Rolling Return vs Point to Point: What Each One Hides
A point to point return measures two dates and nothing between them, so moving either date moves the answer. A rolling return repeats that measurement across every start date in a period. Repeating it removes the choice of start date and puts overlapping windows that share months in its place. Each measure hides something different, and a rolling series cannot be produced from a single year at all.
Two people can look at the same scheme, run the same arithmetic correctly, and come away with different numbers. Neither of them has made a mistake. The two people have measured between different pairs of dates, and the pair of dates is part of the measurement rather than a detail of how it was reported. A figure that changes when the question changes is a figure to interrogate before using, and the pair of dates is where the change comes from.
The worked scheme here is the Girnar Large Cap Equity Fund, an invented open ended equity scheme operated by Girnar Asset Management Limited, with Kalyani Bhagat as its fund manager and Sohail Merchant heading operations. The record behind it holds exactly one measured year: the scheme returned 13.4 per cent, net, measured value to value, against a stated benchmark that returned 12.1 per cent over the same year and carries no cost at all because nobody pays anything to hold an index. A single measured year is enough to demonstrate one of the two measures and not enough to demonstrate the other, and the gap between the two is where most of the teaching sits.
A return, and the fact that a published scheme return is already net of the charge running against the scheme's assets, is set out under the expense ratio. Both measures are named at the opening of this sequence. Compounding and averaging are taken as known. The two measures are set side by side below, against the same five questions, in the same order, and neither is declared the winner.
What is a point-to-point return, and what is it actually a function of?
Two dates. Two values. One proportion. A point-to-point returnA return measured between one dated value and another dated value, using only those two readings and nothing in between. takes the value on the first date, takes the value on the second date, and expresses the movement between them as a percentage of where it started. Those three steps are the entire construction. The construction is simple and exact, and the exactness is what makes it so easy to misread.
One property of that construction decides everything else. The figure is a function of the two dates as much as it is a function of the scheme, and the person quoting it usually chose the dates. Nothing dishonest has to happen for that to matter. Somebody had to pick a start and an end in order to compute anything at all, and every pair of dates produces a different answer from the same unchanged record. A reader handed one number has been handed both the record and somebody's choice.
And what it hides is the entire path between the two ends. A vegetable seller comparing this month's takings with the same month last year is doing the same thing. The comparison is real arithmetic on real amounts, and it is a point-to-point reading. The comparison will not show the week the stall was shut because the road was dug up, or the fortnight when a wedding season doubled the trade. The reading states where the two ends sit relative to each other and stays silent about everything in between, including the parts a person would most want to know about.
What is a rolling return, and what does it produce instead?
Fix a length. Then run that length along the record from every start date available, one step at a time. A rolling returnThe same return measure computed repeatedly over a fixed length, from every start date a record allows, rather than once. is not a different kind of arithmetic; it is the same arithmetic done many times. Each individual reading inside it is an ordinary point to point return. The change is that a rolling return keeps all of those readings rather than one.
The fixed length is called the windowThe fixed span of time a rolling reading measures over, for example twelve months or thirty six months, held constant while the start date moves., and it stays constant while the start date walks. Take a record of eight months and a window of three. A window starting at month seven would need a month nine, and the record stops at month eight. So the windows start at month one, at month two, and so on up to month six. Eight less three plus one is six, so six readings come out of eight months. The counting rule is the same at any size, and it does a great deal of work further below.
A rolling reading produces a spreadThe distance between the highest and the lowest reading in a set, which is what a set of readings has and a single reading cannot have. rather than a number. A set of readings shows the best window in the period, the worst window in the period, and how far apart those two sit, and none of that information exists inside a single reading. A household planning a wedding budget knows this instinctively: knowing what a caterer charged one particular Tuesday is one thing, and knowing the cheapest and dearest quote across a season is a different and more useful thing, even though every quote in the range was computed the same way.
What does a rolling reading give that a single reading does not?
Rolling return vs point-to-point return: is either one the honest measure?
Put them against the same questions in the same order and the differences stop being vague. How many dates decide the answer. Which facts the measure hides. Whether it can be chosen to flatter. How long a record it needs in order to exist at all. And whether the output is one figure or many. Five questions, two columns, and the answers are not symmetrical.
A point to point figure is decided by two dates and hides the path. A rolling figure is decided by a window length and hides that its readings overlap each other. Both can be chosen to flatter: the dates move in one case and the window length moves in the other. Because a point to point figure needs only two dated values, it exists for almost every scheme almost immediately. A rolling reading needs many start dates, and many start dates need a long record. A scheme that has been running a short while has no such record to draw them from.
Neither is the honest measure by its name. A rolling reading with a badly chosen window and a point to point reading with honestly chosen dates are not ranked by their labels, and no amount of preferring one word to the other will fix a badly chosen assumption underneath it. Honesty in either measure comes down to the same thing: the choice that produced the figure is visible, stated beside it, and available to be argued with.
