Answer: If large rate changes occur

## 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:** 1. **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 2. **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 3. **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.

Author: LeetQuiz Editorial Team