On questions that require calculations, you may receive partial credit for answers that are not wholly correct if you include your calculations. On questions that ask for an explanation, be sure to answer the question asked, but do not write more than is necessary to articulate your reasoning or reflect your understanding of the specific topic of the question. Please clearly state any additional assumptions you make. If a question has more than one sub-part (a, b, . . . ), points for the question are equally divided across each sub-part.
All interest rates are stated as annual rates.
1.
a. A bond has a market value of $1006.35 and a duration of 6.42. If the yield on the bond decreases from 2.45% to 2.10%, how much is the value of the bond expected to change?
b. Identify two different reasons the yield on the bond might change in this manner.
2.
a. Explain why the manager of a commercial bank is concerned about gap management.
b. What actions should a financial institution manager take relative to gap if short term interest rates are expected to rise and long term interest rates are expected to decline?
3.
a. Explain how the information revealed by a bank’s duration gap differs from that provided by its re-pricing gap.
b. A bank has assets with a total value of $5.72 billion; $5.02 billion of the assets are rate sensitive. The bank’s liabilities total $4.86 billion, all of which are rate sensitive. If the average duration of its asset portfolio is 5.27 years and its liabilities have a 3.11-year average duration, what is the bank’s leverage adjusted duration gap?
c. What is the expected dollar and percentage change in the value of the bank’s equity if the average interest rate is expected to increase from 3.15% to 3.25%?
4.
For each of the following line items from a depository institution’s balance sheet, indicate (a) whether the line item refers to an asset and/or a liability and (b) what the typical maturity of that asset is (you should say more than “long” or “short”, but it may be enough to generally indicate how long or short, e.g., “one day,” “less than a year,” “more than ten years”.)
i. Repurchase agreement
ii. Commercial loan
iii. Treasury bill
iv. Cash
v. Deposit
vi. Federal fund
vii. Commercial paper
viii. Reserve
ix. Subordinated note
x. Equity
5.
a. What is the lowest contractual rate (base rate plus risk premium) will a financial institution charge for a $75 million loan if all of the following are true:
i. The lender requires a minimum risk adjusted return on capital of 37.5%. Capital subject to risk is calculated using the rate adjustment for the worst 5% of loans.
ii. The loan has a duration of 7.85 years.
iii. The lender’s cost of funds is 3.35%.
iv. Origination fees on the loan are 0.35%.
v. Loans with comparable risk yield 7.25%.
vi. For the period the financial institution uses for comparison, the rate adjustment due to changes in credit risk for the worst 5% of comparable loans was 125 basis points.
b. Explain how requiring a risk adjusted return of 37.5% and setting the credit premium change based on the 5% worst loans protects the financial institution against losses due to credit risk.
6.
a. Explain what is meant by the term intermediation and identify two types of intermediation that financial institutions utilize.
b. What effect does financial intermediation have on a financial market?
7. A company’s assets have a value of $503 billion dollars. It has a debt obligation with a principal balance of $185 billion due in 4 years. If the standard deviation of monthly returns on the company’s stock is .0925, what is the probability that the company will default on the loan?
8. What is the duration of each of the following? Assume the yield to maturity in each case is 4.75%.
a. A bondthat makes a fixed annual coupon payment of $226.75 which represents 4.25% of its par value and never repays the principal.
b. A 20-year bond with a par value of $1000 and 12 years remaining until maturity that pays a 6.25% semi-annual coupon.
c. A 21-year, zero coupon bond with a face value of $2500.
d. A portfolio that includes 100 of each of the bonds from part a, b and c.
9.
a. What is one important way that the assets of a depository institution differ from those of an securities firm such as an investment bank?
b. What is one important way that the liabilities of a depository institution differ from those of an securities firm such as an investment bank?
c. What is the most important source of income for a depository institution?
d. What is the most important source of income for an investment bank?
10.
Identify the regulator or regulators that have principal regulatory authority with respect to (a) commercial banks and (b) investment banks in the United States. For each regulator, indicate what the general objective of its regulation is, and specify one regulatory requirement designed to accomplish that objective.
11.
What is the lowest contractual rate (base rate plus risk premium) a financial institution will charge for a $125 million loan if all of the following are true:
i. The financial institution needs an expected return of 6.85% in order to cover its costs of funds and overhead and to generate a desired profit for its investors.
ii. The expected default rate on loans of this type is 5.25%.
iii. In the event of default, the financial institution expects to recover 70% of the amount it would receive in the absence of a default.
iv. The lender charges an origination fee of 0.225%.
v. The lender requires the borrower to maintain a compensating balance during the full term of the loan in an amount equal to 12.5% of the loan balance.
vi. The lender maintains a reserve balance of 10%.
12.
Using the information from the table below, what is the re-pricing gap for the more than 6-monthto1-year maturity category?
Assets Liabilities
maturity rate amount Maturity rate amount
Cash 120 Demand deposits 820
Fed funds 5.05% 200 Savings accounts 1.50% 40
T-bills 9 month 5.25% 60 Money Market Deposit Accounts 4.50% 360
T-notes 3 year 6.50% 100 CD’s 3 month 4.20% 425
7 year 7.50% 80 6 month 4.30% 780
Munis 5 year floating 8.2%, reset monthly 50 1 year 5.00% 885
2 year 6.50% 275
Consumer loans 6 month 6.00% 800 3 year 6.25% 105
1 year 5.80% 780 4 year 5.50% 70
Car loans 5 year 7.00% 560 5 year 6.00% 120
Commercial and Industrial loans 9 month 5.80% 150 Fed funds 5.00% 440
4 year floating 5.15%;
reset every 3 months 455 Repurchase agreements 5.00% 675
Variable rate mortgages 12 year 5.80%, reset every
6 months 405 Commercial paper 6 month 5.05% 510
15 year 6.10%
reset annually 175 Subordinated notes 3 year 6.55% 85
20 year 6.30%
reset every 3 months 375 Subordinated debt 7 year 7.25% 385
30 year 6.40%
reset in 9 months 140 Total liabilities 5975
Fixed rate mortgages 8 year 5.22% 120
15 year 7.85% 850
30 year 8.20% 1040 Equity 705
Premises and equipment 220
Total assets 6680 Total liabilities and equity 6680