Academic Sophistry: Dart-Throwing Monkeys and the EMH


The other day I did a post on the Efficient Markets Hypothesis (EMH) that generated some discussion. I want to deal with a few of the issues raised in a some upcoming blogposts.

One issue of interest was that many EMH proponents said: “Sure, Warren Buffett and Keynes beat the market over a long-period we’re not saying that this is impossible. Some people might beat the market out of pure luck.” Well that seems like rubbish to me.

Think about this. If the EMH says that no one single person can beat the market over the long-run that is a testable proposition. But if they then say that some people might but this is “by luck” that is not testable. That is, in fact, based on an a priori assumption that anyone who beats the market did not do so by skill.

Now, personally I think that some people beat the market by skill. The fact that very few beat the market is not remotely surprising given this interpretation. Most market participants, by definition, will fall around the average and track the market over the long-run. Some really bad participants will fall way behind (these people would just be “unlucky” according to EMH Gospel, I’d be more inclined to say that they are bad at their jobs). And some people — not very many — will come out ahead.

The same is the case in anything. Most football players will be average. Some will be awful. Some will be top class. Is this “by luck”? Well, in terms of their genetic make-up and the environment they grew up in, it is in some sense. Our skills and talents are partially derived by us through what might be called “luck” or “chance”. But this is not what the EMH proponents mean. They mean that you cannot really apply skill to beat the market.

Personally I think that the EMH is a tautology masking as an argument. By definition the average investor cannot beat the market (which is the average outcome of investor decisions). Just like the average runner in a race cannot beat the average outcome of the race. But particular investors may well beat the market. The EMH says that this is not through skill but due to luck. That is not really a testable proposition. And it seems unlikely if we look at the real world.

If we look at the people who consistently beat the market they seem like very hard-working individuals who know the markets intimately and have very well-developed ideas about how to invest. I don’t see any charlatans amongst these. Nor do I see monkeys throwing darts at the stock indices. This leads me to conclude that these people got there by hard work and ingenuity. The onus should be on EMH proponents to produce dart-throwing monkeys that get the returns of Warren Buffett. My sense is that the laws of probability will not allow this any more than they will allow — in the real world — a monkey with a typewriter to produce the works of Shakespeare.

The EMH proponents want us to basically think that there is no skill involved when people beat the market. But again, this is an a priori assumption. They only think this because they assume it. When we look at the real world it appears unlikely. As I wrote in the last post: is it just a coincidence that one of the most important financial economists of the 20th century just “got lucky” and beat the market in the 1930s? The odds of a person being both one of the major financial economists of the 20th century and one of the few people to beat the market in the 1930s strike me as very low. But they need not be if we assume that there might be a link between Keynes being a brilliant financial economist and a brilliant investor.

So, we have established that this assumption by the EMH proponents is a priori. It has the status not of science — it is not testable — but of dogma. Why then is it held? I think that there is a very simple psychological/sociological reason for this that is actually quite obvious when you think about it.

People who teach the EMH claim to be experts on financial markets. They claim to have knowledge of how the markets work that is objectively correct. Now, this is slippery game indeed. Why? Because if someone jumps up and says “I am an expert on the financial markets and I know how they work” society as a whole can reply “Okay then, go and use this knowledge to play the markets and win”.

This causes a huge problem for financial economists. But if they say that their expertise on the financial markets tell them that anyone who beats the market only does so by luck then they are insulated. They can still claim to be experts while at the same time never having to prove their expertise because their expertise now needs no proof. It is a bit like me walking around saying that I am the best driver of flying cars in the world. Then when people tell me to prove it I turn around and say “Why of course I cannot prove it… everyone knows that flying cars don’t exist!”.

Well, that is all very well and good. Perhaps I can trick some gullible people into believing that I am indeed the best driver of flying cars in the world. That will not do much harm. Unfortunately, these “financial market experts” get into positions where they are allowed to dictate how financial markets are regulated. That will tend to cause enormous problems should I be right and should these people be largely engaged in sophistry.


About pilkingtonphil

Philip Pilkington is a macroeconomist and investment professional. Writing about all things macro and investment. Views my own.You can follow him on Twitter at @philippilk.
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24 Responses to Academic Sophistry: Dart-Throwing Monkeys and the EMH

  1. ivansml says:

    First of all, active fund managers are the ones who charge hefty management fees, so it should be primarily up to them to prove that they can consistently beat the market.

    Second, let’s think about that word “consistently” for a moment. It’s true that in any single period, average investor will earn average return, by definition. But if some managers have skill in picking stocks, or timing markets, or whatever, we would expect that their success is *persistent* over time, while if all success is due to luck, it will be hit or miss. In terms of your marathon analogy – if success is due to luck, random bunch of runners will finish first in each race. If it’s due to skill, some runners will be clearly more likely to finish first than others across many races. EMH proponents claim that financial markets are (unlike marathons) closer to the second case.

