Convexity measures the degree of curvature of the price-yield relationship of a bond. A bond with high convexity will be less affected by changes in interest rates than a bond with low convexity. This means that when interest rates fall, the price of a bond with high convexity will rise more than the price of a bond with low convexity, and when interest rates rise, the price of a bond with high convexity will fall less than the price of a bond with low convexity.

This effect becomes more pronounced with larger changes in interest rates. When yields change a lot (Option C), the added price change due to convexity is more noticeable than when yields change a little (Option B), making bonds with greater convexity more attractive. On the other hand, when yields remain constant (Option A), there are no changes in interest rates for convexity to amplify or dampen, so the level of convexity doesn't matter.

In other words, a bond's convexity can provide some protection against interest rate risk, but the level of protection increases with the magnitude of interest rate changes. This is why securities with greater convexity perform better when yields change a lot.

Things to Remember

• Convexity is a measure of the curvature of the relationship between bond prices and bond yields.
• Bonds with higher convexity are less affected by changes in interest rates compared to bonds with lower convexity.
• Convexity helps to estimate the potential price change of a bond given a change in interest rates.
• Convexity is particularly important for fixed income securities with embedded options, such as mortgage-backed securities.
• Duration and convexity are both measures used to assess the interest rate risk of a bond or portfolio of bonds.