A shipping company expects to purchase 2 million barrels of Marine fuel in three months and decides to use Jet fuel futures for hedging. The standard deviation of monthly changes per barrel spot price of Marine fuel is S =0.0551, and the standard deviation of monthly changes per barrel of Jet fuel futures is F= 0.0721, and the correlation between the two price changes is = 0.949.

a)What is the optimum hedge ratio h* ?

b)If each Jet fuel futures traded on CME is to deliver 50,000 barrels per contract, what is the optimal number of Jet fuel contracts to be hedged? Should they be taking a long or short position?

c) why have to measure the optimum hedge ratio in this case?