Question 9. Price Sensitivity Hedge (9 marks) Mr. Toriop manages a bond portfolio valued at $27,492,045. The bonds in this portfolio have a face value of $25 million. The portfolio has a yield of 8.35 percent and a duration of 7.67. Mr. Toriop is worried that interest rates will rise within the next year. He would like to lower the duration of your bond portfolio to 5 years. He finds a one-year bond futures contract and thinks that it would be an appropriate hedge for your portfolio. This futures contract is priced at 109 17/32, has an implied yield of 8 percent, and has an implied duration of 7.9 years. The futures contract size is $100,000. a. Should Mr. Toriop buy or sell futures? (1 mark) b. How many contracts should Mr. Toriop use? (4 marks) c. Suppose that the portfolios value falls to $26,557,089, and the futures price turns out to be 103 8/32 in one years time. What is the net profit from the hedged position? (3 marks) d. If Mr. Toriop were to liquidate the entire bond portfolio in one years time given the information in part (c), what would be the total proceeds received? (1 mark)