Macaulay Duration using the weighted average method
About this lesson
In this video, I will explain Macaulay’s duration and its calculation using weighted average times for each coupon payment.
The idea
Macaulay duration is a weighted average of the times when a bond pays you. Each payment time is weighted by how much that payment is worth today, as a share of the bond’s price.
Step by step
- List each payment time t and its cash flow.
- Find each payment’s present value: CF ÷ (1 + y)t.
- Add the present values to get the price.
- Divide each present value by the price to get its weight. The weights add up to 1.
- Multiply each time by its weight, and add them up. That’s the duration.
Example
A 3-year bond, 8% annual coupon, $1,000 face value, yield 10%:
| t | Cash flow | PV = CF ÷ 1.10t | Weight = PV ÷ Price | t × Weight |
|---|---|---|---|---|
| 1 | 80 | 72.73 | 0.0765 | 0.0765 |
| 2 | 80 | 66.12 | 0.0696 | 0.1392 |
| 3 | 1,080 | 811.42 | 0.8539 | 2.5617 |
| 950.26 | 1.0000 | 2.7774 years |
Build it in Excel
With t in column A and cash flows in column B (rows 2–4), and the yield in F1:
- C2:
=B2/(1+$F$1)^A2(present value), fill down - C5:
=SUM(C2:C4)(price) - D2:
=C2/$C$5(weight), fill down - E2:
=A2*D2, fill down - E5:
=SUM(E2:E4)→ 2.7774
Semi-annual bonds
For bonds paying every six months, work in half-year periods with the half-year yield, then divide the result by 2 to get the duration in years.