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. Specifically, 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 the
correlation matrix 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.Comment: 37 pages, 9 figures, 3 table
Universidad Nacional de Cordoba. Facultad de Ciencias Exactas, Fisicas y Naturales; Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto Multidisciplinario de Biologia Vegetal
Universidad Nacional de Cordoba. Facultad de Ciencias Exactas, Fisicas y Naturales; Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto Multidisciplinario de Biologia Vegetal
Universidad Nacional de Cordoba. Facultad de Ciencias Exactas, Fisicas y Naturales; Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto Multidisciplinario de Biologia Vegetal
Universidad Nacional de Cordoba. Facultad de Ciencias Exactas, Fisicas y Naturales; Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto Multidisciplinario de Biologia Vegetal
Universidad Nacional de Cordoba. Facultad de Ciencias Exactas, Fisicas y Naturales; Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto Multidisciplinario de Biologia Vegetal
Universidad Nacional de Cordoba. Facultad de Ciencias Exactas, Fisicas y Naturales; Consejo Nacional de Investigaciones Cientificas y Tecnicas. Instituto Multidisciplinario de Biologia Vegetal