Question

Interest Rate Risk. 

Bond J has a coupon rate of 4 percent. Bond Shad coupon rate of 14 percent. Both bonds have 13 years to maturity, make semiannual payments, a par value of $1,000, and have a YTM of 8 per 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? 

Answer 1

The given bonds J and S can be valued in the following manner assuming the current interest rates equal YTM of 8%:

In the above table, we can notice that at the discount rate of 8% the values of Bond-J and Bond-S are $680.34 and $1,479.48 respectively. If the interest rate increases by 2% , i.e., from 8% to 10%, the percentage change in the value of bond-J is -16.40%, whereas the same in case of bond-S is -12.98%. Further, if interest rate decreases by 2%, i.e., from 8% to 6%, the percentage change in the values of bond-J and bond-S are 20.71% and 15.92% respectively.

We can notice from the above that as a result of change in interest rate, the price of bond-J (which has lower coupon) varies more than the price of bond-S (which has higher coupon). And, we know that interest rate risk is the variance in the price of a bond due to change in interest rate. Thus, we can conclude that in this specific case bond-J has more interest rate risk than bond-S. And, in general, we can conclude that, keeping other things same, bonds with low coupon have more interest rate risk as compared to the bonds with high coupon.