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Rajiv Sethi: Information, Beliefs, and Trading

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Yves here. This is a terrific post, and I think readers who are in the unfortunate position of having to invest in the markets* will relate to Sethi’s analysis (personally, I hate trading, I wish it were possible to be a long-term investor, but that’s become an awful lot like driving a Model T on a Nascar track). The use of Intrade data and discussing Obama v. Romney-biased speculators is both clever and makes the discussion accessible. And I must confess to being very attached to my “priors” and too willing to fight the tape!

By Rajiv Sethi, Professor of Economics, Barnard College, Columbia University. Cross posted from his blog

Even the most casual observer of financial markets cannot fail to be impressed by the speed with which prices respond to new information. Markets may overreact at times but they seldom fail to react at all, and the time lag between the emergence of information and an adjustment in price is extremely short in the case of liquid securities such as common stock.

Since all price movements arise from orders placed and executed, prices can respond to news only if there exist individuals in the economy who are alert to the arrival of new information and are willing to adjust positions on this basis. But this raises the question of how such “information traders” are able to find willing counterparties. After all, who in their right mind wants to trade with an individual having superior information?

This kind of reasoning, when pushed to its logical limits, leads to some paradoxical conclusions. As shown by Aumann, two individuals who are commonly known to be rational, and who share a common prior belief about the likelihood of an event, cannot agree to disagree no matter how different their private information might be. That is, they can disagree only if this disagreement is itself not common knowledge. But the willingness of two risk-averse parties to enter opposite sides of a bet requires them to agree to disagree, and hence trade between risk-averse individuals with common priors is impossible if they are commonly known to be rational.

This may sound like an obscure and irrelevant result, since we see an enormous amount of trading in asset markets, but I find it immensely clarifying. It means that in thinking about trading we have to allow for either departures from (common knowledge of) rationality, or we have to drop the common prior hypothesis. And these two directions lead to different models of trading, with different and testable empirical predictions.

The first approach, which maintains the common prior assumption but allows for traders with information-insensitive asset demands, was developed in a hugely influential paper by Albert Kyle. Such “noise traders” need not be viewed as entirely irrational; they may simply have urgent liquidity needs that require them to enter or exit positions regardless of price. Kyle showed that the presence of such traders induces market makers operating under competitive conditions to post bid and ask prices that could be accepted by any counterparty, including information traders. From this perspective, prices come to reflect information because informed parties trade with uninformed market makers, who compensate for losses on these trades with profits made in transactions with noise traders.

An alternative approach, which does not require the presence of noise traders at all but drops the common prior assumption, can be traced to a wonderful (and even earlier) paper by Harrison and Kreps. Here all traders have the same information at each point in time, but disagree about its implications for the value of securities. Trade occurs as new information arrives because individuals interpret this information differently. (Formally, they have heterogeneous priors and can therefore disagree even if their posterior beliefs are commonly known.) From this perspective prices respond to news because of heterogeneous interpretations of public information.

Since these two approaches imply very different distributions of trading strategies, they are empirically distinguishable in principle. But identifying strategies from a sequence of trades is not an easy task. At a minimum, one needs transaction level data in which each trade is linked to a buyer and seller account, so that the evolution of individual portfolios can be tracked over time. From these portfolio adjustments one might hope to deduce the distribution of strategies in the trading population.

In a paper that I have discussed previously on this blog, Kirilenko, Kyle, Samadi and Tuzun have used transaction level data from the S&P 500 E-Mini futures market to partition accounts into a small set of groups, thus mapping out an “ecosystem” in which different categories of traders “occupy quite distinct, albeit overlapping, positions.” Their concern was primarily with the behavior of high frequency traders both before and during the flash crash of May 6, 2010, especially in relation to liquidity provision. They do not explore the question of how prices come to reflect information, but in principle their data would allow them to do so.

I have recently posted the first draft a paper, written jointly with David Rothschild, that looks at transaction level data from a very different source: Intrade’s prediction market for the 2012 US presidential election. Anyone who followed this market over the course of the election cycle will know that prices were highly responsive to information, adjusting almost instantaneously to news. Our main goal in the paper was to map out an ecology of trading strategies and thereby gain some understanding of the process by means of which information comes to be reflected in prices. (We also wanted to evaluate claims made at the time of the election that a large trader was attempting to manipulate prices, but that’s a topic for another post.)

The data are extremely rich: for each transaction over the two week period immediately preceding the election, we know the price, quantity, time of trade, and aggressor side. Most importantly, we have unique identifiers for the buyer and seller accounts, which allows us to trace the evolution of trader portfolios and profits. No identities can be deduced from this data, but it is possible to make inferences about strategies from the pattern of trades.

