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Principal regression analysis and the index leverage effect

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

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 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

  • Reigneron, Pierre-Alain & Allez, Romain & Bouchaud, Jean-Philippe, 2011. "Principal regression analysis and the index leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(17), pages 3026-3035.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:17:p:3026-3035
    DOI: 10.1016/j.physa.2011.04.007
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    Cited by:

    1. Mehdi Tomas & Mathieu Rosenbaum, 2019. "From microscopic price dynamics to multidimensional rough volatility models," Papers 1910.13338, arXiv.org, revised Oct 2019.
    2. Thilo A. Schmitt & Rudi Schafer & Holger Dette & Thomas Guhr, 2015. "Quantile Correlations: Uncovering temporal dependencies in financial time series," Papers 1507.04990, arXiv.org.
    3. 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.
    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. Jean-Philippe Bouchaud & Iacopo Mastromatteo & Marc Potters & Konstantin Tikhonov, 2022. "Excess Out-of-Sample Risk and Fleeting Modes," Papers 2205.01012, arXiv.org.
    7. 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.
    8. 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.
    9. 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).
    10. 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.
    11. 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.
    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. 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.
    14. Jean-Philippe Bouchaud, 2021. "Radical Complexity," Papers 2103.09692, arXiv.org.
    15. Armine Karami & Raphael Benichou & Michael Benzaquen & Jean-Philippe Bouchaud, 2021. "Conditional Correlations and Principal Regression Analysis for Futures," Post-Print hal-02567501, HAL.

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