Hiroshi Takahashi and Takao Terano (2003)
Agent-Based Approach to Investors' Behavior and Asset Price Fluctuation in Financial Markets
Journal of Artificial Societies and Social
Simulation
vol. 6, no. 3
<https://www.jasss.org/6/3/3.html>
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Received: 31-Oct-2002 Accepted: 1-Jun-2003 Published: 30-Jun-2003
Refer to Black (1992) for the detail of the bayes correction model^{[19]}.
Figure 1. Price history (when 100% of investors predict based on the fundamental value) |
Figure 2. Price history (fundamentalists : trend predictors = 500 : 500) |
Figure 3. Cumulative excess returns (fundamentalists : trend predictors = 500 : 500) |
Figure 4. Price history when natural selection works (fundamentalists : trend predictors = 500 : 500) |
Figure 5. History of the number of investors when natural selection works (fundamentalists : trend predictors = 500 : 500) |
Figure 6. Distribution of the number of fundamentalists (t=200) |
Figure 7. Distribution of the number of fundamentalists (t=500) |
Figure 8. Price history (fundamentalists : trend predictors = 100 : 900) |
Figure 9. Cumulative excess returns (fundamentalists : trend predictors = 100 : 900) |
Figure 10. Price history when natural selection works (fundamentalists : trend predictors = 100 : 900) |
Figure 11. History of the number of investors when natural selection works (fundamentalists : trend predictors = 100 : 900) |
Figure 12. Distribution of the number of fundamentalists (t=50) |
Figure 13. Distribution of the number of fundamentalists (t=100) |
Figure 14. Price history (with the investment restriction) |
Figure 15. Cumulative excess returns (with the investment restriction) |
Figure 16. Distribution of the number of fundamentalists (with the investment restriction, t=50) |
Figure 17. Distribution of the number of fundamentalists (with the investment restriction, t=100) |
Figure 18. Price history (when some investors have no restriction) |
Figure 19. Cumulative excess returns (when some investors have no restriction) |
Figure 20. Price history (when overconfident investors [k=0.9] exist) |
Figure 21. Cumulative excess returns (when overconfident investors [k=0.9] exist) |
Figure 22. Price history (when overconfident investors [k=0.8] exist) |
Figure 23. Cumulative excess returns (when overconfident investors [k=0.8] exist) |
Figure 24. Price history (when overconfident investors [k=0.6] exist) |
Figure 25. Cumulative excess returns (when overconfident investors [k=0.6] exist) |
Figure 26. Price history (when fundamental predictors based on Prospect Theory [10 days] exist) |
Figure 27. Price history (when fundamental predictors based on Prospect Theory [max 10 days] exist) |
Figure 28. Price history (when fundamental predictors based on Prospect Theory [max 20days] exist) |
Figure 29. Price history (when trend predictors based on Prospect Theory exist) |
^{2}Even when CAPM was suggested, Simon already pointed that the rationality of human being is bounded (Simon 1955). However, an asset price in financial markets is considered to be priced based on the fundamental value for the reasons that "irrational investors behave random and their behaviors are canceled out" and "arbitrage transactions adjust the market price to the fundamental value". Friedman also insisted that even if the assumptions are unrealistic, the traditional finance is valid while it has enough explanation power (Friedman 1953). On the other hand, Behavioral Finance casts some doubt on the assumptions of traditional financial theories by pointing "there are good reasons to believe that the behavior of irrational investors is biased" and "the capability of arbitrage is limited".
^{3}Hirshleifer (2001)describes how Agent-Based Approach is effective to analyze financial markets.
^{4}Several articles including our paper analyze artificial markets in which investors change their strategies based on their own rules (Kirman and Teyssiere 2001, Lux and Marchesi 1999). Our work focuses the temporal change of the number of investors during the simulation (e.g. see fig. 5-7).
^{5}It is also reported that rational investors adopt the optimal strategy in consideration of irrational investors' behavior. However, in the interests of simplicity, we make analyses based on the investors who do not consider other investors' behavior and always follow the pre-defined rules.
^{6}For example, they try to derive the optimal portfolio strategy under the condition that the lending and borrowing interest rates are different.
^{7}The investors in real markets collect the information from media and information terminals and update their belief based on it.
^{8}Every investor adopts the same benchmark that is buy-and-hold of the portfolio consists of 1,000 CASH and 1,000 STOCK at the initial state (t=0).
^{9}It is conventionally pointed that the typical means-variance models have a problem that "the slight difference in return makes large difference in assets allocation". The bayes correction model has resolved this problem and is closer to the investors' real behavior.
^{10}When a loss arises as against the reference point, the investor estimates the loss larger than the actual and tends to behave more like a risk taker. This behavior vastly differs from the decision-making based on maximization of expected utility. On the other hand, when a profit arises as against the reference point, the form of the value function convexes upward, which is similar to the form of the conventional maximization of expected utility.
