Rationality and asset prices under belief heterogeneity
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Rationality and asset prices under belief heterogeneity Daniele Giachini1 Accepted: 13 October 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract 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 logutility 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. Keywords Belief heterogeneity · Rationality · Investment rules · Heuristics · Financial markets · Asset pricing JEL Classification C60 · D53 · D81 · D83 · G11 · G12
Daniele Giachini
[email protected] 1
Institute of Economics, Department EMbeDS, Scuola Superiore Sant’Anna, Piazza Martiri della Libert`a 33, 56127, Pisa, Italy
D. Giachini
1 Introduction Standard models of asset pricing, such as the one of Lucas (1978), assume that agents are fully rational: they know every detail of the economy and their behavior derives from (or is consistent with) utility maximization. In particular, a fully rational agent has rational expectations and can exactly evaluate the likelihood of every possible future state of the economy. Assuming that a decision maker has such knowledge is a very strong and rather unrealistic assumption. Hence, understanding what happens to asset prices when no one knows the true distribution becomes a relevant topic. Blume and Easley (2009a) address this issue keeping the assumption that agents behave as rationally as they can under their heterogeneous and, possibly, incorrect beliefs. They show that long-run prices generically reflect the beliefs of the most accurate agent.1 This sounds as a second-best: when no one knows exactly the true distribution, prices are at least able to reveal the best evaluation among those of market participants. Moreover, the standard way of thinking about bounded rationality suggests that if we move further away from full rationality (e.g. assuming that agents rely on heuris
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