Question

Modified duration gap of 3 year and market value of assets of 3 million. Manager expects interest rates to go up from 9% to 10%.

Question: show how can the manager immunize the bank assets from interest rate change by using following 2 Swaps: Swap 1: pay T-bill +1% in exchange for 7% fixed rate. Swap 2: pay fixed rate of 7% in exchange for a floating rate of T-bill +1%. Assume modified duration on 7% fixed rate security is 7.5 and the modified duration on T-bill is 1.

Answer 1

a. If the rate sensitive assets are increased by $20m, the total rate sensitive assets (RSA) will become $40m. This will result in the gap - given by (RSA - RSL) - to reduce from negative $30m to negative $10m .

b. After the actions taken in (a), if the interest rates decline by 1% the interest income on RSA and interest outflow on RSL both will decrease however since the RSA (and hence the gap was reduced) was increased, the net interest income for the bank will decrease proportionately. Since the gap reduced from negative $30m to negative $10m, assuming uniform change, the net impact should be 1% of (30-10) $20m.

c. RSL decreased by $30m to $20m and RSA increase to $100m. The resultant duration for the assets increases and liabilities decrease, however since the assets are all rate sensitive, any change in interest rate will accordingly impact the interest income of the bank. The gap between RSA and RSL is $80 m, which is an increase from earlier negative $30m. Thus the interest rate risk has increased and the bank is positioned for increase in interest rates and any decline in rates can have adverse impact on the net interest income of the bank .

d. Assets duration is 4 years and increase of 1% in interest rate will reduce the value of assets by 4%, hence the value of assets will become = $96m. On the liability side the duration is 2 years, the change in value will be -2% or $2m. The net change in net worth will be = $2 million

e. In both a and c, the manager was positioning the bank to benefit from increase in interest rates, since it will boost the interest income on assets more than liabilites in relative terms