  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. 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 such 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 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 or significantly reduced,
so the future risk and return are better estimated and controlled. 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.
