Summary and conclusions

The goal of this section is to model the role of emotions in financial decision making. To this end, we advance a market setting where three distinct categories of economic agents trade a unique risky asset: rational traders, emotional traders, and noise traders. Prices are set by a competitive market maker to be proportional to the current total order flow.

We formally represent and study the formation of individual beliefs, the trader demand strategies, their individual and group wealth, and finally the price formation process.

What makes the distinction among our trader categories is, first, the way in which they interpret public information in order to form subjective beliefs, and, second, the strategy they pursue in order to determine the risky-asset amount to be traded. In particular, rational traders combine past and current information in a traditional Bayesian manner. In so doing, they account for the presence of other trade strategies and for their impact on prices. Moreover, rational demands are shaped to maximize expected utility of wealth. In contrast, emotional traders form beliefs in an unbalanced manner, putting different weights on diverse information sources. Thus, they are prone to thinking heuristics commonly met in practice, such as representativeness and conservatism. Also, emotional traders are not concerned with the existence of other agents. Furthermore, emotional traders blindly follow their beliefs in formulating demands and hence make use of heuristics (in the sense of simplifying rules) also in acting. Noise traders act randomly.

The belief formation relies on the interpretation of information. Our interest is in the role of emotional traders as a distinct type of traders driven by affect and intuition.

We suggest a way to quantify the emotional process of belief formation, showing how emotional traders may balance between past information and new evidence in contrast to the traditional updating employed by rational traders.

Once formed in the trader minds, beliefs flow into demands. In particular, trade

strategies are shaped in linear dependence on subjective opinions. Prices are set to be proportional to the current total order flow and depend thus on the demands of each trader group. We show how the distinct beliefs of different market participants are directly reflected in the informational content of prices. Given the rational strategy and the price setting rule, we derive the equilibrium condition of the market: Rational traders should be able to anticipate the total order flow emanating from the other traders, in other words to adapt to the conditions created by other traders, especially by the emotional ones. Such a strategy appears to be rational not only in classic, but also in an evolutionary sense.

Moreover, we measure the survival chances of our different trader categories by their individual and group wealth, the wealth variation between successive trades, and the growth of individual wealth as a part of the total trader wealth. We infer theoretical conditions on which rational wealth decreases and fluctuates less than the emotional one.

This corresponds to the possibilities that rational traders lose money or make lower profits than their emotional peers, respectively.

The somewhat static setting described sofar is subsequently extended to a particular case of dynamic belief updating. We derive the corresponding market prices both in the short and the long run.

Finally, our model is tested by numerical simulations for different parameter con-stellations and in different market settings. Specifically, we examine the evolution of log-returns, trader demands, and trader wealth for various proportions of rational and emotional traders, distinct behavioral profiles of emotional traders, different relations be-tween the actions of emotional and noise traders, various belief updating rules, and several trade organization possibilities.

Our simulations suggest that markets in which emotionally driven agents are active, can reach stable and closely efficient states. A necessary premise appears to be the existence of other traders, who rationally maximize expected utility of wealth and, in consequence, adapt to the conditions created by emotional trades. Rational traders of this type commit to absorbing the uncertainty generated by other non-strategic trades.

Therefore, their presence guarantees – or at least facilitates – the market stability.

In spite of their simplistic thinking processes and action strategies, emotional traders appear to be not only able to survive, but even to dominate such markets. They are best off – in terms of individual and group wealth, as well as of the growth of individual wealth – when they think conservatively, ascribing a higher importance to past evolutions

than to current information. Markets with conservative emotional traders are closest to efficient, and rational agents constantly lose money. However, when emotional traders are impulsive (and hence more similar to noise traders), rational traders make higher profits but all traders are able to accumulated positive wealth from the trade. With balanced emotional traders (who come thus closest to the rational way of thinking, although in a more simplistic manner), rational traders dominate the market only in the short run but are eventually overtaken by their emotional peers.

These findings support the idea that, under certain circumstances, emotional traders have high chances of continued existence while rational traders might be even forced to quit the market in consequence of too high loses. This comes to contradict the traditional conviction that rational traders can be the sole survivors in financial markets.

CHAPTER 3

How Investors Face Financial Risk:

Loss Aversion and Wealth Allocation

“[...] it is not the loss itself, but the estimate of the loss that troubles us.”

Seneca.

T

Our contribution concerns the integration of behavioral elements into the classic portfolio optimization. We extend a VaR-portfolio model in order to account for individually per-ceived risk. Individual perceptions are modeled according to an extended prospect-theory framework: Losses loom larger than gains of the same size (loss aversion) and the past risky-portfolio performance changes the subjective valuation of risky investments. The utility of financial investments is overemphasized (myopia). The portfolio model with indi-vidual VaR delivers an optimal wealth assignment between risky and risk-free assets.

We proceed in two steps: First, we assume that non-professional investors derive utility exclusively from financial wealth fluctuations. In consequence, they are interested in split-ting their wealth between risky and risk-free assets. We analyze how the past performance and the evaluation frequency of risky performance impact non-professional investors’ be-havior. Estimations based on real market data suggest that myopic loss aversion holds at different evaluation frequencies. One year is the optimal evaluation horizon at which, under practical constraints, risky holdings are maximized. Classic settings using standard VaR-significance levels may underestimate the loss aversion of individual investors.

Second, utility is derived from a twofold source: financial wealth fluctuations and con-sumption. Wealth has to be split now between consumption and financial assets in to-tal. The aggregate market equilibrium is obtained in two distinct settings: under the maximization of expected and of non-expected utility. Our estimations indicate that the non-expected utility setting is more robust and describes better the behavioral profile of non-professional investors. Compared to their peers in the expected-utility setting, the maximizers of non-expected utility are more averse towards financial losses, and allocate lower percentages of their total wealth to financial investments in total, but higher ones to risky assets in particular. With two-dimensional utility, myopic loss aversion is mostly rejected.¹

1This chapter is based on joint work with Erick Rengifo.

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