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

A bond is priced at 100.00. When the benchmark curve shifts down 50 bps, its price is 101.20. When the curve shifts up 50 bps, its price is 98.90. The bond's effective duration is closest to:

Effective duration is closest to 2.3. It equals the price when rates fall minus the price when rates rise, 2.30, divided by twice the initial price times the 0.5% curve shift, which is 1.00. Omitting the factor of two would wrongly give 4.6.

  1. A2.3
  2. B2.8
  3. C4.6Correct

Explanation

Effective duration = (V- − V+)/(2 × V0 × Δcurve) = (101.20 − 98.90)/(2 × 100 × 0.005) = 2.30/1.00 = 2.30. Wait: 2 × 100 × 0.005 = 1.00, so duration is 2.3. The 4.6 option omits the factor of 2 in the denominator, and 2.8 uses an incorrect price base.

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