Since the early 2000s, the economic growth of the BRICS countries, excepting that of Russia during the 2007 financial crisis, has been significantly higher than any other of the developed countries. For example, within the last twenty years, China has registered particularly high growth rates. Brazil, India and South Africa have political systems similar to that of the Western democracies, whereas Russia and China have rather authoritarian regimes. Economically, there are great differences between the States (the hydrocarbons in Russia or the mines in South Africa), and those which have a more diverse industrial tissue, such as Brazil and China. BRICS countries have many points in common which puts them among the emerging countries: trade between the BRICS members is still limited, only 3.5% of Brazil’s exports go to Russia, India and South Africa. These economies are ultimately rather competing, especially between India and China in the industrial sector or South Africa and China in the clothing industry. However, these countries are aware that their unity is crucial to change the political order of the world and facilitate better representation of the developing countries within international organizations. The position of the BRICS in the global economy continues to gain much importance. Today, the BRICS have a GDP exceeding 11,000 billion Euros and account for nearly 3 billion people, or about 40% of the world population.  The global financial crisis had the effect of reducing the performance of the emerging countries making their stock index development more or less similar to that of the financial markets of the developed countries, even less favorable over the previous two years. Our investigation is motivated by the fact that the BRICS countries are the main beneficiaries of the global investment flows and among the world's leading commodity consumers. Consequently, changes in the world economic factors could be a channel through which fluctuations of the economic and financial conditions in the world, like the recent world financial crisis, are transmitted to the stock markets of the BRICS countries by affecting their economic growth. Moreover, international investors are particularly interested in the Co-movements of the stock markets of the BRICs countries with these world factors. argue that the only way BRICS countries would be able to weather the next financial crisis would be by undertaking trade. Through trade and collection, and a large amount of foreign reserves together with fiscal reform, emerging countries would be able to isolate themselves from the external shocks that may negatively impact on the financial markets and economies.  However, it is trade that led the emerging countries into lowered growth from mid-2008. The falling demand of consumption led to a fall in exports. Combined with the pull of the currency contagion, channel presence in the traditional dollar-trading markets and those artificially pegged to the dollar, the financial markets experienced a decrease in market capitalization and liquidity, the performance of which was found to be affected by the intensive bad news from the West. This paper examines the dynamic correlation and the integration level between the BRICS countries. By applying the Asymmetric DCC GARCH approach and the econometric tests (linear correlation, functions of impulse responses, decomposition of the forecasting error variance and tests of causality in the Granger sense), our results show that the linear correlation analysis reveals that the strongest correlation is detected between Brazil and South Africa (0.426) followed by India and South Africa (0.381) and then Brazil and India (0.315). The causality test in the Granger sense shows asymmetrical causality directions between BRICS countries. The results of the variance decomposition emphasize that Brazil proves to be sensitive to the fluctuations undergone by the Indian, South-African and Russian stock markets. The analysis of the impulse response functions highlights that a shock on BOVESPA index involves a positive response on behalf of all the other indices. Nevertheless, the (RTSI and FTSE SA) positively react to a shock exerted on the Indian index but China and Brazil seem independent.  At the empirical stage, we use the Bivariate A-DCC approach with a GJR-GARCH specification to estimate the conditional correlations, the conditional covariances and variances. The choice of this model is motivated by several reasons. First, this model allows us to take into account an important feature of time series namely the asymmetry in the dynamics of markets. Ederington LH Second, some previous studies reveal the asymmetric feature of stock market’s behavior ie negative shocks have more impact than positive shocks of equal magnitude [1]. Our results indicate the high persistence of volatility over time. This dependence structure is often asymmetrical and affected by the emergence of the recent world financial crisis. The remainder of this article is organized as follows: section 2 presents a literature review, section 3 discusses the methodology, section 4 describes the data, sections 5 and 6 represent the  results of econometric tests and Asymmetric DCC GARCH respectively, section 7 focuses on the in the interpretation of DCC graphs and the last section concludes.

