Friday, February 07, 2014

Does trend-chasing explain financial markets?

"How can you know, how can you know/ Which is which, who's doin' what?/ I guess that you can ask 'em"
- Dan Bern, "Tiger Woods"

A lot of interesting unexplained phenomena in finance are related. Bubbles. Long-run reversion. Excess volatility. "Overreaction". All of these have to do with the general thing known as long-run stock return predictability. In other words, it really is possible to know when stocks are "cheap" or "expensive". This is one of the insights for which Robert Shiller won the Econ Nobel this year.

But why do stock prices mean-revert in the long run? This is the subject of an ongoing controversy - perhaps the most important controversy in finance. Some people say that it's because of time-varying risk premia with Rational Expectations; others say that it's because of people's incorrect information processing, and expectations are non-rational. In other words, it could be because what people want is kind of funky, or because how people think is messed up. But without some kind of independent measurement of either A) people's desires, or B) people's expectations, we'll never really resolve the controversy.

So that's why this 2012 paper by Andrei Shleifer and Robin Greenwood is so interesting. They take an extremely simple approach toward measuring people expectations: Just ask people what they think is going to happen! Actually, what they do is to take data from six different surveys of the stock market expectations of individual investors. For those who don't know, this is a pretty maverick thing to do; financial economists traditionally have not trusted survey data to reveal investors' true expectations.

So the first and most obvious question is: Do these "survey expectations" represent people's real beliefs?" The authors answer this in two ways. They first check that the six survey measures are correlated with each other; in fact, they are strongly correlated.

Second, and more importantly, they check that survey expectations are consistent with investors' actions. In fact, they are strongly consistent. Here's a graph displaying reported expectations (according to one of the surveys) alongside the amount of money flowing into equity mutual funds:

As you can see, when people say they expect stocks to do well, they actually put money into stocks.

So it seems as if you really can measure people's expectations about stock performance just by asking them! That is potentially big news for the future of finance research.

OK, so now we get to the really interesting question. What causes people to expect higher stock returns? The authors are behavioral economists, so they try out a behavioral explanation: "extrapolative expectations", also known as trend-chasing. In other words, when recent returns have been high, people expect the recent "trend" to continue, and buy accordingly. (This kind of expectation formation definitely doesn't fit the Rational Expectations hypothesis, but it could still fall under the looser heading of Bayesian rationality, if there is enough underlying structural change in the market.) Trend-chasing - and causes of trend-chasing, such as herd behavior - has received a fair amount of attention in the behavioral literature, though perhaps not as much as it should.

In fact, Greenwood and Shleifer find that the Extrapolative Expectations hypothesis seems to fit the facts very well:

What about the big alternative explanation: Rational Expectations? Well, Rational Expectations suggest that people will expect higher returns when expectations of future fundamentals are high. The authors plug in various measures of fundamentals and find that they don't really help explain the survey expectation measures.

So the authors conclude that Extrapolative Expectations beat Rational Expectations. That result would imply that trend-chasing by quasi-rational investors is the big force behind long-term stock return predictability. If this result is true, it's a big step toward resolving finance's biggest mystery.

So what do I think of this result? I'm very excited about the finding that survey measures of expectations are for real; I had always thought they were extremely unreliable. The finding that expectations are extrapolative doesn't surprise me, though it doesn't look like what we see in "bubble experiments" in the lab.

But I actually have a problem with the theory in this paper. The authors conclude that firms' equity issuance must respond to investors' trend-chasing, because someone needs to take the other side of the trade. But while this may happen, it leaves the turning points unexplained. At some point, prices stop going up and start going down. Since these turning points are brief compared to the trends at the observed frequency, they won't kill the regression results, but the authors' theory can't explain why they happen. Why don't trend-chasing investors push prices to infinity as soon as they see a sufficiently long up-trend?

It seems to me that there must be a role for hetergeneous investor expectations. Investors can't all be the same, and "fundamentalists" can't all be firms. There must be some subset of investors that, at some point, decides that prices are just too egregiously out of line with fundamentals, and acts together to kill the trend.

