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Problem Set
- Repricing Risk
The example below shows a bank where the timing of the repricing differs between assets and liabilities. Consider a bank that borrows $100 million in deposits at a floating rate of T-Bill plus 2%, and lends at T-Bill plus 4%, earning a spread of 2%. Assume by the first quarter, the T-Bill rate increases to 4%. The spread for the second quarter is now ( 3% ).
Yield curve risk
Consider a bank that borrows $100 million in deposits at a floating rate of T-Bill plus 2%, and lends at T-Bill plus 4%, earning a spread of 2%, as shown below. Both rates are reset semi-annually. However, the benchmark T-Bill for deposits is the 6-month T-Bill, while that for loans is the 3-month T-Bill, as shown below.
a.
Assume the 3-month T-Bill rate was 3.0% and the 6-month T-Bill rate was 3.25% when the loan was disbursed. The spread is ( 1.75% ).
b.
If the 6-month T-Bill rate increases to 4.50% while the 3-month T-Bill rate increases to 4.0%, the spread drops from 1.75% to ( 1.5% ).
- Basis Risk
Assume the 3-month LIBOR rate was 3.20% and the 3-month T-Bill rate was 3.0% when the loan was disbursed. The spread is given as follows:
a.
Spread =( 2.20% ).
b.
if the 3-month LIBOR rate increases to 4.10% while 3-month T-Bill rates increase to 4.20%, the spread changes into ( 1.90% ).
- When interest rate changes, the impact on a bank’s earnings depends on the repricing of their assets or liabilities.
Loan A (6%, 1 year) = $100 Deposit A (3%, 3 months) = $250
Loan B (9%, 2 years) = $200 Deposit B (5%, 1 year) = $ 50
Total Assets = $300 Total Liabilities = $300
a.
The average maturity of its assets is larger than that of its deposits, as is typical of most banks. The net interest margin or spread is ( 4.7% ).
b.
Assume that the deposit rates three months later increase from 3% to 4.5%. The spread will be reduced to ( 3.42% ) from 4.7%.
5. Assume a bank has the following balance sheet.
a. Determine the 1-year and 2-year GAP (GAP).
b. What is the net impact on net interest income (NII), if interest rates are expected to change as
specified in the Potential rate change, for the 1- and 2-year GAP?
Asset
|
Potential rate change
|
Amount
|
|
Liability
|
Potential Rate change
|
Amount
|
Cash
|
N/A
|
$100
|
|
90-day CDs
|
0.75%
|
$100
|
6-month Gbonds
|
2.00%
|
$300
|
|
360-day CDs
|
1.00%
|
$200
|
2-year
commercial
loans
|
3.00%
|
$400
|
|
Time Deposits 2- year
|
1.50%
|
$900
|
5-year fixed
rate loans
|
2.00%
|
$500
|
|
Stockholder’
s equity
|
N/A
|
$100
|
Total
|
|
$1,300
|
|
Total
|
|
$1,300
|
|
|
|
|
|
|
|
GAP
6-month
= (RSA
6-month
– RSL
6-month
)
ΔNII = (RSA
1-year
– RSL
1-year
)* (.02)
6. Assume a bank has the following balance sheet.
a. Determine the 1-year and 2-year GAP.
b. What is the net impact on net interest income (NII), if interest rates are expected to change as
specified in the Potential rate change, for the 1- and 3-year GAP?
Asset
|
Potential rate change
|
Amount
|
|
Liability
|
Potential Rate change
|
Amount
|
Reserves at the Fed
|
N/A
|
$200
|
|
90-day CDs
|
0.75%
|
$200
|
6-month T-Bills
|
2.00%
|
$400
|
|
360-day CDs
|
1.00%
|
$300
|
3-year Consumer loans
|
3.00%
|
$600
|
|
Time Deposits 2- year
|
1.50%
|
$1200
|
10-year mortgages
|
2.00%
|
$800
|
|
Stockholder’
s equity
|
N/A
|
$200
|
Total
|
|
$2000
|
|
Total
|
|
$2000
|
6. In the following balance sheet, estimate the impact on the economic value of equity (EVE).
a. If all interest rates increase by 2%
b. If interest rates of assets fall by 1% and deposit rates increase by 1%.
|
|
|
|
|
|
|
Loan A
|
(8%, 3 year)
|
= $100
|
|
Deposit A
|
(5%, 2 years)
|
=$250
|
Loan B
|
(11%, 4 years)
|
= $200
|
|
Deposit B
|
(7%, 3 year)
|
= $ 50
|
Total Assets
|
|
= $300
|
|
Total Liabilities
|
|
= $300
|
7. In the following balance sheet, estimate the impact on the economic value of equity (EVE).
a. if all interest rates decrease by 3%
b. If interest rates of assets increase by 1% and deposit rates decrease by 2%.
