Question

PLEASE NOTE: THIS QUESTION HAS BEEN POSTED BEFORE BUT WRONG ANSWERS WERE PROVIDED. PLEASE DO NOT COPY THOSE ANSWERS AND PASTE THEM HERE AGAIN. I WOULD APPRECIATE A FRESH ATTEMPT. HERE IS THE QUESTION:

A company has a payment due in three and a half years’ time of $50m. The current market interest rate for this company and this maturity is 2.55%. In order to immunise against this liability, they would like to invest in assets. Two bonds with the following characteristics are available:

Bond A
Principal:	$1000
Annual Coupon:	3% (paid once per annum)
Maturity:	6 years
Yield to maturity:	4.25%
Bond B
Principal:	$1000
Annual Coupon:	2.55% (paid once per annum)
Maturity:	3 years
Yield to maturity:	3.00%

Given the above information, how many of each bond would you suggest the company to invest in? Show all calculations.

Answer 1

In order to immunize company's liability follow below steps -

1. Calculate present value of company's liability
2. Calculate Current Bond Price of Both Bonds
3. Calculate Duration of both bonds
4. Construct a Bond Portfolio in such a way that Bond Portfolio's duration is same as Liability duration
5. Once you got proportion of Bond-A and Bond-B in step-5, buy it accordingly.

Please refer to below spreadsheet for calculation and answer. Cell reference also provided.

Cell reference -

Now lets assume Bond-A weight in Bond Portfolio is Wa and Bond-B weight is Wb=(1-Wa). Bond's Portfolio duration is 3.5 years so that Company's liability immunized.

thus,

Thus, Units of Bond-A should be purchased equals to -

Units of Bond-B should be purchased equals to -