Convexity

Modified duration is a linear approximation, while a bond's actual price-yield relationship is generally curved. For a conventional option-free fixed-cash-flow bond with positive convexity, a yield fall raises price more than an equal-sized yield rise lowers it. A common second-order approximation is ΔP/P ≈ −D_modified×Δy + 0.5×convexity×(Δy)², with consistently defined units. Embedded options can alter convexity and may produce negative convexity. Current AFM requires discussion of convexity's effect; the final SCF guide explicitly refers to convexity metrics, so exam depth must be separately mapped.