Signed Graphs for Portfolio Analysis in Risk Management

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.

Department(s)

Electrical and Computer Engineering

Keywords and Phrases

Graph theory; Portfolio management; Risk; Signed graphs

International Standard Serial Number (ISSN)

1471-678X

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2024 Oxford University Press; Institute of Mathematics and its Applications, All rights reserved.

Publication Date

01 Jan 2002

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