Question

Calculate the duration and volatities of 9% coupon and 13% coupon, 5 years bonds whose yields are 8%.

Answer 1

Duration and volatility of 9% coupon Bond

Year (1)	Cash Flow (2)	PVIF at 8% (3)	Present Value (4) = (3)x (2)	Weight (5)	Duration (6) = (1) x (5)
1	$90	0.925926	$83.33	0.0801	0.08
2	$90	0.857339	$77.16	0.0742	0.15
3	$90	0.793832	$71.44	0.0687	0.21
4	$90	0.735030	$66.15	0.0636	0.25
5	$1,090	0.680583	$741.84	0.7134	3.57
			$1,040	1.0000	4.26

Duration of the Bond = 4.26 Years

Volatility of the Bond = Duration / (1 + YTM)

= 4.26 / (1 + 0.08)

= 3.94

Duration and volatility of 13% coupon Bond

Year (1)	Cash Flow (2)	PVIF at 8% (3)	Present Value (4) = (3)x (2)	Weight (5)	Duration (6) = (1) x (5)
1	$130	0.925926	$120.37	0.1003	0.10
2	$130	0.857339	$111.45	0.0929	0.19
3	$130	0.793832	$103.20	0.0860	0.26
4	$130	0.735030	$95.55	0.0796	0.32
5	$1,130	0.680583	$769.06	0.6409	3.20
			$1,200	1.0000	4.07

Duration of the Bond = 4.07 Years

Volatility of the Bond = Duration / (1 + YTM)

= 4.07 / (1 + 0.08)

= 3.77