Abstract
This chapter investigates whether a behaviourally biased agent is able to persistently maintain a positive consumption share when trading in the market with a Bayesian agent. The question is addressed by recasting a popular model of investor sentiment in a general equilibrium framework. Our evolutionary stability analysis complements standard Behavioural Finance studies, where a biased representative agent is usually considered to explain deviations from rational pricing. In fact, if the biased agent asymptotically disappears from the market, then misvaluation patters generated by its behaviour do not survive in the long term. We find that, despite the existence of generic cases in which the biased agent succumbs, the learning process with behavioural biases displays a good degree of evolutionary stability.
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Notes
- 1.
The topic has also been investigated in different frameworks. For instance, Benos (1998) and Kyle and Wang (1997) base their model on Kyle (1985) and analyse the trading of a risky security in a partial equilibrium setting with risk-neutral traders. The price of the security is decided by a risk-neutral market maker; hence, no Walrasian mechanism exists. In a one-stage game, the authors show that an overconfident trader can attain a higher profit than a rational one. Benos (1998) shows that the same result holds when the market maker is risk averse. The choice of a non-Walrasian price fixing condition seems to be essential for these results.
- 2.
In the notation of BSV, the weight w i,1(σ t+1) is the quantity (1 − λ 1)q t+1 + λ 2(1 − q t+1), where the functional form of q t is reported at the end of page 322 of their paper. In this way, the predictive probability in (6) correctly matches the one BSV assume.
- 3.
BSV justify the prescription in (9) as a simil-Bayesian updating with respect to a fictional two-state model the agent has in mind. This justification, admittedly not always convincing, is immaterial for the present analysis. In other terms, we discuss the merits of the behavioural model described by (9) without discussing its degree of rationality with respect to some mental model possibly adopted by the agent.
- 4.
Such a low number of independent replications are due to the extremely low volatility of the estimated average relative entropy across different replicas of 25 × 104 time steps each. In the different replica, we obtain standard errors in order of 10−5. As expected from an ergodic process, a single, sufficiently long, sequence is basically enough to obtain reliable estimates (Vandin et al. 2022).
- 5.
This statement has to be taken with a pinch of salt. The original BSV pricing model is not consistent with the Arrow–Debreu economy we consider here.
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Acknowledgements
We thank the attendance at the “IEAP Meeting: Investor Emotions & Asset Pricing”, IAE Lille University School of Management, February 2022, and in particular Pascal Alphonse for a number of useful comments and suggestions of previous contributions in the literature. The authors also thank an anonymous referee for the insightful review.
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Antico, A., Bottazzi, G., Giachini, D. (2023). On the Evolutionary Stability of the Sentiment Investor. In: Bourghelle, D., Grandin, P., Jawadi, F., Rozin, P. (eds) Behavioral Finance and Asset Prices. Contributions to Finance and Accounting. Springer, Cham. https://doi.org/10.1007/978-3-031-24486-5_7
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