Bond Duration

The valuation of any fixed-income security is just the summation of the present value of all future cash flows to which the security is entitled. It needs to be understood that the present value is calculated based on a discount rate. Hence, if the discount rate changes, the present value will also change. This will ultimately lead to an impact on the valuation of the bond. The prevailing interest rate is generally used as the discount factor while calculating the present value. Hence, when the prevailing interest rate changes, the opportunity cost of bonds also changes. This leads to a change in the present value of the cash flows.

It is important for investors to measure exactly how sensitive a given bond is, to the changes in the interest rate. The bond duration is the measure of such sensitivity. In this article, we will understand what bond duration is, how it is calculated and how it impacts bond valuations.

What is Bond Duration?

Bond duration is often defined as the average lifetime of the future stream of payments that any debt security has to offer. Now, since the duration is measured in time, the output is also expressed in terms of number of years.

The bond duration is also considered to be a measure of interest rate risk. This means that it expresses the impact the changes in interest rate have on the valuation of the bond. First, it is important to understand that bond prices and interest rates are negatively correlated. This means that when interest rates decline, bond prices rise and vice versa. However, it needs to be understood that bonds have a finite life. Hence, the drop in interest rates does not affect all bonds equally.

Let’s assume that we have two bonds. One of these bonds has only one year left for maturity whereas the other bond has ten years left for maturity. If the interest rate falls by 1%, obviously the change in price for both the bonds will not be the same. This is because, in the case of the first bond, most coupon payments have already been received. Hence, the first bond will receive a 1% higher than market interest only for one year.

Under normal circumstances, this means that the price of the bond will go up by 1% in the secondary market. On the other hand, the second bond still has ten years to go. Hence, for these ten years, the issuer is obligated to pay the bondholder a rate of interest that is 1% higher than the market rate. This means that the bondholder will earn 1% extra for each year of the duration. Since the duration is of ten years, in this case, it would mean that the price of the bond will go up by 10%.

It is important to note that the time for maturity is not the only factor that impacts duration. This example has been oversimplified for explanation. For instance, if the prevailing interest rate changes by 1%, it will have a different impact on zero-coupon bonds as compared to bonds that pay regular coupon payments.

Therefore, it can be said that duration is a very important factor that impacts the price of the bond. Duration along with a change in the interest rate determines the sensitivity of the bond to changes in the prevailing interest rate.

How to Interpret Duration Numbers?

The purpose of bond duration is to ensure that even though different types of bonds have different cash flow features, they can be compared for sensitivity. It is for this reason that bond duration eliminates the impact of different cash flow patterns during the calculation stage. The end result is a number that can be used for comparison across different types of bonds.

The value of the duration number is fairly simple to interpret. The higher the value of the duration number, the more sensitive a bond is to interest rate changes. Similarly, if the value is lower, then the bond is less sensitive to interest rate changes as compared to other bonds.

Common Rules Related to Bond Duration

There are certain common rules which are related to bond duration which most seasoned investors know. These rules are just corollaries to the main concept.

• The duration of a zero-coupon bond is equal to its maturity. This is because zero-coupon bonds only pay one single cash flow. This cash flow is paid on maturity and hence the duration is higher which makes sensitivity to interest rates also go higher.

• The duration of a bond that pays coupons earlier has a shorter duration. This is because the bond keeps paying interest at regular intervals which reduces the impact of interest rate changes on those payments

• Also, bonds that have higher coupon payments and yield to maturities also have a shorter duration

All of the above-mentioned rules can be calculated and verified. However, investors have created these heuristics which allow them to make decisions quickly while trading securities.

The bottom line is that fixed income securities tend to be complex. Investors commonly use a wide variety of metrics in order to understand the bond better. The duration is one such metric that is widely used in different parts of the world.

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