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Large Dynamic Covariance Matrices

Author

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  • Robert F. Engle
  • Olivier Ledoit
  • Michael Wolf

Abstract

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroscedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present article marries these two strands of literature to deliver improved estimation of large dynamic covariance matrices. Supplementary material for this article is available online.

Suggested Citation

  • Robert F. Engle & Olivier Ledoit & Michael Wolf, 2019. "Large Dynamic Covariance Matrices," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(2), pages 363-375, April.
  • Handle: RePEc:taf:jnlbes:v:37:y:2019:i:2:p:363-375
    DOI: 10.1080/07350015.2017.1345683
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    References listed on IDEAS

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    1. Ledoit, Olivier & Wolf, Michael, 2004. "A well-conditioned estimator for large-dimensional covariance matrices," Journal of Multivariate Analysis, Elsevier, vol. 88(2), pages 365-411, February.
    2. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    3. Ledoit, Olivier & Wolf, Michael, 2017. "Numerical implementation of the QuEST function," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 199-223.
    4. Ledoit, Olivier & Wolf, Michael, 2015. "Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 360-384.
    5. Yin, Y. Q., 1986. "Limiting spectral distribution for a class of random matrices," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 50-68, October.
    6. Engle, Robert & Colacito, Riccardo, 2006. "Testing and Valuing Dynamic Correlations for Asset Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 238-253, April.
    7. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    8. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    9. Silverstein, J. W., 1995. "Strong Convergence of the Empirical Distribution of Eigenvalues of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 55(2), pages 331-339, November.
    10. Gian Piero Aielli, 2013. "Dynamic Conditional Correlation: On Properties and Estimation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 282-299, July.
    11. Silverstein, J. W. & Choi, S. I., 1995. "Analysis of the Limiting Spectral Distribution of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 54(2), pages 295-309, August.
    12. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1684, August.
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    Citations

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    Cited by:

    1. Zhao Zhao & Olivier Ledoit & Hui Jiang, 2019. "Risk reduction and efficiency increase in large portfolios: leverage and shrinkage," ECON - Working Papers 328, Department of Economics - University of Zurich.
    2. repec:gam:jecnmx:v:7:y:2019:i:2:p:19-:d:229754 is not listed on IDEAS
    3. Marc Hallin & Luis K. Hotta & João H. G Mazzeu & Carlos Cesar Trucios-Maza & Pedro L. Valls Pereira & Mauricio Zevallos, 2019. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: a General Dynamic Factor Approach," Working Papers ECARES 2019-14, ULB -- Universite Libre de Bruxelles.
    4. Niels S. Grønborg & Asger Lunde & Kasper V. Olesen & Harry Vander Elst, 2018. "Realizing Correlations Across Asset Classes," CREATES Research Papers 2018-37, Department of Economics and Business Economics, Aarhus University.
    5. Chen, J. & Li, D. & Linton, O., 2018. "A New Semiparametric Estimation Approach for Large Dynamic Covariance Matrices with Multiple Conditioning Variables," Cambridge Working Papers in Economics 1876, Faculty of Economics, University of Cambridge.
    6. Andries C. van Vlodrop & Andre (A.) Lucas, 2018. "Estimation Risk and Shrinkage in Vast-Dimensional Fundamental Factor Models," Tinbergen Institute Discussion Papers 18-099/III, Tinbergen Institute.
    7. He, Zhongfang, 2018. "A Class of Generalized Dynamic Correlation Models," MPRA Paper 84820, University Library of Munich, Germany.
    8. van Zundert, Jeroen, 2018. "Empirical studies on the cross-section of corporate bond and stock markets," Other publications TiSEM 338205fc-a031-4e06-a636-9, Tilburg University, School of Economics and Management.
    9. Trucíos, Carlos & Hotta, Luiz K. & Valls Pereira, Pedro L., 2019. "On the robustness of the principal volatility components," Journal of Empirical Finance, Elsevier, vol. 52(C), pages 201-219.
    10. Gianluca De Nard & Olivier Ledoit & Michael Wolf, 2018. "Factor models for portfolio selection in large dimensions: the good, the better and the ugly," ECON - Working Papers 290, Department of Economics - University of Zurich, revised Dec 2018.
    11. repec:eee:csdana:v:115:y:2017:i:c:p:199-223 is not listed on IDEAS
    12. Ledoit, Olivier & Wolf, Michael, 2017. "Numerical implementation of the QuEST function," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 199-223.
    13. Olivier Ledoit & Michael Wolf, 2019. "Shrinkage estimation of large covariance matrices: keep it simple, statistician?," ECON - Working Papers 327, Department of Economics - University of Zurich.
    14. Claudio, Morana, 2018. "Regularized semiparametric estimation of high dimensional dynamic conditional covariance matrices," Working Papers 382, University of Milano-Bicocca, Department of Economics, revised 04 Jun 2018.
    15. Olivier Ledoit & Michael Wolf, 2017. "Analytical nonlinear shrinkage of large-dimensional covariance matrices," ECON - Working Papers 264, Department of Economics - University of Zurich, revised Nov 2018.
    16. repec:gam:jijfss:v:6:y:2018:i:2:p:52-:d:146287 is not listed on IDEAS
    17. Liu, Laura & Matthes, Christian & Petrova, Katerina, 2018. "Monetary Policy across Space and Time," Working Paper 18-14, Federal Reserve Bank of Richmond.
    18. Catherine D'Hondt & Rudy De Winne & Eric Ghysels & Steve Raymond, 2019. "Artificial Intelligence Alter Egos: Who benefits from Robo-investing?," Papers 1907.03370, arXiv.org.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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