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

DGAP = Duration of assets - (Liabilities/Assets) * Duration of Liabilities

= 10 - (86/95) * 2 = 8.1895

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Rate-sensitive assets - Rate sensitive liabilities = $95 Mn - $86 Mn = $9 mn

Effect on Net worth = -DGAP * A * Change in rate/ (1+ rate)

Change in value of futures = Duration of futures * Price of futures * Number of futures * Change in rate/ (1+ rate)

Equate Effect on net worth to Change in value of futures

-DGAP * A = Duration of futures * Price of futures * Number of futures

-8.1895 * $95 Mn = 4 * 96.375 * Number of futures

Number of futures = 2018164.72 ~= 2018165

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Hedging is to short futures so as to benefit from fall in price.

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