On the Role of Memory in an Asset Pricing Model with Heterogeneous Beliefs

The paper discusses the role of memory in an asset pricing model with heterogeneous beliefs. In particular, we were interested in how memory in the fitness measure affects the stability of evolutionary adaptive systems and the survival of technical trading. In order to obtain an insight into this matter, two cases were analyzed: a two-type case of fundamentalists versus contrarians and a three-type case of fundamentalists versus opposite biases. It has been established that increasing memory strength has a stabilizing effect on dynamics, though it is not able to eliminate speculative traders’ short-run profit-seeking behaviour from the market. Furthermore, opposite biases do not seem to lead to chaotic dynamics, even when there are no costs for fundamentalists. Apparently some (strong) trend extrapolator beliefs are needed in order to trigger chaotic asset price fluctuations.asset pricing, biased beliefs, contrarians, fitness measure, fundamentalists, heterogeneous beliefs, memory strength, stability

Complex evolutionary systems in behavioral finance

Traditional finance is built on the rationality paradigm. This chapter discusses simple models from an alternative approach in which financial markets are viewed as complex evolutionary systems. Agents are boundedly rational and base their investment decisions upon market forecasting heuristics. Prices and beliefs about future prices co-evolve over time with mutual feedback. Strategy choice is driven by evolutionary selection, so that agents tend to adopt strategies that were successful in the past. Calibration of "simple complexity models" with heterogeneous expectations to real financial market data and laboratory experiments with human subjects are also discussed.

Asset prices and informed traders' abilities: evidence from experimental asset markets

This study reports the results of fifteen experimental asset markets designed to investigate the effects of forecasts on market prices, traders' abilities to assess asset value, and the link between the two. Across the fifteen markets, the authors investigate alternative forecast-generating processes. In some markets the process produces an unbiased estimate of asset value and in others a biased estimate. The processes generating the biased forecasts, though, are less variable than the process generating the unbiased forecast. The authors find that, in general, period-end asset price reflects private forecasts, regardless of the forecast-generating process. Subsequently, they investigate whether traders' abilities to use forecasts differ across the forecast-generating processes. The authors find that most are able to properly use unbiased forecasts. They refer to them as smart traders. By comparison, a significant proportion is unable to properly use biased forecasts (typically traders' adjustments for bias are insufficient). Linking market outcomes and traders' abilities, the authors find that asset price appears to properly reflect unbiased forecasts as long as the market includes at least two smart informed traders who have sufficient ability to influence market outcomes. To obtain a comparable result in markets with the biased forecast, at least three smart informed traders with sufficient ability to influence market outcomes are necessary.Forecasting ; Markets ; Financial markets ; Risk

More hedging instruments may destabilize markets (Revised version, April 2008)

This paper formalizes the idea that more hedging instruments may destabilize markets when traders have heterogeneous expectations and adapt their behavior according to experience based reinforcement learning. In a simple asset pricing model with heterogeneous beliefs the introduction of additional Arrow securities may destabilize markets, and thus increase price volatility, and at the same time decrease average welfare. We also investigate whether a fully rational agent can employ additional hedging instruments to stabilize markets. It turns out that the answer depends on the composition of the population of non-rational traders and the information gathering costs for rationality.

Heterogeneous Agents Models: two simple examples, forthcoming In: Lines, M. (ed.) Nonlinear Dynamical Systems in Economics, CISM Courses and Lectures, Springer, 2005, pp.131-164.

These notes review two simple heterogeneous agent models in economics and finance. The first is a cobweb model with rational versus naive agents introduced in Brock and Hommes (1997). The second is an asset pricing model with fundamentalists versus technical traders introduced in Brock and Hommes (1998). Agents are boundedly rational and switch between different trading strategies, based upon an evolutionary fitness measure given by realized past profits. Evolutionary switching creates a nonlinearity in the dynamics. Rational routes to randomness, that is, bifurcation routes to complicated dynamical behaviour occur when agents become more sensitive to differences in evolutionary fitness.

Is more memory in evolutionary selection (de)stabilizing?

We investigate the effects of memory on the stability of evolutionary selection dynamics based on a multi-nomial logit model in an asset pricing model with heterogeneous beliefs. Whether memory is stabilizing or destabilizing depends in general on three key factors: (1) whether or not the weights on past observations are normalized; (2) the ecology of forecasting rules, in particular the average strength of trend extrapolation and the spread in biased forecasts, and (3) whether or not costs for information gathering of economic fundamentals have to be incurred.

A Study of Neo-Austrian Economics using an Artificial Stock Market

An agent-based artificial financial market (AFM) is used to study market efficiency and learning in the context of the Neo-Austrian economic paradigm. Efficiency is defined in terms of the 'excess' profits associated with different trading strategies, where excess for an active trading strategy is defined relative to a dynamic buy and hold benchmark. We define an Inefficiency matrix that takes into account the difference in excess profits of one trading strategy versus another ('signal') relative to the standard error of those profits ('noise') and use this statistical measure to gauge the degree of market efficiency. A one-parameter family of trading strategies is considered, the value of the parameter measuring the relative 'informational' advantage of one strategy versus another. Efficiency is then investigated in terms of the composition of the market defined in terms of the relative proportions of traders using a particular strategy and the parameter values associated with the strategies. We show that markets are more efficient when informational advantages are small (small signal) and when there are many coexisting signals. Learning is introduced by considering 'copycat' traders that learn the relative values of the different strategies in the market and copy the most successful one. We show how such learning leads to a more informationally efficient market but can also lead to a less efficient market as measured in terms of excess profits. It is also shown how the presence of exogeneous information shocks that change trader expectations increases efficiency and complicates the inference problem of copycats.Neoaustrian economics, Market efficiency, Artificial financial market, Learning, Adaptation

A generalized spin model of financial markets

We reformulate the Cont-Bouchaud model of financial markets in terms of classical "super-spins" where the spin value is a measure of the number of individual traders represented by a portfolio manager of an investment agency. We then extend this simplified model by switching on interactions among the super-spins to model the tendency of agencies getting influenced by the opinion of other managers. We also introduce a fictitious temperature (to model other random influences), and time-dependent local fields to model slowly changing optimistic or pessimistic bias of traders. We point out close similarities between the price variations in our model with $N$ super-spins and total displacements in an $N$-step Levy flight. We demonstrate the phenomena of natural and artificially created bubbles and subsequent crashes as well as the occurrence of "fat tails" in the distributions of stock price variations.Comment: 11 pages LATEX, 7 postscript figures; longer text with theoretical analysis, more accurate numerical data, better terminology, additional references. Accepted for publication in European Physical Journal

On Financial Markets Trading

Starting from the observation of the real trading activity, we propose a model of a stockmarket simulating all the typical phases taking place in a stock exchange. We show that there is no need of several classes of agents once one has introduced realistic constraints in order to confine money, time, gain and loss within an appropriate range. The main ingredients are local and global coupling, randomness, Zipf distribution of resources and price formation when inserting an order. The simulation starts with the initial public offer and comprises the broadcasting of news/advertisements and the building of the book, where all the selling and buying orders are stored. The model is able to reproduce fat tails and clustered volatility, the two most significant characteristics of a real stockmarket, being driven by very intuitive parameters.Comment: 18 pages, submitte