Set out the measures used to gauge risk and return in a bond portfolio and how bonds co-move with other assets
The idea
Portfolio duration, approximated by the market-value-weighted average of holdings' durations, measures sensitivity to parallel yield shifts. Convexity captures curvature, so %ΔP ≈ −D × Δy + ½ × C × (Δy)². Effective duration is used when cash flows depend on rates, as with callable bonds or mortgage-backed securities. Spread duration measures sensitivity to credit spreads, and key rate durations show exposure to shifts at particular maturities. Correlation of government bonds with equities has often been low or negative, but high-yield bonds behave more like equities, and correlations shift across inflation regimes. Applying modified duration to bonds with embedded options misstates their rate sensitivity.
Formulas
Price change with the convexity adjustment
%Δprice ≈ −ModDur × Δyield + ½ × Convexity × (Δyield)²
- %Δprice
- the percentage change in the full price
- ModDur
- modified duration
- Convexity
- the curvature of the price-yield relationship
- Δyield
- the change in yield, as a decimal
For a portfolio use the value-weighted averages of the holdings' durations and convexities, and effective measures for bonds with options. Positive convexity adds to the price change whichever way yields move.
In the app: 1 practice questions on this outcome, a narrated walkthrough with diagrams, spaced review that brings it back before you forget it.
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