Stocks as Lotteries: The Implications of Probability Weighting for Security Prices Nicholas Barberis and Ming Huang NBER Working Paper No. 12936 February 2007 Abstract: This paper studies the asset pricing implications of cumulative prospect theory, focusing on its probability weighting component. The main result is that, in contrast to the prediction of a standard expected utility model, a security's own skewness can be priced: a positively skewed security can be "overpriced," and can earn a negative average excess return. The results offer a unifying way of thinking about a number of seemingly unrelated financial phenomena, such as the low average return on IPOs, private equity, and distressed stocks; the diversification discount; the low valuation of certain equity stubs; the pricing of out-of-the-money options; and the lack of diversification in many household portfolios. Introduction: Over the past few decades, researchers have accumulated a large body of experimental evidence on attitudes to risk. This evidence reveals that, when people evaluate risk, they often depart from the predictions of expected utility. In an effort to capture the experimental data more accurately, economists have developed so-called non-expected utility models. Perhaps the most prominent of these is Tversky and Kahneman's (1992) "cumulative prospect theory." This paper studies 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 effectively, 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 non-expected 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 this 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 for capturing the common preference for a lottery-like, or positively skewed, wealth distribution. Previous research on the pricing implications of prospect theory has focused mainly on the implications of the kink in the value function (Benartzi and Thaler, 1995; Barberis, Huang, and Santos, 2001). Here, we turn our attentionStocks as Lotteries: The Implications of Probability Weighting for Security Prices Nicholas Barberis and Ming Huang NBER Working Paper No. 12936 February 2007 Abstract: This paper studies the asset pricing implications of cumulative prospect theory, focusing on its probability weighting component. The main result is that, in contrast to the prediction of a standard expected utility model, a security's own skewness can be priced: a positively skewed security can be "overpriced," and can earn a negative average excess return. The results offer a unifying way of thinking about a number of seemingly unrelated financial phenomena, such as the low average return on IPOs, private equity, and distressed stocks; the diversification discount; the low valuation of certain equity stubs; the pricing of out-of-the-money options; and the lack of diversification in many household portfolios. Introduction: Over the past few decades, researchers have accumulated a large body of experimental evidence on attitudes to risk. This evidence reveals that, when people evaluate risk, they often depart from the predictions of expected utility. In an effort to capture the experimental data more accurately, economists have developed so-called non-expected utility models. Perhaps the most prominent of these is Tversky and Kahneman's (1992) "cumulative prospect theory." This paper studies 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 effectively, 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 non-expected 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 this 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 for capturing the common preference for a lottery-like, or positively skewed, wealth distribution. Previous research on the pricing implications of prospect theory has focused mainly on the implications of the kink in the value function (Benartzi and Thaler, 1995; Barberis, Huang, and Santos, 2001). Here, we turn our attention