Fund Return vs Benchmark Return: Net Against No Cost

A fund return and its benchmark return are not the same kind of number. The scheme figure is net of its charge. Nobody holds an index and nobody pays to hold one, so the index figure carries no cost at all. Subtracting one from the other compares a net result with a costless one, so restate both onto one basis before reading the gap.

Here is what sits underneath that. 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 an expense ratio of 1.65 per cent a year. For the stated year the Girnar Large Cap Equity Fund returned 13.4 per cent net, measured value to value, against 12.1 per cent for its stated benchmark. Kalyani Bhagat manages the portfolio and Sohail Merchant heads operations.

Three things are settled elsewhere and taken as given. The charge comes out of the scheme's own assets day by day rather than out of the holder's pocket, so a published scheme return is already net of it. A point-to-point figure is decided by its two dates. Hold the two dates completely still, and nothing but the basis is left to work on. And a second invented scheme, the Girnar Broad Market Index Fund, has a record of its own that serves exactly one purpose below: evidence that an investable version of an index is not free. Every comparison below sits inside one fixed pair of dates, so every difference that follows comes from the basis and from nothing else.

The word that does all the work here is basisThe convention a figure is computed on, chiefly whether costs have already been taken out of it or not.. One return has already had money taken out of it and the other never had money in it to take. Two such returns can cover the same year, the same market and the same currency and still refuse to subtract. The mismatch is not a rounding problem or a data problem. It is a difference in what the two numbers are.

What is a benchmark return, and what does it represent?

A benchmarkThe index a scheme names as the yardstick its performance is read against. is the index a scheme names as the yardstick its own record is read against, and a benchmark returnThe change in that index over a period, computed by the index provider from the index's own published rules. is simply the change in that index across a period, computed by the index provider from the index's own published rules. The provider takes the index level at the start of the period and the level at the end, and reports the movement between them. Nothing else enters the calculation.

An index is a measuring stick rather than a holding, and that single property decides everything that follows. Nobody buys an index. Nobody is charged for it. Nobody pays a broker to assemble it, nobody pays a custodian to hold it, nobody pays a registrar to record who has it, and nobody receives its return at the end of the year. Nobody is there to charge in the first place. An index is costlessCarrying no charge of any kind, because there is no holder and therefore nobody to charge. for that reason alone, and no effort went into making it cheap.

There is an everyday version in the price board outside a vegetable market. The board records what tomatoes went for today, and it is genuinely useful: a shopper can tell whether the shop down the road is overcharging. But the board is not a bag of tomatoes. Nobody carried the board home, nobody paid the auto fare, nobody stood in the queue and nobody dropped two of them on the stairs. The board records a level. The bag is a thing a household actually has, and getting it home cost something the board never mentions. A benchmark return is the board and a scheme return is the bag, and the gap between the two is the whole of the problem.

What is a fund return, and on what basis is it published?

A fund returnThe change in a scheme's net asset value across a period, computed from values a holder can actually transact at. is the change in the scheme's net asset value across the same period, computed from values a holder could actually have bought at and redeemed at. For the Girnar Large Cap Equity Fund the stated year produced 13.4 per cent net. The word net is not a decoration on that sentence and it is not a caution bolted on afterwards. Net is part of the number.

A scheme return is net for a structural reason rather than by convention: the charge comes out of the assets every day, so it is already inside both ends of the calculation before anybody does the arithmetic. The value at the start of the year was struck after that day's charge had been taken out of the pool. The value at the end of the year was struck the same way. Every value in between was too. So there is no later step in which somebody deducts 1.65 per cent from 13.4 per cent, and anyone who performs that deduction has taken the charge twice. The scheme's net basisA figure computed after costs have already been taken out, so no further deduction belongs on it. is a fact about how the figure was built.

The everyday version is the amount that lands in a bank account on the first of the month. Provident fund and tax came out before the transfer, so the figure in the account is already net. Nobody sends a separate bill afterwards, and nobody would subtract the deductions a second time from what actually arrived. The 13.4 per cent net is a figure somebody genuinely received. The 12.1 per cent is precisely not that.

Do the two figures treat income the same way?

