Explanation
Barbell vs. Bullet Performance:
A barbell portfolio outperforms a bullet portfolio when large rate changes occur. This is due to the higher convexity of the barbell structure.
Why barbell outperforms with large rate changes:
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Convexity Advantage:
- Barbell portfolios have higher convexity due to the combination of short and long maturities
- Higher convexity means the portfolio's price increases more when rates fall and decreases less when rates rise
- This convexity benefit becomes more significant with larger interest rate movements
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Mathematical Explanation:
- Price change ≈ -Duration × Δy + ½ × Convexity × (Δy)²
- The convexity term (½ × Convexity × (Δy)²) becomes more important when Δy is large
- Since barbell has higher convexity, it benefits more from large rate changes
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Portfolio Structure:
- Barbell: Combines short and long maturities
- Bullet: Concentrated in intermediate maturities
- The barbell's structure provides better convexity characteristics
Why other options are incorrect:
- B: With stable rates, the higher convexity doesn't provide benefits and may even be costly
- C: Small rate changes don't sufficiently activate the convexity advantage
- D: Yield curve flattening affects different portfolio structures differently, but doesn't guarantee barbell outperformance
Practical Implication:
Barbell strategies are particularly effective in volatile interest rate environments where large rate movements are expected.
