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Index tracking problem using risk measures
 Polakovičová, Andrea ; Branda, Martin (advisor) ; Šmíd, Martin (referee)
In this thesis, we will introduce various methods for measuring risk known as Value at Risk (V aR) and Conditional Value at Risk (CV aR). We will use their properties and formulations in deriving a linear optimization problem. The linear programming problem will consist of minimizing the objective function representing the deviation between the portfolio and a chosen index. The calculation will be carried out based on multiple constraints, where one of them will use the aforementioned risk measures V aR and CV aR. The goal is to create a portfolio based on this program that replicates the S&P 500 index. We will perform the entire calculation using Python based on historical data. Subsequently, we will use the optimal solution found by the software and construct a replication portfolio that we will track in the following time periods. In conclusion, we will analyze and discuss the individual results for various input parameters. 1
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