Question

For every $100 in assets, a bank has $40 in interest-rate sensitive assets, and the other $60 in non-interest-rate sensitive assets. The same bank has $50 for every $100 in liabilities in interest-rate sensitive liabilities, the other $50 are in liabilities that are not interest-rate sensitive. Suppose the interest rate on assets increases from 5 to 6 percent, and the interest rate on liabilities increases from 3 to 4 percent.
a.   Determine the impact of the interest rate changes on the bank's profits per $100 of assets. (Show all your calculations and fully explain)

Answer 1

Assets

Value of interest rate sensitive assets = $40

Value of non-interest rate sensitive assets = $60

Rate increases from 5% to 6%

Initial interest income on asset = 5% * 40 = $2

Interest income after a change in interest = 6% * 40 = $2.4

Increase in interest income = $0.4 per $100 assets

Liabilities

Value of interest rate sensitive liabilities = $50

Value of non-interest rate sensitive liabilities = $50

Rate increases from 3% to 4%

Initial interest expense = 3% * 50 = $1.50

Interest expense after a change in interest = 4% * 50 = $2

Increase in interest expense = $0.5 per $100

Hence banks' liabilities increase more than the assets because of change in interest rates.

Loss/Decrease in profit = 0.5 - 0.4 = $0.1 per 100 dollars of assets

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