( a) South East Airlines expects to purchase 6 million gallons of jet fuel in a month, and decides to use heating oil futures to hedge. Using past monthly data, the standard deviation of the change in spot price of jet fuel is found to be 0.0497 and the standard deviation of the heating oil futures price is obtained as 0.0564. The correlation between the spot and futures prices is found to be 0.91. Also, each heating oil contract traded on the New York Mercantile Exchange (NYMEX) is on 42,000 gallons of heating oil. (i) What is the optimal number of futures contracts (and indicate whether long or short) that the airlines should use to hedge its position of purchasing jet fuel in a month? (ii) Explain briefly what cross hedging implies in terms of the situation described for South East Airlines above. What is the significance of optimum hedge ratio in cross hedging?