Question

XYZ Bank has the following balance sheet in millions

Assets	Liabilities and Equity
Cash = $30	Demand deposits = $100
4-year treasury notes = $40	3-year certificates of deposits = $150
20-year mortgages = $230	Equity= $50
Total Assets = $300	Total Liabilities and Equity = $300

a) What is the maturity gap for XYZ?

b) Is XYZ bank more exposed to an increase or decrease in interest rates? Explain why?

Answer 1

Duration gap is the difference between the duration of the assets and the duration of the liabilities of the bank. Since we don’t have other details, we can assume the duration of the financial instruments is equal to their maturity. Total duration of assets (or liabilities) is sum of duration of individual asset (or liability) * $ value of the asset (or liability) divided by the total value of the assets (or liabilities).

Assets	Value	Duration	Weighted Duration		Liability	Value	Duration	Weighted Duration
Cash	30	0	0		Demand deposit	100	0	0
Treasury notes	40	4	160		CD	150	3	450
Mortgage	230	20	4600		Total	250	1.80	450
Total	300	15.87	4760

Duration of assets - liability=

14.07

As it is clear from the above calculation, the duration gap = duration of assets- duration of liability= 14.07 years. Hence, the duration of assets is more than that of the liability.
Duration is the sensitivity of the security to interest rates change. The duration gap of the bank is positive (duration of assets > duration of liability). Hence, in case of increase in interest rates, the value of assets will decrease by a much larger amount than the value of the liabilities. On the other hand, in case of decrease in interest rates, the value of assets will increase by a much larger amount than the value of the liabilities. Its risk arises from decrease in the value of the assets. Hence, it is exposed more to the increase in interest rates.