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Principal Regression Analysis and the index leverage effect

  • Pierre-Alain Reigneron
  • Romain Allez
  • Jean-Philippe Bouchaud
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    We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call `Principal Regression Analysis' (PRA) and for which we provide some analytical (using Random Matrix Theory) and numerical benchmarks. We find that downward index trends increase the average correlation between stocks (as measured by the most negative eigenvalue of the conditional correlation matrix), and makes the market mode more uniform. Upward trends, on the other hand, also increase the average correlation between stocks but rotates the corresponding market mode {\it away} from uniformity. There are two time scales associated to these effects, a short one on the order of a month (20 trading days), and a longer time scale on the order of a year. We also find indications of a leverage effect for sectorial correlations as well, which reveals itself in the second and third mode of the PRA.

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    File URL: http://arxiv.org/pdf/1011.5810
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    Paper provided by arXiv.org in its series Papers with number 1011.5810.

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    Date of creation: Nov 2010
    Date of revision: Feb 2011
    Publication status: Published in Physica A: Statistical Mechanics and its Applications, 390 (2011)
    Handle: RePEc:arx:papers:1011.5810
    Contact details of provider: Web page: http://arxiv.org/

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    1. Giulio Biroli & Jean-Philippe Bouchaud & Marc Potters, 2007. "The Student ensemble of correlation matrices: eigenvalue spectrum and Kullback-Leibler entropy," Papers 0710.0802, arXiv.org.
    2. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    3. Josep Perello & Jaume Masoliver & Jean-Philippe Bouchaud, 2004. "Multiple time scales in volatility and leverage correlations: a stochastic volatility model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(1), pages 27-50.
    4. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1999. "Random matrix theory," Science & Finance (CFM) working paper archive 500052, Science & Finance, Capital Fund Management.
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