Signed graphs for portfolio analysis in risk management

Authors:
  • FHFrank Harary
    Frank Harary
  • MLMeng‐Hiot Lim
    Meng‐Hiot Lim
  • DWDonald C. Wunsch
    Donald C. Wunsch
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Abstract
We introduce the notion of structural balance for signed graphs in the context of portfolio analysis. A portfolio of securities can be represented as a signed graph with the nodes denoting the securities and the edges representing the correlation between the securities. With signed graphs, the characteristics of a portfolio from a risk management perspective can be uncovered for analysis purposes. It is shown that a portfolio characterized by a signed graph of positive and negative edges that is structurally balanced is characteristically more predictable. Investors who undertake a portfolio position with all positively correlated securities do so with the intention to speculate on the upside (or downside). If the portfolio consists of negative edges and is balanced, then it is likely that the position has a hedging disposition within it. On the other hand, an unbalanced signed graph is representative of an investment portfolio which is characteristically unpredictable.