Non-homogeneous volatility correlations in the bivariate multifractal model

In this paper, we consider an extension of the recently proposed bivariate Markov-switching multifractal model of Calvet, Fisher, and Thompson [2006. “Volatility Comovement: A Multifrequency Approach.” Journal of Econometrics 131: 179–215]. In particular, we allow correlations between volatility components to be non-homogeneous with two different parameters governing the volatility correlations at high and low frequencies. Specification tests confirm the added explanatory value of this specification. In order to explore its practical performance, we apply the model for computing value-at-risk statistics for different classes of financial assets and compare the results with the baseline, homogeneous bivariate multifractal model and the bivariate DCC-GARCH of Engle [2002. “Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models.” Journal of Business & Economic Statistics 20 (3): 339–350]. As it turns out, the multifractal model with heterogeneous volatility correlations provides more reliable results than both the homogeneous benchmark and the DCC-GARCH model.     

Financial crisis,Value-at-Risk forecasts and the puzzle of dependency modeling

Forecasting Value-at-Risk (VaR) for financial portfolios is a crucial task in applied financial risk management. In this paper, we compare VaR forecasts based on different models for return interdependencies: volatility spillover (Engle & Kroner, 1995), dynamic conditional correlations (Engle, 2002, 2009) and (elliptical) copulas (Embrechts et al., 2002). Moreover, competing models for marginal return distributions are applied. In particular, we apply extreme value theory (EVT) models to GARCH-filtered residuals to capture excess returns.Drawing on a sample of daily data covering both calm and turbulent market phases, we analyze portfolios consisting of German Stocks, national indices and FX-rates. VaR forecasts are evaluated using statistical backtesting and Basel II criteria. The extensive empirical application favors the elliptical copula approach combined with extreme value theory (EVT) models for individual returns. 99% VaR forecasts from the EVT-GARCH-copula model clearly outperform estimates from alternative models accounting for dynamic conditional correlations and volatility spillover for all asset classes in times of financial crisis.     

Market Risk of Developed and Emerging Countries During the Global Financial Crisis

This study compares the performance of the widely used risk measure, value at risk (VaR), across a large sample of developed and emerging countries. The performance of VaR is assessed using both the unconditional and conditional tests of Kupiec and Christoffersen, respectively, as well as the quadratic loss function. The results indicate that VaR performs much more poorly when measuring the risk of developed countries than of emerging ones. One possible reason might be the deeper initial impact of the global financial crisis on developed countries. The results also provide evidence of the decoupling of the market risk of emerging and developed countries during the global financial crisis.     

Time Variation in Diversification Benefits of Commodity, REITs, and TIPS

Diversification benefits of three “hot” asset classes—Commodity, Real Estate Investment Trusts (REITs), and Treasury Inflation-Protected Securities (TIPS)—are well-studied on an individual basis and in a static setting. Using data from 1970 to 2010, this paper documents both that the three asset classes are in general not substitutes for each other, and that diversification benefits of each asset class change substantially over time. Therefore, all three asset classes ought to be included in investors’ portfolios. Furthermore, we show that the observed time variation in diversification benefits can be explained by time-varying return correlations. To see the implications of these findings for asset allocation in practice, we examine the out-of-sample performance of portfolio strategies, based on a variety of correlation structures. We find that the Dynamic Conditional Correlation (DCC) model (Engle, J Bus Econ Stat 20(3):339–350, 2002) outperforms other correlation structures, such as rolling-window, historical, and constant correlations. Our findings suggest that diversification benefits of the three asset classes should be examined in a dynamic setting, and that investors need to use appropriate correlation estimates to adjust for such time variation.     

