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ETF Basket-Adjusted Covariance estimation

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  • Boudt, Kris
  • Dragun, Kirill
  • Sauri, Orimar
  • Vanduffel, Steven

Abstract

The increase in trading frequency of Exchanged Traded Funds (ETFs) presents a positive externality for financial risk management when the price of the ETF is available at a higher frequency than the price of the component stocks. The positive spillover consists in improving the accuracy of pre-estimators of the integrated covariance of the stocks included in the ETF basket. The proposed ETF Basket-Adjusted Covariance (BAC) equals the pre-estimator plus a minimal adjustment matrix such that the covariance-implied stock-ETF covariation equals a target value. We focus on a truncated pre-averaged version of the (Hayashi and Yoshida, 2005) pre-estimator and derive the asymptotic properties of its implied stock-ETF covariation. The simulation study confirms that the accuracy gains are substantial in all cases considered. In the empirical part of the paper, we show the gains in tracking error efficiency when using the BAC adjustment to construct portfolios that replicate a broad index using a subset of stocks.

Suggested Citation

  • Boudt, Kris & Dragun, Kirill & Sauri, Orimar & Vanduffel, Steven, 2023. "ETF Basket-Adjusted Covariance estimation," Journal of Econometrics, Elsevier, vol. 235(2), pages 1144-1171.
    • Handle: RePEc:eee:econom:v:235:y:2023:i:2:p:1144-1171
    DOI: 10.1016/j.jeconom.2022.10.002
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    as
    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. 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.
    3. Tim Bollerslev & Jia Li & Andrew J. Patton & Rogier Quaedvlieg, 2020. "Realized Semicovariances," Econometrica, Econometric Society, vol. 88(4), pages 1515-1551, July.
    4. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    5. Mancini, Cecilia & Gobbi, Fabio, 2012. "Identifying The Brownian Covariation From The Co-Jumps Given Discrete Observations," Econometric Theory, Cambridge University Press, vol. 28(2), pages 249-273, April.
    6. 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.
    7. Jacod, Jean & Li, Yingying & Mykland, Per A. & Podolskij, Mark & Vetter, Mathias, 2009. "Microstructure noise in the continuous case: The pre-averaging approach," Stochastic Processes and their Applications, Elsevier, vol. 119(7), pages 2249-2276, July.
    8. Potiron, Yoann & Mykland, Per A., 2017. "Estimation of integrated quadratic covariation with endogenous sampling times," Journal of Econometrics, Elsevier, vol. 197(1), pages 20-41.
    9. Andersen, Torben G. & Dobrev, Dobrislav & Schaumburg, Ernst, 2012. "Jump-robust volatility estimation using nearest neighbor truncation," Journal of Econometrics, Elsevier, vol. 169(1), pages 75-93.
    10. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    11. Xin Huang & George Tauchen, 2005. "The Relative Contribution of Jumps to Total Price Variance," Journal of Financial Econometrics, Oxford University Press, vol. 3(4), pages 456-499.
    12. Zhang, Lan, 2011. "Estimating covariation: Epps effect, microstructure noise," Journal of Econometrics, Elsevier, vol. 160(1), pages 33-47, January.
    13. 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.
    14. repec:wyi:journl:002184 is not listed on IDEAS
    15. Christensen, Kim & Podolskij, Mark & Vetter, Mathias, 2013. "On covariation estimation for multivariate continuous Itô semimartingales with noise in non-synchronous observation schemes," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 59-84.
    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. Bj�rn Fastrich & Sandra Paterlini & Peter Winker, 2014. "Cardinality versus q -norm constraints for index tracking," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 2019-2032, November.
    18. Christophe Croux & Sébastien Laurent, 2011. "Outlyingness Weighted Covariation," Journal of Financial Econometrics, Oxford University Press, vol. 9(4), pages 657-684.
    19. Li, Jia & Todorov, Viktor & Tauchen, George, 2016. "Inference theory for volatility functional dependencies," Journal of Econometrics, Elsevier, vol. 193(1), pages 17-34.
    20. 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.
    21. Ole Martin & Mathias Vetter, 2019. "Laws of large numbers for Hayashi–Yoshida-type functionals," Finance and Stochastics, Springer, vol. 23(3), pages 451-500, July.
    22. Kris Boudt & Jin Zhang, 2015. "Jump robust two time scale covariance estimation and realized volatility budgets," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 1041-1054, June.
    23. 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.
    24. Per Mykland, 2012. "A Gaussian calculus for inference from high frequency data," Annals of Finance, Springer, vol. 8(2), pages 235-258, May.
    25. Corradi, Valentina & Silvapulle, Mervyn J. & Swanson, Norman R., 2018. "Testing for jumps and jump intensity path dependence," Journal of Econometrics, Elsevier, vol. 204(2), pages 248-267.
    26. Koike, Yuta, 2014. "Limit theorems for the pre-averaged Hayashi–Yoshida estimator with random sampling," Stochastic Processes and their Applications, Elsevier, vol. 124(8), pages 2699-2753.
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