Duration and Convexity (Intuition)
Duration is first-order rate sensitivity; convexity is the second-order correction.
Duration approximates how bond price changes for small yield changes (linear sensitivity).
Convexity improves the approximation for larger yield moves (curvature).
Higher convexity is generally valuable, but it is not free: it is priced.
A fixed coupon bond reacts to yield moves. Duration gives a first-order linear approximation to the price change; convexity adds a quadratic correction that matters more for larger shifts.
For small yield moves, the orange duration-only bar is close to the blue exact bar. As you increase |Δy|, the gap grows and the green duration+convexity bar stays closer to the true price.
Duration gives a linear sensitivity; convexity corrects this for curvature in the price–yield relationship. Higher convexity improves the approximation but is itself a priced feature of the bond or the portfolio.