Duration and convexity explained

What are duration and convexity for a bond? Describe their main properties and how practitioners use them.

Duration is the price sensitivity to yield; convexity is how that sensitivity changes. Macaulay duration is the PV-weighted average time to the cash flows; modified duration $-\tfrac{1}{P}\tfrac{dP}{dy}$ gives the percentage price change per unit yield move. It rises with maturity and falls with coupon and yield; a zero's Macaulay duration equals its maturity. Convexity $\tfrac{1}{P}\tfrac{d^2P}{dy^2}$ is the second-order term, positive for option-free bonds. Together they approximate price changes and are used to hedge and immunise portfolios.