Income treatment is the second half of a fair comparison, and it is skipped far more often than the cost half. Dividends and interest arriving in the scheme raise the assets and therefore raise the value of a unit, so a scheme return includes the income the scheme received across the period. An index return may or may not include the same thing. An index can be computed on price alone, in which case income is simply absent from it, or it can be computed with income treated as reinvested, in which case income is inside it. Price alone and income reinvested give two different figures for the same index in the same year.

Which of the two the stated benchmark of the Girnar Large Cap Equity Fund uses is nowhere established, and the honest thing to do with a check that cannot be completed is to mark it unresolved rather than to assume the convenient answer. The direction of the effect is worth holding on to even without the figure: a scheme return that carries income set against an index return computed on price alone flatters the scheme, and no figure in hand settles whether that is happening.

The household version is a shop's takings. If one shop counts only what came over the counter and the other counts the counter plus the rent it collects from the room upstairs, the two takings figures are not comparable, however carefully each was added up. Two returns are like for like only when the period matches, the basis for costs matches and the treatment of income matches, and only the first two are settled for the Girnar Large Cap Equity Fund.

Benchmark return vs fund return: why are these two figures not the same kind of number?

Because of one asymmetry, and it is worth stating slowly. The 13.4 per cent net of the Girnar Large Cap Equity Fund for the stated year was computed from values that already carried the 1.65 per cent charge, so nothing is deducted from it afterwards. An index is not something a person can hold, and nobody pays anything to hold one, so the 12.1 per cent of the stated benchmark for the same stated year carries no cost at all. Subtracting the second from the first sets a net result against a costless one, so the 1.3 points it produces is not a like-for-like reading, and both bases belong in the same sentence every single time either figure is written.

Here is the everyday version, and it is worth sitting with. A delivery service quotes a price to move a carton across the city, and that price has fuel in it, wages in it, the cost of the van in it and a driver who has to find parking. Beside that, someone reads the straight line distance off a map. Nobody drives the straight line and nobody is billed for it, so comparing the delivery price with the straight line on the map is not a comparison of two services. The map distance is real, useful and exactly right about what it measures. The distance is simply not a price.

One consequence is worth stating plainly. The distance between the published gap and the honest gap is not some vague error term to worry about in general. The distance is exactly the size of the charge. A scheme charging very little is misread by very little; a scheme charging a great deal is misread by a great deal. Like for likeA comparison in which both figures are computed on the same conventions, so the difference between them means what it appears to mean. is not a style preference here, and the size of the failure is a number anyone can put a finger on.

What does the published gap of 1.3 points actually measure?

Work it first. The Girnar Large Cap Equity Fund returned 13.4 per cent net for the stated year and its stated benchmark returned 12.1 per cent carrying no cost, and 13.4 less 12.1 is 1.3 percentage pointsThe plain arithmetic difference between two percentages, as against a percentage change in one of them.. The 1.3 points is not meaningless and it is not to be thrown away. The gap is what a holder actually got, measured against a stick nobody can hold, and wanting to know that is a perfectly reasonable thing to want.

For a household with Rs 1,00,000/- in the scheme through the whole of that stated year, 1.3 points is Rs 1,300/-. The scheme's 13.4 per cent of Rs 1,00,000/- is Rs 13,400/-, and 12.1 per cent of the same amount is Rs 12,100/-. The Rs 1,300/- is real money on a real holding, before any tax and before any exit load. Nothing that follows makes it disappear.

The selection of holdings was carried out with money that pays a charge and the stick's figure was not, so the 1.3 points is not a measure of that selection. Read as the value of the choices Kalyani Bhagat made across the stated year, it understates them, and it understates them by the whole of the charge. Read as what the holding delivered against a yardstick, it is exactly right. One number, two questions, and only one of them is the question the number answers.

How is the comparison restated on to one basis?

There are exactly two routes, and only one of them can be walked on the figures in hand. Route one puts the scheme on to the index's costless basis by putting the charge back on. Route two puts the index on to a holder's basis by taking off what an investable version of that same index would cost. Both are legitimate. Only the first can be worked from these figures.

