Microscopic Simulation of Financial Markets

From Investor Behavior to Market Phenomena

Haim Levy, Moshe Levy, Sorin Solomon

• Publisher: Academic Press
• Year: 2000
• ISBN:
  9780080511597
• Topic: Business
• Subtopic: Finanza
• Index: Business

Microscopic Simulation (MS) uses a computer to represent and keep track of individual ("microscopic") elements in order to investigate complex systems which are analytically intractable. A methodology that was developed to solve physics problems, MS has been used to study the relation between microscopic behavior and macroscopic phenomena in systems ranging from those of atomic particles, to cars, animals, and even humans. In finance, MS can help explain, among other things, the effects of various elements of investor behavior on market dynamics and asset pricing. It is these issues in particular, and the value of an MS approach to finance in general, that are the subjects of this book. The authors not only put their work in perspective by surveying traditional economic analyses of investor behavior, but they also briefly examine the use of MS in fields other than finance.

Most models in economics and finance assume that investors are rational. However, experimental studies reveal systematic deviations from rational behavior. How can we determine the effect of investors' deviations from rational behavior on asset prices and market dynamics? By using Microscopic Simulation, a methodology originally developed by physicists for the investigation of complex systems, the authors are able to relax classical assumptions about investor behavior and to model it as empirically and experimentally observed. This rounded and judicious introduction to the application of MS in finance and economics reveals that many of the empirically-observed "puzzles" in finance can be explained by investors' quasi-rationality.

Researchers use the book because it models heterogeneous investors, a group that has proven difficult to model. Being able to predict how people will invest and setting asset prices accordingly is inherently appealing, and the combination of computing power and statistical mechanics in this book makes such modeling possible. Because many finance researchers have backgrounds in physics, the material here is accessible.

• Emphasizes investor behavior in determining asset prices and market dynamics
• Introduces Microscopic Simulation within a simplified framework
• Offers ways to model deviations from rational decision-making

1

Classic Models in Finance: Solved and Unsolved Issues

1.1 INTRODUCTION

The classic models in finance, and in particular the studies that constitute the pillars of this relatively young field of research, are mainly analytical. These analytical models deal with investment decision making under uncertainty and, in particular, with the prevailed complex capital market composed of many risky assets. To achieve analytical results, it is necessary to assume a decision framework (e.g., expected utility framework) and to make many specific assumptions, some of which are very unrealistic. The fact that some of the assumptions are very unrealistic was not concealed from the researchers who made them; however, these assumptions were made for the sake of tractability in order to obtain analytical results.

Let us illustrate here with the Sharpe-Lintner Capital Asset Pricing Model (CAPM). The CAPM deals with rational investors who maximize expected utility. To obtain the CAPM, one needs to make many assumptions such as: no taxes, homogeneous expectations regarding future distribution of returns (which are assumed to be normal), no transaction costs, that all investors will have the same holding period, and so on. Obviously, these assumptions do not conform with the actual facts—in particular, taxes and transaction costs do exist. Thus, one may claim that the CAPM is unrealistic because the assumptions are unrealistic. It is also possible that these assumptions are intact, yet investors are irrational.

