Macaulay Duration

A bond pays coupons over its life and repays its face value at maturity. Macaulay duration, named after economist Frederick Macaulay, summarises when, on average, the investor receives the bond's value.

For example, a two-year bond with a 5% annual coupon, priced to yield 5%, pays 5 after one year and 105 after two years. In present value terms, the first payment is worth about 4.76 and the second about 95.24, out of a price of 100. Weighting the times by these values gives a Macaulay duration of about 1.95 years.

A zero-coupon bond's Macaulay duration equals its maturity, because it pays only once. Bonds with coupons have durations shorter than their maturities. Higher coupons and higher yields reduce duration.

Macaulay duration is used in immunisation strategies, where investors match the duration of their assets with the timing of their liabilities. It is the starting point for modified duration, which measures a bond's price sensitivity to changes in interest rates.