Question

1.Assume that the market value assets and liabilities of a bank are $120 million and $220 million, respectively, and their durations are 2 and 3. Find the new market value of assets that eliminates the interest-risk of this bank.

2. Assume that the assets and liabilities of a bank are $150 million and $120 million, respectively, and their durations are 3 and 4. What will be the effect of an increase in interest rate of 5% on the net worth of the bank? ​

please show the steps.

Answer 1

1. Duration gap should be zero to eliminate the interest risk

Duration gap= Duration of assets- Duration of liabilities*Liabilities/ Assets

Let assets be A

0= 2-3*220/A

660/A = 2

660=2A

A=$ 330 million

The new value of assets that eliminates the interest risk= $330 million

2. Change in value = -Change in interest rate*Duration* value

Change in market value of assets= -5%*3*$150 million

=-15%*150 million

=-22.5 million

Change in market value of liabilities= -5%*4* 120 million

= -24 million

Change in Net worth= Change in assets- change in liabilities

=-22.5 -(-24)

=$1.5 million