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 Liability 2yr 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 Calculate the duration and convexity of the both asset and liability sides
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 Liability 2yr 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 Calculate the duration and convexity of the both asset and liability sides
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
|
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 Liability |
|
2yr 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
|
Calculate the duration and convexity of the both asset and liability sides
Expert Solution
Step 1
we will calculate the duration and convexity of both the asset and liability sides by below table
| years | value (A) | weights(B) | duration(C) | effective duration(B*C) | convexity (D) | effective convexity(B*D) |
| assets potion | ||||||
| 5 | 500 | 38.46 | 4.562 | 1.7545 | 12.026 | 4.6251 |
| 12 | 800 | 61.53 | 9.453 | 5.8164 | 53.565 | 32.96 |
| 1300 | 7.5709 | 37.5851 |
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