The Composite: Grouping Portfolios for Honest Reporting

A composite groups every portfolio run to one strategy into a single reported record, so nobody chooses which portfolio to show. The return is weighted by assets rather than by count, and the spread between the best and worst member is reported beside it. A composite holding one portfolio reports a spread of zero, and that zero says nothing at all about consistency.

Start with the situation that makes the idea necessary. A manager runs the same approach for eleven different holders. Eleven portfolios exist. They started on different dates, they carry slightly different cash levels, and by the end of the year they have eleven different returns. Somebody now has to put a number in a presentation. Which of the eleven numbers goes in?

The question has no honest answer, and that is exactly the point. Whoever answers it has an interest in the answer. A compositeA group of portfolios run to the same stated approach, reported together as one record so that no single portfolio can be picked out and presented on its own. is the device that takes the question away, by requiring that all eleven go in, every period, whether they helped or not. The arithmetic that follows is genuinely secondary. Grouping is a governance idea first and a calculation second.

The worked case throughout is the Anantara Multi-Asset Portfolio, an invented discretionary mandate of Rs 500 crore run by Faiz Ahmad Ansari for a charitable endowment whose investment committee is chaired by Rukmini Deshpande. Its stated shape is equity 60.0 per cent at Rs 300 crore, fixed income 30.0 per cent at Rs 150 crore and cash 10.0 per cent at Rs 50 crore, summing to Rs 500 crore exactly. Over one stated twelve month period the mandate returned 14.2 per cent. Its blended benchmark of 60 per cent a broad equity index and 40 per cent a broad bond index, both left unnamed, returned 12.6 per cent.

The word composite does two jobs in this sequence, and confusing them is easy. The benchmark just described is a blend of two unnamed indices, and blends of that kind are sometimes called composites too. A blended benchmark is not the meaning used here. A composite, in the sense that matters for reporting, is a grouping of whole portfolios. One word, two jobs, and the sentence around it settles which is meant.

What problem is grouping actually solving?

Not an arithmetic problem. Grouping solves a problem about who holds a discretion, and it solves it by abolishing the discretion rather than by supervising it. Before a composite exists, a manager presenting a record has a legitimate looking choice at every turn: which portfolio best represents the approach; which one had an unrepresentative cash drag; which one the holder interfered with. Every one of those questions can be asked in complete good faith, and every one of them can also be asked until the answer comes out flattering.

Ordinary life is full of the same shape. A tutor says that a student of theirs cleared a hard entrance examination. True, checkable, and completely uninformative. The number who sat the examination was never given. A caterer shows photographs from one wedding. A stall outside a college displays the one review that praised it. In each case nothing false was said. The missing information was the denominator, and nobody had to lie to keep it back.

A composite is the denominator, made compulsory. It says: here is the population of portfolios run this way, here is what the population did, and here is how far apart the members were. The manager can still argue about whether the approach is any good. The manager can no longer decide, after the fact, what evidence about the approach the reader gets to see. The honesty at stake is narrow and precise rather than a general virtue. The evidence is fixed before anybody argues about it.

Why is the return weighted by money rather than by count?

Because of what a composite return is meant to describe. A composite return is a statement about the experience of the money run to the strategy. If Rs 200 crore was run one way and Rs 50 crore was run the same way, then four times as much money lived through the first portfolio's result, and a figure that describes the money has to say so. That is asset weightingCombining several returns so that each one counts in proportion to the money behind it, rather than counting each portfolio once.: each portfolio enters in proportion to its size.

Take the four invented portfolios from the figure above. Sizes Rs 200 crore, Rs 150 crore, Rs 100 crore and Rs 50 crore, so weights of 40, 30, 20 and 10 per cent of a Rs 500 crore total. Returns of 18.0, 11.0, 7.0 and 2.0 per cent. Weighted by money: 0.40 times 18.0 gives 7.20, 0.30 times 11.0 gives 3.30, 0.20 times 7.0 gives 1.40, and 0.10 times 2.0 gives 0.20. Add them and the composite return is 12.10 per cent.

Now do it the other way. Equal weightingCombining several returns by counting each one once, whatever its size, so a very small portfolio and a very large one carry the same influence. counts each portfolio once: 18.0 plus 11.0 plus 7.0 plus 2.0 is 38.0, divided by four is 9.50 per cent. The gap between the two answers is 2.60 percentage points, and nothing about the portfolios changed. Only the question changed. Equal weighting gives the smallest portfolio exactly the same voice as the largest. The report then describes the accounts rather than the money, and those are two different things that happen to be measured in the same units.

Neither answer is wrong in the abstract. To learn how a typical account run to this approach fared, counting accounts is a reasonable thing to do. To learn what happened to the money, counting accounts is the wrong instrument. The failure is not choosing one. The failure is publishing a figure without saying which one was chosen, and the reader is then unable to tell which question was answered.

The same arithmetic runs inside a single portfolio, and the Anantara mandate shows it without inventing anything new. Its three sleeves are Rs 300 crore of equity, Rs 150 crore of fixed income and Rs 50 crore of cash. By money those are 60.0, 30.0 and 10.0 per cent of Rs 500 crore. Counted instead, each sleeve is one of three, or 33.3 per cent. The cash sleeve's influence rises from 10.0 per cent to 33.3 per cent, or 3.33 times what its size supports. The equity sleeve's falls from 60.0 per cent to 33.3 per cent, a little over half of where it started, at 0.56 times. The fixed income sleeve, sitting near a third already, barely moves, at 1.11 times.

A composite groups whole portfolios rather than sleeves, so three sleeves of one portfolio are not a composite. The weighting arithmetic is identical either way, and the pattern these numbers show is general.

The general result the arithmetic keeps producing is that equal weighting always transfers influence from the large to the small, and the size of the transfer grows exactly with the size gap. Where every portfolio in a composite is roughly the same size, the two weightings give almost the same answer and the choice hardly matters. Where one portfolio is enormous and the rest are small, the two weightings can give answers that argue with each other. So the place to look hardest at the weighting note is the report where the sizes are most uneven. Inconveniently, that is also the report nobody wants to look at.

What does the reported return leave out?

The width. A composite return is a centre, and a centre on its own cannot show whether the members were huddled around it or scattered across the room. DispersionA measure of how far apart the members of a group were over the same period, most simply the best member's return less the worst member's return. is the figure that supplies the width, most simply as the best member's return less the worst member's return over the same period.

Here is why it is not an optional extra. A prospective holder will receive one portfolio, not the average of all of them, so the width between members describes what they might actually get in a way the centre never can. Two composites can report an identical 14.2 per cent and mean completely different things. In one, every member landed between 13.0 and 15.4 per cent, a width of 2.4 points, and a new holder can reasonably expect to land somewhere in that neighbourhood. In the other, members ran from 6.2 to 22.2 per cent, a width of 16.0 points, and the reported 14.2 per cent is a place almost nobody actually was.

Dispersion is as usefully defined by what it is not. Dispersion is not the volatility of the composite over time. Volatility is a different measurement answering a different question, and dispersion is not a claim about which member any particular holder would have received. Dispersion is a cross section taken at one moment: on this date, over this period, the members of this group were this far apart. A single figure, cheaply computed, and it doubles the information content of the line it sits beside.

Who decides which portfolios belong?

Nobody should, and that is the design goal. Membership has to be determined by a written strategy definitionA written description of an approach that is precise enough for anyone to tell, without judgement, whether a given portfolio is being run that way. rather than chosen by a person. The definition describes the approach tightly enough that a clerk with the mandate documents in front of them can say yes or no about any portfolio without exercising discretion. The inclusion ruleThe written test that decides whether a portfolio is a member of a group for reporting, applied the same way to every portfolio and settled before any of them joins. is that test, and its timing matters more than its wording.

Written before any portfolio joins, the definition is a constraint on the manager. Written afterwards, with a year of results on the desk, it becomes an instrument. Consider five equally sized invented portfolios of Rs 100 crore each returning 18.0, 15.0, 12.0, 4.0 and minus 4.0 per cent. All five in, the composite is 45.0 divided by 5, or 9.0 per cent. Now write a definition that happens to require a minimum equity allocation the last two did not carry, or a mandate length the last two did not have, and the composite becomes 45.0 divided by 3, or 15.0 per cent.

The reported figure rose by 6.0 percentage points and not one return was edited, and an inclusion rule written after the fact is therefore invisible to every arithmetic check anybody can run on the report. There is no line in a table to audit. Every number that appears is true. The falsehood lives in the set, not in the values, and the only defence against it is timing: the rule exists before the results do, and the report says when it was written.

What happens to a portfolio that closes?

One fault quietly ruins long records, and it is worth slowing down for because it feels like housekeeping rather than like a distortion. A holder terminates the mandate. The portfolio stops existing. The portfolio is no longer there, so the obvious administrative instinct is to take it out of the reporting group. SurvivorshipThe effect of building a record only from the members that lasted, so that the ones which stopped existing are missing from the history as well as from the present. is the name for what that instinct does to the history.

Work it with three invented portfolios. Portfolio A is Rs 200 crore, portfolios B and C are Rs 100 crore each. In year one they return 12.0, 9.0 and 3.0 per cent, so asset weighted the group returns 0.50 times 12.0 plus 0.25 times 9.0 plus 0.25 times 3.0, or 9.00 per cent. In year two they return 8.0, 5.0 and minus 4.0, giving 4.00 plus 1.25 less 1.00, or 4.25 per cent. At the end of year two, portfolio C closes.

