FRM Part I · FRM Exam Part I · Interest Rates
A bond is priced at 100 with a modified duration of 8.0 and a convexity of 90. Yields rise by 100 basis points. Using the duration-plus-convexity approximation, what is the new price?
The new price is about 92.45. The duration effect is -8.0%, and the convexity adjustment is +0.5 x 90 x 0.0001 = +0.45%, giving a net change of -7.55% on a price of 100. Convexity always adds value, cushioning the loss from a yield rise.
- A92.45Correct
- B92.00
- C91.55
- D92.90
Explanation
ΔP/P = -8.0 x 0.01 + 0.5 x 90 x 0.01^2 = -0.08 + 0.0045 = -0.0755, so the price is 92.45. Duration alone gives 92.00. Subtracting the convexity term gives 91.55, a sign error. Omitting the 0.5 factor gives 92.90.
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