Portfolio theory is a very powerful tool in the modern investment theory. It is helpful in estimating risk of an investor's portfolio, which arises from our 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 is not widely used among investors on Warsaw Stock Exchange. They treat it as a strictly academic tool. The main reason for abandoning this method is a high level of complexity and immense calculations, which one has to impose in order to use the methods of portfolio analysis.

The aim of this paper is to introduce an automatic decision - making system, which allows a single investor to use such complex methods of Modern Portfolio Theory (MPT) as Markowitz's algorithm or Capital Assets Pricing Model (CAPM). The key tool in MPT is an analysis of an empirical covariance matrix. This matrix, obtained from historical data is 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. This 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 for respective 10% loss of the Warsaw Stock Exchange main index WIG.

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