22.8. Suppose you wish to hedge your exposure to oil prices by means of forwards and futures over the next year. You have the following information: the current price of oil is $20 per barrel and the riskfree rate of interest is 10 percent per year

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 $8 million

 $10 million European profitst compounded annually. Assume that the spot price of oil changes instantaneously from $20 to $21 per barrel.

a. Describe the necessary number of one-year forwards you must hold in order to perfectly hedge a long position in 1 barrel of oil. Then describe any changes in the perfectly hedged position of spot oil and forwards, including any cash that changes hands, when the spot price of oil instantaneously increases by $1.00.

b. Repeat part a for a perfectly hedged position using futures contracts.

c. Repeat parts a and

b, assuming that you now want to hedge a short position of 5,000 barrels of oil.