Question

Both Bond A and Bond B have 7.8 percent coupons and are priced at par value. Bond A has 8 years to maturity, while Bond B has 18 years to maturity. If interest rates suddenly rise by 1 percentage points, what is the difference in percentage changes in prices of Bond A and Bond B? (i.e., Bond A - Bond B).  The bonds pay coupons twice a year.

Answer 1

	YTM = [Annual interest +(Face value-Current price)/n]/(Face value + 2*Current Price)/3
		Bond A	Bond B
	Maturity Years =n	8	18
	Face value -suppose	100	100
	Market value	100	100
	Annual Interest amount	7.8	7.8
	Yield to maturity	7.80%	7.80%
	Bond A =[7.8+0/8](100+200)/3=7.8/100=7.8%
	Bond B=[7.8+0/18]/(100+200)/3=7.8/100=7.8%

	Caculation of Modified Duration of Bond A
Period	Cash Flow	Discount factor @3.9% semi annually	PV cash floW	Time period*Cash flow	PV of time adjusted cash flow
1	3.9	0.962	3.7518	3.9	3.7518
2	3.9	0.926	3.6114	7.8	7.2228
3	3.9	0.892	3.4788	11.7	10.4364
4	3.9	0.858	3.3462	15.6	13.3848
5	3.9	0.826	3.2214	19.5	16.107
6	3.9	0.795	3.1005	23.4	18.603
7	3.9	0.765	2.9835	27.3	20.8845
8	3.9	0.736	2.8704	31.2	22.9632
9	3.9	0.709	2.7651	35.1	24.8859
10	3.9	0.682	2.6598	39	26.598
11	3.9	0.656	2.5584	42.9	28.1424
12	3.9	0.632	2.4648	46.8	29.5776
13	3.9	0.608	2.3712	50.7	30.8256
14	3.9	0.585	2.2815	54.6	31.941
15	3.9	0.563	2.1957	58.5	32.9355
16	103.9	0.542	56.3138	1662.4	901.0208
	Total=		100.0		1219.2803

Macaulays duration= sum of PV of time adjusted cash flow/ Sum of PV of cash flows=	12.19593736
Modified duration =Macaulay's duration/(1+YTN/n)	11.73814952
n= no of coupon payment per year

% change in Price = - modified Duration*% interest change

Interest rate rise 1%

So change in Price in Bond A=-11.73*1%=-11.73%

	Caculation of Modified Duration of Bond A
Period	Cash Flow	Discount factor @3.9% semi annually	PV cash floW	Time period*Cash flow	PV of time adjusted cash flow
1	3.9	0.962	3.7518	3.9	3.7518
2	3.9	0.926	3.6114	7.8	7.2228
3	3.9	0.892	3.4788	11.7	10.4364
4	3.9	0.858	3.3462	15.6	13.3848
5	3.9	0.826	3.2214	19.5	16.107
6	3.9	0.795	3.1005	23.4	18.603
7	3.9	0.765	2.9835	27.3	20.8845
8	3.9	0.736	2.8704	31.2	22.9632
9	3.9	0.709	2.7651	35.1	24.8859
10	3.9	0.682	2.6598	39	26.598
11	3.9	0.656	2.5584	42.9	28.1424
12	3.9	0.632	2.4648	46.8	29.5776
13	3.9	0.608	2.3712	50.7	30.8256
14	3.9	0.585	2.2815	54.6	31.941
15	3.9	0.563	2.1957	58.5	32.9355
16	3.9	0.542	2.1138	62.4	33.8208
17	3.9	0.522	2.0358	66.3	34.6086
18	3.9	0.502	1.9578	70.2	35.2404
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