Bond convexity is a measure of the curvature of a bond’s price-yield relation. Convexity is used in the valuation of bonds, to approximate the change in a bond’s duration for a small change in yield. For example, if two bonds have the same coupon rate and maturity date, but one has higher convexity than the other, then the first bond will be more sensitive to changes in interest rates.
Convexity can be thought of as a measure of “interest rate risk.” The greater the convexity, the greater the risk that a bond will lose value if interest rates rise (and vice versa). For this reason, investors typically require a higher yield on bonds with high convexity.
Bond convexity is affected by a number of factors, including the coupon rate, maturity date, and type of interest (fixed or variable). In general, bonds with longer maturities, higher coupon rates, and/or fixed interest rates will have higher convexity than other bonds.
Convexity is measured in “convexity points.” One convexity point is equal to 0.01% (1 basis point) times the square of the bond’s yield. For example, a bond with a 5% yield and 200 convexity points would have a duration of approximately 10 years.
To calculate the duration of a bond using its convexity, the following formula can be used:
D = D0 + CxP/4
D = Duration
D0 = Modified duration
C = Coupon rate
xP = Convexity points