The Long-Term Market Memory: Momentum Effect and EMH Cracks.
This question has troubled scholars and traders for as long as stock markets have existed: does the stock market form some kind of pattern? Well, in 1900 a French doctoral student proposed an absurd idea, which was met by the utmost of confusion. What if we were to model the price of a security through the principle of a drunk man walking. Each step of a drunk man is completely random, just barely holding balance – can we say that the market takes a step, each independent from the next? A step with mostly no direction, no memory, and one which tells us nothing about the previous day or the following day. Louis Bachelier was given a bare pass on his doctorate paper, and his work sat untouched for nearly half a century.
As you can imagine with most groundbreaking discoveries, the paper was rediscovered in the 1970s and hardened the idea of the random walk of the stock market. The so-called random walk then formed into something that is taught to finance students all over the world today – the Efficient Market Hypothesis (EMH). Put simply, EMH is our best idea of how the stock market and its participants behave. It states that the markets, and specifically asset prices, reflect near perfectly all available information. Consequently, from this theory, it is technically impossible for an investor to beat the market on a risk-adjusted basis in the long run. So, this idea became a sort of doctrine that prices of assets already contain everything that there is to factor; therefore, past prices essentially did not matter to predict the future in any systematic way. Burton Malkiel, a legendary economist and financier from Princeton University, told a generation of investors that a blindfolded monkey throwing darts at the stock listings would do about as well as the professionals. Indeed, an astounding humiliation for the field: most of what passed as techniques was purely incorrect.
Burton G. Malkiel (b. 1932), American economist and professor at Princeton University - Author of A Random Walk Down Wall Street (1973), one of the best-known investing books ever written, now in its 13th-plus edition.
You may be asking yourself, but then why would we even be discussing this topic if there wasn't anything of substance? And you would be correct, because there is a principle that has been refusing to die and has tortured academics for the past thirty years. It's so simple that it sounds incredibly insulting: assets that have done well over the past three to twelve months tend to keep doing well over the following months, and assets that have done badly tend to keep doing badly. Winning companies continue to win. And this is known as the momentum effect, and it is probably the most awkward fact in finance. Eugene Fama even won the 2013 Nobel Prize over his empirical work that built the efficient market hypothesis (EMH). The very people who wrote this in 2008, Fama and Kenneth French, stated the momentum as a "premier anomaly." By now we can guess that the architect of market efficiency calls something an anomaly, when the word is doing a great deal of work. So how do we proceed to tackle this anomaly? We run an experiment on our own data and check on our findings. 155 years of data on the S&P 500, then replicating the classic winners vs losers on five years of daily prices for 505 U.S. stocks.
We established the roots of the theory, the main critiques, and the foundational basis for our exploration. Momentum comes in two flavors; both are claims about market memory, and they differ in what the market is remembering against.
The first version is relative momentum. We rank every stock in the market by how well it performed over the last three to twelve months. Momentum dictates: buy the ones at the top and sell the ones at the bottom, and wait. Narasimhan Jegadeesh and Sheridan Titman did so in 1993, taking a sample of stocks and applying the same method discussed above. The results were about 1% per month in growth for a period from 1965–1989. Not a yield of picking prosperous companies, but one of sorting. An important technicality to mention here is the way that we look at the twelve-month period. Within the ranking window, the twelve months end one month ago – skipping the most recent month entirely. That gap exists because very short-horizon returns tend to reverse, and leaving the last month in the signal contaminates it with the opposite effect.
The finding was rather strange, and enough so that Mark Carhart even included a momentum factor in the Fama-French model in 1997. That factor has sat in the premise of the model since it was introduced. A fourth term to the three-factor model that nobody quite knows how to justify. Fama and French themselves never accepted it. When they expanded their own model in 2015 they added profitability and investment - and still left momentum out. A fourth term that the entire industry prices and its own authors decline to endorse.
The second variety of momentum is more absolute. With this principle the asset is measured against nothing but its own past. If the Nasdaq has risen over the twelve-month sample, then it is much more likely to rise next month than if it had fallen. Undeniably, a much easier approach that does not require ranking, short positions, or peer groups. In 2012 scholars Tobias Moskowitz, Yao Hua Ooi, and Lasse Pedersen found that across nearly one hundred futures markets the idea remained. These futures include equities, bonds, currencies, and commodities. There is even a paper by the name of "212 Years of Price Momentum" which tracked stock prices all the way back to 1801. With every single time period, the momentum effect is present and undeniable – and that is the issue itself. A property that occurs so deeply is either a very concrete fact about human nature or a deep flaw in the way we test.
