# What to make of debt fund duration

- by Sammy

Choosing debt funds in a rising interest rate environment is not easy, as rising rates lead to declines in bond prices. Make the wrong choice of duration and you can easily face capital erosion on your debt funds. But if you’re looking to gauge a fund’s maturity profile from its fact sheet, there are three different measures that funds put out – Average maturity, Modified duration and Macaulay duration. What do you make of each?

**Average maturity**: The maturity period of a bond is the period at the end of which your principal is finally returned. When applied to a fund’s portfolio, average maturity is the weighted average of the actual maturities of all the bonds held by it. Consider a debt fund that owns a portfolio worth ₹ 1,000 crore. It holds ₹ 500 crore in 10-year bonds (bonds that will mature in 2032) and ₹ 500 crore in 1-year bonds.

The weighted average maturity of this fund can be calculated by multiplying the value of each type of bond held, by its maturity period and dividing by total portfolio value (500 * 10 plus 500 * 1 divided by 1000). The average maturity of this fund thus comes to 5.5 years. A similar sized fund that holds ₹ 500 crore in 10-year bonds, ₹ 300 crore in 2-year bonds and ₹ 200 crore in 1-year bonds will have an average maturity of 5.8 years. In a rising rate scenario, the second fund may suffer higher capital losses than the first fund. But do note that averages can hide extremes. So a fund with a 50-50 allocation between 10-year bonds and 1-year bonds may carry an average maturity of 5.5 years, but this is not actually the period when any of the bonds will mature.

**Macaulay duration**: Despite its name, Macaulay duration is more useful to gauge the composition of a fund’s portfolio, than its sensitivity to interest rates.

Macaulay duration is the time you need to hold a bond (or a fund) to get back your initial investment by way of interest and principal repayments. Given that future repayments entail a sacrifice on the time value of money, future interest and principal receipts are discounted to present value in calculating Macaulay duration.

Suppose you invest ₹ 1,000 in a 10-year bond with a 7 per cent interest rate. You can expect to receive ₹ 70 in interest every year for the next 10 years with ₹ 1,000 returned in the 10th year. When you calculate its Macaulay duration, assuming you discount the cash flows also at 7 per cent (to account for the time value of money), the first year’s interest will be valued at ₹ 65.42, the second year’s interest will be worth ₹ 61.14, the third year’s 57.14 and so on. Each of these cash flows is then weighted by the time period. Total time-weighted cash flows are divided by the bond price (₹ 1,000) to arrive at the Macaulay duration. The above bond’s Macaulay duration works out to 7.51 years, though the bond’s actual maturity is 10 years. A fund’s Macaulay duration similarly reflects the present value of cash flows of all the bonds in its portfolio. If you are not mathematically inclined, there are several online calculators available to calculate a portfolio’s Macaulay duration.

But for investing purposes, it is more important to note two things in the interpretation of Macaulay duration. One, a fund’s Macaulay duration is always lower than its actual maturity. Two, being a weighted average, Macaulay duration is influenced by the size and timing of interest and principal payments. A fund that holds higher yielding bonds or bonds with front-ended repayments will have a lower Macaulay duration than a fund with lower yielding bonds or back-ended repayments.

Consider two funds A and B with identical portfolio maturity of 10 years, but differing Macaulay durations of 6 and 7 years. If they are wound up, Fund A is likely to make more repayments earlier than Fund B. But the dates on which you get back the last Rupee on both funds may be similar.

**Modified duration**: This is a direct measure of how rate changes affect a bond portfolio’s value. Modified duration tells you how much the value of a bond or fund’s portfolio will change if there is a change in market interest rates. Modified duration is calculated as Macaulay duration divided by 1 plus the bond’s yield-to-maturity. In the above example, modified duration can be arrived at as 7.51 divided by 1.07, which is 7.01 years. Note that modified duration gives you the likely change in the bond’s price for every 100 basis points or 1 percentage point change in interest rates. If interest rates rise by 1 per cent, you can expect the above bond’s price to fall by 7.01 per cent. The reverse works too. If interest rates fall by 1 percentage point, the bond’s price will rise by 7.01 per cent.

Overall, if looking to gauge how much your debt fund’s NAV will be dented by a rising rate scenario, the modified duration is more useful than either average maturity or Macaulay duration.

Published on

April 09, 2022

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Choosing debt funds in a rising interest rate environment is not easy, as rising rates lead to declines in bond prices. Make the wrong choice of duration and you can easily face capital erosion on your debt funds. But if you’re looking to gauge a fund’s maturity profile from its fact sheet, there are three…