Question

You owe a mobster in Chicago money in 5 years. You want to earn a little bit on money you set aside to pay this liability. However, you do not know if interest rates will rise or fall. You have two bonds to choose from with semi-annual coupon payments:

	Bond A	Bond B
Time to maturity (years)	5	6
Annual yield to maturity	4.00%	4.00%
Annual coupon payment	40.00	65.94
Current price	-1000	-1000
Face value	1000	826.02

So we start with two bonds of equal price ($1000) and annual yield to maturity (4.00%).

1. What is the Macaulay duration (in years) for Bond A? The answer is NOT 4.63

2. What is the Macaulay duration (in years) for Bond B? The answer is NOT 5.09

Answer 1

1

Period (in years)	Payment	Present value factor @4%	Present value	Duration
(a)	(b)	(c)	(d): (b) × (c)	(a) × (d)
0.50	$              20.00	0.980392157	$              19.61	$                   9.80
1.00	$              20.00	0.961168781	$              19.22	$                19.22
1.50	$              20.00	0.942322335	$              18.85	$                28.27
2.00	$              20.00	0.923845426	$              18.48	$                36.95
2.50	$              20.00	0.90573081	$              18.11	$                45.29
3.00	$              20.00	0.887971382	$              17.76	$                53.28
3.50	$              20.00	0.870560179	$              17.41	$                60.94
4.00	$              20.00	0.853490371	$              17.07	$                68.28
4.50	$              20.00	0.836755266	$              16.74	$                75.31
5.00	$         1,020.00	0.8203483	$            836.76	$           4,183.78
			$         1,000.00	$           4,581.12
Macaulay duration=	4581.12/1000		4.58

Duration for A is 4.58

2

Period (in years)	Payment	Present value factor @4%	Present value	Duration
(a)	(b)	(c)	(d): (b) × (c)	(a) × (d)
0.50	$              32.97	0.980392157	$              32.32	$                16.16
1.00	$              32.97	0.961168781	$              31.69	$                31.69
1.50	$              32.97	0.942322335	$              31.07	$                46.60
2.00	$              32.97	0.923845426	$              30.46	$                60.92
2.50	$              32.97	0.90573081	$              29.86	$                74.65
3.00	$              32.97	0.887971382	$              29.28	$                87.83
3.50	$              32.97	0.870560179	$              28.70	$              100.46
4.00	$              32.97	0.853490371	$              28.14	$              112.56
4.50	$              32.97	0.836755266	$              27.59	$              124.15
5.00	$              32.97	0.8203483	$              27.05	$              135.23
5.50	$              32.97	0.804263039	$              26.52	$              145.84
6.00	$            858.99	0.788493176	$            677.31	$           4,063.85
			$            999.98	$           4,999.94
Macaulay duration=	4999.94/999.98	5.00

Duration for B is 5 years.