Duration & Convexity
Duration draws a straight tangent to the price-yield curve. Convexity adds the curvature the tangent misses, so it tracks the true price more closely as the yield moves.
Price
$100.00
Macaulay dur.
8.11 yr
Modified dur.
7.72 yr
Convexity
75.00
At Δy = +1.0% (new yield 6.0%)
True new price$92.64
Duration estimate$92.28error -0.36
Duration + convexity$92.65error +0.01
Adding the ½·C·Δy² term shrinks the error: convexity captures the curve the tangent misses, and because the price-yield curve bows toward the origin it always sits above the tangent.