Realized Semi(Co)Variation: Signs that All Volatilities are Not Created Equal

42 Pages Posted: 23 Jun 2021 Last revised: 15 Oct 2021

See all articles by Tim Bollerslev

Tim Bollerslev

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

Date Written: June 17, 2021


I provide a selective review of recent developments in financial econometrics related to measuring, modeling, forecasting and pricing “good” and “bad” volatilities based on realized variation type measures constructed from high-frequency intraday data. An especially appealing feature of the different measures concerns the ease with which they may be calculated empirically, merely involving cross-products of signed, or thresholded, high-frequency returns. I begin by considering univariate semivariation measures, followed by multivariate semicovariation and semibeta measures, before briefly discussing even richer partial (co)variation measures. I focus my discussion on practical uses of the measures emphasizing what I consider to be the most noteworthy empirical findings to date pertaining to volatility forecasting and asset pricing

Keywords: Downside risk; high-frequency data; realized variation; semi(co)variation; semibeta; partial variation; jumps and co-jumps; volatility forecasting; return predictability; cross-sectional return variation.

JEL Classification: C22, C51, C53, C58, G11, G12

Suggested Citation

Bollerslev, Tim, Realized Semi(Co)Variation: Signs that All Volatilities are Not Created Equal (June 17, 2021). Economic Research Initiatives at Duke (ERID) Working Paper No. 306, Available at SSRN: or

Tim Bollerslev (Contact Author)

Duke University - Finance ( email )

Durham, NC 27708-0120
United States
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Duke University - Department of Economics

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

National Bureau of Economic Research (NBER)

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