Consider a bank with the following balance sheet (M means million): Assets 5yr bond bought at a yield of 3.4% (lending money) 12yr bond bought at a yield of 4% (lending money) Liabilities 2yr bond sold at a yield of 2.4% (borrowing money) 4yr bond sold at a yield of 2.8% (borrowing money) Value $550M $800M Duration of the Asset 4.562 9.453 Convexity of the Asset 12.026 53.565 Convexity of the Liability 2.384 8.206 Value $300M 1.941 Duration of the Liability $500M 3.759 1) 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 2）In 1）‘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? 3）Do you agree with the following statement? Explain why. “The information about a bond’s duration and convexity adjustment is sufficient to quantify interest rate risk exposure.”
Question 3. Bond
Consider a bank with the following
Assets
5yr bond bought at a yield of 3.4% (lending money)
12yr bond bought at a yield of 4% (lending money)
Liabilities
2yr bond sold at a yield of 2.4% (borrowing money)
4yr bond sold at a yield of 2.8% (borrowing money)
Value $550M
$800M
Duration of the Asset 4.562
9.453
Convexity of the Asset 12.026
53.565
Convexity of the Liability 2.384
8.206
Value
$300M 1.941
Duration of the Liability
$500M 3.759
1) 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
2）In 1）‘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?
3）Do you agree with the following statement? Explain why.
“The information about a bond’s duration and convexity adjustment is sufficient to quantify interest rate risk exposure.”
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