Another important consideration is the constraint we hold for this article's test. We can imagine momentum as a sort of wave in the sea, that doesn't necessarily hold on forever. The "wave" only holds for a specific time window. Over days, prices tend to bounce back against themselves. Over three to twelve months, they continue. In 1985 Werner DeBondt and Richard Thaler documented, over a three-to-five-year period, another reversal, or what they called the long-horizon overreaction. So, any test that we conduct on this idea will have two clauses: the drift of the wave and the point where the wave expires. A pattern that only goes up is a bull market, and a pattern that rises, fades on schedule, and then turns negative is a memory with a shape.
For the sake of simplicity, we will start with the easier of the two varieties – the absolute one (market against its own). For this test we need only one price series, and a reliable one too. We choose Robert Shiller's monthly S&P 500 composite – 1,866 months from January 1871 to June 2026. The twelve-month look back and the one-month forward return consume thirteen of those, leaving 1,853 usable observations.For each month we asked what the index had done over the previous twelve, then looked at what it did next.
Here we will have a null hypothesis which is worth being stated clearly, because it gives dimension and meaning to our test. Sorting months by their trailing year return does not utilize any extra information except past prices. Applying what we know, if a random walk were to be true, sorting this series would give us forward returns of every bucket coming out the same. Divide the 1,853 usable months into five equal-length groups, from worst year to best year, and the following month looks nothing like that. The shape on the graph from perspective resembles a staircase, so we will refer to it as the staircase climb.
From what we can observe, the staircase climbs almost with no interruption. Following the worst fifth of trailing years, the market lost an average of 0.18% in the following month. Accordingly, after the best fifth month of trailing years, the market returns 1.04%. Statistically, the unconditional sample mean across every month is 0.48%. Knowing nothing but last year's return moves your expectation a full percentage point from one end of the sort to the other.
If we were to collapse the test into a simple sign diagram – following a positive trailing year, the market rose in 62.4 percent of months, averaging +0.83 percent. Following a negative trailing year, it rose in 48.3 percent of months, averaging −0.16 percent. The important part here is the second number: after a losing year, the average month is not worse than the average, but it is negative. A negative figure is notable here; the obvious objection to everything above is that stocks tend to drift upwards and we have discovered nothing but gravity here. The even stranger part is that gravity would not explain why in one instance our "coin" lands heads 62 percent of the time and the other state 49 percent. We observe a spread of 0.99% per month with a Welch t-statistic of 4.58 across 155 years. If we were to believe the idea of previous prices carrying no information, the chance of that gap being this large, with a t=4.58 is on the order of 1 in 200,000.
What's even more bizarre is not the drift of the data itself, but the shape of the graph. A fair test shouldn't only find the continuation but the very point that the graph stops being continuous. Therefore, we extend the holding period after each signal and measure the advantage decay.
With a one-month horizon, the year advantage is 12.3 percentage points per annum (t=4.56). At three months it has fallen to 6.9 (t = 3.76), for six months, to 3.9 (t = 2.94). By twelve months it is gone and marginally negative at −0.5. Past that the sign flips and stays flipped: −1.7 points at two years, −1.2 at five.
While this is all complicated data and numbers that do not necessarily tell us anything at a moment's notice, we can go back to the theories we discussed earlier. If we were to read this sequence again, this data set produces two separate anomalies that were coined as theories and we discussed above. The momentum continuation at the front by Jegadeesh and Titman and the long-horizon reversal at the back by DeBondt and Thaler. The front of the curve is: a t of 4.6 across 155 years is not a coincidence. The back of it is a shape we can see and cannot yet prove, and we would rather say so than let the symmetry cause ambiguity. Turns out that Malkiel's random walk doesn't simply fail but dies with structure.
Having a strategy to predict is a great tool for a financier, but I believe that the burning question concerning all of us is this: if last year's return really does bend next month's odds, can we stand on that fact and make money? Well, we built a rule the evidence allows and tested it across the same period of 155 years.
