In each pair, identify the bond with the greatest price sensitivity to interest

Question

In each pair, identify the bond with the greatest price sensitivity to interest rate changes, and explain why:

A. Both bonds are 20-year maturity with a 6% coupon. One bond is selling at a premium, the other at a discount.

B. Both bonds have a 20-year maturity and a yield to maturity of 6%. One bond has a 4% coupon and the other has a 7% coupon.

A bond has a maturity date of May 15, 2030, a coupon rate of 4% paid semi-annually, and a yield to maturity of 5%. You buy the bond with a settlement date of November 10, 2017.

A. What is the price of the bond on the settlement date?

B. What are the number of days to the next coupon payment on the settlement date?

C. What is the invoice price of the bond on the settlement date?

D. What is the modified duration of the bond on the settlement date?

Explanation / Answer

A - A premium bond is the one which has a coupon rate higher than its yield to maturity. A discount bond is the one which has a coupon rate lower than its YTM.

The discount bond is more sensitivity to the change in interest rate because it offers lower coupon rate in comparison to the YTM. Any further decline in interest rate would have more drastic impact on a discount bond than on a premium bond.

B - Similarly, the bond with a higher coupon rate of 7% is a premium bond and the bond with a lower coupon rate of 4% is a discount bond. The discount bond has greater price sensitivity to interest rate.

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