Suppose you were managing risk for a bank with the

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Suppose you were managing risk for a bank with the following balance sheet: Loans Eurodollar deposits 1 year at 7% 100 M 2 year at 5% 100 M a. Calculate your profit under the 3 interest rate scenarios used in the chapter (assume you can lend at LIBOR + 3%). reinvestment position: borrow long term, lend short term, pay term premium i. LIBOR remains the same: 1. earn the same rate on the new loans as the old 2. 100*(0.07-0.05) = 2 million 3. After year 1, bank earns 100M * 0.07 = 7m 4. can use 7m to fund new 1 year loans at same rate of 7%. 5. Will invest 107m for 1 year at 7%. 6. after year 2, bank earns 107m * 0.07 = 7.49m 7. amt earned = 7 + 7.49 = 14.49m 8. bank also has to pay 100m * (0.05^2) = 10.25m 9. total assets = 14.49m+100m 10. total liabilities = 100m + 10.25m 11. profit = 14.49m - 10.25m = 4.24 m ii. LIBOR rises to 12% 1. earn 15% on the loans, pay the same amount on deposits 2. 100*(0.15-0.05) = 10 million 3. After year 1, bank earns 100M * 0.07 = 7m 4. can use 7m to fund new 1 year loans at new rate of 12+3 = 15%. 5. Will invest 107m for 1 year at 15%.
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6. after year 2, bank earns 107m * 0.15 = 16.05m 7. amt earned = 7 + 16.05 = 23.05 8. bank also has to pay 100m * (0.05^2) = 10.25m 9. profit = 23.05m-10.25m = 12.8m 10. total assets = 23.05m+100m 11. total liabilities = 100m + 10.25 12. profit = 13.05m iii. LIBOR falls to 2% 1. earn 5% on the loans, pay the same amount on deposits 2. 100*(0.05-0.05) = 0 million 3. LIBOR falls to 2%. 4. After year 1, bank earns 100M * 0.07 = 7m 5. can use 7m to fund new 1 year loans at new rate of 2+3 = 5%. 6. Will invest 107m for 1 year at 5%. 7. after year 2, bank earns 107m * 0.05 = 5.35m 8. amt earned = 7m+5.35m = 12.35m 9. bank also has to pay 100m * (0.05^2) = 10.25m 10. profit = 12.35m-10.25m = 2.1m 11. total assets = 12.35m+100m 12. total liabilities = 100m + 10.25m 13. profit = 2.35m b. How would you hedge using futures or FRAs? Calculate your profits under the same three interest rate scenarios. iv. take a long position by buying futures - payoff is (actual price - futures price) * nominal amount; price of each contract is (100 - futures rate)/100; assume futures rate is 6% v. LIBOR remains the same: 1. payoff for purchasing 100 contracts is (0.96 - 0.94)*100 = 2 million 2. 2 million + 2 million = 4 million 3. After year 1, bank earns 100M * 0.07 = 7m 4. actual price = (100-4)/100 = 0.96 5. earn (0.96-0.94) * 100m = 2m bc price > future rate 6. can use 7m to fund new 1 year loans at same rate of 7%. 7. Will invest 107m for 1 year at 7%. 8. after year 2, bank earns 107m * 0.07 = 7.49m 9. amt earned = 7 + 7.49 = 14.49m 10. bank also has to pay 100m * (1.05^2) - 100m = 10.25m 11. profit = 14.49m + (1.04)*2 – 10.25m = 6.32m 12. total assets = 14.49m+100m + 2m(1.04) 13. total liabilities = 100m + 10.25 14. profit = 6.57 vi. LIBOR rises to 12%: 1. payoff is (0.88 - 0.94)*100 = -6 million 2. -6 million + 10 million = 4 million 3. After year 1, bank earns 100M * 0.07 = 7m 4. actual price = 100-12/100 = 0.88 5. pay (0.94-0.88) * 100m = 6m bc price < future rate 6. can use 7m to fund new 1 year loans at new rate of 12+3 = 15%. 7. Will invest 107m for 1 year at 15%.
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8. after year 2, bank earns 107m * 0.15 = 16.05m 9. amt earned = 7 + 16.05 = 23.05 10. bank also has to pay 100m * (1.05^2) - 100m = 10.25m 11. profit = 23.05m – 10.25m - (1.12)*6m = 6.08m 12. total assets = 23.05m+100m 13. total liabilities = 100m + 10.25 + 6m(1.12) 14. profit = 6.33m vii. LIBOR falls to 2%: 1. payoff is (0.98 - 0.94)*100 = 4 million 2. 4 million + 0 million = 4 million 3. After year 1, bank earns 100M * 0.07 = 7m 4. actual price = 100-2/100 = 0.98 5. earn (0.98-0.94) * 100m = 4m bc price > future rate 6. can use 7m to fund new 1 year loans at new rate of 2+3 = 5%.
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