An airline company expects to purchase 5 million gallons of jet fuel in three months' time and decides to use heating oil futures for hedging. The standard deviation of monthly changes in the spot price of jet fuel is S = 0.0256, and the standard deviation of monthly changes in the heating oil futures is F= 0.0351, and the correlation between the two price changes is = 0.934.

(a)What is the optimum hedge ratio h* ? (3 marks)

(b) If the heating oil contract traded on CME is 42,000 gallons per contract, what is the optimal number of heating oil contracts to be hedged? Should they be long or short? (5 marks)

(c) Suppose the company choose to use crude oil futures to hedge, (also 42,000 gallons per contract) instead of the heating oil contract as above, how will this decision change the optimal number of contracts? The standard deviation of monthly changes in the crude oil futures is F= 0.0552, and the correlation between the jet fuel and crude oil futures is = 0.950. (7 marks)