A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The company will lose $1 million for each 1 cent increase in the price per gallon of the new fuel over the next three months. The new fuels price changes have a standard deviation that is 50% greater than price changes in gasoline futures prices.

a) If gasoline futures are used to hedge the exposure, what should the hedge ratio be?

b) What is the companys exposure measured in gallons of the new fuel?

How do you know their exposure is 100 million gallons of the new fuel?

c) What position, measured in gallons, should the company take in gasoline futures?

3.30. It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the December futures contract on a stock index to change the beta of the portfolio to 0.5 during the period July 16 to November 16. The index futures price is currently 2,000 and each contract is on $250 times the index.

(a) What position should the company take and why?

(b) Suppose that the company changes its mind and decides to increase the beta of the portfolio from 1.2 to 1.5. What position in futures contracts should it take and why?