This paper introduces an ARCH model (exponential ARCH) that (1) allows correlation between returns and volatility innovations (an important feature of stock market volatility changes), (2) eliminates the need for inequality constraints on parameters, and (3) allows for a straightforward interpretation of the "persistence" of shocks to volatility. In the above respects, it is an improvement over the widely-used GARCH model. The model is applied to study volatility changes and the risk premium on the CRSP Value-Weighted Market Index from 1962 to 1987. Copyright 1991 by The Econometric Society.

Conditional heteroskedasticity in asset returns: a new approach

Any series of observations ordered along a single dimension, such as time, may be thought of as a time series. The emphasis in time series analysis is on studying the dependence among observations at different points in time. What distinguishes time series analysis from general multivariate analysis is precisely the temporal order imposed on the observations. Many economic variables, such as GNP and its components, price indices, sales, and stock returns are observed over time. In addition to being interested in the contemporaneous relationships among such variables, we are often concerned with relationships between their current and past values, that is, relationships over time.

Time Series Analysis

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility. THE TRADEOFF BETWEEN RISK and return has long been an important topic in asset valuation research. Most of this research has examined the tradeoff between risk and return among different securities within a given time period. The intertemporal relation between risk and return has been examined by several authors-Fama and Schwert (1977), French, Schwert, and Stambaugh (1987), Harvey (1989), Campbell and Hentschel (1992), Nelson (1991), and Chan, Karolyi, and Stulz (1992), to name a few. This paper extends that research.

https://faculty.washington.edu/ezivot/econ589/GJRJOF1993.pdf

On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks

Time varying correlations are often estimated with multivariate generalized autoregressive conditional heteroskedasticity (GARCH) models that are linear in squares and cross products of the data. A new class of multivariate models called dynamic conditional correlation models is proposed. These have the flexibility of univariate GARCH models coupled with parsimonious parametric models for the correlations. They are not linear but can often be estimated very simply with univariate or two-step methods based on the likelihood function. It is shown that they perform well in a variety of situations and provide sensible empirical results.

/pdf/dynamic-conditional-correlation-a-simple-class-of-1s5avcbk8r.pdf

Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models

This paper presents theoretical results in the formulation and estimation of multivariate gen- eralized ARCH models within simultaneous equations systems. A new parameterization of the multivariate ARCH process is proposed and equivalence relations are discussed for the various ARCH parameterizations. Constraints suffcient to guarantee the positive deffniteness of the con- ditional covariance matrices are developed, and necessary and suffcient conditions for covariance stationarity are presented. Identifcation and maximum likelihood estimation of the parameters in the simultaneous equations context are also covered.

https://www.jstor.org/stable/pdfplus/3532933.pdf

Multivariate Simultaneous Generalized ARCH

This paper develops mew robust inference procedures for analyzing the intraday return volatility patterns that constitute a focal point of much market microstructure theory. Our empirical analysis is motivated by the recent lifting of trading restrictions in the interbank foreign exchange (FX) market for Japanese banks during the Tokyo lunch period. Ito, Lyons, and Melvin (1998) (ILM) argue that this deregulation resulted in a highly significant shift in the volatility pattern across the entire Japanese trading day, indicating that private information is an important component of the price formation process in the FX market. In contrast, our robust analysis finds no evidence for any discernible change in the pattern outside of the Tokyo lunch period. Moreover, we document that the standard variance-ratio methodology inference in this high-frequency data context.

/pdf/testing-for-market-microstructure-effects-in-intraday-yac9yd4bnk.pdf

Testing for Market Microstructure Effects in Intraday Volatility: A Reassessment of the Tokyo FX Experiment

We exploit direct model-free measures of daily equity return volatility and correlation obtained from high-frequency intraday transaction prices on individual stocks in the Dow Jones Industrial Average over a five-year period to confirm, solidify and extend existing characterizations of stock return volatility and correlation We find that the unconditional distributions of the variances and covariances for all thirty stocks are leptokurtic and highly skewed to the right, while the logarithmic standard deviations and correlations all appear approximately Gaussian. Moreover, the distributions returns scaled by the realized standard deviations are also Gaussian. Furthermore, the realized logarithmic standard deviations and correlations all show strong dependence and appear to be well described by long-memory processes, consistent with our documentation of remarkably precise scaling laws under temporal aggregation. Our results also show that positive returns have less impact on future variances and correlations than negative returns of the same absolute magnitude, although the economic importance of this asymmetry is minor. Finally, there is strong evidence that equity volatilities and correlations move together, thus diminishing the benefits to diversification when the market is most volatile. By explicitly incorporating each of these stylized facts, our findings set the stage for improved high-dimensional volatility modeling and out-of-sample forecasting, which in turn hold promise for the development of better decision making in practical situations of risk management, portfolio allocation, and asset pricing.

The Distribution of Stock Return Volatility

High-dimensional multivariate realized volatility estimation

We examine the joint predictability of return and cash flow within a present value framework, by imposing the implications from a long-run risk model that allow for both time-varying volatility and volatility uncertainty. We provide new evidence that the expected return variation and the variance risk premium positively forecast both short-horizon returns and dividend growth rates. We also confirm that dividend yield positively forecasts long-horizon returns, but that it cannot forecast dividend growth rates. Our equilibrium-based “structural” factor GARCH model permits much more accurate inference than the reduced form VAR and univariate regression procedures traditionally employed in the literature. The model also allows for the direct estimation of the underlying economic mechanisms, including a new volatility leverage effect, the persistence of the latent long-run growth component and the two latent volatility factors, as well as the contemporaneous impacts of the underlying “structural” shocks.

Stock Return and Cash Flow Predictability: The Role of Volatility Risk

We test for price discontinuities, or jumps, in a panel of high-frequency intraday returns for forty large-cap stocks and an equiweighted index from these same stocks. Jumps are naturally classified into two types: common and idiosyncratic. Common jumps affect all stocks, albeit to varying degrees, while idiosyncratic jumps are stock-specific. Despite the fact that each of the stocks has a b of about unity with respect to the index, common jumps are virtually never detected in the individual stocks. This is truly puzzling, as an index can jump only if one or more of its components jump. To resolve this puzzle, we propose a new test for cojumps. Using this new test we find strong evidence for many modest-sized common jumps that simply pass through the standard jump detection statistic, while they appear highly significant in the cross section based on the new cojump identification scheme. Our results are further corroborated by a striking within-day pattern in the non-diversifiable cojumps.

/pdf/risk-jumps-and-diversification-4nl2hhc7j2.pdf

Tim Bollerslev

Papers

Testing for Market Microstructure Effects in Intraday Volatility: A Reassessment of the Tokyo FX Experiment

The Distribution of Stock Return Volatility

High-dimensional multivariate realized volatility estimation

Stock Return and Cash Flow Predictability: The Role of Volatility Risk

Risk, Jumps, and Diversification