Convexity is defined as what?

• A. The curvature of the price-yield curve.
• B. Duration.
• C. Credit risk.
• D. The slope of the yield curve.

Answer: (A)

Convexity measures the curvature of the price-yield relationship for a bond. As yields move, a bond’s price doesn’t change in a straight line because the price curve is curved. Duration captures the initial slope of that price change for a small yield move, but it assumes linearity. Convexity is the second derivative, describing how duration itself changes as yields change. In practical terms, a bond with higher convexity will gain more in price when yields fall and lose less when yields rise, compared with a bond with lower convexity. The usual price-change approximation uses both duration and convexity: ΔP ≈ -D×Δy + (1/2)×Conv×(Δy)^2. The other concepts—duration as the first-order sensitivity, credit risk as default risk, and the slope of the yield curve as the difference between yields at different maturities—describe different ideas.