Modeling and Forecasting (Un)Reliable Realized Covariances for More Reliable Financial Decisions

Abstract

We propose a new framework for modeling and forecasting common financial risks based on (un)reliable realized covariance measures constructed from high-frequency intraday data. Our new approach explicitly incorporates the effect of measurement errors and time-varying attenuation biases into the covariance forecasts, by allowing the ex-ante predictions to respond more (less) aggressively to changes in the ex-post realized covariance measures when they are more (less) reliable. Applying the new procedures in the construction of minimum variance and minimum tracking error portfolios results in reduced turnover and statistically superior positions compared to existing procedures. Translating these statistical improvements into economic gains, we find that under empirically realistic assumptions a risk-averse investor would be willing to pay up to 170 basis points per year to shift to using the new class of forecasting models. School and Nova SBE Lisbon for helpful comments. Bingzhi Zhao kindly provided us with the cleaned high-frequency data underlying our empirical investigations.Modeling and forecasting of dynamically varying covariances have received much attention in the literature, with numerous multivariate ARCH, GARCH and stochastic volatility specifications been proposed for the job. All of these procedures effectively treat the covariances as latent. More recently, however, the increased availability of reliable high-frequency intraday asset prices have has spurred somewhat of a paradigm shift based on the idea of directly modeling and forecasting expost realized covariance measures constructed from intraday data (see, e.g., Andersen, Bollerslev, Christoffersen, and Diebold, 2013, for a discussion of both the earlier parametric models and the more recent realized volatility literature). The benefits of high-frequency-based realized volatility procedures for practical investment and portfolio allocation decisions have also been extensively documented in the literature (e.g., Fleming, Kirby, and Ostdiek, 2003;Bandi, Russell, and Zhu, 2008;Pooter, Martens, and Dijk, 2008;Liu, 2009;Varneskov and Voev, 2013; Hautsch, Kyj, and Malec, 2015, among others).Even though the use of high-frequency intraday data generally allows for the construction of more accurate realized covariance measures than lower frequency (e.g., daily) data, they are still estimates and as such subject to estimation error. Correspondingly, the use of these covariance estimates in dynamic forecasting models leads to a classical errors-in-variables problem and an attenuation of the parameters towards zero relative to a forecasting model based on the true (latent) covariances. If the measurement errors were homoskedastic, this attenuation would be time invariant, and from a practical forecasting perspective inconsequential. If, however, the measurement errors are heteroskedastic, as we show is the case with realized covariance estimates, all observations are "not equal," and the presence of such heteroskedastic measurement errors can indeed have ...

The Realized Hierarchical Archimedean Copula in Risk Modelling

“…The formal definition of the realized measures is given in Appendix B. Despite the constantly growing research on incorporating the realized measures into multivariate Gaussian models, discussed in Chiriac and Voev (2011) and Bauer and Vorkink (2011), and into GARCH type models, for example, Hansen et al (2014) and Bollerslev et al (2016), there is still a gap in the literature on how the parameters of non-Gaussian copula can be estimated daily based on high-frequency observations. It is important to note here that such standard copula estimation techniques as the Maximum Likelihood (ML) method or the inversion of Kendall's τ can not be directly applied to tick-by-tick observations.…”

“…Many researchers have implemented the obtained realized measures to model financial time series. Most of those studies, however, employ models where the realized correlation matrix directly characterizes the multivariate distribution, see, for example, Bauer and Vorkink (2011), Chiriac and Voev (2011), Jin and Maheu (2012), or address GARCH type models, for example, Hansen et al (2014), Bauwens et al (2012), Noureldin et al (2012), Bollerslev et al (2016). There are only a limited number of studies which discuss the implementation of high-frequency data in copula models.…”