Question

GE has a 7-year, 4.5% coupon bond with semi-annual coupon payments. The current YTM is 3.5%. What is duration of this bond and how much will price change if YTM goes up by 1% using duration approximation method?

Answer 1

Period	Cash Flow	Present [email protected]%	Present value of Cash flow	Period X Cash flow	Period x PV of Cash Flow
a	b	c	d=b*c	e=a*b	f=a*d
1	$        22.50	0.9780	22.00	$                         22.50	$            22.00
2	$        22.50	0.9565	21.52	$                         45.00	$            43.04
3	$        22.50	0.9354	21.05	$                         67.50	$            63.14
4	$        22.50	0.9148	20.58	$                         90.00	$            82.34
5	$        22.50	0.8947	20.13	$                      112.50	$          100.66
6	$        22.50	0.8750	19.69	$                      135.00	$          118.13
7	$        22.50	0.8558	19.25	$                      157.50	$          134.78
8	$        22.50	0.8369	18.83	$                      180.00	$          150.65
9	$        22.50	0.8185	18.42	$                      202.50	$          165.75
10	$        22.50	0.8005	18.01	$                      225.00	$          180.11
11	$        22.50	0.7829	17.62	$                      247.50	$          193.77
12	$        22.50	0.7657	17.23	$                      270.00	$          206.73
13	$        22.50	0.7488	16.85	$                      292.50	$          219.03
14	$ 1,022.50	0.7323	748.82	$                14,315.00	$    10,483.47
			1000		$    12,163.60
Duration = Present value of a bond's cash flows, weighted by length of time to receipt and divided by the bond's current market value.
Duration=$12,163.6/$1,000= 12.16
With a duration of 12.16 years. If market yields increased by 100 basis points (1%), the approximate percentage change in the bond's price would be:
	(- Macaulay Duration x Change in Yield) = Approximate Change in Price
	(- 12.16 x 1%) = 12.16%

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