How crucial are these assumptions and what effect do they have on the derived model? What will be the effect on the theoretical results if one relaxes one or more of these assumptions? To neutralize the effect of these assumptions, and to test expected utility theory or portfolio theory even in the ideal case where such assumptions are intact, one can conduct experimental studies. Thus, one can test the investor’s rationality when all the assumptions are intact. Investment laboratory experiments can be conducted such that all the crucial assumptions mentioned hold. For example, there have been experiments in which the subjects participating had to choose from several securities and were told that there were no transaction costs, no taxes, and that the returns were drawn randomly from normal distributions with known parameters. By conducting the test in such a way, one can test the other ingredients of portfolio theory, in particular the expected utility theory (EUT) models. For example, by Markowitz’s (1952a) portfolio theory, which is the foundation of the CAPM, we expect that when one changes the correlation between two stocks, say, from + 0.8 to –0.8 (with no change in the parameters of the other stocks), generally a higher proportion of the subject’s wealth will be allocated to these two stocks. Also, when returns are drawn randomly from a given distribution with parameters that are known to the subjects, the historical rates of return are irrelevant for future decision making. The behavior found in laboratory experiments contradicts EUT: it was found that investors did not increase their investment proportion in stocks when the correlation between these two stocks was changed from + 0.8 to –0.8, and that investors insist on asking for information on historical rates of return even though they are irrelevant (see Kroll, Levy, and Rappoport, 1988a, 1988b). There are many more experimental findings rejecting EUT even in artificially simplified settings.¹ The deviation of investors from rationality induces deviations in market prices from what theoretical models predict. Indeed, Arrow (1982) asserts: “I hope to have made a case for the proposition that an important class of international markets shows systematic deviation from individual rational behavior” (see Arrow, 1982, p. 8).²

Most experimental studies do not involve securities. The subjects were asked to make some hypothetical choices from which it was concluded that a substantial group of them do not behave as EUT asserts. They behave irrationally, distort probabilities subjectively (but in some systematic way), and make decisions based on changes in wealth rather than total wealth. Kahneman and Tversky (1979), who conducted many of these experiments, suggest prospect theory (PT), which describes how investors behave in a laboratory environment, pinpointing the various contradictions to EUT.

Many experiments follow Kahnemann and Tversky’s 1979 PT paper. Most studies support PT, confirming the basic observations of Kahneman and Tversky.³ Yet a few studies reject the PT or some elements of it. ⁴ As mentioned previously, most PT studies are experimental studies. Yet, in a few exceptions the studies rely on empirical market data: for example, Fiegenbaum and Thomas (1988) and Fiegenbaum (1990) employ the COMPUSTAT data to confirm that risk-seeking behavior exists below a certain level of rate of return. D’Aveni (1989) uses data of bankrupt firms, finding that managers behave according to the predictions of PT, and Benartzi and Thaler (1995) use PT to explain the observed risk-premium in the market. Thus, there are attempts to use market data or to explain market phenomena like the risk premium by using PT.

Prospect theory casts doubt on the EUT, which is the foundation of most theoretical models in finance and economics. In addition, people do not react to changes in the various parameters as EUT predicts. Thus, the assumption that individuals act according to EUT is very problematic. On top of this, many of the specific assumptions underlying classical models are also unrealistic. According to Friedman (1953a), models should not be judged by their assumptions, but by their predictive power. Unfortunately, the empirical evidence either rejects the various theoretical models in finance or supports them only weakly. Thus, the classic models in finance and economics are attacked on several fronts.

There are no analytical tools to measure the effect of various deviations from the EUT assumption and from model-specific assumptions on the results and, in particular, on asset price determination and on the risk-return relationship. It is possible that the fact that some of the assumptions regarding investors’ behavior that underlie a given model are not so crucial, and the fact that they do not hold has only a minor impact on the model’s results. Alternatively, it is possible that even a small deviation from the assumptions may completely reverse the theoretical results. Since it is hard, if not impossible, to analytically test the effects of various deviations from the model’s assumptions on asset prices, in this book we suggest a different approach to investigate these effects.

We suggest employing the microscopic simulation (MS) methodology to analyze the impact of various deviations from EUT and other unrealistic model-specific assumptions on the theoretical results. With the MS methodology one can allow for heterogeneous expectations, various heterogeneous investment holding periods, and even a violation of EUT in favor of prospect theory or other experimentally observed behavior patterns. With MS one can model investors as being quasi-rational or bounded-rational (see Russell and Thaler, 1994, and Black, 1986): they maximize some expected utility or value function but they may make errors in their decision making. The MS methodology allows us to relax one or more of the model’s assumptions and to examine the effects of this relaxation on the results. MS allows us to obtain results that are impossible to obtain analytically.

