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

124 ACTA WASAENSIAProof. See appendix A8.Intuitively, the equilibrium conditions follow quite naturally from the structure of thequasi-meanvalue equations (5.4) as follows. Consider first the subdynamics of theequity investor populations. At fundamental equilibrium both fundamentalist utilitiesequal zero, because all trading prices equal their fundamental values. Also the chartistutilities equal zero when there are equally many equity investors in stock 1 and 2. Alltransition probabilities between equity investments in the quasi-meanvalue equationsequal then v, such that (5.4) simplifies for the subdynamics between equity investorsto4n˙i = v · (n j − n i ), n i ,n j = n c1 ,n c2 ,n f1 ,n f2 . (5.15)j=1It is then immediately clear from (5.15) that zero expected changes for all traderpopulations imply that there are equally many investors in each of the equity strategysubpopulations. The same argument applies for the asset allocation subdynamics,thereby implying equally many equity and bond investors.Employment of absolute values in the fundamentalist utilities (5.6) implies that the systemof differential equations (5.3) and (5.14) contains four subregimes (p 1 >p f1 ,p 2 >p f2 ), (p 1