Macaulay Duration and Modified Duration in Debt Fund: Meaning, Calculation and Importance

First, let us consider the meaning of Macaulay Duration. Macaulay Duration can be defined as the time period (duration) required to fully repay the initial investment of a bond, through the internal cash flows that the bond (or other debt security) generates. Since, a debt mutual fund typically invests in a number of bonds and other debt securities, the weighted average of the Macaulay Duration of all securities held by the scheme is the Macaulay Duration of a debt mutual fund.

The Macaulay Duration of a bond (or debt fund) is directly proportional to its maturity date. It means the longer the bond's maturity, the higher the Macaulay Duration and vice versa. Now that we have completed our basic understanding of Macaulay Duration, let's shift our focus towards gaining an insight into the Modified Duration.

Modified Duration can be defined as a measure of the change in price occurring in the price of a debt instrument such as bonds in India due to fluctuations in the market interest rate. Since bond prices decrease when The Modified Duration tells individuals of changes happening in the price of debt funds as a result of a 1% change in the interest rates.

A Modified Duration follows the principle of the inverse relationship between interest rates and bond prices. For instance, the modified duration of a debt mutual fund scheme is 2 years. In this case, a 1% fall in interest rate would lead to a 2% rise in bond prices leading to higher return on the investment.

Now that we have understood the meaning of Modified Duration, let's move to other segments.

Before we get into the complex formulae of Macaulay Duration and Modified Duration, let's take a look at some basic terms.

 Face Value: This is the price at which the bond is issued.

 Annual Interest: The total interest payout during the entire time span of a bond.

 Coupon Rate: Interest rate offered to bondholders.

Using these basic terms, a simple formula of Macaulay Duration is as follows:

 Macaulay Duration = Face Value/Yearly Interest Payout

Let's find out the Macaulay Duration of Bond X using this formula.

We see that the Macaulay Duration of a bond X is 10 years. But in a practical sense, when we are considering the cash flows generated from a bond, we also need to take into consideration the discounted present value of future cash flows. Suppose the maturity of Bond X is 8 years, and the discount rate is 10%, one can find the present value of future cash flows and the present value of time-weighted cash flows. An illustration of this has been given below:

Using these calculations, the Macaulay Duration of bond X is computed using the following formula: (Total Time-Weighted Cash Flows/Total Present Value of Cash Flows)

Macaulay Duration = 2100/385 = 5.5 years

Don't worry! Individuals do not have to take the pain of computing the Macaulay Duration as all debt funds provide this duration in their consolidated factsheet. However, one must remember the principle that a higher duration implies a higher sensitivity to interest rates and vice versa.

Let's take a look at the calculation formula for Modified Duration. One has to use the Macaulay Duration for the computation of Modified Duration. The formula for Modified Duration is as follows:

**Modified Duration = (Macaulay Duration)/[1+(YTM/F)]**

Here, YTM stands for the year to maturity or, in simple words, the coupon rate.

F stands for coupon frequency, i.e., how frequently the interest is paid to the bondholders. Let's consider an example for a better understanding of the calculation of Modified Duration.

The significance of Macaulay Duration is given below:

• The Macaulay Duration helps in measuring the sensitivity of bond prices with respect to changes in interest rates. One can use this analysis to decide the future course of action, i.e., whether they wish to invest or sell off.
• It also helps in comparing the interest rate sensitivity of bonds having different maturities.

The importance of Modified Duration is as follows:

• Individuals can use the Modified Duration to understand the strategies of a fund manager. For instance, if the fund manager thinks of an increase in the interest rate in future, he will keep a low Modified Duration and invest in short-term maturity instruments.
• Individuals can use the Modified Duration parameter to select the debt funds as well as hybrid funds as per their risk appetite. In case one wants to reduce their interest rate risk, he can invest in debt funds having a low modified duration.

The Macaulay Duration depends on price changes and coupon rates. A longer Macaulay Duration implies a lower interest rate and vice versa. On the other hand, Modified Duration decreases with a decrease in maturity and a rise in interest rate.