    Guess what? This is not a dogma, but a testable hypothesis that has been studied many times (e.g. Jensen, 1968; Carhart, 1997; Fama & French, 2010). Those papers find, across a wide sample of mutual funds, that after adjusting for risk, survivorship bias, etc., there’s little evidence of persistence in returns that could be explained by skill. Sure, maybe Warren Buffet and few others can consistently beat the market, but large majority of professional money managers can’t.

    • (1) They must do that for their clients. In academic debate such a defence is not excusable.

      (2) It’s not “sure, Buffett might beat it”. If you are that cavalier then the EMH says nothing of interest. All it says is “most people will not beat the market consistently (through time)”. But that is banal. I can say that about anything. “Most people will not win Olympic medals”; “most people will not become billionaires” and so on. Given a large enough sample and some strict criteria only a few will come out winners in EVERY field.

      Either the EMH says “no one can beat the market consistently” and this shows that the market is “efficient” in some sense. Or it says nothing. It is shocking that economists do not notice this. But ideologues NEVER notice what they’re engaged in.


      • ivansml says:

        You could try reading what you respond to as well (see, I don’t even need large caps). So again, although you cannot test whether any one single person beat the market by skill or luck (especially when that person is not randomly selected), you can look at performance of many investors and see whether the pattern in persistence of their returns matches the skill hypothesis. Turns out it mostly doesn’t.

        I’ve already said this, your understanding here of how economics is supposed to work is silly. We are not dealing with matters of pure logic that can provide black or white answers. Our hypotheses will always be imperfect descriptions of complicated world. The question of how good (or bad) approximation of the real world is the EMH is an interesting one. The question whether EMH holds 100% of time is not.

      • Again, that has nothing to do with the EMH. Given a large enough sample only a small number of people will significantly outperform in ANY field. From tennis playing, to mathematics test scores, to citations in economic journals. That has nothing to do with any theory. That is simply a statistical truism. It just says: only a small number of people will be far above average in any given field.

        This is so simple it is not even funny. I am shocked that you cannot see this. I can only conclude that you do not even know what it is that you think the EMH says. Or, if you do, you do not understand that it is entirely trivial and without substantial meaning.

        All you are saying is “in a market full of investors only some of these will come out substantially above average over a long-period of time”. Replace “market full of investors” with “clubs full of football players”, “classrooms full of students” or whatever else you want. This has NOTHING to do with economic theory. It is simply a statistical tautology.

      • ivansml says:

        No, that’s not what I’m saying (and you clearly don’t want to understand). Even if by definition only a small group “significantly” outperforms the average, the question is whether it’s the same group every time (skill) or always composed randomly (luck). So a last attempt, with an example:

        Economy A: half of investors just hold the market, other half uses active strategies. Markets are efficient, there’s no room for skill and everyone earns on average the same risk-adjusted return, say 5%. If an investor earns above-market return, he’s just as likely not to in the next period.

        Economy B: half of investors just hold the market, a quarter have high skill and use superior active strategy, other quarter have low skill and use inferior strategy. Market return is on average 5%, superior active investors earn 6%, inferior investors earn 4%. If an investor has earned above-market return, it’s more likely he will do so also in the next period.

        In both economies, there will be some people who have beaten the market over long periods of time, so such anecdotes tell us nothing. But clearly one could study the statistical distribution and persistence of investor returns to distinguish between the two.

      • Yeah. People who beat it over the long-run. Like Buffet etc. That’s what the post SAYS. Reread it and you will see I continuosly refer to the long-run. Even in the first two or three paragraphs.

        The same applies to a game of poker. I may win a hand or two at a poker table of pros. But in the LONG RUN I will not. You don’t need a notion of market efficiency to explain this. It is a simple statistical phenomenon that runs: “if there is a large enough sample only some people will persistently outperform over the long run”. These are the elite in the field. And you explain these guys away… how… I don’t know. You just shrug.

        In the EMH there can be no “elite” because the markets are assumed to be efficient in some sense. For the theory to work there has to be no elite. But in the real world there clearly are.

        The fact that you cannot understand this speaks volumes. I’m literally shocked. You are not a stupid person. Thus there must be something else at work.

      • Let’s take this in steps…


        “Many of us economists who believe in efficiency do so because we view markets as amazingly successful devices for reflecting new information rapidly and, for the most part,
        accurately. Above all, we believe that financial markets are efficient because they
        don’t allow investors to earn above-average risk adjusted returns. In short, we believe that $100 bills are not lying around for the taking, either by the professional or the amateur investor.” (Malkiel 2003, pp60-61)

        (1) How do we falsify this? We look to see if “professional investors” cannot beat the market in the long-run.

