Question

1)Consider a bond selling at par with modified duration of 22-years and convexity of 415. If the yield decreases by 2%, what would be the percentage price change according to the duration-with-convexity rule?

		44%
		52.3%
		60.6%
		80%

2)Bond A has an 8-year duration and is priced at $1,070. Its yield to maturity is 9%. If the yield to maturity falls to 8.42%, you would predict that the new value of the bond will be approximately ________.

		$1,024.5
		$1,070.0
		$1,115.5
		$1,160.1

Answer 1

1)

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

Percentage change in price = (-22 * -0.02) + [0.5 * 415 * (-0.02)^2]

Percentage change in price = 0.44 + [0.5 * 415 * 0.0004]

Percentage change in price = 0.523 or 52.3%

2)

Modified duration = Macaulay duration / (1 + r)

Modified duration = 8 / (1 + 0.09)

Modified duration = 7.33945

Change in yield = 8.42% - 9% = -0.58%

Change in percentage = -Modified duration * change in yield

Change in percentage = -7.33945 * -0.0058

Change in percentage = 0.042569 or 4.2569%

New value of bond = 1070 (1 + 0.042569)

New value of bond = $1,115.5