We focus on contracts referencing the two major party candidates, Obama and Romney. These contracts are structured as binary options, paying $10 if the referenced candidate wins the election and nothing otherwise. The data allows us to compute volume, transactions, aggression, holding duration, directional exposure, margin, and profit for each account. Using this, we are able to group traders into five categories, each associated with a distinct trading strategy.

During our observational window there were about 84,000 separate transactions involving 3.5 million contracts and over 3,200 unique accounts. The single largest trader accumulated a net long Romney position of 1.2 million contracts (in part by shorting Obama contracts) and did this by engaging in about 13,000 distinct trades for a total loss in two weeks of about 4 million dollars. But this was not the most frequent trader: a different account was responsible for almost 34,000 transactions, which were clearly implemented algorithmically.

One of our most striking findings is that 86% of traders, accounting for 52% of volume, never change the direction of their exposure even once. A further 25% of volume comes from 8% of traders who are strongly biased in one direction or the other. A handful of arbitrageurs account for another 14% of volume, leaving just 6% of accounts and 8% of volume associated with individuals who are unbiased in the sense that they are willing to take directional positions on either side of the market. This suggests to us that information finds its way into prices largely through the activities of traders who are biased in one direction or another, and differ with respect to their interpretations of public information rather than their differential access to private information.

Prediction markets have historically generated forecasts that compete very effectively with those of the best pollsters.  But if most traders never change the direction of their exposure, how does information come to be reflected in prices? We argue that this occurs through something resembling the following process. Imagine a population of traders partitioned into two groups, one of which is predisposed to believe in an Obama victory while the other is predisposed to believe the opposite. Suppose that the first group has a net long position in the Obama contract while the second is short, and news arrives that suggests a decline in Obama’s odds of victory (think of the first debate). Both groups revise their beliefs in response to the new information, but to different degrees. The latter group considers the news to be seriously damaging while the former thinks it isn’t quite so bad. Initially both groups wish to sell, so the price drops quickly with very little trade since there are few buyers. But once the price falls far enough, the former group is now willing to buy, thus expanding their long position, while the latter group increases their short exposure. The result is that one group of traders ends up as net buyers of the Obama contract even when the news is bad for the incumbent, while the other ends up increasing short exposure even when the news is good. Prices respond to information, and move in the manner that one would predict, without any individual trader switching direction.

This is a very special market, to be sure, more closely related to sports betting than to stock trading. But it does not seem implausible to us that similar patterns of directional exposure may also be found in more traditional and economically important asset markets. Especially in the case of consumer durables, attachment to products and the companies that make them is widespread. It would not be surprising if one were to find Apple or Samsung partisans among investors, just as one finds them among consumers. In this case one would expect to find a set of traders who increase their long positions in Apple even in the face of bad news for the company because they believe that the price has declined more than is warranted by the news. Whether or not such patterns exist is an empirical question that can only be settled with a transaction level analysis of trading data.

If there’s a message in all this, it is that markets aggregate not just information, but also fundamentally irreconcilable perspectives. Prices, as John Kay puts it, “are the product of a clash between competing narratives about the world.” Some of the volatility that one observes in asset markets arises from changes in perspectives, which can happen independently of the arrival of information. This is why substantial “corrections” can occur even in the absence of significant news, and why stock prices appear to “move too much to be justified by subsequent changes in dividends.” What makes markets appear invincible is not the perfect aggregation of information that is sometimes attributed to them, but the sheer unpredictability of persuasion, exhortation, and social influence that can give rise to major shifts in the distribution of narratives.

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*To be clear, I recognize that having to worry about investing is a high class problem. But the markets are so manipulated and crooked, and as I discuss at length in ECONNED, the “prudent” standard investment approaches actually push not just poor retail saps but even the supposed pros into taking on way too much risk. And now that interest rates are volatile, bonds aren’t the safe haven they used to be either.

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10 comments

  1. marinbelge

    Thanks for this great cross-post. That idea of competing narrative is great and worth debating:)

    The post is certainly bringing useful information on the trading eco-system.

    However is this site not about “naked capitalism”?

    I’d be glad to hear about the justification of the current state of “financial markets”. A thorough discussion of the current mantra in US (and UK as well), the Market deity.

    Do not get me wrong, I certainly like decently efficient markets. But is this what markets are to-day?

    What is indeed the CURRENT justification – both on economical and ethical ground – for the CURRENT setup of financial markets:
    - participants, big or small who use others’ money, essentially driven by a central bank,
    - assymetrical size effects that have grown massively with the introduction of electronics and high freq micro-management.

