We propose a novel and easy-to-implement framework for forecasting timevarying correlations based on a large set of salient realized correlation features and the sparsity-encouraging Least Absolute Shrinkage and Selection Operator technique. Considering the universe of S&P 500 stocks, we find that the new approach manifests in statistically superior out-of-sample forecasts compared with commonly used procedures. We further demonstrate how the forecasts translate into significant economic gains in the form of higher pairs trading profits, better equity premium predictions, more accurate portfolio risk targeting, and superior overall risk control and minimization.

We contribute to the growing literature on high-frequency spot volatility estimation by deriving a new integral representation for the recently introduced asymptotic minimum risk equivariant (AMRE) candlestick-based class of estimators. Our new theoretical representation enables the practical numerical computation of the hitherto impractical to compute optimal estimators based on multiple adjacent candlesticks. We also propose a new exact sampling scheme for high-frequency candlestick data, which facilitates straightforward calculation of the asymptotic risk and confidence intervals for the estimators. The resulting critical values for the highest-density intervals highlight the substantial efficiency gains from incorporating more than one candlestick in the estimation process. We showcase the practical value of the new techniques in elucidating the behavior of financial market volatility around the time of important news announcements.

We propose new refined measures of the local covariation between the return on an asset and a risk factor. Our proposed “granular betas” generalize the notion of up- and down-side betas to multi-factor functional measures of covariation. We show how the resulting granular beta functions may be used in the estimation of new “risk premium functions.” Implementing the proposed methods with a large cross-section of U.S. equity returns, we find evidence against the traditional (non-granular) CAPM, the Fama–French three and five-factor models, and the Fama–French-Carhart model in favor of the new granular versions of these models. Our empirical results in turn provide new insights into where in the factor-space the compensation for exposures to systematic risks is mostly earned.

We provide strong empirical evidence for time-series predictability of the intraday return on the aggregate market portfolio by exploiting lagged high-frequency cross-sectional returns on the factor zoo. Our results rely on the use of modern machine-learning techniques to regularize the predictive regressions and help tame the signals stemming from the zoo together with techniques from financial econometrics to differentiate between continuous and theoretically nonpredictable discontinuous high-frequency price increments. Using the predictions from the model estimated for the aggregate market portfolio in the formulation of simple intraday trading strategies for a set of highly liquid ETFs results in sizeable out-of-sample Sharpe ratios and alphas after accounting for transaction costs. Further dissecting the abnormal intraday returns, we find that most of the superior performance may be traced to periods of high economic uncertainty and a few key factors related to tail risk and liquidity, pointing to slow-moving capital and the gradual incorporation of new information as the underlying mechanisms at work. This paper was accepted by Kay Giesecke, finance. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2023.01657 .

Betas from return regressions are commonly used to measure systematic financial market risks. "Good" beta measurements are essential for a range of empirical inquiries in finance and macroeconomics. We introduce a novel econometric framework for the nonparametric estimation of time -varying betas with high -frequency data. The "local Gaussian" property of the generic continuous -time benchmark model enables optimal " finite -sample" inference in a well-defined sense. It also affords more reliable inference in empirically realistic settings compared to conventional large -sample approaches. Two applications pertaining to the tracking performance of leveraged ETFs and an intraday event study illustrate the practical usefulness of the new procedures. (JEL C22, C58, G12, G23)

Utilizing real-time newswire data, together with a robustly estimated intraday stochastic discount factor (SDF), we identify and quantify the economic news that is priced. News related to monetary policy and finance on average accounts for most of the variation in the SDF, followed by news about international affairs and macroeconomic data. We also document nontrivial temporal variation in the relative importance of the news, along with marked differences in the estimated news risk premiums in the "factor zoo." To further highlight the economic mechanisms at work, we associate the different news effects with interest rate, growth, and risk premium shocks.

We present a general framework for optimal nonparametric spot volatility estimation based on intraday range data, comprised of the first, highest, lowest, and last price over a given time-interval. We rely on a decision-theoretic approach together with a coupling-type argument to directly tailor the form of the nonparametric estimator to the specific volatility measure of interest and relevant loss function. The resulting new optimal estimators offer substantial efficiency gains compared to existing commonly used range-based procedures.

A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented. (c) 2023 Published by Elsevier B.V.

A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.

I provide a brief history of the origins of the GARCH model and my 1986 paper published in the Journal, along with a discussion of how the GARCH model and applications thereof have flourished since then. I also briefly highlight connections to the more recent realized volatility literature. (c) 2023 Elsevier B.V. All rights reserved.

Jumps in asset prices are ubiquitous, yet the apparent high price of jump risk observed empirically is commonly viewed as puzzling. We develop new model-free short-time risk-neutral variance expansions, allowing us to clearly delineate the importance of jumps in generating both price and variance risks. We find that simultaneous jumps in the price and the stochastic volatility and/or jump intensity of the market commands a sizeable risk premium. The existence of “jump leverage” risk premium may be rationalized in the context of equilibrium-based models by jumps in the conditional moments of the underlying fundamentals and/or changes in investors' risk aversion.

