In finance we are sometimes interested in hedging the risk associated with future price changes by using futures contracts. A futures contract allows the buyer of the contract to buy the commodity at a later date at a price that is agreed upon now. By purchasing the correct number of contracts, an investor can reduce or even eliminate his or her risk. The correct number of contracts to purchase is known as the hedge ratio, and it can be estimated by regression analysis. The regression to be estimated is

Suppose you collect 30 daily spot and future prices over a 1-year period and estimate β to be 3.32 with a standard error of 1.12. Construct a 95 % confidence interval around the hedge ratio β.

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AS = a + BAf+e where AS = change in the spot price of the commodity Af = change in the futures price of the commodity = hedge ratio (number of futures contracts used for hedging)