Problem set 3

1. The balance sheet of A. G. Fredwards, a government security dealer, is listed below. Market yields are in parentheses, and amounts are in millions.

Assets Liabilities and Equity

Cash $20 Overnight repos $340

1-month T-bills (7.05%) 150 Subordinated debt

3-month T-bills (7.25%) 150 7-year fixed rate (8.55%) 300

2-year T-notes (7.50%) 100

8-year T-notes (8.96%) 200

5-year munis (floating rate)

(8.20% reset every 6 months) 50 Equity 30

Total assets $670 Total liabilities and equity $670

a. What is the repricing gap if the planning period is 30 days? 3-month days? 2 years?

b. What is the impact over the next three months on net interest income if interest rates on RSAs increase 50 basis points and on RSLs increase 60 basis points?

c. What is the impact over the next two years on net interest income if interest rates on RSAs increase 50 basis points and on RSLs increase 60 basis points?

d. Explain the difference in your answers to parts (b) and (c). Why is one answer a negative change in NII, while the other is positive?

2. An insurance company has invested in the following fixed-income securities: (a) $10,000,000 of five-year Treasury notes paying 5 percent interest and selling at par value, (b) $5,800,000 of 10-year bonds paying 7 percent interest with a par value of $6,000,000, and (c) $6,200,000 of 20-year subordinated debentures paying 9 percent interest with a par value of $6,000,000.

1. What is the weighted-average maturity of this portfolio of assets?

b. If interest rates change so that the yields on all of the securities decrease 1 percent, how does the weighted-average maturity of the portfolio change?

c. Explain the changes in the weighted-average maturity of the portfolio if the yields increase by 1 percent.

d. Assume that the insurance company has no other assets. What will be the effect on the market value of the company's equity if the interest rate changes in (b) and (c) occur?

3. 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?

1. What do the answers to parts (b) and (c) of this question suggest about the use of maturity gap to immunize an FI against interest rate risk?

4. The balance sheet for Gotbucks Bank, Inc. (GBI), is presented below ($ millions):

Assets Liabilities and Equity

Cash $30Core deposits $20

Federal funds 20Federal funds 50

Loans (floating) 105 Euro CDs 130

Loans (fixed) 65 Equity 20

Total assets $220 Total liabilities & equity $220

Notes to the balance sheet: The fed funds rate is 8.5 percent, the floating loan rate is LIBOR + 4 percent, and currently LIBOR is 11 percent. Fixed rate loans have five-year maturities, are priced at par, and pay 12 percent annual interest. The principal is repaid at maturity. Core deposits are fixed rate for two years at 8 percent paid annually. The principal is repaid at maturity. Euros currently yield 9 percent.

a. What is the duration of the fixed-rate loan portfolio of Gotbucks Bank?

b. If the duration of the floating-rate loans and fed funds is 0.36 year, what is the duration of GBI's assets?

c. What is the duration of the core deposits if they are priced at par?

d. If the duration of the Euro CDs and fed funds liabilities is 0.401 year, what is the duration of GBI's liabilities?

e. What is GBI's duration gap? What is its interest rate risk exposure?

f. What is the impact on the market value of equity if the relative change in all interest rates is an increase of 1 percent (100 basis points)? Note that the relative change in interest rates isDR/(1+R) = 0.01.

g. What is the impact on the market value of equity if the relative change in all interest rates is a decrease of 0.5 percent (-50 basis points)?

h. What variables are available to GBI to immunize the bank? How much would each variable need to change to get DGAP equal to zero?