Market Anomalies: Momentum, Reversal and Drift

A market anomaly is a documented return pattern a stated efficiency claim says should not exist. Momentum runs over three to twelve months, reversal over three to five years, and drift follows an earnings announcement for weeks. Momentum and reversal describe different horizons, so they do not contradict each other. None of the three is a mispricing.

Each of these three is commonly named in conversation, and just as commonly named without its horizon. The missing horizon is where most of the confusion in this subject comes from. Two of the three effects run in opposite directions, and they only look like a quarrel once the windows they were measured over have been thrown away. Every one of these effects is a statement about a measured window, and stripped of its window it is not a weaker claim but a different claim altogether. Put the horizon back on each of them and a less comfortable question follows: what does any of it license an investor to do? The honest answer is nothing at all.

Anomalous with respect to what, exactly?

Start with the word. A market anomalyA documented return pattern that a stated claim about efficiency says should not be there. is not a surprise, a shock or a bad quarter. An anomaly is a return pattern that some named model of expected returns says should not be there, and the phrase carries no meaning at all until that model has been named out loud.

A train described as running late makes the point. Late is not a property of the train. Late is the distance between the train and a timetable, and two different timetables produce two different verdicts about the same train arriving at the same minute. Nobody would accept a complaint about lateness that refused to say which timetable was being used. Yet a return pattern gets called anomalous every day of the week with no benchmark stated anywhere in the sentence.

The model of expected returns is that timetable. The model says what return an ordinary holding should be expected to produce, given whatever the model treats as the driver of returns. Only once that is written down can a measured pattern sit above it or below it. Eugene Fama set out that benchmark in Efficient Capital Markets, published in the Journal of Finance in 1970.

And there is a sting in the tail. When a measurement departs from the model, what has been learned is that something in the pair is wrong. Either the market is doing something odd, or the model of expected returns was a poor description of what ordinary holdings should return in the first place. A departure is evidence against the pair of them jointly, never against the market alone, and no amount of extra data separates the two. The joint nature of the test returns below as the second of the four explanations.

The Momentum Effect: over what horizon does it actually run?

The momentum effectThe tendency of recent winners to keep out-performing over three to twelve months. is the finding that holdings which did comparatively well over a recent window went on doing comparatively well over a window of similar length. Narasimhan Jegadeesh and Sheridan Titman set it out in Returns to Buying Winners and Selling Losers, published in the Journal of Finance in 1993. Almost everybody who repeats the finding has quietly changed what it says, so the shape of their test is worth understanding properly.

The test is not about any one holding. The test ranks a large list by how each holding did over a formation window, takes the group at the top and the group at the bottom, then measures how those two groups did on average over a following holding window. Both windows sit in the three to twelve month range. The result is a statement about the average gap between two sorted groups over a stated stretch of time. The finding is not a statement that a particular holding which rose last quarter will rise next quarter, and it never was.

The everyday version runs like this. A row of food stalls outside one office building will do. Reputation moves slowly and people copy each other, so the stall with the longest queue at lunchtime this month will quite often still have the longest queue next month. The queue is a fact about the ranking of a group over a short stretch. Nothing in it says whether any single stall will be busy on Tuesday, and nothing in it says which stall will still be there in five years. Momentum is a claim about a sorted group over a window of months, and it stops being true the moment it is shrunk to one name or stretched to a decade.

The Reversal Effect: what happens when the window becomes years?

Now stretch the window. The reversal effectThe tendency of long-run winners to under-perform over three to five years. is the finding that the group which did comparatively well over a long window of three to five years went on to do comparatively badly over a following window of similar length, and the group that lagged went on to lead. Werner De Bondt and Richard Thaler reported it in Does the Stock Market Overreact, published in the Journal of Finance in 1985, eight years before the momentum paper appeared.

The structure of the test is the same shape as the momentum test. Rank a list, take the top group and the bottom group, wait, then compare the two group averages. The horizonThe period over which an effect is measured. The horizon is part of the definition of the effect, not an incidental detail. is what changes, and stretching it from months to years is not a small adjustment. Months and years pose different questions about different stretches of time.

Take it out of finance again. A student who topped the last three monthly tests is a reasonable bet to be near the top of next month's test. Five years is long enough for the reasons anybody was at the top to have changed completely, so the same student ranked against a whole cohort over five years is a much less reliable bet. Nobody thinks those two statements are in conflict. The reversal finding and the momentum finding are the same experiment run over windows an order of magnitude apart. Both can be true at once for exactly that reason.

Why do momentum and reversal not contradict each other?

