Suppose an oil and gas company expects to purchase 500,000 barrels of petroleum in a month from a refinery, and uses crude oil futures for cross hedging. Each futures contract represents 1000 barrels. The standard deviation of the monthly changes in the market ( or, spot) price of petroleum is 0.0445, and the standard deviation of the monthly changes in the crude oil futures price is 0.0525. The correlation between the spot and futures price is 0.942 . Suppose the spot price is $ 170 per barrel and the futures price is $165 per barrel.

a) What is the minimum variance hedge ratio ? How many gallons of petroleum exposure ( out of the 500,000 barrels) may need to be hedged ?

b) Should the company take a long or short futures position to hedge?

c) What is the optimal number of contracts when adjustments for daily settlement are not considered ? ( used in hedging with forward contracts)

d) What is the optimal number of futures contracts when daily settlement is considered?