Explanation

In bond portfolio management, convexity measures the curvature of the price-yield relationship. For portfolios with the same duration:

• Barbell portfolio: Consists of short-term and long-term bonds, creating a "barbell" shape on the yield curve
• Bullet portfolio: Concentrated in bonds with similar maturities around the target duration

Key Principle: Barbell portfolios typically have higher convexity than bullet portfolios with the same duration because:

1. Convexity increases with the square of time to maturity
2. The long-term bonds in the barbell contribute disproportionately to convexity
3. The combination of short and long durations creates a more curved price-yield relationship

Mathematical Insight:

• Convexity ≈ (Duration² + Duration + Dispersion)
• Barbell portfolios have higher dispersion of cash flows, leading to higher convexity

Practical Implication: The barbell portfolio will benefit more from large interest rate movements (both up and down) due to its higher convexity, while the bullet portfolio performs better for small rate changes due to better duration matching.

Answer: B - Barbell convexity is greater than bullet's convexity