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Vast Volatility Matrix Estimation Using High-Frequency Data for Portfolio Selection

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  • Jianqing Fan
  • Yingying Li
  • Ke Yu

Abstract

Portfolio allocation with gross-exposure constraint is an effective method to increase the efficiency and stability of portfolios selection among a vast pool of assets, as demonstrated by Fan, Zhang, and Yu. The required high-dimensional volatility matrix can be estimated by using high-frequency financial data. This enables us to better adapt to the local volatilities and local correlations among a vast number of assets and to increase significantly the sample size for estimating the volatility matrix. This article studies the volatility matrix estimation using high-dimensional, high-frequency data from the perspective of portfolio selection. Specifically, we propose the use of “pairwise-refresh time” and “all-refresh time” methods based on the concept of “refresh time” proposed by Barndorff-Nielsen, Hansen, Lunde, and Shephard for the estimation of vast covariance matrix and compare their merits in the portfolio selection. We establish the concentration inequalities of the estimates, which guarantee desirable properties of the estimated volatility matrix in vast asset allocation with gross-exposure constraints. Extensive numerical studies are made via carefully designed simulations. Comparing with the methods based on low-frequency daily data, our methods can capture the most recent trend of the time varying volatility and correlation, hence provide more accurate guidance for the portfolio allocation in the next time period. The advantage of using high-frequency data is significant in our simulation and empirical studies, which consist of 50 simulated assets and 30 constituent stocks of Dow Jones Industrial Average index.

Suggested Citation

  • Jianqing Fan & Yingying Li & Ke Yu, 2012. "Vast Volatility Matrix Estimation Using High-Frequency Data for Portfolio Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(497), pages 412-428, March.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:497:p:412-428
    DOI: 10.1080/01621459.2012.656041
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    References listed on IDEAS

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    Cited by:

    1. Fengler, Matthias R. & Gisler, Katja I.M., 2015. "A variance spillover analysis without covariances: What do we miss?," Journal of International Money and Finance, Elsevier, vol. 51(C), pages 174-195.
    2. Veredas, David & Vander Elst, Harry, 2014. "Disentangled jump-robust realized covariances and correlations with non-synchronous prices," DES - Working Papers. Statistics and Econometrics. WS ws142416, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Laurent Callot & Anders B. Kock & Marcelo C. Medeiros, 2014. "Estimation and Forecasting of Large Realized Covariance Matrices and Portfolio Choice," Tinbergen Institute Discussion Papers 14-147/III, Tinbergen Institute.
    4. Trucíos Maza, Carlos César & Hotta, Luiz Koodi & Pereira, Pedro L. Valls, 2018. "On the robustness of the principal volatility components," Textos para discussão 474, FGV/EESP - Escola de Economia de São Paulo, Getulio Vargas Foundation (Brazil).
    5. Michael Ho & Jack Xin, 2016. "Sparse Kalman Filtering Approaches to Covariance Estimation from High Frequency Data in the Presence of Jumps," Papers 1602.02185, arXiv.org, revised Apr 2016.
    6. Kim, Donggyu & Wang, Yazhen & Zou, Jian, 2016. "Asymptotic theory for large volatility matrix estimation based on high-frequency financial data," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3527-3577.
    7. Hautsch, Nikolaus & Voigt, Stefan, 2017. "Large-Scale Portfolio Allocation Under Transaction Costs and Model Uncertainty: Adaptive Mixing of High- and Low-Frequency Information," Annual Conference 2017 (Vienna): Alternative Structures for Money and Banking 168222, Verein für Socialpolitik / German Economic Association.
    8. Aït-Sahalia, Yacine & Fan, Jianqing & Li, Yingying, 2013. "The leverage effect puzzle: Disentangling sources of bias at high frequency," Journal of Financial Economics, Elsevier, vol. 109(1), pages 224-249.
    9. Boudt, Kris & Laurent, Sébastien & Lunde, Asger & Quaedvlieg, Rogier & Sauri, Orimar, 2017. "Positive semidefinite integrated covariance estimation, factorizations and asynchronicity," Journal of Econometrics, Elsevier, vol. 196(2), pages 347-367.
    10. Tim Bollerslev & Andrew J. Patton & Rogier Quaedvlieg, 2016. "Modeling and Forecasting (Un)Reliable Realized Covariances for More Reliable Financial Decisions," CREATES Research Papers 2016-10, Department of Economics and Business Economics, Aarhus University.
    11. BAUWENS, Luc & BRAIONE, Manuela & STORTI, Giuseppe, 2016. "Multiplicative Conditional Correlation Models for Realized Covariance Matrices," CORE Discussion Papers 2016041, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. repec:spr:portec:v:16:y:2017:i:2:d:10.1007_s10258-017-0131-3 is not listed on IDEAS
    13. repec:eee:econom:v:204:y:2018:i:2:p:301-319 is not listed on IDEAS
    14. Oh, Dong Hwan & Patton, Andrew J., 2015. "Modelling Dependence in High Dimensions with Factor Copulas," Finance and Economics Discussion Series 2015-51, Board of Governors of the Federal Reserve System (U.S.).
    15. Xinghua Zheng & Yingying Li, 2010. "On the estimation of integrated covariance matrices of high dimensional diffusion processes," Papers 1005.1862, arXiv.org, revised Mar 2012.
    16. R. P. Brito & H. Sebastião & P. Godinho, 2017. "Portfolio choice with high frequency data: CRRA preferences and the liquidity effect," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 16(2), pages 65-86, August.
    17. repec:oup:biomet:v:104:y:2017:i:2:p:397-410. is not listed on IDEAS
    18. Sun, Edward W. & Chen, Yi-Ting & Yu, Min-Teh, 2015. "Generalized optimal wavelet decomposing algorithm for big financial data," International Journal of Production Economics, Elsevier, vol. 165(C), pages 194-214.
    19. Alberto Ohashi & Alexandre B Simas, 2015. "Principal Components Analysis for Semimartingales and Stochastic PDE," Papers 1503.05909, arXiv.org, revised Mar 2016.
    20. repec:cte:wsrepe:es142416 is not listed on IDEAS
    21. repec:oup:biomet:v:104:y:2017:i:2:p:481-488. is not listed on IDEAS

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