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Motivated by the recent availability of extensive electronic news databases and advent of new empirical methods, there has been renewed interest in investigating the impact of financial news on market outcomes for individual stocks. We develop the information processing hypothesis of return volatility to investigate the relation between firm-specific news and volatility. We propose a novel dynamic econometric specification and test it using time series regressions employing a machine learning model selection procedure. Our empirical results are based on a comprehensive dataset comprised of more than 3 million news items for a sample of 28 large U.S. companies. Our proposed econometric specification for firm-specific return volatility is a simple mixture model with two components: public information and private processing of public information. The public information processing component is defined by the contemporaneous relation with public information and volatility, while the private processing of public information component is specified as a general autoregressive process corresponding to the sequential price discovery mechanism of investors as additional information, previously not publicly available, is generated and incorporated into prices. Our results show that changes in return volatility are related to public information arrival and that including indicators of public information arrival explains on average 26% (9–65%) of changes in firm-specific return volatility.

We model the joint dynamics of intraday liquidity, volume, and volatility in the U.S. Treasury market, especially through the 2007–09 financial crisis and around important economic announcements. Using various specifications based on Bauwens and Giot (2000)’s Log-ACD(1,1) model, we find that liquidity, volume, and volatility are highly persistent, with volatility having a lower short-term persistence than the other two. Market liquidity and volume are important to explaining volatility dynamics but not vice versa. In addition, market dynamics change during the financial crisis, with all variables exhibiting increased responsiveness to their most recent realizations. Our models also reveal different market dynamics around announcements. Finally, we introduce new measures of liquidity risk that are useful for continually monitoring liquidity conditions and the risk of liquidity stress in the market.

Significance This study develops quantitative estimates of the level of systemic risk in the financial sector that precipitates a financial crisis. When financial firms are undercapitalized, they face difficulty in covering losses in a downturn. The natural response to such vulnerability, reducing leverage through asset sales, can start a financial crisis. Perilous excessive credit growth is reflected in the undercapitalization of the financial sector. Market-based indicators of systemic risk such as SRISK, which stands for systemic risk, measure such weakness in real time. We develop a probability of crisis measure and an SRISK capacity measure for 23 developed countries. Our analysis highlights the important global externality whereby the risk of a crisis in one country depends on the undercapitalization of the rest of the world., When financial firms are undercapitalized, they are vulnerable to external shocks. The natural response to such vulnerability is to reduce leverage, and this can endogenously start a financial crisis. Excessive credit growth, the main cause of financial crises, is reflected in the undercapitalization of the financial sector. Market-based measures of systemic risk such as SRISK, which stands for systemic risk, enable monitoring how such weakness emerges and progresses in real time. In this paper, we develop quantitative estimates of the level of systemic risk in the financial sector that precipitates a financial crisis. Common approaches to reduce leverage correspond to specific scaling of systemic risk measures. In an econometric framework that recognizes financial crises represent left tail events for the economy, we estimate the relationship between SRISK and the financial crisis severity for 23 developed countries. We develop a probability of crisis measure and an SRISK capacity measure based on our estimates. Our analysis highlights the important global externality whereby the risk of a crisis in one country is strongly influenced by the undercapitalization of the rest of the world.

We study the crash of bank stock prices during the COVID-19 pandemic. We find evidence consistent with a “credit line drawdown channel”. Stock prices of banks with large ex-ante exposures to undrawn credit lines as well as large ex-post gross drawdowns decline more. The effect is attenuated for banks with higher capital buffers. These banks reduce term loan lending, even after policy measures were implemented. We conclude that bank provision of credit lines appears akin to writing deep out-of-the-money put options on aggregate risk;we show how the resulting contingent leverage and stock return exposure can be incorporated tractably into bank capital stress tests.

We propose a multiplicative factor multi frequency component GARCH model which exploits the empirical fact that the daily standardized forecast errors of one-component GARCH models behave counter-cyclical when averaged at a lower frequency. For the new model, we derive the unconditional variance of the returns, the news impact function and multi-step-ahead volatility forecasts. When applied to the S&P 500, the new component model significantly outperforms the nested one-component GJR-GARCH and the log-HAR model in terms of out-of-sample forecasting.

We study the crash of bank stock prices during the COVID-19 pandemic. We find evidence consistent with a “credit line drawdown channel”. Stock prices of banks with large ex-ante exposures to undrawn credit lines as well as large ex-post gross drawdowns decline more. The effect is attenuated for banks with higher capital buffers. These banks reduce term loan lending, even after policy measures were implemented. We conclude that bank provision of credit lines appears akin to writing deep out-of-the-money put options on aggregate risk; we show how the resulting contingent leverage and stock return exposure can be incorporated tractably into bank capital stress tests.

