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A bond with face value = 6,000 currently trades at par. Its Macaulay duration is 4.91...

A bond with face value = 6,000 currently trades at par. Its Macaulay duration is 4.91 years and its convexity is 63.98.

Suppose yield currently is 2.32%, and is expected to change to 3.65%. Calculate the approximate dollar change in price using both duration and convexity.

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

Solutions

Expert Solution

Modified duration = Macaluay duration / (1 + YTM)

Modified duration = 4.91 / (1 + 0.0232)

Modified duration = 4.798671

Change in yield = 3.65% - 2.32% = 1.33%

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

Percentage change in price = (-4.798671 * 0.0133) + [0.5 *  63.98 * (0.0133)^2]

Percentage change in price = -0.063822 + 0.005659

Percentage change in price = -0.058163 or -5.8163%

Since bond is selling at par, current price is 6000

approximate dollar change = 6000 * -0.058163

approximate dollar change = -$348.98

jeff jeffy answered 2 years ago
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