Asymmetric Arbitage and Normal Backwardation

This paper provides a theoretical explanation for the existence of backwardation on the futures markets, based on Routhakker's work dealing with asymmetry of arbitrage on such markets. The central assumption of the paper is that cash and futures prices tend to be more highly correlated at low than at high cash prices. This assumption reflects the asymmetry in arbitrage opportunities in futures markets; in particular, at the maturity date of a futures contract, the futures price cannot exceed the cash price of any grade-location combination deliverable under the futures contract. The main result of the paper is a proposition that asserts that with identical long and short hedgers, with the same wheat commitments on both sides of the market, and with utility functions exhibiting constant or decreasing absolute risk aversion, if the probability density function over cash and futures prices is sufficiently concentrated at low cash prices, then the resulting market equilibrium will exhibit backwardation, that is, the current future price is a downward biased estimator of the future futures price as well as being a downward biased estimator of the future cash price.