The Benchmark Index: The Yardstick a Scheme Declares

A benchmark index is the rule built portfolio a scheme names in its own documents, before a period starts, as the thing its return will be set against. An index is a computation, so it carries no charge at any point. A scheme's published return is already net of one. A comparison that ignores that difference is measuring the charge as well as the manager.

Every mistake in this subject starts by getting one thing wrong: what kind of object a benchmark indexA published index a scheme names as the reference its own return will be reported against. actually is. A benchmark index is not a scheme, and it is not a portfolio anybody holds. A benchmark index is a rule: take this defined set of holdings, weight them in this defined way, and compute what that arrangement returned over the period. The result is published as a number. Nobody bought anything to produce it, nobody was charged anything, and not one unit changed hands.

Two things settled earlier are load bearing here, and neither is rebuilt. The first is that the expense ratio runs against the scheme's own assets every day, so a scheme's published return is already net of its charge before anyone looks at the value of a holding. The second is that an active scheme is measured against a benchmark named ahead of the period rather than picked at the end of it. Cost is not a side note in the comparison, it is the argument.

Girnar Asset Management Limited, an invented asset manager, 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 of assets a year. For the stated year the Girnar Large Cap Equity Fund returned 13.40 per cent net, against 12.10 per cent for the benchmark it had declared. Girnar Asset Management also runs the Girnar Broad Market Index Fund, which follows a broad index. For the same stated year that index returned 12.40 per cent and the Girnar Broad Market Index Fund returned 12.12 per cent net. Kalyani Bhagat manages the equity scheme and Sohail Merchant heads operations. Each of those figures covers one year and one scheme.

What is a benchmark index?

A benchmark index is a rule built portfolio that a scheme names, in its own documents, before the period it will be reported over. Three parts of that sentence are doing work. Rule built: the holdings and their weights follow a stated method rather than somebody's judgement on the day. Portfolio: an index is a defined arrangement of holdings, and nobody holds it. Named before: a stick chosen once the answer is known is not a stick at all.

Picture a school testing a change to how it teaches. If the school names the comparison class in April, before the year runs, the comparison means something. If it waits until the March results are out and then picks whichever class makes the change look best, the comparison has stopped measuring the teaching and started measuring the picking. An index chosen after the fact measures the choice of index and nothing else. That is why declared in advanceNamed in a document before the period being measured begins, rather than selected once the result is known. is not paperwork. Advance declaration is the whole reason the resulting number carries information.

The declaration is a document fact. The Girnar Large Cap Equity Fund names a benchmark in its own documents, and that name sits there whether the scheme goes on to come out above it or below it. A declaration is not a claim about performance, not a target, and not a promise. A reader who treats the presence of a declared benchmark as a statement about outcomes has read a filing cabinet as a forecast.

What makes an index usable as a benchmark for one particular scheme?

Three conditions, and they are not equally hard to meet. The first is the declaration in advance just described. The second is that the index return covers the same stretch of time as the scheme return being set against it. That sounds obvious, and it goes wrong quietly when one figure runs to the end of March and the other to the end of December. The third condition matters most: the index has to match the holdings the scheme is permitted to hold.

Here is the everyday version. A vegetable seller who works one street corner is compared with the takings of every food stall in the city. The seller cannot open a second stall, cannot sell anything but vegetables and cannot move off the corner, so most of the difference between the two numbers comes from the difference between one corner and a city rather than from anything the seller did. An index that does not match the mandateThe set of holdings a scheme is permitted to invest in, written into its own documents. measures the mandate rather than the manager, so the comparison answers a question nobody asked.

Why are a scheme's return and an index return not the same kind of number?

Because only one of them has ever had a charge taken out of it. An index is computed. There is no pool of assets behind it, no registrar keeping folio records, no custodian holding securities, nobody to pay and nothing to pay them out of. The published index return is what the stated arrangement of holdings produced, and it is a costless figure not because anyone made it cheap but because nobody was ever in a position to charge it anything.

A scheme's published return is a different animal. A scheme return is computed from the values of a unit at two dates, and every one of those values was struck after the day's expenses had already been set against the scheme's assets. So the figure arrives with the charge inside it, in the sense that the charge has already been removed. Removing the charge first is what makes a scheme return a net returnA return computed after the charges running against the assets have already been taken out. and an index return the costless figure it sits next to. Set them side by side without saying so and the difference between them is measuring the charge as well as the selection.

