Convexity

Convexity measures the curvature in the relationship between bond prices and yields, providing a second-order effect beyond duration. While duration assumes a linear relationship, convexity accounts for the fact that this relationship is actually curved. Positive convexity means that as yields fall, price increases accelerate, and as yields rise, price decreases decelerate – favorable for investors. For example, a bond with duration of 10 and convexity of 100 will gain more than 10% if rates fall 1% and lose less than 10% if rates rise 1%. The formula includes a convexity adjustment: price change ≈ -Duration × yield change + 0.5 × Convexity × (yield change)². Bonds with embedded options have negative convexity in certain ranges – callable bonds when rates fall (price gains are capped) and mortgage-backed securities due to prepayment risk. Portfolio managers seek positive convexity to enhance returns. Zero-coupon bonds have the highest convexity for given maturity.