Stability of cross-market bivariate return distributions during financial turbulence

Accepted Manuscript Title: Stability of cross-market bivariate return distributions during financial turbulence Authors: Syeda Rabab Mudakkar, Jamshed Y. Uppal PII: DOI: Reference:

S0275-5319(17)30480-4 http://dx.doi.org/doi:10.1016/j.ribaf.2017.07.170 RIBAF 860

To appear in:

Research in International Business and Finance

Received date: Revised date: Accepted date:

2-4-2015 29-10-2016 6-7-2017

Please cite this article as: Mudakkar, Syeda Rabab, Uppal, Jamshed Y., Stability of cross-market bivariate return distributions during financial turbulence.Research in International Business and Finance http://dx.doi.org/10.1016/j.ribaf.2017.07.170 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

STABILITY OF CROSS-MARKET BIVARIATE RETURN DISTRIBUTIONS DURING FINANCIAL TURBULENCE Author Information: 1.

Syeda Rabab Mudakkar, Ph.D. Assistant Professor of Statistics Centre for Mathematics & Statistical Sciences Lahore School of Economics, Lahore, Pakistan Email: [email protected].

2.

Jamshed Y. Uppal, Ph.D. (corresponding author) Associate Professor of Finance School of Business and Economics, Catholic University of America Washington DC, 20064, USA Phone: 001-202-319-4730 Fax: 001-202-319-4426 Email: [email protected]

Graphical abstract

Upper and Lower Tail Dependency 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0

Pre GFC

Post GFC

Abstract

The paper examines the stability of the bivariate stock return distributions across the G5 and five emerging markets in times of financial crisis using copula models. We find that the volatility dynamics as well as the dependency structures appear to be both country- and periodspecific. Neither the bivariate distributions nor the associated parameters appear to be stable over time. It implies that the usefulness of the copula techniques may be limited particularly in times of financial turbulence. Our results strike a note of caution for the practitioners and policy makers in dealing with the phenomenon of financialization which draws much strength from the quantitative financial models. Keywords: Financialization, Spillover Effects, Global Financial Crisis, GARCH models, Copula theory, Tail Dependence

1. Introduction: The Global Financial Crisis (GFC) of 2008-09 has brought to attention the perils of financialization, which refers to the growing dominance of financial instruments and markets over the traditional industrial and agricultural economies, and is connected with the concomitant development of cyberspace, the global deregulation of financial markets, and the rise of shareholder governance (Lagoarde-Segot, 2016).1 Palley (2007) argues that principal impacts of financialization are to (i) elevate the significance of the financial sector relative to the real sector; (ii) transfer income from the real sector to the financial sector; and (iii) increase income inequality and contribute to wage stagnation. Additionally, financialization may render the economy prone to risk of debt-deflation and prolonged recession. Aalbers et al. (2015) present a case study of the financialization of both housing and the state in the Netherlands documenting its negative consequences. Cloke (2010, 2013) suggests that the global financial crisis “represents a distinctly new form of actor-network capitalism, originating in the hybrid financial innovations since the 1970s, the explosive growth in cyber-space potential during the 1990s and the subsuming of the State by finance that accompanied these two processes.” The author proposes that the evolution of ultra-capital (capital beyond capital) from within the global financial services sector, need to be considered for a proper understanding the recurrent financial crisis. Vitali et al. (2011) suggest that the structure of the control network of transnational corporations creates a small tightly-knit core of financial institutions, an economic “super-entity” which affects global market competition and financial stability. The acceptance and rationalization of the reliance on financial markets and products is to a large extent anchored in mathematical models and the theoretical framework assuming economic rationality. Walter (2016) argues that management tools and beliefs of financial practices are embedded in the structural discourse he terms as the “financial logos.” He hypothesizes that this “discourse contains a specific representation of risk mathematically modelled by probability 1

