Robust portfolios with commodities and stochastic interest rates

Abstract

This paper addresses a gap in the literature concerning robust portfolio analysis for commodity markets in the presence of stochastic interest rates. For generality, we study an ambiguity-averse investor with a Cramér-Lundberg surplus to be allocated into a mean-reverting asset representing a commodity and a bond with a Vasicek interest rate model. Our framework allows for closed-form solutions for the optimal strategy, worst case measure, terminal wealth and value functions. We provide necessary conditions for a well-behaved solution. A full estimation is conducted on two commodity representatives: WTI oil prices and gold prices. We find strong evidence that optimal exposures to commodity risk and interest rate risk, as well as the performance of the portfolio, are significantly affected by the level of ambiguity aversion. Our analyses demonstrate that investors who ignore uncertainty incur drastic equivalent welfare losses, in particular ignoring commodity uncertainty is more costly than neglecting interest rate uncertainty. In a comparison between stocks and commodities, ignoring uncertainty on the latter is also more damaging. We also confirm the importance of working in a complete market (investing in Bonds) for commodity investors, otherwise welfare losses could easily reach 45%. In terms of parameter mis-specifications, we find that incorrect large correlation, smaller variance or simply the wrong market price of commodity risk, can lead to drastically large wealth-equivalent losses.