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CFA Level I · CFA Level I Exam · Curve-Based and Empirical Fixed-Income Risk Measures

A callable bond has a price of 102.00. Using a binomial model, a 20 bps parallel shift in the benchmark curve gives prices of 102.90 for a downward shift and 101.10 for an upward shift. The effective duration is closest to:

Effective duration is about 4.4. It equals the price when the curve falls minus the price when it rises, 1.80, divided by two times the base price times the 0.002 curve shift, 0.408, which yields roughly 4.41.

  1. A2.2
  2. B4.4Correct
  3. C8.8

Explanation

Effective duration = (PV- − PV+)/(2 × PV0 × Δcurve) = (102.90 − 101.10)/(2 × 102 × 0.002) = 1.80/0.408 = 4.41. Using 0.2 instead of 0.002 would understate it, and omitting the 2 in the denominator gives 8.8.

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