Climate change could impose systemic risks upon the financial sector, either via disruptions in economic activity resulting from the physical impacts of climate change or changes in policies as the economy transitions to a less carbon-intensive environment. We develop a stress testing procedure to test the resilience of financial institutions to climate-related risks. Specifically, we introduce a measure called CRISK, systemic climate risk, which is the expected capital shortfall of a financial institution in a climate stress scenario. We use the measure to study the climate-related risk exposure of large global banks in the collapse of fossil-fuel prices in 2020.

Estimation of time-varying covariances is a key input in risk management and asset allocation. ARCH-type multivariate models are used widely for this purpose. Estimation of such models is computationally costly and parameter estimates are meaningfully biased when applied to a moderately large number of assets. Here, we propose a novel estimation approach that suffers from neither of these issues, even when the number of assets is in the hundreds. The theory of this new method is developed in some detail. The performance of the proposed method is investigated using extensive simulation studies and empirical examples. Supplementary materials for this article are available online. Cavit Pakel gratefully acknowledges financial support from the European Commission (Marie Curie Actions Career Integration Grant [Project No 618562])

Using a multi-regime forecasting model, we investigate the impact of COVID-19 pandemic on market volatility. We show that daily number of active cases and the Curvature are significant predictors of daily cross-section of both realized volatility and the GJR-GARCH volatility in global equity markets. We estimate realized volatilities using intraday 5-minute returns for 46 country specific ETFs and daily GARCH volatilities are estimated using the stock market indices of 88 countries around the world. We find that stricter policy responses by individual countries, measured by higher OxCGRT Stringency Index levels, result in lower stock market volatilities while increased negative managerial sentiment, extracted from earnings call transcripts, causes an increase in realized volatilities.

A stress test assesses the value of a firm or asset in the future under an adverse counterfactual scenario. The critical points of stress tests are the valuation model and the scenario. This paper describes some of the difficulties in generating appropriate scenarios and valuing firms under these scenarios. In most cases, these difficulties can be solved if the regulator is better informed than the market. However, if this is not correct at all times and settings, then it is also sensible to carry out stress tests with market scenarios and market data. When these stress tests agree, the results gain added credibility. When they disagree, the parties can discuss whether the market has missed signals, or whether the regulators’ models are wrong or have been politically impacted. Detailed analysis of SRISK, a market based stress test, is presented from an economic, econometric and historical point of view. This is compared with alternative measures such as SES and CoVaR and with regulatory stress tests.

Multivariate GARCH models do not perform well in large dimensions due to the so-called curse of dimensionality. The recent DCC-NL model of Engle et al. (2019) is able to overcome this curse via nonlinear shrinkage estimation of the unconditional correlation matrix. In this paper, we show how performance can be increased further by using open/high/low/close (OHLC) price data instead of simply using daily returns. A key innovation, for the improved modeling of not only dynamic variances but also of dynamic correlations, is the concept of a regularized return, obtained from a volatility proxy in conjunction with a smoothed sign of the observed return.

Geopolitical events can impact volatilities of all assets, asset classes, sectors and countries. It is shown that innovations to volatilities are correlated across assets and therefore can be used to measure and hedge geopolitical risk. We introduce a definition of geopolitical risk which is based on volatility shocks to a wide range of financial market prices. To measure geopolitical risk, we propose a statistical model for the magnitude of the common volatility shocks. Accordingly, a test and estimation methods are developed and studied using both empirical and simulated data. We provide a novel explanation for why idiosyncratic volatilities comove based on a new way to formulate multiplicative factors. Finally, we propose a new criterion for portfolio optimality which is intended to reduce the exposure to geopolitical risk., Part of this work was developed while the second author was visiting the New York University Stern School of Business. The financial support provided by the Luso-American Development Foundation and the Portuguese Foundation for Science and Technology (SFRH/BD/109539/2015) is gratefully acknowledged. This research was supported by the Volatility and Risk Institute at NYU Stern School of Business and the authors are indebted to the Global Risk Institute, the Sloan Foundation, the National Science Foundation, the Norwegian Finance Institute and many individual donors.

