Question

3.

Hedge Row Bank has the following balance sheet (in millions): $ 189 $210 Liabilities Assets Equity 21 $ 210 $210 Total Total The duration of the assets is 7 years and the duration of the liabilities is 5 years. The bank is expecting interest rates to fall from 10 percent to 9 percent over the next year. a. What is the duration gap for Hedge Row Bank? (Round your answer to 2 decimal places. (e.g., 32.16)) b. What is the expected change in net worth for Hedge Row Bank if the forecast is accurate? (Enter your answer in millions rounded to 3 decimal places. (e.g., 32.161)) c. What will be the effect on net worth if interest rates increase 100 basis points? (Negative amount should be indicated by a minus sign. Enter your answer in millions rounded to 3 decimal places. (e.g., 32.161)) d. If the existing interest rate on the liabilities is 6 percent and that on the assets is 10 percent, what will be the effect on net worth of a 1 percent increase in interest rates? (Negative amount should be indicated by a minus sign. Do not round intermediate calculations. Enter your answer in millions rounded to 4 decimal places. (e.g., 32.1616)) Duration gap years а. million Expected change in net worth b. Expected change in net worth million C. Expected change in net worth d. million OO

Answer 1

Solution:

a	Duration Gap	2.5	years
b	Expected Change in net worth	$4.773	million
c	Expected Change in net worth	-$4.773	million
d	Expected Change in net worth	- $4.4485	million

a) Duration Gap (DGAP) = Duration of assets - (market value of liabilities / market value of assets) x Duration of liability

= 7 - (189/210) x 5

= 2.5 years

b) Expected change in net worth= -DGAP [change in interest rates/(1+ R)] x market value of asset

= -2.5(-0.01/1.1) $ 210

= $4.773 million

c) Expected change in net worth= -DGAP [change in interest rates/(1+ R)] x market value of asset

= -2.5(0.01/1.1) $ 210

=  -$4.773 million

d) We need to find the impact on equity of a change in interest rates in both assets and liabilities.We find this by determining difference between the change in interest rates of assets and liabilities.

Expected change in net worth= Change in Asset Value - Change in Liabilities value

Change in Asset Value = -Duration of assets [change in interest rate of assets/(1+ R(a))] x market value of asset

= -7 x [.01/1.1] x $210

= -$13.36363623 million

Change in Liabilities value= - Duration of Liabilities [change in interest rates of liabilities/(1+ R(L)] x market value of liabilities

= -5 x [0.01/1.06] x $189

= -$ 8.915094279 million

Expected change in net worth= -$13.36363623 - (-$ 8.915094279)

= - $4.4485 million