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Solutions for End-of-Chapter Questions and Problems: Chapter Eight
1. How do monetary policy actions made by the Federal Reserve impact interest rates?
Through its daily open market operations, such as buying and selling Treasury bonds and
2. How has the increased level of financial market integration affected interest rates?
Increased financial market integration, or globalization, increases the speed with which interest
3. What is the repricing gap? In using this model to evaluate interest rate risk, what is meant
by rate sensitivity? On what financial performance variable does the repricing model
focus? Explain.
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4. What is a maturity bucket in the repricing model? Why is the length of time selected for
repricing assets and liabilities important when using the repricing model?
The maturity bucket is the time window over which the dollar amounts of assets and liabilities
5. What is the CGAP effect? According to the CGAP effect, what is the relation between
changes in interest rates and changes in net interest income when CGAP is positive? When
CGAP is negative?
6. Which of the following is an appropriate change to make on a bank’s balance sheet
when GAP is negative, spread is expected to remain unchanged and interest rates are
expected to rise?
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Education.
d. Replace equity with demand deposits
No. This change will have no impact on either RSAs or RSLs. So, will have no impact on GAP.
e. Replace vault cash with marketable securities
Yes. This change will increase RSAs, which will increase GAP.
7. If a bank manager was quite certain that interest rates were going to rise within the next six
months, how should the bank manager adjust the bank’s six-month repricing gap to take
advantage of this anticipated rise? What if the manger believed rates would fall in the next
six months.
8. Consider the following balance sheet positions for a financial institution:
• Rate-sensitive assets = $200 million. Rate-sensitive liabilities = $100 million
• Rate-sensitive assets = $100 million. Rate-sensitive liabilities = $150 million
• Rate-sensitive assets = $150 million. Rate-sensitive liabilities = $140 million
a. Calculate the repricing gap and the impact on net interest income of a 1 percent
increase in interest rates for each position.
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b. Calculate the impact on net interest income on each of the above situations assuming a
1 percent decrease in interest rates.
c. What conclusion can you draw about the repricing model from these results?
9. Consider the following balance sheet for MMC Bancorp (in millions of dollars):
Assets Liabilities
1. Cash and due from $ 6.25 1. Equity capital (fixed) $25.00
2. Short-term consumer loans 62.50
(one-year maturity) 2. Demand deposits 50.00
3. Long-term consumer loans 31.25
(two-year maturity) 3. Passbook savings 37.50
4. Three-month T-bills 37.50 4. Three-month CDs 50.00
5. Six-month T-notes 43.75 5. Three-month banker’s
acceptances 25.00
6. Three-year T-bonds 75.00 6. Six-month commercial paper 75.00
7. 10-year, fixed-rate mortgages 25.00 7. One-year time deposits 25.00
8. 30-year, floating-rate
mortgages 50.00 8. Two-year time deposits 50.00
9. Premises 6.25
$337.50 $337.50
a. Calculate the value of MMC’s rate-sensitive assets, rate sensitive liabilities, and
repricing gap over the next year.
Looking down the asset side of the balance sheet, we see the following one-year rate-sensitive
assets (RSA):
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Summing these four items produces one-year RSA of $193.75 million. The remaining $143.75
million is not rate sensitive over the one-year repricing horizon. A change in the level of interest
rates will not affect the interest revenue generated by these assets over the next year. The $6.25
million in the cash and due from category and the $6.25 million in premises are nonearning
Looking down the liability side of the balance sheet, we see that the following liability items
clearly fit the one-year rate or repricing sensitivity test:
Summing these four items produces one-year rate-sensitive liabilities (RSL) of $175 million. The
remaining $162.50 million is not rate sensitive over the one-year period. The $25 million in
equity capital and $50 million in demand deposits do not pay interest and are therefore classified
b. Calculate the expected change in the net interest income for the bank if interest rates
rise by 1 percent on both RSAs and RSLs. If interest rates fall by 1 percent on both
RSAs and RSLs.
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The CGAP would project the expected annual change in net interest income ()NII) of the bank is:
10. What are the reasons for not including demand deposits as rate-sensitive liabilities in the
repricing analysis for a commercial bank? What is the subtle but potentially strong reason
for including demand deposits in the total of rate sensitive liabilities? Can the same
11. What is the gap to total assets ratio? What is the value of this ratio to interest rate risk
managers and regulators?
