FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01
A $200 million bond portfolio has a modified duration of 5 and a convexity of 40. Yields rise by 100 basis points in a parallel shift. Using both duration and convexity, what is the approximate change in portfolio value?
The portfolio falls by about $9.6 million. The duration effect is -5 times 0.01, or -5%, and the convexity adjustment adds 0.5 times 40 times 0.0001, or +0.2%. The net change is -4.8% of $200 million. Duration alone overstates the loss.
- A-$9.6 millionCorrect
- B-$10.0 million
- C-$10.4 million
- D-$9.2 million
Explanation
ΔP/P ≈ -D x Δy + 0.5 x C x (Δy)^2 = -5(0.01) + 0.5(40)(0.0001) = -0.05 + 0.002 = -0.048. Times $200m this gives -$9.6m. The -$10.0m answer uses duration only, and -$10.4m subtracts the convexity term instead of adding it.
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