Loan A (7.5%, 5 year) = $300
Loan B (15%, 10 years) = $200
|
Deposit A (6%, 1 years) =$350
Deposit B (5%, 2 year) = $150
|
Total Assets = $500
|
Total Liabilities = $500
|
8. Assume a 4-year loan with a principal of $5,000 paying 5% interest. The current market yield on the loan is also 5%. What is the duration of the loan? (3.723 years) What is the convexity?
9. Estimate the duration of Loan M and Deposit N
Bank Balance Sheet
|
Cash = $ 50
Loan M (5%, 6 years) = $200
|
Deposit N (3 years, 3%) = $ 200
Equity = $ 50
|
Total Assets = $250
|
Total Liabilities = $ 250
|
a. Estimate the duration of Loan M and Deposit N.
b. Using the duration formula, estimate the change in the value of the equity if interest rates are
expected to increase by 2%.
c. Estimate the convexity of Loan M.
d. Using the duration plus convexity formula, estimate the change in the value of Loan M if interest rates are expected to increase by 2%. There is no need to estimate the convexity of Deposit N.
10. Estimate the duration of Loan A and Deposit B
Bank Balance Sheet
|
Cash = $ 50
Loan A (10%, 5 years) = $500
|
Deposit B (5%, 2 years) = $ 520
Equity = $ 30
|
Total Assets = $550
|
Total Liabilities = $ 550
|
a. Estimate the duration of Loan A and Deposit B.
b. Using the duration formula, estimate the change in the value of the equity if interest rates are
expected to decrease by 3%.
c. Estimate the convexity of Loan A.
d. Using the duration plus convexity formula, estimate the change in the value of Loan A if interest rates are expected to decrease by 3%. There is no need to estimate the convexity of Deposit B.
11. A portfolio of stocks has $800,000 market value. If the recent volatility of the portfolio, as measured by the standard deviation, is 3.2%, what is the estimated 10-day value at risk (VAR) using a 99% level of confidence. Assume the returns are normally distributed.
12.A bank has a short position of ¥5 billion in Japanese yen. The current exchange rate is $0.0098/¥. What is the VAR using a 95% level of confidence if the standard deviation is 3.5%? Assume a 10-day time horizon.
13. A bank has a short position of £500,000 in British pounds. The current exchange rate is $1.45/£. What is the VAR using a 99% level of confidence if the standard deviation has been estimated at 50 basis points? Assume a 10-day time horizon.
14. Assume a bank holds 5-year $1,000,000 face value in corporate bonds paying 5% annual coupons. The yield is currently 6%. If the standard deviation of the returns is estimated at 35 basis points, what is the 10-day VAR if we use a 95% level of confidence? Use the traditional pricing method.
15. A bank is in the process of renegotiating an amortizing $150 million loan that has two annual remaining payments. The agreement requires reducing the interest rates from the existing 7% to 5% and to extend the maturity from two to five years. A grace period of two years is offered during which time only interest will be paid. In the last three years, principal payments of $50 million are expected each year. An up-front fee of 1% will be collected as part of the renegotiating fee.
a. If the cost of funds to the bank is 8% before rescheduling and 8.75% after rescheduling, what is the present value of the old and new loan?
b. What should the approximate up-front fee in percent be in order for the bank to have the present value of the old and new loan be equal?
c. At what costs of funds after rescheduling will the present value of the new and old loan be equal?
16. Assume a company with a loan of $10 million is experiencing cash flow problems and may be unable to make its next interest payments. The bank has estimated that, at the most, it will receive $7 million if the company is declared bankrupt and the assets are liquidated. The other option is to convert the debt to equity and invest an additional $4 million to reorganize the company with new management and a new marketing campaign. The turnaround is expected to generate after-tax cash flows of $2.15 million for the next five years. They also anticipate selling the business (terminal value) at the end of the 5 years for $7 million after taxes. Since the turnaround carries a lot of risk, the bank will accept the debt-to equity conversion if it earns a 15% rate of return.
a. Should they choose the debt-to-equity swap or liquidate the assets?
b. What after-tax terminal value at the end of 5 years will make the bank be better off choosing the debt-to-equity swap?
17. Distinguish between common and civil law.olutions and answers as needed. If you have any questions ask me before submiting.