Portfolio creation using graph characteristics

Abstract

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.

Keywords

• eccentricity
• Markowitz portfolio optimization
• minimum spanning tree
• portfolio
• risk