1.What is a maturity gap? How can the maturity model be used to immunize an FI’s portfolio? What is the critical requirement that allows maturity matching to have some success in immunizing the balance sheet of an FI?
Assets Liabilities and Equity
5-year Treasury notes 60 1-year certificates of deposit 160
30-year mortgages 200 Equity 20
Total assets $320 Total liabilities and equity $320
What is the maturity gap for Nearby Bank? Is Nearby Bank more exposed to an increase or decrease in interest rates? Explain why?
3.County Bank has the following market value balance sheet (in millions, all interest at annual rates). All securities are selling at par equal to book value.
Assets Liabilities and Equity
15-year commercial loan at 10% 5-year CDs at 6% interest,
interest, balloon payment 160 balloon payment 210
balloon payment 300 balloon payment
Equity 50
Total assets $480 Total liabilities & equity $480
a.What is the maturity gap for County Bank?
b.What will be the maturity gap if the interest rates on all assets and liabilities increase by 1 percent?
c.What will happen to the market value of the equity?
4. If a bank manager is certain that interest rates were going to increase within the next six months, how should the bank manager adjust the bank’s maturity gap to take advantage of this anticipated increase? What if the manager believes rates will fall? Would your suggested adjustments be difficult or easy to achieve?
5. Gunnison Insurance has reported the following balance sheet (in thousands):
Assets Liabilities and Equity
15-year munis 165 5-year note 160
Equity 45
Total assets $340 Total liabilities & equity $340
All securities are selling at par equal to book value. The two-year notes are yielding 5 percent, and the 15-year munis are yielding 9 percent. The one-year commercial paper pays 4.5 percent, and the five-year notes pay 8 percent. All instruments pay interest annually.
a.What is the weighted-average maturity of the assets for Gunnison?
b.What is the weighted-average maturity of the liabilities for Gunnison?
c.What is the maturity gap for Gunnison?
d.What does your answer to part (c) imply about the interest rate exposure of Gunnison Insurance?
e.Calculate the values of all four securities of Gunnison Insurance’s balance sheet assuming that all interest rates increase 2 percent. What is the dollar change in the total asset and total liability values? What is the percentage change in these values?
f.What is the dollar impact on the market value of equity for Gunnison? What is the percentage change in the value of the equity?
g.What would be the impact on Gunnison’s market value of equity if the liabilities paid interest semiannually instead of annually?
6.Scandia Bank has issued a one-year, $1million CD paying 5.75 percent to fund a one-year loan paying an interest rate of 6 percent. The principal of the loan will be paid in two installments, $500,000 in six months and the balance at the end of the year.
a.What is the maturity gap of Scandia Bank? According to the maturity model, what does this maturity gap imply about the interest rate risk exposure faced by Scandia Bank?
b.What is the expected net interest income at the end of the year?
c.What would be the effect on annual net interest income of a 2 percent interest rate increase that occurred immediately after the loan was made? What would be the effect of a 2 percent decrease in rates?
d.What do these results indicate about the ability of the maturity model to immunize portfolios against interest rate exposure?
7.EDF Bank has a very simple balance sheet. Assets consist of a two-year, $1 million loan that pays an interest rate of LIBOR plus 4 percent annually. The loan is funded with a two-year deposit on which the bank pays LIBOR plus 3.5 percent interest annually. LIBOR currently is 4 percent, and both the loan and the deposit principal will be paid at maturity.
a.What is the maturity gap of this balance sheet?
b.What is the expected net interest income in year 1 and year 2?
c.Immediately prior to the beginning of year 2, LIBOR rates increased to 6 percent. What is the expected net interest income in year 2? What would be the effect on net interest income of a 2 percent decrease in LIBOR?
8.What are the weaknesses of the maturity model?
9. The current one-year Treasury bill rate is 5.2 percent, and the expected one-year rate 12 months from now is 5.8 percent. According to the unbiased expectations theory, what should be the current rate for a two-year Treasury security?
10. Suppose that the current one-year rate (one-year spot rate) and expected one-year T-bill rates over the following three years (i.e., years 2, 3, and 4, respectively) are as follows:
1R1=6% E(2r1)=7% E(3r1)=7.5% E(4r1)=7.85%
Using the unbiased expectations theory, calculate the current (long-term) rates for one-, two-, three-, and four-year-maturity Treasury securities. Plot the resulting yield curve.