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12. Which of the following assets or liabilities fit the one-year rate or repricing sensitivity test?
3-month U.S. Treasury bills Yes
1-year U.S. Treasury notes Yes
20-year U.S. Treasury bonds No
20-year floating-rate corporate bonds with annual repricing Yes
30-year floating-rate mortgages with repricing every two years No
30-year floating-rate mortgages with repricing every six months Yes
Overnight fed funds Yes
9-month fixed-rate CDs Yes
1-year fixed-rate CDs Yes
5-year floating-rate CDs with annual repricing Yes
Common stock No
13. What is the spread effect?
The spread effect is the effect that a change in the spread between rates on RSAs and RSLs has
14. A bank manager is quite certain that interest rates are going to fall within the next six
months. How should the bank manager adjust the bank’s six-month repricing gap and
spread to take advantage of this anticipated rise? What if the manger believes rates will rise
15. Consider the following balance sheet for WatchoverU Savings, Inc. (in millions):
30-year fixed-rate loans 3-year time deposits
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a. What is WatchoverU’s expected net interest income at year-end?
b. What will net interest income be at year-end if interest rates rise by 2 percent?
c. Using the cumulative repricing gap model, what is the expected net interest income for
a 2 percent increase in interest rates?
d. What will net interest income be at year-end if interest rates on RSAs increase by 2
percent but interest rates on RSLs increase by 1 percent? Is it reasonable for changes in
interest rates on RSAs and RSLs to differ? Why?
16. Use the following information about a hypothetical government security dealer named M.
P. Jorgan. Market yields are in parenthesis, and amounts are in millions.
Assets Liabilities and Equity
Cash $10 Overnight repos $170
1-month T-bills (7.05%) 75 Subordinated debt
3-month T-bills (7.25%) 75 7-year fixed rate (8.55%) 150
2-year T-notes (7.50%) 50
8-year T-notes (8.96%) 100
5-year munis (floating rate)
(8.20% reset every 6 months) 25 Equity 15
Total assets $335 Total liabilities & equity $335
a. What is the repricing gap if the planning period is 30 days? 3 months? 2 years? Recall
that cash is a non-interest-earning asset.
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b. What is the impact over the next 30 days on net interest income if interest rates increase
50 basis points? Decrease 75 basis points?
c. The following one-year runoffs are expected: $10 million for two-year T-notes and $20
million for eight-year T-notes. What is the one-year repricing gap?
d. If runoffs are considered, what is the effect on net interest income at year-end if interest
rates increase 50 basis points? Decrease 75 basis points?
17. A bank has the following balance sheet:
Assets Avg. Rate Liabilities/Equity Avg. Rate
Rate sensitive $550,000 7.75% Rate sensitive $375,000 6.25%
Fixed rate 755,000 8.75 Fixed rate 805,000 7.50
Nonearning 265,000 Nonpaying 390,000
Total $1,570,000 Total $1,570,000
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, gap to total assets ratio, and gap ratio.
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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. Explain how the CGAP and spread effects influenced the change in net interest income.
18. 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, gap to total asset ratio, 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.
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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.
19. 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?
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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?
20. 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.
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Education.
The CGAP affect worked to decrease net interest income. That is, the CGAP was negative while
interest rates increased. Thus, interest income increased by less than interest expense. The result
is a decrease in NII. In contrast, the spread effect worked to increase net interest income. The
spread increased by 10 basis points. According to the spread affect, as spread increases, so does
net interest income. However, in this case, the increase in NII due to the spread effect was
dominated by the decrease in NII due to the CGAP effect.
21. 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?
The repricing model has four general weaknesses:
22. 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?
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23. Nearby Bank has the following balance sheet (in millions):
Assets Liabilities and Equity
Cash $60 Demand deposits $140
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?
24. 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
Cash $20 Demand deposits $100
15-year commercial loan at 10% 5-year CDs at 6% interest,
interest, balloon payment 160 balloon payment 210
30-year mortgages at 8% interest, 20-year debentures at 7% interest, 120
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?
If interest rates increase one percent, the value and average maturity of the assets will be: