Question

What is the duration of a 5 year, 8% semi-annual coupon bond with a face value of $1,000 that is currently selling at a YTM of 10%?

Answer 1

Here n = 5*2 = 10 and semi-annual coupon payment = 8%/2*1000 = $40

YTM = 10%/2 = 5%. Thus 1+r = 1.05

1	2	3	4	5
Time until payment	Cash flow	PV of CF (discount rate = 10%/2)	Weight	Column 1 * column 4
1	40.00	38.10	0.0413	0.04
2	40.00	36.28	0.0393	0.08
3	40.00	34.55	0.0374	0.11
4	40.00	32.91	0.0357	0.14
5	40.00	31.34	0.0340	0.17
6	40.00	29.85	0.0323	0.19
7	40.00	28.43	0.0308	0.22
8	40.00	27.07	0.0293	0.23
9	40.00	25.78	0.0279	0.25
10	40.00	24.56	0.0266	0.27
10	1,000.00	613.91	0.6653	6.65
Total		922.78	1.00	8.36

Thus duration = 8.36/2 = 4.18 years