Trading with securities and stock indices gains a lot of popularity these days. Every investor's dream is to know the future prices of financial instruments. This paper attempts to apply a Markov chain model to forecast the trends in the stock prices. Markov chain models are obtained for the prices of 3 different stocks based on probability transition matrix and initial state vector. Quantitative data on the daily closing share prices of the stocks is obtained for the period 01.01.2019-31.12.2019. The analyzed stocks are further mixed up in an optimal risk portfolio. An analysis of risk aversion coefficient and how it influences the choice of complete portfolio is made. Such an approach could be applied in future studies on this matter as well as in the practice of portfolio managers and investors.
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