Convexity
Convexity measures how a 's duration changes as interest rates move, capturing the curvature in the relationship between a 's price and its yield. Duration alone assumes that relationship is a straight line, but in reality a 's price does not rise or fall by exactly the same amount for every incremental change in yield, and convexity describes that difference.
Most ordinary have positive convexity, meaning their price rises by slightly more when yields fall than it falls when yields rise by the same amount. This works in the investor's favor, since gains from falling rates tend to outpace losses from rising rates of the same size. Some , notably and mortgage-backed securities, can exhibit negative convexity, where the price gain from falling rates is capped because the issuer becomes more likely to call the or borrowers become more likely to refinance, limiting the upside just when it would otherwise be largest.
For an investor comparing two with similar duration, the one with greater positive convexity is generally more attractive, since it offers a better tradeoff between potential gains and potential losses as rates move. Convexity becomes more important the larger the expected swing in interest rates, since duration by itself becomes a less accurate estimate of price change as that swing gets bigger.