The Inaccuracy of Expectations: A Statistical Study of the Liverpool Cotton Futures Market, 1921/2-1937/8

i. The futures price of a commodity is so closely connected with expectations as to its price in the future, that it is possible to make an estimate of how accurate these expectations are. The significance of such an estimate, however, can only be appreciated if the structure of prices in a futures market is understood. This structure is somewhat complicated. The price of every futures contract must satisfy the two conditions expressed in the following equations: (i) FP CP i + c'q (ii) EPFP= r where CP is the current or spot price of the commodity, FP is the price of the futures contract with a certain period to run before maturity,1 i and c' are the marginal interest and carrying charges for holding stocks for this period, and q is the marginal yield in convenience from holding stocks of this size for this period; and where EP is the representative expected price, and r the market risk premium. 2. A fuller discussion of these equations will be found in recent numbers of the Review of Economic Studies.2 There it was shown that the risk premium might take a negative sign either (i) if the risks that were to be hedged were predominantly negative risks, i.e. the sort of risks a man would face who had sold forward more than he owned; or (ii) if, when there was both buying and selling of futures by speculators, the bears were more averse to bearing risks than the bulls, and sufficiently so to outweigh the riskaversion of the hedgers. In a futures market for a raw