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Correlation and volatility in an Indian stock market: A random matrix approach

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  • Varsha Kulkarni
  • Nivedita Deo

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    Abstract

    We examine the volatility of an Indian stock market in terms of correlation of stocks and quantify the volatility using the random matrix approach. First we discuss trends observed in the pattern of stock prices in the Bombay Stock Exchange for the three-year period 2000–2002. Random matrix analysis is then applied to study the relationship between the coupling of stocks and volatility. The study uses daily returns of 70 stocks for successive time windows of length 85 days for the year 2001. We compare the properties of matrix C of correlations between price fluctuations in time regimes characterized by different volatilities. Our analyses reveal that (i) the largest (deviating) eigenvalue of C correlates highly with the volatility of the index, (ii) there is a shift in the distribution of the components of the eigenvector corresponding to the largest eigenvalue across regimes of different volatilities, (iii) the inverse participation ratio for this eigenvector anti-correlates significantly with the market fluctuations and finally, (iv) this eigenvector of C can be used to set up a Correlation Index, CI whose temporal evolution is significantly correlated with the volatility of the overall market index. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

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    File URL: http://hdl.handle.net/10.1140/epjb/e2007-00322-1
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    Bibliographic Info

    Article provided by Springer in its journal The European Physical Journal B.

    Volume (Year): 60 (2007)
    Issue (Month): 1 (November)
    Pages: 101-109

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    Handle: RePEc:spr:eurphb:v:60:y:2007:i:1:p:101-109

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    Web page: http://www.springer.com/economics/journal/10051

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    Keywords: 89.65.Gh Economics; econophysics; financial markets; business and management; 89.65.-s Social and economic systems; 89.75.-k Complex systems;

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    1. Simone Bianco & Roberto Ren\'o, 2006. "Unexpected volatility and intraday serial correlation," Papers physics/0610023, arXiv.org.
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    Cited by:
    1. Cheong, Siew Ann & Fornia, Robert Paulo & Lee, Gladys Hui Ting & Kok, Jun Liang & Yim, Woei Shyr & Xu, Danny Yuan & Zhang, Yiting, 2011. "The Japanese economy in crises: A time series segmentation study," Economics Discussion Papers 2011-24, Kiel Institute for the World Economy.
    2. Wang, Gang-Jin & Xie, Chi & Chen, Shou & Yang, Jiao-Jiao & Yang, Ming-Yan, 2013. "Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3715-3730.
    3. Sandoval, Leonidas, 2012. "Pruning a minimum spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2678-2711.
    4. Matsushita, Raul & Figueiredo, Annibal & Da Silva, Sergio, 2012. "A suggested statistical test for measuring bivariate nonlinear dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4891-4898.
    5. Eterovic, Nicolas A. & Eterovic, Dalibor S., 2013. "Separating the wheat from the chaff: Understanding portfolio returns in an emerging market," Emerging Markets Review, Elsevier, vol. 16(C), pages 145-169.
    6. 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.

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