What is Macaulay Duration?

Macaulay duration is the weighted average life of a portfolio of bonds, also known as the term to maturity or average life. Expressed in years, it is also commonly viewed by traders as a measure of cash flow volatility with respect to prices. Volatility is a measure of risk and how much cash flows from bond portfolios fluctuate over time. As such, Macaulay duration is used as a tool to balance and hedge bond portfolios against the risk associated with changes in bond cash flows.

Created by Frederick Macaulay in 1938, Macaulay duration was not widely used until the 1970s. There are several different types of duration to include: key-rate, modified, and effective. All measures are expressed in years. The difference is in the way each calculation accounts for changes in interest rates or other embedded options in the bond. Macaulay duration uses a weighted average approach.

In general, investors use duration to gauge the sensitivity of a bond, or bond portfolio, to changes in interest rates. This is important because bonds are priced depending on the current level of interest rates. Bonds with a longer term to maturity carry more risk and have more cash flow fluctuations in response to changes in interest rates.

In order to understand the concept of Macaulay duration it is important to understand how changes in interest rates affect bond prices. Par value is the stated value of the bond, and it's usually the amount the bondholder will receive when the bond is redeemed at maturity. A bond trading at par has a coupon which is equivalent to current interest rates.

Bonds trading at a price higher than par, or the future value, are trading at a premium. This also means that current interest rates are trading lower than the rate of interest paid on the bonds. As such, the bonds are more valuable since they pay a higher rate of interest than what is paid on current bonds. On the other hand, a bond trading below par is paying a lower rate of interest than current interest rates. As such, this bond is not as valuable and is therefore priced lower.

Interpreting Macaulay duration is fairly intuitive. In general, if a bond's yield goes up by 200 basis points, or 2.0 percent, the duration or life of the bond will decrease by a certain number of years. That is, the time it takes for the bond to reach maturity and pay back the bondholder is shorter. This is because increases in yield equate to a higher rate of income and so the bond is paid off faster.