# What is the duration of a bond? and How to Calculate It?

A bond is a debt instrument issued to an investor, or holder of the bond, by a borrower. It makes the investor eligible to receive a fixed income after a fixed amount of time. The fixed income comes as a result of the fixed price and interest on bonds. A bond is the most basic unit of debt usually issued by companies.

Bonds have some particular characteristics. They generally have a face value, which is the amount the bond will be worth at maturity. The face value of the bond may not be the same as its issue price, which is the value which the borrower receives for the bond.

Similarly, bonds also have coupon rates and coupon dates, which are the rates and dates of interest payments. Bonds also have a maturity date, which is the date on which the bond is repayable.

## Duration of a Bond

The duration of a bond does not represent the duration for which an investor holds a bond. Instead, it refers to the relationship between the price of a bond and interest rates of the bond after considering its different characteristics such as yield, coupon rate, maturity, etc.

Usually, the duration of a bond shows the number of years in which an investor can recover the present value of the cash flows of a bond. It can also represent a percentage that is a measure of how sensitive the value of the bond is to changes in interest rates.

The duration of a bond is simple to understand. The higher the duration is, the higher is its susceptibility to changes in interest rates. This is mainly because when the interest rates go up, the value of a bond will fall.

Similarly, bonds with a lower duration will not be affected as much by interest rate changes. In the long-term, if an investor expects the interest rates to go up, they will dispose of off their bonds while if they expect them to go down, they will hold on to their bonds. The relationship between the price of a bond and interest rates is inverse.

## Is the duration of bond different from its maturity?

While the duration of a bond and bond maturity may both sound similar because they consider a time related to the bond, they are both different. As discussed above, the duration of a bond represents the average time it takes an investor to receive all cash flows from a bond.

On the other hand, the maturity of a bond is a time in the future on which the investor will receive the last cash flow from the bond.

## How to calculate the duration of a bond?

There are two ways to calculate the duration of a bond. Both of them represent different aspects of the duration of a bond but are interrelated.

### Macaulay duration

The first way to calculate the duration of a bond is by using a model known as the Macaulay duration. Using the model, the aggregate of the present value of all cash flows from a bond is divided by its current market price.

The model calculates the time the present value of cash flows from a bond takes to realize. The simplified formula for Macaulay duration is as below:

Macaulay Duration = Sum of PV of cash flows [PV (CF1) + PV (CF2) … + PV (CFn)] / Market price of the bond

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The cash flows of a bond consist of all interest payments and the final interest and principal payments made to the investors. They are easily calculatable because bonds have a fixed income. The results obtained from this model are in the form of a number of years.

### Modified duration

Another model used to calculate the duration of a bond is the modified duration model. While the Macaulay duration represents the time taken for the present value of cash flows from a bond to realize, the modified duration represents the sensitivity of the price of the bond in relation to the interest rates. The formula used to calculate the modified duration of a bond is as below:

Modified duration = Macaulay duration / (1 + Yield To Maturity of the bond)

The results obtained from this model are in the form of a percentage. As mentioned above, the higher this percentage is, the higher the inverse relationship between the price of a bond and the interest rates will be.

## Conclusion

A bond is a debt instrument issued by a borrower to investors. Bonds come with fixed-income interests payable at predetermined dates. The duration of a bond represents the relationship between the price of a bond and interest rates.

Generally, the relationship between the two is inverse, which means when interest rates are high, the price of the bond will fall and vice versa. The duration of a bond is different from its maturity as both present different time periods of a bond. There are two ways to calculate the duration of a bond, Macaulay duration, and modified duration.