Forecasting market risk of portfolios: copula-Markov switching multifractal approach

This paper proposes a new methodology for modeling and forecasting market risks of portfolios. It is based on a combination of copula functions and Markov switching multifractal (MSM) processes. We assess the performance of the copula-MSM model by computing the value at risk of a portfolio composed of the NASDAQ composite index and the S&P 500. Using the likelihood ratio (LR) test by Christoffersen [1998. “Evaluating Interval Forecasts.” International Economic Review 39: 841–862], the GMM duration-based test by Candelon et al. [2011. “Backtesting Value at Risk: A GMM Duration-based Test.” Journal of Financial Econometrics 9: 314–343] and the superior predictive ability (SPA) test by Hansen [2005. “A Test for Superior Predictive Ability.” Journal of Business and Economic Statistics 23, 365–380] we evaluate the predictive ability of the copula-MSM model and compare it to other common approaches such as historical simulation, variance–covariance, RiskMetrics, copula-GARCH and constant conditional correlation GARCH (CCC-GARCH) models. We find that the copula-MSM model is more robust, provides the best fit and outperforms the other models in terms of forecasting accuracy and VaR prediction.     

Dynamic Correlations Among Asset Classes: REIT and Stock Returns

We use the Dynamic Conditional Correlation model with Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH) developed by Engle (Journal of Business & Economic Statistics 20(3):339–350, 2002) to examine dynamics in the correlation of returns between publicly traded REITs and non-REIT stocks. The results suggest that REIT-stock correlations form three distinct periods. During the first period, ending in August 1991 with the start of the modern REIT era, correlations were high and without trend, never dipping below 59%. During the second period, ending in September 2001 with the inclusion of REITs in broad stock market indexes, correlations declined precipitously to 30%, enabling substantially higher portfolio allocations to both high-return asset classes and therefore higher portfolio returns without increasing portfolio volatility. During the third period, since September 2001, correlations increased steadily but only reached 59% in late 2008. A simple portfolio optimization suggests that asset managers would be willing to pay 20 basis points per year, plus the difference in transaction costs, for the ability to use DCC-GARCH modeling of dynamic correlations in place of rolling 24-month asset correlations.     

European equity market integration and joint relationship of conditional volatility and correlations

We analyse the integration patterns of seven leading European stock markets from 1990 to 2013 using daily data and mismatched monthly macroeconomic data. To study the mismatch of data frequencies we use the DCC-MIDAS (Dynamic Conditional Correlation – Mixed Data Sampling) technique developed by Colacito, Engle and Ghysels (Journal of Econometrics, 2011). We benchmark European integration patterns against the German stock market. The reported integration patterns show a clear divide between large and (relatively) small equity markets' short run and long run return correlations: the small markets display higher short run European convergences than the large markets and vice versa. The across-the-board divergence from Greek risk, during the crisis period, is the most unambiguous conclusion of our study. During this period, cross-country joint relationships of conditional variances and return correlations – a ‘convergence of risks’ resulting in global/regional contagious spillovers – are typically positive. Only exceptions are the German stock market's joint relationships.     

Testing for structural breaks in correlations: Does it improve Value-at-Risk forecasting?

In this paper, we modify the Constant Conditional Correlation (CCC) model and its dynamic counterpart, the Dynamic Conditional Correlation (DCC) model by combining them with a pairwise test for constant correlations, a test for a constant correlation matrix, and a test for a constant covariance matrix. We compare these models to their plain counterparts with respect to the accuracy for forecasting the Value-at-Risk of financial portfolios by a set of distinct backtests. In an empirical horse race of these models based on multivariate portfolios, our study shows that correlation models can be improved by approaches modified by tests for structural breaks in co-movements in several settings.     

中美黄金市场的价格发现和动态条件相关性研究

本文运用向量误差修正模型、Hasbrouck信息份额分析法和Engle(2002)提出的动态条件相关多元GARCH模型,研究从2004年11月18日至2008年11月17日期间,中国黄金市场与美国黄金市场的价格发现和动态条件相关性。实证结果发现:中国黄金市场现货和美国黄金市场期货、ETF三者间存在长期均衡关系,美国黄金市场ETF和期货在价格发现过程中居主导地位;中美黄金市场间的相关性随时间变化而动态改变,上海黄金交易所开设夜市交易及延长夜市交易时间,增加了两个市场的关联性,但中国黄金期货的推出和2008年全球金融危机的加深,又使中美黄金市场间的相关性有所降低。     

