Does Belief Heterogeneity Explain Asset Prices: The Case of the Longshot Bias

Abstract

This paper studies belief heterogeneity in a benchmark competitive asset market: a market for Arrow-Debreu securities. We show that differences in agents' beliefs lead to a systematic pricing pattern, the favorite longshot bias (FLB): securities with a low payout probability are overpriced while securities with high probability payout are underpriced. We apply demand estimation techniques to betting market data, and find that the observed FLB is explained by a two-type population consisting of canonical traders, who hold virtually correct beliefs and are the majority type in the population (70%); and noise traders exhibiting significant belief dispersion. Furthermore, using formal model comparisons and also exploiting variation in public information across markets in our dataset, we show that our belief heterogeneity model empirically outperforms existing preference-based explanations of the FLB, such as risk-loving or prospect theory.JEL Classification: C13, C51, D40, G13, L00.

Estimating Risk Preferences in the Field

“…If one can observe how bettors partition themselves across races with different characteristics, one can draw inference on the distribution of heterogeneity. Gandhi and Serrano-Padial (2015) are motivated by the favorite-longshot bias, and the idea that belief heterogeneity could drive it (as suggested by Ali 1977, theorem 2). They develop a formal model of risk-neutral agents with heterogeneous beliefs, and prove that such a model would generate a favorite-longshot bias.…”

“…Gandhi and Serrano-Padial (2015) had the key insight that this market is isomorphic to a discrete-choice horizontally differentiated products market of the form studied by Berry, Levinsohn, and Pakes (1995) and Berry, Gandhi, and Haile (2013).…”

“…In particular, the assumption of unidimensional heterogeneity that 76 This step is analogous to the approach in Weitzman (1965) and Snowberg and Wolfers (2010), except that they estimate how the probability of horse i winning depends on the full vector of odds R , as opposed to merely depending on R i . 77 Here, they do not pursue a maximum-likelihood approach as in Jullien and Salanié (2000) and Gandhi and Serrano-Padial (2015). Rather, they focus on one particular implication of V that can be non-parametrically identified from p(R) , and which can be used to compute NF .…”

Inference Under Stability of Risk Preferences

“…Examples include, among many others, Manski (2014), who uses revealed preferences arguments and shape restrictions to partially identify preferences for income and leisure and study their consequences for the evaluation of income tax policy; Dominitz and Manski (2011), who analyze probabilistic expectations of equity returns measured at two points in time, and use the partial identification approach to obtain bounds on the prevalence of expectations types in their sample; Chetty (2012), who obtains bounds on price elasticities in the presence of frictions such as adjustment costs or inattention; Ciliberto and Tamer (2009), who estimate payoff functions in a static, complete information entry game in airline markets in the presence of multiple equilibria; Haile and Tamer (2003), who study an incomplete model of English auctions and derive bounds on the distribution function characterizing bidder demand, on the optimal reserve price, and on the effects of observable covariates on bidder valuations, and apply their methodology to U.S. Forest Service timber auctions to evaluate reserve price policy; and Manski and Pepper (2000), who derive sharp bounds in the presence of monotone instrumental variables, and apply them to a study of the returns to education. 8 Gandhi and Serrano-Padial (2015) use data on bets on U.S. horse races to estimate a cumulative prospect theory model by parametric maximum likelihood.…”

The favorite-longshot bias and the impact of experience

“…Recent empirical literature has demonstrated that a plausible explanation for the FLB might be seen in the interplay of casual bettors and (semi-)professionals who benefit from the fact that favorites are underbet (Gandhi and Serrano-Padial 2012). To investigate if the impact of experience on odds and success is exclusively driven by large investors, we divide the population into ten equally large subgroups, sorted by experience.…”