According to Palley (2007) financialization is a process whereby financial markets, financial institutions and financial elites gain greater influence over economic policy and economic outcomes. According to Aalbers (2015) the financialization literature seeks to conjoin real-world processes and practices that are otherwise treated as discrete entities; how the financialization of the global economy is tied to the financialization of the state, economic sectors, individual firms, and daily life. Gupta (2015) provides a brief review of the literature on “financialization” and the causes for the emergence of this phenomenon. For a more detailed treatment, see Epstein (2005).

measures.” Using the concept of performativity, he argues that mathematical modelling plays a concrete role in the framing of financial decisions, and makes contributions to financial practices in the epistemologically and sociologically sense.2 Dupré and Perluss (2016) point out that historically rules and regulations have often taken into consideration the performativity of risk insurance so as to limit the range of insured risks and thus avoid the realization of the claims through embezzlement or kindred corruption. Today, the finance profession takes “risk quantification as an incontrovertible given.” Quantifying risk has become a key feature in modern finance, “a dogma,” ignoring the distinction between risk and uncertainty. The use of mathematical models to reduce the complexity of the financial markets is certainly alluring. However, quantitative models have been shown to poorly predict financial markets; inadequacies of the quantitative models in assessing financial risk arising from extreme events are well discussed; see for example, Salmon (2009), Bernstein (1996),Taleb (2007). The less than satisfactory performance of the quantitative models has been attributed to the difficulties in correctly estimating the parameters of the models, and much research has been devoted to more accurately estimating data driven parameters; for example, Careya, Gath and Hayes (2014) develop a generalized smoothing approach to modeling financial dynamics. However, it is also important to examine the nature and structure of the return distributions underlying the quantitative finance models and how these are affected in times of turmoil. An important genre of quantitative risk models deals with the interdependence of different financial markets that can lead to contagion and the spillover of economic shocks across markets. The Global Financial Crisis period provides us an opportunity to investigate the bi-variate distributions used to model the co-dependence of stock markets and the stability of their structure during times of severe financial turbulence. The GFC had extreme and far-reaching effects on the financial markets across nations. Stock market volatility increased several fold throughout the crisis, all assets experiencing extreme returns. Exceptionally large swings in the stock prices were experienced with a frequency which had never been observed previously. The objective of this study is to examine how the nature and characteristics of cross-market return distributions were impacted during the financial turmoil. This objective is pursued by first examining the effect of the Global Financial Crisis on the structure of volatility dynamics in selected emerging and G5 equity markets (see data section below). We then examine the degree and structure of financial market inter-dependence among the emerging and the G5 economies using the copula framework. Next, we address the question of the stability of the bivariate jointdistributions. Finally, we conclude by drawing implications for the applied usage of quantitative models as well as with respect to a broader perspective on financialization.

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MacKenzie, Muniesa and Siu (2008) examine whether economics is performative - whether, in some cases, economics actually produces the phenomena it analyzes.

