Question

Periods 10 Bond ABC FGH VWX Coupon Maturity 4.600% 12/31/2024 8.490% 12/31/2025 5.000% 12/31/2027 Price 92.401 94.029 97.429 Yield 6.40% 6.00% 5.40% 12 16 Assume that today is December 31, 2019. Each bond pays interest semiannually, on June 30 and December 31 every year. Construct an immunized portfolio for an investor with an investment horizon equal to six (6) years. Compute the expected yield of the portfolio you construct. Compute the total amount an investor must invest in each bond in the portfolio if s/he faces a liability equal to $100,000 in six years.

Answer 1

Portfolio will be immunized when duration of bond portfolio will be equals 6 years

We have to first find out the duration of each Bond

Calculation of duration of Bond 1

Bond 1
Period	Cashflow	Discount Factor		Weight	Weight*Cashflow
1	2.3	0.97	2.23	0.02	0.02
2	2.3	0.94	2.16	0.02	0.05
3	2.3	0.91	2.09	0.02	0.07
4	2.3	0.88	2.03	0.02	0.09
5	2.3	0.85	1.96	0.02	0.11
6	2.3	0.83	1.90	0.02	0.12
7	2.3	0.80	1.84	0.02	0.14
8	2.3	0.78	1.79	0.02	0.15
9	2.3	0.75	1.73	0.02	0.17
10	102.3	0.73	74.66	0.81	8.08
				Total	9.00
				Duration in year	4.50

Similarly duration of other bonds

Particulars	Coupon	Settlement Date	Maturity Date		Price	Yield	MD
Bond 1	4.60	31-Dec-19	31-Dec-24	10	92.401	6.40	4.50
Bond 2	8.49	31-Dec-19	31-Dec-25	12	94.029	6.00	4.90
Bond 3	5.00	31-Dec-19	31-Dec-27	16	97.429	5.40	6.67

Now to have a duration of 6 we will combine Bond 1 and Bond 3 - Let's say we invest x part of our portfolio in Bond 1

Then,

x*4.5 + (1-x)*6.67 = 6

Solving the equation we will get x = 0.31,

So, we will invest 31% in Bond 1 and 69% in Bond 3

Part 2 Expected yield of portfolio =

Weight	Yield
A	B	A*B
0.69	5.40	3.73
0.31	6.40	1.98
Yield of Portfolio		5.71

Part 3

Investment in Bond 1 = 30,874

Investment in Bond 2 = 69,125