# Bond Definition: What is duration and the formula for it

For those who are learning how and where to invest money in Singapore as a beginner, it can be interesting to invest in fixed income. Within Singapore, Fixed Income is not as common an investment vehicle as public equities. However, that does not prevent us from buying Singapore Saving Bonds, Publicly Listed Corporate Bonds and Fixed Income Unit Trusts in general. When buying fixed income instruments, it is important to understand duration, which is a way to measure interest rate risk for your fixed income investment.

When investors refer to duration, they are often talking about modified duration. However, it is important to first understand macauley duration before moving on to modified.

## What is Bond Duration

Duration is the weighted average of the bond’s cash flow discounted to its present value. Each year of cash flow is discounted and weighted, relative to the present value of all the cashflow that is generated by the bond.

There are a few main types of duration: Macauley Duration and Modified Duration.

Macauley duration is the sum of all the cash flows that are discounted by the yield to maturity, and weighted by the time of payment.

Modified duration is the Macaulay duration divided by 1 plus the yield to maturity.

## Why is Bond Duration important

It is an important risk measure as it can give investors an approximation as to how much their returns will be impacted if interest rates change

Apart from being a risk measure, bond duration is also needed to immunize a portfolio.

## Why is interest rate so important

Interest rate is important because it is the discount factor that is being used to discount future cash flows to the present.

## How does coupon rate affect duration

Coupon affects duration for two main reasons.

Firstly, it affects the present value of cash flows. The higher the coupon, the greater the present value of the earlier time periods.

Secondly, with a higher present value, the cashflows in the early years will represent a larger portion of total cashflows. this will cause duration to decrease as duration is mainly concentrated in the later years towards maturity.

There are those that will think that the present value of these periods will not be affected as the coupon paid is always the same. While most of the coupon payments will increase. proportionately, the last payment which includes not just the last interest payment but also the bullet will not have a proportionate increase. For that reason, some of the present value is tilted from the last payment towards the earlier years, resulting in a shorter duration.