1.1 Contagion Studies The spillover of economic shocks across financial markets has been a subject of considerable research and risk modelling. In the past, monetary crisis originating in the developing markets, e.g., the Asian Flu, the Tequila Crisis or the Russian Virus, were considered as infectious, and prompted gigantic bailouts by the global organizations to stem contagion. Among the academic studies, the earliest papers is one by Morgenstern (1959), who inspected the spill-over effects of 23 stock market panics on foreign markets. Later econometric research concentrated on correlation analysis utilizing GARCH-type models to inspect if equity market co-movements become stronger or weaker throughout crashes as compared with non-crash periods. These include among others Lin, Engle, and Ito (1994), and Susmel and Engle (1994). More recently, research has focused on the spillovers and contagion from the Global Financial Crisis. There is well established empirical evidence of increase in inter-market correlations, spillovers and contagion. However, not much scholarship has been devoted to the study of its impact on the nature and characteristics of bivariate distributions underlying the risk models. Several of the contagion studies while documenting an increase in correlations during times of crisis also show the magnitude of contagion to be different for each country pair. Gilenko and Fedorova (2014) examine spillover effects for the BRIC stock markets during the crisis period and find some evidence for the ‘decoupling’ phenomenon. Luchtenberg and Vu (2015) show that both economic fundamentals such as trade structure, interest rates, inflation rates, industrial production, regional effects, and investors’ risk aversion contribute to international contagion. Jin and An (2016) show that during the 2007–2009 GFC, the degree of stock market reactions to shocks originating in the US differs from one BRIC market to another, depending on the level of integration with the international economy. Rejeb and Arfaoui (2016) in a study of volatility spillovers over a longer period 1993 to 2010, find that volatility transmission between the emerging and the developed stock markets is closely associated with geographical proximity as well as with crisis periods, observing that the interdependence increases during bullish markets while decreases during bearish markets. Rothonis, Tran and Wu (2016) find that cultural proximity can intensify volatility linkages across inter-national equity markets; their cultural distance measure is inversely related to the strength in return volatility linkages between country pairs. These linkages are intensified when there is a wider common investor base between two markets, with greater bilateral portfolio investments and the degree of openness in terms of their foreign exchange trading activity. Al Nasser and Hajilee (2016) document the existence of shortrun integration among the emerging and the developed markets. However, the long-run relationship of all emerging countries is significant only with the Germany stock market. Yavas and Dedi (2016) study European exchange traded fund (ETF) and find existence of significant co-movement of returns as well as volatility spillovers. Espinosa-Torres et al. (2016) in a study of how Latin American countries’ term premia responds to changes in United States term premium, find that impulse-response functions vary depending on the country and particular time-length for which premia are computed. Yarovaya and Lau (2016) analyze stock market comovements around recent crises among the UK, the BRICS and the MIST emerging markets. Their results suggest that conditional correlation among the stock markets exhibits higher dependency when it is driven by negative shocks to the market, supporting the decoupling hypothesis. Omrane and Hussain (2016) find that impact of US macroeconomic news on the French index is stronger than that on the German. Burzala (2016) finds that rates of return in the

studied European markets react simultaneously to a much greater extent as a result of interdependencies than as a result of mutual contagion, defined as a significant intensification of lagged reactions. From the above survey of literature, it appears that the contagion/spillover effects are specific to the county pairs and to the study time period. We seek to examine intermarket dependencies by comparing the bivariate distributions in order to get a fuller picture. 1.2 The Copula Approach The traditional approach to capture the co-movement between different financial assets is to examine their correlation structure; however, the method suffers from serious drawbacks. The Pearson correlation analysis is appropriate only when the variables have a linear relationship and the distribution of individual variables is normal. This is particularly problematic in empirical models which seek to compare conditional correlations over calm and turbulent periods. Firstly, results may be misleading because of a spurious relationship between correlation and volatility; Longin and Solnik (2001). Solnik, Boucrelle and Fur (1996) suggest that the contagious nature of volatility may explain why global correlations expand in times of high market volatility. Secondly, as Bae, Karolyi and Stulz (2003) point out, correlations that give equal weight to small and large returns are not appropriate since, “large shocks, because they exceed some threshold or generate panic, propagate across countries, but this propagation is hidden in correlation measures by the large number of days when little of importance happens.” Chan-Lau, Mathieson and Yao (2004) show that “extremal dependence measures of contagion and simple correlation measures are not highly correlated ... suggesting that the use of correlations as a proxy for contagion may be misleading.” It is also evident from different empirical studies, e.g., Embrechts, McNeil, and Straumann (2002), that the distributions of financial assets often exhibit heavy tails, skewness and other features of non-linearity. In the presence of such features, it has, therefore, been suggested that Copulas could be utilized to adequately model the inter-dependence of financial assets. As an alternative, a notable advantage of the Copula models is that they provide the measures of relationship as well as fully describe the joint distribution of the variables. Copulas can be useful not only in portraying the dependence structure between two or more assets when return distributions are well behaved, but also in cases of extreme losses or gains that are typical of the financial assets. For example, Rodriguez (2003) examines the financial contagion of five EastAsian nations throughout Asian crisis and four Latin-American nations throughout Mexican crisis utilizing Copula approach with Markov-switching parameters. The findings show expanded tail reliance and asymmetry in times of high instability for the Asian nations, while symmetry and tail independence in case of Latin-American countries. In the same spirit, Vaz de Melo Mendes (2005) considers extreme value copula function to analyze the degree of integration between 21 Emerging stock markets throughout crisis periods. A more recent work is by Aloui et al. (2012) who use daily return from the Brazil, Russia, India, China (BRIC) and US stock exchanges to investigate the contagion effects of 2007-2009 economic crises on the selected economies.

