A bond has a Macaulay duration of 6.25 years. What will be the percentage change in the bond price if the yield to maturity increases from 6% to 6.4%?

Question

Quizplus · Accepted Answer

The percentage change in the bond price can be estimated using the modified duration formula: $\Delta P/P = -D_{mod} \times \Delta y$, where $\Delta P/P$ is the percentage change in price, $D_{mod}$ is the modified duration, and $\Delta y$ is the change in yield. The modified duration is approximately equal to the Macaulay duration divided by $1 + y$, where $y$ is the yield to maturity. Here, $D_{mod} = 6.25 / (1 + 0.06) = 5.896$. The change in yield, $\Delta y$, is $0.064 - 0.06 = 0.004$ or 0.4%. Thus, $\Delta P/P = -5.896 \times 0.004 = -0.023584$ or -2.36%. The closest answer is −2.43%.

A Bond Has a Macaulay Duration of 6