Market Efficiency: The Three Forms and What They Do Not Claim

Market efficiency says prices already reflect a stated body of information, and that body cannot then be used to do better than the market as a whole. Three forms name three bodies: past prices, everything public, everything including the private. The claim is smaller than its reputation. The claim does not say prices are right, and no test can refute it alone.

Market efficiency is most often met in its damaged form, in one of two sentences. Either markets are efficient, so there is nothing to learn and nothing to look at; or markets are obviously not efficient, look at what happened last quarter, so there is something to go and do. Both sentences are wrong, and they are wrong for the same reason: each one has quietly dropped the four words that carry the whole hypothesis. Put those four words back and market efficiency turns into a careful, narrow, testable claim that recommends absolutely nothing.

What is Market Efficiency, and efficient with respect to what?

Start with a phrase rather than a definition, because the phrase is the idea and the definition is only its packaging. The phrase is efficient with respect to. The phrase cannot be finished without naming something, and the thing named is the claim. Efficiency is never a property a market simply has; it is a relation between a price and a named body of information.

Take it out of finance first, because the shape is easier to feel in a place with no jargon in it. A vegetable market at seven in the morning is efficient with respect to this morning's truck arrivals. Everybody standing on that street can count the crates coming off the tempo, and the price of tomatoes has already moved for it before a buyer arrives with a bag. The same market, at the same hour, is nowhere near efficient with respect to the rain that fell on a growing district four hundred kilometres away last night. Nobody at those stalls has heard about it yet. One market, one moment, two opposite verdicts. The only thing that changed was the information named.

So every efficiency claim has a slot in it, and the slot must be filled before the claim carries any content at all. Filled with yesterday's prices, it is a modest claim most people would grant. Filled with everything ever written down inside every company, including what has not been announced, it is a claim almost nobody would grant. The underlying logic was set out by Paul Samuelson in Proof That Properly Anticipated Prices Fluctuate Randomly, published in the Industrial Management Review in 1965, and the three named forms were assembled by Eugene Fama in Efficient Capital Markets, in the Journal of Finance in 1970. The information setThe named body of information that one particular efficiency claim is about. Change it and the claim itself has changed. is what each of those two papers is careful about and what most retellings of them leave out.

What are the three forms, and what does each one add?

The three forms are three fillings of that slot, arranged so that each one swallows the one before it. The three forms are usually presented as a ladder of strictness. The shorthand is harmless right up to the moment somebody concludes that refuting the top rung has said something about the bottom one. It has not.

The weak form: past prices and volumes

The weak formThe claim that prices already reflect past prices and past traded volumes, so the price record itself holds no further usable pattern. names the smallest set: the price record the market produced itself, and the volumes that went with it. The claim is that whatever pattern can be extracted from that record has already been extracted, priced, and thereby destroyed. The Palash 100, an invented index, shows the shape of it. The index opened at 100.0, reached 131.0 at the second quarter end, fell to 104.0 by the fourth, and stood at 127.0 at the eighth. The weak form says that anybody staring at those nine numbers looking for the shape of the tenth is looking at a record every other reader can also see. The weak form is not a claim that the past is meaningless, only that a pattern visible to everybody has already been competed away by everybody.

The semi-strong form: everything public

The semi-strong formThe claim that prices already reflect all publicly available information, not merely the price record. widens the slot to everything a person could in principle find out without breaking a confidence: results, announcements, filings, the scheme document, the television segment on the nineteenth of February. Notice that this set contains the previous one, because past prices are themselves public. So the semi-strong form is not a competing claim, it is the weak form plus a great deal more, and it can only be true if the weak form is true as well.

The strong form: everything, including the private

The strong formThe claim that prices reflect all information, including information held privately and not yet released. fills the slot with everything, including what somebody inside a company knows this morning and nobody outside will know until Thursday. Almost nobody defends this one as a description, and the interesting part is what its failure does and does not imply. If the strong form fails, it fails because private information is not yet in the price. The failure says nothing whatever about whether the public information is. The nesting runs one way only: a break in the largest set leaves both the smaller sets exactly where they were.

What does the hypothesis refuse to claim?

Four claims get attached to market efficiency by people arguing for it and by people arguing against it, and the hypothesis makes none of them. Each refusal below stands on its own and none of them is hedged.

The hypothesis does not claim prices are correct. It claims prices reflect the named information. Whether that information was any good is a separate question the hypothesis never touches. A market can be flawlessly efficient with respect to everything public and still settle on a number that looks absurd two years later, provided nothing public said otherwise at the time. Efficient means the information got in, not that the information was right.

The hypothesis does not claim investors are rational. It needs something far weaker, and it is the aggregation step: mistakes that scatter in different directions cancel against each other, and only mistakes that share a direction survive to move a price. Sixty people can each be wrong on the invented Palash decision log and the market can still be efficient, so long as they are wrong in different directions. Cancellation is why refuting efficiency by pointing at one careless decision never works.

The hypothesis does not claim a bubble is impossible. Efficiency is silent on whether prices can detach from anything for an extended period, and what a speculative episode looks like is set out under speculative bubbles. Silence is not denial.

The hypothesis does not claim nobody ever does better. It claims that the named information set is not how. Somebody with a private supply chain, a faster pipe or an appetite for a risk other people will not carry may end up ahead, and none of those routes is the information set the hypothesis named. The hypothesis rules out one road, not the whole map.

Why can no test reject efficiency on its own?

Here is the part that gets filed as a technicality and is not one. Testing whether a price reflects the information available requires knowing what the price should have been if it had. The comparison figure does not fall out of the sky. The figure comes from a model of expected returnThe return a holding is supposed to deliver on average, given the risk it carries. It is produced by a model, never observed directly.. Somebody chose that model, and the model could be wrong.

So every test carries two propositions into the room and can only ever reject the pair. The pairing is the joint hypothesis problemAny test of market efficiency is simultaneously a test of the model of expected returns used to say what the price should have been., and it is a structural fact about testing rather than a weakness of any particular study. A rejection establishes that at least one of the two is wrong, and it never establishes which.

Think of a school that tests its students with a paper somebody wrote that morning. The class scores badly. Two explanations are alive and the mark sheet cannot separate them: the students did not know the material, or the paper was a bad paper. The school can argue about it for a term. The school cannot settle it from the marks alone. The missing information was never in the marks, so no amount of statistical care applied to them will change that.

What does that look like worked on the numbers at hand?

Stating the joint hypothesis problem abstractly is exactly what makes readers file it under technicality, so it is worth working through. Suppose the invented Palash 100 is examined to see whether the fall from 131.0 at the second quarter end to 104.0 at the fourth shows the market was inefficient. Answering that requires knowing what the level should have been, and that is a number nobody has supplied.

Supplying one shows what happens. Across the eight quarters as a whole, the index went from 100.0 at the open to 127.0 at the eighth quarter end. The rise is 27.0 points, treated as a simple sum rather than a compounded return so the arithmetic stays visible. Eight quarters at four quarters a year is two years. If the correct expected return were 11.0 per cent a year, matching the invented cohort's gross figure, then two years of it is 22.0 points, and the index at 27.0 points is 5.0 points ahead. The gap looks like something.

Now change one thing, and change nothing about the index. If the correct expected return were 13.5 per cent a year, two years of it is 27.0 points, and the index sits exactly on the line with a gap of zero. The verdict moved entirely with the assumption and not at all with the data, and the joint hypothesis problem is nothing more than that pair of sums.

The second panel carries the point. Nobody handed anybody the true expected return, and working out what a holding ought to return is a valuation question rather than an efficiency one. So the verdict is not a finding. The verdict is an assumption wearing the costume of a finding.

What does the Adaptive Markets Hypothesis change about the question?

Once it is clear that no test settles the matter, the natural next move is to stop asking a question that cannot be answered and ask a better one. Replacing the question is what the adaptive markets hypothesisThe view that how efficient a market is varies with conditions and with competition, rather than holding as a single fixed state. does. Andrew Lo set it out in The Adaptive Markets Hypothesis, in the Journal of Portfolio Management in 2004, and its move is to treat efficiency as a quantity that varies rather than a switch that is either on or off.

The reasoning is borrowed from ecology rather than from physics. How efficient a market is with respect to some body of information depends on how many participants are competing over exactly that information, how expensive it is to get at, and how stable the conditions have been. Where a great many people are working on the same public numbers with the same tools, the information gets into the price fast. Where few are, or where getting at it costs real money and effort, it gets in slowly. Efficiency becomes a level that moves with conditions, so the honest question is how efficient, with respect to what, and for how long.

Notice that this reframing does not repair the joint hypothesis problem. Measuring how efficient a market is still requires knowing what the price should have been, and that still requires a model. The reframing buys a better shaped question and an explanation for something the original framing struggled with: why an apparent pattern can be present for a while and absent afterwards, without anybody having to claim that a law of nature changed.

What can the invented log and the invented index actually settle?

Almost nothing. The Palash 100 is an invented path; it was not produced by anybody buying or selling anything, so it cannot be evidence about how prices behave. The Palash decision log records 240 decisions taken by 60 investors across eight quarters, made up of 96 buys, 84 sells, 36 switches and 24 pauses of a standing instruction, and no price is attached to a single one of them. The log is a record of deciding, not of pricing.

The four holdings inside the case make the same point. At the valuation struck on 30 September, the Vindhya index scheme stood at Rs 3,36,000/- against a cost of Rs 3,00,000/-, the Nilgiri mid-cap scheme at Rs 2,55,000/- against Rs 3,00,000/-, Suvarna Chemicals Limited at Rs 4,60,000/- against Rs 4,00,000/-, and Kesari Logistics Limited at Rs 1,95,000/- against Rs 3,00,000/-. Cost Rs 13,00,000/- against value Rs 12,46,000/-, down Rs 54,000/-, being 4.2 per cent. Every one of those numbers is a fact about one invented holding and none of them is evidence about whether any information was in any price. Four positions cannot test a hypothesis about markets, and neither can four hundred.

How does an adviser use an idea that instructs nobody?

Devika Rao, the adviser at the invented Palash Advisory Services Private Limited, gets no instruction out of any of this, and that turns out to be the useful part. She gets a way of sorting claims that arrive at her desk. When somebody tells her that a holding is mispriced, the idea gives her one question to ask back: mispriced with respect to what information, and who else has it? If the answer is a television segment that ran on the nineteenth of February, then whatever that segment contained is public, tens of thousands of people saw it, and the claim is that everybody who saw it has failed to act on it. The claim is a large thing to assert, and it is now sitting out in the open where it can be examined.

The same question works for a person deciding alone with no adviser and no committee. No model, terminal or committee is needed to ask who else knows this. In the invented log, 41 of the 96 buys followed a media mention within three days, or 42.7 per cent, against roughly 11.0 per cent of the eligible list being mentioned at all in a given week. The value of the idea to a practitioner is not a verdict about any price, it is a habit of naming the information set before taking a claim seriously. Meera Sundaram gets exactly the same use out of it as her adviser does.

Why is none of this a reason to trade, or not to trade?

The boundary here cuts in both directions, and the second direction is easy to miss. Prices reflecting public information is not a reason to stop looking, reading or thinking. The reflecting is done by people who looked, and nothing in the hypothesis says a holder's own reason for holding something has to be an informational edge. Prices possibly not reflecting it is not a reason to start trading either. An explanation of why a price moved is an explanation and never an instruction. Neither half of the hypothesis licenses an action, and a reader who takes one away has assembled it themselves out of parts the hypothesis does not supply.

Three separate things keep that boundary honest, and any one of them would be enough on its own. The first is cost. Take the cohort's five turnoverHow much of a holding is bought and sold over a year, stated as a percentage of what is held. groups, twelve investors each, running at 9, 34, 71, 128 and 210 per cent a year. Their gross returns were 11.2, 11.0, 11.1, 10.9 and 11.0 per cent, a spread of 0.3 points. Their net returns, after dealing charges, spread and tax, were 10.9, 10.4, 9.6, 8.4 and 6.9 per cent, a spread of 4.0 points. The busiest group paid 4.1 points a year to be busy, a toll larger than most documented effects are before costs, and a documented effect is almost always measured before costs. Brad Barber and Terrance Odean examined the relationship between trading and returns in the Journal of Finance in 2000, and the invented figures here illustrate that shape rather than reproduce their findings.

The second thing is publication. An effect that has been written up in a journal is read by everybody who read the journal, which is a large number of well resourced people. Whatever the effect did before it was published is therefore not what it does afterwards, and the finding and its own obsolescence arrive in the same envelope. The third is that the reasons a mispricing can survive are the same reasons a reader cannot capture it. Andrei Shleifer and Robert Vishny set this out in The Limits of Arbitrage, in the Journal of Finance in 1997: the frictions that stop the price being corrected are the frictions that stop anybody correcting it. The explanation and the obstacle are one fact seen from two sides.

There is a fourth consideration that cuts against the pure version of the hypothesis and still licenses nothing. Sanford Grossman and Joseph Stiglitz argued in On the Impossibility of Informationally Efficient Markets, in the American Economic Review in 1980, that if prices reflected everything perfectly then nobody would be paid for gathering information, and if nobody gathered it the prices could not reflect it. Perfect efficiency is self-undermining, and even that argument against the strong version is not an argument for anybody to go and act.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited, the Palash decision log, the Palash 100 index, the Palash investor cohort, the Vindhya index scheme, the Nilgiri mid-cap scheme, Suvarna Chemicals Limited and Kesari Logistics Limited are invented.
Educational material. Not advice on any investment, tax, budget or market position.