2020/29  LEM Working Paper Series  
Selection in incomplete markets and the CAPM portfolio rule 

Giulio Bottazzi and Daniele Giachini 

Keywords  
Selection; Evolution; Capital Asset Pricing Model; Incomplete Markets.


JEL Classifications  
C60, D53, G02, G12, G14


Abstract  
This paper studies whether, and to what extent, trading in an
incomplete competitive market rewards the CAPM portfolio rule over alternative
rules. We find that, if a meanvariance trader faces an agent who invests
in each asset proportionally to expected relative payoffs, in the longrun
only two scenarios are possible: either the meanvariance trader vanishes or
both agents survive with fixed and constant wealth shares. In both cases,
asymptotic prices are proportional to assetsâ€™ expected payoff, and the relation
between prices and returns implied by the CAPM does not generally
hold. Conversely, when a meanvariance trader faces a generic fixedmix
investor, several longrun outcomes are possible, such as dominance of one
trader, survival of both, and generic pathdependency. We provide sufficient
conditions to assess such outcomes. We find that the different outcomes can
be effectively discussed in terms of the effective risk aversion of the
trading strategies, as implied by their portfolio choices conditional on prevailing
market prices. In general, a larger effective risk aversion constitutes a survival advantage.
 
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