The standard deviation ( squareroot of variance) of monthly changes in the spot

Question

The standard deviation ( squareroot of variance) of monthly changes in the spot price of jet fuel is 16.5 cents per gallon. The standard deviation of monthly changes in the futures price of crude oil is $4.5 per barrel. There are 31.5 gallons in 1 barrel. The correlation between the spot and futures price changes is 0.87. It is now October 15. An airline plans to purchase 1'000'000 gallons of jet fuel on November 15 and wants to use the December crude oil futures contracts to hedge risks in the jet rule price. Each futures contract is for delivery of 1'000 barrels of crude oil. How many futures positions does the airline have to take to minimize its exposure to jet fuel price fluctuations? Ignore tailing adjustments to account for daily settlement.

Explanation / Answer

SD (Spot price) in gallons = (16.5^2 * 31.5^2)^0.5 = 5.19

Perfect Hedge ratio = Correlation * SD of Spot price / SD of future price = 5.19 * 0.87 / 4.5 = 1.004

Optimal contract = Size of desirable underlying portfolio / Contract size of one future contract * Perfect hedge ratio

= 1000000 / 10000 * 1.004 =1004 contract

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