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% $550M 4.562 12.026 (lending money) 12yr bond bought at a yield of 4% $800M 53.565 (lending money) 9.453 Liabilities Value Duration of the Liability Convexity of the Liability $300M 2yr bond sold at a yield of 2.4% (borrowing money) 1.941 2.384 4yr bond sold at a yield of 2.8% $500M 3.759 8.206 (borrowing money) a) 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; b) In a)'s scenario, to maintain the equity to asset ratio at 40% which is required by the regulation, the bank decides to raise cash (zero duration and zero convexity) from the equity holders. How much cash does the bank need to raise?
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% $550M 4.562 12.026 (lending money) 12yr bond bought at a yield of 4% $800M 53.565 (lending money) 9.453 Liabilities Value Duration of the Liability Convexity of the Liability $300M 2yr bond sold at a yield of 2.4% (borrowing money) 1.941 2.384 4yr bond sold at a yield of 2.8% $500M 3.759 8.206 (borrowing money) a) 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; b) In a)'s scenario, to maintain the equity to asset ratio at 40% which is required by the regulation, the bank decides to raise cash (zero duration and zero convexity) from the equity holders. How much cash does the bank need to raise?
Chapter7: Types And Costs Of Financial Capital
Section: Chapter Questions
Problem 1bM
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Please answer part a) with proper workings and formula.
![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%
$550M
4.562
12.026
(lending money)
12yr bond bought at a yield of 4%
$800M
53.565
(lending money)
9.453
Liabilities
Value
Duration of the Liability Convexity of the Liability
$300M
2yr bond sold at a yield of 2.4%
(borrowing money)
1.941
2.384
4yr bond sold at a yield of 2.8%
$500M
3.759
8.206
(borrowing money)
a) 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;
b) In a)'s scenario, to maintain the equity to asset ratio at 40% which is required by the regulation,
the bank decides to raise cash (zero duration and zero convexity) from the equity holders.
How much cash does the bank need to raise?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18e2f419-d134-4308-859b-a1f99dafb802%2Fc3658478-9852-4a95-9e93-c23ecdda07ee%2F3fee5oi.jpeg&w=3840&q=75)
Transcribed Image Text: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%
$550M
4.562
12.026
(lending money)
12yr bond bought at a yield of 4%
$800M
53.565
(lending money)
9.453
Liabilities
Value
Duration of the Liability Convexity of the Liability
$300M
2yr bond sold at a yield of 2.4%
(borrowing money)
1.941
2.384
4yr bond sold at a yield of 2.8%
$500M
3.759
8.206
(borrowing money)
a) 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;
b) In a)'s scenario, to maintain the equity to asset ratio at 40% which is required by the regulation,
the bank decides to raise cash (zero duration and zero convexity) from the equity holders.
How much cash does the bank need to raise?
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