Interestingly, this is exactly the refinement that Greenwood and Shleifer make in this 2013 paper, in which they team up with Nicholas Barberis and Lawrence Jin. They make a theoretical model where some investors are extrapolative trend-chasers and some are rational. When the trend-chasers push things too out of wack, the rational fundamentalists step in to correct things. But the result is still a stock market that swings too much. So I suggest reading that paper as well. (Note: Papers in which trend-chasers interact with fundamental traders are not new; for example, see this paper by Hong & Stein or this more recent one by Mark Thoma. The Barberis (2013) paper is new in that it derives CAPM-type equilibrium asset pricing implications.)

So here's the really important question: If people really are trend-chasers, can rational investors make money by exploiting this fact? As John Cochrane shows here, simply taking advantage of long-run stock predictability may not make you a lot of money. You can only strike it rich if you can time those turning points. And simply measuring the aggregate expectations of investors will not be enough to time those turning points (especially because, as the authors show, by the time expectations show up in the surveys, the money is already moving).

Can it be done? Could models be constructed to predict the peaks of bubbles? If so, we would expect those models to gain in popularity until bubbles themselves are suppressed, thus eliminating the models as money-making tools and saving the economy from irrational asset price swings in the process. But I'll believe it when I see it...


  1. They make a theoretical model where some investors are extrapolative trend-chasers and some are rational. When the trend-chasers push things too out of wack, the rational fundamentalists step in to correct things.

    I have a slightly different take. Not a model, but a narrative. Individuals have a varying degree of rationality. When prices are too low, relative to fundamentals, it's because they have been pushed too far down by irrational action in the market.

    Then, on the upsweep, buying is a highly rational decision. Until it eventually goes to far. People gradually realize the price doesn't look attractive, and eventually, the buy side of the trade dries up. That's when the panic happens. At first, selling is rational. Once it has momentum, it overshoots rational value on the downside. Eventually the sell side dries up, and it starts all over again.

    We're all human, all semi-rational, all subject to moods, anger, ecstasy, despair, and changes in atmospheric conditions that vary our rationality over time.

    Is there a real central limit tendency, or a complex series of long and short cycle variations oscillating around a central limit?


  2. That Dan Bern quote is a good one, but it's, like, the single least interesting line in that song.

    1. Actually it's my favorite line. But yeah, they're all pretty awesome. :-)

    2. Oh, no doubt! But cf., "On my really good days, they swell to the size of small dogs." One of those lines, but not the other, is going to inspire the well-intentioned reader of first impression to think, "How interesting, I wonder what that's about. To Google! oh no oh dear god!"

      That, or the digressive interlude about Madonna...

  3. A funny thing about what investors say: high expected returns are associated with low subjective risk. A bull isn't somebody who thinks he's earning a rationally determined risk premium, it's somebody who thinks there's a free lunch available.

    1. This is the next frontier in survey research, I think... :-)

  4. Anonymous3:50 AM

    You state "So here's the really important question: If people really are trend-chasers, can rational investors make money by exploiting this fact?"

    This, I believe, is exactly what happens. But these rational investors are not rational in the sense that they look at the fundamentals. They are rational in the sense that they know that the market tends to swing and that this offers possibilities to make profits. Thus, they look for swing patters to exploit. They try to jump in after market bottoms , ride the trend while it is developing, and jump off when they think the trend is nearing its end.

    In this process of swing trading, money is effectively changing pockets from the less aware market participants to these swing traders. In other words, from the losers of the game (which are probably not even aware that they are in a game) to these winning swing traders. Thus, the rationality of these traders is not the rationality of the fundamental investor, but the rationality of the game player.

    1. Yep, and in a lot of the models in this literature, that's exactly what ends up happening!

    2. Anonymous12:49 PM

      You ask “Can it be done? Could models be constructed to predict the peaks of bubbles?”

      I believe that this is happening all the time, not by scientist, but by traders. Trading is an expectations game. Traders try to predict what others will do and, if they believe the odds are at their side, they will enter the market, long or short. But they will normally use a stop loss, because they could very well be wrong. And if such stops are triggered, new patterns could be created, which could be exploited by other traders.

