Answer: Convexity scales with roughly the square of maturity

## 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

Author: LeetQuiz Editorial Team