    IMHO, these so-called financial markets (“so-gennante” as they use to say in postwar West Germany when talking about the East republic…) do not bring additional capital more. They are an extraction engine. Not the opposite. The Fed does the feeding and backstops most of heavy-weight when necesseray. These carnations of markets do not participate in price discovery. They just massively increase volatility.

    One and only single advantage… The Fed has some control on the pricing mechanics via QE and others. Is that what capitalism and markets are all about? Is this an advantage in view of their handlings of affairs (and predictions as displayed in central banks web site publication history..)?

    When that is the case, please bring me the old Gosplan by the Soviets. I’d prefer to hear about them than Greenspan, Bernanke (and soon Yellen) tuning the markets actions with words and emotion…

  2. Newtownian

    With all this priors and posterior stuff its obvious our friend the fiendish Reverend Bayes at work albeit uncredited.

    Which accounts in turn market irrationality. For anyone interested in the inability of market people to not understand the implications of Bayes, persistently get the implications of complete knowledge wrong, is not familiar with the Monty Hall problem http://en.wikipedia.org/wiki/Monty_Hall_problem and who needs a good laugh can I recommend the following:

    Author: T. Slembeck and J.-R. Tyran
    Year: 2004
    Title: Do institutions promote rationality? An experimental study of the three-door anomaly?
    Journal: Journal of Economic Behavior & Organization
    Volume: 54 Pages: 337-350

    The three-door problem is an example of a systematic violation of a key rationality postulate that has attracted much attention. In this seemingly simple individual decision task, most people initially fail to apply correctly Bayes’ Law, and to make the payoff-maximizing choice. Previous experimental studies have shown that individual learning reduces the incidence of irrational choices somewhat, but is far from eliminating it. We experimentally study the roles of communication and competition as institutions to mitigate the choice anomaly. We show that the three-door anomaly can be entirely eliminated by these institutions.

  3. Newtownian

    “This suggests to us that information finds its way into prices largely through the activities of traders who are biased in one direction or another, and differ with respect to their interpretations of public information rather than their differential access to private information.”

    This is the precise observation you will see in the above paper I’ve cited. People stick to their guns even when its not probabilistically sensible, probably making algorithms smarter on average provided they have good inputs.

    And speaking of Obama v. Romney see also
    Efron, B., 2013. Bayes’ Theorem in the 21st Century. Science 340, 1177-1178.

  4. David Lentini

    Very interesting piece, and the last citation to the “IMH” was very good too.

    One thing that seems amiss to me is the lack of discussion about the definition of “information”. The basic definition of the word implies that “information” refers to statements that are true or are reliable. And, as I recall, EMH at least implies that market prices somehow (as in “then a miracle happens”) reflect everything knowable about a security.

    Clearly, then “information” as commonly defined can’t be the case in the market described in the “second approach”, where parties can differ about the accuracy of statements (the “information”) as much as their implications. And “information” can’t reflect only statements or knowledge about the subject being traded when the actions of the traders may reflect forces on the traders that have no relationship to the market itself (the “first approach”).

    Thus, the idea of “infomration” in the market is far more nuanced and slippery than it would appear on its face, and is often stated in most of the economics writings I’ve seen over the years. In fact, both approaches described here, especially the “first approach” look a lot like Keynes’s famous characterization about the market in which the traders are more concerned about the expectations and actions of other traders than with the actual facts of the subject matter underlying the securities being traded.

  5. from Mexico

    Great stuff!

    This post joins a host of literally hundreds, if not thousands, of other publications over the past few years which demonstrate that most human beings seldom, if ever, behave “rationally,” a la Adam Smith.

    Here’s how Wikipedia describes “the wonderful world of Adam Smith,” as Robert Heilbroner called it — “Smith’s panegyric of a free and unfettered market”:

    Barter is characterized in Adam Smith’s “The Wealth of Nations” by a disparaging vocabulary: “higgling, haggling, swapping, dickering.” It has also been characterized as negative reciprocity, or “selfish profiteering.”[5] By placing barter as the original “state of nature”, Smith is thus asserting that self-interest and greed are at the centre of all successive forms of economic exchange.

    http://en.wikipedia.org/wiki/Barter

    Here’s how Peter Turchin puts it in War and Peace and War:

    During the twentieth century, the ideas of Mandeville, Smith, and many others have been developed and systematized into what is now known as “the theory of raitonal choice.” The core of the theory is the postulate that people — “agents” — behave in such a way as to maximize their “utility function.” In principle, the utility funciton could be almost anything, but in practice almost all applications of the theory in the mainstream economics equate utility with material self-interest. In the most basic version, the utility is simply the dollar amount that an agent expects to get as a result of a certain action. The agent then should perform the action that yeilds the greatest payoff — this is what “maximizing utility” means. Agents that behave in ways that maximize their utility function are “rational.”

