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Realized Semicovariances

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  • Tim Bollerslev
  • Jia Li
  • Andrew J. Patton
  • Rogier Quaedvlieg

Abstract

We propose a decomposition of the realized covariance matrix into components based on the signs of the underlying high‐frequency returns, and we derive the asymptotic properties of the resulting realized semicovariance measures as the sampling interval goes to zero. The first‐order asymptotic results highlight how the same‐sign and mixed‐sign components load differently on economic information related to stochastic correlation and jumps. The second‐order asymptotic results reveal the structure underlying the same‐sign semicovariances, as manifested in the form of co‐drifting and dynamic “leverage” effects. In line with this anatomy, we use data on a large cross‐section of individual stocks to empirically document distinct dynamic dependencies in the different realized semicovariance components. We show that the accuracy of portfolio return variance forecasts may be significantly improved by exploiting the information in realized semicovariances.

Suggested Citation

  • Tim Bollerslev & Jia Li & Andrew J. Patton & Rogier Quaedvlieg, 2020. "Realized Semicovariances," Econometrica, Econometric Society, vol. 88(4), pages 1515-1551, July.
    • Handle: RePEc:wly:emetrp:v:88:y:2020:i:4:p:1515-1551
    DOI: 10.3982/ECTA17056
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    2. Bollerslev, Tim & Medeiros, Marcelo C. & Patton, Andrew J. & Quaedvlieg, Rogier, 2022. "From zero to hero: Realized partial (co)variances," Journal of Econometrics, Elsevier, vol. 231(2), pages 348-360.
    3. Li, Dan & Drovandi, Christopher & Clements, Adam, 2024. "Outlier-robust methods for forecasting realized covariance matrices," International Journal of Forecasting, Elsevier, vol. 40(1), pages 392-408.
    4. Kirill Dragun & Kris Boudt & Orimar Sauri & Steven Vanduffel, 2021. "Beta-Adjusted Covariance Estimation," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 21/1010, Ghent University, Faculty of Economics and Business Administration.
    5. Li, Yuan & Pakkanen, Mikko S. & Veraart, Almut E.D., 2023. "Limit theorems for the realised semicovariances of multivariate Brownian semistationary processes," Stochastic Processes and their Applications, Elsevier, vol. 155(C), pages 202-231.
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    18. Neil Shephard, 2020. "An estimator for predictive regression: reliable inference for financial economics," Papers 2008.06130, arXiv.org.
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