Question

Suppose the First National Bank of Duluth has $500.00 million in total assets with an average asset duration of five years. Assume that the bank’s liabilities are comprised of $86.75 million of demand deposits and $163.75 million in bonds with a 4.00% coupon rate (which pays annually) and a five year time-to-maturity. Further assume that current market interest rates are at 9.00% per annum.

What is this bank’s duration gap? Is the bank asset- or liability-sensitive?

Answer 1

The formula for duration gap is,

$D_{Gap}=D_{A}-D_{L}\times \frac{L}{A}$

Where , D_Gap=Duration gap

D_A = Weighted duration of Asset., A = value of assets

D_L= weighted duration of liablity L= Value of liability

Given, D_A=5 YEARS, D_L= 5 Years, A= $500 , L = $86.75 + $163.75= $250.5

Putting the values in formula above

$D_{Gap}=5-5 \times \frac{250.5}{500}$

$D_{Gap}=5-5 \times 0.501$

$D_{Gap}=5-2.505$

$D_{Gap}=2.495$

Hence, bank's duration gap = 2.495 years answer.

Since ,the duration gap is positive ,In this situation, if interest rates rise, assets will lose more value than liabilities, thus reducing the value of the firm's equity. If interest rates fall, assets will gain more value than liabilities, thus increasing the value of the firm's equity. Hence,bank is asset -sensitive. Answer.