Suppose that you want to hedge your companys oil exposure using oil futures, and you want to be careful and exact about the quantities. You know that you will need to buy 2 million barrels of oil on June 25, 2020. The current spot price of oil is $65.78/barrel. Suppose that tradable oil futures mature on the 15th of every month, the futures price for the chosen contract is $65.60/barrel, and each contract is for 1,000 barrels. If the optimal hedge ratio is 1, how many contracts do you need to hedge your risk?

Follow the question above, now assume that the standard deviation of daily changes in oil futures price is .30, the standard deviation of daily changes in spot prices is .28, and the correlation between those changes is .92. In this case, how many contracts would you need in order to hedge your risk?