Modified Duration in Mutual Funds: Meaning, Formula and Example

An analogy is a simple way to understand a complex concept. Let’s consider the same to help you get a good idea of modified duration -

Saajan ran a cotton clothing business that is best suited for the summer season. Expecting a good season sale, he stocked the items in excess. He was thinking of selling them all before winter began. Unexpectedly, the winter came forward earlier than usual, making him lower the selling price of items to clear the stock. Contrary to this, he would have charged a higher price and made more money if the summer had been prolonged. As you can see here, an external factor can significantly impact the price and profits.

Let’s define modified duration in line with this analogy.

What is Modified Duration?

Modified duration can be defined as the measurable change in the price of security in relation to the change in interest rate. In other words, it covers the effect of 1% or 100 basis points in the interest rate on the price of a bond. Here, the interest rate change can be considered analogous to the season change in the analogy above.

For instance, if the modified duration in mutual funds (debt funds) is less, it is similar to having fewer items in the stock. Even if the interest rate were to change, the price change would be less. On the contrary, if this duration is higher, it is similar to having excess items in the stock. If the interest rates were to change, the price impact would also be significant.

Hence, the higher the modified duration in mutual funds, the higher can be the risk of price fluctuation, and vice versa.

Relationship between Bond Price and Interest Rates

At the core, the price of a bond is inversely proportional to the interest rates. It means the bond price tends to fall when the interest rate rises, and vice versa. In these terms, the modified duration covers the degree of rise and fall in the price of bonds, given the change in interest rates.

In mathematical terms, the change in bond price is the arithmetic product of modified duration in mutual funds and the changes in external interest rates. These technical details might sound a little off-the-course to the basics of mutual fund investing. But here’s an interesting part waiting next for you -

Who Changes the Modified Duration of Mutual Funds?

As part of investing in mutual funds, you might already know that a fund manager oversees the fund’s trading activity and investment strategy. In relation to the interest rates, he is the one who takes the required decision. Here’s how fund managers usually deal with changing interest rates:

If the fund manager expects the interest rates to rise (similar to expecting the start of winters earlier than expected), he would most likely reduce the modified duration of the portfolio.

On the other hand, if the interest rates are expected to fall, he tends to maintain a higher modified duration to benefit more from the fall in the interest rates.

More About Modified Duration Formula

You can calculate modified duration using the following formula:

Modified Duration = (Macaulay Duration)/{1 + (YTM)/n}

Here, YTM equals Yield to Maturity, and n is the number of coupon periods in a year

As in this formula, you can consider modified duration to be an extension of Macaulay duration - a parameter that calculates the weighted average time before you (as the bondholder) will receive the bond's cash flow.