Question

A set of bonds all have the same maturity. Which one has the least percentage price change for given shifts in interest rates: (choose one correct answer)

not enough information to determine.

zero coupon bonds.

pure discount bonds.

low coupon bonds.

high coupon bonds.

Answer 1

We know that a change in the interest rate changes the discount factor in the denominator and hence have an effect on the value of the bonds. Zero discount bond is the same as pure discount bond and both have only one payment at the end of the maturity. Hence, if we compare these with the coupon bonds we observe that their payments are more concentrated towards the end of maturity. These payments towards the end will be discounted by a higher power on the discount rate as compared to the case of coupon bonds. Hence, zero coupon bonds will be most affected by the change in interest rates.

Among low coupon bonds and high coupon bonds, we see that the high coupon bonds will be paying more interest (i.e. coupon) each year. Therefore, the concentration of cash flows for a high coupon bond will be lower towards the end as compared to the low coupon bonds. This can also be understood by the concept of duration. Low coupon bonds will have higher duration than high coupon bonds and hence will be more sensitive with the interest rates. Thereofore, high coiupon bonds will be the answer.