Consensus: How the Aggregated Expectation Is Built

Consensus is the average of the published estimates a set of analysts have filed for a company, together with the range around it. An aggregate is not a view: nobody holds it, the estimates carry different dates and different definitions, and the average hides the spread. A result inside the range that already existed has surprised nobody, however the headline reports it.

Everything below rests on four things already in place. The two research questions are kept apart, and a view has to be checkable, both settled in the opening material. A market figure is dated and scaled before it is described, settled in the market data material. The reported, adjusted and symmetric versions of a profit line are different quantities, settled in the accounting material. And the invented record for Sarvani Coatings Limited supplies nine estimates, a mean, a range and a published result, so every number here can be worked on paper.

One warning at the outset. The difficulty is not a criticism of the people who publish estimates. Every problem in this guide is a property of averaging, and it would appear in exactly the same shape if the nine contributors were the nine most careful forecasters alive. Aggregation loses information. Losing information is what aggregation is for, and that is why the analyst has to know what got lost.

What exactly is consensus, and who puts it together?

Start with a wedding. A household is catering one and needs a headcount. Nine relatives are asked how many people they think will actually turn up, the nine numbers go on the back of an envelope, and the total is divided by nine. The envelope average is a consensus. Notice what now exists and what does not. There is one number. There is no record of the two aunts who guessed before the invitations went out, no record of the cousin who was counting only the bride's side, and the average cannot show whether the nine numbers sat close together or split into a tight camp of six and a wild camp of three.

The market version is the same operation at a different scale. Analysts who cover a company publish their estimates of its revenue, its earnings before interest, tax, depreciation and amortisation (EBITDA)The rung of the profit ladder read before depreciation and financing charges arrive. What that line contains, and the arguments about it, are settled in the accounting material., its profit after taxThe bottom line of the profit ladder, what is left once every cost, interest charge and tax has been taken out. Built and defined in the accounting material. and its earnings per shareProfit after tax divided by the number of shares. How corporate actions restate it across periods was settled in the listings sequence.. Somebody gathers whichever of those estimates they can find, counts them, and computes an average. The average, with the count and sometimes the highest and lowest figures beside it, appears in a headline as the number a company beat or missed.

The set is self selected, its membership changes without anybody announcing it, and its membership is the first thing nobody checks. No committee decides who is in. An analyst publishes and is in. An analyst stops covering the company, or is on leave, or has moved to another employer, and quietly is not. The aggregate for this quarter and the aggregate for last quarter may not be measuring the same nine people, and the published line will look identical either way.

What is one Consensus Estimate, and what does it have to do to get into the set?

A Consensus Estimate is one analyst's published number sitting inside that set. Not the average, the individual contribution. Somebody built a revenue forecast, worked it down a cost structure, arrived at a profit figure, put it in a document and published it. The published number is now a contribution.

Here is the part that surprises people. An estimate becomes part of the aggregate by having been published, not by having been good, and an estimate published eight months ago carries exactly the same weight as one published yesterday. There is no scoring, no track record adjustment, no decay. Nothing in the assembly process asks when the number was made, what the maker knew at the time, or whether the maker has looked at the company since. Nine contributions, each weighted one ninth, whatever their vintage.

Go back to the wedding. Two of the aunts answered before the invitations went out; one answered after the replies came back. All three guesses are one third of the average. Nothing in the average marks the difference. In the market version the difference is larger. Between a stale estimate and a current one there may have been a results filing, a change of guidanceWhat management itself has said it expects. What is committed, what is merely hinted, and how to read the difference is covered separately under management guidance., a capital spending announcement or a change in a shared input price. The stale contributor is not careless. The stale contributor is simply somebody who published, moved on, and never went back.

Why is the mean the weakest summary of the set?

Three different points can be computed from the same nine numbers, and they answer three different questions. The mean is the total divided by the count, and it moves whenever any single contribution moves. The median is the middle number once the nine are sorted, and it barely notices an extreme contribution at either end. The midpoint is simply halfway between the highest and the lowest, and it ignores the seven numbers in between entirely.

