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Random Matrix Application to Correlations Among Volatility of Assets

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  • Ajay Singh
  • Dinghai Xu

Abstract

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

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  • Ajay Singh & Dinghai Xu, 2013. "Random Matrix Application to Correlations Among Volatility of Assets," Papers 1310.1601, arXiv.org.
    • Handle: RePEc:arx:papers:1310.1601
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    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. 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).
    4. 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.

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