Question

Bond J is a 4% coupon bond. Bond K is a 12% coupon bond. Both bonds have 9 years to maturity, make semiannual payments, and have a YTM of 8%.

A. If interest rates suddenly rise by 2%, what is the percentage price change of these bonds?

B. What is rates suddenly fall by 22% instead? What does this problem tell you about the interest rate risk of lower-coupon bonds?22% instead?

C. What does this problem tell you about the interest rate risk of lower-coupon bonds?

Answer 1

Current price of the bonds

Bond J   - coupon 4% semi annual,

                coupon amount   (PMT)    = 1000X4% X1/2   = $20- semi annual

               time to mature    (n)         = 18    (9years X 2)- since semi annual

                YTM      (rate)                =4%   semi annual ( 8 /2- since semi)

             par Vale     (FV)                =1000$

Bond K - coupon 12% semi annual,

                coupon amount   (PMT)    = 1000X 12% X1/2   = $60- semi annual

               time to mature    (n)         = 18    (9years X 2)- since semi annual

                YTM          (rate)            =4%   semi annual ( 8 /2- since semi)

              par Vale     (FV)                =1000$

bond prices are found by using PV formula

excel formula

a)

interest rates suddenly rise by 2%.

2% rise means, the YTM is 10% (8+2)

in our case- since semi annual - YTM is 5% (10/2)

all other things same, bond prices and the change % will be...

a rise in interest rates reduces the prices of bonds.

b)  

interest rates fall by 2%.

2% fall means, the YTM is 6% (8-2)

in our case- since semi annual - YTM is 3% (6/2)

all other things same, bond prices will be...

c)   as seen above, when the interest rates rises by 2 % the bond prices of a 4% coupon falls by 13.06%   as against the bond prices of 12% coupon which fell only by 10.88%

similarly when the interest rates fell by 2 % the bond prices of a 4% coupon increased by 15.49%   as against the bond prices of 12% coupon which increased only by 12.72%

thus it is clearly evident that the bonds with lower coupon rates are more prone to the interest rate risk. that is they fluctuate more than a high coupon bond - when interest rates fluctuates.