sive overview of financial risk management from the point of view of both Wall Street and the Ivory Tower. Most usefully, ABCD discuss a number of recent developments in the econometrics of time varying risk that hold vast promise for risk management applications: the dynamic conditional correlation model of Engle (2002) which permits large-scale, flexi-ble modeling of conditional covariance matrices; the use of high-frequency data to measure realized variances and covariances that has been developed largely by the authors; and the modeling of the full distribution of conditional returns. In this discussion I will just offer a couple of comments and extensions to ABCD’s very well organized survey. Unconditional vs Conditional Risk ABCD discuss extensively the pros and cons of both unconditional and conditional (dynamic) measures of risk. There is however an additional source of risk dynamics that is ignored in the paper and that, in fact, has not been studied much in the literature. Most financial assets are managed over time and it is therefore more important to study the risks of dynamic investment strategies rather than the risks of static portfolios. Especially for supervision and regulation purposes, it matters more to forecast the risk of a portfolio taking into account

We propose two new jump-robust estimators of integrated variance based on high-frequency return observations. These MinRV and MedRV estimators provide an attractive alternative to the prevailing bipower and multipower variation measures. Specifically, the MedRV estimator has better theoretical efficiency properties than the tripower variation measure and displays better finite-sample robustness to both jumps and the occurrence of “zero” returns in the sample. Unlike the bipower variation measure the new estimator allows for the development of an asymptotic limit theory in the presence of jumps. Finally, it retains the local nature associated with the low order multipower variation measures. This proves essential for alleviating finite sample biases arising from the pronounced intraday volatility pattern which afflict alternative jump-robust estimators based on longer blocks of returns. An empirical investigation of the Dow Jones 30 stocks and an extensive simulation study corroborate the robustness and efficiency properties of the new estimators.

of Turkey. The views expressed herein are those of the authors and do not necessarily reflect the views

informs doi 10.1287/mnsc.1060.0520

We provide a set of probabilistic laws for estimating quadratic variation of continu-ous semimartingales with the realized range-based variance; a statistic that replaces every squared return of realized variance with a normalized squared range. If the entire sample path of the process is available- and given weak conditions- our statistic is consistent and has a mixed Gaussian limit with five times the precision of realized variance. In practice, of course, inference is drawn from discrete data and true ranges are unobserved, leading to downward bias. We solve this problem to give a consistent, mixed normal estimator, irre-spective of non-trading. It has varying degrees of efficiency over realized variance, depending on how many observations that are used to construct the high-low. The methodology is ap-plied to TAQ data and compared with realized variance. Our findings suggest the empirical path of quadratic variation is also estimated better with the intraday high-low statistic.

This study reconsiders the role of jumps for volatility forecasting by showing that jumps have a positive and mostly significant impact on future volatility. This result becomes apparent once volatility is separated into its continuous and discontinuous component using estimators which are not only consistent, but also scarcely plagued by small-sample bias. To this purpose, we introduce the concept of threshold bipower variation, which is based on the joint use of bipower variation and threshold estimation. We show that its generalization (threshold multipower variation) admits a feasible central limit theorem in the presence of jumps and provides less biased estimates, with respect to the standard multipower variation, of the continuous quadratic variation in finite samples. We further provide a new test for jump detection which has substantially more power than tests based on multipower variation. Empirical analysis (on the S&P500 index, individual stocks and US bond yields) shows that the proposed techniques improve significantly the accuracy of volatility forecasts especially in periods following the occurrence of a jump.

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Abstract: A large literature over several decades reveals both extensive concern with the question of time-varying betas and an emerging consensus that betas are in fact time-varying, leading to the prominence of the conditional CAPM. Set against that background, we assess the dynamics in realized betas, vis-à-vis the dynamics in the underlying realized market variance and individual equity covariances with the market. Working in the recently-popularized framework of realized volatility, we are led to a framework of nonlinear fractional cointegration: although realized variances and covariances are very highly persistent and well approximated as fractionally-integrated, realized betas, which are simple nonlinear functions of those realized variances and covariances, are less persistent and arguably best modeled as stationary I(0) processes. We conclude by drawing implications for asset pricing and portfolio management. Key Words: quadratic variation and covariation, realized volatility, asset pricing, CAPM, equity betas, long memory, nonlinear fractional cointegration, continuous-time methods. JEL Codes: C1, G1 * We dedicate this paper to Clive W. J. Granger, a giant of modern econometrics, on whose broad shoulders we are fortunate to stand. For useful discussion we thank participants at the UCSD Conference on Predictive Methodology and Applications in Economics and Finance (in honor of Granger), and the London School of Economics Fifth Financial Markets Group Conference on Empirical Finance. We also thank seminar participants at the University of Pennsylvania, as well as Andrew Ang, Michael Brandt, Mike Chernov, Graham Elliott, Eric Ghysels, Rich Lyons, Norman Swanson, and Mark Watson. This work was supported by the National Science Foundation and the Guggenheim Foundation. Roll (1977) critique is also relevant. That is, even if we somehow knew what factor(s) should be priced, it is not clear that the factor proxies measured in practice would correspond to the factor required by the theory. 2 See Keim and Hawawini (1999) for a good discussion of the difficulty of interpreting additional empirically-motivated factors in terms of systematic risk. 3 There are of course qualifications, notably Ghysels (1998), which we discuss subsequently.

The relation between the volatility of stocks and bonds and their price valuations is strongly time-varying, both in magnitude and direction, defying traditional asset pricing models and conventional wisdom. We construct and estimate a model in which investors ’ learning about regular and unusual fundamental states leads to a non-monotonic V −shaped relation between volatilities and prices. Structural forecasts from our model predict future return volatility and covariances with R2 ranging between 40 % and 60 % at the 1-year horizon. The model’s success stems largely from backing out the endogenous and time-varying pro (counter) cyclical weights that investors assign to earnings (inflation) news. While it is intuitive that the volatilities and comovements of stocks and bonds are strongly related to the state of economic fundamentals, it is surprising that the financial literature has been unable to empirically demonstrate such a strong link between them, as evidenced in the following quote from a recent paper by Nobel prize laureate Robert Engle.