Lesson 5 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 5 of 5 · 12 min
Macaulay duration between coupon dates and the closed-form formula
Between coupon dates every cash flow is closer by the fraction of the period already elapsed, so Macaulay duration simply falls by t/T while the weights stay the same.
In short
- Between coupon dates, the time to receipt of the first cash flow is , then , and so on.
- Discount with those fractional times; the sum of the PVs is the full price.
- The PV weights do not change: every PV is scaled up by the same factor .
- So MacDur between coupons = MacDur at the last coupon date − (in periods). Macaulay duration falls as time passes.
- A closed-form formula gives the same answer without a table.
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