Macaulay duration is an investment measure used primarily by fixed-income strategists to gauge the sensitivity of a bond portfolio to changes in interest rates. It is named after American mathematician and financier William F. Macaulay and is used to compare and measure the safety of different bonds.

Macaulay duration is an important tool for investors to use when determining the degree of interest rate risk in their portfolios. It is used to calculate both the average maturity of a series of fixed income bonds, as well as the pattern of cash flows from those bonds. Essentially, Macaulay duration measures the amount of time it takes for the market value of a bond portfolio to be repaid.

The Macaulay duration of a bond is the weighted-average time it takes for the bond's cash flows to be received. This is determined using the present value of each payment and its time to maturity. Bonds with longer durations tend to have a greater degree of sensitivity to interest-rate changes. This is because, as the duration of a bond increases, so does the amount of time needed for the investment to recover from rising interest-rates. As a result, when the general level of interest rates is expected to increase, investors should prefer bonds with shorter Macaulay durations.

Macaulay duration is also used to estimate the amount of price volatility that a bond may experience when interest rates change. This is because bonds with longer durations will tend to have more price volatility due to their greater sensitivity to changes in interest rates. Therefore, an investor who is looking for a bond with less price volatility should prefer those that have a shorter Macaulay duration.

Additionally, Macaulay duration can tell us about the expected rate of return from a security if it is held to maturity. This is because long duration bonds tend to have a higher expected rate of return than short duration bonds. Therefore, an investor looking for a higher return should consider holding bonds with a longer duration.

Finally, Macaulay duration is a useful tool for measuring the duration of a bond fund, or a package of different bonds. It seeks to compare bonds of different maturities along with their respective yields. To accurately measure the portfolio's duration, one must calculate the weighted average of the duration of all the bonds that make up the portfolio.

In conclusion, Macaulay duration is a widely used measure of a bond portfolio's sensitivity to interest rate fluctuations. It is most useful for comparing the duration of different bonds and for estimating the expected rate of return from holding a bond. By using Macaulay duration, investors can better manage their interest rate risk and gain an insight into the volatility of their portfolio.