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 as a benchmark the pricing derived under rational expectations (fully rational pricing), I compare the long-run pricing performance in terms of accuracy of an economy in which agents behave according to the Subjective Generalized Kelly rule (Bottazzi et al., Economic Theory, 66(2)407–447, 2018), which is not optimal under agents’ beliefs, with the one emerging from an economy where agents maximize logarithmic preferences under the same heterogeneous and incorrect beliefs. I find that, in the long-run, the Subjective Generalized Kelly economy prices either match those attained in the log-utility maximizers economy or, on average, approximate the fully rational pricing better. Moreover, in the limit of agents having a discount factor equal to one, asset 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 improve the pricing performance when agents have biased and heterogeneous beliefs. This is due to the evolutionary process of wealth reallocation taking place among agents, which lets non-optimality of rules compensate for biases in beliefs.