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FINM7407 –Financial Institutions and Markets
Semester 2 2023 Sample Final Examination
This exam has 55 marks in total and carries 55% of the total mark of this course. There are five
(5) questions. Answer all questions.
Question 1 [11 marks]
A bank is planning to make a loan of $5,000,000 to a firm in the steel industry. It expects to charge
a servicing fee of 50 basis points. The loan has a maturity of 8 years with a duration of 7.5 years.
The cost of funds (the RAROC benchmark) for the bank is 10 percent. The bank has estimated the
maximum change in the risk premium on the steel manufacturing sector to be approximately 4.2
percent, based on two years of historical data. The current market interest rate for loans in this sector
is 12 percent.
a. Using the RAROC model, determine whether the bank should make the loan?
b. What should be the duration in order for this loan to be approved?
c. Assuming that duration cannot be changed, how much additional interest and fee income
will be necessary to make the loan acceptable?
d. Given the proposed income stream and the negotiated duration, what adjustment in the
loan rate would be necessary to make the loan acceptable?
Question 2 [14 marks]
Consider $100 million of 30-year mortgages with a coupon of 5 percent per year paid quarterly.
a. What is the quarterly mortgage payment?
b. What are the interest and principal repayments over the first year of life of the
mortgages?
c. Construct a 30-year CMO using this mortgage pool as collateral. The pool has three
tranches, where tranche A offers the least protection against prepayment and tranche C
offers the most protection against prepayment. Tranche A of $25 million receives
quarterly payments at 4 percent per year, tranche B of $50 million receives quarterly
payments at 5 percent per year, and tranche C of $25 million receives quarterly
payments at 6 percent per year.
d. Assume nonamortization of principal and no prepayments. What are the total promised
coupon payments to the three classes? What are the principal payments to each of the
three classes for the first year?
e. If, over the first year, the trustee receives quarterly prepayments of $5 million on the
mortgage pool, how are these funds distributed?
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Question 3 [10 marks]
A. A manager decides not to lend to any firm in sectors that generate losses in excess of 5 percent
of capital.
a. If the average historical losses in the automobile sector total 8 percent, what is the
maximum loan a manager can lend to firms in this sector as a percentage of total capital?
b. If the average historical losses in the mining sector total 15 percent, what is the
maximum loan a manager can lend to firms in this sector as a percentage of total capital?
B. Suppose that an FI holds two loans with the following characteristics.
Annual
Spread between Loss to FI Expected
Loan Rate and FI’s Annual Given Default
Loan Xi Cost of Funds Fees Default Frequency
1 0.45 5.5% 2.25% 30% 3.5% ρ12 = -0.15
2 0.55 3.5 1.75 20 1.0
Calculate of the return and risk on the two-asset portfolio using Moody’s Analytics
Portfolio Manager.
Question 4 [10 marks]
Hedge Row Bank has the following balance sheet (in millions):
Assets $150 Liabilities $135
Equity 15
Total $150 Total $150
The duration of the assets is six years and the duration of the liabilities is four years.
The interest rate on both the assets and the liabilities is currently at 10 percent.
The bank is expecting that the interest rates will increase in the near future.
a. What is the duration gap for Hedge Row Bank?
b. What will be the effect on net worth if next year interest rates increase by 110
basis points?
c. Suppose that the FI plans to use futures contracts with the following
characteristics to hedge its position: a one-year futures is currently price at $97
per $100 of face value for a 20-year, 8 percent coupon bond underlying the
futures contract, the minimum contract size is $100,000, and the duration of the
bond underlying the futures contract is 9.5 years. How many futures contracts
that the FI should use and whether the FI should buy or sell these future
contracts?
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Question 5 [10 marks]
National Bank has the following balance sheet (in millions) and has no off-balance-sheet
activities.
Assets Liabilities and Equity
Cash $20 Deposits $960
Treasury bills 40 Subordinated debentures 25
Residential mortgages Common stock 45
(category 1; loan-to-value Retained earnings 40
ratio = 70%) 600 Total liabilities and equity $1,090
Business loans 430
Total assets $1,090
a. What is the CET1 risk-based ratio?
b. What is the Tier I risk-based capital ratio?
c. What is the total risk-based capital ratio?
d. What is the leverage ratio?
e. In what capital risk category would the bank be placed?