Lesson 1 of 5 · 14 min
From Macaulay duration to modified duration
Modified duration is Macaulay duration divided by one plus the yield per period, and it tells you roughly what percentage of its full price a bond loses or gains when its yield moves.
In short
- Yield duration measures price sensitivity to a change in the bond's own YTM, with cash flows assumed certain. Curve duration (later modules) uses a benchmark curve instead.
- Macaulay duration = PV-weighted average time to receipt of the cash flows, with weights = each cash flow's share of the full price.
- Modified duration = MacDur ÷ (1 + yield per period). It is the slope of the price-yield curve expressed as a percentage of price.
- Estimated % change in full price ≈ −AnnModDur × ΔYield. Higher modified duration → steeper curve → more interest rate risk.
- The estimate is linear, so it gives the same size of move for a rise and a fall in yield; the true curve is convex.
- With a negative yield, 1 + r < 1, so modified duration is larger than Macaulay duration.
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