2. Hypothesis, Data and Methodology Having laid out the nexus between the financialization phenomenon and the quantitative finance models, the study considers three aspects of these models relating to the international stock return dependencies and how these were affected by the Global Financial Crisis. The first one examines the volatility dynamics for country for the pre-GFC and the GFC periods. We examine if the structure of volatility dynamics and its characterizing distribution is the same in the two periods, noting differences across countries. The second aspect investigates the modeling of the co-dependence of equity returns. Here, the null hypothesis is that the parameters of the joint return distributions are equal in the pre-GFC and the crisis periods. The third one examines the modeling of co-dependencies in country pairs, examining in particular the co-movements in the extreme values using copula models. Here, our focus is on the adequacy of the copula models to describe the tail dependencies over the two periods. The study considers the stock markets of the G5 nations - France, Germany, Japan, the United Kingdom, and the United States, and also of the leading five rising economies - Brazil, People's Republic of China, India, Mexico, and South Africa. Considering the timeframe of the GFC, we mark the onset of the down turn in the financial markets as the first of July, 2007. We backpedal about four years to establish a base case. Therefore, our study spans a time period from July 1, 2003 to June, 2011, subdivided as follows: 1. July 1, 2003 to June 30, 2007 – the Base Period 2. July 1, 2007 to June 30, 2011 – the GFC Period We compare the stability of bivariate time-varying dependence across the markets for the base and the GFC periods of time in the following manner. i. We first compare the volatility clustering and conditional mean phenomenon with various AR-GARCH specifications for each univariate time series in both periods and identify the best model for each pair of countries.3 The model with the best fit is selected by examining whether the standardized residuals are independently and identically distributed using ARCH-LM test. ii. We then apply Canonical Maximum Likelihood method that transforms the standardized residuals (𝑧1 , 𝑧2 , … . 𝑧𝑛 ) of each time series into pseudo observations i.e., (𝑢1 , 𝑢2 , … , 𝑢𝑛 ), where each 𝑢𝑖 ∈ [0,1]. iii. We test for bi-variate independence across all pairs using two measures: (a) a nonparametric measure of association, and (b) independence test using pseudo copula data. iv. We next fit a variety of copulas (see Appendix) using maximum likelihood estimation to the pseudo observations across all pairs markets for the base and crisis periods. We consider the two well-known parametric families of Copulas i.e., Elliptical and Archimedean class in our analysis. The Elliptical family includes the copulas with elliptical distributions which exhibit the properties of the multivariate Normal distribution. The well-known members of this family are the Gaussian and the Student’s-t Copula. Archimedean copulas are the most popular copulas in terms of practicability. In comparison to the Elliptical copulas, the Archimedean copulas are expressed by a specific generator. Archimedean class of copulas 3

The methodology is discussed also in Mudakkar and Uppal (2012).

