Question

Suppose that you have a bond position worth $100 million. Your position has a modified duration of 8 years and a convexity of 150. By how much does the value of the position change if interest rates increase by 25 basis points?  Use the duration-convexity rule.

		a. ($1,953,125)
		b. ($1,906,250)
		c. ($2,046,875)
		d. ($2,187,500)

Answer 1

25 basis point = 0.25%

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

Percentage change in price = (-8 * 0.0025) + [0.5 * 150 * (0.0025)^2]

Percentage change in price = -0.02 + [0.5 * 150 * 0.00001]

Percentage change in price = -0.02 + 0.00047

Percentage change in price = -0.02047 or -2.047%

Change in value of the position = 100,000,000 * -0.02047

Change in value of the position = (2,046,875)