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Predictive Patterns in Financial Markets

by Allan Timmermann

Ever wondered why it is so difficult to forecast stock prices, movements in exchange rates, or the direction of the gold market? It is certainly not for lack of trying. Legions of professional fund managers, institutional investors, laymen, and market gurus are constantly scouring for any empirical evidence, news story, mathematical model, or computer algorithm that might give them an edge in profiting from higher returns by identifying predictable patterns in financial payoffs.

This quest for predicting future stock, oil, or gold prices will only get more intense in a world with big data. After the recent announcement that one study of Facebook Likes found that a preference for eating curly fries was linked to a higher IQ, undoubtedly we will soon be submerged in reports of novel predictability patterns.

It is exactly investors’ attempts at predicting future stock prices that make their objective of beating the market so difficult to achieve. Suppose that through data collection and extensive number crunching an investor comes up with a model that gives her a slight edge in forecasting daily stock returns. For example, instead of facing even odds that the market will move up or down, the model could improve the investor’s odds from 50-50 to, say, a 50.1 percent success rate versus a 49.9 percent failure rate.

Presumably, the investor would take advantage of this improvement in odds by buying slightly more stocks when there is a better than even chance that their price will go up the next day. As more money gets allocated to this strategy, the stock price will be pushed up on days with favorable return prospects and gets reduced otherwise. If only a single investor knows of the forecasting model, this investor might not buy sufficiently many stocks to push their price up to the point where the odds are again 50-50. However, as more and more investors learn of the model, it becomes increasingly likely that the stock price will quickly adjust ahead of the predicted event. At this point, the forecasting model ceases to work – it has become a victim of its own (past) success.

Physics & Finance

The Heisenberg uncertainty principle from quantum mechanics holds that there are limits on how precisely the position and momentum of a particle can be jointly measured. The analogy to forecasting financial market phenomena is that there are limits on how precisely stock prices can be forecasted and how much money a forecaster can make when acting on these forecasts. This is akin to the well-known observer effect from scientific studies – the act of observing a phenomenon may lead to a change in the phenomenon. The forecaster is part of the system whose law of motion she is attempting to predict.

A similar phenomenon arises in opinion polls. Suppose that an opinion poll accurately measures voters’ opinions and gets its predictions spot on. Unfortunately, when people see the opinion poll, they may decide to change their voting behavior and vote strategically (perhaps because their favorite stands to lose, and so they move their vote to another candidate). This means that the opinion poll will end up not being right – because of the effect it had on voting behavior after it got published. What is needed is a sophisticated opinion poll that takes into account the effect it has on voting behavior.

Recent research papers have found evidence that is consistent with these observations. One 2012 study1 examined 82 cross-sectional return predictability patterns. These involved ways to sort stocks by various criteria such as past returns or firm characteristics (such as price-earnings ratios), forming portfolios of the most desirable stocks, and earning outsized returns, even after adjusting for risk. The researchers looked at what happened to payoffs on such “anomalies” after knowledge of their existence became publicly available. On average the postpublication decay in predictability was found to be 35 percent, although it did not disappear entirely. Upon publication, most predictability that could be converted into abnormally high profits appeared to vanish, however.

Another study2 looked at the socalled accruals anomaly from financial accounting. The accruals anomaly holds that stocks of firms with larger accounting accruals (non-cash earnings) on average earn lower future returns. The study found that, once published, this anomaly largely disappeared as a result of inflows of capital by large investors such as hedge funds that aimed at exploiting this investment opportunity. Interestingly, the accruals anomaly did not vanish immediately after the initial study had documented its presence. It took about five years for this to happen, so outsized profit opportunities existed for a while.

These studies reveal a fundamental challenge facing researchers working on forecasting security prices. The more people become aware of your forecast – and act on it – the less likely it is that future forecasts will be accurate. Hence, there is no such thing as an accurate and stable prediction model for security prices. To be successful, the forecasting rule must account for its own impact. This means having an adaptive strategy for how to evolve and change over time. The forecasting method becomes a mutating organism, constantly on the lookout for pockets in time with predictability patterns large and stable enough to be pounced on before they self-destruct because of the markets’ learning. It is equally important for the forecasting method to know when to quit as a result of the prior signals ceasing to be accurate. Poor decisions will be made if the forecast is dominated by noise. Strategies that might have worked in the past cannot be expected to continue to work indefinitely.