For Sarvani Coatings the mean is Rs 268 crore. The range runs from Rs 255 crore to Rs 284 crore, so the midpoint is Rs 269.50 crore. The midpoint sits Rs 1.50 crore above the mean, and the gap between the two establishes something at no cost. If the mean sits below the midpoint of the range, the numbers are not symmetric, and at least one contribution has to sit well below the rest to pull the average down that way.

The median, however, cannot be recovered. A mean and a range do not determine a median, so the usual disclosure cannot show whether the nine estimates cluster tightly together or split into two opposed camps. A set of nine sitting between Rs 265 crore and Rs 271 crore with two outliers, and a set of nine split into a group of five near Rs 258 crore and a group of four near Rs 280 crore, can produce the same mean and the same range. The two sets say completely different things about how settled the view is, and the published line reports them identically.

What does one contributor who has not looked up do to the number?

This is where the arithmetic stops being an abstraction. Do not take staleness as a general caution. Work it.

Suppose one of the nine has not revised since before something relevant happened, and their number consequently sits Rs 20 crore below where they would put it today. The mean is a sum divided by nine. One number therefore drags the whole mean by its distance divided by nine: Rs 20 crore over nine is about Rs 2.22 crore. The mean therefore reads Rs 265.78 crore instead of Rs 268 crore.

Now feed that into the beat. The published result was Rs 278 crore. Against the true mean of Rs 268 crore that is a beat of Rs 10 crore, or 3.73 per cent. Against the dragged mean of Rs 265.78 crore it is a beat of Rs 12.22 crore, or 4.60 per cent. With a set this small, one contributor who never looked up adds nearly nine tenths of a percentage point to the headline. Nine tenths of a point is close to a fifth of the whole reported beat. Put it the other way round and it is starker still: of the Rs 12.22 crore the result now appears to be above the view, Rs 2.22 crore is one person's inattention. Nothing about the company changed to produce it.

What if the contributors are not even estimating the same thing?

Staleness is a problem of dates. Definitions are worse, and a problem of definitions cannot be fixed by anybody being more diligent.

Sarvani Coatings' year three EBITDA has three defensible values. The reported figure is Rs 446 crore, straight off the statements. Management's adjusted figure adds back a restructuring chargeA one time cost booked when a business reorganises, for example closing a line or writing down a site. What may be treated as one time, and the arguments about it, belong to the accounting material. of Rs 6 crore, so it reads Rs 452 crore. The symmetric figure applies the same treatment in both directions and therefore also removes a provision write backA credit that appears when a liability set aside earlier turns out to be unnecessary, so an old charge is reversed. Its accounting treatment is settled elsewhere. of Rs 4 crore, giving Rs 448 crore. Three numbers, one year, no dishonesty anywhere.

Now put nine contributors across those three definitions. Say three estimated the adjusted figure and six estimated the reported figure. The average comes out at Rs 448 crore. By pure accident that lands exactly on the symmetric figure, and nobody in the set actually estimated it. Nothing in a published aggregate line records which definition each contributor used, so an average across a split set is an average of different quantities and measures nothing in particular. A result then gets compared against it, and the comparison inherits the confusion without ever disclosing it.

Work the whole thing once, on Sarvani Coatings' year three

Every step here is arithmetic that can be done on paper, and every input is in the invented record. The share count is 24.00 crore shares. The count checks against the published book value per share of Rs 61.92/- on a net worth of Rs 1,486 crore.

Read step nine again, because it is the quietest line in the table. The same event reports as a 3.73 per cent beat or a 3.67 per cent beat depending only on whether somebody rounded the per share figures to the paisa before dividing. Six basis pointsOne hundredth of one percentage point. A convention for talking about small differences in rates and margins without ambiguity. of that headline came from a rounding convention and from nothing else. Nobody is at fault and nobody could fix it, and six basis points is roughly the size of a gap that gets written up as a company having done slightly better than expected.

