Question

Bond with:

Par Value: $1,000

Maturity: 4 years

Coupon Rate: 6%

Current Annualized 6-month yield of 9%.

Assume that coupon payments are made semiannually to bondholders and that the next coupon payment is expected in 6 months.

1.) What is the bond's duration (annualized)? Compare this with the approximate duration.

Answer 1

Duration = Sum [ Weight * Period ]

Period	CF	PVF @4.5%	Disc CF	Weight	Duration
1	$      30.00	0.9569	$   28.71	0.0319	0.0319
2	$      30.00	0.9157	$   27.47	0.0305	0.0610
3	$      30.00	0.8763	$   26.29	0.0292	0.0875
4	$      30.00	0.8386	$   25.16	0.0279	0.1117
5	$      30.00	0.8025	$   24.07	0.0267	0.1336
6	$      30.00	0.7679	$   23.04	0.0256	0.1534
7	$      30.00	0.7348	$   22.04	0.0245	0.1713
8	$      30.00	0.7032	$   21.10	0.0234	0.1873
8	$ 1,000.00	0.7032	$ 703.19	0.7804	6.2432
Duration ( In Six Months)					7.1807

Duration in Years = DUration in SIx Months / 2

= 7.1807 / 2

= 3.59 Years