«Abstract In this paper, we study the long-run wealth distribution regarding different trading strategies in an artificial stock market. An artificial ...»
Relationship between Trader Types and Their Long-run Wealths in an
Artificial Financial Market
Akira Namatame1,Kazuya konno2, Taisei Kaizouji 3
National Defense Academy
International Christian University
In this paper, we study the long-run wealth distribution regarding different trading strategies in an
artificial stock market. An artificial stock market is designed consisting with two broad types of
agents, "rational traders” and "imitators. Rational traders trade to optimize their short-term income and they invest based on their expectation on both trend follow and reverse of it. We also include imitators, i.e., traders that mimic behavior of the majority of rational traders. We investigate the performances of various traders by changing the ratio of rational traders and imitators. In the region where rational traders are in the minority, they can come to dominate the market, in that they eventually have a high share of wealth. On the other hand, in the region where rational traders are in the majority and imitators are in the minority, imitators can come to dominate the market. We conclude that the survival in a finance market is a kind of the minority game at the meta-level between rational traders and imitators.
1 Introduction Economists have long asked whether traders who misperceive the future price can survive in a competitive market such as a stock or a currency market. The classic answer, given by Friedman, is that they cannot. Friedman argued that mistaken investors buy high and sell low, as a result lose money to rational trader, and eventually lose all their wealth.
Shleifer and his coleagues questioned the presumption that traders who misperceive returns do not survive. Since noise traders who are on average bullish bear more risk than do investors holding rational expectations, as long as the market rewards risk-taking such noise traders can earn a higher expected return even though they buy high and sell low on average. The relevant risk need not even be fundamental: it could simply be the risk that noise traders’ asset demands will become even more extreme tomorrow than they are today and bring losses to any investor betting against them.
Because Friedman’s argument does not take account of the possibility that some patterns of noise traders’ misperceptions might lead them to take on more risk, it cannot be correct as stated. But this objection to Friedman does not settle the matter, for expected returns are not an appropriate measure of long run survival. To adequately analyze whether noise traders are likely to persist in an asset market, one must describe the long run distribution of investors’ wealth, not just the level of expected returns.
Understanding if there are winning and losing market strategies and determine their characteristics is an important question from the point of view of investors and regulators alike. On one side, it seems obvious that different types of investors exhibit different investing behavior which is, at least partially, responsible for the time evolution of market prices. On the other side, it is difficult to reconcile the regular functioning of financial markets with the coexistence of different types of investors. If there is a consistently winning market strategy than it is reasonable to assume that the losing traders disappear in the long run. It was Friedman who first advanced the hypothesis that in the long run irrational investors cannot survive as they tend to lose wealth and disappear. Offering an operational definition of rational investors, however, presents conceptual difficulties as all investors are boundedly rational. No agent can realistically claim to have the kind of supernatural knowledge needed to formulate rational expectations. The fact that different types of traders with different trading strategies prone to forecast errors can coexist in the long run is a fact that still requires an explanation.
In this paper we take an approach in considering the long run distribution of wealth. We examine how traders with various trading strategies affect prices and the long run accumulation of the wealth. We show that mimic traders as a group might survive and come to dominate rational investors in wealth when the proportion of imitators is much less than that of rational traders. Generally, in a market where rational traders are minority, we found that they could win and accumulate their wealth, whereas in a market where rational traders become majority, they lose and imitators win and accumulate their wealth.
2 An Agent-based Financial Market The variety of applications, the different types of learning mechanisms used in such applications and the different types of markets that one could simulate suggest a rich field of research. However, all this flexibility and freedom comes at a cost. One of the main criticisms to agent based markets is the large number of parameters and the tuning needed to get “realistic price behavior”. In some situations, small changes in the parameter settings could lead to significant changes in the market's behavior, both quantitatively and qualitatively. For any results to be creditable, changes in the parameters settings must not lead to significantly different results.
In recent economic and finance research, there is a growing interest in marrying the two viewpoints, that is, in incorporating ideas from social sciences to account for the facts that markets reflect the thoughts, emotions, and actions of real people as opposed to the idealized economic investors who under lies the efficient markets and random walk hypotheses. A real investors may intend to be rational and may try to optimize his or her actions, but that rationality tends to be hampered by cognitive biases, emotional quirks, and social influences. The behaviors of financial markets is thought to result from varying attitudes towards risk, the heterogeneity in the framing of information, cognitive errors, self-control and lack thereof, regret in financial decision making, and the influence of mass psychology. Assumptions about the frailty of human rationality and the acceptance of such drives as fear and greed are underlying the recipes developed over decades by so-called technical analysis. There is growing empirical evidence of the existence of herd or "crowd" behavior in speculative markets. Herd behavior is often said to occur when many people take the same action, because some mimic the actions of others. The term "herd" obviously refers to similar behavior observed in animal groups. Other terms such as "flocks" or "schools" describe the collective coherent motion of large numbers of self- propelled organisms, such as migrating birds and gnus, lemmings and ants. In recent years, physicists have shown that much of the observed herd behavior in animals can be understood from the action of simple laws of interactions between animals.
