Question

6. Suppose a one year oil forward price is $60 per barrel. Suppose further that there are two equally likely outcomes in one year---an oil spot price of $40 and an oil price of $80. If the oil price is $40, the firm’s revenue will be $150 million with 75% probability and $200 million with 25% probability. If the oil price is $80, the firm’s revenue will be $200 million with 50% probability and $250 million with 50% probability. What position in oil forward contracts minimizes the variance of the firm’s revenue (with the underlying asset being a barrel of oil)?

Answer 1

In case Oil price becomes $40 after one year

Expected value of Firm's Revenues = $150 million *75%+ $200 million *25% =$162.5 million

In case Oil price becomes $60 after one year

Expected value of Firm's Revenues = $200 million *50%+ $250 million *50% =$225 million

As the firm will have less revenues in case Oil price goes down to $40, to reduce variance of Firm's Revenues, a Short position in forward Contracts should be undertaken

This short position will increase the expected Revenues in case Oil becomes $40 and decrease the expected Revenues in case Oil becomes $80, thereby reducing the variance of Firm's Revenues.