Abstract
Random matrix theory (RMT) has been used to great effect in analysing the structure of the stock return cross-correlation matrix. Common results have been found in various markets: only a few eigen-modes (or portfolios) appear significant and the rest resemble that of a random matrix. Specifically, the eigenvalues spectrum consists of an outstanding large eigenvalue representing the whole market mode, followed by several other large ones, plus the bulk which mostly agrees with the theoretical spectrum distribution predicted by the RMT. The body of work on eigenvector components is not as abundant however. In this work, we analyse in detail the components of the eigenvectors and found that the market mode components depend linearly on what we called the correlation weights of the stocks. Therefore, the corresponding market portfolio must be viewed as a market-correlation-portfolio rather than a market-cap-portfolio. Other informative eigenvectors also show important structures. Those results could be very meaningful in analysing the structure of financial markets and their applications.
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References
Mantegna, R.N.: Hierarchical structure in financial markets. Eur. Phys. J. B 11, 193 (1999)
Laloux, L., Cizeau, P., Bouchaud, J.P., Potters, M.: Noise dressing of financial correlation matrices. Phys. Rev. Lett. 83(7), 1467 (1999)
Laloux, L., Cizeau, P., Potters, M., Bouchaud, J.P.: Random matrix theory and financial correlations. Int. J. Theoret. Appl. Finance 3(03), 391–397 (2000)
Plerou, V., Gopikrishnan, P., Rosenow, B., Amaral, L.A.N., Guhr, T., Stanley, H.E.: Random matrix approach to cross correlations in financial data. Phys. Rev. E 65(6), 066126 (2002)
Utsugi, A., Ino, K., Oshikawa, M.: Random matrix theory analysis of cross correlations in financial markets. Phys. Rev. E 70, 026110 (2004)
Wilcox, D., Gebbie, T.: On the analysis of cross-correlations in South African market data. Phys. A 344, 294 (2004)
Oh, G., Eom, C., Wang, F., Jung, W.S., Stanley, H.E., Kim, S.: Statistical properties of crosscorrelation in the Korean stock market. Eur. Phys. J. B 79, 55 (2011)
Cukur, S., Eryigit, M., Eryigit, R.: Cross-correlation in an emerging market financial data. Physics A 376, 555 (2007)
Shen, J., Zheng, B.: Cross-correlation in financial dynamics. Europhys. Lett. 86, 48005 (2009)
Jiang, X.F., Zheng, B.: Anti-correlation and subsector structure in financial systems. EPL 97, 48006 (2012)
Pan, R.K., Sinha, S.: Collective behavior of stock price movements in an emerging market. Phys. Rev. E 76, 046116 (2007)
Kulkarni, V., Deo, N.: Volatility of an Indian stock market: a random matrix approach, e-print arXiv:physics/0512169 (2005)
Nguyen, Q.: One-factor model for cross-correlation matrix in the Vietnamese stock market. Phys. A 392, 2915–2923 (2013)
Marchenko, V.A., Pastur, L.A.: Distribution of eigenvalues for some sets of random matrices. Matematicheskii Sbornik 114(4), 507–536 (1967)
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This research is funded by Vietnam National University Ho Chi Minh City (VNU-HCM) under grant number B2017-42-01.
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Nguyen, H.T., Tran, P.N.U., Nguyen, Q. (2018). An Analysis of Eigenvectors of a Stock Market Cross-Correlation Matrix. In: Anh, L., Dong, L., Kreinovich, V., Thach, N. (eds) Econometrics for Financial Applications. ECONVN 2018. Studies in Computational Intelligence, vol 760. Springer, Cham. https://doi.org/10.1007/978-3-319-73150-6_40
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DOI: https://doi.org/10.1007/978-3-319-73150-6_40
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