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Risks of large portfolios

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  • Fan, Jianqing
  • Liao, Yuan
  • Shi, Xiaofeng

Abstract

The risk of a large portfolio is often estimated by substituting a good estimator of the volatility matrix. However, the accuracy of such a risk estimator is largely unknown. We study factor-based risk estimators under a large amount of assets, and introduce a high-confidence level upper bound (H-CLUB) to assess the estimation. The H-CLUB is constructed using the confidence interval of risk estimators with either known or unknown factors. We derive the limiting distribution of the estimated risks in high dimensionality. We find that when the dimension is large, the factor-based risk estimators have the same asymptotic variance no matter whether the factors are known or not, which is slightly smaller than that of the sample covariance-based estimator. Numerically, H-CLUB outperforms the traditional crude bounds, and provides an insightful risk assessment. In addition, our simulated results quantify the relative error in the risk estimation, which is usually negligible using 3-month daily data.

Suggested Citation

  • Fan, Jianqing & Liao, Yuan & Shi, Xiaofeng, 2015. "Risks of large portfolios," Journal of Econometrics, Elsevier, vol. 186(2), pages 367-387.
    • Handle: RePEc:eee:econom:v:186:y:2015:i:2:p:367-387
    DOI: 10.1016/j.jeconom.2015.02.015
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    Cited by:

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    5. Noureddine Kouaissah & Sergio Ortobelli Lozza & Ikram Jebabli, 2022. "Portfolio Selection Using Multivariate Semiparametric Estimators and a Copula PCA-Based Approach," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 833-859, October.
    6. Fan, Jianqing & Wang, Weichen & Zhong, Yiqiao, 2019. "Robust covariance estimation for approximate factor models," Journal of Econometrics, Elsevier, vol. 208(1), pages 5-22.
    7. Christian M. Hafner & Oliver Linton & Haihan Tang, 2016. "Estimation of a multiplicative covariance structure in the large dimensional case," CeMMAP working papers 52/16, Institute for Fiscal Studies.
    8. Matteo Barigozzi & Marc Hallin, 2016. "Generalized dynamic factor models and volatilities: recovering the market volatility shocks," Econometrics Journal, Royal Economic Society, vol. 19(1), pages 33-60, February.
    9. Yu, Long & He, Yong & Kong, Xinbing & Zhang, Xinsheng, 2022. "Projected estimation for large-dimensional matrix factor models," Journal of Econometrics, Elsevier, vol. 229(1), pages 201-217.
    10. HAFNER, Christian & LINTON, Oliver B. & TANG, Haihan, 2016. "Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case," LIDAM Discussion Papers CORE 2016044, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    11. Christis Katsouris, 2023. "Statistical Estimation for Covariance Structures with Tail Estimates using Nodewise Quantile Predictive Regression Models," Papers 2305.11282, arXiv.org, revised Jul 2023.
    12. Barigozzi, Matteo & Hallin, Marc, 2020. "Generalized dynamic factor models and volatilities: Consistency, rates, and prediction intervals," Journal of Econometrics, Elsevier, vol. 216(1), pages 4-34.
    13. Kouaissah, Noureddine, 2021. "Using multivariate stochastic dominance to enhance portfolio selection and warn of financial crises," The Quarterly Review of Economics and Finance, Elsevier, vol. 80(C), pages 480-493.
    14. Ding, Yi & Li, Yingying & Zheng, Xinghua, 2021. "High dimensional minimum variance portfolio estimation under statistical factor models," Journal of Econometrics, Elsevier, vol. 222(1), pages 502-515.
    15. Yu-Min Yen, 2016. "Sparse Weighted-Norm Minimum Variance Portfolios," Review of Finance, European Finance Association, vol. 20(3), pages 1259-1287.
    16. Ma, Shujie & Su, Liangjun, 2018. "Estimation of large dimensional factor models with an unknown number of breaks," Journal of Econometrics, Elsevier, vol. 207(1), pages 1-29.
    17. Christis Katsouris, 2021. "Optimal Portfolio Choice and Stock Centrality for Tail Risk Events," Papers 2112.12031, arXiv.org.
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    More about this item

    Keywords

    High dimensionality; Factor models; Principal components; Sparse matrix; Volatility;
    All these keywords.

    JEL classification:

    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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