The general DV01 of Lesson 1 makes no assumption about what moves. This lesson specialises to the most common case in practice: the rate factor is the bond's own yield-to-maturity, so the sensitivity is called yield-based DV01 (or modified duration). The result is a closed-form formula — the sum of time-weighted present values — that practitioners compute in a spreadsheet from observable yields and cash flows.
Macaulay duration then emerges as a simple transformation that has one unique interpretation: it equals the cash-flow-weighted average maturity of the bond, and for a zero-coupon bond it equals the bond's maturity exactly. This interpretation makes duration a measure of the effective "centre of mass" of the bond's cash flows in time.
Learning objectives. By the end of this note you should be able to:
- derive the yield-based DV01 formula by differentiating the price-yield equation;
- compute modified duration from a cash-flow table;
- state the Macaulay duration formula and explain its interpretation as a weighted average maturity;
- derive the Macaulay duration of a zero-coupon bond and of a perpetuity;
- list three features that determine a bond's duration: coupon, maturity, and yield.
In this lesson
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- Yield-based DV01 derived
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- Modified duration
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- Macaulay duration
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- Determinants of duration
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- Duration of a portfolio
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- Convexity in the yield-based framework
Before you start
- DV01, Dollar Duration, and One-Factor Price Sensitivity
- Yield-to-Maturity: Definition, Interpretation, and the Coupon Effect
The full lesson, with worked examples and exercise solutions, is for members.
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