Ten years ago, the financial crisis spurred research focused on systemic risk. This article examines the history and application of the SRISK measure, which was developed at that time and is now widely used in monitoring systemic risk around the globe. The concept is explained and a variety of ways to measure SRISK are developed. In this article, new results are presented on the uncertainty associated with the SRISK measure and on how it compares with other related measures from both academics and regulators. By focusing on the mechanism by which undercapitalization of the financial sector initiates a financial crisis, new research examines how the probability of a financial crisis is affected by the level of SRISK and, consequently, how much SRISK a country can stand without having a high probability of crisis. The model used to evaluate this probability recognizes the externalities between financial institutions that make an undercapitalized firm or country more fragile if other firms and countries are also undercapitalized.

Recent episodes of stress in the financial system have fostered a great deal of discussion regarding new supervisory and regulatory tools for financial institutions. The recent introduction of additional capital requirements for systemically important financial institutions is one example of the concrete measures that are being taken by regulators to mitigate systemic risk. In order to assist market participants in assessing and tracking systemic risk in the financial system, the Volatility Laboratory of the NYU Stern School of Business developed a quantitative indicator, called SRISK, which estimates the expected capital shortfall faced by a firm in a potential future financial crisis. Conceptually, SRISK is similar to the stress tests that are regularly applied to financial institutions; however, it is based exclusively on publicly available information (market and accounting data) and is quick and inexpensive to compute. Those firms with a high capital shortfall in a crisis – that is, when capital is low in the financial system – are the ones with the potential to extend the crisis and impact the broader economy. We use SRISK to quantify the estimated capital shortfalls of financial institutions under three relevant stress events that occurred in 2016: Brexit, the Trump election and the Italian referendum. We refer to these events collectively as BRUMPIT. Our empirical results confirm the usefulness of SRISK in assessing the sensitivity of individual financial institutions to the BRUMPIT events. This highlights the transmission channels in terms of systemic risk.

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroscedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present article marries these two strands of literature to deliver improved estimation of large dynamic covariance matrices. Supplementary material for this article is available online.

We propose a statistical model of the term structure of U.S. treasury yields tailored for long-term probability-based scenario generation and forecasts. Our model is easy to estimate and is able to simultaneously reproduce the positivity, persistence, and factor structure of the yield curve. Moreover, we incorporate heteroskedasticity and time-varying correlations across yields, both prevalent features of the data. The model also features a regime-switching short-rate model. We evaluate the out-of-sample performance of our model in terms of forecasting ability and coverage properties, and find that it improves on the standard Diebold and Li model.

We propose a new model of volatility where financial leverage amplifies equity volatility by what we call the “leverage multiplier”. The exact specification is motivated by standard structural models of credit; however, our parametrization departs from the classic Merton (1974) model and is, as we show, flexible and accurate enough to capture environments where the firm’s asset volatility is stochastic, asset returns can jump, and asset shocks are non-normal. As a result, our model also provides estimates of daily asset returns and asset volatility. In addition, our specification nests both a standard GARCH and the Merton model, which allows for a simple statistical test of how leverage interacts with equity volatility. Empirically, the Structural GARCH model outperforms a standard GARCH model for approximately 75% of the financial firms we analyze. We then apply the Structural GARCH model to two empirical applications: the leverage effect and systemic risk measurement.

William Shakespeare's Tragedy of King Richard III, written approximately in 1592, is the story of evil acts by the detested and misshapen hunchback, Richard, who plots to sow discontent among his brother, the King, and others, and has his brother murdered along with other wicked deeds in order to gain the throne. It opens with the line, “Now is the winter of our discontent” (p. 111, ed. Wright 1936). “The Winter of Our Discontent” is also the title of John Steinbeck's (1961) novel of a man who trades his moral convictions to reclaim lost family wealth. “Globalization and Its Discontents” is the title of Joseph Stiglitz's (2002) book that critiques rigid adherence by major economic institutions—such as the International Monetary Fund—to economic orthodoxy in the promotion of globalization. (JEL F6, D72, D3, O23, O24, L17, K33)

We propose and implement a procedure to dynamically hedge climate change risk. We extract innovations from climate news series that we construct through textual analysis of newspapers. We then use a mimicking portfolio approach to build climate change hedge portfolios. We discipline the exercise by using third-party ESG scores of firms to model their climate risk exposures. We show that this approach yields parsimonious and industry-balanced portfolios that perform well in hedging innovations in climate news both in sample and out of sample. We discuss multiple directions for future research on financial approaches to managing climate risk.

