Abstract
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.
Highlights
The covariance matrix is computed for each portfolio and the weights of shares, which minimize the standard deviation of the portfolio determined by Generalized Reduced Gradient Method (GRG)
After the implementation of this method, we are looking for portfolios that offer the lowest risk at predefined performance conditions
The portfolio created by minimal risk strategy is not the portfolio with minimal risk in either case
Summary
The second question that occurs after solving the first one is what should be the amount of resources invested in each selected underlying asset, so that the resulting portfolio would have the lowest expected risk? Authors have studied the effect of asset risk, return, correlation and diversification on expected investment portfolio returns. If we invest in the larger number of high-risk assets, we can use the reverse stock split method, which allows us to effectively merge these assets to form a smaller number of proportionally more valuable shares. This method was used by Manuela Raisová, Martin Užik and Christian M. In the first step by using the Minimum Spanning Tree method we select the most appropriate underlying assets in the portfolio and in the second step by using Generalized Reduced Gradient method we calculate their weights in the proposed portfolio
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