Rationality and asset prices under belief heterogeneity

In this paper I study the relationship between rationality and asset prices when agents have heterogeneous and incorrect beliefs about future events. Using the fully rational pricing as a benchmark, I show that when agents behave according to the Subjective Generalized Kelly rule (Bottazzi et al., 2017), which is not optimal under agents' beliefs, the long-run pricing performance is at least as good as the one emerging from an economy where agents maximize their preferences under rational price expectations. Indeed, there exist generic cases in which expected long-run prices of the Subjective Generalized Kelly economy approximate better the rational pricing than those attained by the utility maximizers economy. Moreover in the limit of agents having a discount factor equal to one the prices of the Subjective Generalized Kelly economy converge to those of the fully rational economy. Hence the fact that agents use non-optimal (heuristic) decision rules may correct for biases in beliefs and, as a consequence, improve the pricing performance of the economy.