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Consider the following balance sheet (in millions) for an Fl: Assets Duration - 11 years $ 890 Liabilities Duration - 7 years Equity $ 810 80 a. What is the Fl's duration gap? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) b. What is the Fl's interest rate risk exposure? c. How can the Fl use futures and forward contracts to create a macrohedge? d. What is the impact on the Fl's equity value if the relative change in interest rates is an increase of 2 percent? That is, A R/(1+R) = 0.02. (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in dollars not in millions.) e. Suppose that the Fl in part (c) macrohedges using Treasury bond futures that are currently priced at 97. What is the change in value per futures contract used to hedge if the relative change in all interest rates is an increase of 2 percent? That is, A R/(1+ R) = 0.02. Assume that the deliverable Treasury bond has a duration of ten years. The bonds underlying the futures contract have a par value of $100,000. (Negative amount should be indicated by a minus sign. Enter your answer in dollars not in millions.) f. If the FI wants to macrohedge, how many Treasury bond futures contracts does it need? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round down your answer to the nearest whole number.) years a. interest rates. b. futures or forward contracts. Duration gap The Fl would be hurt by The FI could hedge its interest rate risk by Impact on the FI's equity value Change in value per futures contract Number of Treasury bond d. e. f. An Fl has a $360 million asset portfolio that has an average duration of 90 years. The average duration of its $320 million in liabilities is 5.4 years. Assets and liabilities are yielding 10 percent. The Fl uses put options on T-bonds to hedge against unexpected interest rate increases. The average delta (b) of the put options has been estimated at -0.3 and the average duration of the T-bonds is 9.5 years. The current market value of the T-bonds is $96,000. Put options on T-bonds are selling at a premium of $1.25 per face value of $100. a. What is the modified duration of the T-bonds if the current level of interest rates is 10 percent? (Do not round intermediate calculations. Round your answer to 4 decimal places. (e.g., 32.1616) b. How many put option contracts should the Fl purchase to hedge its exposure against rising interest rates? The face value of the T- bonds is $100,000. (Do not round intermediate calculations. Round your answer to the nearest whole number.) c. If interest rates increase 50 basis points, what will be the change in value of the equity of the Fl? (Enter your answer in dollars not in millions. Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to the nearest dollar amount.) d. If interest rates increase 50 basis points, what will be the change in value of the T-bond option hedge pos n? (Enter your answer in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.) e. What must be the change in interest rates before the change in value of the balance sheet (equity) will offset the cost of placing the hedge? (Do not round intermediate calculations. Negative value should be indicated by a minus sign. Round your answer to 2 decimal places. (e.g., 32.16)) f. How much must interest rates change before the payoff of the hedge will exactly cover the cost of placing the hedge? (Do not round intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) years a. Modified duration Number of contracts b. c. If interest rates increase 50 basis points, what will be the change in value of the equity of the FI? (Enter your answer in dollars no in millions. Negative amount should be indicated by a minus sign. Do not round Intermediate calculations. Round your answert the nearest dollar amount.) d. If interest rates increase 50 basis points, what will be the change in value of the T-bond option hedge position? (Enter your answ in dollars not in millions. Do not round intermediate calculations. Round your answer to the nearest dollar amount.) e. What must be the change in interest rates before the change in value of the balance sheet (equity) will offset the cost of placingt hedge? (Do not round intermediate calculations. Negative value should be indicated by a minus sign. Round your answer to 2 decimal places. (e.g., 32.16)) f. How much must interest rates change before the payoff of the hedge will exactly cover the cost of placing the hedge? (Do not ro intermediate calculations. Round your answer to 2 decimal places. (e.g., 32.16)) years . Modified duration b. Number of contracts C d. Change in equity value Change in T-bond value Change in interest rates Change in interest rates % e. % f