Convexity.
A definition, in plain English — with the books that teach it.
What it means
Convexity measures the curvature in the relationship between a bond's price and interest rates. Duration provides a linear approximation of price sensitivity, but as rates move significantly, the actual price change diverges from the linear estimate — convexity captures that curvature. Bonds with positive convexity gain more in price when rates fall than they lose when rates rise by the same amount, which is a desirable property. Callable bonds and mortgage-backed securities can exhibit negative convexity, making them riskier in volatile rate environments.
Example
Two bonds have the same duration of 7 years. Bond A has convexity of 80; Bond B has convexity of 40. If rates fall 2%, Bond A gains about 0.4% more than the linear estimate would predict, while Bond B's bonus is only 0.2%. In a volatile rate environment, Bond A's higher convexity is worth paying a slight yield premium.
