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High-dimensional minimum variance portfolio estimation based on high-frequency data

Author

Listed:
  • Cai, T. Tony
  • Hu, Jianchang
  • Li, Yingying
  • Zheng, Xinghua

Abstract

This paper studies the estimation of high-dimensional minimum variance portfolio (MVP) based on the high frequency returns which can exhibit heteroscedasticity and possibly be contaminated by microstructure noise. Under certain sparsity assumptions on the precision matrix, we propose estimators of the MVP and prove that our portfolios asymptotically achieve the minimum variance in a sharp sense. In addition, we introduce consistent estimators of the minimum variance, which provide reference targets. Simulation and empirical studies demonstrate the favorable performance of the proposed portfolios.

Suggested Citation

  • Cai, T. Tony & Hu, Jianchang & Li, Yingying & Zheng, Xinghua, 2020. "High-dimensional minimum variance portfolio estimation based on high-frequency data," Journal of Econometrics, Elsevier, vol. 214(2), pages 482-494.
    • Handle: RePEc:eee:econom:v:214:y:2020:i:2:p:482-494
    DOI: 10.1016/j.jeconom.2019.04.039
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    2. Bodnar, Taras & Parolya, Nestor & Thorsén, Erik, 2023. "Is the empirical out-of-sample variance an informative risk measure for the high-dimensional portfolios?," Finance Research Letters, Elsevier, vol. 54(C).
    3. Taras Bodnar & Nestor Parolya & Erik Thorsen, 2021. "Dynamic Shrinkage Estimation of the High-Dimensional Minimum-Variance Portfolio," Papers 2106.02131, arXiv.org, revised Nov 2021.
    4. Ruijun Bu & Degui Li & Oliver Linton & Hanchao Wang, 2022. "Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data," Working Papers 202212, University of Liverpool, Department of Economics.
    5. Bu, R. & Li, D. & Linton, O. & Wang, H., 2022. "Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data," Cambridge Working Papers in Economics 2218, Faculty of Economics, University of Cambridge.
    6. Sumanjay Dutta & Shashi Jain, 2023. "Precision versus Shrinkage: A Comparative Analysis of Covariance Estimation Methods for Portfolio Allocation," Papers 2305.11298, arXiv.org.
    7. Bian, Zhicun & Liao, Yin & O’Neill, Michael & Shi, Jing & Zhang, Xueyong, 2020. "Large-scale minimum variance portfolio allocation using double regularization," Journal of Economic Dynamics and Control, Elsevier, vol. 116(C).
    8. Zhonghui Zhang & Huarui Jing & Chihwa Kao, 2023. "High-Dimensional Distributionally Robust Mean-Variance Efficient Portfolio Selection," Mathematics, MDPI, vol. 11(5), pages 1-16, March.
    9. 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.
    10. Kim Christensen & Mikkel Slot Nielsen & Mark Podolskij, 2021. "High-dimensional estimation of quadratic variation based on penalized realized variance," Papers 2103.03237, arXiv.org.
    11. Jalshayin Bhachech & Arnab Chakrabarti & Taisei Kaizoji & Anindya S. Chakrabarti, 2022. "Instability of networks: effects of sampling frequency and extreme fluctuations in financial data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(4), pages 1-14, April.
    12. Christis Katsouris, 2021. "Optimal Portfolio Choice and Stock Centrality for Tail Risk Events," Papers 2112.12031, arXiv.org.
    13. Taras Bodnar & Mathias Lindholm & Vilhelm Niklasson & Erik Thors'en, 2020. "Bayesian Quantile-Based Portfolio Selection," Papers 2012.01819, arXiv.org.
    14. Maaz Mahadi & Tarig Ballal & Muhammad Moinuddin & Tareq Y. Al-Naffouri & Ubaid Al-Saggaf, 2022. "Portfolio Optimization Using a Consistent Vector-Based MSE Estimation Approach," Papers 2204.05611, arXiv.org.
    15. Chen, Xin & Yang, Dan & Xu, Yan & Xia, Yin & Wang, Dong & Shen, Haipeng, 2023. "Testing and support recovery of correlation structures for matrix-valued observations with an application to stock market data," Journal of Econometrics, Elsevier, vol. 232(2), pages 544-564.
    16. Kim Christensen & Mikkel Slot Nielsen & Mark Podolskij, 2023. "High-dimensional estimation of quadratic variation based on penalized realized variance," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 331-359, July.
    17. Alfelt, Gustav & Bodnar, Taras & Javed, Farrukh & Tyrcha, Joanna, 2020. "Singular conditional autoregressive Wishart model for realized covariance matrices," Working Papers 2021:1, Örebro University, School of Business.
    18. Bodnar, Olha & Bodnar, Taras & Parolya, Nestor, 2022. "Recent advances in shrinkage-based high-dimensional inference," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    19. Donggyu Kim & Minseog Oh, 2023. "Dynamic Realized Minimum Variance Portfolio Models," Papers 2310.13511, arXiv.org.

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    More about this item

    Keywords

    Minimum variance portfolio; High dimension; High frequency; CLIME estimator; Precision matrix;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C55 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Large Data Sets: Modeling and Analysis
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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