Given the various interest reasons of the contagion study and the volatility transmission of the financial crises on the stock markets, there is a vast literature relating to the analysis of the relation between the financial crises and the evolution of the relation between the BRICS countries. Ono.2011 examined the systemic impact of the oil prices on the stock market outputs for the four BRIC countries (Brazil, Russia, India and China). He found that oil price increases raise the stock index prices for all these countries, except for Brazil. The studies which dealt with the BRICS’ stock markets use various methods to explain contagion or the extreme co-movements involving these markets. Applied the copulas to examine the extreme interdependences of the BRIC’s countries with the US markets and highlighted a dynamic dependence between them [2]. By applying the ARCH (DCC-FIAPARCH) model, Dimitriou noted a growing co-movement between the BRICS and the US markets during the post-crisis period which implies that dependence is larger on the bullish markets than on the bear ones [3]. Similarly, Hwang examined the dynamic conditional correlations between the United States and ten emerging stock markets (the BRICS countries, South Korea, Thailand, Philippines, Taiwan and Malaysia)[4]. The authors concluded a transmission from volatility in the crisis period towards the emerging economies. Using a new process of DCC decomposition, Zhang provide solid evidence that the recent financial crisis changes the conditional correlations between the developed countries (the United States and Europe) and the BRICS’ stock markets. They also noted that 70% of the conditional correlation of the BRICS’ stock markets showed a long-term upwards trend with the developed stock markets during the world-wide crisis [5-6]. Gilenko and Fedorova  used the BEKK-GARCH-in-MEAN model with four dimensions to study the links of the BRIC group with the rest of the world during the pre- and post-crisis period [7]. They suggested that the links between the developed countries and BRIC stock markets changed considerably after the crisis. By using both a regime-switching model of the multivariate Gaussian copulate and the approach of the generalized asymmetrical conditional dynamic correlation (AG-DCC), Kenourgios showed that the BRIC emerging markets are more prone to financial contagion. Hentschell has proposed a model which encompasses these three effects and provides an overview of the above mentioned univariate asymmetric GARCH parameterization [8]. Recent evidence Hansen and Lunde has shown that not only do these models perform better in-sample, but they also produce superior forecasts. While asymmetries in conditional volatilities have been thoroughly empirically verified, the efforts to capture asymmetric effects in multivariate settings, however, have been far rarer. Presently, there are only two models capable of capturing asymmetric effects in correlation in a multivariate GARCH model. The first to model asymmetric effects was Kroner and Ng. The model they proposed allows for asymmetric effects in both the variances and covariance. An alternative multivariate GARCH parameterization which permits to capture asymmetries in variances (but not in correlations) is the Dynamic Conditional Correlation (DCC) GARCH model of Engle. Sheppard has extended the DCC model to allow for asymmetric dynamics in the correlation in addition to the asymmetric response in variances (which were available in the original DCC model). Moreover, while the original DCC model assumed that all assets shared the same news impact curve for correlation, Sheppard’s specification is able to accommodate different news impact curves for correlations across distinct assets (Figure 1).

Many previous studies use the dynamic conditional correlation (DCC) GARCH model to analyze dynamic correlations Hammoudeh, Chang, Ciner Creti. For instance, Chang use DCC-GARCH approach to investigate time-varying correlations between precious metals and exchange rates. Suggest that this specification is appropriate to examine time-varying correlations between commodity and economic variables. In this paper we use the asymmetric dynamic conditional correlation (A-DCC) model introduced by Cappiello [9]. It allows us to investigate asymmetric responses in conditional variances and correlations during periods of shocks. The conditional mean process is expressed as follows:

Rt = μ + ? Rt-1 + εt                                                                                                                                

εt = et √Ht                                                                                                                                          

Where Ht is the variance-covariance matrix defined as follows:

Ht = D_t P_t D_t                                                                                                                                                                                     

Where D_t = diag ( , )                                                                                                                       

Represents a diagonal matrix of standard deviations obtained from the estimation of the univariate Glosten, Jagannathan and Runkle’s (1993) (JGR-GARCH) model expressed by:

h_t = ω + α₁ε²_t-1+β₁ h_t-1 + γ s_t-1 ε² _t-1                                                                                                     

and P_t is a positive matrix given by:

