# Macaulay Duration: Definition, Formula, Example, and How It Works.

Macaulay Duration: Definition, Formula, and Example How is Macaulay duration Modified duration calculated? Macaulay duration is the weighted average of the cash flows from a bond, where the weights are determined by the present value of each cash flow. Modified duration is a measure of a bond's price sensitivity to changes in interest rates. It is calculated by dividing the Macaulay duration by (1 + yield to maturity).

What is the duration or how long is the duration? The duration of a financial asset is the time it takes for the asset to mature and can be used as a measure of the asset's sensitivity to changes in interest rates. The longer the duration, the greater the sensitivity. For example, a one-year bond has a duration of one year, while a five-year bond has a duration of five years.

### How do you calculate duration of a bond portfolio in Excel?

To calculate the duration of a bond portfolio in Excel, first determine the weighted average maturity of the bonds in the portfolio. To do this, multiply the face value of each bond by its maturity date, then add these products together and divide by the sum of the face values of all the bonds. This will give you the weighted average maturity.

Next, calculate the weighted average coupon of the bonds in the portfolio. To do this, multiply the face value of each bond by its coupon rate, then add these products together and divide by the sum of the face values of all the bonds. This will give you the weighted average coupon.

Finally, use the following formula to calculate the duration of the bond portfolio:

Duration = weighted average maturity x weighted average coupon / 2

In this formula, the weighted average maturity is in years and the weighted average coupon is a percentage.

### How do you calculate time duration?

The time duration of a bond is the measure of a bond's sensitivity to changes in interest rates. The longer the duration, the greater the sensitivity. To calculate the time duration of a bond, you need to know the coupon rate, the current market price, the par value, and the yield to maturity.

First, calculate the present value of the bond's future cash flows using the current market price and the yield to maturity. This will give you the bond's "dirty price."

Next, calculate the present value of the bond's future cash flows using the par value and the coupon rate. This will give you the bond's "clean price."

Finally, subtract the clean price from the dirty price. This difference is the time duration of the bond.

### How do you calculate duration on a financial calculator?

There are a few different ways to calculate the duration of a fixed income security, depending on the type of security and the information that is available. For example, for a simple bond with a face value of \$1,000 and a coupon rate of 5%, the duration can be calculated using the following formula:

Duration = (face value + coupon payments) / (yield to maturity)

For a more complex security, such as a mortgage-backed security, the duration may be calculated using a different formula.

It is important to note that the duration of a security is affected by factors such as the coupon rate, the yield to maturity, and the time to maturity. As such, it is important to consider these factors when calculating the duration of a security.