Convexity

Convexity measures the rate of change of a bond's duration as interest rates change, capturing the non-linear (curved) relationship between bond prices and yields. While duration provides a linear approximation of price sensitivity, convexity accounts for the fact that this relationship is actually curved — bond prices rise more when rates fall than they decline when rates rise by the same amount. Positive convexity is desirable for bondholders because it means the bond gains more from falling rates than it loses from rising rates. Standard "bullet" bonds (non-callable, fixed-rate) have positive convexity. Callable bonds exhibit negative convexity at low yields because the call option caps upside price appreciation — as rates fall, the bond's price approaches the call price ceiling rather than continuing to rise. Convexity is particularly important for large interest rate movements where duration alone becomes an insufficient predictor. Portfolio managers use convexity alongside duration to more accurately hedge and manage interest rate risk.