IDEAS home Printed from https://ideas.repec.org/a/spr/annopr/v346y2025i1d10.1007_s10479-024-06238-4.html
   My bibliography  Save this article

Model-based vs. agnostic methods for the prediction of time-varying covariance matrices

Author

Listed:
  • Jean-David Fermanian

    (ENSAE-CREST, Finance Department)

  • Benjamin Poignard

    (Osaka University, Graduate School of Economics
    RIKEN-AIP)

  • Panos Xidonas

    (ESSCA School of Management)

Abstract

This article is written in memory of Harry Markowitz, the founder of modern portfolio theory. We report a few human perspectives of his character, we review a large number of his contributions, published both in operations research and finance oriented journals, and we focus on one of the most critical, and still open, portfolio theory issues, the forecast of covariance matrices. Our contribution in this paper is placed exactly towards this direction. More specifically, we compare the performances of several approaches to predict the variance-covariance matrices of vectors of asset returns, through simulated and real data experiments: some dynamic models such as Dynamic Conditional Correlation (DCC) and C-vine GARCH on one side, and several agnostic methods (Average Oracle, usual “Sample” matrix) on the other side. The most robust methods seem to be DCC and the Average Oracle approaches.

Suggested Citation

  • Jean-David Fermanian & Benjamin Poignard & Panos Xidonas, 2025. "Model-based vs. agnostic methods for the prediction of time-varying covariance matrices," Annals of Operations Research, Springer, vol. 346(1), pages 511-548, March.
    • Handle: RePEc:spr:annopr:v:346:y:2025:i:1:d:10.1007_s10479-024-06238-4
    DOI: 10.1007/s10479-024-06238-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10479-024-06238-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10479-024-06238-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Olivier Ledoit & Michael Wolf, 2022. "The Power of (Non-)Linear Shrinking: A Review and Guide to Covariance Matrix Estimation [Design-Free Estimation of Variance Matrices]," Journal of Financial Econometrics, Oxford University Press, vol. 20(1), pages 187-218.
    2. Xidonas, Panagiotis & Mavrotas, George & Zopounidis, Constantin & Psarras, John, 2011. "IPSSIS: An integrated multicriteria decision support system for equity portfolio construction and selection," European Journal of Operational Research, Elsevier, vol. 210(2), pages 398-409, April.
    3. Olivier Ledoit & Michael Wolf, 2017. "Nonlinear Shrinkage of the Covariance Matrix for Portfolio Selection: Markowitz Meets Goldilocks," The Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4349-4388.
    4. Louis K.C. Chan & Jason Karceski & Josef Lakonishok, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," NBER Working Papers 7039, National Bureau of Economic Research, Inc.
    5. Weiming Li & Jing Gao & Kunpeng Li & Qiwei Yao, 2016. "Modeling Multivariate Volatilities via Latent Common Factors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(4), pages 564-573, October.
    6. John B. Guerard & Ganlin Xu & Harry Markowitz, 2021. "A further analysis of robust regression modeling and data mining corrections testing in global stocks," Annals of Operations Research, Springer, vol. 303(1), pages 175-195, August.
    7. Peter R. Hansen & Asger Lunde & James M. Nason, 2011. "The Model Confidence Set," Econometrica, Econometric Society, vol. 79(2), pages 453-497, March.
    8. Robert D. Arnott & Jason C. Hsu & Jun Liu & Harry Markowitz, 2015. "Can Noise Create the Size and Value Effects?," Management Science, INFORMS, vol. 61(11), pages 2569-2579, November.
    9. Markowitz, Harry M & Perold, Andre F, 1981. "Portfolio Analysis with Factors and Scenarios," Journal of Finance, American Finance Association, vol. 36(4), pages 871-877, September.
    10. Bai, Jushan & Liao, Yuan, 2016. "Efficient estimation of approximate factor models via penalized maximum likelihood," Journal of Econometrics, Elsevier, vol. 191(1), pages 1-18.
    11. Massimiliano Caporin & Michael McAleer, 2013. "Ten Things You Should Know about the Dynamic Conditional Correlation Representation," Econometrics, MDPI, vol. 1(1), pages 1-12, June.
