Portfolio theory is a very powerful tool in the modern investment theory. It is helpful in estimating risk of an investor's portfolio, arosen from lack of information, uncertainty and incomplete knowledge of reality, which forbids a perfect prediction of future price changes. Despite of many advantages this tool is not known and not widely used among investors on Warsaw Stock Exchange. The main reason for abandoning this method is a high level of complexity and immense calculations. The aim of this paper is to introduce an automatic decision-making system, which allows a single investor to use complex methods of Modern Portfolio Theory (MPT). The key tool in MPT is an analysis of an empirical covariance matrix. This matrix, obtained from historical data, biased by such a high amount of statistical uncertainty, that it can be seen as random. By bringing into practice the ideas of Random Matrix Theory (RMT), the noise is removed or significantly reduced, so the future risk and return are better estimated and controlled. These concepts are applied to the Warsaw Stock Exchange Simulator {http://gra.onet.pl}. The result of the simulation is 18\% level of gains in comparison with respective 10\% loss of the Warsaw Stock Exchange main index WIG.

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