Is a rolling return the more honest measure of the two?
What does the choice of start date actually do to a reported figure?
The choice of start date moves the answer without touching the record. Written down the claim sounds obvious, and in practice it is routinely forgotten. So state it as a mechanism rather than as a warning. The record is a sequence of values that happened. The figure is a comparison of two of those values. Change which two are compared and the figure changes. Every value in the record stays exactly where it was.
The movement is not uniform, either. A point to point figure moves most when the value at one end happens to sit at an unusual level. Start the measurement at a low point and the figure is flattered by the recovery that follows. Start it at a high point and the same record reports something much duller. The effect has a name worth carrying: start date sensitivityHow much a reported figure changes when only the starting date is moved, with the underlying record left completely untouched., and the size of it is a property of the record rather than of the arithmetic.
A reader who is handed a point to point figure has been handed somebody's choice of dates, and the polite question is not whether the figure is right but why those two dates. The figure is almost certainly right. Being right is what makes the question necessary rather than rude. A customer puts the same question to a shopkeeper whose window compares prices with last Diwali rather than last month. Most of the time the answer is reasonable. Occasionally it is revealing.
Somebody quotes a point to point return and picked the two dates themselves. What is the useful question to ask?
Predict before counting. Across sixty months, how many twelve month windows can be drawn?
Why are overlapping windows not separate observations?
Most treatments of rolling readings skip the overlap, and the overlap is what changes how a rolling reading should be read. Neighbouring windows share nearly all of their months. A window starting in January and a window starting in February, both twelve months long, have eleven months in common and differ by one month at each end. The two windows are not independent evidence about separate stretches of time. The second is very nearly the first, written down twice.
Work the counting rather than accepting the phrase. Take a bare strip of sixty months, carrying no returns at all, belonging to no scheme. A window starting at month fifty would need a month sixty one, so a twelve month window can begin at month one and as late as month forty nine. Sixty less twelve plus one is forty nine start positions. Now ask a different question of the same strip: how many twelve month windows fit end to end without sharing a single month with each other. Sixty divided by twelve is five, and five twelve month blocks use up exactly sixty months with nothing left over.
Put the two counts side by side. Forty nine readings, and only five of them that could be described as separate. Forty nine numbers carry roughly the information of five. Calling them forty nine observations overstates the evidence by a factor of 9.8. The overlapThe months that two neighbouring windows have in common, which is what stops them being separate pieces of evidence about the same record. is not a flaw anybody introduced; it is a consequence of stepping one month at a time, and it is the price a rolling reading pays for removing the choice of start date.
The factor checks from the other side too. A count this important should not rest on one route. Forty nine windows, twelve months each, is 588 month slots. The strip holds only sixty months. 588 divided by 60 is 9.8, so the average month on that strip has been counted 9.8 times over. Dividing the counts instead, 49 by 5, gives 9.8 again. Both routes land on exactly the same figure with no rounding at any step, and the reason they agree is that twelve divides sixty exactly. Where the window does not divide the strip, the two routes separate, and the honest course then is to quote the count of non-overlapping windows and the months left over rather than a single tidy ratio.
The everyday version is a street survey. Someone stands outside one office building at lunchtime and asks a hundred people what they think of the new footbridge. The survey gives a hundred answers and one office building. If forty of those people work on the same floor and share the same commute, the result is not a hundred independent views of the footbridge but a handful of views, repeated. The count is real and the evidence behind it is thinner than the count suggests. Overlapping windows do exactly this to a return record, and it is why an independent observationA reading that shares none of its underlying data with another reading, so the two can be treated as separate pieces of evidence. is worth so much more than a repeated one.
A scheme is reported as positive in 98 of 100 rolling windows. How many independent results is that?
How the window length changes the count
The strip below is sixty months long. The strip carries no returns and belongs to no scheme, and sixty months is a round length chosen to keep the counting easy. Move the window length and watch two things at once: the stack of every window that fits, and underneath it the far shorter row of windows that share no month with each other. Click any month on the strip to start a window there and see how far it reaches.
A 12 month window on a sixty month strip gives 49 windows, of which 5 share no month with each other, and any neighbouring pair shares 11 of its 12 months. The average month on the strip is counted 9.8 times over. The highlighted window starts at month 1 and ends at month 12.
Educational illustration. The counts are arithmetic about windows on a strip of months and say nothing about any scheme's performance. For a window of w months on this strip the number of windows is 60 less w plus 1, the number that share no month is the whole number part of 60 divided by w, and a neighbouring pair shares w less 1 months.
What does a rolling reading still not fix?