^{11}The models for biases on decision-making are proposed in De Long (1990a), De Long (1990b), Barberis and Shleifer (1998), Kyle (1997), and Hong and Stein (1999). Although Behavioral Finance is sometimes considered ad hoc, it may be not in accordance with the reports that say that the emotion plays a key role in decision-making of human being (Damasio 1994, LeDoux 1996, Loewenstein 1996).
^{12}Chiarella (1992) and Lux (1998) analyze the influences of heterogeneous investors with differential equations formulation, but the analyses lack the constraints assumptions about investors. On the other hand, agent-based approach deal with various kinds of analysis hard to analyze with differential equations. This is one of the advantages of our agent-based approach to financial market analysis.
^{13}Behavioral finance tries to explain non-standard investors, such as trend followers, noise traders, overconfident investors, and loss avert investors from psychological view points. Several researchers have analyzed the effects of trend predictors and noise traders on asset prices with agent-based approach (Kirman and Teyssiere 2001, Lux and Marchesi 1999). In our paper, we deal with trend predictors, overconfident investors, and loss avert investors. One of the novelties of this research is to analyze the effects of overconfidence and loss aversion.
^{14}See http://www.rr.iij4u.or.jp/~taishi/research
^{15}We also analyze the case that the investment ratio of the risk asset is restricted (see section 4).
^{16}For the simplicity, the investor models in this paper make investment decisions based on single period model. The analysis based on investors who consider multi- period is one of our future works. It is reported that rational investors adopt the strategy in consideration of irrational investors' behavior. However, for the simplicity, we assume that the behavior of each investor does not change according to the other investors' behavior. The analysis of the market that contains the investors who consider other investors' behavior is also one of our future works.
^{17}Every investor adopts the same benchmark that is buy-and-hold of the portfolio consists of 1,000 cash and 1,000 stock at the initial state (t=0).
^{18}When the most recent price is higher than the price at the reference point, the original predicted price remains as the ultimate predicted price.
^{19}Appendix B at the end of this paper shows the outline of the bayes correction model.
^{20}Although there are other determination methods of traded prices, we adopt the simplest method in accordance with Arthur et al. (1997). We expand traditional financial theory such as CAPM by adopting an equation based price determination because, in this paper, we will explore the limitation of conventional financial theory by Agent-Based Simulation. Elaboration of the price determination method is one of our future works. At the price determination, we change the value of (P_{t}) in increments of 0.1 and search the price to satisfy the equality condition. Although we adopt the simplest price determination method, consideration of other methods is also one of our future works.
^{21}Every experiment described in this paper is repeated more than fifty times in each condition so that the reproducibility of the results is confirmed. We also analyzed the volatility of this market including the comparison of simulation data with empirical data. The detail is discussed elsewhere Takahashi and Terano (2002).
^{22}When every investor is fundamentalist, the valuation of the asset price completely agrees among all investors. Therefore, the stock price fluctuates according to the fluctuation of the corporate profit, but the number of stock held by each investor does not change and no transaction occurs.
^{23}As for the trend prediction investor, we have illustrated typical three trend investors (Trend1, Trend2, Trend3).
^{24}Even if the traded price deviates from the fundamental value, it is adjusted by the fundamentalists.
^{25}We obtain the same result even when we increase the ratio of the trend predictors up to 70%.
^{26}At the beginning, the price fluctuation does not show the extreme trend so that the influence of fundamentalists is relatively large and the traded price fluctuates around the fundamental value. After a certain terms, however, the price fluctuation shows the extreme trend in many cases so that the traded price largely deviates from the fundamental value. Note that we abort the experiment when the traded price becomes fivefold or fifth part of the fundamental value because the computation takes too long and the extreme deviation of the prices is unrealistic.
^{27}In this paper, every investor initially has the same amount of assets. It is also one of our future works to analyze the cases that each investor initially has different amount of assets.
^{28}This experiment shows two types of results: one is the case the fundamentalists are eliminated and another is the case they are not. The main factor that brings different results is how the situation of excess returns was when the natural selection principle worked for the first time. For example, the fundamentalists tend to be eliminated from the market if the trend predictors obtain excess returns when the natural selection principle works for the first time.
^{29}In the experiments on this investor ratio without the investment restriction, we have obtained the results that conform to the conventional financial theories.
^{30}For example, if the ratio of the stock to the total market value at the term t-1 is 50%, the investment ratio of the stock at the term t must be 50%±5%. Such both over and lower risk limits are usually found in the business area of asset management of pension.
^{31}This tendency is accelerated when the degree of overconfidence is increased.
^{32}We set the reference point of Prospect Theory at ten days before.
^{33} e^{ricum} corresponds to the fitness of genetic algorithm.
The short term expected rate of return of the investor i is calculated from the predicted stock price and the current stock price P_{t} as , where are the stock price and the predicted return of the investor respectively. The short term expected rate of return contains the error term to reflect the fact that the in-depth prospects are different even among the investors of the same prediction type.
The expected rate of return on the stock is calculated as . As described above, the expected rate of return on the stock can be calculated based on the corporate profit at the term t and the information (such as prices) available from the market at and before the term t-1.
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