"تراژدی منابع مشترک" معامله گران اساسی: هزینه های اطلاعات و عوامل دیگر برای بقای کارشناسان و معامله‌گران اختلال‌زا در بازارهای مالی

This study explores the long-standing question about the survival of noise traders in financial markets through the relatively new method of agent-based modeling. We find that, in the normal case, there are two attractors for the ratio of experts versus noise traders. Either experts disappear almost entirely from the market, or they account for a certain fraction, with noise traders still being present. In the dynamic framework, the dynamics switches between these attractors, which leads to the emergence of some typical statistical features of financial markets, such as long memory, leptokurtic returns, and bubbles and crashes. Furthermore, we achieve a general approximation of the attractors and of the switching point in between from relevant determinants.

Studies on financial markets commonly distinguish between two kinds of traders. Independent of their denotation (some studies call them rational, sophisticated or informed, others speak of arbitrageurs, smart money traders or fundamentalists), the common characteristic of the first group is that they derive their transactions from the analysis of true fundamental information. Though not trading arbitrarily, for the second group, this is not true. For example, so-called technical traders (or “chartists”) seek to identify patterns in the evolution of prices and extrapolate them. Yet, because of the myriad of behavioral patterns in this group and the unpredictability of their transactions, the second group has been known as “noise traders” (Black, 1986). It has been a long time since Milton Friedman (1953) stated that noise traders cannot survive in a market — a proposition which has been replicated in different model setups such as Figlewski (1978), Sandroni (2000) and Blume and Easley (2006). The unifying logic is that noise traders would lose money compared to rational agents as they trade on wrong beliefs (see also Alchian, 1950; Fama, 1965, for early proponents of this view). The opposite view is represented by a profound body of theoretic evidence which indicates that, under more or less restrictive assumptions, the long-run survival of noise traders is possible. Examples include DeLong et al., 1990 and DeLong et al., 1991, Blume and Easley (1992) and Evstigneev et al. (2002). One of the most popular arguments for this belief has been proposed by DeLong et al. (1991), who construct an overlapping-generations model. If noise traders overestimate returns or underestimate risk, they tend (unconsciously) to accept higher risks than arbitrageurs and thus achieve superior returns on average. Finally, Black (1986) states that noise trading is the very condition for rational arbitrage because if everyone had the same correct beliefs, there would hardly be any trading. Our study explores the survival of noise versus expert traders in a dynamic agent-based model. Financial market models from this field have proven to be quite successful in improving our understanding of real market dynamics; for surveys, see Hommes (2006), LeBaron (2006) or Westerhoff (2008). The relatively new, simulation-based approach enables us to uncover some dynamic effects in the ratio of trader groups which have been vastly ignored so far. A key feature of our model is the implementation of information costs. According to Merton (1987), information costs arise from “gathering and processing data”. Several studies have found such costs to be influential in investment decisions (e.g. Ahearne et al., 2004, Gregoriou and Ioannidis, 2006 and Kang et al., 1999). We can assume that information costs are particularly relevant for expert trading. Our model finds information costs to be a crucial determinant for the ratio of experts versus noise traders. Another new insight is that the share of experts, denoted by K, can alternate between two different attractors. The first attractor is K = 0. In such intervals, experts avoid the market because, due to the prevalence of noise traders, the tendency of the market towards a fundamental correction is too low to cover information costs. Experts incur profits if K exceeds some level K1, and the second attractor K2 becomes active. In K2, noise traders may still be numerous. The reason is that once K exceeds K2 the average mispricing becomes too small to make the experts' strategy profitable. One goal of this study is to derive these conditions of the existence and the value of the two critical points K1 and K2. We can do this analytically within a simple static framework (Section 2). In Section 3, the static setup is transformed into a dynamic agent-based model. The value of the agent-based model is to extend the analytical findings and to review their implications under more realistic conditions. It will be shown that the dynamics of the model switches between K1K1 and K2K2, and this produces volatility clustering, heavy tails of returns, and speculative bubbles and crashes — three of the most important stylized facts of financial markets. The two-staged approach illustrates the potential of agent-based modeling in combination with static analyses and yields some new insights into the question at stake.