P_t = (diag (Q_t) )^-1/  Q_t (diag (Q_t)) ^-1/2                                                                                                  

With reference to Cappiello et al (2006) correlation evolution is defined as follows:

Q_t = (P – A’PA – B’PB – G’NG) + A’ε_t-1 ε’_t-1 A + B’Q_t-1 B + G’η _t-1 η’_t-1 G   

Where A, B and G are k×k parameter matrices,

P = [ε_t ε_t’]; ηt = [ε_t<0]°ε_t                                                                                                                                                            

Where I [] is a k×1 indicator function which takes on value 1 if the argument is true and 0 otherwise, whearas N = [η_t,η’_t ].

Cappiello et al (2006) note that the sufficient condition for Q_t to be positive definite for all possible realizations is that the intercept (P – A’PA – B’PB – G’NG) is positive semi-definite and the initial covariance matrix Q₀ must be positive definite.

Data

Our database covers daily returns of stock market indices for the BRICS group (Brazil, Russia, India, China and South Africa). The period chosen covers from August 14th 2001 until June 1st 2015. This choice is motivated by the inclusion of three important events: the terrorist attacks of 11/09/2001, the subprime crisis and the European sovereign debt. The results of econometric tests (stationary, descriptive statistics, correlation matrix, causality test Granger, Variance Decomposition and Impulse Responses Functions) and the estimated coefficients of Bivariate ADCC GARCH (1, 1) have been obtained using the Eviews 8 software (Figure 2).

Results of the stationary and unit root tests

Stationary significantly affects the behavior of the time series. However, for non-stationary time series prediction is only valid for a given period of time without generality Gujarati. There are some empirical methods for testing the stationary time series as ADF Dickey and Fuller, Phillips and KPSS Kwiatkowski.

Descriptive Statistics

Table 2 shows that China has the best daily stock exchange profitability followed by India and Brazil. The Chinese stock market has the highest risk level followed by Brazil and India. The asymmetry coefficient (Skewness) is negative in Brazil, India, South Africa and Russia whereas it is positive in China, which shows that the stock market of this country has more positive than negative shocks. The statistics of Jarque-Bera (JB) test strongly rejects the normality hypothesis [10]. The Kurtosis coefficient suggests that all the series follow a leptokurtic distribution.

The linear correlation

The analysis of the linear correlation reveals that the strongest correlation is detected between Brazil and South Africa (0.43) followed by India and South Africa (0.38) and then Brazil and India (0.31). (Forbes and Rigobon, 2002) showed that contagion tests based on the correlation coefficients are skewed because of the heteroscedasticity. In order to solve this problem and at the same time model the conditional variances and correlations of several series, Engle, like Tse and Tsui, proposed the extended DCC method (Dynamic Conditional Correlation) and thereafter a treatment of asymmetries by Cappiello the results of which will be presented in what follows.

Lag length selection

Before carrying out the causality test in the Granger sense, the variance decomposition and the analysis of the responses Impulse Functions, first we need to select the P delay magnitude. This selection is based mainly on the information criteria since there are several restrictions on the likelihood-ratio test (LR). If two criteria show contradictory results, the information SBIC criterion is retained because it is more reliable. By retaining Schwartz (SC), as a selection criterion, it is found according to the following table that the detected delay magnitude is equal to 2.

Results of the causality test in the Granger sense

Granger, considers that a series “causes” another series if the past knowledge of the first manages to improve the forecasting of the second. It consists in detecting the improvement of the predictability of a variable. Sekkat, supports the idea according to which temporal succession is central and therefore causality cannot be discussed without taking time into account. These tests make it possible to know the movement of a given stock market volatility on another market after a random and positive shock on the first. In other words, knowing the past values of Y enables better prediction of the current value of X. The examination of the causal relationships (interactions) between the BRICS countries is of prime concern. The causality test in the Granger sense helps, on the one hand, understanding these countries’ stock market functioning in a context of international financial market globalization and integration and, on the other hand, provide enhanced information as a crucial factor in reducing risk. The results show asymmetrical causality directions between the 

