The Risk of Expected Utility under Parameter Uncertainty
(2024) Management science — Vol. 70, n° 11, p. 7644-7663 (2024)
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- 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.
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Citations
Lassance, N., Martín-Utrera, A., & Simaan, M. (2024). The Risk of Expected Utility under Parameter Uncertainty. Management science, 70(11), 7644-7663. https://hdl.handle.net/2078.5/273036 (Original work published 2024)