Set the three effects on one time axis and the apparent quarrel disappears in about two seconds. Drift lives in the weeks after a dated announcement. Momentum lives in the three to twelve month range. Reversal lives in the three to five year range. The three windows do not overlap, and a claim about one stretch of time is simply not the same proposition as a claim about a different stretch.

Dropping the horizons manufactures the confusion entirely, and dropping them is exactly what happens when a finding is repeated at second hand. Somebody says winners keep winning. Somebody else says winners eventually lose. Both are half a sentence, and half sentences contradict each other constantly without any of the underlying research doing so.

There is a second point hiding here that is worth more than the first. If two effects with different horizons are both real, no single mechanism can be producing both of them. A mechanism that produces continuation over months and a mechanism that produces correction over years run on different logic. Two effects at two horizons is a demand for two explanations, and a reader offered one story covering both is being sold a simplification.

Post-Earnings Announcement Drift: what makes it hardest to explain away?

The third effect is the tidiest of the three, and the most awkward. Post-earnings announcement driftPrices continuing to move in the direction of an earnings surprise for weeks after the announcement. is the finding that after a company reports earnings that differ from what was expected, the price moves on the day and then keeps moving in the same direction for weeks afterwards. Ray Ball and Philip Brown documented it in the Journal of Accounting Research in 1968, and Victor Bernard and Jacob Thomas returned to it in the same journal in 1989 and found it still there.

Why should that be uncomfortable? Because the information arrived on a known date, in public, in a document everybody could read at once. A market that absorbs public information quickly should have finished absorbing it by the end of the day. A move that continues for weeks after the document was published is a slow reaction to something that was never secret.

The everyday version is a wedding invitation that arrives in the post. Everybody in the household reads it on the same evening, and the plans should change that evening. If the household is still adjusting its arrangements six weeks later in response to a card everybody read at once, something in the way the household processes news is worth examining. The card was not hidden. The delay is the finding.

One feature of drift matters more than the rest. The announcement date is fixed by the calendar and set by somebody other than the person doing the research. A researcher hunting for patterns has enormous freedom over where to look, but no freedom at all over when a company reported. Drift is anchored to a dated public event that the researcher did not choose. The fixed date strips away most of the room needed for a pattern to be searched into existence.

Market Anomaly vs Mispricing: which of the two implicates the market?

The distinction between an anomaly and a mispricing is the one everything else turns on, and it gets lost more often than any other idea in the subject. A mispricingA departure of price from underlying value. is a departure of price from value. An anomaly is a departure of returns from a model. A departure from a model and a departure from value are not two ways of saying one thing. The two claims are measured against different yardsticks, and only one of them says the market got something wrong.

Each of the two claims needs something different before it can be asserted. Claiming a mispricing requires a value. A value requires a method that produces one, and any such method rests on a whole apparatus of assumptions about future cash and what it is worth today. Valuation itself is covered separately. Claiming an anomaly requires only a model of expected returns and a measurement, and both can be had without ever forming a view about what anything is worth.

So the two claims sit at very different heights. An anomaly is fully consistent with a market that has priced everything correctly and a model that has described expected returns badly. The combination is not a technicality but the leading explanation for several documented effects. Reading an anomaly as though it were a mispricing skips the entire question of whether the benchmark was any good.

Why should any of these persist, and what are the four explanations?

Ask the obvious question. If a pattern is documented in a widely read journal, why does anybody still find it there decades later? Something that reliably paid should attract enough attention to remove itself. Persistence is a genuine puzzle, and part of the answer belongs under limits to arbitrage, where the conditions that let a gap survive are taken apart properly.

Four explanations compete, and all four deserve equal standing. For most documented effects every one of them remains live, and no measurement yet made has picked a winner. The first is that the pattern is a real mispricing that ordinary participants have not removed. The second is that the model of expected returns is wrong, so there was never anything to explain. The third is that the pattern is payment for a risk the model does not capture, in which case the extra return is a fee being collected rather than something for nothing. The fourth is data snoopingFinding a pattern by testing very many possible patterns against one history until something fits.: test enough patterns against one history and some of them fit by arithmetic necessity.

Notice how different the world looks under each. Under the second and third, the market is behaving perfectly and the description of it was faulty. Under the fourth, there is no pattern at all outside the sample it was found in. Only the first implicates the market, and it is one of four rather than the default. A reader who has settled on any single explanation has stopped too early, and settling on the mispricing explanation is the most common way of stopping too early.

What can eight quarters of an invented index actually detect?

