Explanation

Convexity Scaling:

Convexity scales with roughly the square of maturity. This means that as the maturity of a bond increases, its convexity increases at an accelerating rate (quadratically).

Why this matters for barbell portfolios:

• In a barbell portfolio, the long-duration bond (15-Year Treasury in this case) has significantly higher convexity due to its longer maturity
• The convexity contribution from the long-duration bond disproportionately increases the overall convexity of the barbell portfolio
• This is because convexity ≈ (maturity)², so a bond with 15-year maturity has much higher convexity than one would expect from a linear relationship

Mathematical Insight:

• Convexity formula: C ≈ (1/P₀) × (P₊ - 2P₀ + P₋)/(Δr)²
• For zero-coupon bonds, convexity is approximately equal to (maturity)²
• Even for coupon bonds, the relationship remains roughly quadratic

Why other options are incorrect:

• A: Convexity does not scale linearly; it scales quadratically
• C: Convexity actually increases with longer maturities
• D: Convexity is highly dependent on maturity and is not constant