are useful in investigating different tail dependencies i.e., only the upper/right tail or the lower/left tail or both upper and lower tail dependencies having different magnitude. We consider Gumbel, Clayton, BB1 and BB7 Copulas from the family of Archimedean Copulas. v. Finally the tail dependence is investigated. The details of these Copulas families and the relevant measure of association and test for independence are provided in the Appendix. 3. Empirical Results and Discussion The returns in each equity market are measured as the first log differences of the stock price index series. The geometric returns thus calculated yield stationary series which is confirmed by the Dickey-Fuller tests for both periods (not included here). Table1 panel A and B provide the descriptive statistics of the log returns for the emerging and the G5 economies respectively. The results clearly show that the return distributions have heavier tails than of a Normal distribution in both the base and the GFC periods. The JarqueBera statistic is significant even at low levels in all cases. High values of the kurtosis statistic indicate that the distributions have fat tails. However, the coefficients of skewness are not high, yet the negative value indicates that the upper tail of loss distribution is of specific interest. We, therefore, dismiss the null hypothesis that the stock returns are normally distributed, and consider the copula models to be applicable. 3.1 Models of Volatility Dynamics Most of the market risk models start with specifying the volatility dynamics of the asset returns. We examine which models best describe the volatility structure of the G5 and the five emerging market returns in both the base and the GFC periods. The best fit is determined by the F-statistic and the p-values from the ARCH-LM tests that the residuals extracted from the fitted models are independent and identically distributed. The time series plots (not shown here) of all markets in both the base and the GFC period clearly exhibit the volatility clustering phenomenon which leads us to consider GARCH group of models. Our results (presented in Table 2) indicate that a GARCH (1, 1) model with normal innovations is appropriate to represent the dynamic volatility of most of the markets throughout the base period. However, the conditional mean structure is found in the Indian and the South African stock returns during the base period. This necessitates including an AR(1) term in the models for these two markets. Comparing the volatility structure of the five emerging economies in the GFC period from the base period, we observe that it is not different for the market returns series of Brazil, China and Mexico. However, for South Africa and India, the GARCH(1,1) model with normal innovations but without a conditional mean term, is also adequate to capture the dynamic volatility during the GFC period as for the other emerging economies. Examining the volatility structure of G5 countries during the Global Financial crisis, we find that, excluding Japan, it is remarkably different from the base period. In case of France, Germany and FTSE 100, GARCH(1,1) with t-innovations was found to be appropriate for capturing the innovation distribution. It is notable that in case of the S&P500 the serial dependence of the return series increased i.e., it follows a GARCH(2,2) process with normal innovations. None of the other G5 series exhibits conditional mean. It is notable that the

volatility structure of the Japanese market remains the same as that in the base period. These observations most likely reflect more extreme movements during the GFC period. Comparing with the stock returns of the emerging economies during GFC, the results also indicate that the GFC hit the developed stock markets more severely. Thus, our results in this section show that the models to capture the volatility dynamics seem to be market and period specific, and may not be structurally stable over different periods. 3.2 Stability of Bivariate Dependency We next examine bivariate dependence of stock returns in countries pairs for both the base and the crises periods in two ways: a) we consider Kendall’s Tau as the nonparametric measure of association for examining the correlation structure between the markets; b) we model the bivariate dependency structure using the Copula approach. The tests are conducted on the residuals (rendered iid) from the GARCH models as in the previous section. Nonparametric measure of association: Results are shown in Table 3. In the case of the emerging economies, the results indicate that except for the Brazil and Mexico pair (South American region), all other markets indicate weak inter-market correlation (ρ<0.20). The correlations among the European Union countries UK, France and Germany are strong (ρ >0.50) in the base and the GFC periods. The correlations of the European countries with the USA market is moderate (UK-Germany) to strong (USA-France). However, the correlation of the Japanese market with the other G5 countries is rather weak. Next, we examine the bivariate relationships of each of the emerging economies with the largest developed market i.e., the US (S&P 500). The results show that Brazil exhibits the highest correlation with S&P 500, whereas China the least during the Base period. The correlation between the Indian and the US market is on the other hand very weak during the Base period. The results indicate that the G5 economies seem to be more integrated as compared to the emerging economies in terms of the correlation values. The degree of correlation also seems to be related to regional proximity. To test whether the estimated correlations are significantly different across the two periods, we use the z-statistic. The rejection of the null hypothesis against the one-sided alternative indicates that the GFC period correlation is greater than in the base period. The results show, the correlations between most of markets seem to have increased. However, there are notable exceptions in case of China and Japan; the z-score is not statistically significant for China paired with Brazil, Mexico, and the USA, and for Japan paired with France, UK and the USA.

