With the development of the economy and the flourishing of the stock market, stock indexes have been identified as important social and economic indicators that can comprehensively reflect the overall trends and performance of the stock market. Based on the sheer size and breadth, global stock markets play a decisive role in global financial performance. Along with the increasingly closer economic ties amongst all countries, rapid capital flows are not rare in modern global stock markets, allowing for fast and frequent transactions, resulting in markets that tend to have higher dependencies on each other. Economic globalization has created accessibility and convenience for investors, managers, and relevant officers in financial markets, with the drawback being the acceleration of the risk contagions.
Global stock markets play a decisive role in global financial performance. Along with increasingly closer economic ties amongst all countries, rapid capital flows are not rare in modern global stock markets, which enable fast and frequent transactions, resulting in markets having higher dependencies amongst themselves. The financial crisis of 2008 is considered as the worst financial crisis since the Great Depression, and its consequences not only included production curtailment but also rapid destruction of the financial system in a short timespan. It has also triggered renewal of the notion of financial regulation (e.g., macro-prudential policy) and the concept of systemic risk. Systemic risk includes the potential fluctuations, losses, and crises of the whole financial system influenced by relevant financial activities, policies, transactions, and so on [1
]. Influenced by the financial crisis, global stock markets faced a huge slump. Among all possible explanations for this catastrophe, mis-prediction and ignorance of potential risk are the main topics (see [2
] and others). To reduce the risk of a financial crisis, measuring and monitoring the potential risk of global stock markets is important. Therefore, studies that focus on measurement of systemic risk in global stock markets are essential.
Systemic risk is defined as the risk of distress in a various group of institutions. Different from systematic risk, systemic risk represents a severe degree of loss and a large proportion of the institutions [5
]. Measurements of systemic risk were examined from various perspectives. Many scholars focused on measuring or forecasting systemic risk. For example, Bartram et al. [6
] estimated the risk of systemic failure in the global banking system. Song et al. [7
] used stock markets in G20 nations to represent global financial market and estimated financial risk from 2007 to 2018. However, most other studies measured systemic risk in some countries or regions. For example, Acharya et al. [8
], Browlees and Engle [9
], and Banulescu and Dumitrescu [10
] used a similar dataset of stock market to forecast systemic risk for the USA financial market. Reboredo and Ugolini [11
] measured systemic risk in the European sovereign debt market. Bartels and Ziegelmann [12
] measured systemic risk in Brazil Sao using 44 time series of financial assets from the Sao Paulo Stock Exchange. Shahzad et al. [13
] analyzed spillover effect and systemic risk of Islamic equity markets. Other studies focused on the systemic risk of special financial markets, such as securities markets [14
], banking system [15
], and default swap [5
]. Scholars have considerably contributed to regional financial markets in terms of examining systemic risk.
Scholars have also contributed by developing quantitative models to measure or forecast systemic risk. Studying the dependence between a large collection of assets is required for general analysis of systemic risk [5
]. Thus, most scholars proposed methods that are a combination of dependence modelling and risk measuring methods to measure or forecast systemic risk. With regard to dependence modelling, mainstream models, such as Dynamic Conditional Correlation-GARCH and copula-GARCH, reduce the dimensions of data to two: Individual firm and stock market index, e.g., Browlees and Engle [9
], Wu et al. [16
], Yun and Moon [17
], Banulescu and Dumitrescu [10
], Calabrese and Osmetti [18
], and Wei et al. [19
]. These methods have the clear benefit of being parsimonious. To handle large collections of data, some researchers applied vine copula-GARCH approaches into dependence and risk analysis, such as Liu et al. [20
], Reboredo and Ugolini [21
], Pourkhanali et al. [22
], Shahzad et al. [13
], and Song et al. [7
]. In vine copula-GARCH approaches, the number of parameters exponentially increase with an increase in the number of variables, which restricts their application to high-dimensional data. Recently, factor copula-GARCH models have been proposed and extended to the application of systemic risk analysis [5
]. Different types of factor copula-GARCH approaches were proposed by Oh and Patton [23
] and Krupskii and Joe [24
]. The factor copula of Krupskii and Joe [24
] can be easily interpreted and is able to capture linear or nonlinear correlations between any asset and latent variables compared to the one proposed by Oh and Patton [23
Under the measurement framework of systemic-risk-based dependence modelling, some scholars proposed some methods of risk measurement that can be widely applied to various financial markets. One prominent measurement method is the marginal expected shortfall (MES) proposed by Acharya et al. [25
], which has been widely applied by many, such as Tiwari et al. [26
], Kleinow et al. [27
], and Benoit et al. [28
]. The MES measures marginal contribution of one financial institution or firm to total loss, but it cannot accurately reflect total loss or systemic risk. The other systemic risk measure is the delta conditional value-at-risk (CoVaR), proposed by Adrian and Brunnenneier [29
]. The delta CoVaR method can be used to measure the spillover effects of systemic risk, but lacks sub-additive calculations. For instance, Reboredo [21
] investigated systemic risk and dependence between oil and renewable energy markets in the United States; Reboredo and Ugolini [30
] examined systemic risk in European sovereign debt markets before and during the Greek debt crisis; Reboredo et al. [31
] studied systemic risk spillovers between currency and stock markets in emerging economies. On the basis of MES and CoVaR, the component expected shortfall (CES) was developed by Banulescu and Dumitrescu [10
]. The CES can be used to measure a system’s aggregate loss using expected shortfall (ES), and also allows us to measure the contribution of one institution to systemic risk [15
]. Therefore, this method is conductive to identifying important institutions systematically, thereby providing guidelines for formulating more relevant policies for governments and financial institutions.
