Realized Semicovariances

50 Pages Posted: 8 Sep 2017 Last revised: 31 Jan 2020

See all articles by Tim Bollerslev

Tim Bollerslev

Duke University - Finance; Duke University - Department of Economics; National Bureau of Economic Research (NBER)

Jia Li

Duke University

Andrew J. Patton

Duke University - Department of Economics

Rogier Quaedvlieg

Erasmus University Rotterdam (EUR) - Department of Business Economics

Date Written: January 23, 2020

Abstract

We propose a new decomposition of the realized covariance matrix into components based on the signs of the underlying high-frequency returns. Under an asymptotic setting in which the sampling interval goes to zero, we derive the asymptotic properties of the resulting realized semicovariance measures. The first-order asymptotic results highlight how the concordant components and the mixed-sign component load differently on economic information concerning stochastic correlation and jumps. The second-order asymptotics, taking the form of a novel non-central limit theorem, further reveals the fine structure underlying the concordant semicovariances, as manifest in the form of co-drifting and dynamic ``leverage'' type effects. In line with this anatomy, we empirically document distinct dynamic dependencies in the different realized semicovariance components based on data for a large cross-section of individual stocks. We further show that the accuracy of portfolio return variance forecasts may be significantly improved by using the realized semicovariance matrices to ``look inside'' the realized covariance matrices for signs of direction.

Keywords: High-frequency data; realized variances; semicovariances; co-jumps; volatility forecasting

JEL Classification: C22; C51; C53; C58

Suggested Citation

Bollerslev, Tim and Li, Jia and Patton, Andrew J. and Quaedvlieg, Rogier, Realized Semicovariances (January 23, 2020). Economic Research Initiatives at Duke (ERID) Working Paper No. 252. Available at SSRN: https://ssrn.com/abstract=3033993 or http://dx.doi.org/10.2139/ssrn.3033993

Tim Bollerslev (Contact Author)

Duke University - Finance ( email )

Durham, NC 27708-0120
United States
919-660-1846 (Phone)
919-684-8974 (Fax)

Duke University - Department of Economics

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Box 90097
Durham, NC 27708-0204
United States

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
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Jia Li

Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

Andrew J. Patton

Duke University - Department of Economics ( email )

213 Social Sciences Building
Box 90097
Durham, NC 27708-0204
United States

HOME PAGE: http://econ.duke.edu/~ap172/

Rogier Quaedvlieg

Erasmus University Rotterdam (EUR) - Department of Business Economics ( email )

Netherlands

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