Wealth-Driven Competition in a Speculative Financial Market: Examples with Maximizing Agents

This paper demonstrates how both quantitative and qualitative results of general, analytically tractable asset-pricing model in which heterogeneous agents behave consistently with a constant relative risk aversion assumption can be applied to the particular case of ``linear'' investment choices. In this way it is shown how the framework developed in Anufriev and Bottazzi (2005) can be used inside the classical setting with demand derived from utility maximization. Consequently, some of the previous contributions of the agent-based literature are generalized. In the course of the analysis of asymptotic market behavior the main attention is paid to a geometric approach which allows to visualize all possible equilibria by means of a simple one-dimensional curve referred as the Equilibrium Market Line. The case of linear (particularly, mean-variance) investment functions thoroughly analyzed in this paper allows to highlight those features of the asymptotic dynamics which are common to all types of the CRRA-investment behavior and those which are specific for the linear investment functions.Asset Pricing Model, CRRA Framework, Equilibrium Market Line, Rational Choice, Expected Utility Maximization, Mean-Variance Optimization, Linear Investment Functions.

Wealth-Driven Competition in a Speculative Financial Market: Examples With Maximizing Agents

This paper demonstrates how both quantitative and qualitative results of a general, analytically tractable asset-pricing model in which heterogeneous agents behave consistently with a constant relative risk aversion assumption can be applied to the special cases of optimizing behavior. The analysis of the asymptotic properties of the market is performed using a geometric approach which allows the visualization of all possible equilibria by means of a simple one-dimensional Equilibrium Market Curve. The case of linear (particularly, mean-variance) investment functions is thoroughly analyzed. This analysis highlights the features which are specific to the linear investment functions. As a consequence, some previous contributions of the agent-based literature are generalized.

Behavioral Consistent Market Equilibria under Procedural Rationality

In this paper we analyze a dynamic, asset pricing model where an arbitrary number of heterogeneous, procedurally rational investors divide their wealth between two assets. Both fundamental dividend process and behavior of traders are modeled in a very general way. In particular, agents' choices are described by means of the generic smooth functions defined on a commonly available information set. The choices are consistent with (but not limited to) the solutions of the expected utility maximization problems. As a natural rest point of the corresponding dynamics we propose the notion of the Behavioral Consistent Equilibria (BCE) where the aggregate dynamics are consistent with the agents' investment choices. We show that provided that the dividend process is given, all possible equilibria of the system can be characterized by means of one-dimensional Equilibrium Market Line (EML). This geometric tool allows to separate the effects of dividend process and agents' behaviors on the aggregate dynamics. Namely, the precise shape of this line depends on the character of the dividend process, but the realized equilibrium, i.e.~a point on the line, is determined by the ecology of agents' behaviors. We argue that the EML can be useful in investigation of the questions of existence, multiplicity and stability of the BCE and provide corresponding examples. The EML also allows to make the comparative static exercises in a framework with heterogeneous agents and discuss the relative performances of different strategies. The notion of BCE can be considered as a generalization of the Rational Expectations Equilibrium on the framework with heterogeneous traders. It can be, therefore, useful also in other fields of economics where heterogeneity of actors plays an important role for the aggregate outcomeAsset Pricing Model, Procedural Rationality, Heterogeneous Agents, CRRA Framework, Equilibrium Market Line,, Stability Analysis, Multiple Equilibria.

Price and Wealth Dynamics in a Speculative Market with Generic Procedurally Rational Traders

An agent-based model of a simple financial market with arbitrary number of traders having relatively general behavioral specifications is analyzed. In a pure exchange economy with two assets, riskless and risky, trading takes place in discrete time under endogenous price formation setting. Traders' demands for the risky asset are expressed as fractions of their individual wealths, so that the dynamical system in terms of wealth and return is obtained. Agents' choices, i.e. investment fractions, are described by means of the generic smooth functions of an infinite information set. The choices can be consistent with (but not limited to) the solutions of the expected utility maximization problems. A complete characterization of equilibria is given. It is shown that irrespectively of the number of agents and of their behavior, all possible equilibria belong to a one-dimensional "Equilibrium Market Line". This geometric tool helps to illustrate possibility of different phenomena, like multiple equilibria, and also can be used for comparative static analysis. The stability conditions of equilibria are derived for general model specification and allow to discuss the relative performances of different strategies and the selection principle governing market dynamics.

