Price Discovery: How Information Becomes Price

Price discovery is the process by which information held separately by many people becomes one public number. Hayek's point is that no participant holds what the price ends up containing. Grossman and Stiglitz added the sting: if prices reflected everything, nobody would pay to gather information, so prices could not reflect everything. The wrongness left over is exactly what capture costs.

Start with the thing itself rather than with the theory. A number appears on a screen. The number changes during the day, sometimes by a little and occasionally by a lot, and thousands of people look at it and treat it as though it were a fact about the world. Where did it come from? Nobody wrote it. No committee met to set it. No survey was taken of what everybody thought. The number is a residue: it is what is left behind when people who disagree act on their disagreement, and it carries information that not one of those people ever held on their own. The process has a name, price discovery, and it produces a summary of what many people knew separately without ever producing a verdict on what anything is worth.

What does price discovery actually accomplish?

Friedrich Hayek, writing in The Use of Knowledge in Society in the American Economic Review in 1945, set out the problem in a form that had nothing to do with markets in shares. He asked how an economy decides what to do when the knowledge it needs is not held in any one place. The person who knows a machine is idle this week is not the person who knows a shipment is delayed, and neither of them knows what a household three towns away has decided to stop buying. All of that knowledge is real, all of it is relevant, and none of it is written down anywhere in a form anybody could collect.

Hayek's answer was that a price does the collecting. Each holder of a fragment acts on their own fragment, the acts meet, and the level at which they meet carries a summary of the lot. Price discoveryThe process by which scattered information becomes one public number. is that collecting, seen as a process rather than as a result. Its accomplishment is not accuracy. Its accomplishment is aggregation of knowledgeMany partial views combining into a figure no one of them held.: a single figure that summarises what many separate people knew separately, produced without any of them ever telling anybody what they knew.

Take it out of finance for a moment. The point is easier to feel at a vegetable market. Thirty sellers arrive at dawn. One of them knows the rain flattened a field in her village. One knows a wedding hall has ordered heavily for Saturday. One knows nothing at all and is only copying the stall beside him. By nine in the morning there is a price for a kilogram of tomatoes, and that price is higher than yesterday. No single seller in that market could have said why the price rose, yet the price rose for a reason, and the reason is inside it. The tomato price is the whole of Hayek's insight, and the fact that it works without anybody understanding it is precisely what he found remarkable.

How does knowledge scattered across many people become one number?

The mechanism is narrower than most readers expect, and that narrowness is what every limitation of a price comes from. Knowledge reaches a price through exactly one channel: somebody acts on it. Not thinks it, not believes it, not mentions it to a colleague. Acts. Places an order, accepts an offer, moves money. A conviction that never turns into a transaction has exactly the same effect on a price as no conviction at all, which is none.

The single channel of acting does an enormous amount of filtering, and the filter is not random. The filter removes everybody who is uncertain, everybody who is busy, everybody who has no money free this month, everybody who already holds as much as they want, and everybody who thinks the price is roughly right and therefore has nothing to do. Through the filter passes only the small group whose view was different enough from the current level, and held firmly enough, to be worth acting on today.

The invented Palash decision log makes the size of that filter visible. The log records 240 decisions taken by 60 investors over eight quarters. The arithmetic is 4 decisions each across two years, or one decision every other quarter on average. Sixty people held opinions continuously for eight quarters; the record of those opinions reaching anything at all runs to 240 lines. Everything else those sixty people believed, feared, hoped and noticed over two years left no mark anywhere.

Notice where the narrowness stops. Narrow filtering does not mean the price is badly informed. A market where only the well informed bother to act, and everybody else sits still because they have nothing to add, is exactly the market Hayek was describing, and the filtering is helping. The trouble starts only when a reader forgets that the filtering happened and treats the number as though it had polled everybody.

What does a price contain, and whose view is it?

One question separates a reader who understands prices from one who merely watches them. When a screen shows a level, whose opinion is that? The instinctive answer is that it is everybody's, averaged somehow. The correct answer is that it belongs to two people, and those two are not typical of anybody.

A price is the level at which the last buyer to agree and the last seller to agree found each other. The last buyer and the last seller are the marginal participantThe buyer or seller whose agreement sets the price. on each side: the buyer who would not have paid a rupee more and the seller who would not have taken a rupee less. Everybody who thought the level was far too low and bought hours ago is not in it. Everybody who thought it far too high and sold last week is not in it. Everybody who thought it about right and therefore did nothing is not in it at all. A price is a marginal agreement between the two least convinced participants on either side, and treating it as the settled view of a crowd misreads which two people made it.