Quite a lot, and this is where a reader who has just been convinced by rolling readings needs to slow down. A rolling reading still needs a window length, and the window length is a choice made by somebody. Twelve months, thirty six months, sixty months: each produces a different spread from the same record, and whoever reported the figure decided which one appears. One arbitrary choice has been removed and another has been put in its place.
A rolling series still starts and ends somewhere. Somebody decided that the last five years were the interesting five years, so a rolling series computed over them is itself a point to point selection at a higher level. And it still says nothing whatever about the basis of the figures inside it. Every reading in a rolling series built from a scheme's own published values is a net returnA return computed from values that already carry the charge running against the scheme's assets, so no fee is taken off afterwards., already carrying the charge. A series built from an index carries no cost at all. Rolling one of them does not make them comparable with each other.
Removing one arbitrary choice does not remove all of them, and a rolling reading quoted without its window length is as bare as a point to point figure quoted without its dates. That is the practical rule to carry away. The window length is the label a rolling figure cannot travel without, in the same way that the two dates are the label a point to point figure cannot travel without, and a figure that arrives without its label is not usable yet.
A rolling figure arrives with no window length attached. Is it usable as it stands?
Predict before answering. The record behind the worked scheme holds one measured year. Can its rolling returns be shown?
Can a rolling return be produced for the Girnar Large Cap Equity Fund?
No, and the reason for the absence teaches more than a filled row would. The record behind this sequence holds one measured year for the Girnar Large Cap Equity Fund: 13.4 per cent, net, value to value, over the one stated year. One window is exactly enough for a point to point reading. A rolling reading needs many start dates, and therefore a record long enough to hold them. There is no second year here, no month by month series, and no other scheme's series either. The Girnar Broad Market Index Fund exists in this teaching record as a separate scheme, and no figure of any kind from it is used here.
So the rolling row of the table below is written as not computable rather than filled, and the reason that matters is worth saying out loud: a plausible rolling series invented for the occasion would look exactly like a real one. It would have a best window and a worst window and a sensible looking spread, and a reader would have no way at all of telling it from a disclosed series. Inventing a series nobody could tell from a disclosed one is the failure worth preventing, so the row stays empty and the emptiness does the teaching instead.
The same absence covers more than the series. The record carries no holdings, weights, cash position or flow data for either scheme, and the mechanism is teachable without any of them. An invented weight would read exactly like a disclosed one, the same failure wearing different clothes.
What does the record actually support, worked end to end?
The comparison runs on what is genuinely here, and the gap does the teaching. The Girnar Large Cap Equity Fund returned 13.4 per cent, net, measured value to value across the one stated year. Its stated benchmark returned 12.1 per cent over the same year. An index is not investable and nobody pays anything to hold one, so that benchmark figure carries no cost at all. The two figures therefore sit on different bases, and the benchmark comparison is taken apart under its own heading in this sequence. The point that matters is that the scheme's figure is a point to point reading and behaves like one.
Work it as one. Two dates, two values, one proportion, and no information whatever about the path between them. The scheme could have risen evenly through the year. The scheme could have fallen a long way in the middle and come back. Or it could have done almost nothing for eleven months and everything in the twelfth. In all three of those worlds the reported figure is 13.4 per cent, net, and nothing in the figure distinguishes them. The silence is not a defect in the arithmetic but the definition of the measure.
The difference between what the record itemises and what it does not is easy to slide past, so be precise about it. The record holds one dated value for the scheme: net assets of Rs 4,200 crore across 120.00 crore units in issue, dividing to Rs 35.00 a unit exactly. Rs 35.00 is one value on one date. A point to point reading needs two of them, and the 13.4 per cent net figure is the result of a pair this record never itemises. So even the point to point reading here arrives as a finished figure rather than as a calculation that can be rerun. Keep its basis and its period attached to it wherever it travels.
The rolling reading fails next, and it fails honestly. A rolling reading needs many start dates. The record holds one window and no monthly series behind it. So the rolling row is not a number waiting to be computed. It is an absence, named rather than filled. The overlap arithmetic runs instead on a bare strip of months, needing no scheme at all, and the table below sets both counts against each other.
Two numerals below look alike and are nothing alike. The 12 in a twelve month window is a count of months on a bare strip that belongs to no scheme. The 12.1 per cent is the stated benchmark's return over the one stated year, on a basis that carries no cost at all. The two share two digits and nothing else, and wherever one ends up beside the other in a sentence, one of them is in the wrong sentence.
| The counting | The arithmetic | Result |
|---|---|---|
| Start positions | A strip of 60 months, a window of 12 months, stepping one month | 60 less 12 plus 1, so 49 |
| Windows that share nothing | 60 months divided into blocks of 12, end to end | 5, with 0 months left over |
| Shared by a neighbouring pair | Two windows one month apart, of 12 months each | 11 of 12 months |
| Check, route one | 49 windows times 12 months, divided by the 60 months on the strip | 588 over 60, so 9.8 |
| Check, route two | 49 readings divided by the 5 that share no month | 9.8, the same figure |
| Rolling reading for the scheme | Needs many start dates. This record holds one window | not computable |
Both routes reach 9.8 exactly, with no rounding at any step, and they agree because twelve divides sixty without remainder. Forty nine readings carry roughly what five independent ones would, and that is the sentence to carry away. Notice too what the last row of that table does: it is the only row with no number in it, and it is there precisely so that the absence is visible rather than quietly skipped.
