Active and Passive Funds: The Trade, Not the Verdict

An active fund employs a manager who selects the holdings and aims to beat a benchmark declared in advance. A passive fund follows the rule of an index it has declared it will track, so nobody selects anything, and it aims only to match that index less its own costs. The trade is a known higher charge against an unknown difference in result, and it stays a trade rather than a settled question.

Here is what sits underneath that answer, and it is smaller than most treatments of this question make it sound. An active fundA scheme in which a person selects what it holds, inside limits the scheme has stated in advance. and a passive fundA scheme whose holdings are fixed by the rule of an index it has declared it will follow. are the same object with one part exchanged. Both are schemes. Both issue units. Both strike a value once a day by dividing net assets by the units in issue. Both process an application the same way, and both take their charge the same way, out of the scheme's own assets rather than out of the holder's pocket. Exactly one part differs between them, and that part decides what the scheme holds.

Two schemes carry every figure below. Girnar Asset Management Limited, an invented fund house, runs the Girnar Large Cap Equity Fund, an open ended equity scheme with net assets of Rs 4,200 crore and 120.00 crore units in issue. Dividing the first by the second makes one unit worth Rs 35.00 exactly. Kalyani Bhagat manages that scheme's portfolio and Sohail Merchant heads operations at Girnar Asset Management. The same manager also runs the Girnar Broad Market Index Fund, a tracker of a broad market index.

Four things are covered separately and taken as settled here: which day's value an order gets, what a scheme is and who stands behind it, how a value per unit is struck, and what an expense ratio is and how it reaches that daily value. Cost turns out to be the argument, so cost is used below rather than explained again.

What is actually different between the two, once everything they share is stripped out?

One part. Setting the two schemes side by side and going through them row by row, four of the five rows come out identical. The unit is the same kind of object. The daily value is struck the same way. An application is processed the same way. The charge accrues daily against the scheme's own assets in both, so in both the published value a holder sees is already after it. Then comes the row where they part: in the Girnar Large Cap Equity Fund a person decides what the scheme holds, and in the Girnar Broad Market Index Fund the rule of a declared index decides and nobody selects anything.

Two identical kitchens in the same building make the point. Same stove, same gas connection, same bill, same hours. In one, a cook decides each morning what to make from whatever looked good in the market that day. In the other, a printed menu that never changes decides, and the person in the kitchen simply follows it. Everything visible about the two kitchens is the same, and the only real difference is who is holding the decision. A reader who is told that active and passive are two different worlds learns two sets of machinery where there is one machine and one swapped part. Saying so at the start saves the second set.

What is an Active Fund, and what is the higher charge actually buying?

An active fund is a scheme in which a named person selects what the scheme holds, inside a mandateThe written limits a scheme sets for itself, saying what kind of thing it may hold and what it may not. the scheme has written down in advance, and the result is set against a benchmarkA published index a scheme names in advance as the yardstick its result will be read against. named in advance as well. On the Girnar Large Cap Equity Fund that person is Kalyani Bhagat. She works inside the mandate the scheme has stated, and the scheme has stated which benchmark its result will be read against before the year starts, not afterwards. How she selects anything is a portfolio question and is covered separately; what matters here is that the selection exists and that a person is answerable for it.

This is where most explanations go soft, so be precise about what a holder has bought. A holder has not bought a list of holdings. The list will be different in six months and the holder was not consulted about any of it. A holder of an active fund has bought a decision process running for a year, and the charge is the price of that process, agreed in advance and taken whether the decisions turn out well or badly. The Girnar Large Cap Equity Fund charges 1.65 per cent of that scheme's assets a year. On net assets of Rs 4,200 crore that is Rs 69.30 crore for the year, or Rs 69,30,00,000/- written out in full.

A tailor is the cleaner comparison than anything from finance. A customer who goes to a tailor pays for the measuring, the cutting and the judgement, not for a specific shirt chosen off a rail. If the shirt does not fit, the tailor was still paid for the work of making it. The arrangement is not a scandal and nobody hides it; it is the deal. An active fund is that deal, in a scheme.

What is a Passive Fund, and if nobody selects the holdings, what is left to manage?

A passive fund is a scheme whose holdings are decided by the rule of an index it has declared it will follow. Nobody sits down and picks. The index has a rule for what goes into it and in what proportion, and the scheme's job is to hold that. The Girnar Broad Market Index Fund follows a broad market index, and the rule of that index fixes what the scheme holds.

Here is the part most treatments skip, and it is the reason a trackerEveryday word for a scheme that follows an index rather than selecting holdings of its own. is not simply an active fund with the manager removed. The manager's job does not disappear in a passive fund, it changes: it becomes following a published rule at the lowest cost and with the least slippage. Following a rule cheaply is an operational job with an output anybody can measure. Money arrives on days the index does not change. Some cash is held to meet redemptions and cash is not in the index. When the index itself changes, the scheme has to deal, and dealing costs something. None of that is selection. All of it moves the result.

