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Principal Regression Analysis and the index leverage effect


  • Pierre-Alain Reigneron
  • Romain Allez
  • Jean-Philippe Bouchaud


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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  • Pierre-Alain Reigneron & Romain Allez & Jean-Philippe Bouchaud, 2010. "Principal Regression Analysis and the index leverage effect," Papers 1011.5810,, revised Feb 2011.
  • Handle: RePEc:arx:papers:1011.5810

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    References listed on IDEAS

    1. 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.
    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. Giulio Biroli & Jean-Philippe Bouchaud & Marc Potters, 2007. "The Student ensemble of correlation matrices: eigenvalue spectrum and Kullback-Leibler entropy," Papers 0710.0802,
    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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    1. repec:eee:jeborg:v:140:y:2017:i:c:p:18-34 is not listed on IDEAS
    2. Thilo A. Schmitt & Rudi Schafer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering temporal dependencies in financial time series," Papers 1507.04990,
    3. Thilo A. Schmitt & Rudi Schäfer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering Temporal Dependencies In Financial Time Series," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-16, November.
    4. da Gama Batista, João & Massaro, Domenico & Bouchaud, Jean-Philippe & Challet, Damien & Hommes, Cars, 2017. "Do investors trade too much? A laboratory experiment," Journal of Economic Behavior & Organization, Elsevier, vol. 140(C), pages 18-34.
    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. repec:eee:phsmap:v:486:y:2017:i:c:p:618-627 is not listed on IDEAS
    7. repec:kap:compec:v:51:y:2018:i:2:d:10.1007_s10614-016-9596-x is not listed on IDEAS

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