The limit belongs in the same breath as the figure rather than in a closing caution. The record holds one year for one scheme. There is no second year, no monthly series and no other scheme's figures behind it. A single year cannot be annualised into anything, cannot be extended forward or backward, cannot be set against any real fund or index, and is not evidence about what selecting holdings or tracking an index delivers. The arithmetic on it is exact and its reach is tiny, and both of those are true at the same time. The record does support a point to point figure with its basis and its dates attached, and that figure is the object taken apart under the benchmark comparison.
Who reaches for this distinction on a working day, and how?
Three people, and none of them is doing it out of curiosity. A figure whose dates cannot be reconstructed cannot be checked by anybody afterwards, so Sohail Merchant, heading operations at Girnar Asset Management, has to be able to say which dates produced any figure that leaves the building. The dates are part of the record, not decoration on it, and they are filed with the number.
An analyst reading a scheme's published figures does something narrower than most readers expect. The analyst does not ask whether the number is good. The question is what the number measures: which declared values, over which dates, on which basis, and how many separate stretches of time sit behind it. Asking it is the whole practitioner move, and it converts a quoted figure into a statement whose evidence can be counted. A rolling range with a stated window is a different object from a rolling range without one, and an analyst treats them differently.
A household reading a leaflet at a bank counter has the same two questions available and can ask them in ordinary words. How long is the window. How many of these readings do not overlap. Neither question needs any arithmetic, and between them they separate evidence about a scheme from evidence about a date. None of the three can say anything at all about the next year from a single measured one, and neither measure changes that.
The error that gets made, and what it costs
A reader is shown a scheme's rolling three year returns and told the reading was positive in 98 of 100 windows. The claim sounds like a hundred separate tests, ninety eight of which passed. The report is nothing of the kind. If the windows step one month at a time, a hundred thirty six month windows need a record of a hundred and thirty five months. A hundred plus thirty six less one is a hundred and thirty five. Ask how many thirty six month windows fit into a hundred and thirty five months without sharing anything, and the answer is three, with twenty seven months left over.
So a single strong stretch inside that record lifts dozens of readings at once. On the strip drawn below, an eighteen month stretch sits inside 53 of the 100 windows, so more than half the readings contain it. The reader has counted one stretch of evidence many times and has become confident on the strength of the counting rather than on the strength of the record. The mirror error sits on the other measure entirely: a reader accepts a point to point figure without asking why those two dates, and whoever chose them had every reason to choose well.
Both errors end in the same place: a reader who believes they have evidence about a scheme when they actually have evidence about a date, or about one stretch of months. The cost is a decision taken with more confidence than the record can support, and confidence is the expensive part. The fix is two questions and they are short: how long is the window, and how many of these readings do not overlap.
Who decides which periods a scheme has to publish?
The Securities and Exchange Board of India (SEBI) does. Which return periods a scheme must disclose, over what spans, in what form, and alongside which comparator, is fixed by rules SEBI makes, and those rules are revised. A printed period, list of periods or prescribed format does not merely become dated when the rule changes, it becomes wrong. The current position is read at sebi.gov.in on the day it is needed.
Industry level material on how schemes present their figures sits with the Association of Mutual Funds in India (AMFI) at amfiindia.com. The association publishes and coordinates rather than making the rule. The tax treatment of any gain sits with the tax authority at incometaxindia.gov.in.
The mechanism above this block does not depend on any of that. Counting how many windows fit on a strip of months is arithmetic that works the same way under any rulebook. A second market would add to the mechanism rather than rewrite it.
Two short questions cover most of the ground with either measure. What are they?
References
| Source | Document | Where |
|---|---|---|
| Securities and Exchange Board of India | The rules fixing which return periods a mutual fund scheme must disclose, over what spans and in what form, and the comparator that must accompany them | sebi.gov.in |
| Association of Mutual Funds in India | Industry level material on how schemes present return figures | amfiindia.com |
| Income Tax Department | The treatment of any gain on units | incometaxindia.gov.in |
Girnar Asset Management Limited, the Girnar Large Cap Equity Fund, the Girnar Broad Market Index Fund, Kalyani Bhagat and Sohail Merchant are invented.
Educational material. Not advice on any investment, tax, budget or market position.