Figure 1: Impulse responses functions of BRICS.

studied stock markets. They also suggest a bidirectional and significant causal relationship between each pair of following countries: Brazil/India, South Africa/India, and Russia/India. In accordance with the linear correlation test, Brazil/India, South Africa/India seem to be interdependent than the other nations. Brazil succeeded in unilaterally causing South Africa, China and Russia, in the Granger sense. Therefore, the previous values of the volatility realized by BOVESPA have an explanatory and significant power, which enables to forecast the carried out volatility of indices; FTSE SA, SHANGHAI and RTSI. From the results of the Granger causality test, we can underline that the shockwaves of the collapse of major financial institutions affected global financial markets and resulted in the spread of the financial crisis [11]. The resulting global recession has affected demand for imports in the developed world. This has caused a slowdown of growth in the export-led economies of the BRICS countries. This is particularly true to natural resources export countries like Russia, Brazil and South Africa where the contagion was found during the post crisis period. There was some insulation of contagion for manufactured and service export countries like China and India as these countries experienced a delay of slowdown of economic growth that only occurred in the late stage of 2009 [12]. This resulted in the decreased level of investment and the outflow of liquidity in the financial markets of the BRICS countries. As a result, the capitalization of the financial markets in the BRICS decreased and they also experienced a crisis directly caused by the sub-prime mortgage crisis in the USA. Moreover, the decreased price of commodities from mid-2008 also affected the confidence of the financial markets. This significantly affected the resource export-led countries such as Russia, South Africa and Brazil. Hence the financial performance of the major enterprises that are listed in their respected financial markets decreased. Thus the performance of the index was affected, and confidence for the future was dented during 2008 and 2009 within the BRICS. Apart from China, the value of all four currencies depreciated against the dollar from 2008 as a result of low confidence in the midst of the recession. This somehow did not augment exportation for the BRICS; hence it caused major concern regarding the capacity to earn foreign currencies in the emerging countries. Furthermore, the depreciation of local currencies is one of the pieces of evidence of the outflow of liquidity of financial markets. This further caused the decreased value of capitalization of the financial markets in the BRICS.

Analysis of the variance decomposition

In order to study the links between the stock markets of the BRICs countries, the analysis of the variance decomposition enables us to examine the impact of the previous market shocks on another specific market. Since our investigation deals with the bivariate case, the analysis of the variance decomposition in our study reveals very important results. Regarding the Brazilian index BOVESPA, the forecasting error variance is due for 99.69% to its own innovations against 0.27% only for India. However, the other markets seem to be independent from the shock suffered by the Brazilian stock market. The RTSI index makes clear that from the fifth day (of the shock), it is possible to explain 73.20% of its own variance forecasting errors against 20.96% for Brazil, whereas India, with (2.67%), South-Africa, with (3.08%) and China, with (0.08%) do not seem to react to the shock on the Russian stock market.  On the other hand, the BSE Indian index suggests some interdependence with the BOVESPA insofar as this last succeeded in explaining 13.93% of the variance forecasting errors compared to the Indian stock index. The Chinese market appears independent from the other stock market places since it presents an explanatory power of about 95.87% of its own variance forecasting errors. The South-African stock index (FTSESA) demonstrated its ability to explain 72.62% of its own forecasting errors against 21.67% due to the Brazilian stock market.  The results of the variance decomposition showed that Brazil is sensitive to the fluctuations undergone by the Indian, South-African, and the Russian stock markets insofar as it succeeded in explaining, respectively 13%, 21,6% and 20,96% of the Indian, South African and Russia variance forecasting error[13-15]. These results can be justified by the fact that Brazil number of assets. It has one of the most diversified economies alongside a dynamic agro-alimentary sector (which ensures 30% of exports) which is a mining and aeronautical industry with world-sized companies like CVRD and Embraer. The Brazilian vast territory helps the country be one of the main world ore producers (iron, tin, bauxite) like paper pulp. Actually, within a few years, Brazil should appear among the first oil producers due to the development of the mine fields in its territorial waters. On the political level, Brazil is a democracy, but is sensitive to the dehydration of the South countries. Brazil, which is one of the world countries that masters the technology of uranium enrichment, defends the idea of an access to civil nuclear technologies for all, but under an international supervision. It is also a foreground agricultural supplier for many countries that cannot or do not wish to buy from the United States, the EU or Australia. At the same time, Brazil keeps friendly relationships with the Western nations. It can speak on behalf of the South countries acceptable for the Westerners, but the ambition of which would be limited to represent South America and Africa [16-18].  These findings should be of interest to policy makers in BRICS as well international investors and portfolio managers who intend to invest in BRICS. Policy makers in South Africa, in particular, should be cautious in attempting to pursue the agenda of full capital market liberalization with other BRICS countries with the possibility of scrapping the existing exchange control. Such a move may result in capital flight from South Africa to other BRIC countries, especially during periods of financial instability in South Africa. However, South Africa may attempt the full capital market liberalization embarked on by Brazil, which is already South Africa’s most important trade partner in the BRIC grouping. The two countries are also both members of the IBSA (India, Brazil and South Africa) grouping [19]. For international investors and portfolio managers, these findings should inform on the possibility of portfolio diversification and equity and option pricings when investing in the BRICS bloc. South Africa is shown to be far from a safe haven during crises originating from Russia, India and China.

