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 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.”

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
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Question 3. Bond

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

a) Calculate the equity (total asset – total liability) to asset ratio of the bank (Hint: equity to asset ratio = total equity/total asset) 

  1. b)  Calculate the duration and convexity of the both asset and liability sides; 

  2. 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; 

  3. 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? 

  4. 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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