Question

Both bond Sam and bond Dave have 7.3 percent coupons, make semiannual payments, and are priced at par value. Bond Sam has three years to maturity, whereas bond Dave has 20 years to maturity. If interest rates suddenly rise by 2 percent, what is the percent change in price of Bond Sam? of Bond Dave? If rates were to suddenly fall by 2 percent instead, what would the percentage change in the price of Bond Sam be then? Of Bond Dave? Illustrate your answers by graphing bond prices versus YTM What does this problem tell you about interest rate risk of longer term bonds ? (without using excel) Thank you very much

Answer 1

		ANALYSIS OF BOND Sam
		Face Value (Assumed)	$1,000
	Nper	Semi annual period to maturity=3*2	6
	Pmt	Semi -annual coupon payment=(1000*7.3%)/2	$36.50
	Pv	Bond Price	$1,000	(Using PV function of excel with Rate =3.65%,Nper=6, Pmt=-36.50,Fv=-1000)
	Fv	Payment at maturity	$1,000
	Rate	Semi annual Yield to maturity=(7.3/2)%	3.65%
			A	B=A/2
			YTM	Semi annual Yield	Bond Price	(Using PV function of excel with Rate =B, Nper=6,Pmt=-36.50,Fv=-1000)
						% Change in Price
			1.30%	0.65%	$1,175.97
			3.30%	1.65%	$1,113.36
			5.30%	2.65%	$1,054.81	5.48%	(1054.81/1000)-1
			7.30%	3.65%	$1,000.00
			9.30%	4.65%	$948.67	-5.13%	(948.67/1000)-1
			11.30%	5.65%	$900.56
			13.30%	6.65%	$855.45
		Change in Price with 2% increase in YTM	-5.13%
		Change in Price with 2% decrease in YTM	5.48%
		ANALYSIS OF BOND Dave
		Face Value (Assumed)	$1,000
	Nper	Semi annual period to maturity=20*2	40
	Pmt	Semi -annual coupon payment=(1000*7.3%)/2	$36.50
	Pv	Bond Price	$1,000	(Using PV function of excel with Rate =3.65%,Nper=40, Pmt=-36.50,Fv=-1000)
	Fv	Payment at maturity	$1,000
	Rate	Semi annual Yield to maturity=(7.3/2)%	3.65%
			A	B=A/2
			YTM	Semi annual Yield	Bond Price	(Using PV function of excel with Rate =B, Nper=40,Pmt=-36.50,Fv=-1000)
						% Change in Price
			1.30%	0.65%	$2,053.69
			3.30%	1.65%	$1,582.25
			5.30%	2.65%	$1,244.80	24.48%	(1244.80/1000)-1
			7.30%	3.65%	$1,000.00
			9.30%	4.65%	$819.86	-18.01%	(819.86/1000)-1
			11.30%	5.65%	$685.30
			13.30%	6.65%	$583.22
		Change in Price with 2% increase in YTM	-18.01%
		Change in Price with 2% decrease in YTM	24.48%
		Longer term bonds will have higher interest rate risk