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

118 ACTA WASAENSIAby Lux (1998). The key difference is that Lux follows the order-based literature inusing this expression to describe stocks to trade rather than target positions in stocksto hold, as is the case here. We do therefore expect traders holdings–unlike those inthe simulations of Lux & Marchesi (2000)–to remain bounded due to level stationarityof the number of chartists n ci and the mispricing p i − p fi . This claim will be verifiedin section 5.2.I assume the target holding parameters t c and t f and the fundamental prices p f1 andp f2 to be constant over the time period considered. Trading demand for the stocks isgenerated by changes in desired aggregate holdings due to changes in mispricing or thecomposition of tradersED i = d dt E i = n˙ci t c + n˙fi t f (p fi − p i ) − n fi t f p˙i , i =1, 2. (5.2)Market clearing (ED i = 0) yields for the logarithmic trading prices of the stocksp˙i = 1 t cn˙ci + n˙fi (p fi − p i ) , i =1, 2. (5.3)n fi t fWe see from equation (5.3) that fast changes in the composition of traders and largemispricings speed up price changes, whereas large fundamentalist populations slowthem down. On the chartist side, the speed of price adjustment depends on the targetexposures of chartists relative to fundamentalists. Large chartist exposures speed upprice changes whereas large fundamentalist exposures have the opposite effect. Overall,we recover the recurrent theme from the interacting agent literature, that fundamentalistshave a stabilizing effect and that noise traders have a destabilizing effect uponprices, without having made any specific assumptions yet about how to model changesin the traders populations.Another important conclusion from equations (5.1) to (5.3) is that our trading processconserves the number of shares traded, a feature not necessarily present in order basedmodels including a market maker, as was demonstrated in section 4.3.2. This may beseen as follows: Because we assume market clearing, the aggregate target holdings E 1and E 2 inequation(5.1)mustequalthenumberofsharesissuedbycompanies1and2.