The technical rule remains: at the start of each month, we look at the index's trailing twelve-month return. From here we follow another basic principle – if the market predicts positive, we hold, and if the market signals red, we sit in cash. We have even included an additional aspect which veers away from reality but makes our experiment that much harsher to the Momentum Effect. During the time we sit in cash we would not be earning any dividends or profits on it, unlike what a real investor would do – no treasury yields, no interest accounts, literally zero profit. So, we will take the most punishing assumption to observe if the effect really allows us to profit.
Unfortunately, we will state the saddening part out loud: on pure raw return, the rule will lose to the buy-and-hold position. B&H compounded 9.1% per annum for the entire duration of our sample, whereas the trend rule managed to compound only 8.4%. Having a pile of cash even in good months costs a lot, and no amount of clever investment tactics will mitigate the lack of growth on the cash.
But for that 0.7% difference you bought something else entirely. If we look at the statistical data on the two different strategies, the numbers speak differently. The trend rule's volatility was 9.8% per year, while the buy-and-hold's was 14.1% per year. Strictly speaking, the peak-to-trough loss was 38% for the trend rule and the opponent's was 82%. As a matter of fact, this constitutes a near-complete wipeout from 1929 to 1932. It took nearly twenty-five years to recover from this near-wipeout for the buy-and-hold position. As to why this happens, there is a single plausible explanation: the rule itself allows for the user to steer away from bad years. As expected, following a financial crash, we wouldn't expect to have good months exactly following the downturn. The rule doesn't forecast good times but sidesteps the worst ones.
With that in mind, we go back to the foundational pillar of finance – at the level of the whole index, the story isn't about return but more about risk. The model isn't going to beat the market in the long run, but it will keep you from catastrophic events that are likely to wipe out your portfolio. So, back to reality: a rational investor wouldn't just sit on cash and wait for the correct time to buy; they would invest in accounts with interest or yields from treasury bills. If we were to pay a realistic yield to cash, the rule will roughly match the buy-and-hold on return while keeping the investor safer. We opted to report on the worst possible version just to avoid the flattery of a magical rule that beats the market.
Momentum was not discovered in a single index through measuring its own history. It was more of a covariation method where stocks were measured against each other – the relative memory. In simple terms, winners and losers are ranked side by side. In order to close the loop, we ran the original experiment ourselves, and the contrast we saw in the previous section is the most important takeaway from this article.
The method used is rather mechanical and straightforward – taking daily closing prices of 505 constituents from the S&P 500 in the period Feb. 2013 to Feb. 2018. At the end of each month in the period, we ranked every stock by the return it yielded over the twelve months, with the same technicality of skipping the most recent month. We sorted the ranked stocks into ten deciles, held the top decile and the bottom decile in equal weights for the coming month, and then did the whole thing again the next month. Forty-eight times over.
Looking at the data, we can make the following implication: by every measure of direction, the method worked. Last year's winners beat last year's losers. The advantage equates to 0.43%/month – meaning a little over 5% per annum. If we take a dollar and we place it in the winning decile, month by month it will grow to $1.61, whereas the same dollar in the losing bracket will only reach $1.27. Interestingly, every formation window we tried, from three to twelve months, produced the same positive spread. Winner-minus-loser return had a negative correlation, like the market itself, at around −0.23. It made money during the selloffs of August 2015, behaving exactly like the momentum spread suggests. In magnitude, temperament, and shape, we had produced the same anomaly.
Rather problematically, the t-statistic on our winner-minus-loser spread is 0.6. Over the period of these 48 months, we cannot statistically distinguish momentum from luck. While the reason isn't so obvious, there is a logical explanation: momentum isn't fake, but very faint. Since the market is extremely loud and unpredictable, the faint edge that momentum has is of the order of one percent a month, while the noise around it is approaching six percent. To separate a signal that is so small from this much static requires many observations. Enforcing the statistical certainty would mean stretching time even further. In essence, you would need two decades of data before the edge from the momentum effect reliably clears the statistical bar. Five years isn't enough, and for the same reason, Jegadeesh and Titman needed twenty-five years to make their case, other researchers went as far back as 1801, and our own test ran across a century and a half. The phenomenon appears regardless of time, but the length of the ruler (the test) dictates whether we could see it.