      All in all, I believe the markets are some sort of arena where traders try to outsmart each other and which change all the time due to the interactions of these traders. And thus, the characteristics of these peaks (and bottoms) could very well change all the time.

  5. I think you would like Soros' Alchemy of Finance. Soros' Theory of Reflexivity tries to explain the relationship between market participants' sentiment and fundamentals. He wrote a brief essay for the FT that explains it in part, though the book obviously has more depth.

    1. Should've added this quote: “The prevailing wisdom is that markets are always right. I take the opposition position. I assume that markets are always wrong. Even if my assumption is occasionally wrong, I use it as a working hypothesis. It does not follow that one should always go against the prevailing trend. On the contrary, most of the time the trend prevails; only occasionally are the errors corrected. It is only on those occasions that one should go against the trend.” – George Soros

  6. Anonymous10:20 AM

    What most any market participant would say upon reading this post:


    Seriously, though, Noah, you didn't mention arbitrage conditions. Theoretically, all it takes is one investor with rational expectations to stop trend-chasing. This fundamentalist would have infinite access to margin with which to short stocks, as well as no margin calls, no ornery clients, and the ability to sleep eight hours a night while being billions in the hole. Of course, such an investor doesn't exist in real life. To which any market participant would respond:


    1. That's right, but remember, Shleifer has a large body of work in which he explores how limits to arbitrage affect markets...

    2. Long Term Capital tried to be such a rational fundamentalist...those pesky margin calls got in the way.

    3. ZOMG thars quants and technical traders out there making a mockery of Lucas! Who knew?

    4. Diego Espinosa12:56 PM

      Since you're buying the idea of herding behavior...

      Wouldn't the main transmission for Fed policy be its effect on that behavior?

      For instance, QE signals to bond traders that they should herd into duration. Forward guidance tells them the liability side of the carry trade is guaranteed. Have at it!

      So, if the above is true, where does that leave monetary policy? I'd say it causes the diversity of the financial ecosystem to fluctuate (more like mimicry than herding, so as not to mix metaphors here). These fluctuations take it from robustness to fragility and back. The shift from fragility to robustness, of course, is what we subjective observers label a "crisis".

      In this formulation, the 2007 crisis was a short-term repo panic caused by a Fed-induced carry trade, which lowered ecosystem diversity to unprecedented levels and away from the strategy of using insured deposits. "Measured pace" and "extended period" were the "take duration" signals, and shadow banking (funding short, lending AAA long) was the mimicked strategy.

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  8. Anonymous1:58 PM

    Tiny note: the third author on the paper by Barberis, Greenwood, Jin, and Shleifer is Lawrence Jin, not Robin Jin.

    1. Ahh, thanks. Fixed!

    2. Predating Hong and Stein and others in generating exactly the sort of model you prescribe were those coming out of the early 90s Santa Fe stock market model exercise. Two published articles on that with models of these types changing their relative balances over time due to changing relative returns with switching points and the works are

      William A. Brock and Cars H. Hommes, "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, 1998, 22, 1236-1274

      Blake LeBaron, W. Brian Arthur, and R. Palmer, "Time series properties of a artificial stock market," Journal of Economic Dynamics and Control, 1999, 23, 1487-1516.

      I could add a paper in Macroeconomic Dynamics by Mauro Gallegati, Antonio Palestrini, and someone else (guess who) from 2011 along similar lines that showed one could get not only speculative bubbles and crashes, but also those curious "periods of financial distress" that have happened in the vast majority of major bubbles where prices decline for a period past the peak before they finally crash...

      Barkley Rosser

    3. Great links, thanks!!

    4. You're welcome, Noah. I would note that this most recent study you cite is based on actual surveys of expectations rather than a simulation model. Surveys are gradually becoming more respectable in econ and finance, after a long period of simply ignoring them, arguing that behavior more important than what people say, even if we find what they say helps explain behavior. One area where surveys have been used a lot has been the happiness literature, although that is controversial and has complications.

