Portfolio optimization models aim to optimally distribute capital among selected stocks, bonds and other securities and financial products offered on financial markets. An important factor in the optimization is the risk, which is by definition very abstract concept and is very difficult to quantify. Robust portfolio optimization model is based on the general robust binary model. The robustness of this model lies in a two-stage optimization, where every solution is subject to maximization of losses and from these pessimistic estimates such a solution is selected that best meets the user's criteria, in our case total return of the portfolio.

The thesis deals with current opportunities for investing in precious and industrial metals. The literature overview introduces the reader with the current knowledge about commodity investments and provides results of various authors dealing with factors important for commodity price develop and with relation of commodity prices and inflation. Trough metal markets analysis identifies key factors with impact on sup-ply, demand and price of specific metal. Based on historical prices explores the relationship of metal prices, relationship of metal prices and stock market and business cycle. Quantify risk, which the investor has to accept in the case of investing in metals by using Value at Risk methods. The risk is compared with the level of risk on stock market. The thesis summarises all these results and formulate investment recommendation.

The diploma thesis deals with energy commodities investments. The content of thesis is trough analysis of markets to identify key factors affecting supply, demand and prices of energy commodities. By correlation analysis examines the relationships between energy commodities, stocks and the business cycle. Processing time series models create predictions of energy commodities prices. Using the Value at Risk method to quantify the risk, which investor has to accept in the case of investing in energy commodities. In conclusion, based on the results obtained, formulates investment recommendation.

This master thesis aims to describe and apply in practice solutions of basic tasks in portfolio management- portfolio optimization, portfolio modelling and risk management. As value of financial assets in future is a random variable, it is necessary to use mathematic tools resulting from probability theory and statistics. Basic terms from this area are for example stochastic Wiener process or geometric Brownian motion, which are described in first part of this thesis. Next parts of thesis describe the Markowitz model or method Value at Risk. In the last part of thesis is application of calculation VaR using Monte Carlo simulation for stock portfolio constructed as optimal portfolio according to Markowitz model from real data.

Diploma thesis focuses on the issue of an appropriate selection of securities and the subsequent establishment of a portfolio of these securities. Follow detailed discussion about analysis of portfolio and investor’s preferences. Below is a description of the CAPM model, its assumptions and usage of this model to build a portfolio. Then there is the actual calculation of characteristics of securities traded on the Prague Stock Exchange and on the basis of these calculations is made the proposal of several portfolios and their evaluation.

The thesis deals with modern portfolio theory. The theoretical part of the thesis describes the historical development of portfolio optimization and presents the basic theoretical background of the Markowitz model, the Tobin model and the Capital asset pricing model. In the practical part of the thesis, the models are applied to real data from two Czech securities markets, PSE and RM-S. An optimal portfolios composition is proposed by the three models mentioned above and then the outputs of the models are compared to the real datas from the next period. Finally, the benefits and drawbacks of the used models are evaluated.