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This homework assignment is due at the beginning of class on Monday, August 3. Late homework assignments cannot be accepted because I will be reviewing the homework assignment and handing out solutions in class on Monday, August 3. All answers must be typed on the answer sheet at the end of this assignment with all supporting work clearly numbered and attached to the answer sheet. Supporting work can be handwritten. No credit will be given unless all work is shown and clearly numbered. You may work in pairs on this assignment. If you work in pairs, please hand in one copy with both names on it.
Chapter 15 – Market Risk
Use the following information to answer problems 1 through 5.
BaldwinTronics Bank has a $1 million position in a five-year, zero-coupon bond with a face value of $1,402,552. The bond is trading at a yield to maturity of 7.00 percent. The historical mean change in daily yields is 0.0 percent, and the standard deviation is 12 basis points.
1. What is the modified duration of the bond? (4 pts.)
2. What is the maximum adverse daily yield move assuming we desire no more than a 5 percent chance that yield changes will be greater than this maximum? (4 pts.)
3. Using the modified duration, what is the price volatility of this bond? (4 pts.)
4. What is the daily earnings at risk for this bond? (4 pts.)
5. What would be the VAR for a 10-day period? (2 pts.)
Use the following information to answer problems 6 through 8.
Export Bank has a trading position in Japanese Yen and Swiss Francs. At the close of business on February 4, the bank had ¥300,000,000 and Swf10,000,000. The exchange rates for the most recent six days are given below:
Exchange Rates per U.S. Dollar at the Close of Business
2/4 2/3 2/2 2/1 1/29 1/28
Japanese Yen 112.13 112.84 112.14 115.05 116.35 116.32
Swiss Francs 1.4140 1.4175 1.4133 1.4217 1.4157 1.4123
6. On a dollar basis, calculate the foreign exchange (FX) positions using the FX rates on February 4. (4 pts.)
7. Calculate the volatility (standard deviation) of the change in exchange rates for each currency over the five-day period (1/29-2/4). To do so, calculate the % change on a daily basis and then calculate the standard deviation for each position. (8 pts.)
8. Determine the bank’s DEAR for both positions assuming a 90% confidence level. (2 pts.)
Chapter 16 – Off-Balance-Sheet Risk
9. BaldwinTronics has been approved for a $75,000 loan commitment from its local bank. The bank has offered the following terms: term = 1 year, up-front fee = 85 basis points, back-end fee on the unused portion = 35 basis points, and rate on the loan = 7.75%. BaldwinTronics expects to immediately take down $70,000 and no more during the year unless there is some unforeseen need. Calculate the total interest and fees BaldwinTronics can expect to pay on this loan commitment. (6 pts.)
Chapter 12 – Liquidity Risk
10. A FI has the following assets in its portfolio: $30 million in cash reserves with the Fed, $20 million in T-Bills, and $50 million in mortgage loans. If the assets need to be liquidated at short notice, the FI will receive only 99 percent of the fair market value of the T-Bills and 90 percent of the fair market value of the mortgage loans. Estimate the liquidity index using the above information. (4 pts.)
Chapter 22 – Futures and Forwards
Use the following information to answer problems 11 through 15.
Consider the following balance sheet (in millions) for a FI
Duration = 5.72 years $950 Duration = 3 years $860
11. What is the FI’s leveraged adjusted duration gap? (4 pts.)
12. What is the FI’s interest rate risk exposure? (4 pts.)
13. How can the FI use futures and forward contracts to set up a macrohedge? (4 pts.)
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14. What is the impact on the FI’s equity value if the change in interest rates is DR/(1+R) = 0.015? (4 pts.)
15. Suppose that the FI macrohedges using Treasury bond futures that are currently priced at 96 ($96,000 per contract), how many Treasury bond futures contracts does it need to enter into? Assume that the deliverable Treasury bond has a duration of nine years. (4 pts.)
16. Village Bank has $240 million of assets with a duration of 14 years and liabilities worth $210 million with a duration of 4 years. In the interest of hedging interest rate risk, Village Bank is contemplating a macrohedge with interest rate futures contracts with a duration of 9 years, which are currently selling for $102,656. If the spot and futures interest rates move together, how many futures contracts must Village Bank sell to fully hedge the balance sheet? (4 pts.)
Chapter 23 – Options, Caps, Floors, and Collars
Use the following information to answer problems 17 through 19.
A FI manager purchases a zero-coupon bond that has two years to maturity. The manager paid $76.95 per $100 for the bond. The current yield on a one-year bond of equal risk is 12 percent and the one-year rate in one year is expected to be either 16.65 percent or 15.35 percent. Either rate is equally probable.
17. Given the expected one-year rates in one year, what are the possible bond prices in one year? (4 pts.)
18. If the manager buys a one-year option with an exercise price equal to the expected price of the bond in one year, what will be the exercise price of the option? (2 pts.)
19. Given the exercise price of the option, what premium should be paid for this option? (4 pts.)
Use the following information to answer problems 20 through 22.
A bank purchases a 3-year, 6 percent $5 million cap option on interest rates.
20. Assume interest rates are 5 percent in year 2 and 7 percent in year 3, what is the amount that the bank will receive at the end of year 2 and at the end of year 3? (4 pts.)
21. Instead of a cap, if the bank had purchased a 3-year 6 percent floor with the same notional value and interest rates are 5 percent and 6 percent in years 2 and 3, respectively, what are the payoffs to the bank in each year? (4 pts.)
22. In addition to purchasing the cap, if the bank also purchases a 3-year 7 percent floor and interest rates are 5 percent and 7 percent in years 2 and 3, respectively, what are the payoffs to the bank in each year? (4 pts.)
Chapter 24 – Swaps
Use the following information to answer problems 23 and 24.
A U.S. bank agrees to a swap making fixed-rate interest payments of $12 million to a UK bank in exchange for floating-rate payments of LIBOR + 4 percent in British pounds on a notional amount of £100 million. The current exchange rate is $1.50/£. The interest payments will be exchanged at the end of the year at the prevailing rates.
23. At the end of year 1, LIBOR is 6 percent and the exchange rate is $1.50/£. What is the net payment paid or received in dollars by the U.S. bank? (4 pts.)
24. At the end of year 2, LIBOR is 4 percent and the exchange rate is $1.10/£. What is the net payment paid or received in dollars by the U.S. bank? (4 pts.)
Chapter 25 – Loan Sales
Use the following information to answer problems 25 and 26.
Cash $200 Deposits $1,000
Good loans $1,000 Purchased funds $300
Bad Loans $380 Equity $280
Total $1,580 $1,580
Cash $240 Bonds $120
Loans 0 Preferred stock $40
Common stock $80
Total $240 $240
Bad Bank buys the bad loans for $232. The proceeds of the loan sale are used by Good Bank to pay off purchased funds.
25. What will be the total assets of Good Bank after the sale of the loans? (2 pts.)
26. What will be the amount of equity on the balance sheet of Good Bank after the sale of the loans? (2 pts.)
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