1. A bank has the following balance sheet:
Assets Avg. Rate Liabilities/Equity Avg. Rate
Rate sensitive $550,000 7.75% Rate sensitive $575,000 6.25%
Fixed rate 755,000 8.75 Fixed rate 605,000 7.50
Nonearning 265,000 Nonpaying 390,000
Total $1,570,000 Total $1,570,000
Suppose interest rates fall such that the average yield on rate-sensitive assets decreases by 15 basis points and the average yield on rate-sensitive liabilities decreases by 5 basis points.
a. Calculate the bank’s CGAP and gap ratio.
b. Assuming the bank does not change the composition of its balance sheet, calculate the resulting change in the bank’s interest income, interest expense, and net interest income.
c. The bank’s CGAP is negative and interest rates decreased, yet net interest income decreased. Explain how the CGAP and spread effects influenced this decrease in net interest income.
2.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 75 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?
3. A bank has the following balance sheet:
Assets Avg. Rate Liabilities/Equity Avg. Rate
Rate sensitive $225,000 6.35% Rate sensitive $300,000 4.25%
Fixed rate 550,000 7.55 Fixed rate 505,000 6.15
Nonearning 120,000 Nonpaying 90,000
Total $895,000 Total $895,000
Suppose interest rates rise such that the average yield on rate-sensitive assets increases by 45 basis points and the average yield on rate-sensitive liabilities increases by 35 basis points.
a. Calculate the bank’s repricing GAP.
b. Assuming the bank does not change the composition of its balance sheet, calculate the net interest income for the bank before and after the interest rate changes. What is the resulting change in net interest income?
c.Explain how the CGAP and spread effects influenced this increase in net interest income.
4.What are some of the weakness of the repricing model? How have large banks solved the problem of choosing the optimal time period for repricing? What is runoff cash flow, and how does this amount affect the repricing model’s analysis?
5.33. 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?