Preface

The classical models in finance are analytical models. These models make assumptions regarding the market and the behavior of individuals operating in the market and derive their results by mathematical analysis. For example, the Capital Asset Pricing Model (CAPM) assumes that investors maximize their von Neuman and Morgenstern (1944) expected utility, in addition, it makes specific assumptions of a perfect market with no taxes and no transaction costs, normal rate of return distributions, a one-period investment horizon, and homogeneous expectations.

Many of the assumptions made in the CAPM, as well as in most other models in finance, are admittedly false. First, there are experimental findings that cast doubt on the expected utility paradigm, which is the foundation of most models in finance. Second, there are also many model-specific assumptions that have been criticized. For instance, the assumption of no taxes and no transaction costs does not conform to the actual facts. It is also clear that, in contrast to the homogeneous expectation assumption, investors differ in their expectations, holding periods, decision-making processes, and so on. Although false, these assumptions are required to obtain analytical tractability. Thus, most of the cornerstone models in finance, such as the CAPM, the Arbitrage Pricing Theory, the Black and Scholes Option Pricing Model, and the Modigliani and Miller Capital Structure and Valuation Model, are based on underlying assumptions that are, at best, problematic.

There are several arguments in defense of models based on unrealistic assumptions. The first is that a model with unrealistic assumptions is better than no model at all, and one should not reject a model unless a better one is found (see Stigler, 1966). In addition, although some of a model’s assumptions may not hold in reality, it is possible that the model still provides realistic results. According to Friedman (1953a), a model’s quality should be measured by the model’s explanatory power, not by its (possibly unrealistic) assumptions. For example, even though investors do not sit down to calculate their expected utilities, the market may behave “as if” investors were expected utility maximizers. Unfortunately, the empirical results that test the various theoretical models in finance are, at best, controversial. Moreover, there are several anomalies (e.g., the January effect, the small-firm effect) that contradict the prediction of theoretical models. Thus, in the case of most finance models, the empirical findings do not support the “as if” argument.

The expected utility models mentioned previously are normative. Given a set of assumptions or axioms, the model tells us how investors should behave and how the end result (e.g., the pricing of an asset) is determined. In contrast, experimental studies analyze how investors, or more precisely laboratory subjects, actually do behave and make no normative claims regarding how investors should behave. The leading candidate to compete with the expected utility paradigm is Prospect Theory, advocated by Kahneman and Tversky (1979). Kahneman and Tversky conducted a series of experiments revealing that decision-making behavior is in sharp contradiction to the predictions of expected utility theory. In particular, the subjects make choices according to change in wealth rather than total wealth and employ decision weights (which do not obey the probability rules) rather than objective probabilities.

Thus, expected utility models in finance have been attacked on the following fronts:

1. Some of the model-specific assumptions that are commonly made(no taxes, homogeneous expectations, etc.) are unrealistic.

2. Even if the model-specific assumptions are intact (or if we justify these assumptions by the “as if” argument), experimental studies, particularly Prospect Theory, cast doubt on the validity of the expected utility paradigm, which is the foundation of these models.

3. Empirical studies either do not support or only weakly support the various models in finance.

Prospect Theory and other descriptive models of investor behavior attempt to capture some systematic elements of investor behavior. Unfortunately, there does not seem to be a single theory that makes sense of the mixed empirical and experimental data (see Davis and Holt, 1993). In addition, the mathematics of these descriptive models is typically cumbersome, and therefore the implications of these models for pricing are difficult to analyze.

It seems that theoretical research in finance may have a problem: on the one hand, unrealistic simplifying assumptions are needed to ensure analytic tractability; on the other hand, these assumptions lead to results that cannot be convincingly supported by the empirical evidence. Perhaps we have been searching for the lost coin only under the lamppost.

In this book we suggest a research methodology that may expand the realm of investigation in finance. This methodology is called Microscopic Simulation (MS). MS is a methodology that was developed in the physical sciences as a tool for the study of complex systems with many interacting “microscopic” elements. Such complex systems generally do not yield to analytical treatment. The main idea of the MS methodology is to study complex systems by representing each of the microscopic elements individually on a computer and simulating the behavior of the entire system, keeping track of all of the elements and their interactions in each time period. Throughout the simulation, global, or “macroscopic,” variables that are of interest can be recorded, and their dynamics can be investigated. For example, in physics, in order to study and predict the behavior of a nuclear reactor, the multitude of atomic particles interacting in the reactor can be simulated, and the dynamics of the system’s temperature, pressure, and so on, can be investigated. The main advantage of the MS method is that, unlike analytical methods, it does not force one to make simplifying assumptions for the sake of tractability. Thus, virtually any system with heterogeneous elements and complicated interactions can be investigated.

The idea of studying complex systems by simulating all of the systems’ microscopic elements is very natural, and as such it has been reinvented in various fields of science. As a consequence, this methodology is known by several different names, such as microscopic simulation, microsimulation, and agent-based simulation. Although there may be nuances differentiating these various methods, the basic idea behind all of them is the same1.

We believe that MS has a great potential as a research tool in finance and in economics. There is no doubt that financial markets, in which a multitude of heterogeneous quasi-rational investors operate, are very complex systems. MS allows the modeling and investigation of such systems without unrealistic simplifying assumptions. Indeed, the unrealistic assumptions can be relaxed one by one, and the effect of each simplifying assumption on the results can be investigated.

Although MS is a standard tool in most natural sciences, it is not yet commonly employed in the social sciences. Indeed, physicists who realize that the powerful MS machinery they possess can solve problems in social science are starting to conduct microscopic simulations of social science systems. The purpose of this book is to present the MS methodology to the finance and economics community and to suggest ways in which this methodology can be implemented in these areas.

We believe that MS holds promise in two main research avenues:

1. Extension of existing models. With MS, one can extend the existing analytical cornerstone models in finance and investigate the robustness of these models. Namely, one can study the effect of relaxing each of the models’ assumptions on the results. Do the results of the model approximately hold when unrealistic simplifying assumptions are replaced with more realistic assumptions? Which of the important models are robust, and which break down with a slight change of the underlying assumptions?

2. New models. MS allows the researcher to explore new models without having to make restricting assumptions. In particular, one can model markets as realistically as desired. For instance, if the experimental and empirical evidence suggests that the behavior of 60% of the investors is best described by expected utility maximization, whereas for 20% of the investors Prospect Theory provides a better description, and for 20% of the investors noise or liquidity trading seems to be the best explanation, these findings can easily be incorporated into an MS model. Various fundamentalist and technical trading strategies which are observed in experiments and in actual markets can also all be modeled with MS in a realistic setting where transaction costs and taxes prevail. Finally, while classical models typically deal with static equilibrium in a market of homogeneous rational agents, with MS one can investigate dynamic models, models in which investors are heterogeneous in many respects, and models in which investors are constantly learning and changing strategies as time goes by.

This book is organized as follows. Chapter 1 reviews the main models in finance and some of their problematic underlying assumptions....