## Friday, November 20, 2009

### Judgment under uncertainty: heuristics, cognitive bias, and correlation

In a seminal paper that first appeared in 1974 (“Judgment under uncertainty: Heuristics and biases”) Amos Tversky and Daniel Kahneman describe three heuristics that people use to make judgments under uncertainty and the cognitive biases to which they give rise: “(i) representativeness, which is usually employed when people are asked to judge the probability that an object or event A belongs to class or process B; (ii) availability of instances or scenarios, which is often employed when people are asked to assess the frequency of a class or the plausibility of a particular development; and (iii) adjustment from an anchor, which is usually employed in numerical prediction when a relevant value is available.”

Today I want to focus on a single theme from this paper—cognitive bias and flawed correlation. I’ll look at two examples, the first from the heuristic of representativeness, the second from the heuristic of availability.

Let’s say we are asked to predict the final grade point average of a student who has all B’s in his first year and the final GPA of a student whose first-year record includes a lot of A’s and C’s. Most people would be more confident in predicting the final result for the straight-B student. But, the authors counter, “Highly consistent patterns are most often observed when the input variables are highly redundant or correlated. . . . However, an elementary result in the statistics of correlation asserts that, given input variables of stated validity, a prediction based on several such inputs can achieve higher accuracy when they are independent of each other than when they are redundant or correlated. Thus, redundancy among inputs decreases accuracy even as it increases confidence, and people are often confident in predictions that are quite likely to be off the mark.”

This statistical reasoning underlies the call for portfolio diversification. Although, as we have learned only too well, seemingly uncorrelated assets can becoming frighteningly correlated during market disruptions, for the most part it still makes sense to diversify. Who would presume to predict the outcome of a portfolio consisting solely of high beta tech names or of municipal bonds? You’d probably say that no good could come of it, but you would have nothing but common sense on which to base your judgment. You couldn’t make even a wild stab at quantifying your prediction. Common sense is sometimes good enough, but we mustn’t forget that common sense relies on heuristics to make its judgments under uncertainty, so we’re caught in a vicious circle.

From the heuristic of “availability” comes the cognitive bias of illusory correlation. For example, psychologists often ask a patient to draw a person, believing that how the patient draws the eyes is particularly telling. They believe, for instance, that there is a correlation between drawing big eyes and paranoia. Not so, but this illusory correlation effect is extremely resistant to contradictory data. “Availability provides a natural account for the illusory-correlation effect. The judgment of how frequently two events co-occur could be based on the strength of the associative bond between them. When the association is strong, one is likely to conclude that the events have been frequently paired. Consequently, strong associates will be judged to have occurred together frequently. According to this view, the illusory correlation between suspiciousness and peculiar drawing of the eyes, for example, is due to the fact that suspiciousness is more readily associated with the eyes than with any other part of the body.”

Pattern traders are particularly prone to the pitfalls of illusory correlation. It’s extraordinarily easy to mark up a chart with nothing but winning patterns and ignore all the instances in which these same patterns failed. Shift a line a little and the trader can yo-yo between winning and losing. Thomas Bulkowski undertook the monumental task of “documenting” chart pattern performance in his Encyclopedia of Chart Patterns but, despite the alleged probabilities, how often are we looking at big eyes and indulging in illusory correlation?