The paper analyzes the process of market selection of investment strategies in an incomplete asset market. The payoffs of the as-sets depend on random factors described in terms of a discrete-time Markov process. Market participants make dynamic investment de-cisions based on their observations and time. We show that a trader distributing wealth across available assets according to the relative expected returns eventually accumulates the entire market wealth. The result obtains under the assumption that the trader's strategy is asymptotically distinct from the CAPM strategy (prescribing in-vestment in the market portfolio). This assumption turns out to be essentially necessary for the conclusion.