Prospect theory and fat tails

Abstract

A behavioral representative investor who evaluates a single risky asset based on cumulative prospect theory will often induce high kurtosis, negative skewness, and persistent autocorrelation into the distribution of market returns even if the asset payoffs are merely a sequence of independent coin tosses. These findings continue to hold even when the investor is simply loss averse. What causes fat tails and extreme events in market returns? One possibility is that the market prices ac- curately reflect the underlying business risk, and that business risk itself has rare but extreme possibilities. This possibility is the implicit assumption in statistical models of market returns. The business risks are pre- sumed to be reflected in the market and so we study the market process to deduce the distribution of the under- lying business risks. The alternate possibility, and the one I follow here, is that the market process itself may augment the possi- bility of extreme risks, even when the underlying busi- ness risk has no rare but extreme events. How do we know which possibility is the right one? The second does makes a specific but hard to test pre- diction: if we could observe two markets on the same asset, one by human traders subject to standard behav- ioral tendencies and psychological biases, and one by risk neutral robots, the behavioral market would have more extreme events than the risk neutral one. Experi- mental results do suggest that bubbles and crashes are a product of human trading and can dissipate as expe- rience and group familiarity grows, cf. (3) for a review of 72 such experiments. The aim of this paper is to see if applying standard behavioral models of investor psychology and decision making to the repeated evaluation of a sequence of bi- nomial gambles generates new extreme events in the market prices that do not occur in the underlying busi- ness risk. Suppose there is a single representative investor trading a single market asset whose fundamental risk is as benign as a coin toss, with no extreme events, and known probabilities. If the investor is risk neu- tral, the asset will always be worth its expected value, and because the expected value will not change in any extreme way over time, neither will the returns of the market asset. Similarly, if the investor maxi- mizes the expected utility of his total wealth, for stan- dard utility functions, no new extreme events are intro- duced.