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The increasing availability of high-frequency asset return data has had a fundamental impact on empirical financial economics, focusing attention on asset return volatility and correlation dynamics, with key applications in portfolio and risk management. So-called "realized" volatilities and correlations have featured prominently in the recent literature, and numerous studies have provided direct characterizations of the unconditional and conditional distributions of realized volatilities and correlations across different assets, asset classes, countries, and sample periods. For overviews see Andersen et al. (2005a, b).
In this paper we selectively survey, unify and extend that literature. Rather than focusing exclusively on characterization of the properties of realized volatility, we progress by examining economically interesting functions of realized volatility, namely, realized betas for equity portfolios, relating them both to their underlying realized variance and covariance parts and to underlying macroeconomic fundamentals.
Meanwhile, key empirical findings for realized volatility include lognormality and long memory of volatilities and correlations (Andersen et al., 2001a, b), as well as normality of returns standardized by realized volatility (Andersen et al., 2000). Those properties, as distilled in the lognormal/normal mixture model of Andersen et al. (2003), have important implications for risk management and asset allocation.
II. Realized Beta and Its Components
Although characterizations of the properties of realized variances and covariances are of interest, alternative objects are often of greater economic significance with a leading example being the market beta of a portfolio. If either the market volatility or its covariance with portfolio returns is time-varying, then the portfolio beta will generally be time-varying. Hence it is clearly of interest to explore the links between time-varying volatilities, time-varying correlations, and time-varying betas. One may construct realized betas from underlying realized covariance and variance components, or conversely, decompose realized betas into realized variance and covariance components.
By comparing the properties of directly measured betas to those of directly measured variances and covariances, we can decompose movements in betas in informative ways. In particular, because the long memory in underlying variances and covariances may be common, it is possible that betas may be only weakly persistent (short-memory, I(d), with d [asymptotically =] 0), despite the widespread finding that realized variances and covariances are long-memory (fractionally integrated, I(d), with d [asymptotically =] 0.4). Recent work (Andersen et al., 2005d)...