The simulation studies by Lux and Marchesi (1999),(2000) of the noise trader infection model invented by Lux (1998) were among the first to demonstrate detailed agreement of the simulated time series of an artificial market with the main stylized facts of empirical asset returns, e.g. heteroscedastic returns with a realistic tail index and long memory in clustered return volatility despite uncorrelated returns. I extend their univariate model into a multivariate setup containing a second risky asset and a riskless bond, which was not available in their original model. In order to add some further realism, the investment process will be split up into asset allocation and security selection, as is common practice in financial institutions.
This study is not the first to tackle the impact of heterogeneous expectations upon more than one risky asset. Böhm and Wenzelburger (2005) extend the classical capital asset pricing model (CAPM) to a dynamic context with heterogeneous beliefs. Chiarella et al. (2005) extend the concept of adaptive belief systems (predictors of future prices which are periodically updated based upon past forecasting performance) introduced by Brock and Hommes (1998) to multiple risky asset. However, their focus is not on demonstrating concordance of simulated time series with real financial returns as in this study.
Westerhoff (2004) considers the interaction of chartists and fundamentalists on multiple assets and generates return series similar to those observed in real markets. My main contribution relative to his study and those by Lux and Marchesi consists in removing inconsistencies concerning traders inventories and wealth resulting from the order-based setup of their models. Both Lux and Westerhoff consider trading at disequilibrium prices in order driven markets following the tradition initiated by Beja and Goldman (1980) and Day and Huang (1990). That is, traders place orders proportional to the expected profits of their investments, while a market maker adjusts prices proportional to net excess demand, filling any imbalances between demand and supply from his inventory. The consequences of such a setup upon traders inventories remained unexplored until Farmer and Joshi (2002) discovered that order-based trading implies non-stationary positions and traders can accumulate unbounded inventories, which appears unrealistic from a risk management point of view.
Order-based trading appears also unrealistic because it is well established standard in the academic literature at least since Markowitz (1959), that investors consider portfolio holdings rather than orders as the relevant object of profit and risk considerations. The inconsistencies of an order-based setup become particularly obvious when extending a univariate model into a multi asset framework. Suppose for example that a trader has favoured asset A over asset B for a while, but receives now a signal which favours asset B over asset A. A consistent model would require the trader to close or at least diminish his position in asset A before entering a new position in asset B. That is, a new signal favouring B over A would not only generate buying orders for B, but also selling orders for A, until the desired new positions in assets A and B are established. This is not achieved by na?vely extending the order-based setup by Beja and Goldman (1980) to multiple assets, as it would falsely neglect any acquired position in A when producing new orders for asset B.
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Asset Allocation, Position Based Trading, And The Stylized Facts