Asset Prices, Traders' Behavior, and Market Design

The dynamics in a financial market with heterogeneous agents is analyzed under different market architectures. We start with a tractable behavioral model under Walrasian market clearing and simulate it under more realistic trading protocols. The key behavioral feature of the model is the switching of agents between simple forecasting rules on the basis of fitness measure. Analyzing the dynamics under order-driven protocols we show that behavioral and structural assumptions of the model are closely intertwined. High responsiveness of agents to a fitness measure causes excess volatility, however the frictions of the order-driven markets may stabilize the dynamics.

Evolution of Market Heuristics

The time evolution of aggregate economic variables, such as stock prices, is affected by market expectations of individual investors. Neo-classical economic theory assumes that individuals form expectations rationally, thus enforcing prices to track economic fundamentals and leading to an efficient allocation of resources. However, laboratory experiments with human subjects have shown that individuals do not behave fully rational but instead follow simple heuristics. In laboratory markets prices may show persistent deviations from fundamentals similar to the large swings observed in real stock prices. Here we show that evolutionary selection among simple forecasting heuristics can explain coordination of individual behavior leading to three different aggregate outcomes observed in recent laboratory market forecasting experiments: slow monotonic price convergence, oscillatory dampened price fluctuations and persistent price oscillations. In our model forecasting strategies are selected every period from a small population of plausible heuristics, such as adaptive expectations and trend following rules. Individuals adapt their strategies over time, based on the relative forecasting performance of the heuristics. As a result, the evolutionary switching mechanism exhibits path dependence and matches individual forecasting behavior as well as aggregate market outcomes in the experiments. Our results are in line with recent work on agent-based models of interaction and contribute to a behavioral explanation of universal features of financial markets.

Wealth-driven Selection in a Financial Market with Heterogeneous Agents

We study the co-evolution of asset prices and individual wealth in a financial market populated by an arbitrary number of heterogeneous boundedly rational investors. Using wealth dynamics as a selection device we are able to characterize the long run market outcomes, i.e. asset returns and wealth distributions, for a general class of investment behaviors. Our investigation illustrates that market interaction and wealth dynamics pose certain limits on the outcome of agents' interactions even within the ``wilderness of bounded rationality''. As an application we consider the case of heterogenous mean-variance optimizers and provide insights into the results of the simulation model introduced in Levy, Levy and Solomon (1994).Heterogeneous agents, Asset pricing model, Bounded rationality, CRRA framework, Levy-Levy-Solomon model, Evolutionary Finance.

Evolutionary Selection of Individual Expectations and Aggregate Outcomes

In recent 'learning to forecast' experiments with human subjects (Hommes, et al. 2005), three different patterns in aggregate asset price behavior have been observed: slow monotonic convergence, permanent oscillations and dampened fluctuations. We construct a simple model of individual learning, based on performance based evolutionary selectionor reinforcement learning among heterogeneous expectations rules, explaining these different aggregate outcomes. Out-of-sample predictive power of our switching model is higher compared to the rational or other homogeneous expectations benchmarks. Our results show that heterogeneity in expectations is crucial to describe individual forecasting behavior as well as aggregate price behavior.

Price and Wealth Dynamics in a Speculative Market with an Arbitrary Number of Generic Technical Traders

We consider a simple pure exchange economy with two assets, one riskless, yielding a constant return, and one risky, paying a stochastic dividend, and we assume trading to take place in discrete time inside an endogenous price formation setting. Traders demand for the risky asset is expressed as a fraction of their individual wealth and is based on future prices forecast obtained on the basis of past market history. The general case is studied in which an arbitrary large number of heterogeneous traders operates in the market and any smooth function which maps the infinite information set to the present investment choice is allowed as agent's trading behavior. A complete characterization of equilibria is given and their stability conditions are derived. We find that this economy can only possess isolated generic equilibria where a single agent dominates the market and continuous manifolds of non-generic equilibria where many agents hold finite wealth shares. We show that irrespectively of agents number and of their behavior, all possible equilibria belong to a one dimensional "Equilibria Market Line". Finally we discuss the relative performances of different strategies and the selection principle governing market dynamics.Asset Pricing Model, CRRA Framework, Equilibria Market Line, Market Selection Principle