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Financial Applications of Random Matrix Theory: a short review

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  • J. P. Bouchaud
  • M. Potters

Abstract

We discuss the applications of Random Matrix Theory in the context of financial markets and econometric models, a topic about which a considerable number of papers have been devoted to in the last decade. This mini-review is intended to guide the reader through various theoretical results (the Marcenko-Pastur spectrum and its various generalisations, random SVD, free matrices, largest eigenvalue statistics, etc.) as well as some concrete applications to portfolio optimisation and out-of-sample risk estimation.

Suggested Citation

  • J. P. Bouchaud & M. Potters, 2009. "Financial Applications of Random Matrix Theory: a short review," Papers 0910.1205, arXiv.org.
    • Handle: RePEc:arx:papers:0910.1205
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    Cited by:

    1. F. Pozzi & T. Matteo & T. Aste, 2012. "Exponential smoothing weighted correlations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 85(6), pages 1-21, June.
    2. 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.
    3. Esteban Guevara Hidalgo, 2015. "Bin Size Independence in Intra-day Seasonalities for Relative Prices," Papers 1501.05176, arXiv.org, revised Dec 2016.
    4. Mattia Guerini & Duc Thi Luu & Mauro Napoletano, 2023. "Synchronization patterns in the European Union," Applied Economics, Taylor & Francis Journals, vol. 55(18), pages 2038-2059, April.
    5. Duc Thi Luu, 2022. "Portfolio Correlations in the Bank-Firm Credit Market of Japan," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 529-569, August.
    6. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Sparsity and Stability for Minimum-Variance Portfolios," Papers 1910.11840, arXiv.org.
    7. repec:hal:spmain:info:hdl:2441/5q8fnecj1u87ka099dc571bhi2 is not listed on IDEAS
    8. Yongcheng Qi & Mengzi Xie, 2020. "Spectral Radii of Products of Random Rectangular Matrices," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2185-2212, December.
    9. Raphael Douady & Antoine Kornprobst, 2018. "An Empirical Approach To Financial Crisis Indicators Based On Random Matrices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 1-22, May.
    10. Vincent Tan & Stefan Zohren, 2020. "Estimation of Large Financial Covariances: A Cross-Validation Approach," Papers 2012.05757, arXiv.org, revised Jan 2023.
    11. Zeng, Xingyuan, 2017. "Limiting empirical distribution for eigenvalues of products of random rectangular matrices," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 33-40.
    12. Liu Ziyin & Kentaro Minami & Kentaro Imajo, 2021. "Theoretically Motivated Data Augmentation and Regularization for Portfolio Construction," Papers 2106.04114, arXiv.org, revised Dec 2022.
    13. M. Raddant & T. Di Matteo, 2023. "A look at financial dependencies by means of econophysics and financial economics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 18(4), pages 701-734, October.
    14. Nguyen, Q. & Nguyen, N.K.K., 2019. "Composition of the first principal component of a stock index — A comparison between SP500 and VNIndex," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    15. 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.
    16. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2022. "Sparsity and stability for minimum-variance portfolios," Risk Management, Palgrave Macmillan, vol. 24(3), pages 214-235, September.
    17. Tiberiu Teşileanu & Lucy J Colwell & Stanislas Leibler, 2015. "Protein Sectors: Statistical Coupling Analysis versus Conservation," PLOS Computational Biology, Public Library of Science, vol. 11(2), pages 1-20, February.
    18. Gabriele Torri & Rosella Giacometti & Sandra Paterlini, 2019. "Sparse precision matrices for minimum variance portfolios," Computational Management Science, Springer, vol. 16(3), pages 375-400, July.
    19. Sandoval, Leonidas Junior & Bruscato, Adriana & Venezuela, Maria Kelly, 2012. "Building portfolios of stocks in the São Paulo Stock Exchange using Random Matrix Theory," Insper Working Papers wpe_270, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
    20. Dalibor Eterovic & Nicolas Eterovic, 2012. "Separating the Wheat from the Chaff: Understanding Portfolio Returns in an Emerging Market," Working Papers wp_025, Adolfo Ibáñez University, School of Government.
    21. Thomas Lux & Duc Thi Luu & Boyan Yanovski, 2020. "An analysis of systemic risk in worldwide economic sentiment indices," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 47(4), pages 909-928, November.
    22. Lars Heinrich & Antoniya Shivarova & Martin Zurek, 2021. "Factor investing: alpha concentration versus diversification," Journal of Asset Management, Palgrave Macmillan, vol. 22(6), pages 464-487, October.
    23. Sakae Oya, 2022. "A Bayesian Graphical Approach for Large-Scale Portfolio Management with Fewer Historical Data," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 29(3), pages 507-526, September.
    24. Luu, Duc Thi & Yanovski, Boyan & Lux, Thomas, 2018. "An analysis of systematic risk in worldwide econonomic sentiment indices," Economics Working Papers 2018-03, Christian-Albrechts-University of Kiel, Department of Economics.
    25. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2013. "A nested factor model for non-linear dependences in stock returns," Papers 1309.3102, arXiv.org.

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