Question

A) The price of which of the following will be more sensitive to changes in interest rates. Explain your answer. Proper explanation / calculations required

Bond  X. 2-year 15% coupon bond with a face value of $1000 that pays semi-annual coupons and is trading at a yield of 26%

Or

Bond Y. A Zero-Coupon Bond that has a maturity of 18 months

B)  What is the price of the Bond X . above ?

C) Would your answer to part A change if bond X were trading at par?

Answer 1

A)

As we know that Bond with longer term to maturity or more number of cash flows/coupon payments is more sensitive to chage in the interest rate. i.e. there will be more price change of bond which is having longer term to maturity or more number of cash flows. The bond with higher

In this case, Bond X: 2-year 15% coupon bond with a face value of $1000 that pays semi-annual coupons has longer term to maturity as compared to Bond Y. A Zero-Coupon Bond that has a maturity of 18 months.

Hence, Bond X is more sensitive to change in interest rate.

B)

Formula:

C)

As stated in part A, Hence, Bond X is more sensitive to change in interest rate due to its longer time to maturity and more number of cash flows.

If bond X were trading at par, it will not chage the fact that Bond X has longer time to maturity and more number of cash flows compared to Bond Y. Price of bond will not have any effect/impact on the sensitiveness of Bond to changes in interest rates.

Hence, the answer remains the same as in Part A.