We propose and implement a procedure to dynamically hedge climate change risk. We extract innovations from climate news series that we construct through textual analysis of newspapers. We then use a mimicking portfolio approach to build climate change hedge portfolios. We discipline the exercise by using third-party ESG scores of firms to model their climate risk exposures. We show that this approach yields parsimonious and industry-balanced portfolios that perform well in hedging innovations in climate news both in sample and out of sample. We discuss multiple directions for future research on financial approaches to managing climate risk.

We propose and implement a procedure to dynamically hedge climate change risk. We extract innovations from climate news series that we construct through textual analysis of newspapers. We then use a mimicking portfolio approach to build climate change hedge portfolios. We discipline the exercise by using third-party ESG scores of firms to model their climate risk exposures. We show that this approach yields parsimonious and industry-balanced portfolios that perform well in hedging innovations in climate news both in sample and out of sample. We discuss multiple directions for future research on financial approaches to managing climate risk.

We introduce SRISK to measure the systemic risk contribution of a financial firm. SRISK measures the capital shortfall of a firm conditional on a severe market decline, and is a function of its size, leverage and risk. We use the measure to study top financial institutions in the recent financial crisis. SRISK delivers useful rankings of systemic institutions at various stages of the crisis and identifies Fannie Mae, Freddie Mac, Morgan Stanley, Bear Stearns, and Lehman Brothers as top contributors as early as 2005-Q1. Moreover, aggregate SRISK provides early warning signals of distress in indicators of real activity.Received June 7, 2011; accepted April 18, 2016 by Editor Geert Bekaert.

In this article, the authors provide a nontechnical discussion of a number of practical and theoretical issues associated with implementing factor models used to explain or forecast equity returns. The first issue is determining the number of factors (i.e., the number of variables needed to explain or forecast returns). In finite markets such as stock markets, the problem of determining the true number of factors cannot be solved theoretically. Instead, asset managers must be content with approximations using model selection criteria. The authors then discuss the questions of overfitting and dimensionality reduction—both of which can lead to poor out-of-sample performance of investment or trading strategies. Overfitting entails using a model that is too complex for the data available to the modeler; thus, the resulting model fits noise. Dimensionality reduction solves the problem of dimensionality by using approximate models of reduced dimensionality that can be estimated with small samples. An important instance of applying dimensionality reduction techniques is using factor GARCH models to forecast covariance matrices. Finally, the authors discuss problems associated with backtesting. In trying to choose the best-performing model or strategy, a modeler may be tempted to run multiple backtests, thereby creating the risk of using out-of-sample backtesting as a form of in-sample testing. In turn, this leads to overfitting.

When financial firms are under-capitalized, they are vulnerable to external shocks. This is commonly measured by stress tests or market-based measures of systemic risk such as SRISK. The natural response to such vulnerability is to raise capital and this can endogenously start a financial crisis. Excessive credit growth can be interpreted as under-capitalization of the financial sector. Hence, we can assess how much SRISK an economy can stand, and measure the probability of a crisis. Using a crisis intensity variable constructed by Romer and Romer (2017), we estimate a Tobit model for 23 developed economies. We develop a probability of crisis measure and an SRISK capacity measure from the Tobit estimates. These reveal the important global externalities since the risk of a crisis in one country is strongly influenced by the under-capitalization of the rest of the world.

We discuss several multivariate extensions of the Multiplicative Error Model to take into account dynamic interdependence and contemporaneously correlated innovations (vector MEM or vMEM). We suggest copula functions to link Gamma marginals of the innovations, in a specification where past values and conditional expectations of the variables can be simultaneously estimated. Results with realized volatility, volumes and number of trades of the JNJ stock show that significantly superior realized volatility forecasts are delivered with a fully interdependent vMEM relative to a single equation. Alternatives involving log-Normal or semiparametric formulations produce substantially equivalent results.

We investigate the sources of skewness in aggregate risk factors and the cross section of stock returns. In an ICAPM setting with conditional volatility, we find theoretical time series predictions on the relationships among volatility, returns, and skewness for priced risk factors. Market returns resemble these predictions; however, size, book-to-market, and momentum factor returns are not always consistent with our predictions. We find evidence that size and book-to-market may be priced post-crisis but not in the decade before. Momentum does not appear priced by our test. We link aggregate risk and skewness to individual stocks and find empirically that the risk aversion effect manifests in individual stock skewness. Additionally, we find several firm characteristics that explain stock skewness. Smaller firms, value firms, highly levered firms, and firms with poor credit ratings have more positive skewness.

