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FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

A portfolio is 60% invested in Bond A (modified duration 4.0, convexity 20) and 40% in Bond B (modified duration 12.0, convexity 100), by market value. Yields rise by 200 basis points in a parallel shift. Using the duration-plus-convexity approximation, what is the estimated percentage change in portfolio value?

The estimated change is -13.36%. Portfolio duration is 7.2 and portfolio convexity is 52, both value-weighted averages. The duration effect is -14.40%, and the convexity effect adds back 1.04%, leaving a net fall of 13.36%.

  1. A-14.40%
  2. B-13.36%Correct
  3. C-15.44%
  4. D-12.32%

Explanation

Portfolio duration = 0.6×4 + 0.4×12 = 7.2. Portfolio convexity = 0.6×20 + 0.4×100 = 52. Change = -7.2×0.02 + 0.5×52×0.0004 = -0.144 + 0.0104 = -0.1336, or -13.36%. Duration alone gives -14.40%. Subtracting the convexity term gives -15.44%. Omitting the 0.5 factor gives -12.32%.

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