# Rolling Return Analyzing Mutual Fund Performance Over Time

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We can view how the ‘n year’ growth has progressed over the past few years using a rolling return. This may sound complicated, so let’s simplify it: we’ll examine the development of the ‘n year’ return.

Let’s take up an example and discover the rolling return calculation. Knowing the math behind this concept certainly helps make understanding it simpler.

Rather than looking up the rolling returns on many websites, it may be more beneficial to understand the concept by knowing the maths behind it. This will make grasping the idea of rolling returns quite simple.

So let us get started.

I have the historical NAV data of AB Frontline Equity Growth-Direct from 2nd January 2013, spanning seven years until 2nd January 2020.

My goal is to work out the 2-year rolling return for this fund. Starting in 2015 will be necessary to achieve that.

I calculate the return by taking the NAV on 2nd January 2015 and comparing it to the NAV 2 years prior, on 2nd January 2013. Then, I shift the date by one day and compare the NAV on 3rd January 2015 with that of 3rd January 2013. Finally, when I move the date one more day, i.e. 4th January 2015 and 2013, I record the return between those dates as well.

So on and so forth, such that I have a time series of 2-year return.

Let us calculate the first rolling return –

NAV on 2nd January 2013 – 100.83

NAV on 2nd January 2015 – 161.83

Since its two years, we apply CAGR –

[161.83/100.83]^(1/2)-1

26.69%

The 2nd rolling return in this series would be –

NAV on 3rd January 2013 – 101.29

NAV on 3rd January 2015 – 161.45

=[161.45/101.29]^(1/2)-1

26.25%

I have organised the data on Excel side-by-side, and this is the result. Do you comprehend?

The starting date is 2nd January 2015, right up to 2nd January 2020.

You can observe the most recent date and NAV (highlighted in blue), followed by the date and NAV from two years ago (shaded in pale yellow). By calculating the CAGR between these, I’m able to generate a time series of the daily 2-year return beginning on 2nd January 2015.

Before continuing, let’s recap this statement about rolling return – ‘Rolling return helps understand the growth seen over the last ‘n years’. Does that make sense?

I certainly wish that is not the case!

Note that NAV data for 5th January 2013 cannot be obtained, due to the weekend factor. Fret not, however, as the NAV data for 3rd January 2013 has been used instead and can safely be disregarded.

By now, it should be clear that determining the 1-year rolling return requires me to begin at 2014, while computing a three-year rolling return necessitates that I start at 2016.

With the Rolling Return time series starting from 2015, we can now look to do a few things. Calculating the range of returns is certainly one task that can be done with this data. Estimating the range involves simply computing the maximum and minimum values.

Here is the max –

And here is the min –

This means that someone who invested in the AB Frontline Equity fund on 19th August 2013 and withdrew their funds two years later, on 19th August 2015, earned a return of 37.76%.

This unfortunately unsuccessful investor put their money in on 19th September 2017, keeping it there for two years until the very same date in 2019 but ended up coming away with a loss.

I’m aiming to emphasise that no two 2-year returns are the same; it all depends on when you decide to invest and exit your investment.

This graph shows the rolling two-year return from 2015.

You could have achieved returns ranging from 37% to nearly -1.0%, depending on how long you invested for two years.

Gaining insight into the potential return over a two-year period can be achieved by taking an average of rolling returns; this is also known as the ‘Rolling Return Average’.

The average is 15.35%.

Evidently, the rolling return provides greater insight than a point to point return.

When assessing a mutual fund investment, remember to consider these two elements in your research.

1. Identify the period you are interested in investing
2. Find out the historical rolling return min, max, and average for the period

I’ll take a look at the historical 7-year rolling return for this large-cap equity fund to get a sense of its average performance as well as its range of returns.

In my view, rather than point to point returns, a 2-year rolling return can be used as an example. If you’re thinking of investing in equity funds, then it is advisable to look at a 5-year rolling return or longer.

Let us now turn our attention to other MF metrics that are important.

– Point to Point return

In the preceding chapter, we had an outlook of how returns are figured out, depending on the duration taken into account. Therefore, if I offer you this information –

Fund – Aditya Birla Frontline Equity

Starting date – 2nd January 2013

Starting investment value – Rs.1,00,000/-

Starting NAV – 100.83

Ending date – 2nd January 2015

Ending NAV – 161.83

And asked to find out the returns, you’d probably do it with ease. Let us do the math –

Number of units = 1,00,000/ 100.83

= 991.7683

The ending value of investment  = 991.7683 * 161.83

= Rs.1,60,497.9

The growth in this lumpsum investment over two years can be calculated by applying the  CAGR formula –

= [160497.9/100000]^(1/2) – 1

=26.69%.

Which as would recognize is a phenomenal growth rate.

Now, let us suppose you are rather pleased with your investment, and decide to spread the word about it. A friend then approaches you and inquires about its performance – to which you happily reply that the 2-year growth rate is a whopping 26.69%.

Your friend is so taken by what they have seen that they decide to put their money in.

Please take some time to consider this. What do you believe is the key issue?

Did you lie or mislead your friend by letting him know the returns you’ve enjoyed? – No

What do you consider to be the issue here?

This growth rate of 26.69% is an impressive representation of two-year performance. Mention it to your friend and they will likely be convinced that they can achieve similar success.

The 26.69% return is only applicable when the money is invested on 2nd January 2013 and assessed on 2nd January 2015. Therefore, this growth rate applies specifically for these two dates. It offers a personalised experience.

If I invest and assess the yields at different points in time, the results will be distinct.

When measuring returns or growth between two separately defined periods, the resulting calculation is only valid for those two years. This type of return is known as ‘Point to point’.

To obtain a correct rendering of the two-year return (growth rate), one needs to compute the ‘Rolling Returns’.