Correlation, hierarchies, and networks in financial markets

We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Here, we discuss how to define and obtain h...

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Bibliographic Details
Published in:Journal of economic behavior & organization 2010-07, Vol.75 (1), p.40-58
Main Authors: Tumminello, Michele, Lillo, Fabrizio, Mantegna, Rosario N.
Format: Article
Language:English
Subjects:
Bootstrap validation
Capital market theory
Capital mobility
Correlation
Correlation analysis
Correlation based networks
Factor models
Financial market
Fluctuations
Hierarchical clustering
Kullback–Leibler distance
Matrices
Matrix
Matrix calculus
Multivariate analysis
Multivariate analysis Hierarchical clustering Correlation based networks Bootstrap validation Factor models Kullback-Leibler distance
Optimization
Portfolio management
Portfolios
Securities markets
Studies
Trees
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Summary:We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Here, we discuss how to define and obtain hierarchical trees, correlation based trees and networks from a correlation matrix. The hierarchical clustering and other procedures performed on the correlation matrix to detect statistically reliable aspects of it are seen as filtering procedures of the correlation matrix. We also discuss a method to associate a hierarchically nested factor model to a hierarchical tree obtained from a correlation matrix. The information retained in filtering procedures and its stability with respect to statistical fluctuations is quantified by using the Kullback–Leibler distance.
ISSN:0167-2681
1879-1751
DOI:10.1016/j.jebo.2010.01.004