Answer the simple finance/accounting related question. Disregard writing on page

Question

Answer the simple finance/accounting related question. Disregard writing on page.
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 o event of an inc contracts. Right now, there are plenty of T-bond futures in the market, with duration rease in interest rates, it is contemplating a macrohedge with interest rate futures trading at 96-12 (i.e., $96,375). Assume that the spot and futures interest rates move together. 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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