Question

4.

Consider the following balance sheet (in millions) for an FI: Assets Duration = 10 years $ 910 Liabilities Duration = 4 years Equity $ 810 100 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 FI'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 96. 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 nine 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 Fl 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 interest rates. futures or forward contracts. a. Duration gap b. The Fl would be hurt by c. The Fl could hedge its interest rate risk by d. Impact on the Fl's equity value e. Change in value per futures contract f. Number of Treasury bond

Answer 1

a). Duration gap = asset duration - (liabilities/assets)*liability duration = 10 - (810/910)*4 = 6.44 years

b). The FI will be hurt by increase in interest rates as gap would increase.

c). The FI can hedge its interest rate risk by selling futures or forward contracts.

d). Change in equity value = -duration gap*asset value*relative change in interest rates

= -6.44*910,000,000*0.02 = -117,200,000 (Equity value will decrease by this amount)

e). Change in equity = duration of Treasury bond*Bond price*relative change in interest rates

= -9*96000*0.02 = -17,280 (No negative sign as it is a short hedge so results in a profit.)

f). Number of Treasury bond futures contract = expected loss/expected profit per contract

= 117,200,000/17,280 = 6,782.41 or 6,782