in a Simulated Multi‐Agent Stock Market
Paolo Tasca
Advanced School of Economics, Ca’ Foscari University of Venice
Visiting Fellow Chair of Systems Design, ETH Zürich
First Draft: September 2008
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1. Introduction
In this paper we analyze the financial price dynamics emerging from the heterogeneous behaviours of traders interacting in an experimental asset market in presence of asymmetric information. The understanding of the behavior of partially informed agents in experimental settings is a critical step toward understanding behavior in real markets.
Access to qualitative private information gives the traders the opportunity to exploit a dominant position when trading with uninformed agents. This in turn motivates not only the search for information but also the communication of misleading information. For the uninformed traders, a situation of general uncertainty may also lead to imitation and ultimately to herding behaviour. As Grossman (1976) has observed, when confidence in fundamentals disappears, naive imitative behaviour may actually be the best option.
According to the theories of information aggregation (Grossman 1976, 1981; Grossman and Stiglitz 1980; Jordan 1982; Diamond and Verecchia 1981; Verecchia 1982), traders have and use different information about the value of assets and through the process of their aggregation, market prices effectively reveal all the information present in the market. Then, in equilibrium traders cannot learn nothing more than prices. In line with the rational expectations (RE) hypothesis, aggregation of diverse information is in general difficult because no single agent possesses full information. Traders can identify the state of nature with certainty only by sharing their individual information in the process of trading. Plott & Sunder (1982) and Forsythe, Palfrey & Plott (1982) study markets with insiders and uninformed traders. They show that the equilibrium prices do reveal insider information after repetition of experiments and conclude that the markets disseminate information efficiently. Plott & Sunder (1982) further show that convergence to the rational expectation equilibrium (REE) occurs in markets that pays diverse dividends to different traders. They attribute the success of the RE model to the fact that traders learn about the equilibrium price and the state simultaneously from market conditions. The results by Plott & Sunder (1988) and Forsythe & Lundholm (1990), on the other hand, show that a market aggregates diverse information efficiently only under certain conditions: identical preferences, common knowledge of the dividend structure, complete contingent claims. These studies provide examples of failure of the RE model and suggest that information aggregation is a more complicated situation. In another related study, O'Brien & Srivastava (1991) find that market efficiency in terms of full information aggregation depends on complexity of the market. In particular, complexity is induced by market parameters such as the number of stocks and the number of periods in the markets.
In a variety of situations the market may actually fail to aggregate information correctly. Salient reasons are information mirages and bubbles (see Camerer C. 1989, Camerer C. and Weigelt, 1991), information traps (see Nöth et al., 1999), and pricemanipulations (see Veiga and Vorsatz, 2008).
In this paper we investigate whether, in a market composed by informed and uninformed agents, uninformed agents may overreact to uninformative trades during the process of information aggregation. Once an agent occurs in such a mistake, she may trade as informed trader causing other traders to wrongly infer that she is an insiders. The misleading path of market prices resulting from such mistakes is what Camerer and Weigelt (1991) has referred to be “price mirages” because prices reveal information which is not really there. Information mirages is an important phenomenon to be analyzed as one explicative cause of some well known stylized facts in financial markets such as excess volatility (Shiller R.J., 1981). As Fisher Black (1986), French and Roll (1984) have considered, volatility of asset prices may be induced by traders overreaction to trades that are not informative, creating self-generated information mirages. We can imagine for example that just by chance, in the first daily trading sessions the most part of the orders are on the sell side. Uninformed traders entering the market later, may reasonable infer that the market sentiment is negative and may be induced to sell. Thus the market price should fall. Others uninformed traders who pay attention on the recent price path may be attracted by the price drop and be induced to enter the market on the sell side as well. This cycle exactly describe what we mean by an information mirage: a sort of mini-bubble which is typically temporary, and possibly small in size. Imitative behaviour may be responsible for a significant proportion of the price volatility observable in real-world asset markets: in inferring information from the trades of others, traders sometimes go wrong and their errors cause others to overreact, creating price paths that falsely reveal information that no one has.
Previous studies (e.g. Camerer and Weigelt, 1991) consider the dynamics of price mirages in the short run (few minutes). Whereas, in this paper we will analyse this phenomenon in the long run (around 1200 trading days): a sufficiently large horizon during which mini-bubbles may grow into big-bubbles.
2. Artificial Financial Market with Noisy and Insider Traders
Information mirages are difficult to detect in natural data because researchers usually do not know what information traders had at any point in time, so it is difficult to know whether prices incorporate all information or not. Instead, in the artificial financial market introduced here we model the flow through which information enter the market allowing the existence of asymmetric information. This arise the problem of what Fischer Black (1986) has referred to as noise trading:
“Noise trading is trading on noise as if it were information. People who trade on noise are willing to trade even though from an objective point of view they would be better off not trading. Perhaps they think the noise they are trading on is information. Or perhaps they just like to trade” (Black F., 1986, p.531)
The experimental approach is ideally suited to investigations of this kind, since it is possible to control both the structure of the market and the signals through which information is disseminated. Two classes of investors will be allow to trade contemporaneously in the market: insider traders and noisy traders. Insider traders, quickly will trade on the received unbiased signals revealing the variation of asset’s true fundamental value. While, noisy traders will behave as boundedly rational agents. They will trade upon indications of external biased signals and will be influenced by other investors’ sentiments. This lead us away from the Efficient Market Hypothesis (EMH) towards the Adaptive Market Hypothesis (AMH)1 and Coherent Market Hypothesis (CMH) of Vaga T. (1990) through the theory of social imitation (Callen,
Shapiro 1974) and the Ising model.
Market prices will be the product of the interplay between insider traders (called “rational arbitrageurs” in Shiller model, 1984) and noisy traders operating under different decision rules. With continuous information flows, the model encourage the interchange of the role between insiders and noisy traders. Insiders, making ex ante rational trades may nevertheless lose money ex post on any given trade. In real financial markets, investors may trade on the right side of the market performing as insider once they receive the right signal. But they can frequently be engaged in noise trades when receiving signals not carrying the true state of nature.
We frame the model into two classes of rules: microstructure rules and behavioral rules. Microstructure rules are all those ones describing the system design and the mechanisms characterizing the functionality of the market. Behavioral rules instead, describe the agents decisions models.
