Estimating price changes with duration and convexity

In short

• $\%\Delta PV^{Full} \approx (-\text{AnnModDur} \times \Delta y) + \tfrac{1}{2} \times \text{AnnConvexity} \times (\Delta y)^2$.
• The first term is the duration effect; its sign depends on the direction of the yield change.
• The second term, the convexity adjustment, is always added for an option-free bond, because $(\Delta y)^2$ is positive.
• So the estimated gain when yields fall is bigger than the estimated loss when yields rise by the same amount.
• The improvement matters most for large yield changes, long maturities and low coupons.