Information, Beliefs, and Trading

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.