Lesson 4 of 5 · All lessons in this module
- The three sources of return on a fixed-rate bondVideo lesson
- Horizon yield: the realized return when rates moveVideo lesson
- Reinvestment risk, price risk and the duration gapVideo lesson
- Calculating Macaulay duration on a coupon dateVideo lesson
- Macaulay duration between coupon dates and the closed-form formula
Lesson 4 of 5 · 13 min
Calculating Macaulay duration on a coupon date
Macaulay duration is the average time until you receive a bond's cash flows, with each time weighted by that cash flow's share of the bond's price.
In short
- Macaulay duration = weighted average time to receipt of the cash flows; weight = PV of the cash flow ÷ the bond's full price.
- Recipe: list times and cash flows → discount each at the YTM → weights = PV ÷ total → multiply each time by its weight → add.
- For a coupon bond, Macaulay duration is less than maturity; for a zero-coupon bond (on a coupon date) it equals maturity.
- For semiannual (or quarterly) bonds, the sum is in periods: divide by 2 (or 4) to annualize into years.
- Interpretation: the holding period that balances reinvestment and price risk.
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