Introduction

actions are therefore guided by a (somewhat) strategic view over the course of action to be taken and how this affects the entire market evolution.

However, numerous empirical studies have emphasized the perpetuated existence of traders who employ a small number of simple and quick rules of thumb in order to make decisions under uncertainty. These traders are referred to as “not fully” or “quasi rational”

and their action rules as heuristics. Heuristics appear to be based on strong emotional components. They can sometimes lead to systematic mistakes, denoted as biases. Nev-ertheless, heuristics have proved to be useful in practice, especially when decisions have to be made under time constraints, uncertainty, or huge amounts of information. More details on what heuristics are and on their role in decision making can be found in the above Section 2.1.2.

Within the last years, a new paradigm which tries to integrate the classical finan-cial theory with the behavioral perspective has been developed in Lo (2004) under the name of the adaptive markets hypothesis. As stressed in the same Section 2.1.2, it is based on Darwin’s theory of evolution and considers individuals as organisms that try to maximize the survival of their species. During the decision making process, they develop heuristics in order to maximize the efficiency of their responses to uncertainty. However, since the environment is constantly changing, we can observe behavioral biases given the maladaptation to new circumstances.

The natural question arising in this context is if traders who follow their intuition and affect – in particular their emotions – and use heuristics can survive when confronted with rational traders and if so, under which conditions. This section attempts to further explore this question and hence to determine if the rational decision making represents the unique path towards survival in uncertain environments such as financial markets. To this end, we rely on market microstructure features and incorporate the role of emotions in financial decision making.

Specifically, we design a market with three groups of traders: rational traders, emo-tional traders, andnoise traders. These categories – which can be viewed in an evolution-ary perspective, as species – differ in the way they form beliefs and make decisions.

In essence, the belief formation is based on how information is perceived. In this con-text, rational traders consider both prior and current information to be equally important in order to infer price evolutions. They perform what we denote as a balanced combi-nation of elements of information, in the Bayesian spirit. In addition, rational traders

account for the existence of other traders with specific beliefs and their possible influence on prices. In contrast, emotional traders remain unconcerned with the existence of other traders and tend to under- or over-weight the prior relative to the current information.

Thus, they act either impulsively or conservatively, being guided by their affective per-sonality traits.⁴⁵ Such behaviors represent manifestations of frequent thinking heuristics.

Note that, as noise traders are assumed to trade randomly, we are not interested in their beliefs.⁴⁶

Emotional traders differ from their rational peers also with respect to the way in which they act, in particular to their demand strategy. In the vein of classical Economics, rational traders maximize the expected utility of wealth. Emotional traders simply follow their intuition. Specifically, they trade in accordance with their subjective beliefs in the price evolution. The emotional demand strategy can be considered as an example of action heuristics. As mentioned above, noise traders act randomly. Further details on the theoretical foundation, the intuition, and the implications of these assumptions can be found in Section 2.1.3.

We show that emotional traders exert an important influence on prices. The market equilibrium can be reached if rational traders adapt to the conditions created by emotional traders and their noise peers. In other words, the best rational strategy is to take into account the existence of other strategies. This appears to be indeed the most “rational”

way, both in the classic sense (since thereby the goal of expected utility maximization is reached) and in an evolutionary sense (since adaption should ensure survival). How-ever, rational traders are not necessarily accumulating the highest wealth in the market.

They can be worse off than emotional traders and even systematically lose money. We theoretically derive the conditions under which such a situation occurs. In addition, we empirically explore possible parameter constellations that facilitate an emotional lead over rational traders. For instance, rational traders perform better than impulsive emotional traders but worse than conservative ones. In sum, our results support the possibility that emotional traders can survive – and even dominate the market – in spite of their apparently simplistic strategy and “distorted” belief formation processes.

Moreover, our simulations indicate that market evolutions are not necessarily

per-45In essence, emotional traders can be considered to be quite young and self confident and having no formal education concerning financial markets. Thus, they do not analyze the market development using sophisticated tools but instead rely on their own intuition and experience in the market.

46Since these beliefs cannot affect their actions.

turbed by the emotional presence. Our markets are always stable in response to singular shocks (in particular, log-returns are stationary). They even come close to efficiency when emotional traders perceive past evidence to be at least as important as new one, in other words when they think conservatively. A too elevated presence of emotional traders in the market can yet destabilize the trade of insufficiently liquid assets.

The remainder of the section is organized as follows: Section 2.2.2 presents our the-oretical model following the main steps of the price emergence. In particular, we first formalize the formation of group specific beliefs by combination of prior and current el-ements of information. Second, we show how traders formulate their demands based on these subjective beliefs. To this end, we detail the price setting rule and subsequently the demand strategies of each trader group. The price formation is thirdly addressed.

Fourthly, we derive the individual wealth of the different trader categories. Finally, we study an extension of the model in a particular case with dynamic belief updating. The applicative Section 2.2.3 comments on the simulation results – in particular log-returns, individual demands, and individual wealth and wealth growth – obtained under various parameter constellations. The final Section 2.2.4 summarizes the main findings. Interme-diate mathematical proofs and further graphical results are included in Appendix A.2.