Question

Both Bond A and Bond B have 8 percent coupons, make semiannual payments, and are priced at par value. Bond A has 2 years to maturity, whereas Bond B has 11 years to maturity.

(a) If interest rates suddenly rise by 1 percent, what is the percentage change in the price of Bond A? [3 points]

(b) If interest rates suddenly rise by 1 percent, what is the percentage change in the price of Bond B?

(c) If rates were to suddenly fall by 1 percent instead, what would the percentage change in the price of Bond A be then? [3 points]

(d) If rates were to suddenly fall by 1 percent instead, what would the percentage change in the price of Bond B be then? [3 points]

(e) What relation is illustrated? Interpret your results [4 points]

Answer 1

Semi annual coupons =8%*1000/2 =40

Since it is priced at Par YTM =8%
Semi annual YTM =8%/2 =4%
Price of both bonds =1000

a) Number of Periods =2*2 =4
New YTM =8%+1% =9%
Semi annual YTM =9%/2 =4.5%
Price of Bond A =PV of Coupons +PV of Par Value =40*((1-(1+4.5%)^-4)/4.5%)+1000/(1+4.5%)^4 =982.0624
Percentage Change of Price A =(982.0624-1000)/1000 =-1.79%

b) Number of Periods =11*2 =22
New YTM =8%+1% =9%
Semi annual YTM =9%/2 =4.5%
Price of Bond B =PV of Coupons +PV of Par Value =40*((1-(1+4.5%)^-22)/4.5%)+1000/(1+4.5%)^22 =931.0079
Percentage Change of Price B =(931.0079-1000)/1000 =-6.90%

c)Number of Periods =2*2 =4
New YTM =8%-1% =7%
Semi annual YTM =7%/2 =3.5%
Price of Bond A =PV of Coupons +PV of Par Value =40*((1-(1+3.5%)^-4)/3.5%)+1000/(1+3.5%)^4 =1018.3654
Percentage Change of Price A =(1018.3654-1000)/1000 =1.84%

d) Number of Periods =11*2 =22
New YTM =8%-1% =7%
Semi annual YTM =7%/2 =3.5%
Price of Bond B =PV of Coupons +PV of Par Value =40*((1-(1+3.5%)^-22)/3.5%)+1000/(1+3.5%)^22 =1075.8356
Percentage Change of Price B =(1075.8356-1000)/1000 =7.58%