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Set out the measures used to gauge risk and return in a bond portfolio and how bonds co-move with other assets

CFA® Level III · Portfolio Construction · Overview of Fixed-Income Portfolio Management · L3.PC.2.b

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.

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