This paper proposes a generalization of the class of realized semivariance and semi -covariance measures introduced by Barndorff-Nielsen et al. (2010) and Bollerslev et al. (2020a) to allow for a finer decomposition of realized (co)variances. The new "realized partial (co)variances"allow for multiple thresholds with various locations, rather than the single fixed threshold of zero used in semi (co)variances. We adopt methods from machine learning to choose the thresholds to maximize the out-of-sample forecast performance of time series models based on realized partial (co)variances. We find that in low dimensional settings it is hard, but not impossible, to improve upon the simple fixed threshold of zero. In large dimensions, however, the zero threshold embedded in realized semi covariances emerges as a robust choice.(c) 2021 Elsevier B.V. All rights reserved.

We rely on newly-developed realized semicorrelations constructed from high-frequency returnstogether with hierarchical clustering and cross-validation techniques to identify groupsof individual stocks that share common features. Implementing the new procedures basedon intraday data for the S&P 100 constituents spanning 2019-2020, we uncover distinctchanges in the "optimal" groupings of the stocks coincident with the onset of the COVID-19 pandemic. Many of the clusters estimated with data post-January 2020 evidence cleardifferences from conventional industry type classifications. They also differ from the clustersestimated with standard realized correlations, underscoring the advantages of "lookinginside" the correlation matrix through the lens of the new realized semicorrelations.

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

We propose a new decomposition of the traditional market beta into four semibetas that depend on the signed covariation between the market and individual asset returns. We show that semibetas stemming from negative market and negative asset return covariation predict significantly higher future returns, while semibetas attributable to negative market and positive asset return covariation predict significantly lower future returns. The two semibetas associated with positive market return variation do not appear to be priced. The results are consistent with the pricing implications from a mean-semivariance framework combined with arbitrage risk driving a wedge between the risk premiums for long and short positions. We conclude that rather than betting against the traditional market beta, it is better to bet on and against the "right" semibetas.

Jumps in asset prices are ubiquitous, yet the apparent high price of jump risk observed empirically is widely viewed as puzzling. Importantly however, in addition to direct price risks, jumps may also trigger simultaneous changes in other distributional features of asset returns. We develop model-free short-time expansions for two alternative risk-neutral variance measures, allowing us to more clearly delineate the role played by jumps in generating both price and variance risks and the pricing of "jump leverage" in particular. Relying on high-frequency S&P 500 index and options data, we find that the jump leverage effect commands a sizeable risk premium.

We develop new high-frequency-based inference procedures for analyzing the relationship between jumps in instantaneous moments of stochastic processes. The estimation consists of two steps: the nonparametric determination of the jumps as differences in local averages, followed by a minimum-distance type estimation of the parameters of interest under general loss functions that include both least-square and more robust quantile regressions as special cases. The resulting asymptotic distribution of the estimator, derived under an infill asymptotic setting, is highly non-standard and generally not mixed normal. In addition, we establish the validity of a novel bootstrap algorithm for making feasible inference including bias-correction. The new methods are applied in a study on the relationship between trading intensity and spot volatility in the U.S. equity market at the time of important macroeconomic news announcement.

We present a new theory for the conduct of nonparametric inference about the latent spot volatility of a semimartingale asset price process. In contrast to existing theories based on the asymptotic notion of an increasing number of observations in local estimation blocks, our theory treats the estimation block size k as fixed. While the resulting spot volatility estimator is no longer consistent, the new theory permits the construction of asymptotically valid and easy‐to‐calculate pointwise confidence intervals for the volatility at any given point in time. Extending the theory to a high‐dimensional inference setting with a growing number of estimation blocks further permits the construction of uniform confidence bands for the volatility path. An empirically realistically calibrated simulation study underscores the practical reliability of the new inference procedures. An empirical application based on intraday data for the S&P 500 equity index reveals highly significant abrupt changes, or jumps, in the market volatility at FOMC news announcement times, validating recent uses of various high‐frequency‐based identification schemes in asset pricing finance and monetary economics.

This paper studies the nonparametric estimation of occupation densities for semimartingale processes observed with noise. As leading examples we consider the stochastic volatility of a latent efficient price process, the volatility of the latent noise that separates the efficient price from the actually observed price, and nonlinear transformations of these processes. Our estimation methods are decidedly nonparametric and consist of two steps: the estimation of the spot price and noise volatility processes based on pre-averaging techniques and in-fill asymptotic arguments, followed by a kernel-type estimation of the occupation densities. Our spot volatility estimates attain the optimal rate of convergence, and are robust to leverage effects, price and volatility jumps, general forms of serial dependence in the noise, and random irregular sampling. The convergence rates of our occupation density estimates are directly related to that of the estimated spot volatilities and the smoothness of the true occupation densities. An empirical application involving high-frequency equity data illustrates the usefulness of the new methods in illuminating time-varying risks, market liquidity, and informational asymmetries across time and assets.