The Risk of Expected Utility Under Parameter Uncertainty

• 成果类型: Article
• 署名作者: Lassance, Nathan; Martin-Utrera, Alberto; Simaan, Majeed
• 署名单位: Iowa State University; Stevens Institute of Technology
• 刊物名称: MANAGEMENT SCIENCE
• ISSN/ISSBN: 0025-1909
• DOI: 10.1287/mnsc.2023.00178
• 发表日期: 2024
• 关键词: Parameter uncertainty; mean-variance portfolio; shrinkage

摘要

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.