CFA Level I · CFA Level I Exam · Curve-Based and Empirical Fixed-Income Risk Measures
A bond has key rate durations of 0.40 at the 2-year point, 1.10 at the 5-year point, and 3.50 at the 10-year point. The bond's effective duration is closest to:
The effective duration is about 5.00. Key rate durations sum to the effective duration because a parallel shift changes all key rates by the same amount, so the total price sensitivity is the sum of 0.40, 1.10 and 3.50. Averaging them would understate the sensitivity.
- A1.67
- B5.00Correct
- C6.00
Explanation
Effective duration approximately equals the sum of the key rate durations, since a parallel shift moves every key rate equally. 0.40 + 1.10 + 3.50 = 5.00. Averaging them gives 1.67, which is wrong because the contributions are additive, not averaged.
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