Suppose a bank has $500 million in interest rates sensitive assets, with a durat

Question

Suppose a bank has $500 million in interest rates sensitive assets, with a duration of 5 years, and $600 million of interest rate sensitive liabilities with a duration of 2 years.

a. If interest rates increase from 3% to 4%, what is the percentage change in net worth of the bank? Enter your response as a percent without the percent sign (for example, enter a numerical answer of 0.0525 = 5.25%, as 5.25).

b. Given the information in the previous question, what duration of assets would lead to a duration gap of zero?

c. Given the information in question part a above, what duration of liabilities would lead to a duration gap of zero?

Explanation / Answer

A

Change in net worth of bank = Change in Value of assets - Change in value of liabilities

Change in asset value = $500 * 5 * 1% = $25 Mn

Change in liabilities value = $600 * 2 * 1% = $12 Mn

Change in net worth of bank = $25 Mn - $12 Mn = $13 Mn

% Change in net worth of bank = Change in net worth/ Original Asset value = $13 Mn/ $500 Mn = 0.026 = 2.6 %

Ans = 2.6

B

Let Duration Gap be 0 for X value of duration of Assets

Duration gap = $500 Mn * X - $600 Mn * 2 = 0

X = $600 Mn * 2 / $500 = 2.4 years

C

Let Duration Gap be 0 for Y value of duration of Liabilities

Duration gap = $500 Mn * 5 - $600 Mn * Y = 0

Y = $500 Mn * 5 / $600 = 4.17 years

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