Through reviewing the aforementioned literature, we summarize the main points of the existing literature as follows: First, systemic risk has been a major concern and many scholars have conducted related researched from various perspectives. No study to date has investigated the systemic risk of global financial markets using high-dimensional data. Second, a variety of rich analytical methods are available for analyzing systemic risk, and have solved the problems of high-dimensional distribution, spillover effects, contribution of individual institutions to total risk, and magnitude of systemic risk. However, most of the methods do not allow for nonlinear correlation of financial assets in high-dimensional data.
Given this backdrop, we investigated the systemic risk of the global financial markets using the factor copula-GARCH models of Krupskii and Joe [24
] and CES method. The stock markets of 43 major countries (G20 and European Union (EU) nations) were used to represent the global financial markets. The factor copula-GARCH models allow for better flexibility in joint distributions than vine copula, and capture nonlinear dependence and tail dependence between financial assets and latent variables. The latent variables were aggregated from many exogenous variables, such as crude oil price, political factors, interest rates, debt-to-GDP ratio, etc. For example, the co-movement and the spillover effect between crude oil price and the stock market performance were demonstrated in different countries [34
]; and government debt and debt-to-GDP ratios are also key factors that influence the stock returns [36
]. A large collection of assets representing global financial markets would improve the accuracy of systemic risk measurement. Therefore, there are three main contributions in this paper. First, to the best of our knowledge, this is one of the earliest attempts to investigate the systemic risk of the global financial markets using high-dimensional data. Second, we combine the factor copula-GARCH models with the CES approach for the first time, and applied the method to measure the systemic risk of global financial markets. Third, the measurement of systemic risk of global financial markets was used to diversify portfolios. A deeper understanding of the systemic risk and Banulescu portfolios may help investors and policymakers to design sound investment and risk management strategies and efficient macroeconomic policies.
The remainder of the paper is structured as follows: Section 2
describes models for marginals, factor copulas, and component expected shortfall. Section 3
describes the data. Section 4
presents the results. Section 5
provides our conclusions and policy implications.
The main objectives of this study were to measure and forecast systemic risk in the global financial markets and then construct a trade decision model based on the results of CES predictions for investors and financial institutions to assist them in forecasting risk and potential returns. To this end, the GJR-GARCH (1,1), factor copula-GARCH models, and component expected shortfall (CES) were combined for the first time. A high-dimensional dataset of daily stock market indices of 43 countries covering the period 2003 to 2019 were used to represent the global financial markets.
The results revealed the practicality of the factor copula models and their ability to catch tail dependence even during the financial crisis period. Firstly, the parameters used to measure sensitivity to the latent variables are consistent with common knowledge, which indicates the accuracy of the estimations. Secondly, ES predictions are in line with the graph showing a higher level of risk during the crisis period than the other two periods. Thirdly, the functionality of the predictions with regard to high-dimensional data was proven. The CES% varied from the pre-crisis to the post-crisis period, which indicated structural changes in systemic risk, that is, the CES% of the USA continued to decrease, but it still contributed more than 60% to total systemic risk. Generated from the minimization of the CES notion, CES portfolios were examined, which performed well for all crisis periods for our dataset. This illustrated the importance of risk diversification and proved that even during the crisis period, there are still opportunities to gain a profit.