Lesson 2 of 5 · 12 min
Approximate modified duration
Reprice the bond a few basis points above and below its yield, and the price difference divided by twice the yield change and the starting price gives an accurate estimate of modified duration.
In short
- Approximate modified duration = (PV₋ − PV₊) ÷ (2 × ΔYield × PV₀), all full prices.
- It estimates the slope of the tangent line using two nearby points on the price-yield curve.
- The result is already annualized if ΔYield is an annual figure; coupon frequency is handled inside the price calculations.
- It works when Macaulay duration is unknown, e.g. for bonds with contingent cash flows or default risk.
- Approximate Macaulay duration = approximate AnnModDur × (1 + yield per period).
- For large yield changes, duration overstates losses and understates gains, because the curve is convex.
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