Expected commodity returns and pricing models

Stochastic models of commodity prices have evolved considerably in terms of their structure and the number and interpretation of the state variables that model the underlying risk. Using multiple factors, different specifications and modern estimation techniques, these models have gained wide acceptance because of their success in accurately fitting the observed commodity futures' term structures and their dynamics. It is not well emphasized however that these models, in addition to providing the risk neutral distribution of future spot prices, also provide their true distribution. While the parameters of the risk neutral distribution are estimated more precisely and are usually statistically significant, some of the parameters of the true distribution are typically measured with large errors and are statistically insignificant. In this paper we argue that to increase the reliability of commodity pricing models, and therefore their use by practitioners, some of their parameters — in particular the risk premium parameters — should be obtained from other sources and we show that this can be done without losing any precision in the pricing of futures contracts. We show how the risk premium parameters can be obtained from estimations of expected futures returns and provide alternative procedures for estimating these expected futures returns.