Measure the curvature of a bond’s price-yield relationship that duration alone misses.
Duration is a straight-line approximation, which understates gains when yields fall and overstates losses when they rise. Convexity is the correction term, and it always works in the bondholder’s favour for ordinary bonds. For large yield moves the convexity term matters materially, which is why long bonds gain more in a rally than duration alone predicts.
Bond Convexity
Price change % ≈ −modified duration × Δy + ½ × convexity × (Δy)²
Price change % ≈ −modified duration × Δy + ½ × convexity × (Δy)² Duration is a straight-line approximation, which understates gains when yields fall and overstates losses when they rise. Convexity is the correction term, and it always works in the bondholder’s favour for ordinary bonds.
For large yield moves the convexity term matters materially, which is why long bonds gain more in a rally than duration alone predicts.
This calculator takes 5 inputs: Face value, Market yield, Years to maturity, Modified duration, Yield change to model. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.