Which leads us to a few important, final test considerations. The honest version of the result we stated has some admissions. Firstly, the firms we used, or as we call our universe, were those still in the index in 2018. Since then, some companies have been delisted; therefore the very worst losers are missing, which flatters the loser line. This would imply our spread line is more likely understated than exaggerated. Further, 2014 to 2018 was a placid bull market, a kind of market that doesn't pay well and doesn't punish you with its worst. The anomaly is found, but with five years we cannot prove it.
Since we have our test and our observations, we must have some sort of narrative to explain the momentum effect. Here is where, after thirty years, our field has split into three camps trying to explain it. The debate isn't about the existence of the phenomenon, but about what kind of event it is.
The behavioural camp of scholars and professionals claim that momentum is a mistake caught in the act – a mispricing of assets happening in slow motion. Because information doesn't reach everyone at the same time, it spreads through the market unevenly. Analysts anchor on their old estimates and revise them grudgingly, a little at a time. Private investors tend to fall prey to another phenomenon called the disposition effect – the well-documented habit of selling winners to lock in a momentary gain, while clinging to losers for too long in order to avoid losses. Good news is absorbed into rising prices too slowly, and bad news into falling prices too slowly. Both frictions drag the adjustment out over months instead of seconds, and a drift is exactly what a delayed adjustment looks like. Then, as the trend becomes obvious, a second force takes over: overconfidence and herding push the price past where it should have stopped, until it eventually snaps back.
But the important consideration is what the second force buys us. It's not just an explanation for the continuation over the 155 years, but it gives justification to the reversal on the other side. The horizon chart in section two (one rising for a few months and then going negative at two and five years) isn't just an outlier for the theory to accommodate, but the theory's own prediction. Under reaction from the market side produces the drift, while the overreaction produces a reversal. On this view, the term structure of momentum returns is a very quantifiable pattern, being a two-stage adjustment process. The correspondence between the shape of the anomaly and the shape of the proposed mechanism is the camp's principal source of support.
In our case, the risk camp compensates for a specific tail risk through the momentum returns. Looking at the winner-minus-loser portfolio, we observe consistent stretches of positive movement, accompanied by low-volatility returns punctuated by severe, infrequent losses. Tracing a decline in the market, the loser stretch becomes concentrated in high-beta, distressed firms. Equity in such firms becomes a call option on the firm's survival. Accordingly, during periods of sharp recovery of the market, said securities appreciate disproportionately, imposing large losses on a short-leg portfolio. Daniel and Moskowitz (2016) document the two largest such episodes: approximately −91 percent over two months in 1932 and approximately −73 percent over three months in 2009. Considering everything mentioned above, the interpretive question – whether these drawdowns represent an adequate/rational premium for bearing crash risk or the periodic failure of a crowded position – remains the key unresolved issue between the two camps of the momentum effect.
By contrast, the data-mining hypothesis stands on little ground when looking at the evidence. Our phenomenon has been documented out of a sample about a century in each direction from the original study. It occurs in equity, fixed income, currency, and commodity markets, in most markets, and most definitely for three decades following the original publication. What gives us assurance is that by now arbitrage capital could have competed the effect away, and indeed its magnitude has declined as more participants join, furthered by consistency with partial correction of the genuine mispricing, but it has not disappeared. Yet, three decades later, the model still operates and the premium persists, while the two camps have not yet reconciled.
How can we summarise this storm of data we just witnessed? The random walk made a very simple and straightforward claim: the past is a variable that does not give us any information regarding the future. Set against 1,853 months of American stock market history, the random walk does not survive the claim. What predicted the drift was the trailing year and the month that followed. Subsequently, the drift fades on schedule, and with a longer horizon scope it reverses. All in perfect coordination with how a two-stage human-error theory says it should behave.
While this all sounds perfectly sound, pegged against our data – none of the aforementioned properties of momentum hides a fortune waiting to be collected. The five years we explored did not clear the bar that should separate a real edge from a lucky one. All of the bleeds that the market experiences aren't mere mistakes but the price we pay for admission, for our inability to trade efficiently. Arguably, the most prominent conclusion we can derive is the fact that for near a century the orthodoxy that the past didn't carry information was false. And the reason isn't mathematical, but the very human errors we operate on. Prices of assets do not follow a random walk, because they do not move on their own – they are moved by people absorbing the news slowly and reacting inadequately, selling soon-to-be winners. The market is efficient enough to humble almost everyone who tries to beat it, and human enough to leave a trail while doing so. Momentum is that trail, very slight but unmistakable, still visible after 155 years.
