Signed graphs for portfolio analysis in risk management |
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Authors: | Harary, Frank Lim, Meng-Hiot Wunsch, Donald C. |
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Affiliation: | 1 Computer Science Department, New Mexico State University, Las Cruces, NM 88003, USA 2 School of EEE, Block S1, Nanyang Tech University, Singapore 639798, Singapore 3 Department of ECE, University of Missouri - Rolla, Rolla, MO 65409-0040, USA |
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Abstract: | We introduce the notion of structural balance for signed graphsin the context of portfolio analysis. A portfolio of securitiescan be represented as a signed graph with the nodes denotingthe securities and the edges representing the correlation betweenthe securities. With signed graphs, the characteristics of aportfolio from a risk management perspective can be uncoveredfor analysis purposes. It is shown that a portfolio characterizedby a signed graph of positive and negative edges that is structurallybalanced is characteristically more predictable. Investors whoundertake a portfolio position with all positively correlatedsecurities do so with the intention to speculate on the upside(or downside). If the portfolio consists of negative edges andis balanced, then it is likely that the position has a hedgingdisposition within it. On the other hand, an unbalanced signedgraph is representative of an investment portfolio which ischaracteristically unpredictable. |
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Keywords: | graph theory portfolio management risk signed graphs |
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