Consider a bank with the following balance sheet (M means million): Assets Value Duration of the Asset Convexity of the Asset Syr bond bought at a yield of 3.4% $550M (lending money) 4.562 12.026 $800M 53.565 12yr bond bought at a yield of 4% (lending money) 9.453 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
Using the image attached:
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?
e) 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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