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.
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