    5. This survey work is great to see. And not surprising, I think, unless you're predisposed to disbelieve it!

      You probably already know these, but some other early papers on interaction of trend followers and fundamentalists (that I happen to know by chance, since I'm hardly an expert on the literature) are:

      Lux and Marchesi (
      In this one, trend followers become more likely to get skittish and turn into fundamentalists if a trend goes on too long. Likewise, fundamentalists are more likely to feel like losers and jump in to profit from a trend if it continues for a good while. So the two types aren't wholly fixed; people flow from one type to the other and back.

      And of course one of the earliest papers by Alan Kirman in 1992:

  9. Anonymous3:23 PM

    Here is a good starting point:

    the LPPL model in my practical experience is the only one who had decent ex-ante performance. See also

    The latest example was the SP500, which followed a textbook bubble

    Hope this can help the discussion.

  10. Our research has found that if we want precise and confident tactical asset allocation decision making, we must transcend / discard the use of the "usual suspects" ( data sets that have been regurgitated for the last 25+ years in the financial world : sentiment, fundamental, economic, most technical analysis.) and concentrate on price action itself. We believe that as long as there is a Federal reserve, a 4 year election cycle, and free stock market mechanism, then there will be repeatable and consistent "effects" that occur in the markets.
    God article !

  11. On exchange markets, the Post Keynesian theory of exchange rate determination, based mainly on the work of John Harvey in the early 1990s, already recognizes the importance of heterogeneous agents. See the following works by Harvey: "A Post Keynesian view of exchange rate determinations" (Journal of Post Keynesian Economics, 14(1), 1991); "The institution of foreign exchange trading" (Journal of Economic Issues, 27 (3), 1993); and "Currency, capital flows and crises". Also, along these lines, by Imad Moosa, "International financial operations" (chapter 8) and De Grauwe & Gimaldi, "The exchange rate in a behavioral finance framework" (chapter 2).

  12. Check out these two blog posts for I guess "proof" that you can make money with an autoregressive model in the stock market -
    I realize that this message comes to many as might a communication from the Flat Earth Society.
    The problem is that what I maintain is completely (a) transparent, and (b) replicable. I develop autoregressive models with Matlab (and Excel spreadsheets earlier), using data from the early 1990 through early 2008. Then, I apply the model coefficients to next-trading-day forecasts of daily returns of the SPY (or earlier S&P500), showing that a simple trading program thus constituted beats a Buy & Hold strategy. I also have explored whether these successes could be due to "pure chance" and found that to be an unlikely explanation.
    I think your post on this research is an outstanding contribution, and thanks.

  13. I would assume period doubling leading to a chaotic end. Someone did a paper on prices going super exponential prior to a crash.

  14. Good post overall, but I take issue with:

    "it really is possible to know when stocks are "cheap" or "expensive"."

    I don't think it is as easy as you imply. For example, are stocks "cheap" or "expensive" right now? Inquiring minds want to know!

    Before you answer, consider that if stock prices "mean revert," how do you know what mean they revert to? Should we use the last 30 years, or go all the way back to 1870? Maybe the last 30 years were anomalous, but on the other hand maybe 100 years ago things were just different in a long list of ways. And consider that we used to have something called the "equity premium puzzle" that said (basically) that the long term average observed price level for stocks was too low to make sense. And consider that other things like demographic trends will probably play a roll, as will inflation and real interest rates, and accounting standards which define earnings, etc. etc.

  15. Noah,

    If I might ask about Fama's explanation for the apparent mean-reversion over perhaps a century or two (see Wharton's Jeremy Siegel's "Stocks for the Long Run", with a data set going all the way back to 1802!). Is he saying that yeah, it does mean-revert, but still the market is efficient – Long live extreme libertarianism! – It's just that people's risk aversion keeps changing and changing back again cyclically and regularly, and that's what makes the expected return keep going up and down, and mean-reverting.