1.2 EUT, ALTERNATIVE MODELS, AND NOISE TRADERS

One of the most famous violations of EUT is the Allais paradox (1953) (see Chapter 2). There are a variety of modifications of EUT that may explain this paradox. Machina (1982) proposes a generalized expected utility theory, Kahneman and Tversky suggest prospect theory, Chew and MacCrimmon (1979) develop weighted utility theory, Bell (1982), Fishburn (1982), and Loomes and Sugden (1982) suggest the regret theory, and Quiggin (1982) proposes the rank dependent utility theory. The states of all these theories is best summarized by Davis and Holt (1993):

For a variety of reasons, none of these alternatives has become widely accepted. First, the pattern of violations of expected utility theory is not as clear as was once believed, and no rival theory persuasively organizes the somewhat mixed data. Second, their application involves complicated specifications of utility functions, which theorists find rather cumbersome. (p. 448)

Thus, it is not obvious that any of the other proposed theories are better than EUT, in particular because they do not provoke simple testable hypotheses or even do not suggest an equilibrium price determination model. We do not reject a theory unless there is a better one. Therefore we do not reject the EUT. This idea was summarized as early as 1966 by George Stigler:

When we assume that consumers, acting with mathematical consistency, maximize utility, ... it is not proper to complain that men are much more complicated and diverse than that. So they are, but, if this assumption yields a theory of behavior which agrees tolerably well with the facts, it must be used until a better theory comes along. (Stigler, 1966, p. 6)

Thus, it seems that the correct approach is not to reject EUT but to improve it, either by relaxing some of the assumptions or by adding some components to the decision-making process (e.g. some sort of irrationality). Indeed, this is the approach adopted in this book.

Generally, the investment decision process can be classified into two extreme regimes: one asserting that all investors maximize some utility function and act exactly as implied by EUT. The other is the complete opposite—a chaos in which investors buy or sell stock randomly, completely unrelated to the asset’s fundamental value. Nowadays, more and more economists believe in quasi-rationality or bounded-rationality, which lies between these two extremes scenarios. It is believed that quasi-rationality best describes how individuals in financial markets operate.⁵ In the quasi-rationality framework, investors still maximize some utility or value function (act according to some model) but may have some degree of irrationality. For example, they can act on wrong signals or incorrect information, rely on technical analysis that is not related to the fundamental value of the asset, and so on. Such investors, who do not conform with EUT, are sometimes referred to as “noise traders.” Friedman (1953b) argues against the importance of noise traders. According to his view, irrational investors are met in the market with rational arbitrageurs who trade against them, and in the process the rational investors drive the asset price close to its fundamental value. Moreover, the irrational investors, according to Friedman’s view, lose money to the rational investors and so eventually disappear from the market.

DeLong, Shleifer, Summers, and Waldmann (1990) show that this may not be the case. Arbitrage does not eliminate the effect of noise traders. Moreover, noise traders who are bullish earn a higher expected return than the sophisticated rational investors who trade with them. The noise traders also affect the volatility of prices and certainly do not disappear from the market. DeLong et al. assert that noise traders select their portfolio on the basis of incorrect information, such as information from technica...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright page
• Dedication
• Preface
• Acknowledgments
• 1: Classic Models in Finance: Solved and Unsolved Issues
• 2: Decision Weights, Change of Wealth, and Value Function: The Experimental Evidence
• 3: Empirical and Experimental Evidence Regarding Preferences: Absolute and Relative Risk Aversion
• 4: Inefficient Choices and Investors’ Irrationality
• 5: The Microscopic Simulation Method
• 6: Microscopic Simulations in Various Fields
• 7: The LLS Microscopic Simulation Model
• 8: Various Financial Microscopic Simulations
• 9: Prospect Theory, Asset Pricing, and Market Dynamics
• 10: Application of Microscopic Simulation to the CAPM: Heterogeneous Expectations and the Number of Assets in the Portfolio1
• 11: Application of Microscopic Simulation to Option Pricing: Uncertainty and Disagreement About the Volatility
• Bibliography
• Index