Abstract
This paper shows that a stock market is evolutionary stable if and only if stocks are evaluated by expected relative dividends. Any other market can be invaded by portfolio rules that will gain market wealth and hence change the valuation. In the model the valuation of assets is given by the wealth average of the portfolio rules in the market. The wealth dynamics is modelled as a random dynamical system. Necessary and sufficient conditions are derived for the evolutionary stability of portfolio rules when (relative) dividend payoffs form a stationary Markov process. These local stability conditions lead to a unique evolutionary stable strategy according to which assets are evaluated by expected relative dividends.
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