    12. Xidonas, Panos & Mavrotas, George & Hassapis, Christis & Zopounidis, Constantin, 2017. "Robust multiobjective portfolio optimization: A minimax regret approach," European Journal of Operational Research, Elsevier, vol. 262(1), pages 299-305.
    13. Cavit Pakel & Neil Shephard & Kevin Sheppard & Robert F. Engle, 2021. "Fitting Vast Dimensional Time-Varying Covariance Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 652-668, July.
    14. Das, Sanjiv & Markowitz, Harry & Scheid, Jonathan & Statman, Meir, 2010. "Portfolio Optimization with Mental Accounts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 45(2), pages 311-334, April.
    15. Peter Reinhard Hansen & Asger Lunde & James M. Nason, 2003. "Choosing the Best Volatility Models: The Model Confidence Set Approach," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 65(s1), pages 839-861, December.
    16. John B. Guerard & Harry Markowitz & Ganlin Xu & Ziwei Wang, 2018. "Global portfolio construction with emphasis on conflicting corporate strategies to maximize stockholder wealth," Annals of Operations Research, Springer, vol. 267(1), pages 203-219, August.
    17. Edwin J. Elton & Martin J. Gruber & Jonathan Spitzer, 2006. "Improved Estimates of Correlation Coefficients and their Impact on Optimum Portfolios," European Financial Management, European Financial Management Association, vol. 12(3), pages 303-318, June.
    18. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    19. Brechmann, Eike Christian & Schepsmeier, Ulf, 2013. "Modeling Dependence with C- and D-Vine Copulas: The R Package CDVine," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i03).
    20. 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.
    21. Ledoit, Olivier & Wolf, Michael, 2021. "Shrinkage estimation of large covariance matrices: Keep it simple, statistician?," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    22. Guerard, John B. & Markowitz, Harry & Xu, GanLin, 2015. "Earnings forecasting in a global stock selection model and efficient portfolio construction and management," International Journal of Forecasting, Elsevier, vol. 31(2), pages 550-560.
    23. Honaker, James & King, Gary & Blackwell, Matthew, 2011. "Amelia II: A Program for Missing Data," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 45(i07).
    24. Harry M. Markowitz & Erik L. van Dijk, 2003. "Single-Period Mean–Variance Analysis in a Changing World (corrected)," Financial Analysts Journal, Taylor & Francis Journals, vol. 59(2), pages 30-44, March.
    25. Markowitz, Harry, 2014. "Mean–variance approximations to expected utility," European Journal of Operational Research, Elsevier, vol. 234(2), pages 346-355.
    26. De Nard, Gianluca & Engle, Robert F. & Ledoit, Olivier & Wolf, Michael, 2022. "Large dynamic covariance matrices: Enhancements based on intraday data," Journal of Banking & Finance, Elsevier, vol. 138(C).
    27. 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.
    28. Ledoit, Olivier & Wolf, Michael, 2003. "Improved estimation of the covariance matrix of stock returns with an application to portfolio selection," Journal of Empirical Finance, Elsevier, vol. 10(5), pages 603-621, December.
    29. Harry M. Markowitz, 2011. "Investment for the Long Run: New Evidence for an Old Rule," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 35, pages 495-508, World Scientific Publishing Co. Pte. Ltd..
    30. Harry M. Markowitz, 1999. "The Early History of Portfolio Theory: 1600–1960," Financial Analysts Journal, Taylor & Francis Journals, vol. 55(4), pages 5-16, July.
    31. Gianluca De Nard & Olivier Ledoit & Michael Wolf, 2021. "Factor Models for Portfolio Selection in Large Dimensions: The Good, the Better and the Ugly [Using Principal Component Analysis to Estimate a High Dimensional Factor Model with High-frequency Data," Journal of Financial Econometrics, Oxford University Press, vol. 19(2), pages 236-257.
    32. Harry M. Markowitz, 2009. "Proposals Concerning the Current Financial Crisis," Financial Analysts Journal, Taylor & Francis Journals, vol. 65(1), pages 25-27, January.
