Question

Which of the following bonds would have the largest change in price (in percentage terms) for a given change in interest rates (that is, in yield to maturity) – for example, if the yield to maturity on a bond decreases from 8% to 6%, all else constant, which of the following bond prices will change the most (in percentage terms)? a. A $1000 par value bond with a 10% coupon rate (annual payments) that matures in 2 years. b. A $1000 par value bond with a 10% coupon rate (semi-annual payments) that matures in 25 years. c. A $1000 par value bond with a 2% coupon rate (annual payments) that matures in 4 years. d. A $1000 par value bond with a 2% coupon rate (semi-annual payments) that matures in 30 years. e. The bond that changes the least (in price percentage terms) cannot be determined from the information given.

Answer 1

The bond that would have the largest change in price (in percentage terms) for a given change in interest rates (that is, in yield to maturity) is the bond with the lowest coupon rate and longest maturity, which would be Bond D: A $1000 par value bond with a 2% coupon rate (semi-annual payments) that matures in 30 years.

This is because the lower the coupon rate, the higher the sensitivity to changes in yield (the higher the duration). Longer maturities also increase the sensitivity to changes in yield.

Therefore, Bond D would have the largest change in price (in percentage terms) for a given change in interest rates.

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