Question

A bond with face value = 6,000 currently trades at par. Its Macaulay duration is 5.66 years and its convexity is 67.35.

Suppose yield currently is 4.26%, and is expected to change to 2.45%. Calculate the approximate dollar change in price using both duration and convexity.

Assume annual compounding. Round your answer to 2 decimal places.

Answer 1

Modified duration = Macaluay duration / (1 + YTM)

Modified duration = 5.66 / (1 + 0.0426)

Modified duration = 5.428736

Change in yield = 2.45% - 4.26% = -1.81%

Percentage change in price = (-modified duation * change in yield) + [0.5 *  convexity * (change in yield)^2]

Percentage change in price = (-5.428736 * -0.0181) + [0.5 *  67.35 * (-0.0181)^2]

Percentage change in price = 0.09826 + 0.011032

Percentage change in price = 0.10929 or 10.929%

Since bond is selling at par, current price is 6000

approximate dollar change = 6000 * 0.10929

approximate dollar change = $655.74