CFA Level I · CFA Level I Exam · Yield-Based Bond Convexity and Portfolio Properties
A portfolio manager holds three bonds with market values of 40%, 35% and 25% of the portfolio. Their modified durations are 4.0, 6.0 and 8.0, respectively. The portfolio modified duration is closest to:
The portfolio modified duration is about 5.7. It is the market-value-weighted average of the individual durations: 0.40×4.0 plus 0.35×6.0 plus 0.25×8.0 equals 5.7. A simple average of 6.0 is wrong because it ignores the weights.
- A5.7
- B5.9Correct
- C6.0
Explanation
Portfolio duration is the market-value-weighted average of the bond durations: 0.40×4.0 + 0.35×6.0 + 0.25×8.0 = 1.60 + 2.10 + 2.00 = 5.70. Wait, recomputed: 1.6+2.1+2.0 = 5.7, so the key is 5.7. Taking the simple average of 6.0 is wrong because it ignores the weights.
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