Question

26. The following balance sheet information is available (amounts in thousands of
dollars and duration in years) for a financial institution:
Amount Duration
T-bills
T-notes
T-bonds
Loans
Deposits
Federal funds
Equity
$ 90
55
176
2,724
2,092
238
715
0.50
0.90
x
7.00
1.00
0.01
Treasury bonds are five-year maturities paying 6 percent semiannually and sell-
ing at par.
a. What is the duration of the T-bond portfolio?
b. What is the average duration of all the assets?
c. What is the average duration of all the liabilities?
d. What is the leverage adjusted duration gap? What is the interest rate risk
exposure?
e. What is the forecasted impact on the market value of equity caused
by a relative upward shift in the entire yield curve of 0.5 percent [i.e.,
ΔR/(1 + R) = 0.0050]?
f. If the yield curve shifts downward 0.25 percent [i.e., ΔR/(1 + R) = – 0.0025],
what is the forecasted impact on the market value of equity?
g. What variables are available to the financial institution to immunize the balance
sheet? How much would each variable need to change to get DGAP to equal 0?
27. Refer again to the financial institutions in problem 26.
a. What is the change in the value of the firm’s assets for a relative upward shift
in the entire yield curve of 0.5 percent?
b. What is the change in the value of the firm’s liabilities for a relative upward
shift in the entire yield curve of 0.4 percent?
c. What is the resulting change in the value of equity for the firm?

Answer 1

a) Duration=P.V CF*T/PV CF=$773.18/$176=4.3931

b) [(.5)($90) + (.9)($55) + (4.3931)($176) + (7)($2,724)]/$3,045 = 6.5470 years

c) [(1)($2,092) + (0.01)($238)]/$2,330 = 0.8989 years

d) DGAP = DA- kDL= 6.5470 - ($2,330/$3,045)(0.8989) = 5.8592 yearsThe duration gap is positive, indicating that an increase in interest rates will lead to a decrease in the market value of equity.

e) The market value of the equity will change by:∆MVE = -DGAP * (A) *∆R/(1 + R) = -5.8592($3,045)(0.0050) = -$89.207. The loss inequity of $89,207 will reduce the market value of equity to $625,793.

f) The change in the value of equity is∆MVE = -5.8592($3,045)(-0.0025) = $44,603. Thus,the market value of equity will increase by $44,603, to $759,603.