The word that keeps this straight is basisThe statement of what has and has not been taken out of a figure before it was reported.. A figure's basis is what has already been removed from it. The Girnar Large Cap Equity Fund's 13.40 per cent for the stated year is on a net basis. The 12.10 per cent for its declared benchmark is on a basis where nothing was ever removed. There was never anything to remove. The corresponding gross returnA return stated before the charges running against the assets have been taken out. for that scheme, the figure before its charge, is about 15.05 per cent for the stated year, and getting from one to the other is the next section.

How large is that difference on one scheme and one year?

Large enough that it is most of the headline. Work it on the Girnar Large Cap Equity Fund and keep the basis in every line. On a net basis, 13.40 less 12.10 is plus 1.30 percentage points for the stated year. Now put the scheme on a gross basis by adding the charge back. The scheme charged 1.65 per cent of its assets across the year, which on net assets of Rs 4,200 crore is Rs 69.30 crore. Its gross figure is about 15.05 per cent, and 15.05 less 12.10 is about plus 2.95 percentage points for the same year against the same benchmark.

Both figures are correct, both belong to the same scheme and the same stated year, and they differ by 1.65 points. That distance is exactly the charge, and the match is not a coincidence but the arithmetic closing on itself. Use it as a check: if a net excess and a gross excess for one scheme over one period do not differ by that scheme's charge, one of the two was computed wrongly. The charge is 1.65 points of a 2.95 point figure, about 55.9 per cent of it, so more than half of what the gross comparison shows is not about the selection at all.

One caution before that 15.05 per cent is used for anything. Adding a charge straight back is the simple route, and it is an approximation. The charge accrues day by day against a moving pool rather than as a single deduction at the year end. Backing it out properly gives a slightly larger gross figure and a slightly larger gross excess. Neither route is worth an exact bridge. Both leave the honest gross excess on this record somewhere near three points rather than near one and a third. The word about stays attached to 15.05 and to 2.95 everywhere they appear.

Which of the two comparisons should be run?

The answer depends on the question, and unlike most answers of that shape it names exactly what it depends on. A holder's question is what they received. The charge came out of the pool before the value of a unit was struck, so a holder received the net figure, and a holder's comparison is the net return against the declared benchmark: plus 1.30 points for the Girnar Large Cap Equity Fund over the stated year. Nothing further was paid, so nothing further needs adjusting.

A question about the selection is a different question. Deciding what the scheme should hold is one activity and paying for the running of the scheme is another, and the charge is not a selection decision. So a question about what the selection produced compares the gross figure with the same declared benchmark: about plus 2.95 points for the Girnar Large Cap Equity Fund over the same stated year. Both comparisons are legitimate, they give different sizes, and the fault is running one and reporting it as the other.

Attach the basis to the number and this stops being difficult. The two available sizes on this record differ by more than the smaller one, so an excess returnThe distance between a scheme's return and its declared benchmark's return over the same period. travelling without a basis label is a figure whose size is unknown to the person holding it.

What must the index include before the comparison means anything?

The same things the scheme actually received. Holdings pay income along the way, and an index can be computed two ways: on the movement in prices alone, or with that income treated as reinvested. Both are legitimate methods and both get published. The income arrives in the scheme's own pool, so a scheme receives it whatever the index does.

So the pairing has to match. Setting a scheme against an index computed without the income charges the scheme for something it did receive, and the gap that produces has nothing to do with any decision anybody made. The gap is not the manager, not the charge, not the market. The gap is two different methods of computing sitting in one subtraction, and it flatters the scheme every time.

Which of the two methods the Girnar Large Cap Equity Fund's declared benchmark uses is not established, and neither is the size of the income it pays. The check is real and it is unresolved. Before the plus 1.30 points or the about plus 2.95 points is used for anything, the basis of the stated benchmark has to be established from the scheme's own documents.

Why can two figures that look almost alike not be swapped?

Because looking alike is not the test. Two benchmark figures for the stated year appear above, and they are not the same object. The Girnar Large Cap Equity Fund declared a large capitalisation benchmark, and that benchmark returned 12.10 per cent for the stated year. The Girnar Broad Market Index Fund follows a broad market index, and that index returned 12.40 per cent for the same year. Two different measuring sticks, covering different ground, and neither one describes the other's market.

A yardstickWhatever a result is measured against, chosen and named before the measuring starts. only works while everyone agrees what is being measured with it. A tailor and a carpenter can both hold a measure marked in the same units and still produce nonsense if one hands their reading to the other without saying what was measured. Crossing the two sticks produces a comparison with no meaning at all. The subtraction is the same shape either way, so the arithmetic gives no sign of it.

