BERND PAPE Asset Allocation, Multivariate Position Based Trading ...

116 ACTA WASAENSIAOverall, we can at least not reject the concerns brought forward by Farmer and Joshi,that order based strategies violate fundamental risk management constraints by theirimplicit tendency to build up infinite holdings over time. In the model by Lux &Marchesi (2000) the problems of order based trading became particularly evident forthe inventories of the market maker. This may be not so surprising, given that themarket makers inventories provide the loophole for the modeller to replace equilibriumwith disequilibrium trading.Obviously, it would require considerable additional effort to include market makerswealth and positions into a consistent model of the price discovery process. One mayalso ask whether the disequilibrium trading provided by the market maker is reallysuch an important feature of financial markets to model for return periods of a fulltrading day and above, as was the intention in Lux’ model. In markets without 24hours trading such as stock markets closing prices must be quite close to equilibriumprices, since otherwise market participants wouldn’t be prepared to sleep with themuntil next morning.I shall therefore drop the marketmaker in a simplified version of Lux’ model withposition-based trading in the next chapter. Because the model is position based, it iseasy to generalize to multiple assets, avoiding the inconsistencies of order based tradingdiscussed in the introduction and demonstrated in this section. In order to add furtherrealism to the model, I will also include a riskless bond (cash), and separate the securityselection decision between different stocks from the asset allocation decision betweenequity and bonds.