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% (lending money) $550M 4.562   12.026 12yr bond bought at a yield of 4% (lending money) $800M   9.453   53.565   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   Required  a) Calculate the equity (total asset – total liability) to asset ratio of the bank 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;

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
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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% (lending money)

$550M

4.562

 

12.026

12yr bond bought at a yield of 4% (lending money)

$800M

  9.453

 

53.565

 

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

 

Required 

a) Calculate the equity (total asset – total liability) to asset ratio of the bank

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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