    If so, this does not look efficient to me. If everyone suddenly gets very risk averse, and the expected-return shoots up – but everyone being forward-looking, ultra rational, know all public information, prefect expertise, supermen, knows that in coming years they will shift back again and be not so risk averse, as always happens. And then they will kick themselves for not having bought when the expected return was so high. Then being so forward looking and perfectly rational and expert, they will buy now.

    If you're scared to do something now, but you know you will be glad you did it in the future when it won't be available anymore, then being a perfectly forward looking superbeing, as libertarians know everyone is, with perfect self-discipline, calculating ability, and expertise, you will do it now.

    Is this what Fama is saying? If so what about the potential flaw I ask about?

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  17. Check the easily checkable: the real question here is this: does technical analysis work or is random walk correct? The simplest way to answer this is simply to test this: if today's price is higher than yesterday's, buy, else sell and sell short. Do this with the SP500, and you will find that you could have made money for a very long time, then suddenly, in the first years of this century, it stopped working. The peak returns for this simple and stupid method were in the year 1975.
    So, that means technical analysis "worked" right up until this century. Why? Interesting question.
    Here's another one: recently, this "method" has begun to more or less break even again. Does that mean technical analysis is going to start working again? And if so, why?

  18. it could still fall under the looser heading of Bayesian rationality

    Trend following may make sense if an investor thinks: (1) he is not smart enough to do fundamental analysis; or (2) there are too many unknowable unknowns to do fundamental analysis; or (3) the financial statements issued by publicly traded companies are not reliable enough to do fundamental analysis.

    The one certain fact in a world of smoke and lies is the recent performance of the market.

  19. why Aren't Markets Themselves Surveys Of ExpectationS?
    WhicH As You Point Out Brings You Right Back To Inflections Being The Challenge.

  20. There must be some subset of investors that, at some point, decides that prices are just too egregiously out of line with fundamentals, and acts together to kill the trend.

    You will have subsets of investors who: (1) have a fixed allocation between stocks and bonds and periodically rebalance; or (2) when money is flowing into stock mutual funds pull money out and vice versa. Those investors are not really trading on fundamentals but rather are reacting to movements in the market in a way which tends to act against the trend.

  21. Great post.

    "The authors conclude that firms' equity issuance must respond to investors' trend-chasing, because someone needs to take the other side of the trade. But while this may happen, it leaves the turning points unexplained."

    This is a particularly important point and should be researched. My own feeling is that the points at which Private Equity guys (Schwartzman etc.) launch public or take private, on some or all of their holdings, mark the turning points (top and bottom respectively)

    "You can only strike it rich if you can time those turning points. And simply measuring the aggregate expectations of investors will not be enough to time those turning points"

    This is a call to shorter-term movements and a number of buy side firms have developed timing models that predict correctly for 60%-80% of the time for brief periods, then break down, and the search for the next Timer starts.

  22. The paper is interesting. The problem with all survey research however is that the word "expect" means a different thing to laypeople than it does to academics. We are so indoctrinated that we forget the average person does not know that statisticians coopted the colloquial term "expect" to the mathematical concept "true-measure conditional mean." If you ask a survey respondent what he "expects" stock prices to do, you follow up with "is that true measure or risk neutral measure?" and he responds "wtf?" well, we don't really know what we have do we.

    Probability and marginal utility always enter symmetrically in asset pricing formulas. A good sufficient statistic for most decisions is the product. So it makes a lot of sense for people to respond "what do you expect to happen?" with the product of probability and marginal utility.

    To be a bit behavioral, suppose people are feeling risk tolerant, because times are good, they're searching for yield, and are willing to accept low expected returns. If you ask "do you expect stocks to go up a lot" they respond with words that confirm their decisions, "sure, I wouldn't have bought otherwise."

    Colloquially, poke around in class sometime and see if your students understand that "expected value" is true measure conditional mean, not risk neutral mean, not median, not mode. See if they understand that "risk" includes the chance of making more money than they "expected." I find most people think of "expected" as the risk-adjusted 90% quantile, "what will happen if everything goes right", and "risk" is all downside risk.