The question of if noise traders can survive in financial markets has long been discussed in research. The present article enriches the debate by means of agent-based modeling. The dynamic model shows that the ratio between noise traders and experts in a market, K, is subject to dynamic effects which are hard to discover by static equilibrium analyses only. In particular, we have seen that, in the normal case, there are two equilibria for this ratio that work as attractors in a dynamic framework. One equilibrium is always K = 0, meaning that there are intervals in which experts largely disappear from the market. In the second equilibrium, K2, experts control the market, but the number of noise traders in this equilibrium can still be significant. In the dynamic framework, the dynamics switches between the two attractors. Switching occurs whenever the ratio of experts surpasses some critical level K1. In our analysis, we have identified several determinants for the break-even point K1 as well as for carrying capacity K2. A crucial determinant is information costs. We found that higher information costs lead to a rise of K1 and a decrease of K2. Other determinants for K1 and K2 are the aggressiveness of noise traders and the variability of the fundamental value of the asset traded. Because both variables impact the profit potential for experts, their increase creates room for more experts in K2. On the other hand, the critical level K1 rises, because a larger number of experts are needed to take control of the market. A similar effect occurs if experts have greater trading power, for example, because fundamental trading is undertaken mostly by institutional investors with significant transaction volumes. Then, K1 is lower, meaning that the probability that noise traders completely take over declines. With regard to K2, there is a mixed effect. We have found that for certain values of the relevant determinants, the equilibrium K2 does not exist at all. As a result, the only existent equilibrium is K = 0. Accordingly, experts, and not noise traders (!), are not able to survive in the market. The probability of this alarming situation is affected positively by information costs and by the volatility of value. In contrast, it is affected negatively by the experts' trading power and, surprisingly, by the aggressiveness of noise traders. The causes for all these findings were uncovered in the study. From a broader perspective, our findings suggest some analogies. The mispricing tendency of the market, which is produced by the transactions of noise traders and by changes of fundamentals, can be interpreted as the ‘common good’ of experts, as it represents the very condition for the profitability of fundamental trading and, hence, for the survival of experts. If experts exploit their common good too much, their persistence is endangered. The analogy to the “tragedy of the commons” (Hardin, 2009) is unmistakable. It is because of another tragedy that experts sometimes remain almost entirely out of the market. Agents will only bet on the fundamental strategy if they believe that there is a clear tendency of prices to return to value. However, provided that singular agents can influence prices only marginally, this is only the case if there are enough others who rely on this strategy. A similarity to the so-called “coordination game” (e.g. Cooper, 1999) becomes apparent. In sum, the existence of fundamental trading appears to be its own condition and its dilemma simultaneously. The method agent-based modeling was valuable as we could show switches between the regimes of experts and noise traders to produce some important stylized facts of financial markets such as leptokurtic distribution of returns, long memory, as well as bubbles and crashes. This insight is not completely new. However, we could achieve general approximations of the attractors and the threshold value in between, based on relevant determinants, which were then confirmed in simulation experiments. This underlines the benefit of a combination of algebraic methods and agent-based modeling. The findings sharpen our understanding of the inefficiencies of financial markets and are fundamental to derive regulative measures. The model made very clear that we have to distinguish between two types of inefficiency which have completely different origins: (i) Intervals of turbulent volatility in which prices depart from fundamentals. (ii) A base inefficiency which is the very condition for fundamental trading. Facilitating fundamental trading by means other than information cost can mitigate type (i) inefficiency, but does not necessarily reduce the inefficiency of type (ii). Reducing information cost, however, has a positive effect on both types. This shows the importance of any measure leading to a reduction of information cost, not only in order to improve efficiency in general but also to prevent financial instability. Let us conclude by commenting on two limitations of this study. First, our model only considered speculative profits. Dividends, opportunities for arbitrage between markets, and other returns were ignored, even though seeking such profits constitutes important motives for fundamental trading. Second, the profits of noise traders were not computed endogenously due to the variety of behavioral patterns in this group. However, some studies (e.g. Friedman, 1953) argue that noise traders lose money on average as they tend to buy high and sell low. In sum, the fundamental strategy could be more attractive than presumed in our model. We did not implement these aspects in order to preserve the algebraic tractability of the model. Future research should investigate how they affect the results obtained.