Model uncertainty on commodity portfolios, the role of convenience yield

Abstract

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).