Question

Using the following information to answer the following questions?

Both Bond A and Bond B have 8 percent coupons, make semiannual payments, and are priced at par value. Bond A has 3 years to maturity, whereas Bond B has 20 years to maturity.

a. If interest rates suddenly rise by 2 percent annually (to 10% annually right now), what would be the percentage changes in the prices of Bond A and Bond B?

b. If rates were to suddenly drop by 2 percent instead (to 6% right now), what would be the percentage changes in the prices of Bond A and Bond B?

c. What does this problem tell you about the interest rate risk of long-term bonds?

Answer 1

Bond A
Let Par Value =1000
Coupon =8%*1000/2 =40
Number of Periods =2*3 =6
Price =1000

Bond B
Number of Periods =2*10=20

a. New YTM =8%+2% =10%
Semi annual YTM =5%
New Price of Bond A =PV of Coupons + PV of Par Value =40*(1-(1+5%)^-6)/5%+1000/(1+5%)^6 =949.24

Percentage change in price of A =(949.24-1000)/1000 =-5.08%
Bond B
Number of Periods =2*10=20
New Price of Bond B =PV of Coupons + PV of Par Value =40*(1-(1+5%)^-20)/5%+1000/(1+5%)^20 =875.38

Percentage change in price of B =(875.38-1000)/1000 =-12.46%

b. a. New YTM =8%-2% =6%
Semi annual YTM =3%
New Price of Bond A =PV of Coupons + PV of Par Value =40*(1-(1+3%)^-6)/3%+1000/(1+3%)^6 =1054.17

Percentage change in price of A =(1054.17-1000)/1000 =5.42%
Bond B
Number of Periods =2*10=20
New Price of Bond B =PV of Coupons + PV of Par Value =40*(1-(1+3%)^-20)/4%+1000/(1+3%)^20 =1148.77

Percentage change in price of B =(770.60-1000)/1000 =14.88%

c. Long term bond fluctuates more with increase or decrease with YTM.