Macaulay Duration
Weighted-average time to a bond's cash flows, where weights are the present values of those cash flows divided by the bond price. Expressed in years; the older of the two duration measures.
When to use: Use as the building block for modified duration. Macaulay duration also equals the holding period at which a bond's price-risk and reinvestment-risk balance for a parallel yield shift — the "immunization horizon" in classical fixed-income theory.
Formula
Variables
| Symbol | Name | Description | Unit |
|---|---|---|---|
| MacDur | Macaulay Duration | Weighted-average time to cash flows, in years | years |
| F | Face Value | Par value paid at maturity | $ |
| CR | Coupon Rate | Annual coupon rate as a decimal (e.g. 0.05 for 5%) | % |
| y | Yield | Annual yield as a decimal; periodic yield is y/m | % |
| N | Years to Maturity | Years remaining until the bond matures | years |
| m | Coupons per Year | Number of coupons paid per year (e.g. 2 for semi-annual) | integer |
Real-Life Examples
Example 1: Par Bond, 5y, 5%, Semi-Annual
5-year, 5% coupon, semi-annual, $1,000 face. YTM = 5%, so the bond prices at par.
Given
Step-by-Step
Macaulay duration is 4.49 years — meaningfully shorter than the 5-year maturity because intermediate coupons pull the cash-flow weighted average forward in time.
Frequently Asked Questions
Yes — a zero has a single cash flow at maturity, so the weighted-average time IS the maturity. That's why zeros are the most rate-sensitive bonds for a given maturity.
Because coupons paid before maturity contribute weight at earlier dates. Higher coupons → more cash flow up front → shorter duration. Lower coupons → more weight at maturity → longer duration.
For a small parallel yield shift, an investor with a holding period equal to Macaulay duration sees price risk and reinvestment risk offset to first order. This is the basis of liability-matching pension portfolio strategies.