A delivery driver handed a fixed route in the morning is the everyday version. The driver chooses nothing about where to go; the route is printed. The whole job is to run it without wasting fuel, without missing a turn and without leaving parcels behind. Whether that job was done well is measurable at the end of the day against a route published before the driver set off. A decision to hold one thing rather than another allows no such measurement.

Active Fund vs Passive Fund: what happens when both are run against the same five criteria?

Criteria in the same order for both, or the comparison is rigged before it starts. Take five: what decides the holdings, what the scheme aims at, what it charges, what happens if the deciding goes wrong, and what happens if the market the scheme sits in falls. On the first four the two structures give genuinely different answers. On the fifth they give the same answer, and that fifth row is the one readers get wrong most often.

Run them. The holdings are decided by a person on one side and by a published rule on the other. The aim is to beat a stated benchmark on one side and to match a stated index less costs on the other. The charge is 1.65 per cent of the Girnar Large Cap Equity Fund's assets a year against 0.20 per cent of the Girnar Broad Market Index Fund's assets a year. If the deciding goes wrong on the active side, the result can miss the benchmark by any amount in either direction. On the passive side there is no selection to be wrong about, so a shortfall is operational rather than a judgement that failed.

Then the fifth row. If the index falls, both fall: the tracker follows it down because following is the whole undertaking, and the active scheme may fall more or less than the index but has undertaken nothing at all about the direction, so neither structure is a defence against a market going down. Words like tracking and following sound safe, and the fifth row is where that language does the most damage. Following describes nothing more than obedience to a rule that can point downwards.

Why does cost sit at the centre of this argument rather than off to one side?

Not because it is large. Because of when it is known. The Girnar Large Cap Equity Fund charges 1.65 per cent of that scheme's assets a year and the Girnar Broad Market Index Fund charges 0.20 per cent of its own assets a year, a difference of 1.45 percentage pointsThe plain difference between two percentages. Going from 4 per cent to 5 per cent is one percentage point, not one per cent. a year. The 1.45 point gap is fixed by the two scheme documents before the year begins. Nobody has to wait to find out what it is.

The other half of the trade is not like that at all. Whether the more expensive scheme ends the year ahead of the cheaper one, and by how much, is not knowable in advance by anybody, including the person running it. One side of this trade is contracted before the year starts and the other side is only visible after the year ends, and that asymmetry, rather than the size of the charge, is what puts cost at the centre of the argument.

The same comparison runs through ordinary life without being called anything. In a job, the salary is in the letter and the promotion is not. In a shop tenancy, the rent is in the agreement and the footfall is not. Nobody thinks the rent is the most important thing about a shop. The rent is the one number that is settled, and it is still the line everybody reads first. An expense ratio has exactly that standing in this comparison, and it is why any treatment of active and passive keeps coming back to it.

Put the gap in rupees on a base that exists, and be careful about which base that is. The Girnar Large Cap Equity Fund has net assets of Rs 4,200 crore. Charged at 1.65 per cent of those assets, Rs 69.30 crore leaves that pool in a year. Charged at 0.20 per cent instead, the same pool would give up Rs 8.40 crore. The difference is Rs 60.90 crore a year, written out as Rs 60,90,00,000/-. On one unit worth Rs 35.00 that same 1.45 point difference is Rs 0.5075 a year. The average folio in this scheme is Rs 4,200 crore divided across 3,80,000 folios, or about Rs 1,10,526/-, and on that folio the difference is about Rs 1,602.63/-. The Girnar Broad Market Index Fund's own net assets are nowhere in this record, so the rupee gap above is what a difference in rate does to one known pool, and not a comparison of what the two schemes actually collect.

What does a tracker actually hand the holder, if not the index itself?

The index less its charge, and then less something else again. Start with the honest statement of what a tracker undertakes: to follow a published rule. A tracker does not undertake to deliver the index, and cannot. Holding the index costs money and the index costs nothing to be. Nobody can hold an index. An index is a calculation, not a thing, and no charge has ever been taken out of one.

Watch it happen on the invented figures. In the one stated year the index that the Girnar Broad Market Index Fund follows returned 12.40 per cent. The Girnar Broad Market Index Fund itself returned 12.12 per cent net for the same year. The shortfall is 0.28 percentage points. Its charge for the year was 0.20 per cent of its own assets. The charge accounts for a good deal of that shortfall and plainly not all of it. The part left over is a residualThe part of a difference that is still there after the parts that can already be named have been taken out., and it is a separate thing from the charge, so any account that has a tracker falling behind by its costs alone has stopped one step short of the truth.

