One framing I keep coming back to is 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: A useful review question is which funding, incentive or cash-flow channel is actually doing the work. A lot of confusion disappears once you separate the headline from the mechanism.