An airline company expects to purchase 5 million gallons of Jet fuel in three months and decides to use Heating oil futures for hedging. The standard deviation of monthly changes in the spot price of Jet fuel is S =0.0356, and the standard deviation of monthly changes in the Heating oil futures is F= 0.0451, and the correlation between the two price changes is = 0.924.

a)What is the optimum hedge ratio h*?

b)If each Heating oil futures contract traded on CME is to deliver 45,000 gallons, what is the optimal number of Heating oil contracts to be hedged? Should they be taking long or short position?

c)Explain why such hedging strategy is not a perfect hedge?