Question

The following two (2) questions are based on the following semi-annual coupon payment bonds:

	Bond X	Bond Y
N (semi-annual)	10	12
Rd (semi-annual)	3.5%	3.5%
PMT (semi-annual)	35	35
PV	-1000	-1000
FV	1000	1000

1.  

If interests rates rise 1.25% on an annual basis, what will be the change in value of price due to duration for Bond X?  Include a negative (-) sign if the price change is a decline. For example, enter -123.45 for a $123.45 price drop.

[Hint: you need to calculate Macaulay and Modified duration first]

2.

If interests rates rise 1.25% on an annual basis, what will be the change in value of price due to duration for Bond Y? Include a negative (-) sign if the price change is a decline. For example, enter -123.45 for a $123.45 price drop.

[Hint: you need to calculate Macaulay and Modified duration first]

Answer 1

1)

We first calculate the bond duration in excel

Yield	3.5%
	Year	Cash-flow	PV of cash-flow	Weight	t*Weight
	1	35	$33.82	0.033816	0.033816
	2	35	$32.67	0.032673	0.065346
	3	35	$31.57	0.031568	0.094704
	4	35	$30.50	0.0305	0.122002
	5	35	$29.47	0.029469	0.147345
	6	35	$28.47	0.028473	0.170835
	7	35	$27.51	0.02751	0.192568
	8	35	$26.58	0.026579	0.212635
	9	35	$25.68	0.025681	0.231125
	10	35	$24.81	0.024812	0.248122
	10	1000	$708.92	0.708919	7.089188
			$1,000.00	Duration	8.607687

We get Duration = 8.6076/2 = 4.3038 ( Since all the parameters are semi-annual)

Modified duration (D) = Duration/(YTM/n) = 4.3038/(1.035) = 4.1583

Dollar change in bond price for Bond X = -D*(Change in YTM)* Initial price of bond

Dollar change in bond price for Bond X = -4.1583*0.0125*1000

Dollar change in bond price for Bond X = -$51.98

2)

We first calculate the bond duration in excel

Yield	4%
	Year	Cash-flow	PV of cash-flow	Weight	t*Weight
	1	35	$33.82	0.033816	0.033816
	2	35	$32.67	0.032673	0.065346
	3	35	$31.57	0.031568	0.094704
	4	35	$30.50	0.0305	0.122002
	5	35	$29.47	0.029469	0.147345
	6	35	$28.47	0.028473	0.170835
	7	35	$27.51	0.02751	0.192568
	8	35	$26.58	0.026579	0.212635
	9	35	$25.68	0.025681	0.231125
	10	35	$24.81	0.024812	0.248122
	11	35	$23.97	0.023973	0.263704
	12	35	$23.16	0.023162	0.277949
	12	1000	$661.78	0.661783	7.9414
			$1,000.00	Duration	10.00155

We get Duration = 10.0015/2 = 5.00075 ( Since all the parameters are semi-annual)

Modified duration (D) = Duration/(YTM/n) = 5.00075 /(1.035) = 4.8316

Dollar change in bond price for Bond X = -D*(Change in YTM)* Initial price of bond

Dollar change in bond price for Bond X = -4.8316*0.0125*1000

Dollar change in bond price for Bond X = -$60.395