What we usually infer from the English word ‘duration’ is a little different from what it means, in the context of bonds - but to pave the path for clarity and financial literacy, we explain to you what Bond Duration means, and the depth of the role it plays, in bond investments.

Not to be confused with a bond’s term or time to maturity, Bond Duration essentially measures the sensitivity of the security to change in interest rates. Higher the sensitivity, the higher is the risk associated with the investment in that particular bond. Bond prices share an inverse relationship with interest rates, i.e. when interest rates go up, bond prices go down and when interest rates go down, bond prices go up. This very fluctuation of the price in relation to its interest rates can be gauged by Duration. For an investor, this becomes an important variable to take into account, while investing in fixed income securities, as it helps to determine how the market price of a bond will change as a result of a change in interest rates. While we won’t go as far as to call this is a prediction, understanding bond duration offers an investor a much-needed foresight into the future of their investments. Factors such as time to maturity and coupon rate help determine what the duration of the bond could be.

Why Bother with Bond Duration?

Okay, so what gives? As an investor, why can’t you just park your money in well-performing security and leave the rest to market fate? You could, but that wouldn’t be the most responsible way of investing your money. While one can’t really foresee how the market will react to changing circumstances, one can do their due diligence and gain insights into what security suits their needs the best. And this is why before investing in bonds, understanding the duration could be beneficial.

• Risk Impact on Bond Value: As we’ve already established, the duration is a measure of how sensitive a bond is to change in interest rates, which in turn lets an investor determine the market price of said bond, should there be ups and downs in the interest rates. For example, if you are an investor with a low-risk appetite and a short term investment horizon then you may be advised to look into investing in low Duration bonds as these securities are less sensitive to changes in the interest rates; thereby allowing you to tailor your portfolio to match your investment needs.
• Duration also helps you assess the risk between your varied investments in bonds. If an investor has two bonds with the same maturity date, and the same coupon rate, but different frequencies of coupon payments - they will have different risks attached to them. Duration can offer a good comparison while evaluating one bond’s interest rate risk with that of another.

Types of Duration

When it comes to Bonds Duration, there are three kinds of durations to consider: Macaulay, Modified and Effective. We tell you what each of these individually signifies and how they differ, in relation to calculating the bond’s risk sensitivity.

Macaulay Duration

As an investor, if you ask the question: how long will it take for me to recover the initial investment in a bond security along with the interest payouts, your answer lies in the Macaulay Duration. Essentially, the Macaulay duration weighs the present value of all cash flows (which includes timely coupon payments and the maturity amount) with the time period at which these cash flows will occur and this value is divided by the bond price presenting to you the duration by when you can stand to recover your whole investment amount. Quite naturally, owing to the nature of the answer - the formula is measured in units of time - years.

So, the formula for Macaulay Duration could be written as follows:

So for example, if you invest 1 lakh rupees, for the time period of three years, at an interest rate of 10% with annual payouts - the equation would consider coupon payments made over the three years, ie. Rs 10,000 along with the maturity amount of Rs 1 lakh.

Going by the definition of the Macaulay Duration, it can be safely inferred that bonds that have a higher frequency of coupon payments will have a shorter Macaulay Duration and bonds whose coupon payments are spread over a longer period will have a high Macaulay Duration, which means that the equation also depends on the frequency of the cash flows, its interest rate and maturity amount notwithstanding. And with zero-coupon bonds in consideration, the Macaulay Duration always equals the time to maturity, because as the name suggests - there are no coupon payments scheduled to be made so the only amount the investor is eligible to receive is the whole maturity amount.

Modified Duration

If an investor’s first question on duration is how long would it take for them to recover the amount they are owed, the second should be - what would be changed in the price of the bond, if there are fluctuations in the interest rate. You’ll note, that just as both questions are linked to each other, modified duration is, in theory - an extension of the Macaulay Duration. Macaulay Duration measures the time aspect of the bond investment, and Modified Duration measures a bond’s sensitivity to interest rate changes - basically recording how the price responds to change in rates.

However, in contrast to the Macaulay duration, where the equation is measured in years, modified duration is measured in percentages - as it records a degree of change.

An investor will find it prudent to also have the modified duration with them, as it offers them insight into the possibilities of the bond valuation and how their asset may perform in turbulent market conditions. To calculate the modified duration, one must first assert what the Macaulay duration is, based on which the equation can be completed.

Effective Duration

What is a given while calculating both the Macaulay Duration and the Modified Duration is that all variables of the equation are known and stable. But what happens when the bond an investor has invested in has embedded options and can be called back by the issuer at any given time? The problem this presents is the uncertainty of the time variable and the frequency of the cash flows, making it difficult to nail it down to one simple equation.

For example, you may have invested in a callable bond that is due to pay you coupon interest through the course of three years, at the end of which you will receive the maturity amount. But in the advent of the issuer recalling the bond, and paying off the maturity amount in full, before its time - the loss of the stipulated time and due coupon payments threaten to throw off duration predictions. In a case such as that, only Effective Duration is applied, as it accommodates changes and unforeseen events.

Effective Duration is a simple calculation that is executed using a numerical method by incorporating different scenarios of increase and decrease in interest rates and yield while determining the price sensitivity. To put it mathematically, we may need to rearrange our original definition of Duration, as follows:

Effective Duration too prepares an investor for all bond possibilities, as they would now anticipate which way the bond’s performance may lean towards, given the circumstances. Going into making an investment, an investor ought to entertain all possible options and foresee all the directions towards which their investment might be headed.

Examples:

Let’s assume that a bond has a face value of Rs. 1,00,000 with a 10% annual coupon, the interest rate of 10% p.a. and with maturity after 5 years. The Macaulay and Modified Duration would be calculated as below:

Let’s start with mapping the cashflows:

To calculate Modified Duration for the same bond, we use the following formula:

This implies that for every movement of 1% in interest rate, the bond price would move by 4.11% inversely.

However, if the bond had a call option after 3 years, we won’t be able to use the aforementioned formulas for calculation of any kind of duration. For such a bond, we would have to calculate Effective Duration.

This means that, if there is a call option embedded in the aforementioned bond, the price of the bond would move by 1.89% inversely.