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 (lending money) 4.562 12.026 $800M 12yr bond bought at a yield of 4% (lending money) 9.453 53.565 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) Calculate the equity (total asset – total liability) to asset ratio of the bank (Hint: equity to asset ratio = total equity/total asset) b) Calculate the duration and convexity of the both asset and liability sides; c) 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; d) In c)'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 (lending money) 4.562 12.026 $800M 12yr bond bought at a yield of 4% (lending money) 9.453 53.565 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) Calculate the equity (total asset – total liability) to asset ratio of the bank (Hint: equity to asset ratio = total equity/total asset) b) Calculate the duration and convexity of the both asset and liability sides; c) 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; d) In c)'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?
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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Please answer c) & d). Thanks
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
(lending money)
4.562
12.026
$800M
12yr bond bought at a yield of 4%
(lending money)
9.453
53.565
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) Calculate the equity (total asset – total liability) to asset ratio of the bank
(Hint: equity to asset ratio = total equity/total asset)
b) Calculate the duration and convexity of the both asset and liability sides;
c) 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;
d) In c)'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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