Proposal of creation of a portfolio with minimal risk


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The aim of this work is to propose a method for creating portfolios with a minimal expected risk. The proposed method consists of two steps. In the first step, the authors use a method for finding a minimum spanning tree. It is a graph theory tool, which is the field of discrete mathematics. Graph is defined as a set of vertices and edges. By this method the authors distribute assets, for example a stock index, into several subgroups. From each group it is then chosen an asset, from which most of the edges come out. These selected assets will be used to create a portfolio. In the second step, the authors will use a method of minimizing the standard deviation of the portfolio to calculate the weight of its assets. By this method, first it is found the weight of each asset so that the resulting portfolio would have the lowest possible expected risk. Then the authors find the portfolio with the lowest possible expected risk at required yield and create investment strategies. These strategies are compared during the time and between each other based on the variation coefficient. The article can be a practical guide for an individual investor during the minimal risk portfolio creation and shows him, which assets (and which asset weights) of the selected index to purchase.

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    • Figure 1. Comparison between minimum spanning trees of 5 and 30-year historical yield with color-coded sectors
    • Table 1. Criterion for classification of companies into different price histories
    • Table 2. The representatives of each sector according to time period
    • Table 3. Results analysis for the 5-year historical yield
    • Table 4. Analysis results for the 30-year historical yield
    • Table 5. Riskiness of individual portfolios measured by the variation coefficient