Analysis of the Impulse response functions

After a shock on the Brazilian stock market, the BOVESPA index positively reacts to its own shock at a rather important magnitude. The other indices also positively react to it but at more reduced amplitude, then, the shock effect is dissipated the fourth day. This report shows that the BOVESPA index realized volatility spread to the other markets. This result reflects that the integration level between these markets is justified by an increasing participation in the international trade, an opening of their economy to foreign investments, a regular rise of the income per capita, an increasingly visible presence in research and innovation and the dynamism of their companies which very present on the overseas markets. Finally, the essential common point between the BRICS countries lies in the confidence in the future. It is trust that feeds optimism and maintains growth, notably, through the use of the consumer credit. The analysis of the impulse response functions relating to the RTSI index strongly underlines the independence of the Brazilian, Indian, South-African and Chinese stock markets from the shock to the Russian market which positively reacts to its own shock for two days. The Indian stock market shows the independence of China and Brazil whereas Russia and South Africa answer it but at a low magnitude compared to the one recorded by the BSE index. As a result, the rise of the volatility realized by the Indian index increases the uncertainty in the Russian and South-African stock markets. The Chinese stock market proves to be independent from the other markets of BRICS group insofar as no reaction is recorded on behalf of the latter following a shock in SHANGHAI. The South-African stock index (FTSESA) positively reacts to its own shock for two periods. The Russian index positively reacted but a lower magnitude; hence, the effect of the shock gets more obscure after four days. It is worth noting that South Africa is Russia’s potential customer in nuclear and industry soldier. Finally South Africa carried out a very active diplomacy, since the introduction of the democracy in 1994. It seems also that the South African currency crisis had a negligible influence on Russia and, thus, the absence of contagion of the South African equity market to the Russian equity market. As in the case of Brazil, the two equity markets commove to different external shocks.

