Sequential Hedging

This paper addresses a problem faced by the producer of a commodity for which futures are traded. The producer wishes to reduce his exposure to the random fluctuations in spot prices; however, the futures markets extend out for fewer time periods than the revenue stream that he wants to hedge. The main result of the paper is that under certain conditions on the relationship between the futures prices and past spot prices, it is still possible to hedge perfectly; in other words, there exists a sequence of futures positions that entirely eliminates the risk in the present value of the producer's revenues. Under those conditions—which are necessary as well as sufficient—the paper shows explicitly the futures positions that achieve the exact hedge.