        (2) We turn to the real world and find that quite a few investors DO beat the market in the long-run.


        We tested the hypothesis against the data and found that some investors CAN beat the market in the long-run. Therefore, the hypothesis has been falsified.

        This is not complicated.

      • ivansml says:

        “It is a simple statistical phenomenon that runs: “if there is a large enough sample only some people will persistently outperform over the long run”. These are the elite in the field.”

        So if I see some people persistently outperforming, is it just a mechanical statistical phenomenon, or an indication of being elite? Can’t be both, so you are the one that’s confused, but I really don’t know how to explain it more clearly.

      • So if I see some people persistently outperforming, is it just a mechanical statistical phenomenon, or an indication of being elite?

        It is both.

        In a large enough sample people that continuously perform well will be in the minority. This is the mechanical statistical phenomenon.

        These people are the elite in the field.

        Of course it can be both.

        You can’t explain it better because you’re in a muddle and have been for about two comments.

      • ivansml says:

        “We turn to the real world and find that quite a few investors DO beat the market in the long-run.”

        Yes, this is rather crucial. The research I cited shows that’s not true and only very few investors beat the market in the long run. You on the other hand have provided nothing but a name of Warren Buffet.

      • I named Buffett, Keynes and linked to paper where Buffett gives the track record of nine other investors. Don’t try that BS on here buddy.


        I’m done with this. You’ve wrapped yourself up in a discourse full of tautologies and you can’t see outside it. Others can. I will speak to them. Feel free to have the last word. Try not to lie about the evidence I have or have not provided. It makes you come across as opportunistic.

    • ivansml says:

      “In a large enough sample people that continuously perform well will be in the minority. This is the mechanical statistical phenomenon.

      These people are the elite in the field.”

      If I put thousand people in front of roulette tables, small minority will be continuously successful. Does that make them elite roulette players?

      • No. Over the long-run, if the table is balanced, they will all tend to average. Duh!

        Jesus! Obvious! There is no skill involved. UNLIKE POKER OR MARKETS WHICH ARE DIFFERENT.

        Fuck this. I’m done here. This is ridiculous. You’re not even thinking any more.

      • ivansml says:

        And yet with large enough sample, over any *finite* period you will also get a minority that’s consistently winning. So how can you distinguish luck and skill, given that you always observe such minority? That’s what I’ve been writing all along, but you’re not listening. It’s been a bit bizarre discussion indeed.

      • You can’t. Hence you cannot test whether the EMH is accurate or not. You can’t test whether the minority are skilled or lucky. Hence the EMH is non-falsifiable. All this is in the piece.

      • ivansml says:

        Heh, I can’t resist, sorry. This discussion would make much more sense if you actually made up your mind:

        – either the success of Buffet, Keynes and those 9 other guys can be attributed to skill and thus disproves EMH (comment from 6:04 pm),

        – or it’s impossible to distinguish whether the cause of success was skill or luck, and thus EMH is not falsifiable from this direction (comment from 6:43 pm).

        Needless to say, both arguments cannot be legit.

      • I think that its about skill. But I can’t prove it using statistics. I think this because it is more reasonable given the non-statistical data. That is what the piece is about.

        BUT even if you disagree with this, it is uncontroversial that you cannot PROVE it either way in a statistical manner as the EMH people do.

        That’s the end of the story. Again read the piece, that’s what its about.

      • LK says:

        Roulette is **not** like investing in stocks and shares, so the analogy does not work.

        In any fair game of roulette, there really are stable long run relative frequencies for outcomes that mean, in the long run, people cannot be successful.

        In investing in secondary financial asset markets, you do NOT have stable long run relative frequencies: there is a role for skill and ability, and those who really understand how these markets work might be successful in the long run.

  2. LK says:


    On a completely unrelated point, could please I ask you a favour, and pick your brain on just a couple of issues related to the quantity theory of money, namely the Cash Balance equation?

  3. LK says:

    Could I possibly email you with it?

  4. GrkStav says:

    Hate to go old-school ’empiricist’ here but here it goes:

    The question to pose to EMH is the following:

    What set of data, which verifiable evidence would provide empirical refutation of one or more of the empirically testable hypotheses logically entailed by your theory?

    Therefore, for it to be an actual theory, at least one empirically testable/disprovable hypothesis must be derivable from it. Furthermore, to ensure that attempts to disprove that/those hypothesis/es, the theorist must publicly state the empirical data that would constitute an empirical refutation of the hypothesis/es in question.

    Until and unless those can be provided, EMH is not a ‘scientific’ theory.

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