The exercise that follows is meant to fail, and the failure is its point. The invented Palash 100 index runs across eight quarter ends: 118.0, 131.0, 112.0, 104.0, 116.0, 124.0, 121.0 and 127.0, from an opening level of 100.0. The eight levels give eight quarter-on-quarter changes: up 18.0 per cent, up 11.0 per cent, down 14.5 per cent, down 7.1 per cent, up 11.5 per cent, up 6.9 per cent, down 2.4 per cent and up 5.0 per cent.

A one-quarter momentum test asks a simple question: does a change tend to be followed by another change of the same sign? So take each change and the one after it. The last change has nothing following it, so there are seven such pairs, not eight. Get the off-by-one wrong and every count that comes afterwards is inflated.

Work the seven. Up then up, same. Up then down, opposite. Down then down, same. Down then up, opposite. Up then up, same. Up then down, opposite. Down then up, opposite. The seven pairs give three same and four opposite.

Now comes the tempting bit. Four opposite against three same looks like a lean towards reversal, and a reader who wanted to find reversal would announce it. Do not. Seven tosses of a fair coin land three-and-four or four-and-three more often than they land anything else, so this result is the single most ordinary thing a process with no pattern in it can produce. Three against four out of seven is not weak evidence of reversal, it is the exact reading a fair coin gives more often than any other, and it detects nothing whatever in either direction.

The scale gap here is what makes the point stick. The three effects were measured across thousands of holdings over decades of history. The test here has seven pairs. Eight numbers from one invented index cannot detect an effect of that kind in either direction, and no amount of staring at them changes that.

How does a practitioner read a documented effect without acting on it?

There is a professional use for all of this, and it is not the use most people expect. An analyst, an adviser or a person deciding alone reads a documented effect the way a doctor reads a study: as something that changes what questions get asked, not as something that changes what gets done this afternoon.

The first question is whether the benchmark has been named. A finding with no stated model of expected returns behind it is a description of history and cannot be anything else. The second is whether the effect was measured before costs, and it almost always was. The third is how long the finding has been in print. A finding published in 1985 or 1993 has been read by everybody competing over the same prices for a very long time.

Devika Rao uses those three questions with Meera Sundaram in a specific and rather deflating way. When Meera arrives having read about an effect, the three questions are worked through out loud, and the conversation usually ends with the observation that nothing about the holding needs to change. The professional value of understanding an anomaly is almost entirely defensive: it is what lets an adviser decline to reorganise a holding around a summary of a study. That is a smaller claim than most people want and it is the true one.

What does documenting an anomaly license?

Nothing. Three independent reasons stand behind that answer, and any one of them would be sufficient on its own.

The first reason is arithmetic. Documented effects are measured before costs. The tests are built that way. Costs are not a footnote. In the invented Palash decision log, sixty investors sorted into five groups by annual turnover paid 0.3, 0.6, 1.5, 2.5 and 4.1 points a year in dealing charges, spread and tax together. Their gross returns sat inside 0.3 points of one another, at 11.2, 11.0, 11.1, 10.9 and 11.0 per cent. Their net returns ran 4.0 points apart, from 10.9 down to 6.9 per cent. On a holding the size of Meera Sundaram's, at a cost of Rs 13,00,000/-, the lowest turnover group's 0.3 points is Rs 3,900/- a year and the highest group's 4.1 points is Rs 53,300/- a year. The top figure of 4.1 points a year exceeds several documented effects outright, and it is paid with certainty while the effect is not.

The second reason is publication. Momentum has been in print since 1993 and reversal since 1985. Everybody who read those papers has known about them for the whole of that time, and prices are set by people competing with each other. Whatever an effect did before it was published is not evidence about what it does now, and nothing turns a historical measurement into a present expectation.

The third reason is the one that closes the loop. The conditions that let a gap persist without being removed are the same conditions that stop a reader capturing it. The explanation and the obstacle are one fact seen from two sides. The conditions themselves are set out under limits to arbitrage, where the work of Andrei Shleifer and Robert Vishny in the Journal of Finance in 1997 belongs.

Put those three together and the sentence most readers want to build will not stand up. The sentence is that an effect exists, therefore it should be traded. Every joint in that sentence has already given way: the effect is measured against a model that may be wrong, the measurement is taken before costs that are certain, and the record it rests on predates its own publication. Explaining a pattern and acting on one are different activities, and the second does not follow from the first.

Meera Sundaram, Devika Rao, Palash Advisory Services Private Limited, the Palash decision log and the Palash 100 index are invented.
Educational material. Not advice on any investment, tax, budget or market position.