Monday, April 26, 2010

Behavioral Finance and Extreme Event Risk 1: The Information Cascades

The Rational Madness of Crowds

Alice: But I don't want to go among mad people.
The Cheshire Cat: Oh, you can't help that. We're all mad here. I'm mad. You're mad.
Alice: How do you know I'm mad?
The Cheshire Cat: You must be. Or you wouldn't have come here.
Alice: And how do you know that you're mad?
The Cheshire Cat: To begin with, a dog's not mad. You grant that?
Alice: I suppose so,
The Cheshire Cat: Well, then, you see, a dog growls when it's angry, and wags its tail when it's pleased. Now I growl when I'm pleased, and wag my tail when I'm angry. Therefore I'm mad.

Lewis Carroll, Alice in Wonderland

Behavioral finance is a field that has been gaining in importance over the past two plus decades of its existence. This growth has accelerated since the 07-08 credit crunch due to the apparent inability of the traditional finance models to anticipate or even to account for such tremendous and sudden market swings on the basis of precepts of rationality and models of equilibrium. Our goal is to look for aspects of BF that are relevant to the investors and, in particular, to the practitioners of risk management. Before we get to the useful aspects of BF, let us point out an area which we believe has been extremely overrated in terms of its applicability to the financial markets. We are talking about the field of inquiry pioneered by Daniel Kahneman and Amos Tversky, which is primarily based on the psychological experiments in a controlled setting. They are usually based on pre-defined questionnaires based on the answers to which the researchers determine some flaws in the decision making patterns of subjects. To begin with, these experiments are almost always designed with an apparent goal of achieving a specific result and as such can be worded in a somewhat suggestive manner. We do not imply any bad faith on the part of researchers; however this problem is always present in psychological testing. We intend to write a separate section with examples in the future, but this discussion is not appropriate here, since these design flaws do not play any important role in our argument. Even if we completely accept both the design and interpretation of the results of such tests, we must conclude that they are irrelevant for finance practitioners. The reason is that the stated objective of this branch of BF, as expressed by Kahneman and Tversky is to study how “intuitive predictions violate the statistical rules of prediction in systematic and fundamental ways”, see Kahneman & Tversky (1982A). As they conclude in Kahneman and Tversky (1982B), “The fundamental notion of statistics is evidently not part of people’s repertoire of intuitions”.

This powerful observation led to the development of an old line of thinking, where investors are thought of as an ‘irrational herd’ or a ‘crowd’. Popular and entertaining books on the subject have been written such as “Mobs, Mobsters and Financial Markets” by William Bonner and Lila Rajiva and “Black Swan” by Nasseem Taleb. The reality of the irrationality research is less exciting. While the study of deviations from statistical rules may be useful in some fields of study, it is not much use in the financial risk management. The problems of sharp market reversals do not stem from the impaired statistical judgments, but rather come from the lack of information or lack of confidence in the information that is available. This lack or unreliability of information is a primary cause of what is termed “information cascades”. Roughly speaking, an information cascade can form when investors, instead of basing their judgment only on the information in their possession give some weight to the decisions of others that they observe. In the financial markets, they observe these decisions most frequently as the moves in market prices, so they are immediately placed in the minority, if their views are different. The temptation to discard one’s own information and judgment is very strong in such a case.
This lack of information is severely exacerbated by the lack of separation between investor’s judgments and the fundamental market facts about which they are deciding. This is what a famous speculator George Soros in his books “The Alchemy of Finance” and “The New Paradigm Of Financial Markets” called ‘reflexivity’.