Independence Test Using Pseudo Copula Data: Next, we model the bivariate dependency structure of the markets using the Copula approach. Since the underlying distribution function of each of the filtered residual series is not known, we use the empirical distribution function to transform the innovations into pseudo copula observations. This yields data vectors of values within the interval [0, 1]. We then perform the independence test for bivariate copula data. The independent tests examine whether there exists any bivariate dependence in the data vectors.

The Test Statistic and the p-values (in parentheses) for the emerging and the G5 economies are given in Table 4. The p-values of the independence tests in the table clearly rejects the null hypothesis of independence of the data series pairs, and indicate that there exists dependence structure among all bivariate pairs of all markets, except in cases of South Africa-China and S&P500-China during base period. However, during the GFC period the results imply existence of dependence structure between South Africa and China markets as well. The results in Table 4 indicate that there exists bivariate dependence among all pairs during the base period as well as the GFC period in the developed markets group. The bivariate relationships of emerging markets with the US market, excepting China, are also affirmed by the results of the independence test reported in Table 4(c). China and US market seems to function independently during Base period, as indicated by the insignificant p-value of the independence test statistic. The linkage is somewhat stronger during the GFC period. The Table 4 results are not directly comparable with those reported in Table 3. However, the bivariate relationships from the pseudo-copula tests appear to be much stronger than is shown by the non-parametric tests. The results indicate that the markets may be much more integrated and linked together than implied by the correlations parameters. 3.3 Selection of Appropriate Copula Model: As explained in the earlier section, because of issues with the distributional properties of the return distributions, Copula functions have been advocated for modeling bivariate distributions across pairs of markets. However, the challenges remain as to the correct selection of the copula function and accurate estimation of its parameters. The issue is addressed in this section. We fit six different copulas (see Appendix for details) using the maximum likelihood estimation method to the pseudo pairs. The Akaike (AIC) and the Bayesian information criteria (BIC) are then applied to the different families of copula and the family with the lowest AIC and BIC is selected. Finally, we run bivariate Copula Goodness-of-Fit test based on the Kendall’s procedure to check the appropriateness of selection of copulas. Table 5 presents the selected copula for the Base and GFC periods, and the statistics show that the selected copulas are appropriate to model the dependency structure for particular time regime. It appears that the appropriate copula differs from one market to another. In the base period for all market pairs, except two i.e., South Africa-China and S&P500-China, copula model are appropriate. These two pairs indicate bivariate independence. The choice of the correct copula model is important as the family of copula conveys inform as to the nature of the relationship. Almost all bivariate pairs exhibit heavy tails dependence except in three cases of India-Mexico, Japan-S&P500 and S&P500-South Africa which are modeled by the Gaussian distribution. More interestingly, we notice that the dependency in left tail (i.e., losses) is particularly present. This is indicated by the choice of Clayton copula in a large number of the cases (7 and 9 out of 25 in the base and GFC periods respectively). However, the dependency for losses as well as for gains (i.e., in both tails), as is indicated by the selection of Student’s t Copula, is also found in almost equal of cases (8 and 10 out of 25 in the base and GFC periods