    33. Lewandowski, Daniel & Kurowicka, Dorota & Joe, Harry, 2009. "Generating random correlation matrices based on vines and extended onion method," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 1989-2001, October.
    34. William F. Sharpe, 1963. "A Simplified Model for Portfolio Analysis," Management Science, INFORMS, vol. 9(2), pages 277-293, January.
    35. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
    36. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    37. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    38. Bruce I. Jacobs & Kenneth N. Levy & Harry M. Markowitz, 2005. "Portfolio Optimization with Factors, Scenarios, and Realistic Short Positions," Operations Research, INFORMS, vol. 53(4), pages 586-599, August.
    39. Christian Hafner & Philip Hans Franses, 2009. "A Generalized Dynamic Conditional Correlation Model: Simulation and Application to Many Assets," Econometric Reviews, Taylor & Francis Journals, vol. 28(6), pages 612-631.
    40. Dißmann, J. & Brechmann, E.C. & Czado, C. & Kurowicka, D., 2013. "Selecting and estimating regular vine copulae and application to financial returns," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 52-69.
    41. Bruce I. Jacobs & Kenneth N. Levy & Harry M. Markowitz, 2006. "Trimability and Fast Optimization of Long–Short Portfolios," Financial Analysts Journal, Taylor & Francis Journals, vol. 62(2), pages 36-46, March.
    42. Panos Xidonas & Ralph Steuer & Christis Hassapis, 2020. "Robust portfolio optimization: a categorized bibliographic review," Annals of Operations Research, Springer, vol. 292(1), pages 533-552, September.
    43. Brechmann, Eike C. & Joe, Harry, 2015. "Truncation of vine copulas using fit indices," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 19-33.
    44. Lam, Clifford, 2020. "High-dimensional covariance matrix estimation," LSE Research Online Documents on Economics 101667, London School of Economics and Political Science, LSE Library.
    45. 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.
    46. 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.
    47. Harry M. Markowitz, 2002. "Efficient Portfolios, Sparse Matrices, and Entities: A Retrospective," Operations Research, INFORMS, vol. 50(1), pages 154-160, February.
    48. Harry Markowitz, 1956. "The optimization of a quadratic function subject to linear constraints," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 3(1‐2), pages 111-133, March.
    49. Harry M. Markowitz, 2005. "Market Efficiency: A Theoretical Distinction and So What?," Financial Analysts Journal, Taylor & Francis Journals, vol. 61(5), pages 17-30, September.
    50. Fermanian, Jean-David & Malongo, Hassan, 2017. "On The Stationarity Of Dynamic Conditional Correlation Models," Econometric Theory, Cambridge University Press, vol. 33(3), pages 636-663, June.
    51. Harry Markowitz & Joseph Blasi & Douglas Kruse, 2010. "Employee stock ownership and diversification," Annals of Operations Research, Springer, vol. 176(1), pages 95-107, April.
    52. Bruce I. Jacobs & Kenneth N. Levy & Harry M. Markowitz, 2010. "Simulating Security Markets in Dynamic and Equilibrium Modes," Financial Analysts Journal, Taylor & Francis Journals, vol. 66(5), pages 42-53, September.
    53. Hanqing Jin & Harry Markowitz & Xun Yu Zhou, 2006. "A Note On Semivariance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 53-61, January.
    54. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    55. Chan, Louis K C & Karceski, Jason & Lakonishok, Josef, 1999. "On Portfolio Optimization: Forecasting Covariances and Choosing the Risk Model," The Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 937-974.
    56. Kroll, Yoram & Levy, Haim & Markowitz, Harry M, 1984. "Mean-Variance versus Direct Utility Maximization," Journal of Finance, American Finance Association, vol. 39(1), pages 47-61, March.
    57. Levy, H & Markowtiz, H M, 1979. "Approximating Expected Utility by a Function of Mean and Variance," American Economic Review, American Economic Association, vol. 69(3), pages 308-317, June.
    58. Christian Bongiorno & Damien Challet & Grégoire Loeper, 2023. "Filtering time-dependent covariance matrices using time-independent eigenvalues," Post-Print hal-03481441, HAL.