A price is not a consensusGeneral agreement, which a price is not., though consensus is the word most often used for it. Consensus means general agreement, and a price requires disagreement to exist. If everybody agreed on the level, there would be no reason for anybody to transact and no transaction to record. Every trade is two people who disagree about whether the thing is worth more or less than the money. The price is the place where their disagreement was priced, not the place where it was resolved.

Meera Sundaram sold Suvarna Chemicals Limited whole on 12 October at Rs 4,60,000/-, against a cost of Rs 4,00,000/-. The number Rs 4,60,000/- is now a fact in a record. The record says that on that day one buyer agreed at that level. The record does not say what the other 59 investors in the log thought of it, and 58 of them expressed no view on it whatsoever. One agreement makes a price, and the silence of everybody else is not disagreement with it and not endorsement of it, because silence is not in the number.

What does a price leave out?

Three things, and each one is larger than a reader expects. Take them separately. The three fail in different ways, and a reader who has only noticed one of them will still misread the number.

First, everybody who did nothing

InactionChoosing not to act, which leaves no trace in any price. is the single largest thing a price omits, and it is invisible precisely because there is nothing to see. Work it out from the log. Sixty investors observed over eight quarters gives 480 investor quarters in total. The log carries 240 decisions. Even in the extreme case where no investor ever took two decisions in the same quarter, that leaves 240 investor quarters, being 50.0 per cent of them, in which somebody watched the whole quarter go by and did nothing at all. Wherever two decisions did fall in the same quarter, the silent share is larger still. At least half of all the time held by all the people in this record produced no act, and therefore left no trace in any price anywhere.

A household will recognise the shape of this immediately. A household holds an opinion about the price of the flat it lives in, and has held that opinion for years. The household has never once entered the property market, having neither sold nor bought, and the recorded prices in the area were made entirely by the handful of neighbours who did. Their transactions are the data. The household's view, however well founded, is not in it.

Second, why anybody acted

A price records that a transaction happened. A price cannot record why, and no amount of studying it will recover the reason. The buyer may have read three years of statements. The buyer may have watched a television segment the previous evening. The buyer may have needed cash for a hospital bill and sold the first thing available. All three produce the same mark in the same record at the same level.

The log can see what a price cannot. Of the 240 decisions, 71 were taken within 48 hours of a news item, being 29.6 per cent. Of the 240, only 84 carried a written reason of any kind, being 35.0 per cent. Of the 96 buys, 41 followed a media mention within three days, being 42.7 per cent, against 11.0 per cent of the eligible list being mentioned at all in a given week. The three measurements describe the process behind the acts in some detail. Not one of the three could be recovered from any price, at any resolution, by anybody, because a price has no field for the reason.

Third, how confident anybody was

A price is one number, and one number has no width. Two participants who agree at Rs 4,60,000/- may be equally certain, or one may be sure to the last rupee while the other is guessing within a range of a lakh and simply needed the money today. The agreement is identical either way, and so is the mark it leaves.

A number carries an air of precision that its manufacture does not support, so the missing width is the omission that does the most damage to careful readers. A price arrives with no error bar, no dispersion and no sample size, and a reader who supplies those from imagination has invented the most important part of what they are reading. The width was there in the heads of the participants. The width was destroyed at the moment the transaction fixed a single level.

Why can a price never reflect all information?

Everything so far has been about what a price is. Now comes the argument that decides what a price can be. Sanford Grossman and Joseph Stiglitz set it out in On the Impossibility of Informationally Efficient Markets, in the American Economic Review in 1980. The argument is short enough to state in three sentences and strong enough that nobody has escaped it in the decades since.

The impossibility resultGrossman and Stiglitz's finding that fully efficient prices cannot exist. begins from one observation that everybody accepts and nobody follows through: gathering information costs something. Somebody has to read the statements, visit the site, telephone the supplier, build the model, or pay a person who does. The gathering cost is real, it recurs every year, and it comes out of the return of whoever bears it.

Step one. Suppose prices already reflect everything there is to know. Then a person who gathers information learns nothing the price did not already contain, so their gross return matches everybody else's, and they finish behind by exactly what the gathering cost. A rational gatherer stops gathering. Step two. Suppose instead nobody gathers anything. Then prices reflect nothing at all, and the first person to gather anything finds a great deal worth finding, far more than the gathering cost. Gathering becomes worth doing, so somebody starts. Step three. Neither state can hold, because each one destroys itself. So the market settles between the two, at prices wrong by just enough to pay back the cost of the gathering that corrects them, and no more than that.

What does that argument look like with the log's own cost figures?

