Which one of the following par-value 12% coupon bonds experiences a price change of $23 when the market yield changes by 50 basis points?

Question

Quizplus · Accepted Answer

The price change of a bond due to a change in yield can be estimated using the bond's duration and the change in yield (in decimal form). The formula for the price change is: Price Change = -Duration * Change in Yield * Initial Price. Given a $23 price change and a 50 basis points (or 0.50%) change in yield, we can rearrange the formula to solve for duration: Duration = Price Change / (Change in Yield * Initial Price). Since the initial price is not given, and all options are in terms of duration, we directly relate the price change to duration and yield change. The bond with a duration closest to the calculated duration for a $23 price change with a 50 basis points change will be the correct answer. Among the given options, the bond with a duration of 5.15 years is the one that would experience a $23 price change for a 50 basis points change in yield, assuming all else equal. This is because the duration measures the sensitivity of a bond's price to changes in interest rates, and a bond with a duration of 5.15 years strikes the balance needed for this specific price change.

Which One of the Following Par-Value 12% Coupon Bonds Experiences