Convexity is what reminds you that bond price sensitivity is not perfectly linear. What is happening: Duration gives the first approximation. Convexity tells you how that approximation changes when the move is large. Why it matters: That matters most when portfolios are built assuming small yield changes and reality refuses to stay small. $$ \frac{\Delta P}{P} \approx -D\Delta y + \frac{1}{2}C(\Delta y)^2 $$ Plain English: Convexity adds the curvature term that improves the duration estimate on larger moves. In practice: On bigger rate moves, the second-order effect can materially change how a supposedly simple duration bet behaves. Watch for: The mistake is relying on first-order intuition when the regime is delivering second-order moves. Useful lens: Before reacting, ask what mechanism would still matter here if the headline disappeared tomorrow. That is usually where the edge is: not in the vocabulary, but in the structure underneath it.