We compare the capital shortfall measured by regulatory stress tests,to that o fa benchmark methodology — the “V-Lab stress test” — that employs only publicly available market data.We find that when capital shortfalls are measured relative to risk-weighted assets, the ranking of financial institutions is not well correlated to the ranking of the V-Lab stress test, whereas rank correlations increase when required capitalization is a function of total assets. We show that the risk measures used in risk-weighted assets are cross-sectionally uncorrelated with market measures of risk, as they do not account for the “risk that risk will change.” Furthermore, the banks that appeared to be best capitalized relative to risk-weighted assets were no better than the rest when the European economy deteriorated into the sovereign debt crisis in 2011.

Systemic risk may be defined as the propensity of a financial institution to be undercapitalized when the financial system as a whole is undercapitalized. In this article, we investigate the case of non-US institutions, with several factors explaining the dynamics of financial firms returns and with asynchronicity of time zones. We apply this methodology to the 196 largest European financial firms and estimate their systemic risk over the 2000–12 period. We find that, for certain countries, the cost for the taxpayer to rescue the riskiest domestic banks is so high that some banks might be considered too big to be saved.

We revisit the relation between stock market volatility and macroeconomic activity using a new class of component models that distinguish short-run from long-run movements. We formulate models with the long-term component driven by inflation and industrial production growth that are in terms of pseudo out-of-sample prediction for horizons of one quarter at par or outperform more traditional time series volatility models at longer horizons. Hence, imputing economic fundamentals into volatility models pays off in terms of long-horizon forecasting. We also find that macroeconomic fundamentals play a significant role even at short horizons. © 2013 The President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Building models for high dimensional portfolios is important in risk management and asset allocation. Here we propose a novel and fast way of estimating models of time-varying covariances that overcome an undiagnosed incidental parameter problem which has troubled existing methods when applied to hundreds or even thousands of assets. Indeed we can handle the case where the cross-sectional dimension is larger than the time series one. The theory of this new strategy is developed in some detail, allowing formal hypothesis testing to be carried out on these models. Simulations are used to explore the performance of this inference strategy while empirical examples are reported which show the strength of this method. The out of sample hedging performance of various models estimated using this method are compared.

The Multiplicative Error Model (Engle (2002)) for nonnegative valued processes is specified as the product of a (conditionally autoregressive) scale factor and an innovation process with nonnegative support. A multivariate extension allows for the innovations to be contemporaneously correlated. We overcome the lack of sufficiently flexible probability density functions for such processes by suggesting a copula function approach to estimate the parameters of the scale factors and of the correlations of the innovation processes. We illustrate this vector MEM with an application to the interactions between realized volatility, volume and the number of trades. We show that significantly superior realized volatility forecasts are delivered in the presence of other trading activity indicators and contemporaneous correlations.

Second moments of asset returns are important for risk management and portfolio selection. The problem of estimating second moments can be approached from two angles: time series and the cross-section. In time series, the key is to account for conditional heteroskedasticity; a favored model is Dynamic Conditional Correlation (DCC), derived from the ARCH/GARCH family started by Engle (1982). In the cross-section, the key is to correct in-sample biases of sample covariance matrix eigenvalues; a favored model is nonlinear shrinkage, derived from Random Matrix Theory (RMT). The present paper aims to marry these two strands of literature in order to deliver improved estimation of large dynamic covariance matrices.

In financial time series analysis we encounter several instances of non‐negative valued processes (volumes, trades, durations, realized volatility, daily range, and so on) which exhibit clustering and can be modeled as the product of a vector of conditionally autoregressive scale factors and a multivariate iid innovation process (vector Multiplicative Error Model). Two novel points are introduced in this paper relative to previous suggestions: a more general specification which sets this vector MEM apart from an equation by equation specification; and the adoption of a GMM-based approach which bypasses the complicated issue of specifying a general multivariate non‐negative valued innovation process. A vMEM for volumes, number of trades and realized volatility reveals empirical support for a dynamically interdependent pattern of relationships among the variables on a number of NYSE stocks.

Financial markets are considered to be liquid if a large quantity can be traded quickly and with minimal price impact. Although the idea of a liquid market involves both a cost as well as a time component, most measures of execution costs tend to focus on only a single number that reflects average costs and do not explicitly account for the temporal dimension of liquidity. In practice, trading takes time because larger orders are often broken up into smaller transactions or because of price limits. Recent work shows that the time taken to transact introduces a risk component in execution costs. In this setting, the decision can be viewed as a risk–reward trade-off faced by the investor who can solve for a mean-variance utility-maximizing trading strategy. Engle, Ferstenberg, and Russell introduce an econometric method to jointly model the expected cost and risk of the trade, thereby characterizing the mean-variance tradeoffs associated with different trading approaches, given market and order characteristics. They apply their methodology to a novel dataset and show that the risk component is a nontrivial part of the transaction decision.

