Realized Semi(co)variation: Signs That All Volatilities are Not Created Equal

Abstract

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.