Question

1Find the duration of a bond with a settlement date of May 27, 2020, and maturity date November 15, 2031. The coupon rate of the bond is 9.5%, and the bond pays coupons semiannually. The bond is selling at a bond-equivalent yield to maturity of 9.0%. Use

Answer 1

Price of Bond = PV of CFs from it.

Period	CF	PVF @4.5%	Disc CF
1	$      47.50	0.9569	$      45.45
2	$      47.50	0.9157	$      43.50
3	$      47.50	0.8763	$      41.62
4	$      47.50	0.8386	$      39.83
5	$      47.50	0.8025	$      38.12
6	$      47.50	0.7679	$      36.48
7	$      47.50	0.7348	$      34.90
8	$      47.50	0.7032	$      33.40
9	$      47.50	0.6729	$      31.96
10	$      47.50	0.6439	$      30.59
11	$      47.50	0.6162	$      29.27
12	$      47.50	0.5897	$      28.01
13	$      47.50	0.5643	$      26.80
14	$      47.50	0.5400	$      25.65
15	$      47.50	0.5167	$      24.54
16	$      47.50	0.4945	$      23.49
17	$      47.50	0.4732	$      22.48
18	$      47.50	0.4528	$      21.51
19	$      47.50	0.4333	$      20.58
20	$      47.50	0.4146	$      19.70
21	$      47.50	0.3968	$      18.85
22	$      47.50	0.3797	$      18.04
23	$      47.50	0.3634	$      17.26
23	$ 1,000.00	0.3634	$    363.35
Price of Bond	$ 1,035.37

Duration in Periods:

Duration = Sum [ Wt * Period ]

Period	CF	PVF @4.5%	Disc CF	Weight	Wt * Period
1	$      47.50	0.9569	$      45.45	4.39%	0.0439
2	$      47.50	0.9157	$      43.50	4.20%	0.0840
3	$      47.50	0.8763	$      41.62	4.02%	0.1206
4	$      47.50	0.8386	$      39.83	3.85%	0.1539
5	$      47.50	0.8025	$      38.12	3.68%	0.1841
6	$      47.50	0.7679	$      36.48	3.52%	0.2114
7	$      47.50	0.7348	$      34.90	3.37%	0.2360
8	$      47.50	0.7032	$      33.40	3.23%	0.2581
9	$      47.50	0.6729	$      31.96	3.09%	0.2778
10	$      47.50	0.6439	$      30.59	2.95%	0.2954
11	$      47.50	0.6162	$      29.27	2.83%	0.3110
12	$      47.50	0.5897	$      28.01	2.71%	0.3246
13	$      47.50	0.5643	$      26.80	2.59%	0.3365
14	$      47.50	0.5400	$      25.65	2.48%	0.3468
15	$      47.50	0.5167	$      24.54	2.37%	0.3556
16	$      47.50	0.4945	$      23.49	2.27%	0.3630
17	$      47.50	0.4732	$      22.48	2.17%	0.3690
18	$      47.50	0.4528	$      21.51	2.08%	0.3739
19	$      47.50	0.4333	$      20.58	1.99%	0.3777
20	$      47.50	0.4146	$      19.70	1.90%	0.3805
21	$      47.50	0.3968	$      18.85	1.82%	0.3823
22	$      47.50	0.3797	$      18.04	1.74%	0.3832
23	$      47.50	0.3634	$      17.26	1.67%	0.3834
23	$ 1,000.00	0.3634	$    363.35	35.09%	8.0716
Duration	14.6242

Duration = 14.6242 Periods i.e. 1[ 4.6242 / 2 ] Years

= 7.3121 Years