    John Gray calls classical and neoclassical economics our “ruling mythology.” And he’s absolutely right, since classical and neoclassical economics are now being shown to be based on a partial truth, that partial truth representing a very, very small slice of reality.

    1. s spade

      Classical and neoclassical economics are variants of a single religion which ignores reality as inconvenient and employs mumbo jumbo to justify gratuitous disparities in wealth and income, most of which arise out of exploitation, chicanery and fraud. If the religion made any sense the last five years of reality would have been impossible. Nevertheless, faith in the religion remains inviolate among those whose interest it continues to serve. For others there is propaganda, patriotic hoopla and team sports.

  6. allcoppedout

    The notion of rational man is as dated as the lack of gender inclusion in our collective noun. If one compares this piece with what we get from main media on markets (blather), one has to wonder why they dare not to tell the truth in detail to an audience of rational people. I agree with Mexico, but think what he says a synopsis of about half the story. The rest concerns why we have trading institutions in which only those in its highly self-centred microculture have access to technology, low fees and information with which to trade.

    Deep in this is the fact that humans will practice highly self-interested behaviour not in the wider interest. This ‘capacity’ is in all of us. This, of course, is not to say we do not have other capacities – for cooperation (selfish version cartels), compassion … but it is also the case we should not forget the selfish aspects in a bleeding heart version of human nature.

    I can fix your old car, but am about half as good as a decent mechanic. I know what trading is about from books and university teaching – and have no practical experience and would have to learn the real rules from scratch, including whether I could morally do any of it, suspecting my ethics would rule me out – which is now the case for me in university teaching (Charles Hugh Smith makes the argument I feel right).

    The evidence that in-groups commit fraud is clear. There is a ‘ruling mythology’ (one I see as a religious control fraud) that tells us we must give up to this ‘inevitability’. This is nonsense. To combat the nonsense we need more practical information from the ground on what traders do – as per this piece. This is true across the financial sector. We need to understand the mechanics’ skills. My guess is the traders do little more than a dishonest mechanic charging for an engine overhaul when actually replacing a broken spark plug.

    The underlying research here lacks ‘benchmarking’ – say, considering the trading system as bookmaking. Bookmakers rarely fail, yet are in apparent competition. All gamblers (investors?) without key inside information fail. How is this cartel maintained?

  7. JEHR

    Readers at NC have commented on the use of business terms to describe almost every transaction that takes place in the world, the most egregious one being the description of buyers or patrons as “consumers” which suggests that everything is ingested into human beings, especially in the world according to business.

    In this article, I notice the use of environmental terms to describe the business of financial types: evolution, ecosystem and ecology to describe aspects of trading in the marketplace. So the description of the environment, too, is subsumed by business, even though the author uses them parenthetically to show us he knows what he is doing. These uses of words mean something and to me it means that even the environment is not sacrosanct and is being used for the description of the world of business. Business needs its own usages as does the environment.

    Interesting co-optations, however.

  8. s spade

    All trading theories premised on rationality and information are nonsense. Traders have positions and they have hunches and they respond emotionally to changes in bid and asked prices, justifying their reactions with extrapolations from the noise which they mistake for information. Most of them are running other people’s money and fear only being left behind when values appear to change. Nobody knows what tomorrow’s price of anything will be, except for those having inside information about corporate events guaranteed to surprise the market.

    You can watch CNBC all day long and never learn a single thing of any value whatsoever. You can scour the SEC reports, the Wall Street Journal, every research paper and tout sheet. I will bet my dart throwing monkey out performs you every time, because he moves faster and doesn’t need any time to aim before he lets that dart go.

  9. Chauncey Gardiner

    With the benefit of hindsight of the past five years, it has become self evident that these financial markets are highly manipulated and controlled, and that the ramp in prices benefits a narrow segment of society. Prices have been and continue to be reliant on enormous ongoing injections of trillions of dollars of Cash money by central banks. Without that Cash, these market prices would evaporate like raindrops on a Scottsdale sidewalk. To pretend that this is some never ending battle between the Bulls and the Bears in some sort of perpetual WWF match strains the imagination.

    And what about those who are simply disgusted by the whole charade?…

    Take a look at declining trading volumes even given the huge increase in trading by HFT bots if you need to quantify something. Oh, and while you’re at it, you might study the declining Velocity of Money and the broken transmission mechanism. It all kinda goes together, ya know.

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