Stated in the abstract, the impossibility result reads like a puzzle. Worked with money, it reads like a finding, so work it with money. The invented Palash log gives five cost figures, one for each turnover group: 0.3, 0.6, 1.5, 2.5 and 4.1 points a year, covering dealing charges, spread and tax together. Take 0.5 points a year as the cost of gathering. The figure sits between the lowest two of those five. On Meera Sundaram's holding of Rs 13,00,000/-, 0.5 points is Rs 6,500/- a year.

Step one, in figures. If prices already reflect everything, a gatherer and a non gatherer both earn the same gross return. The log's five groups all sat within 0.3 points of one another on gross return, between 11.2 and 10.9 per cent, so call it 11.0 per cent for both. The gatherer pays Rs 6,500/- and nets 10.5 per cent. The person who reads nothing pays nothing and nets 11.0 per cent. In a market that already reflects everything, the reward for doing the work is to finish 0.5 points behind the person who did none, which is a state that cannot survive its own second year.

Step two, in figures. Now suppose the work has stopped everywhere and prices reflect nothing. Nobody has corrected anything for a long time, so the first person to gather information faces a large residual error. Say prices are wrong by 3.0 points. The first gatherer pays 0.5 points and captures 3.0, netting 2.5 points ahead. Netting 2.5 points is worth doing, so they do it, and so does the next person who notices. Each new gatherer's transactions push part of what they found into the price, and the residual error shrinks.

Watch the ladder descend. At a residual of 3.0 points, the gatherer nets 2.5. At 2.0, they net 1.5. At 1.0, they net 0.5. At 0.5, they net exactly nothing, and at that point the entry stops, because there is no longer anything in it for the next person. The residual error stops falling precisely when it equals the cost of gathering. At that level nobody has a reason either to start or to stop.

What is the equilibrium degree of inefficiency, and why must there be one?

The level the argument settles at has a name. Equilibrium inefficiencyThe residual wrongness that pays for information gathering. is the amount of wrongness that has to remain in prices in order to pay the people whose work is what makes prices informative in the first place. Equilibrium inefficiency is not a defect that better technology or better regulation would remove. Remove it and the gathering it funds disappears, and the prices stop containing anything worth removing.

The identity repays care. Everything else about equilibrium inefficiency follows from it. In equilibrium, the residual error equals the cost of capturing it. A gatherer's gross gain is the residual error, and the residual error is all there is to find. A gatherer's cost is the cost of capturing it. The gross gain and the cost are equal. The expected net gain from capturing the inefficiency is therefore zero by construction, not because gatherers are unlucky and not because they lack skill, but because the equality is what defines the resting point.

Nothing about that depends on the number being 0.5. The log's five turnover groups paid 0.3, 0.6, 1.5, 2.5 and 4.1 points a year in dealing costs, and if any of those five is substituted as the cost of gathering, the equilibrium residual moves to match it and the net gain stays where it was. A market where information is expensive to gather is a market with a lot of wrongness left in its prices, and the people who remove that wrongness are paid exactly what removing it cost them. The size of the inefficiency shows how expensive the information is, and says nothing whatsoever about how much is there to be won.

What are the log's flat gross returns consistent with, and what do they not show?

The invented log carries one measurement that sits close to this argument, and it needs handling with care, because the temptation to over read it is strong. The 60 investors were sorted into five groups of twelve by annual turnover: 9, 34, 71, 128 and 210 per cent. Their gross returns came out at 11.2, 11.0, 11.1, 10.9 and 11.0 per cent. Their costs ran 0.3, 0.6, 1.5, 2.5 and 4.1 points. Their net returns therefore came out at 10.9, 10.4, 9.6, 8.4 and 6.9 per cent.

Look at the two spreads rather than the levels. Across a turnover range running from 9 per cent to 210 per cent, more than twenty times as much activity, gross returns varied by 0.3 points. Net returns varied by 4.0 points. The gross line is flat and the net line falls away. The difference between these investors was made almost entirely by what their activity cost them and almost not at all by what they picked.

Now the discipline. The flat gross line is consistent with the impossibility result, in the sense that a world where the reward to activity nets out to nothing would look rather like this. The line is not evidence for it, and the distinction matters more than the observation. Terrance Odean, in the Journal of Finance in 1998, and Brad Barber and Terrance Odean, in the Journal of Finance in 2000, are where the finding that trading costs eat returns was established on real records; this invented log only illustrates the shape of it.

Three reasons the log cannot carry the weight. Turnover is not information gathering, and the two are not even close: somebody can transact twice a year after months of reading, and somebody else can transact weekly having read nothing. Sixty people over eight quarters is far too small a record for a 0.3 point difference to mean anything at all. And the five groups were not randomly assigned; people sorted themselves into them. The measurement is consistent with the argument and is not evidence for it, and the two are different things that must not be allowed to blur.

Why does this settle the boundary arithmetically rather than as a caution?

