Question

A company is considering constructing a new factory and is considering funding it by issuing a corporate bond to the value of $9m. The bond would have a term to maturity of 12 years, a coupon rate of 3.0% and the bond would be sold into the market at expected yield of 2.8%. Show how an immunisation portfolio could be constructed from the bonds below if the CB cut interest rates by 0.50% over the next year. Show how this strategy would work and explain the nature of the risk and how the protection is created.

2.3% US Treasury 2030, @ Yield to Maturity of 1.50%

2.5% US Treasury 2030, @ Yield to Maturity of 1.67%

3.2% USTreasury 2035, @ Yield to Maturity of 1.71%

3.6% US Treasury 2038, @ Yield to Maturity of 1.73%

2.5% US Treasury 2039, @ Yield to Maturity of 1.74%

5.5% USTreasury 2042, @ Yield to Maturity of 1.78%

Answer 1

	Bond A	Bond1	Bond2	Bond3	Bond4	Bond5	Bond6
Settlement date	11-Apr-20	11-Apr-20	11-Apr-20	11-Apr-20	11-Apr-20	11-Apr-20	11-Apr-20
Maturity date	11-Apr-32	11-Apr-30	11-Apr-30	11-Apr-35	11-Apr-38	11-Apr-39	11-Apr-42
Coupon	3%	2.30%	2.5%	3.2%	3.6%	2.5%	5.5%
Yield	2.80%	1.50%	1.67%	1.71%	1.73%	1.74%	1.78%
Duration	10.273	9.087	9.015	12.429	14.152	15.595	15.338
Initial investment (in $m)		1	1	1	1	1	4
%investment		11.11%	11.11%	11.11%	11.11%	11.11%	44.44%
Duration immunization portfolio	13.51429

Bond A is the bond the company is planning to issue. It's value is $9m & its duration is 10.273

Bond 1 to 6: These are the bonds available for us to create an immunization portfolio

The immunization strategy is that duration of immunization portfolio = 10.273 (ie duration Bond A)

Duration of immunization portfolio =

Where D(i) is duration of bond i & w i is the weightage of bond i.

To start with, we have distributed $9m randomly between bond 1 to 6

Now we will use solver in excel, to decide the exact weightage we should give to each bond

	Bond A	Bond1	Bond2	Bond3	Bond4	Bond5	Bond6
Settlement date	11-Apr-20	11-Apr-20	11-Apr-20	11-Apr-20	11-Apr-20	11-Apr-20	11-Apr-20
Maturity date	11-Apr-32	11-Apr-30	11-Apr-30	11-Apr-35	11-Apr-38	11-Apr-39	11-Apr-42
Coupon	3%	2.30%	2.5%	3.2%	3.6%	2.5%	5.5%
Yield	2.80%	1.50%	1.67%	1.71%	1.73%	1.74%	1.78%
Duration	10.273	9.087	9.015	12.429	14.152	15.595	15.338
Initial investment (in $m)		3.926426	2.547698	1.393182	0.810347	0.322351	0
%investment		43.63%	28.31%	15.48%	9.00%	3.58%	0.00%
Duration immunization portfolio	10.27301
Sum of investment	9.00000

Invest $9 m in above weightage in bond 1 to 6