Asymmetries and Interaction cycles in Financial Markets

Roberto Leombruni, Domenico Delli Gatti and Mauro Gallegati

No 3B.4, CeNDEF Workshop Papers, January 2001 from Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance

Abstract: This paper investigates the dynamics in a stock market where investors have heterogeneous beliefs about future prices of a risky asset, due both to information asymmetries on the "fundamentals", and to an investor specific vector of parameters that defines the strategy adopted to generate a forecast. This latter, is a weighted average of the investor private forecast made according on its beliefs about the fundamentals, and an interaction term accounting for a conformist behaviour in the investor trade activity. In the literature, the pure rational expectations hypothesis (REH) has mainly been relaxed introducing some "noise traders" in the market, to test whether the Friedman's hypothesis that they would be ruled out by the "smart ones" holds, and whether their explicit consideration could outperformance traditional modelling in describing real stock market dynamics (De Long et al. [1990], Brock-Hommes [1997ab, 1998], Goldbaum [2000]). Many studies have been conducted also with an agent based computational approach (ACE), considering again different prediction strategies - a fundamentalist one and some "chartists-like" ones - or letting the agents follow simpler adaptive rules (Arthur et al [1998], Terna [2000]). In all these studies the switch between different forecasting strategies, or the trigger to the correction of the adaptive behaviour, is governed by some fitness function defined at the individual level. Kirman-Teissière (2000) too consider a market populated by chartists and fundamentalists, but let the proportion of the two groups be determined by the interaction between individuals, where the adoption of one of the two strategies is driven by an epidiemiologic process of diffusion derived from Föllmer. In our work, we relax the distinction between chartists and fundamentalists, and put the focus on the role of interaction among individuals. Every investor follows its beliefs about the fundamentals, but adapt them and takes its buy or sell decisions taking into account the behaviour of the other investors. The strength of the interaction is endogenous: when the price is far from the individual expectations, the investor is less confident in the mood present in the market, and gives a smaller weight to the interaction term of its forecast. In equilibrium, on the opposite, the coherence between individual and market behaviour reinforce the credit the investor puts in the market signals. The non-linear dynamics emerging in the simulation of the model - implemented using the Santa Fe Institute's Swarm Simulation Toolkit - can then be attributed more than to different forecasting strategies adopted by the investors at different point of time, to an endogenous cycle in the interaction among individuals: the lower (higher) are the departures from an average belief about the fundamentals, the higher (lower) will be the confidence with which the market signals will be read. And in the periods of high confidence (interaction), the market will be more sensible to any "noisy" signal that can get it out of the equilibrium.

Date: 2001-01-04
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