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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 selected portfolios among a vast pool of assets, as demonstrated in Fan et al (2008). 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 vast number of assets and to increase significantly the sample size for estimating the volatility matrix. This paper 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 proposed by Barndorff-Nielsen et al (2008) for estimation of vast covariance matrix and compare their merits in the portfolio selection. We also 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, 2010. "Vast Volatility Matrix Estimation using High Frequency Data for Portfolio Selection," Papers 1004.4956, arXiv.org.
  • Handle: RePEc:arx:papers:1004.4956
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    References listed on IDEAS

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    1. Nijman, T.E. & de Roon, F.A. & Werker, B.J.M., 2001. "Testing for Mean-Variance spanning with short sales constraints and transaction costs : The case of emerging markets," Other publications TiSEM f4a3551a-d7ae-4c22-8813-b, Tilburg University, School of Economics and Management.
    2. O. E. Barndorff-Nielsen & P. Reinhard Hansen & A. Lunde & N. Shephard, 2009. "Realized kernels in practice: trades and quotes," Econometrics Journal, Royal Economic Society, vol. 12(3), pages 1-32, November.
    3. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    4. Yingying Li & Per A. Mykland, 2007. "Are volatility estimators robust with respect to modeling assumptions?," Papers 0709.0440, arXiv.org.
    5. Yacine Aït-Sahalia, 2005. "How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise," The Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 351-416.
    6. Christensen, Kim & Kinnebrock, Silja & Podolskij, Mark, 2010. "Pre-averaging estimators of the ex-post covariance matrix in noisy diffusion models with non-synchronous data," Journal of Econometrics, Elsevier, vol. 159(1), pages 116-133, November.
    7. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    8. Ravi Jagannathan & Tongshu Ma, 2003. "Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps," Journal of Finance, American Finance Association, vol. 58(4), pages 1651-1683, August.
    9. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    10. Fan, Jianqing & Wang, Yazhen, 2007. "Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1349-1362, December.
    11. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    12. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    13. Fan, Jianqing & Fan, Yingying & Lv, Jinchi, 2008. "High dimensional covariance matrix estimation using a factor model," Journal of Econometrics, Elsevier, vol. 147(1), pages 186-197, November.
    14. de Roon, F.A. & Nijman, T.E. & Werker, B.J.M., 1998. "Testing for mean-variance spanning with short sales constraints and transaction costs : The case of emerging markets," Discussion Paper 1998-07, Tilburg University, Center for Economic Research.
    15. Frans A. De Roon & Theo E. Nijman & Bas J. M. Werker, 2001. "Testing for Mean‐Variance Spanning with Short Sales Constraints and Transaction Costs: The Case of Emerging Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 721-742, April.
    16. Aït-Sahalia, Yacine & Fan, Jianqing & Xiu, Dacheng, 2010. "High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 105(492), pages 1504-1517.
    17. Jianqing Fan & Jingjin Zhang & Ke Yu, 2008. "Asset Allocation and Risk Assessment with Gross Exposure Constraints for Vast Portfolios," Papers 0812.2604, arXiv.org.
    18. repec:bla:jfinan:v:58:y:2003:i:4:p:1651-1684 is not listed on IDEAS
    19. Jean Jacod & Yingying Li & Per A. Mykland & Mark Podolskij & Mathias Vetter, 2007. "Microstructure Noise in the Continuous Case: The Pre-Averaging Approach - JLMPV-9," CREATES Research Papers 2007-43, Department of Economics and Business Economics, Aarhus University.
    20. Rothman, Adam J. & Levina, Elizaveta & Zhu, Ji, 2009. "Generalized Thresholding of Large Covariance Matrices," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 177-186.
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