Modeling Multivariate Returns and Volatilities of Three Important Groups of Stock Indices in the World Stock Markets

Abstract

Stock markets are one among the most influential forms of physical economy in the today’s world. They play a prominent role in all economies because many kinds of investors, including financial institutions invest in financial markets. This entails risk or volatility of returns, and these which are among the most important factors in portfolio or risk management. Volatility across stock markets around the world is linked to the behavior of investment decisions and behavior of investment made by investors. The study of the variance, covariance and correlations in stock market indexes is a useful means of providing information to investors seeking to efficiently build and maintain their portfolios over time. To accomplish their intention that end, some specific tools such as market models and based on historical data are needed required. This thesis proposes the use of financial econometrics which is the multivariate of returns and volatilities models to find the volatility and dependency of behavior in investment and financial data. The major contribution of this thesis is that it proposes and compares appropriate financial econometric models employing multivariate GARCH, comprising DVECH-GARCH, BEKK-GARCH, CC-GARCH, DCC-GARCH, VARMA GARCH, and VARMA AGARCH models. In particular, the study notes that the C-vine copula based ARGARCH model employing one-step estimation allows greater flexibility in accommodating joint distributions since a copula with two-step estimation may fail to efficiently capture the parameters of an AR GARCH model, which are assumed to be independent in two-step estimation, but is dependent in one-step estimation, and can thus be used to predict the volatilities of returns in the stock markets. Hence, the study examined the performance of various competing financial econometric models, which could be empirically applied to stock market data from around the world. The thesis adopted as case studies three important groups of stock markets around the world comprised of 1) the ASEAN stock market group 2) the BRICS stock market group and 3) the world stock market group which consist two groups of countries and three main stock markets in the world as a proxy for the returns during the period, 2008 to 2019. Each segment is carried out through the financial econometric models which stated above. Consequently, the study concluded that the C-vine copula is the most suitable model among these models investigated, for estimating the return, volatility and dependency of the stock markets, since the results show that the C-Vine copula-based AR-GARCH model with one step estimation outperform the existing multivariate returns and volatilities models based on the lowest value of model selection. In the first group studied, the volatilities and linkages between the stock markets of five ASEAN countries (Thailand, the Philippines, Indonesia, Malaysia and Singapore) were diagnosed using a C-Vine copula-based AR (3)-GARCH model with Frank copulas through one-step estimation. The empirical findings reveal that volatility in any period in these countries’ markets was significantly influenced by events occurring in previous periods which Thailand and the Philippines have highest volatility in term of ARCH and GARCH terms, respectively. Moreover, Thailand’s highly integrated investment showed significant linkage of the Philippines, and this has become much stronger than the other economies. Therefore, the stock market of the Philippines is one to which investors in Thailand should pay special attention in terms of its risk and stability, in order to avoid the potential for asymmetric risk caused by the spillover effect between the two markets. It was notable however, that the correlation between Malaysia and Singapore was the lowest among the ASEAN countries and their respective governments should endeavor to encourage a closer investment relationship between these two countries.The second group of stock markets studied was the BRICS group consisting of Brazil, Russia, India, China and South Africa and data relating to the stock indexes of those nations were used to explore the volatilities and relationships among them using a C-Vine copula-based AR (1)-GARCH model with Frank copulas. The empirical results showed that the estimation results obtained from the one-lagged AR model of stock market returns based on the stock market indexes for the five countries, was able to predict the current index values as well as the volatility of those indexes, showing how past information can cause volatility in the current level of stock market indexes. In respect of the dependencies traced among these five countries, it was found that Brazil is highly correlated with China, which is currently one of the markets with the highest potential for growth in the world. Meanwhile, the correlation between India and South Africa was the smallest and the governments of these two countries should provide incentives to encourage the development of investment linkage between them. Furthermore, the investors who are risk averters can divide their investment into these two countries in order to avoid some risk or big losses that may happen in one of these stock markets. The final group studied consisted of the world stock market group with the volatility and dependence structure being identified based on the correlations between three national stock markets (the US, Japanese and Chinese) and two regionally grouped stock markets (European and ASEAN) using the C-Vine copula-based AR (1)-GARCH model with a mixture of student-t and Frank copulas through one-step estimation. The results showed that the parameters of the mean and variance model of marginal distribution provided either definitive or very strong evidence that past events have an influence on market behavior in a current period in terms of both returns and volatility. Furthermore, the investigation of the dependence structure showed that among the five markets studied, the USA and Europe had the strongest relationship, due to the fact that the USA and Europe are advanced economies and powerful countries. Therefore, information about the policies of developed countries and negative events occurring in them is crucial for investors in planning their investments and for policymakers to improve the policies they adopt because the advanced economy is the more spillover effect it likely to produce across the global economy since these two countries are the leader in the global stock market.