Take route one, and say the approximation out loud rather than hiding it. Adding the 1.65 per cent charge back on to the 13.4 per cent net gives about 15.05 per cent on a gross basisA figure stated before costs are taken out, so a charge still has to be deducted from it to reach what anybody received., and about 15.05 per cent against 12.1 per cent carrying no cost is a gap of about 2.95 points. The add-back is arithmetic and it is not exact. The charge accrues day by day against an asset base that moves every day. The accrual is multiplicative rather than additive, so a stricter restatement divides instead of adding: 1.134 over 0.9835 is about 1.1530, or about 15.30 per cent gross, and the gap on that route is about 3.20 points rather than about 2.95.

Even the stricter route treats a daily accrual as one flat annual deduction, so it is an approximation too. The two routes disagree by roughly a quarter of a point. Neither route ties exactly on either figure, and what survives both is the finding rather than a number: the honest gap sits near three points, more than twice the 1.3 the headline shows.

A build that only works forwards has not been checked, so the add-back row reads backwards too. About 15.05 per cent less the 1.65 per cent charge is 13.4 per cent net, the figure the row began with. About 15.05 less 12.1 is about 2.95, the gap in the last column. On the stricter route the unrounded value is 15.30249 per cent, rounded down to about 15.30, and its unrounded gap is 3.20249 points which rounds down to about 3.20. Both roundings go down, and neither is an equality.

The rupee version of the same two rows, on Rs 1,00,000/- held through the stated year: the published gap is Rs 1,300/-, and the like-for-like gap on the add-back route is about Rs 2,950/-. Nobody received the gross figure, so the first of those is money a household actually had and the second is not. Holding that distinction is the difference between using the restatement and misusing it. The restatement shows how far the selection got before the charge; it does not hand anybody Rs 2,950/-.

One year for one scheme is the whole of the evidence. There is no second year, no monthly series, no other scheme in the range and no real vehicle in the arithmetic. A single year cannot be annualised into anything, cannot be extended forward or backward and cannot be set against any real fund or index. The arithmetic on it is exact and its reach is tiny, and both of those are true at once.

Why can the index side not be restated on this record?

Because step two of route two needs one number that is nowhere available: what an investable version of that particular benchmark would cost. There is a tempting substitute sitting one shelf along, and taking it would be a fabrication.

Here is the temptation, named rather than merged. The stated benchmark of the Girnar Large Cap Equity Fund returned 12.1 per cent for the stated year. The index that the Girnar Broad Market Index Fund follows returned 12.40 per cent for the same year. The benchmark and the index are two different measuring sticks. One is the large capitalisation benchmark a particular scheme has declared and the other is a broad market index a particular tracker follows, and nothing establishes that they are the same index or measure the same segment. The two figures read alike and measure different things, and reading alike is not evidence of anything at all.

There is a second near miss one step along, and it catches readers the same way. The Girnar Broad Market Index Fund itself returned 12.12 per cent net for the stated year, within a fiftieth of a point of the 12.1 per cent stated benchmark. The pair sets a scheme's result after its own charge against a costless yardstick for a different segment. Two mismatches sit in that pairing rather than one. Never set 12.12 per cent against 12.1 per cent, and never set 13.4 per cent against 12.40 per cent. The rule is about what each figure measures and never about how near two numbers happen to sit, so it holds unchanged in a year when they read alike and in a year when they do not.

The tracking record does establish one mechanism worth carrying, on its own index and nowhere else: an investable version of an index falls short of the index, and by more than its charge alone. The Girnar Broad Market Index Fund returned 12.12 per cent net for the stated year against its own index at 12.40 per cent, a shortfall of 0.28 of a point. A perfect tracker charging 0.20 per cent would have returned 12.20 per cent, so 0.20 of that shortfall is the charge and the remaining 0.08 is everything else: cash held, the timing of money coming in and going out, and the cost of following an index when the index itself changes. The costs explain most of the shortfall and not all of it, so an account that says a tracker falls behind by its costs has stopped one step early. How that tracking differenceThe gap between what an index returned and what a fund following it returned over the same period. splits is worked through separately; the shortfall matters here only as evidence that route two would have a real number in it wherever such a cost is published.