The distance between the two sticks is 0.30 points, and that number needs a warning label of its own. The 0.30 is not a fact about markets, it does not say one segment did better than another, and it is not a finding of any kind. The 0.30 is simply the size of the error a swap injects, and that size is worth knowing. Crossing the sticks in one direction makes an excess fall by 0.30 points, and crossing them in the other makes it rise by 0.30. Two figures standing near each other mean nothing on their own, and each has to be read with what it measures attached.

What happens to both answers when the sticks are crossed?

The size of the mistake is the lesson, so work it rather than take it on trust. Pair the Girnar Large Cap Equity Fund's 13.40 per cent net with the index the Girnar Broad Market Index Fund follows, at 12.40 per cent, and the subtraction gives plus 1.00 points instead of the legitimate plus 1.30. About 0.30 points of the excess has vanished, close to a quarter of it, and nothing on the face of the figure says where it went.

Now go the other way. Pair the Girnar Broad Market Index Fund's 12.12 per cent net with the benchmark the Girnar Large Cap Equity Fund declared, at 12.10 per cent, and the subtraction gives plus 0.02 points instead of the legitimate minus 0.28. Those two figures are unrelated. One is a scheme's result after its own charge and the other is a costless stick for a different segment of the market. The crossed pairing turns a scheme that finished behind the index it does follow into one that appears to have edged ahead of an index it does not follow. Both wrong answers are arithmetically clean, both are the same shape of subtraction as the legitimate one, and neither reveals that the two numbers came from different sticks.

The 0.30 check explains both distortions with one number rather than two. Hold on to it. Swapping a stick does not scramble the answer unpredictably. It shifts the answer by the distance between the sticks, with the sign decided by which way the swap ran. The check still belongs before the subtraction rather than after it. Once the arithmetic has been done, there is nothing left in the result to inspect: plus 1.00 points looks exactly as reasonable as plus 1.30.

Take what the two legitimate figures do and do not establish. Plus 1.30 points net for the Girnar Large Cap Equity Fund and minus 0.28 points net for the Girnar Broad Market Index Fund are each one year on one scheme, each measured against a stick that scheme itself declared, and the two schemes are not even measured against the same stick. Neither figure is evidence about selecting holdings as an approach, neither is evidence about following an index as an approach, and setting the two schemes against each other on this record would be adding a third mistake to the two just demonstrated.

Why can two schemes' excess figures not be set against each other?

Because an excess is a distance, and a distance is measured from somewhere. If two schemes declare different benchmarks, then one scheme's excess is a distance from one starting point and the other's is a distance from a different one. Subtracting the second from the first produces a number, and that number describes nothing. The two distances were never measured from the same place.

The everyday version is two people reporting how far they walked past a landmark. One says four hundred metres past the temple, the other says three hundred metres past the bus stand. Subtracting gives a hundred metres of nothing at all. Who walked further depends entirely on where the temple sits relative to the bus stand, and neither figure mentions that. The trap holds even when both excess figures are perfectly computed, and perfect computation is exactly what makes it easy to miss. Neither number is wrong. The subtraction between them is the error, and nothing in either input gives any warning of it.

What can a benchmark never tell?

Three things, and they matter more than anything a benchmark does report. Each is a place where a reader most often takes a benchmark further than it goes. The first is whether the mandate was worth holding. A benchmark is chosen to match the holdings the scheme may take, so it covers the same ground the scheme covers. A benchmark can report how the scheme did inside that ground. It was picked to describe the ground rather than to assess it, so it cannot pass judgement on the ground.

The second is whether one period is evidence about anybody. Plus 1.30 points net for the Girnar Large Cap Equity Fund is one year on one scheme. One year is a reading, not a finding, and Kalyani Bhagat is not established as anything by it in either direction. The third is which of two schemes with different mandates did better, the subtraction refused above. A benchmark is a measuring stick, not a verdict, and every one of the three questions above is a verdict.

Why is the tool below a check rather than a calculator?

Because the work is not a computation. Every subtraction above has been shown in full, and none of them is hard: two numbers go in, one comes out, and a reader can do any of them in their head. The hard work all happens before the subtraction, and that work has a yes and a no rather than a quantity. Are these two figures on the same basis? Do they belong to the same declared stick? A control that slid the answer along a range would suggest the matching is a matter of degree, and it is not.

So the interactive below computes nothing that could not be computed by hand, and instead runs the check that has to happen first. A figure from this record and a stick from this record are selected, and the pairing is reported as available or not before any subtraction is shown at all. Three of the six combinations are legitimate and three are crossed. That ratio is worth noticing on its own.

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.