Information Cascades
We will deal with the price-fundamentals feedback loop a bit later, and for now we will focus on a pure information cascade. In one of the best empirical studies of information cascades at work during the extreme financial events, Robert Schiller (2000) sent out questionnaires asking investors what was on their minds during the 1987 Black Monday stock market crash. And astonishing result was that there were not any fundamental news or issues troubling investors, but rather they were thinking of the previous week’s market declines. It is clear that investors treated previous week’s declines as information signals coming from other participants, which prompted them to discard their own information and beliefs. In fact, Bickhchandani, Hirshleifter and Welch (1992) defined information cascade as “a sequence of decisions where it is optimal for agents to ignore their own preferences and imitate the choices of the agent or agents ahead of them”. Schiller also studied news media before 1929 crash and found very similar pattern. Clearly, the crash of 08 cannot be characterized as coming on the heels of no news, since Lehman’s collapse constituted a drastic development, which stunned the market. However, Lehman’s collapse is also an example of an cascade, albeit of a different kind, which we will discuss in the next post. The complicating, and in fact, a key factor in the crash of 08 was the unprecedented leverage taken on by the financial sector. We will discuss the crash of 08 in much more detail when we get to the price-fundamentals feedback loops and the Financial Instability Hypothesis in the next two posts. Information cascades are not purely financial phenomena, there are present in a multitude of social system settings. For example, there is a sizable literature dealing with information cascades in sales of movie tickets. The best hypothetical example of such a cascade is given by Robert Schiller in the “Irrational Exuberance”. Consider a hungry person standing before two empty restaurants with no knowledge about the quality of food in either one of them. Clearly, his choice is random. If now a second person is in the same position, she will see one restaurant with one customer and one without any customers. The single customer will serve as the only piece of information differentiating between the two choices. The odds may now be slightly tilted in the favor of the restaurant that received one random customer. If two people choose the same restaurant, the tilt toward it will be even higher. If this game repeated many times, as it usually happens in the social systems, the probability of an information cascade forming can be very high. This intriguing example makes it appear that the information problems are the sole source of the heavy tales formed as the result of the cascades and that financial markets will necessarily be more stable when more information is available. Even though this is partially true, this line of thinking disregards another problem that is even more serious than the interdependence of decisions, a problem which can magnify price moves by affecting the very fundamentals that form the basis for such independent thinking that does exist. Before we get to the price-fundamentals feedback loops in the next posts, let us spell out some preliminary implications for risk managers based on the concept of information cascades:
1. Information cascades are ubiquitous in finance and by their very nature necessarily lead to fat tailed distributions, even though these tails may not be apparent for long periods of time. This means that risk models must account for them and it also suggests that long periods of low risk premiums in any market should be a major cause for concern at the risk management departments, since the return of the tails is inevitable when the trend reverses. There are no ‘new eras’ of low risk premiums, only periods when cascades work to prop up the market and artificially dampen volatility (we are clearly in one of those periods now).
2. Another important implication is that there are very similar mechanisms at work during all extreme events. This doesn’t mean that they are identical in their details or caused by similar triggers, but it does mean that extreme samples can to some degree be treated as ‘homogenous’ for the purposes of stress testing and distribution estimation.
We will develop these conclusions further into a formidable new framework after we discuss price-fundamentals feedback loops and the Financial Instability Hypothesis.

Next Posts:
Behavioral Finance and Extreme Event Risk 2: The Price-Fundamentals Feedback Loops

Funny Financial Quotes (a break from behavioral finance to take a look at some amusing financial quotes that I have collected over the years)

Behavioral Finance and Extreme Event Risk 3: Hyman Minsky and the Financial Instability Hypothesis

Behavioral Finance and Extreme Event Risk 4: Practical Conclusions for a Risk Manager

Tversky, A., Kahneman, D., 1982A, On the Psychology of Prediction, in
Judgement under Uncertainty: Heuristics and Biases, D Kahneman, P Slovic and A Tversky

Tversky, A., Kahneman, D., 1982B, Judgement under uncertainty: heuristics and biases, in
Judgement under Uncertainty: Heuristics and Biases, D Kahneman, P Slovic and A Tversky

Shiller, Robert J., 2000, Irrational Exuberance, Princeton University Press

Soros, G., 1987, The Alchemy of Finance, Simon & Schuster

Soros, G., 2008, The New Paradigm for Financial Markets: The Credit Crisis of 2008 and What it Means, Public Affairs

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