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Composition of the first principal component of a stock index — A comparison between SP500 and VNIndex

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  • Nguyen, Q.
  • Nguyen, N.K.K.

Abstract

We analyzed the components of the eigenvector corresponding to the largest eigenvalue of a cross-correlation matrix of stock price change (the 1st eigenvector) using the Principle Components (PCs) analysis method. We found that the components of the 1st eigenvector are not uniformly distributed. In fact, they are proportional to the correlations of individual stocks and the 1st PC, and could be negative if the corresponding stock is ”in average” negatively correlated to other stocks. By analyzing data from the world stock index in a developed country (SP500) and an emerging one such as Vietnam (VNIndex) from 2013 to 2017, we found negative components in the 1st eigenvector in the VNIndex (and their distribution is also broader than that of SP500). Furthermore, we found that the largest components correspond to stocks of financial services (brokerage or investment advisory firms) firms in both indices. Those stocks are found to be center hubs in a Minimum Spanning Tree (MST) analysis and play an important role whenever a systemic breakdown happens. Finally, we found a phenomenological linear dependence between the components of the 1st eigenvector and the average stock correlation in both indices, and derived an approximation of this dependency using empirical stylized facts of the data. This result provides an estimation of how the PC1 is composed.

Suggested Citation

  • Nguyen, Q. & Nguyen, N.K.K., 2019. "Composition of the first principal component of a stock index — A comparison between SP500 and VNIndex," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    • Handle: RePEc:eee:phsmap:v:536:y:2019:i:c:s0378437119305862
    DOI: 10.1016/j.physa.2019.04.216
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    References listed on IDEAS

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    1. G. Bonanno & F. Lillo & R. N. Mantegna, 2001. "High-frequency cross-correlation in a set of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 96-104.
    2. J. P. Bouchaud & M. Potters, 2009. "Financial Applications of Random Matrix Theory: a short review," Papers 0910.1205, arXiv.org.
    3. M. Potters & J. P. Bouchaud & L. Laloux, 2005. "Financial Applications of Random Matrix Theory: Old Laces and New Pieces," Papers physics/0507111, arXiv.org.
    4. Bernd Rosenow & Vasiliki Plerou & Parameswaran Gopikrishnan & Luís A. Nunes Amaral & H. Eugene Stanley, 2000. "Application Of Random Matrix Theory To Study Cross-Correlations Of Stock Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 399-403.
    5. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
    6. C. Coronnello & M. Tumminello & F. Lillo & S. Miccich`e & R. N. Mantegna, 2005. "Sector identification in a set of stock return time series traded at the London Stock Exchange," Papers cond-mat/0508122, arXiv.org.
    7. Laurent Laloux & Pierre Cizeau & Marc Potters & Jean-Philippe Bouchaud, 2000. "Random Matrix Theory And Financial Correlations," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 391-397.
    8. Tian Qiu & Bo Zheng & Guang Chen, 2010. "Adaptive financial networks with static and dynamic thresholds," Papers 1002.3432, arXiv.org.
    9. Daniel J. Fenn & Mason A. Porter & Stacy Williams & Mark McDonald & Neil F. Johnson & Nick S. Jones, 2010. "Temporal Evolution of Financial Market Correlations," Papers 1011.3225, arXiv.org, revised May 2011.
    10. Vasiliki Plerou & Parameswaran Gopikrishnan & Bernd Rosenow & Luis A. Nunes Amaral & H. Eugene Stanley, 1999. "Universal and non-universal properties of cross-correlations in financial time series," Papers cond-mat/9902283, arXiv.org.
    11. G. Bonanno & G. Caldarelli & F. Lillo & S. Micciché & N. Vandewalle & R. Mantegna, 2004. "Networks of equities in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 38(2), pages 363-371, March.
    12. Nguyen, Quang, 2013. "One-factor model for the cross-correlation matrix in the Vietnamese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(13), pages 2915-2923.
    13. A. Z. Górski & S. Drożdż & J. Kwapień, 2008. "Scale free effects in world currency exchange network," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 66(1), pages 91-96, November.
    14. Raj Kumar Pan & Sitabhra Sinha, 2007. "Collective behavior of stock price movements in an emerging market," Papers 0704.0773, arXiv.org, revised Nov 2007.
    15. Wang, Gang-Jin & Xie, Chi & Han, Feng & Sun, Bo, 2012. "Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4136-4146.
    16. A. Z. Gorski & S. Drozdz & J. Kwapien, 2008. "Scale free effects in world currency exchange network," Papers 0810.1215, arXiv.org.
    17. William Meredith & Roger Millsap, 1985. "On component analyses," Psychometrika, Springer;The Psychometric Society, vol. 50(4), pages 495-507, December.
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