncertainty

Nathan Lassance (), Alberto Martín-Utrera () and Majeed Simaan ()
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Nathan Lassance: LFIN/LIDAM, UCLouvain, 7000 Mons, Belgium
Alberto Martín-Utrera: Iowa State University, Ames, Iowa 50011
Majeed Simaan: Stevens Institute of Technology, Hoboken, New Jersey 07030

Management Science, 2024, vol. 70, issue 11, 7644-7663

Abstract: We derive analytical expressions for the risk of an investor’s expected utility under parameter uncertainty. In particular, our analysis focuses on characterizing the out-of-sample utility variance of three portfolios: the classic mean-variance portfolio, the minimum-variance portfolio, and a shrinkage portfolio that combines both. We then use our analytical expressions to study a robustness measure that balances out-of-sample utility mean and volatility. We show that neither the sample mean-variance portfolio nor the sample minimum-variance portfolio exhibits maximal robustness individually, and one needs to combine both to optimize portfolio robustness. Accordingly, we introduce a robust shrinkage portfolio that delivers an optimal tradeoff between out-of-sample utility mean and volatility and is more resilient to estimation errors. Our results highlight the importance of considering out-of-sample performance risk in designing and evaluating investment strategies and stochastic discount factor models.

Keywords: parameter uncertainty; mean-variance portfolio; shrinkage (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ormnsc:v:70:y:2024:i:11:p:7644-7663

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