Adapting to Change

In my past work, I have developed adaptive forecast combination methods that combine a predictability monitoring algorithm with a method for forecasting stock returns conditional on having identified some “local” predictability. The figure to the right and above3 uses financial and macro variables to predict monthly U.S. stock returns. The figure shows periods where return predictability is identified by this adaptive forecast combination approach. Periods with some predictability are listed at the top under “combined,” while periods with no predictability detected are listed at the bottom (prevailing mean). While some of the episodes where predictability is detected are quite long-lived, it should be borne in mind that they typically are associated with predictive power (R2-values) on the order of on the order of 1 percent or so. Hence, the signal is very weak relative to the noise.

Predicting Risk

Despite these limitations, there are several ways that stock market prediction can be successful. Most notably, forecasting has proven successful in the area of risk management. While it is difficult to predict levels or directions of stock returns, it is easier to predict squared returns. This was pointed out in the work on volatility modeling conducted at UC San Diego in the early 1980s by Robert F. Engle and was cited as a reason for the 2003 Nobel prize in Economics awarded to Engle and his UC San Diego colleague, Clive Granger, the latter for work on cointegration.

Returns on many financial securities behave in a manner similar to air turbulence: It is difficult to predict the initial jolt in turbulence, but once it has occurred, it is likely that the turbulence will persist for a while. “Fasten your seatbelts” after an initial bout of high turbulence is sound advice that applies not simply to air travel but also to risk management.

While financial forecasts can be self-destructive, they can also be self-fulfilling, at least for a while. Suppose that investors act on forecasts of higher future prices by buying more of an asset, thereby bidding up its price. If there is considerable uncertainty about the price in the first place, the increased stock price could itself induce higher future prices if there are many so-called momentum or feedback investors who project past price patterns into the future.

Which pattern will emerge – self-destructive or self-fulfilling – is a matter of the degree of uncertainty surrounding an asset’s “fair” price and the proportion of rational versus momentum or feedback traders. No prize for guessing which type of investor dominated in the recent Bitcoin bubble.

Contrast the difficulty in forecasting stock returns with another task such as forecasting the growth of the U.S. economy. Suppose that some experts are very good at this task and so produce more accurate forecasts. Will this lead to a similar demise in their forecasts? Probably not, although it might. For example, if the forecasts came from the International Monetary Fund, then predictions of low future growth rates might cause a country to change its fiscal or monetary policy, thereby leading to a less dismal outcome. However, in general, we would not expect such ‘observer effects’ to be as large as in the financial markets, where prices can move very rapidly.

Perhaps it is really true that economic forecasters were created to make weather forecasters look good. In fairness, weather forecasters do not face the difficulty that publishing their forecasts leads to a change in the weather. Bear this in mind the next time you check the weather forecasts or when you hear a self-professed stock market guru pronounce with great confidence the latest forecasts or stock pickings.

Allan Timmermann is the Atkinson/Epstein Endowed Chair Professor of Finance at the Rady School of Management and also holds an appointment as a professor in the Department of Economics at UC San Diego. He uses a mix of theory, data, and econometric techniques to understand the behavior of prices and expectations in financial markets. His objective is to understand what determines the movement of security prices and to use this in managing risk, forming portfolios, and forecasting future price movements.


  1. McLean, R.D., and J. Pontiff. 2012. “Does Academic Research Destroy Stock Return Predictability?” Unpublished working paper, MIT and Boston College.
  2. Green, J., J.R.M. Hand, and M.T. Soliman. 2011. “Going, Going, Gone? The Apparent Demise of the Accruals Anomaly.” Management Science 57: 797-816.
  3. Timmermann, A. 2008. “Elusive Return Predictability.” International Journal of Forecasting 24: 1?18.