Dobrislav Dobrev

The Information Content of High-Frequency Data for Estimating Equity Return Models and Forecasting Risk

We demonstrate that the parameters controlling skewness and kurtosis in popular equity return models estimated at daily frequency can be obtained almost as precisely as if volatility is observable by simply incorporating the strong information content of realized volatility measures extracted from high-frequency data. For this purpose, we introduce asymptotically exact volatility measurement equations in state space form and propose a Bayesian estimation approach. Our highly efficient estimates lead in turn to substantial gains for forecasting various risk measures at horizons ranging from a few days to a few months ahead when taking also into account parameter uncertainty. As a practical rule of thumb, we find that two years of high frequency data often suffice to obtain the same level of precision as twenty years of daily data, thereby making our approach particularly useful in finance applications where only short data samples are available or economically meaningful to use. Moreover, we find that compared to model inference without high-frequency data, our approach largely eliminates underestimation of risk during bad times or overestimation of risk during good times. We assess the attainable improvements in VaR forecast accuracy on simulated data and provide an empirical illustration on stock returns during the financial crisis of 2007-2008.

A Robust Neighborhood Truncation Approach to Estimation of Integrated Quarticity

We provide a first in-depth look at robust estimation of integrated quarticity (IQ) based on high frequency data. IQ is the key ingredient enabling inference about volatility and the presence of jumps in financial time series and is thus of considerable interest in applications. We document the significant empirical challenges for IQ estimation posed by commonly encountered data imperfections and set forth three complementary approaches for improving IQ based inference. First, we show that many common deviations from the jump diffusive null can be dealt with by a novel filtering scheme that generalizes truncation of individual returns to truncation of arbitrary functionals on return blocks. Second, we propose a new family of efficient robust neighborhood truncation (RNT) estimators for integrated power variation based on order statistics of a set of unbiased local power variation estimators on a block of returns. Third, we find that ratio-based inference, originally proposed in this context by Barndorff-Nielsen and Shephard (2002), has desirable robustness properties in the face of regularly occurring data imperfections and thus is well suited for empirical applications. We confirm that the proposed filtering scheme and the RNT estimators perform well in our extensive simulation designs and in an application to the individual Dow Jones 30 stocks.

Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors

We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in and are present also in at least thirty other papers referencing it, including the recent survey on estimation methods for expected shortfall. In particular, we show that the correction we provide in the popular multivariate Student t setting eliminates understatement of expected shortfall by a factor varying from at least 4 to more than 100 across different tail quantiles and degrees of freedom. As such, the resulting economic impact in financial risk management applications could be significant. We further correct such errors encountered also in closely related results in for mixtures of elliptical distributions. More generally, our findings point to the extra scrutiny required when deploying new methods for expected shortfall estimation in practice.