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Principal Regression Analysis and the index leverage effect

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

Abstract

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.

Suggested Citation

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

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    1. J. P. Bouchaud & M. Potters, 2009. "Financial Applications of Random Matrix Theory: a short review," Papers 0910.1205, arXiv.org.
    2. 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.
    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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    6. Lisa Borland & Yoan Hassid, 2010. "Market panic on different time-scales," Papers 1010.4917, arXiv.org.
    7. Emeric Balogh & Ingve Simonsen & Balint Zs. Nagy & Zoltan Neda, 2010. "Persistent collective trend in stock markets," Papers 1005.0378, arXiv.org.
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    Cited by:

    1. 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.
    2. Mehdi Tomas & Mathieu Rosenbaum, 2019. "From microscopic price dynamics to multidimensional rough volatility models," Papers 1910.13338, arXiv.org, revised Oct 2019.
    3. Thilo A. Schmitt & Rudi Schafer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering temporal dependencies in financial time series," Papers 1507.04990, arXiv.org.
    4. Armine Karami & Raphael Benichou & Michael Benzaquen & Jean-Philippe Bouchaud, 2020. "Conditional Correlations And Principal Regression Analysis For Futures," Working Papers hal-02567501, HAL.
    5. Armine Karami & Raphael Benichou & Michael Benzaquen & Jean-Philippe Bouchaud, 2019. "Conditional Correlations and Principal Regression Analysis for Futures," Papers 1912.12354, arXiv.org, revised Jan 2020.
    6. Ma, Rong & Zhang, Yin & Li, Honggang, 2017. "Traders’ behavioral coupling and market phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 618-627.
    7. Jean-Philippe Bouchaud & Iacopo Mastromatteo & Marc Potters & Konstantin Tikhonov, 2022. "Excess Out-of-Sample Risk and Fleeting Modes," Papers 2205.01012, arXiv.org.
    8. 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.
    9. Jean-Philippe Bouchaud, 2021. "Radical Complexity," Papers 2103.09692, arXiv.org.
    10. Aboura, Sofiane & Chevallier, Julien, 2018. "Tail risk and the return-volatility relation," Research in International Business and Finance, Elsevier, vol. 46(C), pages 16-29.
    11. Heckens, Anton J. & Guhr, Thomas, 2022. "New collectivity measures for financial covariances and correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    12. 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.
    13. Armine Karami & Raphael Benichou & Michael Benzaquen & Jean-Philippe Bouchaud, 2021. "Conditional Correlations and Principal Regression Analysis for Futures," Post-Print hal-02567501, HAL.
    14. Kaihua Deng, 2018. "Another Look at Large-Cap Stock Return Comovement: A Semi-Markov-Switching Approach," Computational Economics, Springer;Society for Computational Economics, vol. 51(2), pages 227-262, February.
    15. Jacopo Rocchi & Enoch Yan Lok Tsui & David Saad, 2017. "Emerging interdependence between stock values during financial crashes," PLOS ONE, Public Library of Science, vol. 12(5), pages 1-15, May.

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