A behavioural account of why a price moved is an explanation and never an instruction to act. Under investor sentiment, market anomalies and speculative bubbles that boundary is asserted and argued from evidence. Here it can be derived, and a derivation is a different kind of thing from a warning.

The two quantities run side by side one last time. The residual inefficiency in a market, in equilibrium, equals the cost of gathering the information that would capture it. A gatherer would gain the residual inefficiency by capturing it. A gatherer would spend the cost of gathering to capture it. The gain and the spend are the same quantity. Subtracting one from the other leaves zero. The expected net gain from acting on any explanation of market behaviour is therefore zero by construction rather than by misfortune.

The zero is a finding and not a caution, and the difference is worth stating plainly. A caution is bolted on at the end and could be dropped without touching the argument. A finding is what the argument produces whether anybody wanted it or not. Grossman and Stiglitz did not set out to warn readers away from anything; they set out to show that a particular idealisation was internally inconsistent, and the zero fell out of the algebra. Two things the zero does not say. The zero does not say nobody ever gains. An equilibrium is an average, and individuals scatter around averages in both directions. The zero does not say the gathering is pointless either. The gathering is what makes prices informative, and the gatherers are paid for it, in full, exactly and only.

What does price discovery not mean?

Two misreadings survive everything written above, and both are worth naming separately because they fail in different places. The first treats a price as a consensus, and the marginal argument has already dealt with that. The second treats a price as a correct figure, and that one needs its own paragraph.

A price is not a verdict about value. A price is the level at which the last agreement happened, and a level is a fact about a transaction rather than a fact about the thing transacted. Being later is not the same as being right, and being earlier is not the same as being wrong. The log makes this uncomfortably concrete. Meera Sundaram sold Suvarna Chemicals Limited at Rs 4,60,000/- on 12 October. By 31 March following, it had risen 8.0 per cent, so the same holding would have been worth Rs 4,96,800/-, a forgone Rs 36,800/-. The March level does not make the October price a mistake; it makes it an October price, and the two numbers were produced by two different sets of people acting on two different sets of information.

One case is never evidence that a rule works, and this one is no exception. Suvarna Chemicals Limited rose after the sale and Kesari Logistics Limited, which she kept, fell a further 20.0 per cent from Rs 1,95,000/- to Rs 1,56,000/-. Both outcomes are single draws. If the March levels had gone the other way, the decision of 12 October would have been exactly as well or badly made as it actually was. The worth of a decision is settled by what was known when it was taken.

How is the discovery itself measured?

If price discovery is a process, a natural question is whether anybody has measured it happening, and the answer is yes, though not in the form most readers expect. Joel Hasbrouck, in the Journal of Finance in 1995, worked on the problem of the same thing being priced in more than one place at once, and asked where a lasting move first appears. The method separates a move into the part that stays and the part that comes back, and treats the part that stays as the discovery.

The separation of the lasting part from the reversing part is the useful idea to carry away, and it has nothing to do with venues. A move that reverses within the hour carried no information; something happened, and then unhappened. A move that stays is the price having learned something. Measuring discovery means measuring the part of a move that survives. A large move and an informative move are therefore not the same thing, and they cannot be told apart at the moment they occur. The difficulty sits in that last condition: the separation is only available afterwards.

How does anybody actually use this?

Nobody trades on the impossibility result, and not trading on it is exactly its use. People use it to read prices differently, and that changes four quite ordinary jobs.

A household reading a valuation on a statement now knows what it is holding: a marginal agreement from whenever the last transaction happened, carrying no width and no reason. A marginal agreement is enough for the questions a household actually has, such as whether the total is roughly on track for a stated goal of Rs 40,00,000/- in 11 years. A marginal agreement is not enough to settle whether the number is right. An adviser at a place like the invented Palash Advisory Services Private Limited uses it differently. Devika Rao cannot promise a client that any explanation of a market move will convert into a gain, and the reason she cannot is now arithmetic rather than caution. Arithmetic is a far easier thing to say honestly to somebody who has just read an article. Where a duty applies to how an adviser may describe an expected outcome, that duty is set by the Securities and Exchange Board of India and published at sebi.gov.in.

An analyst uses it as a budget. If gathering information on something costs a certain amount a year, the analyst is asking whether the residual error in that price is larger than that, and the impossibility result says the honest default answer is no, so any yes needs a specific reason attached to it. A lender uses it as a warning about collateral. A quoted level on a security pledged against a loan is a marginal agreement made by two people who may have had nothing to do with each other's reasoning, so a lender who needs to know what could be realised on a sale of size is asking a question the quoted number does not answer.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited, the Palash decision log, Suvarna Chemicals Limited and Kesari Logistics Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.