BOVESPA: stock index of Brazil

RTSI: stock index of Russia

BSE: stock index of India

SHANGHAI: stock index of China

FTSE SA: stock index of South Africa

The Asymmetric Dynamic Conditional Correlation (ADCC) GARCH model (Cappiello et al. 2006) was carried to examine the asymmetric effect in conditional variance, as well as in conditional correlation. The estimation results for the Bivariate A-DCC model are reported in Table 7. As shown, the magnitude of the GARCH coefficient (β) is high and varies between 0.73 (Brazil-China) and 0.995 (Russia-China), indicating the high persistence of volatility over time. All markets satisfy the stationarity condition since the sum (α+γ/2+β) is less than one for all cases. In addition, for all cases, the sum of ARCH and GARCH coefficients is less than unity suggesting the great long run persistence of volatility. The coefficient γ is significant for all selected stock markets indicating the asymmetric behavior of the volatility.  Moreover, using the ADCC model, we investigate asymmetries in conditional variances and correlation dynamics for all countries during crises periods. We find that conditional volatilities of equity indices returns show widespread evidence of asymmetry. The ADCC results provide further evidence for higher joint dependence during stock market crises. When bad news hits stock markets, equity correlation among BRICS increases dramatically. This finding has important implications for international investors, as the diversification sought by investing in multiple markets is likely to be lowest when it is most desirable. Finally, news impact surface show that crises are spread through equity markets rather than through changes in macroeconomic fundamentals. Our results imply that a crisis in one market may induce investors to sell their holdings in other markets in order to maintain certain proportions of a country’s stock index in their portfolios. This implication is supported in Boyer at al. (2006). Similarly, an increase in risk aversion (which could be caused by a crisis in one country) can lead investors to sell assets in which they are overweight in order to track their benchmarks.

The dynamic aspect of both positive and negative correlation is observed through time for (Brazil/Russia, Russia/South Africa, India/China and South Africa/China). This finding is consistent with what Forbes and Rigobon, underlined, namely a correlation growth during the crisis periods when there is a strong volatility increase of the world stock markets [20]. This correlation fall suggests a phenomenon of flight to quality identifying a transfer of the invested capital towards safer instruments linked to uncertainties on the stock markets. Such a phenomenon is usually preceded by the bursting of a speculative bubble. Hence, investors would rush to sell their riskiest securities and fall back on the government bonds which have high prices. The analysis of the Dynamic Conditional Correlation evolution shows that for Brazil/China, Russia/China and Russia/India, this value is positive but limited (not exceeding 0.28 in most studied cases) [21-22]. Almost stable for Brazil/India, the Dynamic Conditional Correlations had strong fluctuations having as an important value the one coinciding with the beginning of the studied period by developing the impact of the 9/11/2001 terrorist attack which took place in the United States. Regarding Brazil/South Africa, the correlation is almost stable (about 0.37), excepting two with a value of 0.7, which shows the impact of the 9/11/2001 terrorist attack for the first, and the coinciding date of the subprime crisis for the second: the correlation between equity markets in Brazil and South Africa increases during crisis periods emanating from other countries and regions, such as the Russian, Asian and subprime crises. This indicates that the synchronization of the two equity markets is also triggered by external shocks. The correlation between the South African and Chinese equity markets is characterized by periods of negative correlation, indicating that the two markets occasionally decouple. The results show also that there seems to be weak evidence of an increasing correlation between South Africa and each of the BRICS countries during a period of crisis that stems from South Africa, which may lead to the conclusion that South Africa is a receiver rather than transmitter of financial shocks to other BRICS countries during periods of financial crisis [23].

