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Risks of large portfolios


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


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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    References listed on IDEAS

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    Cited by:

    1. Fan, Jianqing & Han, Fang & Liu, Han & Vickers, Byron, 2016. "Robust inference of risks of large portfolios," Journal of Econometrics, Elsevier, vol. 194(2), pages 298-308.
    2. 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.
    3. repec:eee:econom:v:201:y:2017:i:2:p:307-321 is not listed on IDEAS
    4. Hafner, C. M. & Linton, O., 2016. "Estimation of a Multiplicative Covariance Structure in the Large Dimensional Case," Cambridge Working Papers in Economics 1664, Faculty of Economics, University of Cambridge.
    5. Li, Kunpeng & Li, Qi & Lu, Lina, 2016. "Quasi Maximum Likelihood Analysis of High Dimensional Constrained Factor Models," MPRA Paper 75676, University Library of Munich, Germany.
    6. Barigozzi, Matteo & Hallin, Marc, 2017. "Generalized dynamic factor models and volatilities: estimation and forecasting," Journal of Econometrics, Elsevier, vol. 201(2), pages 307-321.
    7. Matteo Barigozzi & Marc Hallin & Stefano Soccorsi, 2017. "Identification of Global and National Shocks in International Financial Markets via General Dynamic Factor Models," Working Papers ECARES ECARES 2017-10, ULB -- Universite Libre de Bruxelles.

    More about this item


    High dimensionality; Factor models; Principal components; Sparse matrix; Volatility;

    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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