Consider a bank with the following balance sheet (M means million):Assets Value Duration of the Asset Convexity of the Asset 5yr bond bought at a yield of 3.4% (lending money) $550M 4.562 12.026 12yr bond bought at a yield of 4% (lending money) $800M 9.453 53.565 Liabilities Value Duration of the Liability Convexity of the Liability2yr bond sold at a yield of 2.4%(borrowing money) $300M 1.941 2.384 4yr bond sold at a yield of 2.8%(borrowing money) $500M 3.759 8.206 If the interest rates go up by 1%, using the duration and convexity rule to determine the networth of the bank and the equity to asset ratio
Consider a bank with the following balance sheet (M means million):Assets Value Duration of the Asset Convexity of the Asset 5yr bond bought at a yield of 3.4% (lending money) $550M 4.562 12.026 12yr bond bought at a yield of 4% (lending money) $800M 9.453 53.565 Liabilities Value Duration of the Liability Convexity of the Liability2yr bond sold at a yield of 2.4%(borrowing money) $300M 1.941 2.384 4yr bond sold at a yield of 2.8%(borrowing money) $500M 3.759 8.206 If the interest rates go up by 1%, using the duration and convexity rule to determine the networth of the bank and the equity to asset ratio
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Question
Consider a bank with the following balance sheet (M means million):
Assets Value Duration of the Asset Convexity of the Asset 5yr bond bought at a yield of 3.4% (lending money) $550M 4.562 12.026 12yr bond bought at a yield of 4% (lending money) $800M 9.453 53.565 Liabilities Value Duration of the Liability Convexity of the Liability2yr bond sold at a yield of 2.4%(borrowing money) $300M 1.941 2.384 4yr bond sold at a yield of 2.8%
(borrowing money) $500M 3.759 8.206
If the interest rates go up by 1%, using the duration and convexity rule to determine the net
worth of the bank and the equity to asset ratio
Expert Solution
Step 1
we will calculate in the below table
| year | yield% | value (A) | duration(B) | convexity(C) |
change (t) |
bond price P = A*B |
(t2)/2 | new bond price |
| asset portion | ||||||||
| 5 | 3.40 | 500 | 4.562 | 12.03 | 1 | 2281 | 0.5 | 5590.73 |
| 12 | 4.00 | 800 | 9.453 | 53.57 | 1 | 7562.4 | 0.5 | 138615.01 |
| 1300 | 9843.4 | 144205.74 |
Step 2
| year | yield% | value (A) | duration(B) | convexity(C) |
change (t) |
bond price P = A*B |
(t2)/2 | new bond price |
| asset portion | ||||||||
| 2 | 2.4 | 300 | 1.941 | 2.38 | 1 | 582.3 | 0.5 | 146.157 |
| 4 | 2.8 | 500 | 3.759 | 8.21 | 1 | 1879.5 | 0.5 | 2526.04 |
| 800 | 2461.8 | 2672.197 |
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