Duration: How Far a Bond's Price Moves with Yield

Sketch price against yield as downward-sloping and convex, identify the slope as the risk measure, and record that longer maturity means a larger price move per basis point.

Define the weights $\omega_k = \text{PV}(C_k)/P$, show that they sum to one, and state that a zero-coupon bond's duration equals its maturity.

Differentiate the price formula with respect to $y$ to derive $\frac{1}{P}\frac{\partial P}{\partial y} = -D_m^*$, and state how duration extends to a portfolio using present-value weights.

Build the semi-annual table for the note priced at 103.50 to yield 6%, reach $D = 7.13$ and $D^* = 6.92$ half-years, and convert modified duration to annual units.