The standard deviation (square root 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 fuel 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.
Additional Information
The question lies from Statistics and it is a calculation of standard deviation and correlation of spot price and futures prices of jet fuel. This question requires both the understanding of Finance and Statistics to arrive at the solution.