    59. Poignard, Benjamin & Fermanian, Jean-David, 2019. "Dynamic Asset Correlations Based On Vines," Econometric Theory, Cambridge University Press, vol. 35(1), pages 167-197, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Caporin, Massimiliano & McAleer, Michael, 2014. "Robust ranking of multivariate GARCH models by problem dimension," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 172-185.
    2. Ahmed, Shamim & Bu, Ziwen & Symeonidis, Lazaros & Tsvetanov, Daniel, 2023. "Which factor model? A systematic return covariation perspective," Journal of International Money and Finance, Elsevier, vol. 136(C).
    3. John Guerard, 2025. "Investments: the (almost) century of Markowitz Harry Markowitz: portfolio selection scholar, simulation creator, and applied investment researcher and consultant extraordinaire," Annals of Operations Research, Springer, vol. 346(1), pages 1-8, March.
    4. De Nard, Gianluca & Zhao, Zhao, 2023. "Using, taming or avoiding the factor zoo? A double-shrinkage estimator for covariance matrices," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 23-35.
    5. Massimiliano Caporin & Michael McAleer, 2011. "Ranking Multivariate GARCH Models by Problem Dimension: An Empirical Evaluation," Working Papers in Economics 11/23, University of Canterbury, Department of Economics and Finance.
    6. Mörstedt, Torsten & Lutz, Bernhard & Neumann, Dirk, 2024. "Cross validation based transfer learning for cross-sectional non-linear shrinkage: A data-driven approach in portfolio optimization," European Journal of Operational Research, Elsevier, vol. 318(2), pages 670-685.
    7. Sébastien Lleo & Leonard C. MacLean, 2025. "Dual dominance: how Harry Markowitz and William Ziemba impacted portfolio management," Annals of Operations Research, Springer, vol. 346(1), pages 181-216, March.
    8. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," CARF F-Series CARF-F-219, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    9. Hafner, Christian M. & Wang, Linqi, 2024. "Dynamic portfolio selection with sector-specific regularization," Econometrics and Statistics, Elsevier, vol. 32(C), pages 17-33.
    10. Morana, Claudio, 2019. "Regularized semiparametric estimation of high dimensional dynamic conditional covariance matrices," Econometrics and Statistics, Elsevier, vol. 12(C), pages 42-65.
    11. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    12. Hafner, Christian M. & Reznikova, Olga, 2012. "On the estimation of dynamic conditional correlation models," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3533-3545.
    13. Emilija Dzuverovic & Matteo Barigozzi, 2023. "Hierarchical DCC-HEAVY Model for High-Dimensional Covariance Matrices," Papers 2305.08488, arXiv.org, revised Jul 2024.
    14. Bruce I. Jacobs & Kenneth N. Levy, 2025. "Portfolio insurance, portfolio theory, market simulation, and risks of portfolio leverage," Annals of Operations Research, Springer, vol. 346(1), pages 67-97, March.
    15. Luc Bauwens & Edoardo Otranto, 2023. "Modeling Realized Covariance Matrices: A Class of Hadamard Exponential Models," Journal of Financial Econometrics, Oxford University Press, vol. 21(4), pages 1376-1401.
    16. 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.
    17. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2018. "Modeling and forecasting (un)reliable realized covariances for more reliable financial decisions," Journal of Econometrics, Elsevier, vol. 207(1), pages 71-91.
    18. Benjamin Poignard & Manabu Asai, 2023. "High‐dimensional sparse multivariate stochastic volatility models," Journal of Time Series Analysis, Wiley Blackwell, vol. 44(1), pages 4-22, January.
    19. Thomas Conlon & John Cotter & Iason Kynigakis, 2021. "Machine Learning and Factor-Based Portfolio Optimization," Papers 2107.13866, arXiv.org.
    20. De Nard, Gianluca & Engle, Robert F. & Ledoit, Olivier & Wolf, Michael, 2022. "Large dynamic covariance matrices: Enhancements based on intraday data," Journal of Banking & Finance, Elsevier, vol. 138(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:annopr:v:346:y:2025:i:1:d:10.1007_s10479-024-06238-4. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.