Finding statistical relationship between Markowitz portfolios and Eigen portfolios

Abstract

This study aims to nd a statistical relationship between the Markowitz portfolios and Eigen portfolios using concepts from graph theory as the linkage between them. The former is constructed using a risk-return framework while the latter is constructed using the decomposition of the variance-covariance matrix of the returns into its principal components. In our earlier research, we found that centrality of an asset in the asset graph measured using eigen- vector centrality (EVC) score is statistically related to the portfolio weight of that asset in a Markowitz portfolio. In this paper, we search for a statistical relationship between the EVC scores of assets in a portfolio with the leading eigenvector portfolios. The analysis is carried out in two steps - rst, we establish that the information carried by EVC centrality measure is similar to that of the excess return Fama-French factor and second, we and that the excess return factor explains a large proportion of portfolios generated using eigen decomposition.