Bond has a coupon rate of 3 percent and Bond K has a coupon

Bond ] has a coupon rate of 3 percent and Bond K has a coupon rate of 9 percent. Both bonds have 13 years to maturity, make semiannual payments, and have a YTM of 6 percent. If interest rates suddenly rise by 2 percent, what is the percentage price change of these bonds? What if rates suddenly fall by 2 percent instead? What does this problem tell you about the interest rate risk of lower-coupon bonds? 4.

Solution

Priceof bond formula is given as below

P = C * (1 - (1+r/m)^(-m*n))/(r/m) + FV/(1 + r/m)^(m*n)

Price of bond J = $731.84

Price of bond K = $1268.15

If interest rate rise by 2 % then price of bonds will be equal to as below

Price of J = $600.43

Proce of bond K = $1079.91

Percentage change in bond price of J = (731.84 - 600.43)/731.84 = 17.96%

Percentage change in bond price of K = (1268.15 - 1079.91)/1268.15 = 14.84%

If interest rate fall by 2% then

Price of J = $899.39

Price of K = $1503.03

Percentage change in priceof bond J = (899.39 - 731.84)/731.84 = 22.89%

Percentage change in price of bond K = (1503.03 - 1268.15)/1268.15 = 18.52%

There is higher interest rate risk for lower coupon bond becasue per unit change in yield will result in higher deviation in bond price of J.