Question

The statement of financial position for Michael Bank is shown below. Assets	Duration (years)	Market yield (%)	Market Value ($ in millions)	Liabilities and Equity	Duration (years)	Market yield (%)	Market Value ($ in millions)
Cash	100	Demand account deposits	120
Consumer loans	3.0	5.4	300	Term deposits	3.3	4.8	160
Commercial and industrial loans	6.6	6.6	600	Investment account deposits	1.2	3.2	150
Variable-rate mortgages	0.3	7.2	150	Fed funds	0.02	4.4	330
Fixed-rate mortgages	18.8	8.3	160	CDs	4.2	4.3	450
Other assets	100	Equity	200

(a) Calculate overall duration of all the assets.

(b) Calculate overall duration of all the liabilities.

(c) Calculate the leverage adjusted DGAP.

(d) Calculate overall change in values for all the assets for a 3% increase in interest rate.

(e) Calculate overall change in values for all the liabilities for a 3% increase in interest rate.

(f) Using the results from (d) and (e), compute the change in equity value for a 3% increase in interest rate.

(g) The director of Michael Bank wants to immunize the balance sheet completely by setting a new value of duration of all the assets. However, if it is impossible to change the duration of all the liabilities, and the top management does not want to change the total values of assets and liabilities. In that case, calculate a new value of duration of all the assets for the director so that immunization can be carried out.

Answer 1

Duration of a portfolio = sum of weighted durations

a). Duration of assets = 5.61 years

b). Duration of liabilities = 1.85 years

c). Leverage adjusted DGAP = Da - k*Dl where Da = duration of assets; Dl = duration of liabilities; k = total liabilities/total assets

DGAP = 5.61 - ((1,410-200)/1,410)*1.85 = 4.0268

d). Change in market value = - current market value*change in interest rate*modified duration where change in interest rate = +0.003; modified duration = duration/(1+current yield)

For a 3% increase in interest rates, total asset value declines by 221.64 million

e).

For a 3% increase in interest rates, total liabilities decline by 74.90 million

f). Change in equity = change in asset value - change in liability value

= -221.64 -74.90 = -146.75 million

g). Since duration of liabilities and market values of assets and liabilities cannot be changed, the new asset duration should be

DGAP = Da - k*Dl = 0

Da = k*Dl = ((1,410-200)/1,410*1.85 = 1.59 years (For immunization, duration of assets has to equal the duration of liabilities)