Now remove C from the group entirely. Year one recomputes across A and B alone at weights of two thirds and one third: 8.00 plus 3.00 is 11.00 per cent. Year two recomputes to 5.333 plus 1.667, or 7.00 per cent. Two years that were published as 9.00 and 4.25 per cent are now 11.00 and 7.00 per cent, and nobody edited a single return. The dispersion improves in step: year one narrows from 9.0 points to 3.0, and year two from 12.0 points to 3.0.

The correction is a rule about history rather than about arithmetic. People who are careful with numbers miss it for exactly that reason. A portfolio stays in the group for every period during which it was actually being run that way, and it leaves only the periods after it stopped. No recalculation of any earlier year is permitted just because a member later went away. The rule about history is most of what makes a ten year record mean anything, and none of it is a calculation.

What does a composite of one portfolio report?

A record containing exactly one portfolio is the awkward case, and it is worth working out loud rather than skipping to a bigger example. The Anantara Multi-Asset Portfolio is a single Rs 500 crore mandate that returned 14.2 per cent over one stated twelve month period. Group it. Membership is every portfolio run to this strategy, and here that is one portfolio. The composite return is therefore 14.2 per cent. Rs 500 crore of Rs 500 crore is the whole of it, so the asset weighting carries a single weight of 100 per cent. The best and the worst member are the same portfolio, so the dispersion between them is zero.

Every one of those statements is arithmetically correct, and the last one is the most dangerous sentence a performance report can contain. A dispersion of zero on a group of one describes an absence of members rather than a presence of consistency, and a reader who has not been told the member countHow many portfolios are in a reporting group for the period being shown. Without it, a spread figure cannot be interpreted at all. has no way at all to tell the two apart. A zero looks like a measurement. It sits in the same column as measurements, printed in the same typeface, with the same number of decimal places. Nothing about it announces that it is a structural artefact of having one member.

So the treatment is to print the member count beside the figure every time, and where the count is one, to say so in words rather than leaving a reader to infer it from a blank. A line reading dispersion zero, one member in the group is honest and unremarkable. A line reading dispersion 0.0 with nothing beside it is an invitation, and it does not stop being an invitation because the person who wrote it did not intend one.

The six things that belong beside the return

Put the whole apparatus together and a grouped performance line carries six items, not one. The strategy definition, so a reader knows what was being grouped. The member count, so a spread figure can be read. The assets in the group, so the size behind the number is visible. The weighting used, so the reader knows whether the money or the accounts were counted. The dispersion, so the centre has a width. And the treatment of portfolios that closed, so the history can be trusted.

How does an investment committee use this on a Tuesday?

Concretely, and in about four questions. When a manager presents a record to a committee like the one Rukmini Deshpande chairs, the committee does not begin by arguing about whether the return was good. The committee begins by establishing which portfolios the return came from. How many portfolios are behind this figure. What is the written definition that decides membership, and when was it written. Were the portfolios weighted by money or counted. And what happened to any mandate that ended during the period shown.

Those four questions take under a minute and they are the cheapest diligence available anywhere in this subject area. They cannot tell the committee whether Faiz Ahmad Ansari is any good. The four questions establish whether the evidence in front of the committee is evidence about the approach or evidence about a selection, and that distinction has to be settled before any judgement about quality is worth making at all.

A lender looking at a borrower's track record runs the identical routine without calling it anything. How many projects, not how did the flagship project go. An analyst reading a peer table asks whether every peer's whole set is in it. And a household hiring a tuition centre asks how many students sat the examination. The question is the same one in a different costume. In every one of those settings the useful move is the same: the number is not evaluated until the population it came from is known.

What can grouping never fix?

Almost everything else, and being clear about that is what keeps the idea useful. Grouping addresses one fault: selective presentationShowing some of the available evidence and not the rest, where the choice of which part to show was made by somebody with an interest in how it looks., the choice of which record is shown. Grouping does that completely. It does nothing whatever about the other three faults that make a performance report uninformative.

Grouping cannot make a short record long. One year grouped across forty portfolios is still one year, and the appraisal material earlier in this sequence already settled that a single record cannot separate skill from a draw. Grouping cannot repair a benchmark that does not match the mandate, because a grouped return compared with the wrong yardstick is still a return compared with the wrong yardstick. And it cannot say what happens next, a limit that belongs to the entire enterprise rather than to grouping.

A report can be perfectly grouped, correctly weighted, honestly dispersed and completely uninformative about whether the approach is worth anything, and recognising that combination is what stops a reader from treating a well constructed presentation as evidence it never claimed to be. The measures that carry the names of William F. Sharpe, Jack L. Treynor, Michael C. Jensen, Gary P. Brinson, K. J. Martijn Cremers and Antti Petajisto all try to judge a record. A composite decides which record gets judged. Those are different jobs, and doing the second one well does not do the first one at all.