In the first part of the master's thesis a short introduction to stocks and stock market indexes is presented. The most well-known stock market indexes in the USA are described. After that, the most significant capital market theories are described and the stress is put on the modern portfolio theory. Calculation of efficient portfolio and efficient frontier is shown. On the example of the portfolio which is comprised of stocks which are also members of the stock market index Dow Jones industrial average, calculation of the efficient frontier is presented. In the method used to calculate the efficient frontier, neither short sales nor riskless lending and borrowing are allowed. Using that method efficient frontier is calculated by minimising risk i.e. standard deviation for any given level of expected return. The process of optimisation is derived using software tool Solver which is available as a part of Microsoft Excel. Since one of the tasks in this master's thesis is to prove that it is possible to create a portfolio which is better than the stock market index from the aspect of expected return and the aspect of risk, one efficent portfolio that lies on the graph of the efficient frontier is chosen as an optimal portfolio. Using the period of the next two years a test of the optimal portfolio is made to prove that optimal portfolio is better than the stock market index. As a proof, a Sharp's index is used. Since the value of the Sharp's index for the optimal portfolio is greater than the value of the Sharp's index for the stock market index Dow Jones industrial average, it is proven that it is possible to create a portfolio which is better than the stock market index from the aspect of expected return and the aspect of risk. In the second part of the master's thesis the risk from financial aspect is defined. The break-down of financial risks is given and all of the types of financial risks are explained. It is also explained why it is important to manage financial risks. Then the definition of Value-at-Risk is given and the methodology of Value-at-Risk is explained. The calculation of VaR of the optimal portfolio is shown using the method of historical simulation. The testing of the model is made and it is proven that the calculation of Value-at-Risk using the method of historical simulation represents an adequate model for the calculation of market risk of the stock portfolio.