Now place the result rather than just measuring it. The highest contributor was at Rs 284 crore. The result came in at Rs 278 crore, Rs 6 crore below the most optimistic estimate on the list. Somebody in that set of nine had already written down a number better than what happened, published it, and was not vindicated. And the whole event sits inside a range from Rs 255 crore to Rs 284 crore that existed before the result was announced.

So what does beating consensus actually mean?

Beating consensus means the result came in above the arithmetic average of a self selected set of published numbers of mixed vintage and mixed definition. The comparison against that average is the entire content of the statement. No single person holds the expectation the mean represents, so a beat is not a statement that the company did better than people expected, and a beat is certainly not a statement that anything about the business has changed.

Two comparisons are worth making, and the mean is neither of them: the result against the range that existed before the result, and the result against the analyst's own build, the only expectation that can actually be accounted for. The range at least shows whether what happened had already been contemplated by somebody. The analyst's own build shows which assumption was wrong, and by how much, and therefore what to change. There is no set of assumptions behind an average nobody holds, so it shows neither thing.

Thin content makes the beat a poor trigger for doing anything. Suppose the result had come in at Rs 256 crore instead. A result of Rs 256 crore is a miss of 4.48 per cent against the mean, and it sits inside the same pre-existing range, one crore above the lowest contributor. The headline would read as a shock. The information content would be almost identical: somebody had already written down a number that low.

Why does the direction say more than the number?

Here is the distinction that matters and almost never gets made. A level is what a set of people have not yet got around to changing. A movement is somebody actively deciding that what they wrote before is no longer right. A level and a movement are not the same kind of fact at all. The first is partly inertia; the second is a decision, taken by a person who had to justify it to somebody.

So the interesting question is not what the aggregate reads today. The interesting question is which way the aggregate has been travelling, how fast, and whether the movement is broad or is one contributor catching up. Three contributions cut in the same fortnight after a filing indicate that something happened which several people independently thought material. The level after those cuts is the arithmetic average of nine numbers, and an average is a fact about arithmetic.

The direction of revisions carries information that the level does not, and the level is what gets reported. The mismatch is structural, not accidental. A level fits in a headline and a revision history does not.

What is the aggregate structurally blind to?

Three blindnesses, and none of them is cured by adding contributors. The instinctive fix is always more coverage, and more coverage makes the mean steadier without making it see anything new.

The aggregate is blind to anything nobody modelled. If no contributor wrote down a possible change in a shared input price, or a new line coming on stream, or a rule change, then that possibility is simply not represented anywhere in the aggregate. The mean of nine forecasts that all missed the same thing is a forecast that missed that thing, computed to two decimal places.

The aggregate is also blind to the shape of its own distribution. A tight cluster and two opposed camps generate the same mean and can generate the same range. And it is blind to its own membership changing, so the aggregate this period and the aggregate last period may be two different sets of people, compared as though they were one.

How does somebody actually use this on a Tuesday morning?

Watch what a working analyst does when a result lands, because it is almost the opposite of what the headline invites. Meghna Iyer, who carries her own build for Sarvani Coatings, does not open the aggregate first. She opens her model, puts the published revenue, gross margin and profit lines into it beside her own assumptions, and looks at which of her assumptions was wrong. The wrong assumptions make a list she can act on: volume was a point light, gross margin came in higher than she assumed, other expenses were where she put them.

Only then does she look at the aggregate, and she looks at two things in it. Where the result sat in the range tells her whether anybody had already contemplated it. Which way the contributions have been moving tells her whether other people have been changing their minds and in what direction. She does not need the mean at all, and she never writes a sentence whose subject is the mean.

A household investor can do a smaller version of the same thing in five minutes. Before the result, the two or three expected figures go down on paper: revenue roughly this, margin roughly that, and one item of genuine uncertainty. When the filing appears, those three are checked against it. The comparison that teaches something is the one whose other side the investor built, the only one whose assumptions can be inspected when it turns out wrong. An inspectable other side is exactly what the aggregate cannot offer, and building one costs nothing.