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Random matrix application to correlations amongst the volatility of assets

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  • Ajay Singh
  • Dinghai Xu

Abstract

In this paper, we apply tools from random matrix theory (RMT) to estimates of correlations across the volatility of various assets in the S&P 500. The volatility inputs are estimated by modelling price fluctuations as a GARCH(1,1) process. The corresponding volatility correlation matrix is then constructed. It is found that the distribution of a significant number of eigenvalues of the volatility correlation matrix matches with the analytical result from RMT. Furthermore, the empirical estimates of short- and long-range correlations amongst eigenvalues, which are within RMT bounds, match with the analytical results for the Gaussian Orthogonal ensemble of RMT. To understand the information content of the largest eigenvectors, we estimate the contribution of the Global Industry Classification Standard industry groups to each eigenvector. In comparison with eigenvectors of correlation matrix for price fluctuations, only few of the largest eigenvectors of the volatility correlation matrix are dominated by a single industry group. We also study correlations between ‘volatility returns’ and log-volatility to find similar results.

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  • Ajay Singh & Dinghai Xu, 2016. "Random matrix application to correlations amongst the volatility of assets," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 69-83, January.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:1:p:69-83
    DOI: 10.1080/14697688.2015.1014400
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    Cited by:

    1. Longfeng Zhao & Wei Li & Andrea Fenu & Boris Podobnik & Yougui Wang & H. Eugene Stanley, 2017. "The q-dependent detrended cross-correlation analysis of stock market," Papers 1705.01406, arXiv.org, revised Jun 2017.
    2. Sebastiano Michele Zema & Giorgio Fagiolo & Tiziano Squartini & Diego Garlaschelli, 2021. "Mesoscopic Structure of the Stock Market and Portfolio Optimization," Papers 2112.06544, arXiv.org.
    3. Anshul Verma & Riccardo Junior Buonocore & Tiziana di Matteo, 2017. "A cluster driven log-volatility factor model: a deepening on the source of the volatility clustering," Papers 1712.02138, arXiv.org, revised May 2018.
    4. Nie, Chun-Xiao, 2021. "Analyzing financial correlation matrix based on the eigenvector–eigenvalue identity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).

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