# What is Bond Duration

A bond is a debt instrument issued by an entity, the borrower, to an investor, the lender. The bond gives the holder a right to receive a fixed income at regular intervals of time based on a predetermined rate. Similarly, it provides the lender with the right to receive a predetermined payment, known as its face value, after a specific future time, known as its maturity period.

The maturity of a bond is different from the duration of a bond, between which people often get confused. Therefore, it is critical to understand what bond duration is.

### What is bond duration?

The duration of a bond represents the relationship between its interest rate and price. Investors use bond duration as a sensitivity analysis tool to determine the dependency of the price of a bond to the changes in interest rates. Through the bond duration, investors can also calculate the number of years it will take them to recover the present value of the cash flows from the bond.

The price of a bond has an inverse relationship with the changes in interest rates. When the interest rates rise, the price of a bond will decrease. Similarly, when the interest rates go down, the price of the bond will increase. Usually, investors can use this information to make decisions on when to buy and sell bonds to make a profit from it or avoid losses.

### How to calculate bond duration?

There are two models used in the calculation of the duration of a bond. The formula for both of them are different, and both present the bond duration in different terms. First of all, the most commonly used model in the calculation of bond duration is the Macaulay Duration.

### Macaulay Duration

According to this model, the bond duration is the aggregate of the present value of all its cash flows divided by its current market value. This model shows bond duration in terms of the number of years it takes for the cash flows from a bond to realize. The formula used by the model to calculate bond duration is as follows.

Macaulay Duration = Sum of the present value of cash flows / Market price of the bond

### Modified Duration

The Modified Duration depends on the calculation of Macaulay Duration. It represents the sensitivity of the price of the bond to the interest rates. The model also requires investors to calculate the Yield to Maturity of the bond. The formula used by this model to calculate bond duration is as follows.

Modified Duration = Macaulay Duration / (1 + Yield to Maturity (YTM) of a bond)

### Importance of bond duration

Bond duration is an important metric used by investors around the world. Investors use the bond duration of various bonds to compare and make decisions on where they want to invest. Similarly, as mentioned above, it plays a crucial role in the decision-making process of investors regarding bonds. Apart from these decisions, the bond duration can also help investment decisions made by lenders.

### Conclusion

Bond duration shows the relationship between the price of a bond and the interest rates. It helps investors determine the time it takes for the present value of all cash flows from the bond to realize. There are two ways to calculate bond duration, using Macaulay Duration or Modified Duration.