Question

Consider the following two bond issues.

Bond M: 4% 30-year bond

Bond N: 6% 30-year bond

Neither bond has an embedded option. Both bonds are trading in the market at the same yield.

Which bond will fluctuate more in price when interest rates change? Why?

Answer 1

	Bond M: 4% 30-year bond
	Face Value=$1000
	N	C	A=C*N	B=A/(1.04^N)
	Year	Cashflow	Year*casflow	PV of A
	1	$40	$40	38.46154
	2	$40	$80	73.9645
	3	$40	$120	106.6796
	4	$40	$160	136.7687
	5	$40	$200	164.3854
	6	$40	$240	189.6755
	7	$40	$280	212.777
	8	$40	$320	233.8209
	9	$40	$360	252.9312
	10	$40	$400	270.2257
	11	$40	$440	285.8156
	12	$40	$480	299.8066
	13	$40	$520	312.2985
	14	$40	$560	323.386
	15	$40	$600	333.1587
	16	$40	$640	341.7012
	17	$40	$680	349.0938
	18	$40	$720	355.4122
	19	$40	$760	360.7282
	20	$40	$800	365.1096
	21	$40	$840	368.6202
	22	$40	$880	371.3207
	23	$40	$920	373.2682
	24	$40	$960	374.5166
	25	$40	$1,000	375.1168
	26	$40	$1,040	375.1168
	27	$40	$1,080	374.5619
	28	$40	$1,120	373.4948
	29	$40	$1,160	371.9556
	30	$40	$1,200	369.9824
				8734.155
	Bond duration			8.734155	(8734.155/1000)
	Bond N: 6% 30-year bond
	Face value=$1000
	N	C	A=C*N	B=A/(1.04^N)
	Year	Cashflow	Year*casflow	PV of A
	1	$60	$60	56.60377
	2	$60	$120	106.7996
	3	$60	$180	151.1315
	4	$60	$240	190.1025
	5	$60	$300	224.1775
	6	$60	$360	253.7858
	7	$60	$420	279.324
	8	$60	$480	301.1579
	9	$60	$540	319.6252
	10	$60	$600	335.0369
	11	$60	$660	347.6798
	12	$60	$720	357.8179
	13	$60	$780	365.6944
	14	$60	$840	371.5328
	15	$60	$900	375.5386
	16	$60	$960	377.9004
	17	$60	$1,020	378.7917
	18	$60	$1,080	378.3713
	19	$60	$1,140	376.7848
	20	$60	$1,200	374.1657
	21	$60	$1,260	370.6358
	22	$60	$1,320	366.3067
	23	$60	$1,380	361.2802
	24	$60	$1,440	355.6491
	25	$60	$1,500	349.4979
	26	$60	$1,560	342.9036
	27	$60	$1,620	335.9361
	28	$60	$1,680	328.6586
	29	$60	$1,740	321.1287
	30	$60	$1,800	313.3982
				9367.417
	Bond duration			9.367417	(9367.417/1000)
		Duration of M		8.734155
		Duration of N		9.367417
	Bond duration indicates sensitivity of a bond pice to change in interest rate
	Higher the bond duration higher will be the sensitivity to change in interest rate
	Hence Bond N will flatuate more in price with interest rate change