Noise Dressing of Financial Correlation Matrices

By L. Laloux, P. Cizeau, Jean-Philippe Bouchaud, Marc Potters. 1998

We show that results from the theory of random matrices are potentially of great interest to understand the statistical structure of the empirical correlation matrices appearing in the study of price fluctuations. The central result of the present study is the remarkable agreement between the theoretical prediction (based on the assumption that the correlation matrix is random) and empirical data concerning the density of eigenvalues associated to the time series of the different stocks of the S&P500 (or other major markets). In particular the present study raises serious doubts on the blind use of empirical correlation matrices for risk management.

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Citations in the corpus

The Fitness Landscape of HIV-1 Gag: Advanced Modeling Approaches and Validation of Model Predictions by In Vitro Testing (2014, neutral): “In analogy with past studies on the economic markets and enzymes [13–15], we termed these groups of residues ‘‘sectors’’.”
Correlation structure and dynamics of international real estate securities markets: A network perspective (2015, methodology): “correlation structure among financial assets, such as random matrix theory [23,24], detrended cross-correlation analysis (DCCA) method [25], and multifractal DCCA method [26].”
A methodology for index tracking based on time-series clustering (2004, methodology): “An elegant illustration of this fact was provided recently by Laloux et al (1999a), Ormerod and Mounfield (2000), and Plerou et al (1999) using the random matrix theory, a mathematical theory developed in the 1950s in the context of quantum mechanics.”
Cluster analysis for portfolio optimization (2005, unknown): “…to the unavoidable statistical uncertainty (in the econophysics literature the term of noise dressing has been used) (Galluccio et al., 1998; Laloux et al., 1999, 2000; Plerou et al., 1999, 2002; Gopikrishnan et al., 2001; Drozdz et al., 2001; Rosenow et al., 2002; Pafka and Kondor, 2003,…”
Correlation, Hierarchies, and Networks in Financial Markets (2008, unknown): “In these cases, Laloux et al. (1999) propose to modify the null hypothesis so that correlations can be explained in terms of a one factor model and σ2 = 1 − λ1/N .”
A Network Approach to Portfolio Selection (2016, unknown): “…since the empirical evidence indicates that only eigenvector elements corresponding to the largest eigenvalue have informational content (Green and Hollifield, 1992; Laloux et al., 1999; Trzcinka, 1986), we focus on 𝑣1 and 𝜆1 by defining 𝛤𝑚𝑖𝑛𝑣 and 𝛤𝑚𝑣 in terms of 𝑣𝑗 and 𝜆𝑗 for 𝑗 > 1.”
Spectrum estimation for large dimensional covariance matrices using random matrix theory (2006, background): “They essentially measure what is the minimum risk one can take by investing in a portfolio of certain stocks (see [27] and [13], Chapter 5).”
ENHANCEMENT OF THE APPLICABILITY OF MARKOWITZ'S PORTFOLIO OPTIMIZATION BY UTILIZING RANDOM MATRIX THEORY (2009, methodology): “Laloux et al. (1999) and others suggest that the determination of the correlation matrix and its eigenvalues could be the reason for the poor estimation.”
A new approach to quantify power-law cross-correlation and its application to commodity markets (2011, background): “Many simultaneously recorded time series in various real world commodity or financial markets are found to exhibit spatial or temporal cross-correlations [3, 7-17].”
Random Matrix Theory and Fund of Funds Portfolio Optimisation (2007, methodology): “However, since our aim here is to demonstrate how Random Matrix Theory can be used to improve the risk/return profile for a portfolio of Hedge Funds, we assume that the eigenvalues corresponding to the noise band in RMT, λ− ≤ λ ≤ λ+, are not expected to correspond to real information following [6,7,”
Denoising of diffusion MRI using random matrix theory (2016, methodology): “Beyond dMRI Noise analysis using random matrix theory has previously been explored in the context of finance (Laloux et al., 1999), wireless communication systems (Ahmed et al.”