Convexity is a financial metric that measures the curvature of the relationship between bond prices and bond yields.
Understanding bond convexity
Bond prices move inversely to interest rates. Investors use a metric called duration to estimate how much a bond’s price will change when interest rates change. Duration assumes this relationship is a straight line. The actual price-yield relationship is curved. Convexity measures this curve and accounts for the inaccuracy of duration.
Most standard fixed-rate bonds have positive convexity. When interest rates fall, the price of a bond with positive convexity increases at an accelerating rate. When interest rates rise, the bond’s price decreases, but the rate of the price decline slows down. This asymmetrical price movement means the bond gains more value as rates drop than it loses when rates rise by the exact same amount.
Bonds with embedded options often exhibit negative convexity. Mortgage-backed securities and callable bonds are common examples in global debt markets. If interest rates fall, the issuer is likely to call the bond to refinance the debt at a lower rate. This limits the price appreciation of the bond. The price-yield curve flattens out at lower yields, meaning the price does not rise as much as duration predicts.
Convexity is a standard risk measurement in fixed-income trading. Elephants constructing bond portfolios use it to compare bonds with identical durations and yields. A bond with higher convexity is generally more desirable because it offers better protection against rising rates and greater potential for price gains when rates fall.
Example
Suppose you are evaluating bonds issued by the Savannah Watering Hole Corporation to fund new reservoirs for local herds. You hold a 10-year bond with a duration of seven years and a high level of positive convexity. A central bank decides to lower interest rates by 1%. The duration metric predicts your bond price will rise by exactly 7%. The convexity of the bond pushes the actual price increase to 7.8%.
If the central bank instead raises interest rates by 1%, duration predicts a 7% drop in the bond’s price. The positive convexity cushions this decline, resulting in an actual price drop of only 6.2%. Elephants investing in this debt receive a mathematical advantage, as the bond yields a larger upside and a restricted downside compared to a purely linear price model.