Normal backwardation

Abstract: We examine two models of commodity futures prices. The theory of storage explains the difference between contemporaneous futures and spot prices (the basis) in terms of interest changes, warehousing costs, and convenience yields. We find evidence of variation in the basis in response to both interest rates and seasonals in convenience yields. The second model splits a futures price into an expected premium and a forecast of the maturity spot price. We find evidence of forecast power for 10 of 21 commodities and time-varying expected premiums for five commodities.

Abstract: SUMMARY Despite their widespread use as predictors of the spot price of oil, oil futures prices tend to be less accurate in the mean-squared prediction error sense than no-change forecasts. This result is driven by the variability of the futures price about the spot price, as captured by the oil futures spread. This variability can be explained by the marginal convenience yield of oil inventories. Using a two-country, multi-period general equilibrium model of the spot and futures markets for crude oil we show that increased uncertainty about future oil supply shortfalls under plausible assumptions causes the spread to decline. Increased uncertainty also causes precautionary demand for oil to increase, resulting in an immediate increase in the real spot price. Thus the negative of the oil futures spread may be viewed as an indicator of fluctuations in the price of crude oil driven by precautionary demand. An empirical analysis of this indicator provides evidence of how shifts in the uncertainty about future oil supply shortfalls affect the real spot price of crude oil. Copyright ! 2010 John Wiley & Sons, Ltd.

Abstract: R ISK transfer and price discovery are two of the major contributions of futures markets to the organization of economic activity (Working (1962), Evans (1978, p. 80), and Silber (1981)). Risk transfer refers to hedgers using futures contracts to shift price risk to others. Price discovery refers to the use of futures prices for pricing cash market transactions (Working (1948), Wiese (1978, p. 87), and Lake (1978, p. 161)). The significance of both contributions depends upon a close relationship between the prices of futures contracts and cash commodities. This paper examines the characteristics of price movements in cash (or spot) markets and futures markets for storable commodities. Section II presents an analytical model of simultaneous price dynamics which suggests that, over short intervals of time, the correlation of price changes is a function of the elasticity of arbitrage between the physical commodity and its counterpart futures contract. Greater elasticity fosters more highly correlated price changes, and thereby facilitates the risk transfer function. The elasticity of supply of arbitrage services is constrained by, among other things, storage and transaction costs. Thus, futures contracts will not, in general, provide perfect risk transfer facilities over short time horizons. The essence of the price discovery function of futures markets hinges on whether new information is reflected first in changed futures prices or in changed cash prices (Hoffman (1932, pp. 258259)). The model in section II provides a framework for analyzing whether one market is dominant in terms of information flows and price discovery. In section III we develop a model based on section II which is appropriate for estimating the lead-lag relationship between cash prices and futures prices. Section IV presents empirical estimates of the parameters of the model for seven different storable commodities: wheat, corn, oats, frozen orange juice concentrates, copper, gold, and silver. The cost of arbitrage between cash and futures differs across these commodities. For this reason we are not surprised to find inter-commodity differences in the correlation of short-run price changes and in the substitutability of futures contracts for cash market positions. With respect to the price discovery function of futures markets, we find that while futures markets dominate cash markets, cash prices do not merely echo futures prices; there are reverse information flows from cash markets to futures markets as well.

Abstract: C OMMODITY futures markets provide the economist with abundant data for studying the behavior of individuals coping with uncertainty. However, relatively little empirical work has been undertaken to test some of the theories of uncertainty developed for futures markets, and relatively little theoretical explanation of the empirical results can be found in the more factual studies of futures markets.2 This article combines a theoretical approach with an examination of the evidence and develops a theory of stockholding and futures markets capable of predicting the relations among some of the data collected in futures markets. The evidence presented is inconsistent with a theory of futures markets advanced by J. M. Keynes and J. R. Hicks. The first part of the article presents the theory of stockholding for a competitive industry. Since most of the commodities traded on futures markets