Contango

Abstract: In this article we compare three models of the stochastic behavior of commodity prices that take into account mean reversion, in terms of their ability to price existing futures contracts, and their implication with respect to the valuation of other financial and real assets. The first model is a simple one-factor model 'in which the logarithm of the spot price of the commodity is assumed to follow a mean reverting process. The second model takes into account a second stochastic factor, the convenience yield of the commodity, which is assumed to follow a mean reverting process. Finally, the third model also includes stochastic interest rates. The Kalman filter methodology is used to estimate the parameters of the three models for two commercial commodities, copper and oil, and one precious metal, gold. The analysis reveals strong mean reversion in the commercial commodity prices. Using the estimated parameters, we analyze the implications of the models for the term structure of futures prices and volatilities beyond the observed contracts, and for hedging contracts for future delivery. Finally, we analyze the implications of the models for capital budgeting decisions. THE STOCHASTIC BEHAVIOR OF commodity prices plays a central role in the models for valuing financial contingent claims on the commodity, and in the procedures for evaluating investments to extract or produce the commodity. Earlier studies, by assuming that interest rates and convenience yields are constant allowed for a straight forward extension of the procedures developed for common stock option pricing to the valuation of financial and real commodity contingent claims. The assumption, however, is clearly not very satisfactory since it implies that the volatility of future prices is equal to the volatility of spot prices, and that the distribution of future spot prices under the equivalent martingale measure has a variance that increases without bound as the horizon increases. In an equilibrium setting we would expect that when prices are relatively high, supply will increase since higher cost producers of the commodity will enter the market putting a downward pressure on prices. Conversely, when prices are relatively low, supply will decrease since some of

Abstract: For this study of the simple properties of commodity futures as an asset class, an equally weighted index of monthly returns of commodity futures was constructed for the July 1959 through December 2004 period. Fully collateralized commodity futures historically have offered the same return and Sharpe ratio as U.S. equities. Although the risk premium on commodity futures is essentially the same as that on equities for the study period, commodity futures returns are negatively correlated with equity returns and bond returns. The negative correlation is the result, primarily, of commodity futures' different behavior over a business cycle. Commodity futures are positively correlated with inflation, unexpected inflation, and changes in expected inflation.

Abstract: The authors found that, concurrent with the rapidly growing index investment in commodity markets since the early 2000s, prices of non-energy commodity futures in the United States have become increasingly correlated with oil prices; this trend has been significantly more pronounced for commodities in two popular commodity indices. This finding reflects the financialization of the commodity markets and helps explain the large increase in the price volatility of non-energy commodities around 2008.

Abstract: Investors face numerous challenges when seeking to estimate the prospective performance of a longonly investment in commodity futures. For instance, historically, the average annualized excess retu...