Realized Semicovariances

Tim Bollerslev*, Jia Li, Andrew J. Patton, Rogier Quaedvlieg

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

1 Citation (Scopus)


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.

Original languageEnglish
Pages (from-to)1515-1551
Number of pages37
Publication statusPublished - Jul 2020


  • co-jumps
  • High-frequency data
  • realized variances
  • semicovariances
  • volatility forecasting


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