Portfolio creation using graph characteristics

The aim of this work is by combination of the graph theory and Markowitz portfolio theory to illustrate how some graph characteristics are related to the diversification potential of individual portfolio-forming stocks. Using the graph characteristic, the vertex eccentricity, individual stocks are divided into two groups: a group of large and group of small eccentricity. Eccentricity in this context is considered to be a very suitable metric of the centrality of individual vertices. Different price histories (5 to 30 years) of the Standard and Poor’s index are analyzed. Using the simulation analysis, samples of mentioned groups are generated and then tested by means of comparison to show that larger eccentricity samples, representing stocks on the periphery of the minimum spanning tree of the graph, have a higher potential for diversification than those found in the center of the graph. The results published in the article can be a practical guide for an individual investor during the portfolio creation process and help him/her with decision-making about stock selection. Jakub Danko (Slovak Republic), Vincent Soltes (Slovak Republic) BUSINESS PERSPECTIVES LLC “СPС “Business Perspectives” Hryhorii Skovoroda lane, 10, Sumy, 40022, Ukraine www.businessperspectives. org Portfolio creation using graph characteristics Received on: 17th of October, 2017 Accepted on: 9th of February, 2018 INTRODUCTION The goal of the investor is to create a portfolio that has a high expected return and the low risk level. The first problem is that the investor needs to solve the selection of the stocks into the portfolio and then he has to determine the weights of the individual stocks. In the paper, for the stock selection process, it is proposed to use graph characteristic known as the vertex eccentricity. Every vertex of the graph represents an individual stock, which can form a portfolio. The eccentricity of the graph vertex can identify the so-called centrality of stocks and, as shown in the paper, this measure is very effective in identifying certain stocks that are more suitable for diversifying the risk the investor requires. 1. LITERATURE REVIEW Harry Markowitz (1952, 1959) and William Forsyth Sharpe (1992) are those authors, by whom pioneering work in modern portfolio theory was done. The effect of asset risk, return, correlation, as well as diversification on expected investment portfolio returns, are issues, which were studied by them. Methods of Markowitz portfolio optimization are used in this paper. Approach to portfolio optimization used in this article is based on network theory. Network theory is the tool and methodology approach, which can be used to explain and better understand financial markets. When talking about financial markets, the mutual development © Jakub Danko, Vincent Soltes, 2018 Jakub Danko, Ing. , Department of Finance, Faculty of Economics, Technical University in Košice, Slovak Republic. Vincent Soltes, Professor, Department of Finance, Faculty of Economics, Technical University in Košice, Slovak Republic. This is an Open Access article, distributed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International license, which permits re-use, distribution, and reproduction, provided the materials aren’t used for commercial purposes and the original work is properly cited. portfolio, risk, minimum spanning tree, eccentricity, Markowitz portfolio optimization