    Rats in cages do a pretty good job of utility maximizing. Yet, when you ask them why they're doing things they just chew up the survey forms. Are we really so much more self-aware?

    Data are data. But just because you ask what people "expect" doesn't mean they use the word the same way you do.

    1. Very true! Which is why I never expected survey research of this type to yield anything useful...and I was surprised when the authors reported the conclusions they did, especially about the correlation of expectations and fund flows. I am still pretty skeptical of this result, and I want to see if it replicates and generalizes...

    2. Also, excellent quote about the rats...I'm going to use that.

    3. On those fund flows... remember, money cannot collectively flow in to stocks. If mutual funds expand, direct holdings must contract. Flows into mutual funds only change how stocks are held and a bit by whom. For every buyer there is a seller.

    4. Is that true? Suppose there's only one share of stock in the world and you own it. And we each have $100. Suppose I buy the share of stock from you for $3, so that its quoted price is $3. Now we collectively have $100 in cash and $3 in stock. Now suppose you buy it back from me for $5. Now we collectively have $100 in case and $5 in stock. Is it wrong, from an accounting perspective, to say that "money collectively flowed into stocks"?

    5. Flows into mutual funds only change how stocks are held

      Flows into and out of mutual funds are a measure of what the dumb money is doing. :-)

    6. ". Is it wrong, from an accounting perspective, to say that "money collectively flowed into stocks"?"

      You would be correct (even though shares outstanding remained the same, the price, therefore market value went up).

      In today's markets, especially with leveraged ETF's that are constantly issuing, this effect is magnified.

  23. Anonymous11:22 AM

    "But why do stock prices mean-revert in the long run?"

    Prices do not "mean revert"... the "mean" line is drawn after the prices have happened. So the mean is the slave of prices, not the other way around.

  24. Get to know the credit cycle -- it is highly correlated with the equity cycle, and you can time bottoms to some extent, but tops are a mystery, though you can get an idea by looking at spreads on arbitrages.

  25. The hard wiring of economic theory is a bit much to take, with its perfect information and rational participants. I'm surprised that Kahneman's book, Thinking Fast and Slow, hasn't been mentioned in this discussion. In it, he explains how humans fear loss twice as much as gain. Fear = 2 x Greed (hmm)

    Why the long look at one asset class? My research indicates, and my trading models count on, that humans systematically chase trends across asset classes (finite dimensions of earth). It looks more like trend hopping than trend following, as they chase the best return, and run from risk.

    Fear or greed can drive a market in either direction, quickly. In a bubble, one can hand off to the other seamlessly. The 1998-2008 real-estate bubble & bursting started as the byproduct of a new technology bubble (wealth effect $7T), which was then fueled by the fear of the bursting tech bubble (losing $7T? no way) and the 9/11 attacks (real-estate safe haven). The timing was perfect. Greed was replaced by fear, which was replaced again by greed, which was ultimately replaced by fear.

    In the aftermath of the new technology breakthrough in the mid-1800's, the railroad, there were 50 years riddled with market "panics", many of which can be traced back to the railroad's introduction. The railroad's impact was clearly disruptive (writ large), but the nature and magnitude of the disruption wasn't comprehensible because it was "new". I think the same type of situation exists with the "Web/Internet" today. We've already experienced its first wave of disruption, and it was a doozey. If history is any guide, we should expect more, but what and how much, is tough to call. Do we need to know the specifics to profit from it? No. I think it's safe to say that a long period of disorder is expected after a technological breakthrough that has already transformed economies, and will likely change the nature of government and the concepts of country. We see the word "disruptive" too often tied to new technology. The frequency of its use has numbed us to its meaning. Disruptive is some very nasty stuff. As are bubbles, for that matter. (disruptive blowing bubbles)

    Now, with this as a backdrop, with fear and greed fed a high calorie diet lately, should we expect rational behavior from humans?

    (comments on two different subjects: could the money flow be driving expectations - or, at least coincidentally occurring? were transaction costs factored into the arima trading model?)

  26. I have added on to the debate (and referenced the range of comments here) in a posting about the investment industry, a business of herding: