Multivariate GARCH Models for Portfolio Risk Management: A Comparative Study

Regularized semiparametric estimation of high dimensional dynamic conditional covariance matrices

PurposeThis paper aims to test whether the latest global financial crisis propagated contagiously from the USA to the rest of the world.Design/methodology/approachIf the reason of the propagation of a crisis is a normal time interdependence with the crisis origin country due to real linkages, the spread of crisis can be limited by implementing well-defined preventive policies. On the other hand, if a crisis propagates because of the speculative attacks or irrational behaviors, the “national policymakers will face difficulties in protecting their markets from such a crisis” (Kleimeier et al., 2003, p. 2). Therefore, separation of contagion and interdependence may provide crucial insights for policymakers to implement appropriate policies to prevent and/or stop the financial crisis. Hence, this paper compares the heteroscedasticity-corrected conditional correlations and dynamic conditional correlations in the tranquil and shock periods.FindingsThe findings were quite straightforward and consistent for both Forbes and Rigobon heteroscedasticity correction technique and dynamic conditional correlation (DCC) model. The Forbes and Rigobon technique failed to reject the null of no contagion for 25 countries in our data sample, while the DCC model failed to reject the null of no contagion for 21 countries. While heteroscedasticity-corrected correlation technique confirmed the presence of a contagion for six countries, the DCC technique confirmed the presence of a contagion for ten countries.Originality/valueThis study particularly investigates whether the subprime mortgage crisis spilled over contagiously to the rest of the world. To investigate whether there is a significant increase in the cross-market correlations between the crisis origin country, the USA and the rest of the world markets during the latest financial crisis, both heteroscedasticity-corrected correlation technique and DCC model are used.Therefore, this study possibly contributes well to the literature using a large country set and conducting the analysis from different angles for important properties.

금융 시계열 자료들 간의 상관계수는 자산의 배분, 위험관리 그리고 포트폴리오의 선택에 있어서 중요한 역할을 한다. 이러한 상관계수들을 모형화하기 위해 단변량-GARCH 모형을 다변량-GARCH 모형으로 확장시킨 MGARCH류 모형들에 대한 많은 연구들이 진행되고 있다. 특히, CCC 모형 (Bollerslev, 1990)과 DCC 모형 (Engle, 2002)은 다른 모형들에 비해 추정해야 할 모수의 수가 작다는 이점으로 인해 분석에 널리 쓰이고 있다. 본 논문에서는 국내 주가자료에 대해 CCC 모형과 DCC 모형을 적합시킨 후, 각 모형들에 대한 VaR(value at risk)와 사후검증(back-testing), 결합예측영역(joint prediction region) 등을 통하여 두 모형의 예측 능력을 비교해 보고자 한다. Conditional correlation between financial time series plays an important role in risk management, asset allocation and portfolio selection and therefore diverse efforts for modeling conditional correlations in multivariate-GARCH processes have been made in last two decades. In particular, CCC (cf. Bollerslev, 1990) and DCC(dynamic conditional correlation, cf. Engle, 2002) models have been commonly used since they are relatively parsimonious in the number of parameters involved. This article is concerned with DCC modeling for multivariate GARCH processes in comparison with CCC specification. Various multivariate financial time series are analysed to illustrate possible advantages of DCC over CCC modeling.

This paper introduces the Flexible Dynamic Conditional Correlation
\n(FDCC) multivariate GARCH model which generalizes the Dynamic
\nConditional Correlation (DCC) multivariate GARCH model proposed by Engle (2002). The FDCC model relax the assumption of common dynamics among all assets used in the DCC model. In fact, we cannot impose that the correlation dynamics of, say, European sectorial stock indexes are identical to the corresponding US ones. We thus extend the DCC model introducing a block-diagonal structure; in the FDCC the
\ndynamics are constrained to be equal among groups of variables.
\nWe present an application to a sectorial asset allocation problem.

Correlations and volatility spillovers between oil prices and the stock prices of clean energy and technology companies

The uncertainty of conditional returns, volatilities and correlations in DCC models

A Model of Price Correlations between Clean Energy Indices and Energy Commodities

Purpose This paper analyzes conditional correlations and volatility transmission between Latin American and US stock markets during the pre- and post-COVID-19 periods. Design/methodology/approach The study employs a range of econometric techniques, including six-dimensional BEKK-GARCH models and the Dynamic Conditional Correlation (DCC) model, to examine market interdependencies through spillover effects–specifically mean-to-mean, volatility-to-mean and volatility-to-volatility transmissions. It also conducts hedge ratio and optimal portfolio analyses to develop informed investment strategies. Findings The results reveal that while correlations between the markets are generally positive, they are moderate in strength and become more pronounced after the onset of the pandemic. Volatility transmission is particularly strong between the USA and Brazilian markets. Mexico, exhibiting lower correlations, presents opportunities for cost-effective hedging. In contrast, the Argentine market's high volatility reduces its suitability for inclusion in optimal portfolios. Originality/value This study offers a novel contribution by integrating BEKK and DCC models with hedging and portfolio optimization frameworks, enhancing the understanding of spillovers and conditional correlations among Latin American and US equity markets. The research highlights the rise in market correlations following the COVID-19 crisis, suggesting reduced market decoupling during periods of global stress. It also considers the political and economic implications of these dynamics, including the influence of US Federal Reserve interest rate movements on conditional correlations across countries.

The paper develops two Dynamic Conditional Correlation (DCC) models, namely the Wishart DCC (WDCC) model and the Matrix-Exponential Conditional Correlation (MECC) model. The paper applies the WDCC approach to the exponential GARCH (EGARCH) and GJR models to propose asymmetric DCC models. We use the standardized multivariate t-distribution to accommodate heavy-tailed errors. The paper presents an empirical example using the trivariate data of the Nikkei 225, Hang Seng and Straits Times Indices for estimating and forecasting the WDCC-EGARCH and WDCC-GJR models, and compares the performance with the asymmetric BEKK model. The empirical results show that AIC and BIC favour the WDCC-EGARCH model to the WDCC-GJR and asymmetric BEKK models. Moreover, the empirical results indicate that the WDCC-EGARCH-t model produces reasonable VaR threshold forecasts, which are very close to the nominal 1% to 3% values.

The commonality in idiosyncratic volatility cannot be fully explained by time-varying volatility; correlated idiosyncratic volatility shocks are an important contributing factor. We empirically document this fact for various characteristic-sorted portfolios and industry portfolios. To capture the commonality in idiosyncratic volatility, we propose a novel multivariate generalized autoregressive conditional heteroscedasticity (GARCH) model called dynamic factor correlation (DFC). The DFC model has a closed-form likelihood function that allows computationally cheap estimation, even for a large number of assets. The DFC model improves statistical fit compared with existing multivariate GARCH models such as the dynamic conditional correlation model and the dynamic equicorrelation (DECO) model, achieving the lowest root mean square error and mean absolute error in simulations. Empirical tests also corroborate simulations in demonstrating the improved statistical fit of the DFC model. Mean--variance portfolio optimization using the DFC model outperforms alternative volatility models such as the historical covariance matrix and the DECO model. Out-of-sample mean--variance-efficient portfolios using the DFC model have the lowest volatility and the highest Sharpe ratios, thereby improving the investor's opportunity set. Under parametric restrictions, the DFC model reduces to the constant conditional correlation model or the DECO model.

Modeling volatility and correlations between emerging market stock prices and the prices of copper, oil and wheat

The purpose of this paper is to investigate dynamic changes of the volatilities among stock indices, exchange rates, and interest rates in Taiwan, America, and South Korea during and after the period of American 9/11 terrorist attacks. Using sample data from October 1, 1999 to January 24, 2006, this study applies the Dynamic Conditional Correlation Multivariate GARCH model proposed by Engle (2002) to estimate the volatilities of markets themselves and the dynamic conditional correlations between different markets. The empirical results show: (1) during the period of 9/11 incident, both the short-run volatilities of every market and the short-run dynamic correlations between different markets enlarged significantly, but all correlations with a time lag of one day; (2) after 9/11 incident, the long-run volatilities of stock and exchange markets in all countries enlarged significantly, but the volatilities of interest rate markets diminished significantly or changed insignificantly; the long-run dynamic correlations between the same markets of different countries changed significantly, but the correlations between different markets of the same countries changed insignificantly.

As the nexus between Islamic financial market indexes and energy commodities becomes more global, the question of whether any specific shock considerations are still relevant that might affect this relationship arises. In order to answer it, our paper examines this question by testing the dynamic conditional correlation (DCC) betwee the Qatar Exchange Al Rayan Islamic Index and two energy commodities (crude oil and natural gas) by including structural breaks in the DCC-generalized autoregressive conditional heteroscedasticity (GARCH) model, as introduced by Engle in "Dynamic conditional correlation: a simple class of multivariate GARCH models" (2002), over the period from March 15, 2011 to December 25, 2014. Our findings reveal that the volatility of commodity returns is strongly correlated to that of the Al Rayan Islamic Index, and the volatility persistence decreases by its lowest amount after incorporating structural breaks. Interesting implications emerge from this paper for both policy makers and portfolio risk managers.

PurposeThis study aims to investigate the possibilities of cryptocurrencies as hedges and diversifiers in the Indian stock market before and during financial crisis due to the pandemic and the Russia–Ukraine war.Design/methodology/approachResearchers have used daily data on cryptocurrencies and Indian stock prices from March 10, 2015 to August 26, 2022. The researchers have used the dynamic conditional correlations (DCC)-GARCH model to determine the volatility spillover and dynamic correlation between stocks and digital currencies. Further, researchers have explored hedge ratio, portfolio weight and hedging effectiveness using the estimates of the DCC-GARCH model.FindingsThe findings indicate a negative conditional correlation between equities and cryptocurrencies before the crisis and a positive conditional correlation except for Tether during the crisis. Which implies that cryptocurrencies serve as a hedging asset in the stock market before a crisis but are not more than a diversifier during the crisis, except for Tether. Notably, Tether serves as a safe haven during times of crisis. Finally, the study suggests that Bitcoin, Ethereum, Binance Coin and Ripple are the most effective diversifiers for Indian stocks during the crisis.Originality/valueThis study makes several contributions to the existing literature. First, it compares the hedge and diversification roles of cryptocurrencies in the Indian stock market before and during crisis. Second, the study findings provide insights on risk hedging and can serve as a guide for investors. Third, it may help rational investors avoid underestimating risk while constructing portfolios, particularly in times of financial turmoil.

The effects of commodity financialization on commodity market volatility