پویایی های اولویت ریسک، پیش بینی دقت و بقا : شبیه سازی بازار سهام مصنوعی بر اساس چند دارایی عامل محور

The relevance of risk preference and forecasting accuracy to the survival of investors is an issue that has recently attracted a number of theoretical studies. By using agent-based computational modeling, this paper extends the existing studies to an economy where adaptive behaviors are autonomous and complex heterogeneous. Specifically, a computational multi-asset artificial stock market corresponding to Blume and Easley [Blume, L., Easley, D., 1992. Evolution and market behavior. Journal of Economic Theory 58, 9–40] and Sandroni [Sandroni, A., 2000. Do markets favor agents able to make accurate predictions? Econometrica 68, 1303–1341] is constructed and studied. Through simulation, we present results that contradict the market selection hypothesis.

Agent-based computational economic (hereafter ACE) modeling is distinguished from the conventional economic modeling by its great flexibility in terms of agents’ heterogeneity and the associated population dynamics. This advantage may be very helpful in studying the survivability of different types of agents, specifically when they are placed in a complex interactive environment. In this paper, the ACE approach is applied to address a debate that can be related to the market selection hypothesis, according to which markets favor rational traders over irrational traders Alchian, 1950 and Friedman, 1953. The debate, if we trace its origin, started as a result of the establishment of what become known as the Kelly criterion (Kelly, 1956), which basically says that a rational long run investor should maximize the expected growth rate of his wealth share and, therefore, should behave as if he were endowed with a logarithmic-utility function. In other words, the Kelly criterion implicitly suggests that there is an optimal preference (rational preference) that a competitive market will select and that is logarithmic-utility. The debate on the Kelly criterion has a long history, so not surprisingly, there is a long list of both pros and cons with regard to it as the literature develops. 1 A possible implication of the Kelly criterion is that an agent who maximizes his expected utility under the correct belief may be driven out by an agent who maximizes his expected utility under an incorrect belief, simply because the former does not maximize a logarithmic-utility function, whereas the latter does. Blume and Easley (1992) were the first to show this implication of the Kelly criterion in a competitive asset market. In their seminal study, they questioned the survivability of rational investors. In a nutshell, they showed that rational investors who are characterized by their selection of a portfolio that maximizes their expected utility with respect to the correct belief may not be good enough to survive. To enhance their survivability, their preference over risk (utility function) must also be “optimal.” If not, an even more striking result is that these rational agents may be driven out of the market by those agents who base their decisions on incorrect beliefs, but have a “nearly optimal” preference. 2 The market selection hypothesis, therefore, fails because agents with accurate beliefs are not necessarily selected. A consequence of this failure is that asset prices may not eventually reflect the true value of the asset and may fail to converge to the rational expectations equilibrium. Nonetheless, a series of recent studies indicates that the early analysis of Blume and Easley (1992) is not complete. Sandroni (2000) shows that, if the saving behavior is endogenously determined, then the market selection hypothesis is rescued, and in the long-run, only those optimizing investors with correct beliefs survive. The surviving agents do not have to be log-utility maximizers, and they can have diverse preferences over risk. Sandroni’s analysis is further confirmed by Blume and Easley (2006) in a connection of the market selection hypothesis to the first theorem of welfare economics. They show that in a dynamic complete market Pareto optimality is the key to understanding selection for or against traders with correct beliefs: in any optimal allocation the survival or disappearance of a trader is determined entirely by beliefs and not by risk preference. Sandroni (2000)’s and Blume and Easley (2006)’s studies are largely analytical. They both take a Pareto optimal allocation as a starting point to work with. The dynamic process converging to a Pareto optimal allocation itself is, nonetheless, beyond the scope of their analysis. Issues related to the dynamic process are twofold. First, there is individual dynamic optimization. A Pareto optimal allocation rests upon the optimization of all individuals. In this specific context, this requires that all agents are able to solve the infinite-time stochastic dynamic optimization problem facing them, regardless of their preferences over risk or utility functions. However, analytical solutions known to us are severely restricted to certain classes of preferences. In general, one has to rely on numerical approximation, which means that Pareto optimality may not always be attainable. What makes this problem even more complex is, however, the second issue: trading at an equilibrium consistent with price expectations. Notice that what we study here is not a simple representative-agent optimization problem, but a market composed of heterogeneous agents. Each one of them, upon maximizing his expected utility, has to know the prices of assets in the future. These prices are, nonetheless, endogenously generated by agents’ own perceptions. As a result, a typical fixed-point problem occurs. The market, as a distributed decentralized processor, may fail to coordinate its participants to such a fixed point. In general, it will depend on agents’ forecasting rules and the associated learning schemes, and it is likely that agents will trade at prices that are inconsistent with their ex ante expectations of the prices. In this case, Pareto optimality is also not attainable. Both of the two issues discussed above are directly related to the attainability of Pareto optimality. However, Pareto optimality per se was only taken by Sandroni and Blume and Easley as a convenient starting point for their analytical work. To facilitate their further analysis, the learning dynamics concerned with the updating of agents’ beliefs are also needed to be simplified. Sandroni, for example, did not deal with learning dynamics directly; instead, he assumed that there will be a day when some agents can eventually make accurate predictions or eventually make accurate next period predictions and started his major analytical work from there. Nevertheless, a plausible process to show the appearance of these sages was absent. It is, therefore, not entirely clear whether these types of agents will ever emerge. What happens when no trader has correct beliefs? 3 Blume and Easley (2006) do recognize that the market selection hypothesis would be of little interest if it were to address only selection for traders with correct beliefs. Their delicate analysis of learning leads to two major findings as to the superiority of Bayesians. First, a Bayesian almost surely survives for almost all possible truths in the support of her prior. Second, in the presence of a Bayesian trader, any traders who survive are not too different from Bayesians. We admire the beauty of the analysis of the Bayesians, but are not entirely easy about traders being simply Bayesians. The experimental evidences are certainly not always in favor of Bayesian learning.4 Therefore, this consideration does not stop us from asking: what happens when no traders are Bayesians? This review and discussion of the early literature now seems to indicate clearly where we are moving. Needless to say, the above-mentioned analytical work on the market selection hypothesis has already provided us with an interesting benchmark to reflect upon, namely, the irrelevance of risk preference. However, since the conclusive statement is very interesting, it would be useful to see how strongly we can put it by relaxing some tight constraints. In this paper, we do not assume Pareto optimality, the emergence of the sages, or the Bayesians. This relaxation allows for a more extensive class of bounded-rational behaviors, and we examine whether the irrelevance of risk preference still holds with this enlargement. Concretely speaking, what is proposed here is a computational model, namely, an agent-based computational version of Blume–Easley–Sandroni’s model. The rest of the chapter is organized as follows. Section 2 briefly reviews the Blume–Easley–Sandroni model. An agent-based computational version of the model, provided in Section 3, can be regarded as an extension of the single-asset artificial stock market to its multi-asset version. The debate then proceeds with the experimental designs given in Section 4. The simulation results and analysis are provided in Section 5, followed by the concluding remarks in Section 6.

