Copper and the negative price of storage

Commodities are often stored during periods in which storage returns a negative price. Further, during periods of"backwardation,"the expected revenue from holding inventories will be negative. Since the 1930s, the negative price of storage has been attributed to an offsetting"convenience yield."It has been argued that inventories are a necessary adjunct to business and that increasing inventories from some minimal level reduces overall costs. This theory has always been criticized by proponents of cost-of-carry models, who argue that a negative price for storage creates arbitrage opportunities. Proponents of the cost-of-carry model have asserted that storage will occur only with positive returns. They offer a set of price-arbitrage conditions that associate negative returns with stockouts. Still, stockouts are rare in commodity markets, and storage appears to take place during periods of"backwardation"in apparent violation of the price-arbitrage conditions. For copper, inventories have always been available to the market regardless of the price of storage. The author argues that although inventories may provide a cost-reducing convenience yield, inventories also have value because of uncertainty. Just as the price of a call option contains a premium based on price variability, so the shadow price of inventories contains a dispersion premium associated with the unplanned component of inventories. The author derives a generalized price-arbitrage condition in which either a convenience and/or a dispersion premium may justify inventory holding even during an expected price fall. He uses monthly observations of U.S. producer inventories to estimate the parameters of the price-arbitrage condition. The estimates and simulations he presents are ambiguous with regard to the existence of a convenience yield but strongly support the notion of a dispersion premium for copper. And although the average value of such a premium is low, the value of the premium increases rapidly during periods when inventories are scarce.