Convexity: The Bend That Duration Misses

Take the second derivative of the bond price with respect to yield, write its percentage version $V_m$, and record that it is positive for an ordinary bond.

Derive $P(y') \approx P(y)\left[1 - D_m^*(y'-y) + \frac{1}{2}V_m(y'-y)^2\right]$ from the Taylor expansion, and write a portfolio's convexity as the price-weighted average of its bonds' convexities.

Note the tools' 1970s pre-spreadsheet origin, assign the linear term to the rate level and the quadratic term to rate volatility, and state that higher volatility, other things equal, raises a bond's value.

Compute $D_m^* = 3.509846$ and $V_m = 14.805972$ from the semi-annual table, apply the approximation at 8%, and compare 93.276427 with the exact price 93.267255.