Calculate Percentage Change in Bond Price

What is the percentage change in the bond price when the yield falls from 6% to 5.5%?

If a 19-year semi-annual pay bond has a Macaulay duration of 15.5 and yield to maturity of 6%, calculate the approximate percentage change in the bond's price.

Answer:

The approximate percentage change in the bond's price when the yield falls from 6% to 5.5% is approximately -8.06%.

Macaulay duration measures the weighted average time until the bond's cash flows are received, and it is used to estimate the bond price sensitivity to changes in yield. To calculate the percentage change in price, we can use the modified duration formula:

Percentage change in price = - (Modified duration) x (Change in yield)

Given that the Macaulay duration is 15.5, the modified duration is slightly different and can be approximated as (Macaulay duration) / (1 + Yield to maturity).

For the initial yield of 6%, the modified duration is 15.5 / (1 + 0.06) = 14.62.

When the yield falls to 5.5%, the change in yield is 0.055 - 0.06 = -0.005.

Therefore, the approximate percentage change in price is -14.62 x (-0.005) = 0.0731, which is approximately -8.06%.

Please note that this is an approximate calculation using modified duration, and it assumes a linear relationship between price and yield.