5. (6 points) A bank has $95 million of assets with duration of 10 years, and li

Question

5. (6 points) A bank has $95 million of assets with duration of 10 years, and liabilities worth $86 million with duration of 2 years. Since the bank is concerned about preserving the value of its equity in event of an increase in interest rates, it is contemplating a macrohedge w contracts. Right now, there are plenty of T-bond futures in the market, with duration of 4 years, trading at 96-12 (i.e., $96,375). Assume that the spot and futures interest rates move together. the ith interest rate futures The duration gap (DGAP) of the bank is Workout To hedge the risk, the number of futures contract to enter is Workout: Is the hedging position to long or to short futures? Workout

Explanation / Answer

Assets =$95 million

Liabilities =$86 million

k =86/95 =0.9052

Equity =$95-86 =$9 million

1.) DGAP = Dassets - k x DLiabilities

              = 10 - 0.9052 x 2

              = 10 - 1.8105

              = 8.1895

2.) Number of Contracts Required = DGAP x Assets / (DBill x Pbill)

                                                 = 8.1895 x 95,000,000 / (4 x 96,375)

                                                 = 2,018 contracts

3.) The bank should sell futures contracts since an increase in interest rates would cause the value of the equity and the futures contracts to decrease. These sold contracts will be later bought back at later date to offset the looses in equity value due to interest rate increase.

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