Dynamic correlations and volatility effects in the Balkan equity markets

This paper investigates the presence of time-varying comovements, volatility implications and dynamic correlations in major Balkan and leading mature equity markets, in order to provide quantified responses to international asset allocation decisions. Since asset returns and correlation dynamics are critical inputs in asset pricing, portfolio management and risk hedging, emphasis is placed on the respective (constant and dynamic) equity market correlations produced by alternative multivariate GARCH forms, the Constant Conditional Correlation and the Asymmetric Dynamic Conditional Correlation models. The Balkan stock markets are seen to exhibit time-varying correlations as a peer group, although correlations with the mature markets remain relatively modest. In conjunction with sensitivity analysis on the asymmetric variance–covariance matrix, active portfolio diversification to the Balkan equity markets indicates to potentially improve investors’ risk-return trade-off.     

The factor structure of time-varying conditional volume

We document a set of instruments that explain a large fraction of the time series variation in turnover between 1966 and 2003. We use these relations in latent variable tests that examine the number of predictable factors that drive conditional expected time-varying turnover. After refining the weighting matrix as suggested by Ferson and Foerster [Ferson, W. and S. Foerster, 1994. “Finite Sample Properties of the Generalized Method of Moments in Tests of Conditional Asset Pricing Models.” Journal of Financial Economics 36, 29–55.] and Bekaert and Urias [Bekaert, G. and M.S. Urias, 1996. “Diversification, Integration and Emerging Market Closed-End Funds.” Journal of Finance 51, 835–869.] and accounting for dimensionality as suggested by Gallant and Tauchen [Gallant, R. and G. Tauchen, 1991. “Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications.” Econometrica 57, 1091–1119.], we reject a one-factor model. However, this rejection is partially driven by non-stationarity. When we correct for non-stationarity by using normalized turnover, we reject a single-factor model in the second half of our sample but not in the first. Our work extends recent work by Tkac [Tkac, P.A., 1999. “A Trading Volume Benchmark: Theory and Evidence.” Journal of Financial and Quantitative Analysis 34, 89–114.] and by Lo and Wang [Lo, A. and J. Wang, 2000. “Trading Volume: Definitions, Data Analysis, and Implications of Portfolio Theory.” Review of Financial Studies 13, 257–300.] who develop and test implications of share turnover for asset pricing relations.     

A Bayesian encompassing test using combined value-at-risk estimates

The Value at Risk (VaR) is a risk measure that is widely used by financial institutions in allocating risk. VaR forecast estimation involves the conditional evaluation of quantiles based on the currently available information. Recent advances in VaR evaluation incorporate conditional variance into the quantile estimation, yielding the Conditional Autoregressive VaR (CAViaR) models. However, the large number of alternative CAViaR models raises the issue of identifying the optimal quantile predictor. To resolve this uncertainty, we propose a Bayesian encompassing test that evaluates various CAViaR models predictions against a combined CAViaR model based on the encompassing principle. This test provides a basis for forecasting combined conditional VaR estimates when there are evidences against the encompassing principle. We illustrate this test using simulated and financial daily return data series. The results demonstrate that there are evidences for using combined conditional VaR estimates when forecasting quantile risk.     

The intertemporal capital asset pricing model with dynamic conditional correlations

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.     

Financial forecasts in the presence of asymmetric loss aversion, skewness and excess kurtosis

We present closed-form results for the out-of-sample forecasts under the joint presence of asymmetric loss and non-normality, extending the results of Granger [1969. Operations Research Quarterly 20, 199–207; 1999. Spanish Economic Review 1, 161–173] and Christoffersen and Diebold [1997. Econometric Theory 13, 808–817]. We consider the LinEx and Double LinEx loss functions and non-normal distributions in the form of the Gram–Charlier class. We show how the preference asymmetries interact with the distribution asymmetries to determine optimal forecasts which contain the optimal predictors under symmetry and normality as special cases. We also examine the implications of our results for the development of forecast rationality tests, extending the work of Batchelor and Peel [1998. Economics Letters 61, 49–54]. Our results are relevant for the design of efficient investment and risk management policies.     

