Stocks as Lotteries: The Implications of Probability Weighting for Security Prices

Over the past few decades, economists and psychologists have accumulated a large body of experimental evidence on attitudes to risk. This evidence reveals that, when people make decisions under risk, they often depart from the predictions of expected utility. In an effort to capture the experimental data more accurately, researchers have developed a number of so-called nonexpected utility models. Perhaps the most prominent of these is Amos Tversky and Daniel Kahneman’s (1992) “cumulative prospect theory.” In this paper, we study the pricing of financial securities when investors make decisions according to cumulative prospect theory. Our goal is to see if a model like cumulative prospect theory, which captures attitudes to risk in experimental settings very well, can also help us understand investor behavior in financial markets. Of course, there is no guarantee that this will be the case. Nonetheless, given the difficulties the expected utility framework has encountered in addressing a number of financial phenomena, it may be useful to document the pricing predictions of nonexpected utility models and to see if these predictions shed any light on puzzling aspects of the data. Cumulative prospect theory is a modified version of “prospect theory” (Kahneman and Tversky 1979). Under cumulative prospect theory, people evaluate risk using a value function that is defined over gains and losses, that is concave over gains and convex over losses, and that is kinked at the origin; and using transformed rather than objective probabilities, where the transformed probabilities are obtained from objective probabilities by applying a weighting function. The main effect of the weighting function is to overweight the tails of the distribution it is applied to. The overweighting of tails does not represent a bias in beliefs; it is simply a modeling device that captures the common preference for a lottery-like, or positively skewed, wealth distribution. Stocks as Lotteries: The Implications of Probability Weighting for Security Prices