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