This paper examines the dynamic relationships between BRICS’S stock markets. We employ the Bivariate A-DCC model. We find a time-varying correlation between stock markets during the turbulent period 2007-2012 (Global Financial Crisis and Sovereign Debt in Europe). The BRICS countries, which are in full economic and financial transformations, are classified in little time among the richest countries of the world. Growth of the emerging countries is significantly associated with the growth level of their business partners, namely that of the other large emerging countries, such as the BRICS countries (Brazil, Russia, India, China and South Africa), and with the global funding conditions. The BRICS caught up with the developed economies in the 2000s. They are continuing their rise while other industrialized or developing countries are following. In spite of this sustained favorable consumption dynamics in the BRICS, their growth is significantly moving slowly today. This apparent paradox is explained by the supply constraints from which they now suffer. In fact, the investment decline reflects the fact that the local companies have no more sufficient production capacities to meet this surging demand. In the slowdown context of the large emerging countries, in particular of the BRICS, and the globalization and financial turbulence phenomenon, we attempted to highlight the interdependence and integration level between the BRICS’ stock markets. In order to answer this question, we applied the Bivariate Asymmetric DCC GARCH model between all the pairs of countries included in BRICS group so as to show a possible contagion between the countries and carry out econometric tests to insist on the integration importance within these countries (the analysis of the Impulse Response Functions). The obtained results inform about a strong correlation between Brazil and South Africa (0.426) followed by India and South Africa (0.381) and Brazil and India (0.315). However, (Forbes and Rigobon, show that contagion tests based on the correlation coefficients are skewed because of the heteroscedasticity [24-29]. The Asymmetric Dynamic Conditional Correlation (ADCC) GARCH model Cappiello et al was carried to examine the asymmetric effect in conditional variance, as well as in conditional correlation [8]. The estimation results for the Bivariate A-DCC model show that the magnitude of the GARCH coefficient (β) is high and varies between 0.73 (Brazil-China) and 0.995 (Russia-China), indicating the high persistence of volatility over time. All markets satisfy the stationary condition since the sum (α+γ/2+β) is less than one for all cases. In addition, for all cases, the sum of ARCH and GARCH coefficients is less than unity suggesting the great long run persistence of volatility [30-33]. Also, the coefficient (γ) is significant for all selected stock markets indicating the asymmetric behavior in volatility. Moreover, using the ADCC model, we investigate asymmetries in conditional variances and correlation dynamics for all countries during crises periods. We find that conditional volatilities of equity indices returns show widespread evidence of asymmetry. The ADCC results provide further evidence for higher joint dependence during stock market crises (Global Financial Crisis and Sovereign Debt Crisis). When bad news hits stock markets, equity correlation among BRICS increases dramatically. This finding has important implications for international investors, as the diversification sought by investing in multiple markets is likely to be lowest when it is most desirable. The analysis of the impulse response functions shows that the realized BOVESPA index volatility spread to the other markets. This result reflects the integration level between these markets, as being justified by a rising participation in the international trade, an openness of their economy to foreign investments, a regular rise of the per capita income, an increasingly visible presence in the research and innovation as well as the dynamism of their companies which are very present on the overseas markets. No answer was recorded after a shock about the RTSI and SHANGHAI indices [34-35]. Only Russia and South Africa reacted to a shock on the BSE SENSEX index. Consequently, a rise of the realized volatility of the Indian index raises uncertainty in the Russian and South-African stock markets. Russia also seems to deal with a shock exerted on the FTSE SA index. The results of the variance decomposition show that Brazil seems to be sensitive to the fluctuations undergone by the Indian, South-African and Russian stock markets insofar as it succeeds in respectively explaining 13%, 21.6% and 20.96% of the forecasting error variance of India, South Africa and Russia. The Indian BSE index suggests some kind of interdependence with the BOVESPA index insofar as this latter can explain 13.93% of the variance forecasting errors relating to the Indian stock index. The Chinese market seems not to depend on the other marketplaces since it has an explanatory power of about 95.87% of its own forecasting error variance. The South-African (FTSESA) stock index can explain 72.62% of its own forecasting errors against 21.67% caused by the Brazilian stock market. The causality test in the Granger sense stresses a bidirectional and significant causal relationship between each pair of following countries: Brazil/India, South Africa/India and Russia/India. Moreover, the former values of the realized volatility of the BOVESPA index appear to have an explanatory and significant power for predicting the realized volatility of the FTSE SA, SHANGHAI and RTSI indices. Similarly, the South-African, Chinese and Russian investors can diversify their portfolios in Brazil. The BSE SENSEX and FTSE SA indices appear to have an explanatory power for predicting the development of the Chinese index. The South-African investors have opportunities to diversify their portfolios in China. It is worth noting that the absence of causality in the Granger sense implies growth prospects through diversification. Moreover, the findings of this paper should inform international investors and portfolio managers on the possibility of portfolio diversification and equity and option pricings when investing in BRICS. It should be pointed out that a solid growth of the BRICS countries may result in a price rise of the raw materials exported by the European Union (EU) countries as well as an increase of the IDE. The EU countries could also profit from the setting up of companies of the BRICS countries seeking higher outputs. The study of the interdependences between the BRICS countries and those of the European Union will be the object of our next research.

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