Convexity

The exam rarely asks you to compute convexity; it tests ranking and direction. A classic item gives two bonds with identical (or nearly identical) duration and asks which is preferable — the higher-convexity bond wins, because for equal-sized yield moves it gains more when yields fall and loses less when they rise. The tell that convexity matters is a large yield move or the phrase “more accurate estimate,” signaling you must add the ½ × convexity × (ΔY)² term, which is positive for option-free bonds and therefore improves the duration-only estimate in both directions.

The trap is treating convexity as a substitute for duration: it is a second-order correction, so apply the duration (first-order) term first, then adjust. Duration is the slope; convexity is the curvature. Also distinguish effective convexity — which reprices the bond at shifted (higher and lower) yields and is the required measure for bonds with embedded options — from yield-based (approximate) convexity, and remember a callable bond can turn negative-convex when low yields make the call likely.