Summary and conclusions

Our paper extends the model of Glosten and Milgrom (1985) in order to capture better nuanced information asymmetries. In particular, we are interested in the impact of imper-fect information on prices, when traders acting on both perimper-fect and no information are also active in the market. We rely on the same main assumptions as in Glosten and Milgrom (1985): The trade takes place sequentially; At each time, a trader is stochastically chosen from the totality of traders and can submit (only) market orders for buying or selling one single unit of risky asset; The true value of the risky asset remains unknown to the market until the end of the trade, but some traders may receive information about it already dur-ing the trade interval; Submitted orders are executed by a competitive and risk-neutral market maker; Prices are competitively set, so that the market maker expects zero total profits; Inventory and order processing costs are considered to be constant. Moreover, as in Easley and O’Hara (1987), information arrives randomly in the market.

Our contribution consists in refining the view over information asymmetries, by intro-ducing a supplementary category of informed traders. Specifically, instead of the common, but somewhat coarse, twofold categorization of traders in informed and uninformed, we consider three trader groups: the usual informed traders (who dispose here of perfect information about the true risky value); the usual uninformed traders (motivated by ex-ogenous trade reasons, such as liquidity needs); and a new group of imperfectly informed traders who derive some information, the accuracy of which is explicitly modeled. We consider that our threefold trader-type setting resembles better real markets, where, be-sides liquidity traders and insiders which have access to perfect information, there is also

128In an evolutionary environment, where traders can switch between groups, we expect that more uninformed traders start using practical rules. This would render groupbeven more numerous and thus reinforce the impact on prices.

a relatively high proportion of users of practical trading methods, such as technical or fundamental analysis. The users of practical rules derive information from the system-atical analysis, that employs specific tools, of market-specific and/or market-exogenous data. This information is imperfect – more exactly imperfectly accurate – in the sense that it can be more or less valuable, depending on the deployed method and the skills of the respective traders. However, this information is used in a rational manner, since all traders forming expectations in line with the Bayes rule. We are interested in how this imperfect information affects prices.

Our “threefold” setting replicates the main theoretical results of the settings with only two categories of traders: In consequence of the information asymmetry, the market maker is confronted with adverse selection. Therefore, she sets two different prices for buying and selling the risky asset at each trading time, namely the ask and the bid, respectively.

We theoretically show that a positive gap, denoted as spread, forms between these prices on the condition that the imperfect information is somewhat accurate. General prices are Martingales, but, when imperfect information is derived from past market data, the single prices are not Markovian. In other words, prices as a whole are efficient while the ask and bid sequences can be informative relative to single transaction prices. We also analyze how prices evolve with respect to public beliefs and determine the public belief level at which the spread is maximized.

We subsequently detail the impact of imperfectly information on prices. In so doing, we distinguish a twofold effect: qualitative, i.e. given by the accuracy of imperfect infor-mation, and quantitative, i.e. due to the dimension of the group of imperfectly informed traders. These two influences are studied separately, by considering first- and second-order effects on prices of all variables that characterize the imperfectly informed trade.

Our main finding is that an intensification of the imperfectly informed trade, either in the qualitative or in the quantitative sense, entails worse overall trading conditions, i.e. higher spreads. The same conclusion holds with respect to the impact of perfect information on prices, although several differences manifest with respect to second-order effects.

Finally, we analyze how prices evolve in time when three simple trading strategies are employed, one at a time, for generating imperfect information. All these strategies belong to groups of heuristical methods of wide practical use, such as the technical and fundamental analysis. In particular, we account for the simplified forms of two chartist strategies, namely of a momentum and a moving average one, and of one fundamentalist

strategy. When imperfectly informed traders use the fundamentalist strategy, prices do not always converge within the considered trading interval or, as the case may be, the convergence necessitates longer intervals. When prices do converge, they constantly reach the true risky value. Yet, for both chartist strategies, we observe price convergence across all considered cases (with different proportions of chartists and different chartist infor-mation accuracy). Moreover, the momentum strategy always ensures positive profits, the moving-average one yields merely losses for its supporters, and the fundamentalist strat-egy makes money only during shorter time intervals or under specific market conditions.

In sum, (some) practical trading rules appear to be able to provide, at least under certain circumstances and when they are employed in a rational manner, the opportunity of mak-ing profits; and, in line with Lo (2004), of survivmak-ing in the market.¹²⁹ This supports the claim of the same author that survival can be reached, among others, through heuristics.

129Lo (2004) argues that in financial markets the most fit for survival are the richest.

CHAPTER 2

Emotions and Financial Decision Making

”All learning has an emotional base.”

Plato.

T

We contribute to the theoretical study of the emotions’ role in financial markets by devel-oping a model in which three categories of traders face each other: rational, emotional, and noise traders. Each of these categories is guided by different perceptions of informa-tion and different acinforma-tion principles. We suggest a method for quantifying belief formainforma-tion, which conforms to the Bayesian logic for the rational traders and complies with affective in-tuition for the emotional ones. Rational traders maximize expected wealth utility, demands develop proportionally to subjective beliefs, and prices are linear in the total order flow. Un-der these assumptions, the best rational strategy in equilibrium is to perfectly adapt to the market conditions created by the other market participants. In spite of their apparently simplistic demand strategy and distorted revision of beliefs, emotional traders not only de-cisively influence prices, but can even make more money than their rational peers. Thus, prices in (certain) financial markets may represent a thermometer of the market mood and emotions, rather than informative signals as stated in traditional financial theory.¹

1The main ideas of this chapter are based on joint work with Diego Salzman. The current version has been developed with the help of Michel Baes.

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