Lesson 1 of 5 · 13 min
Effective duration: why curve duration replaces yield duration
When a bond's cash flows depend on future interest rates, its yield-to-maturity is not well defined, so we measure its price sensitivity to a parallel shift in a benchmark yield curve instead: effective duration.
In short
- Yield duration (Macaulay, modified, approximate modified) assumes the cash flows are certain and only the bond's own YTM moves.
- A callable or putable bond, or a mortgage-backed security, has cash flows that depend on whether an option is exercised, so it has no single well-defined YTM.
- Effective duration = (PV₋ − PV₊) ÷ (2 × ΔCurve × PV₀). It is a curve duration: the shift is in the benchmark curve, not in the bond's yield.
- PVâ‚Š and PVâ‚‹ come from an option pricing model in which only the benchmark curve is moved; call schedule, credit spread and volatility are held constant.
- Effective duration also works for option-free bonds, but it usually differs slightly from modified duration; the two are equal only if the yield curve is flat.
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