Where does a residual come from? Cash sits in the scheme and cash is not in the index. Money arrives from holders on days the index has not moved and leaves on days it has. When the index itself changes what it contains, the scheme has to deal, and dealing is never free. None of that is anybody selecting anything, and all of it moves the result away from the rule the scheme is following. How that shortfall is measured and split into its parts is covered separately and is not run here.

What did the two schemes actually do in the one stated year, and on what basis?

Two figures, and both of them are the same kind of number: a net returnA return computed from values that already have the charge taken out, so nothing further is deducted from it.. The Girnar Large Cap Equity Fund returned 13.4 per cent net for the stated year while charging 1.65 per cent of that scheme's assets. The Girnar Broad Market Index Fund returned 12.12 per cent net for the same year while charging 0.20 per cent of its own assets. Subtract and the difference is 1.28 percentage points, in favour of the more expensive scheme, for that one year.

Now the error made most often at this exact point. Both of those figures are computed from daily values that already had the charge taken out of them before the value was struck. Nothing at all is deducted from either figure, and a reader who subtracts a fee from a published scheme return has charged the same expense twice and understated the scheme by its whole expense ratio. A gross returnA return measured before costs are taken out. It has to be labelled, because a net figure looks identical in print. is a different kind of number and has to be labelled as one.

Where do 1.45 percentage points go between the gross reading and the net one?

Run the same pair of schemes on both bases and watch the size of the answer change. On a net basis the Girnar Large Cap Equity Fund's 13.4 per cent less the Girnar Broad Market Index Fund's 12.12 per cent is 1.28 percentage points, both for the stated year. Now put both back on a before charge footing. Add 1.65 to 13.4 and the equity scheme is at about 15.05 per cent gross; add 0.20 to 12.12 and the index fund is at about 12.32 per cent gross. The difference is 2.73 percentage points.

The addition is not exact, so say the word approximate out loud. A charge accrues daily against the assets. Daily accrual makes the charge multiplicative rather than a single subtraction at the end of the year, so adding the ratio straight back is a good approximation and not an identity. Backing it out properly gives a slightly larger figure again. The finding survives both routes even where the decimal does not: the honest gap between these two schemes on one basis is roughly twice what it looks like on the other.

The two lines at the bottom of that table were built from completely different inputs and landed on the same number. Agreement from different inputs is what shows the arithmetic to be right rather than merely plausible. One came from four return figures. The other came from two charges and no returns at all. The gross reading and the net reading of the same pair of schemes differ by the cost gap and by nothing else whatsoever.

Splitting the gross difference shows what the charge did to the number. Of the 2.73 points, 1.45 points is nothing more than the difference between the two charges, and 1.28 points is the difference the two sets of holders actually saw in their own values. As shares of 2.73 that is 53.1 per cent and 46.9 per cent, and the two add to 100 per cent because the difference contains nothing else at all. More than half of the gap between these two schemes on a before charge basis is a difference in what they charged rather than a difference in what reached anybody.

There is a second thing that table quietly settles, and it is worth pulling out. Two of the four ways these figures can be paired are legitimate and two are not. Net against net is legitimate and gives 1.28 points. Gross against gross is legitimate and gives 2.73 points. The equity scheme's 13.4 per cent net against the index fund's about 12.32 per cent gross gives 1.08 points, wrong by exactly 0.20, the index fund's own charge. The equity scheme's about 15.05 per cent gross against the index fund's 12.12 per cent net gives 2.93 points, wrong by exactly 1.65, the equity scheme's own charge. Each mismatched pairing is wrong by precisely one charge. Knowing that is useful, because the error never announces itself as an error, only as a different and equally tidy looking number.

One more thing about that 12.32 per cent. The 12.32 above is the Girnar Broad Market Index Fund's approximate gross equivalent for the stated year. Under discretionary mandates, 12.32 per cent net is what one mandate was left with after its own fees were charged separately. The two 12.32 figures come from different schemes, on different bases, in different structures, and the fact that the digits match is a coincidence produced by arithmetic that cannot be adjusted to avoid it. A reader who has met 12.32 per cent net before met a different number wearing the same face as the index fund's approximate 12.32 per cent gross, and joining the two would invent a connection.

Are the two schemes even being measured against the same stick?

No, and this is the quiet limitation sitting underneath every figure above. The Girnar Large Cap Equity Fund names its own benchmark, and for the stated year that benchmark returned 12.1 per cent, so the scheme's excess over the stick it declared is 1.3 percentage points net against a costless yardstick. The Girnar Broad Market Index Fund follows a different index altogether, a broad market one, and that index returned 12.40 per cent for the same year. The 12.40 is again a costless yardstick rather than a scheme result. Two schemes, two different measuring sticks, and nothing in this record says the two sticks are the same thing or move together.

