A useful way to think about this: 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. That matters most when portfolios are built assuming small yield changes and reality refuses to stay small. In practice: On bigger rate moves, the second-order effect can materially change how a supposedly simple duration bet behaves. $$ \frac{\Delta P}{P} \approx -D\Delta y + \frac{1}{2}C(\Delta y)^2 $$ Plain English: Convexity adds the curvature term that improves the duration estimate on larger moves. 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. The point is not to memorize the label. The point is to know what variable is actually doing the work.