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

122 ACTA WASAENSIAprocessing valuation relevant information as efficiently as their portfolio managers atsecurity selection level do. The utility of equity investments for the sponsor is thereforemodeled in the same spirit as that of the chartists asE = n E − n BN . (5.10)That is, the more equity (bond) investors there are already in the market, the moreattractive equity (fixed income) investment becomes for the sponsor.For the sake of simplicity, the perfectly elasticallysuppliedbond(cash)isassumedtopay no interest, such that its utility is zero. The resulting transition rates betweenequities and bonds read then in analogy to (5.9)p BE = v B e α B(n E −n B )/Nand p EB = v B e −α B(n E −n B )/N , (5.11)where α Bis the strength of infection parameter between equity and bonds and v Bdenotes the frequency at which asset allocators reconsider their strategy.In the next step we need to specify, how the transitions between equity and bonds onasset allocation level translate into transition probabilities between the individual stockinvestors and the bondholders. Keeping in mind that institutional investment practicedemands asset allocation and security selection to be modeled as separate processes,I shall assume here that the asset allocation decision leaves the internal compositionof stock investors unchanged. That is, the transition rates from each individual stockinvestor to bondholders equal just the transition rates between equity and bondsp ciB = p fiB = p EB , i =1, 2, (5.12)whereas transitions from the bondholders to the equity investors must be weighted bythe relative frequency of the relevant stock investor typep Bci = n cin Ep BE ,p Bfi = n fin Ep BE , i =1, 2. (5.13)These may then be inserted into the quasi-meanvalue equations (5.4) in order to obtain