The most important design question faced in market building comes in the representation and structure of the actual trading agents. Agents can vary from simple budget constrained zero intelligence agents to sophisticated genetic programming models. This variation in design is due to the fact that trading agents must solve a poorly defined task. Given that there are many ways to process this past data, there must be as many ways to construct trading agents. The simplest and most direct route is to model agents as well defined dynamic trading rules modeled more or less as strategies used in the real world. This method can lead to very tractable precise results, which gives incites about the interactions between trading rules?
Many markets of this type assume that the trading strategies will continue without modification, although the wealth levels under their control may be diminishing to zero.
This leaves some open questions about co-evolutionary dynamic with only a limited amount of new speciation. A second critique is that agents in these markets do not operate with any well defined objective function. There is some usefulness to having well defined objective functions for the agents. There may be important tradeoffs involved which only a model with well defined objective functions can answer.
The second most important part of agent-based markets is the actual mechanism that governs the trading of assets. Once one leaves the relatively simple world of equilibrium modeling, it is necessary to think about the actual details of trading. This can be both a curse and a blessing to market designers. On the bad side it opens up another poorly understood set of design questions. However, it may have the beneficial effect of allowing one to study the impact of different trading mechanisms, all of which would be inconsequential in an equilibrium world.
This has been interpreted as evidence that as a forecaster age, evaluators develop tighter prior beliefs about the forecaster's ability, and hence the forecaster has less incentive to herd with the group. On the other hand, the incentive for a second-mover to discard his private information and instead mimics the market leader increases with his initial reputation, as he strives to protect his current status and level of pay. In a practical implementation of a trading strategy, it is not sufficient to know or guess the overall direction of the market.
There are additional subtleties governing how the trader is going to enter (buy or sell) the market. For instance, A trader will want to be slightly ahead of the herd to buy at a better price, before the price is pushed up for the bullish consensus. Symmetrically, she will want to exit the market a bit before the crowd, that is, before a trend reversal. In other words, she would like to be a little bit contrarian by buying when the majority is still selling by selling when the majority is still buying, slightly before a change of opinion of the majority of her "neighbors” This means that she will not always want to follow the herd, at least at short time scales. At this level, Anne cannot rely on the polling of her "neighbors" because she knows that they, as well as the rest of the crowd, will have similar ideas to try to out guess each other on when to enter the market. More generally, she ideally likes to be in the minority when entering market, in the majority while holding her position, and again in the minority when closing her position.
3 Design of an Artificial Market
3.1 A Market Mechanism and Performance Measures One of the most important part of agent based markets is the actual mechanism that governs the trading of assets. In most agent based markets they assume a simple price response to excess demand. Most markets of this type poll traders for their current demands, sum the market demands, and if there is an excess demand, increase the price.
If there is an excess supply they decrease the price. Simple form of this rule would be where D(t) and S(t) are the demand and supply at time t respectively. The agent is maintaining the stock and the capital in the artificial market model in this research. The agent loses the capital by obtaining the stock and gets it by selling off the stock.
It explains fluctuations in the value of stocks as follow: The unit of handling of the stock is assumed to be one unit.
where P(t) is stock prices at time t, N1(t) is a number of agents to buy and N2(t) is a number of agents to sell respectively at time t, χ is a constant. This expression implies that "the stock price is a n function of the excess demand”, and the price rises when there are more agents to buy, and it descend when more agents to sell it.
A Stock Volatility We define the price volatility as
where P(t) is stock prices at time t.
Individual Wealth The stock one agent can buy and sell in one trading is one unit. We introduce a notional wealth Wi(t) of agent i as follows.
where Φi is the number of assets held and Ci is the amount of cash held by agent i.
It is clear from equation that an exchange of cash for assets at any price does not in any way affect the agent’s notional wealth. However, the point is in the terminology :the wealth Wi(t) is only notional and not real in any sense. The only real measure of wealth Ci(t), the amount of capital the agent has available to spend. Thus, it is evident that an agent has to do a “round trip”(i.e.buy(sell)an asset then sell(buy)it back) to discover whether a real profit has been made.
The Profit Rate The coefficient is actually used for the value of this normal distribution putting it.
Next, it explains the rate of profit that becomes the standard of loss and gain.
The rate of profit of agent i is shown with γi, and γi(t) at time t is
The mode of dealing and the rate of profit are as mentioned above defined, Which agent is obtaining a higher profit is clarified by the simulation.
3.2 Modeling of Trader Types For modeling purposes, we have (rational traders) who make rational decision in the following stylized terms: If they expect the price goes up then they will buy, and if they expect the price goes down then they will sell right now. But what happens if every trader behaves the same way? Suddenly, some noises or disturbances are introduced exogenously. Given this uncertainty, the individually is modeled to behave differently.
One body of research has sought to explain the data with aggregate models in which a representative agent solves this optimization problem. If the goal is simply to fit the data, it is not unreasonable to attribute to agents the capacity to explicitly formulate and solve dynamic programming problems. However, there is strong empirical evidence that humans do not perform well on problems whose solution involves backward induction.
For this reason, these models fail to provide a realistic account of the phenomenon.
The model we describe will not invoke a representative agent, but will posit a heterogeneous population of individuals. Some of these will behave "as if" they were fully informed optimizers, while others will not.
The traders who enters the market forecasts, and has dealings over stock prices by various techniques. It is a linear forecast of past price data, and a forecast by information from media like news etc. The type of a investor is described from the difference of the forecast method.