One number turns up twice here, and it means nothing both times

Say the coincidence out loud. Adding the Girnar Broad Market Index Fund's 0.20 per cent charge back on to its 12.12 per cent net gives about 12.32 per cent, and that figure is a gross equivalent for that tracker. A discretionary mandateAn arrangement in which a manager runs a client's own portfolio under an agreed mandate, with fees billed to the client rather than taken inside the vehicle. recorded in portfolio material elsewhere is also 12.32 per cent, and that one is a net figure: 14.2 gross less 1.88 of fees. A reader who has met both will meet 12.32 twice.

The two are equal and they mean nothing whatever to each other: different vehicles, unconnected records, and opposite bases, one built by adding a charge back on and one left over after fees were taken out. The arithmetic is forced by the figures and cannot be adjusted to avoid the match, so the match is stated here as a coincidence. Joining them would manufacture a connection out of nothing but a shared pair of digits.

What happens to a ranking when one side is gross and the other is net?

The ranking reverses, and it reverses on no new information at all. The mandate returned 14.2 per cent gross for its stated year, and its fees of 1.88 per cent were billed to the client separately. Taking those fees off leaves 12.32 per cent net. Set 14.2 against the scheme's 13.4 per cent net and the mandate is ahead by 0.8 of a point. Set 12.32 against 13.4 per cent net and the scheme is ahead by 1.08 points. Two vehicles, one year each, and the ranking flips.

A different treatment of the same fee is all that arrived between those two subtractions, and the habit is the most expensive of them all for exactly that reason. The person doing the first subtraction usually has no idea that a fee convention decided the answer, and would defend the conclusion energetically, because both numbers are correct and the arithmetic is correct. Only the pairing was wrong.

Two limits belong beside those figures. The mandate's fee is a separate bill to a client, so the 12.32 per cent net is used directly rather than restated; the multiplicative caution that applies to the scheme's daily accrual does not apply to a figure the record already supplies. And even the honest pairing of 13.4 against 12.32 is one stated year on one vehicle each side, and one year on each side decides nothing about either kind of vehicle in general.

What survives once both sides are honest?

Two gaps survive, and each answers a different question. On the published route the gap is 1.3 points, and it answers what a holder in the Girnar Large Cap Equity Fund got against a stick nobody can hold. On the gross route the gap sits near three points, and it answers how far the selection got before the charge was taken out. The two answer different questions, so neither replaces the other and neither is the honest one. Both need the word about wherever the restatement is involved.

The rule that falls out of all of it is a pairing rule: a gross figure belongs beside a gross figure and a net figure beside a net figure, and a comparison whose two sides differ on that point is arithmetic without a subject. The rule is binary. Two figures on the same basis may be subtracted. Two figures on different bases must be restated first, and the restatement is labelled approximate. And where the basis of either side cannot be established at all, the subtraction is not performed. A difference between two numbers of unknown kind describes nothing.

The last case is the one people find hardest. Two numbers sit there, and refusing to subtract them feels like failing to answer. The refusal is the opposite. The number produced would be confidently wrong, and confidently wrong numbers travel further than honest silences.

How far does one stated year actually reach?

Not far, and the reach belongs in the same breath as the arithmetic rather than in a closing caution. The evidence runs to one year for one scheme. There is no second year, no month by month series, no other scheme in the range and no real vehicle anywhere in it.

There is nothing to annualise across, so a single year cannot be annualised into anything. Nothing sits on either side of it, so the year cannot be extended forward or backward. No real fund or index enters the arithmetic, so the year cannot be set against one. And one observation of anything is not evidence about a process, so the year says nothing about what selecting holdings delivers or what following an index delivers. The arithmetic here is exact and its reach is tiny, and both of those are true at once without contradicting each other.

Girnar Asset Management Limited, the Girnar Large Cap Equity Fund, the Girnar Broad Market Index Fund, their stated benchmarks and indices, the discretionary mandate, Kalyani Bhagat and Sohail Merchant are invented.
Educational material. Not advice on any investment, tax, budget or market position.