The sticks therefore need handling with care. Each scheme's excess figure is only meaningful against the stick that scheme itself declared. Setting the tracker's after charge result against the equity scheme's benchmark, or the equity scheme's result against the broad market index, silently swaps the yardstick and changes the answer with nothing in the record to say it has happened. The two schemes can be compared with each other: a holder really could have held either. Neither scheme's gap over its own benchmark can be set against the other's. Those two gaps are measured from different starting lines. The distinction matters whenever two figures happen to look close to one another. A benchmark figure is a costless yardstick for the market segment a scheme declared, and a scheme figure is an after charge result. Two such numbers can land near each other, and the nearness carries no meaning at all: they are not measuring the same quantity, on the same basis, for the same set of holdings.

There is one more thing this record does not settle. A scheme's return includes the income the scheme received on what it held. An index may be computed on price alone or with income treated as reinvested, and this record does not say which convention the equity scheme's stated benchmark uses. The convention behind the benchmark figure is therefore unresolved, and an unresolved convention is better written down than assumed.

Set the control back to 1.65 and the panel reproduces the worked example exactly: 13.40 per cent net against 12.12 per cent net, a gap of 1.28 percentage points for the stated year. Now push it up. The bar comes down one hundredth of a point at a time and the dashed line stays where it is, and the two finally meet at 2.93 per cent of that scheme's assets. The meeting point is 15.05 less 12.12, and there is no cleverness in it at all.

Notice what that number is not. The 2.93 is not a threshold, it is not a rule and it is nothing anybody set. The figure is simply the amount of gross return the more expensive scheme had to give away before its holders ended the stated year level with the tracker's holders, and on this one year's figures that amount was roughly twice the 1.45 point gap between what the two schemes actually charge.

2.93 has appeared already, a few paragraphs above, as the wrong answer produced by pairing a gross figure with a net one. The subtraction is the same one, and the repeat is not a coincidence: asking what charge brings a scheme's gross return down to another scheme's net result mixes the two bases on purpose. Mixing them is right when that is the question and wrong when the intention was to compare two results. The arithmetic cannot tell the difference. Only the person reading it can.

What does one year on one scheme each side actually establish?

Two things are true at the same time and both have to be held together. The arithmetic above is exact. Its reach is tiny. Neither of those statements weakens the other, and dropping either one either dismisses a correct calculation or promotes it into evidence it cannot carry.

The record contains one year. One scheme on the active side and one on the passive side. Two schemes measured against two different sticks, and those two sticks need not be the same or move together. No second year, no series of months behind either figure, no other scheme from the same manager or anybody else's, and no study of any kind. A sample of one observation on each side cannot rank two structures, and the exactness of the subtraction has nothing to do with it. Precision and reach are entirely separate properties of a number.

A shop that had a good Tuesday is the everyday version. The takings for Tuesday are exact to the rupee; the till does not lie. The shopkeeper cannot say that Tuesdays are good, or that this shop is better than the one across the road. A single day says nothing about either. Nobody finds this confusing about a shop. The same claim becomes confusing about a fund because the number arrives with two decimal places and a printed document behind it, and precision in print is very easy to mistake for weight.

There is a much older idea sitting behind this argument and it deserves its name. The proposition that the prices of traded things already reflect the information available about them is associated with Eugene Fama, whose 1970 review of the theory and the evidence is the standard reference and is findable through ideas.repec.org. If prices already carry what is known, then finding a difference by selecting is hard rather than routine, and that proposition is what gives the selection argument its shape. Running the argument needs evidence about many schemes across many years, a separate subject.

Comparisons of how schemes that select have done against the yardsticks they declared are published, and they depend strongly on which period and which set of schemes was measured. A result from one window is routinely reversed in another. The regulator's own disclosures sit at sebi.gov.in and industry level aggregation sits with AMFI at amfiindia.com, and the period and the coverage of anything found there matter as much as the number does.

Why does the comparison stop at the trade instead of settling it?

Because the trade is what the material supports and the verdict is not. Written out plainly, the evidence is lopsided across the two halves. On one side: a charge of 1.65 per cent of the Girnar Large Cap Equity Fund's assets a year against 0.20 per cent of the Girnar Broad Market Index Fund's, a difference of 1.45 percentage points, contracted, printed, and known before anybody commits anything. On the other side: whatever difference the two schemes produce, unknown until the year is over, and observed here exactly once.

Stopping at the trade is the correct ending and not a hedge. Going further would recommend a structure on the strength of a single observation, the same error the three blocks above are about. A question that is genuinely open may be left open. Closing it with material that cannot close it, and then sounding confident about it, is what may not be done.

The comparison leaves not a preference but a habit: name the basis before comparing, name the period before concluding, and name the size of the sample in the same breath as the number it produced. Followed, it makes both structures legible. Skipped, even correct arithmetic points wherever the reader was already leaning.

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.