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## Macaulay Duration

Source: Investopedia

### What is The 'Macaulay Duration'

The Macaulay duration is the weighted average term to maturity of the cash flows from a bond. The weight of each cash flow is determined by dividing the present value of the cash flow by the price. Macaulay duration is frequently used by portfolio managers who use an immunization strategy.

### Explaining 'Macaulay Duration'

The metric is named after its creator, Frederick Macaulay. The Macaulay duration can be viewed as the as the economic balance point of a group of cash flows. Another way to interpret the statistic is that it is the weighted average number of years an investor must maintain a position in the bond until the present value of the bond's cash flows equals the amount paid for the bond.

### Factors Affecting Duration

A bond's price, maturity, coupon and yield to maturity all factor into the calculation of duration. All else equal, as maturity increases, duration increases. As a bond's coupon increases, its duration decreases. As interest rates increase, duration decreases and the bond's sensitivity to further interest rate increases goes down. Also, sinking fund in place, a scheduled prepayment before maturity and call provisions lower a bond's duration.

### Example Calculation

The calculation of Macaulay duration is straightforward. Assume there is a bond priced at \$1,000 that pays a 6% coupon and matures in three years. Interest rates are at 6%. The bond pays the coupon twice a year, and pays the principal on the final payment. Given this, the following cash flows are expected over the next three years:   