We propose a new approach to model high and low frequency components of equity correlations. Our framework combines a factor asset pricing structure with other specifications capturing dynamic properties of volatilities and covariances between a single common factor and idiosyncratic returns. High frequency correlations mean revert to slowly varying functions that characterize long-term correlation patterns. We associate such term behavior with low frequency economic variables, including determinants of market and idiosyncratic volatilities. Flexibility in the time-varying level of mean reversion improves both the empirical fit of equity correlations in the United States and correlation forecasts at long horizons.

The financial crisis of 2007-2009 has given way to the sovereign debt crisis of 2010-2012, yet many of the banking issues remain the same. We discuss a method to estimate the capital that a financial firm would need to raise if we have another financial crisis. This measure of capital shortfall is based on publicly available information but is conceptually similar to the stress tests conducted by US and European regulators. We argue that this measure summarizes the major characteristics of systemic risk and provides a reliable interpretation of the past and current financial crises.

This paper proposes a new intraday volatility forecasting model, particularly suitable for modeling a large number of assets. We decompose volatility of high-frequency returns into components that may be easily interpreted and estimated. The conditional variance is a product of daily, diurnal, and stochastic intraday components. This model is applied to a comprehensive sample consisting of 10-minute returns on more than 2500 US equities. Apart from building a new model, we obtain several interesting forecasting results. We apply a number of different specifications. We estimate models for separate companies, pool data into industries, and consider other criteria for grouping returns. In general, forecasts from pooled cross-section of companies outperform the corresponding forecasts from company-by-company estimation. For less liquid stocks, however, we obtain better forecasts when we group less frequently traded companies together. Copyright The Author 2011. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

Financial risk management has generally focused on short-term risks rather than long-term risks, and arguably this was an important component of the recent financial crisis. Econometric approaches to measuring long-term risk are developed in order to estimate the term structure of value at risk and expected shortfall. Long-term negative skewness increases the downside risk and is a consequence of asymmetric volatility models. A test is developed for long-term skewness. In a Merton style structural default model, bankruptcies are accompanied by substantial drops in equity prices. Thus, skewness in a market factor implies high defaults and default correlations even far in the future corroborating the systemic importance of long-term skewness. Investors concerned about long-term risks may hedge exposure as in the Intertemporal Capital Asset Pricing Model (ICAPM). As a consequence, the aggregate wealth portfolio should have asymmetric volatility and hedge portfolios should have reversed asymmetric volatility. Using estimates from VLAB, reversed asymmetric volatility is found for many possible hedge portfolios such as volatility products, long- and short-term treasuries, some exchange rates, and gold. JEL: G01 Copyright The Author 2011. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

The intertemporal capital asset pricing model of Merton (1973) is examined using the dynamic conditional correlation (DCC) model of Engle (2002). The mean-reverting DCC model is used to estimate a stock’s (portfolio’s) conditional covariance with the market and test whether the conditional covariance predicts time-variation in the stock’s (portfolio’s) expected return. The risk-aversion coefficient, restricted to be the same across assets in panel regression, is estimated to be between two and four and highly significant. The risk premium induced by the conditional covariation of assets with the market portfolio remains positive and significant after controlling for risk premia induced by conditional covariation with macroeconomic, financial, and volatility factors.

Seasonal patterns in economic time series are generally examined from a univariate point of view. Using extensions of the unit root literature, important classes of seasonal processes are deterministic, stationary stochastic or mean reverting, and unit root stochastic. Time series tests have been developed for each of these. This paper examines seasonality in a multivariate context. Systems of economic variables can have trends, cycles and unit roots as well as the various types of seasonality. Restrictions such as cointegration and common cycles are here applied also to examine multivariate seasonal behaviour of economic variables. If each of a collection of series has a certain type of seasonality but a linear combination of these series can be found without seasonality, then the seasonal is said to be ‘common’. New tests are developed to determine if seasonal characteristics are common to a set of time series. These tests can be employed in the presence of various other time series structures. The analysis is applied to OECD data on unemployment for the period 1975.1 to 1993.4, and it is found that four diverse countries (Australia, Canada, Japan and USA) not only have common trends in their unemployment, but also have common deterministic seasonal features and a common cycle/stochastic seasonal feature. Such a collection of characteristics were not found in other groups of OECD countries.