What's the best way to showcase performance of any mutual fund scheme to your clients? What can they relate most to? Here are three charts which showcase the performance of BSE Sensex for the period 1-Jan-2013 to 1-Sep-2017.

The first is a typical chart that shows how the index has moved in this period - this is very similar to the NAV charts you see in most fund fact sheets. The second is the annual point-to-point returns from the Sensex - this is very similar to the performance numbers tables that are available in all fund fact sheets.

So, the picture one gets from both these charts is that the Sensex has in general been on an upward journey, albeit with some corrections (chart 1) and that the range of returns in this period has been between +30% and -5%.

Both these charts however do not tell the actual story of past performance that most investors will relate to. Investors do not invest in the beginning of a calendar year (or financial year) - they invest at any point of time during the year. So, when they want to know the range of annual returns in the past, they need the full picture - not just a point to point snapshot based on beginning of calendar or financial years. They need to know how volatility within the year impacted returns for people who invested at different points of time each year.

That is what the third chart below gives you:

This is the same Sensex, for the same period. But what it shows you is the annual return that investors made for money they invested at any point of time. So, when the 1-Jan-14 return shows 8%, it means 1 year returns as of 1-Jan-14 were 8% (investment made on 1-Jan-13). Likewise, a 1-Sep-14 return of 50% means that an investor who invested on 1-Sep-13 made 50% in the Sensex over the next 1 year. And a -20% on 1-Mar-16 means an investor who came in on 1-Mar-15, saw a 20% depreciation in his investment over the next 1 year.

This now gives an investor who is looking for annual returns numbers a much clearly picture of the past - a picture that he can relate to more - a picture he ought to see before making an investment in a volatile asset class. This picture is called rolling returns.

Rolling returns are actually returns that are, for a defined period of time, calculated on a continuous basis. In effect, rolling returns are calculated as the averaged annual returns for the selected period. The calculation is done for every day/week/month of the target period.

Annualised returns

Normally, annualised returns would be calculated from the same date of the previous year to the current year. In turn the current year's return would be calculated to the 1st of the succeeding year.

Annualised returns are calculated as follows. Assume that the investment is made for the period of one year from April1st to 31st March of the next year. Supposing there is a return of 10%, it means that there is an increase of that magnitude in the fund in the yearlong period. On 31st March the fund would be 110% calculated from the 1st April of the previous year.

It can be quickly and clearly seen that during this one year period, there might have been periods when the fund value had soared above the annual average at some times anddipped below that average at other times.Thus at these times the return of the fund would have been different from that of the earlier calculation, based on the first and last dates of the investment period. This average return tells us little about how the fund behaved during the year. This isimportant information to evaluate how the fund has performed. Importantly it does not capture volatility, that is, the variations from the average.

Rolling returns

On the other hand, the concept of rolling returns, lays down that returns be calculated for each day of the year. Let us take for example rolling returns for a one year period from 1st January to 31st December. Rolling returns would be calculated from not only the 1st day but also from 2nd, 3rd days and so on. The return for the 2nd would be calculated from the 2nd of January of the earlier year. Further, the intervals can be every day, every week or every month or any other period. Thus we would be able to calculate annualised returns for every day of the given time period.

Rolling returns vs. Annualised returns

In contrast to annual returns, rolling returns analysis for a year-long period would reveal the best one year as well as the worst one year a fund has experienced based on not just the first day of the investment but also on subsequent days. In point of fact an investment that has an 8% annual return might have experienced a best one year return of 16% and worst case of - 4% within the defined time period.

Not surprisingly, such a calculation can give one a much deeper insight into the functioning of funds than the normal method of calculating annual returns. Checking and tracking data regularly would give one a much better idea of how a fund has performed on a one year basis. This facilitates the analysis of the performance of the fund, independent of the day on which the investment is made.Rolling returns give a realistic picture of how the investment has fared.

Point to point returns may warp analysis as the metric merely measures as on a particular day. Thus many relevant factors may be missed when analysis is made in this way. This will not give the whole picture in respect of fund performance.

Judging fund performance

Appraising performance of assets over any time period be it one year, three years, five years or ten years is difficult. Looking at data from the perspective of just the first day and the last day of period tends to obscure a lot of vital information. For example there can be many ups and downs in the chosen time period in between the two dates. Further, funds might have performed better or worse than the market. These variations will go completely unnoticed in a point to point scenario. Thus one cannot really decide on how well a fund is performing.

Alternatively, rolling returns take into account performance of the particular fund every day, week, month or any other interval of a defined period. Thus one can have a view of the performance on a continuous basis. This will throw much needed light on the various movements of the fund. These movements can be analysed in the light of market movements as well, to see if the fund has outperformed or underperformed the market. Hence the performance of the fund can be properly analysed. Such an analysis also shows how the investment would have done irrespective of when the investment was made within the given time period.

Further, the rolling returns metric can be used to study if a fund is performing consistently and if there are volatile periods; and if so the length of the periods of volatility. By turning the lens on returns for every day of the year, rolling returns reveals how much the fund is able to fetch, in spite of the market environment and extraneous factors. It also shows whether the returns run on a smooth line or if there is volatility. For example, one should be cautious if the rolling returns are volatile. To further clarify the picture, one can compare rolling returns with the rolling returns of its benchmark. For people about retire, these are key metrics to judge a fund's performance.

Closing comments

Nassim Taleb, in his book The Black Swan (Penguin, 2008), has a section called "Don't cross a river if it is (on average) four feet deep." It is a statement worth pondering. Most financial projections use averages.

There is no guarantee that your investments will achieve the average return.

For example, from 1926-2015,historical stock market returns, as measured by the S&P 500 Index, averaged 10% a year. But that average encompassed years where it was down 43.3% (1931) and up 54% (1933), as well as more recent years like 2008 when it was down 37%, and 2009 when it went up 26.5%. This variation of returns from the average shows up as sequence risk. You may project one outcome based on your expected average return but experience an entirely different outcome because of the volatility of the actual returns incurred. (The balance, Dana Anspach, Updated October 17, 2016)

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