Economic Linkages, Relative Scarcity, and Commodity Futures Returns

Abstract

This paper shows that economic linkages among commodities create a source of long-term correlation between futures returns. We extend the Theory of Storage to a multi-commodity level and find that the convenience yield of a commodity depends not only on its own scarcity level, but also on its relative scarcity with respect to other economically-related commodities. This result implies a positive feedback effect from one commodity to another that is necessary to replicate the upward-sloping correlation term structure of futures returns observed from the related commodities. Our empirical Multi-Commodity Feedback Affine model (MCFA) allows for a flexible correlation term structure and validates our theoretical prediction. An out-of-sample test using short-maturity crack spread options data shows that our model considerably reduces the pricing error generated by traditional models.