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FRM Part II · FRM Exam Part II · Risk Management for Changing Interest Rates: Asset-Liability Management and Duration Techniques

A bond has a price of 100, a modified duration of 7.0 and a convexity of 60. Yields increase by 100 basis points. Using both duration and convexity, what is the approximate new price?

The approximate new price is 93.30. Duration implies a 7% fall, but convexity adds back 0.5 × 60 × 0.01² = 0.3%, giving a net fall of 6.7% from 100. Ignoring convexity would understate the price at 93.00.

  1. A93.30Correct
  2. B93.00
  3. C93.60
  4. D107.30

Explanation

Percentage change ≈ -D×Δy + 0.5×C×Δy² = -7.0×0.01 + 0.5×60×0.0001 = -0.07 + 0.003 = -0.067. New price = 100 × 0.933 = 93.30. The 93.00 option ignores convexity; 93.60 subtracts the convexity term instead of adding it.

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