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Sparse precision matrices for minimum variance portfolios

Author

Listed:
  • Gabriele Torri

    (University of Bergamo
    VŠB-TU Ostrava)

  • Rosella Giacometti

    (University of Bergamo)

  • Sandra Paterlini

    (University of Trento
    EBS Universität für Wirtschaft und Recht)

Abstract

Financial crises are typically characterized by highly positively correlated asset returns due to the simultaneous distress on almost all securities, high volatilities and the presence of extreme returns. In the aftermath of the 2008 crisis, investors were prompted even further to look for portfolios that minimize risk and can better deal with estimation error in the inputs of the asset allocation models. The minimum variance portfolio à la Markowitz is considered the reference model for risk minimization in equity markets, due to its simplicity in the optimization as well as its need for just one input estimate: the inverse of the covariance estimate, or the so-called precision matrix. In this paper, we propose a data-driven portfolio framework based on two regularization methods, glasso and tlasso, that provide sparse estimates of the precision matrix by penalizing its $$L_1$$ L 1 -norm. Glasso and tlasso rely on asset returns Gaussianity or t-Student assumptions, respectively. Simulation and real-world data results support the proposed methods compared to state-of-art approaches, such as random matrix and Ledoit–Wolf shrinkage.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:16:y:2019:i:3:d:10.1007_s10287-019-00344-6
    DOI: 10.1007/s10287-019-00344-6
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    References listed on IDEAS

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    Cited by:

    1. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2019. "Cross-validated covariance estimators for high-dimensional minimum-variance portfolios," Papers 1910.13960, arXiv.org, revised Oct 2020.
    2. Sumanjay Dutta & Shashi Jain, 2023. "Precision versus Shrinkage: A Comparative Analysis of Covariance Estimation Methods for Portfolio Allocation," Papers 2305.11298, arXiv.org.
    3. Paola Stolfi & Mauro Bernardi & Davide Vergni, 2022. "Robust estimation of time-dependent precision matrix with application to the cryptocurrency market," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 8(1), pages 1-25, December.
    4. Francesca Mariani & Gloria Polinesi & Maria Cristina Recchioni, 2022. "A tail-revisited Markowitz mean-variance approach and a portfolio network centrality," Computational Management Science, Springer, vol. 19(3), pages 425-455, July.
    5. Sakae Oya, 2021. "A Bayesian Graphical Approach for Large-Scale Portfolio Management with Fewer Historical Data," Papers 2103.05880, arXiv.org, revised Mar 2022.
    6. Amedeo Argentiero & Giovanni Bonaccolto & Giulio Pedrini, 2024. "Green finance: Evidence from large portfolios and networks during financial crises and recessions," Corporate Social Responsibility and Environmental Management, John Wiley & Sons, vol. 31(3), pages 2474-2495, May.
    7. Sven Husmann & Antoniya Shivarova & Rick Steinert, 2021. "Cross-validated covariance estimators for high-dimensional minimum-variance portfolios," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 35(3), pages 309-352, September.
    8. 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.

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