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

Abstract

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