Question

An 6% annual coupon bond with (face value = 3,000) currently trades at par. Its Macaulay duration is 5.16 in years and its convexity is 56.34 in years.

Suppose yield goes from 5.88% to 2.42% one day. Calculate the approximate dollar change in price using both duration and convexity.

Assume annual compounding. Round your answer to 2 decimal places. If your answer is a price decline, then include the negative sign in your answer.

Answer 1

Since bond is selling at par, YTM will be equal to coupon rate

Modified duration = Macaluay durartion / (1 + YTM)

Modified duration = 5.16 / (1 + 0.06)

Modified duration = 4.8679

Change in yield = 2.42% - 5.88% = -3.46%

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

Percentage change in price = (-4.8679 * -0.0346) + [0.5 * 56.34 * (0.0346)^2]

Percentage change in price = 0.168429 + [0.5 * 56.34 * 0.001197]

Percentage change in price = 0.168429 + 0.033724

Percentage change in price = 0.202135 or 20.2153%

Dollar change in price = 3000 * 0.202135

Dollar change in price = $606.46