Earlier theoretical studies have already shown the irrelevance of risk preference to survivability. They have also shown that what matters is forecasting accuracy. After introducing bounded-rational behavior, we have almost the opposite: risk preference matters, and it is even more important than forecasting accuracy. Why does risk preference matter? The paper examines three interdependent possibilities: forecasting accuracy, portfolio, and saving among different types of bounded-rational agents. While being bounded rational, all of these agents are at least potentially equally smart in the sense that they are all equipped with the same adaptive search scheme, namely, the genetic algorithm. The neutrality of GA, in that GA does not make one type of agent smarter than the others, is also supported in Sections 5.1.2 and 5.1.4. Therefore, the forecasting accuracy and portfolio performance are excluded, and what is left is only the saving behavior. Therefore, the significance of risk preference is manifested by the saving behavior. While earlier studies recognized the importance of saving behavior to this issue, the attention has been restricted to the rational-equilibrium path. Various moments of saving behavior are not a concern as long as they are on the rational-equilibrium path. However, when they are not, this paper shows that such moments have strong implications for survivability. In addition to the first moment, which has already been explicitly noticed by Blume–Easley–Sandroni, we also find the significance of other high-order moments. Downside saving rates as well as the dispersion of saving rates can both be important. Since the saving decision in general is dependent upon the belief, errors in forecasting accuracy can propagate through the saving decision and manifest themselves in moments of saving. This observation generally applies to all types of agents, except type-1 agents, the log-utility agents, whose saving decisions are independent of their beliefs and are only determined by the exogenously given discount rate. That is what makes the log-utility agent so different from other agents. The conventional wisdom characterized by the Kelly criterion also works on this, but has not successfully established its validity, in particular, in the general equilibrium context. This paper shows that incorporating learning dynamics is one way of demonstrating its validity.