Do past returns matter? Does it make any sense to choose a mutual fund that has performed consistently in the past? After all, there is no guarantee that it would continue to perform well in future.

Let us try out a simple exercise.

- Download returns data from Value Research Online of all equity funds currently open for subscription, except direct funds.
- Plot the 10-year returns (distant past) of all funds against their 3/5/1-year (recent past) returns and visually observe correlations.

The idea is to determine the extent of correlation between a funds 10-year trailing return with its 5/3/1-year trailing return.

If there is a strong correlation, then choosing a fund with impressive ‘history’ makes perfect sense. If there is no correlation, there is no point relying on past performance.

Since life is more of grey than black or white, even before we start, we should expect the correlation to be neither be too strong nor to weak!

While the idea lacks sophistication, I think that it is good enough for the retail investor to check how return from an investment made in the distant past correlates with the return from an investment made in the recent past

Before we begin, let us bear in mind that we are working with trailing returns which means the returns will change from day to day. The data here is as on 11^{th} July 2014.

So here goes nothing

**3-year vs. 5-year returns**

Let us start with 3-year versus 5-year returns as it is the simplest to understand.

Each point in the graph represents a different mutual fund.

Notice the linear correlation. A higher 5-year trailing returns implies an higher *average *3-year trailing return.

‘Average’ because for a single 5-Y return, multiple 3-Y returns are possible.

The blue rectangle represents all the 5-Y returns within one standard deviation of the mean.

That is the mean 5-Y return is 16%. The standard deviation (measure of deviation from the mean) is 4.5%. So the rectangle approximately extends from (16%-4.5%) to (16%+4.5%)

Similarly, the red rectangle represents all the 3-Y returns within one standard deviation of the mean.

Notice that most of the points (funds) are found at the intersection of the two rectangles: a good 67% of the funds.

If you had chosen funds with high 5-year correlation, to the right of the blue rectangle, the 3-year return would either be within the red rectangle or above it. Not bad at all.

Thus one could conclude that there is pretty decent correlation between 3-Y and 5-Y trailing returns. Decent performers in one category are like be decent performers in the other.

**5-year vs. 10-year returns**

Notice that correlation has visually reduced significantly. For a given 10-year return within the blue rectangle, the 5-year return can vary by a much wider margin than the 3Y-5Y graph.

In spite of this, a good 55% of the funds can be found in the intersection between the two rectangles (that is within one standard deviation of the mean)

This means if your fund had 5-Y return within one standard deviation of the mean 5-Y return of all equity funds, there is a good chance that it will be found within one standard deviation of the mean 3-Y return.

If you had have chosen funds with high 10-year trailing returns, to the right of the blue box, you would have got a 5-year return above or within the red rectangle (with the exception of one fund). Again, not bad at all, right?

Yes the correlation has decreased and there is a huge spread in returns but the spread is still favourable. Most of the funds either are above average or close enough to the average.

**3-year vs. 10-year returns**

The spread (range of 3-Y returns for a single 10-Y return) has widened further.

However, still a good 56% in the intersection of the two rectangles.

A high10-Y return to the right of blue rectangle has resulted in a return that is either in the red rectangle or above it. Which is quite decent. A high 10-Y return has produced a high enough 3-Y return.

## **1-year vs. 10-year returns**

About 48% of funds found in the intersection of the rectangles.

The spread, especially within the blue rectangle has considerably increased, and thanks to the bull run, it is on the higher side. One should not take this graph too seriously and it can change a lot depending on when choose to plot the data.

Since we work with trailing returns, the same could perhaps be said of all of the above graphs.

That said, there appears to be a reasonable correlation between returns of the distant past and returns of the recent past.

To me, this is good enough to short-list consistent performers based on 3-year, 5-year and 10-year data listed by Value Research Online as explained in the **step-by-step guide to choosing an equity mutual fund**.

The past seems to be prologue.

If my definition of consistency is combined with reasonable return expectations (~ 10%), the chances of disappointment are significantly lowered.

Would you agree?

Rajanikant Gajjaryou are doing good job by putting common sense ideas to statistical scrutiny.excellent

dr r v gajjar

rkhgajjar@gmail.com

Rajanikant Gajjaryou are doing good job by putting common sense ideas to statistical scrutiny.excellent

dr r v gajjar

rkhgajjar@gmail.com

BanerjeeThanks. Excellent analysis.

pattuPost authorThank you.

BanerjeeThanks. Excellent analysis.

pattuPost authorThank you.

ashalanshuThe over all DATA point is still less. Not many funds are there who are 15+Y old. I w'd like to see this same thing in 2024 or 2034.

Thanks

Ashal

pattuPost authorUnfortunately, yes. The graphs could look different at different times as well.

ashalanshuThe over all DATA point is still less. Not many funds are there who are 15+Y old. I w'd like to see this same thing in 2024 or 2034.

Thanks

Ashal

pattuPost authorUnfortunately, yes. The graphs could look different at different times as well.

Pattabiraman MurariThank you.

Pattabiraman MurariThank you.

KarthikGreat analysis sir..Always wonder how you are able to analyse in so many different ways! Top notch ..