Question

An 5% annual coupon bond with (face value = 2,000) currently trades at par. Its Macaulay duration is 4.62 in years and its convexity is 62.63 in years. Suppose yield goes from 5.74% to 2.89% 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 = 4.62 / (1 + 0.05)

Modified duration = 4.4

Change in yield = 2.89% - 5.74% = -2.85%

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

Percentage change in price = (-4.4 * -0.0285) + [0.5 * 62.63 * (0.0285)^2]

Percentage change in price = 0.1254 + [0.5 * 62.63 * 0.000812]

Percentage change in price = 0.1254 + 0.025436

Percentage change in price = 0.150836 or 15.0836%

Dollar change in price = 2000 * 0.150836

Dollar change in price = $301.67