Oil vs. gasoline: The dark side of volatility and taxation

This paper investigates the relation between gasoline volatility and crude oil volatility. The objective is to examine whether the so-called asymmetric relation between gasoline and oil prices still holds for volatility, particularly, when considering the taxation effect. The approach hinges on the Volatility Threshold Dynamic Conditional Correlation (VT DCC) model. An application to the U.S. WTI oil volatility and the U.S. premium gasoline volatility is provided from 1990 to 2015. The main results reveal that oil volatility influences gasoline volatility, but without any form of asymmetry. The role of taxation seems to particularly affect the volatility of volatility for gasoline.     

Forecasting Value-at-Risk using high frequency data: The realized range model

Current studies on financial market risk measures usually use daily returns based on GARCH type models. This paper models realized range using intraday high frequency data based on CARR framework and apply it to VaR forecasting. Kupiec LR test and dynamic quantile test are used to compare the performance of VaR forecasting of realized range model with another intraday realized volatility model and daily GARCH type models. Empirical results of Chinese Stock Indices show that realized range model performs the same with realized volatility model, which performs much better than daily models.     

Asian Pacific Stock Market Volatility Modeling and Value at Risk Analysis

The potential for stock market growth in Asian Pacific countries has attracted foreign investors. However, higher growth rates come with higher risk. We apply value at risk (VaR) analysis to measure and analyze stock market index risks in Asian Pacific countries, exposing and detailing both the unique risks and system risks embedded in those markets. To implement the VaR measure, it is necessary to perform "volatility modeling" by mixture switch, exponentially weighted moving average (EWMA), or generalized autoregressive conditional heteroskedasticity (GARCH) models. After estimating the volatility parameters, we can calibrate the VaR values of individual and system risks. Empirically, we find that, on average, Indonesia and Korea exhibit the highest VaRs and VaR sensitivity, and currently, Australia exhibits relatively low values. Taiwan is liable to be in high-state volatility. In addition, the Kupiec test indicates that the mixture switch VaR is superior to delta normal VaR; the quadratic probability score (QPS) shows that the EWMA is inclined to underestimate the VaR for a single series, and GARCH shows no difference from GARCH t and GARCH generalized error distribution (GED) for a multivariate VaR estimate with more assets.     

International stock markets interactions and conditional correlations

This paper investigates the transmission of price and volatility spillovers across the US and European stock markets in bivariate combinations. The framework used encompasses the most popular multivariate GARCH models, with News Impact Surfaces employed for interpretation. By using synchronous data the dynamic conditional correlation model (Engle, R., 2002. Dynamic conditional correlation: a simple class of multivariate GARCH models. Journal of Business and Economic Statistics 20, 339–350) is found to best capture the relationships for over half of the bivariate combinations of markets. Other findings include volatility spillovers from the US to European markets, and a reverse spillover. In addition, the magnitude of the correlation between markets is higher not only for negative shocks in both markets, but also when a combination of shocks of opposite signs occurs.     

Intraday risk management in International stock markets: A conditional EVT approach

The study compares the predictive ability of various models in estimating intraday Value-at-Risk (VaR) and Expected Shortfall (ES) using high frequency share price index data from sixteen different countries across the world for a period of seven and half months from September 20, 2013 to May 07, 2014. The main emphasis of the study has been given to Extreme Value Theory (EVT) and to evaluate how well Conditional EVT model performs in modeling tails of distributions and in estimating and forecasting intraday VaR and ES measures. We have followed McNeil and Frey's (2000) two stage approach called Conditional EVT to estimate dynamic intraday VaR and ES. We have compared the accuracy of Conditional EVT approach to intraday VaR and ES estimation with other competing models. The best performing model is found to be the Conditional EVT in estimating both the quantiles for the entire sample. The study is useful for market participants (such as intraday traders and market makers) involved in frequent intraday trading in such equity markets.