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# 6. Suppose a one year oil forward price is \$60 per barrel. Suppose further that there...

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)?

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.

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