Why can duration be shorter than maturity?
Maturity is not duration: coupons return value earlier and change rate sensitivity.
Same ten-year maturity: what changes when coupons arrive earlier?
Face 1,000, 6% YTM, semiannual periods. Compare with and without coupons.
What did you just see?
A zero-coupon bond pays only at maturity, so its equals maturity. Coupons return some value earlier. Higher means greater sensitivity to the same yield change.
Model assumptions
Valuation is on a coupon date. Fixed coupons and face redemption; nominal annual yield is divided by frequency. No default or options. Maturity must span whole coupon periods.
Another example
- Compare ten-year maturity with duration.
- Convert 50 bps to 0.005 and multiply by negative modified duration.
- Use price sensitivity analysis for exact repricing under larger shifts.
Show formal definition and formula
Macaulay duration is the present-value-weighted time to cash flows. Modified duration measures price sensitivity to a small yield change.
D_Mac = Σ[(t/m) × CF_t/(1+y/m)^t] / P; D_Mod = D_Mac/(1+y/m); ΔP/P ≈ −D_Mod × ΔyMacaulay duration is the present-value-weighted time to cash flows. Modified duration measures price sensitivity to a small yield change.
Common mistakes
Maturity is not duration. A 50 bps increase is 0.50 percentage points; Δy is 0.005, not 0.5.
Frequently asked questions
Why use duration for small changes?
Duration approximates the slope of the price curve, excluding curvature. Larger changes may increase approximation error.
You can now explore…
- Duration versus maturity
- Estimate small yield-shock price changes
Term reference4 terms
Open a term when you need a reminder. Underlined words in the article work too.