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The difference between the average maturity and Macaulay duration of a debt fund

Macaulay duration is a superior measure of duration as compared to average maturity, says Ashutosh Gupta

What is the difference between the average maturity and Macaulay duration of a debt fund? Should we match the investment time horizon with average maturity or Macaulay duration for debt funds?
- Anant Garg

These are relatively technical terms but let me try and provide a more simplistic explanation. Average maturity is simply the weighted average of maturities of all bonds in a portfolio. For example, a portfolio consists of two bonds - one maturing in 10 years and the other maturing in five years and both these bonds have an equal weightage. So, the average maturity of this portfolio would simply be 7.5 years, that's the average of both maturities. Since both of the bonds have equal weight, both have been assigned 50 per cent weightage.

But a better depiction of duration is possible through Macaulay duration because it also considers the periodic bond cash flows instead of only total maturity. Let me again give an example. Let's say there is a 10-year zero-coupon bond which doesn't pay any coupon intermittently but only makes a bullet payment at the end of the tenure, which is 10 years. Now in the case of this bond, the maturity and the Macaulay duration will be the same which is 10 years, since there are no intermittent cash flows. Let's say there is another 10-year coupon-paying bond, i.e., which pays you intermittent cash flow say annually in this case. In the case of this bond, the maturity will still be 10 years, but the Macaulay duration will be a bit lower than the maturity, taking into account some of the cash flows that come to you before the 10-year period in terms of annual coupon payments.

So typically, the Macaulay duration will be lower than the average maturity in any bond portfolio, but the magnitude of the difference may differ depending on the composition of these periodic bond cash flows. If you look at the bond fund portfolios, the difference between Macaulay duration and average maturity can vary widely from just a few months to even three-four years. And as I said, a better depiction of duration is by the way of Macaulay duration. So if you want to eliminate the interest-rate risk, it's ideal to map your investment horizon to the Macaulay duration of a fund. But remember, this would typically work in the case of funds that are following a roll-down maturity strategy. Now a roll-down strategy is a passive kind of a strategy in debt funds where the fund manager creates a portfolio with a certain maturity profile in mind, let's say a portfolio of about a four-year duration and then the fund manager simply buys and holds the portfolio and lets it run down naturally from four years to three years and eventually down to zero and then the fund manager resets the portfolio and makes fresh investments to take the duration back up to four years. If you match your investment duration to the Macaulay duration of this portfolio, then effectively, you would eliminate the interest-rate risk from your investment. So, that's how you can make use of Macaulay duration.

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