This paper investigates the effect of model uncertainty on the performance of commodity-based portfolios. We consider a constant relative risk aversion (CRRA) utility maximizer investor in a complete market, with independent ambiguity-aversion levels for the three factors explaining the term structure of future prices, namely, spot prices, convenience yield (CY) and interest rates (IRs), as proposed in the seminal work of Schwartz (J Finance 52(3): 923–973, 1997). This generic investor is interested in the speculative component of the investment rather than possessing/consuming the physical commodity. We obtain closed-form solutions for optimal investments, optimal perturbations (alternative model) and value functions in line with the robust portfolio setting of Maenhout (Rev Financial Stud 17(4): 951–983, 2004). Our main focus is on the effect of convenience yield’s uncertainty on the optimal analysis. We estimate the model by applying a combination of maximum likelihood estimation (MLE) and Kalman Filter (KF) techniques, to two commodities: West Texas Intermediate (WTI) and copper future prices. The analysis demonstrates that uncertainty on the CY factor could be the largest contributor to the under-performance of a commodities portfolio, with wealth equivalent losses (WELs) in the ranges of 33% to 88% (WTI), and 7% to 31% (copper). Moreover, small variations, of up 25%, on CY’s covariance parameters could lead to a WEL of up to 40% (WTI, lesser volatility of CY).

本文研究了模型不确定性对基于商品的投资组合绩效的影响。我们考虑完整市场中的恒定相对风险厌恶（CRRA）效用最大化投资者，对解释未来价格期限结构的三个因素（即现货价格、便利收益率（CY）和利率）具有独立的模糊厌恶水平。 IR），如 Schwartz 的开创性著作中所提出的（J Finance 52(3): 923–973, 1997）。这种一般投资者对投资的投机部分感兴趣，而不是拥有/消费实物商品。我们获得了符合 Maenhout 稳健投资组合设置的最优投资、最优扰动（替代模型）和价值函数的封闭式解决方案（Rev Financial Stud 17(4): 951–983, 2004）。我们主要关注便利收益率的不确定性对最优分析的影响。我们通过将最大似然估计 (MLE) 和卡尔曼滤波器 (KF) 技术组合应用于两种商品来估计模型：西德克萨斯中质原油 (WTI) 和铜期货价格。分析表明，CY 因素的不确定性可能是导致大宗商品投资组合表现不佳的最大因素，财富等值损失 (WEL) 范围为 33% 至 88%（WTI）和 7% 至 31% （铜）。此外，CY 协方差参数的小幅变化（高达 25%）可能导致 WEL 高达 40%（WTI，CY 波动性较小）。