respectively). There is also evidence of asymmetry in the relationships as BB7 or BB1 families of copulas seem more appropriate in modeling the dependency in 3 cases in both periods. A linear dependency structure is also supported as the Gaussian copula seems appropriate for modeling the relationship, for example in case of China with India, China with Brazil and China with South Africa. Surprisingly, China exhibits insignificant dependency with S&P 500 in both periods, indicating independence in Copula models. However, South Africa and China markets which exhibit independence in the base period are characterized by the Gaussian copula during the GFC. Comparing the base period with the Global Financial Crisis period, the results exhibit entirely different structures of dependence. Only in four cases out of twenty-five the selected copula is the same in both periods, i.e., the Student’s-t copula. For example, the dependency of Brazil with India and South Africa or Mexico is characterized by Clayton copula indicating lefttail dependence. But for the GFC period, the asymmetric dependence is indicated in both tails of the distribution as BB7 or BB1 families of copulas seem to be more appropriate fits. Similarly, the dependency structure between France and Germany during the GFC period is found to be symmetric in both tails and can be modeled by Student’s t-Copula, but it is best described as the BB1 copula in the base period. Again, for Japan and Germany lower tail dependency (i.e., loss dependency) is modeled by Clayton copula during the Global Financial crisis period which is a different dependence structure (Student’s t) from the one in the base period. 3.4 Stability of Estimated Copula Parameters Once the appropriate copula family is identified, the parameters of the function need to be accurately estimated. The practical usefulness of the quantitative models critically depends on the stability of these estimates. We, therefore, compare the estimates of the parameters of the identified copula models from the base period to the estimates of parameters for the GFC period. Values of the parameters are estimated from fitting various copula models to the pseudo data pairs using maximum likelihood estimation method. In order to make a valid comparison between the parameter value obtained in the base period and those estimated for the GFC period, we use the same copulas model for both periods. Table 6 presents estimates of copula parameters for the markets under study. A comparison of the estimated values of model parameters for the two periods indicates that during the GFC, bivariate dependency across all five emerging markets increased from the base period. Hence, the values of these parameters estimated in the base period may not be a reliable guide for implementing risk models in the GFC period in emerging markets. During GFC, the estimated value of at least one of the parameters increased compared to its value in the base period. The results in Table 6 indicate that there exist significant differences in the value of estimated parameters during the two periods for both emerging and the developed markets. 3.5 Modeling Upper and Lower Tail Dependency Table 7 presents the results of estimates for upper and lower tail dependency across markets. Note that for the Gaussian and independent copula models the tails dependencies are not estimated, while for the Student’s-t copulas the upper and lower tail estimates are equal. The

results depict a variety of tail dependencies patterns and the impact of the GFC also seems to be varied. The emerging markets group (Table 7a) generally exhibits no upper tail dependence except in the case of the Brazil-Mexican pair and to a weaker extent the South Africa-India pair. In the GFC period, the correlation for positive jumps between the Brazil and the Mexican stock markets decreased, whereas it increased for India-South African pair. On the other hand for this group, the dependency structure between the negative moves existed even in the base period. However, the degree of the dependence is varied; the South Africa-Mexico pair exhibits the highest dependency estimate of 0.1991, whereas the China-India pair exhibits the least dependency value of 0.0021. During the GFC period the magnitude of lower-tail dependency is higher for all emerging market pairs except for the Brazil-Mexico pair. Table 7(b) presents the upper and lower tail dependency estimates for the G5 Economies. The results show that the group generally exhibited dependence in both tails; there seems to be a strong symmetry within the European group (also indicated by the Student’s-t copula). On the other hand, Japan when paired with European markets seems to show little or a small degree of lower tail dependence. The results also indicate that these dependencies in the lower or upper tails increased during the GFC period for all G5 pairs, except for Germany and Japan. Finally, Table 7(c) shows the tail dependency parameter estimates of the emerging markets with the S&P 500 during the base and the GFC periods. Brazil and Mexico seems to be symmetrically dependent on the movements of S&P 500, which increased appreciably in the GFC period. The structure of the US market with the Chinese and the South African markets is characterized by independence and the Gaussian copula respectively. Therefore, the tail dependencies are not relevant. However, the Indian economy seems to have weak correlation with S&P 500 but only in terms of losses; it seems to have increase appreciable in the GFC. 4. Conclusions and Implications Financial quantitative models have provided epistemological and sociological underpinning for the phenomenon of financialization, which many regard as having unacceptable disruptive and undesirable aspects. The Global Financial Crisis furnishes us with an authentic historical experiment to evaluate the foundations of the quantitative financial models. In this paper we have sought to evaluate the efficacy of the Copulas to model the joint bivariate stock return distributions and analyze the stability of the model parameters in times of severe financial turbulence. The co-movement of asset returns across financial market and the related risk arising from spillover and contagion has been a major concern for risk and portfolio management. The copula models are thought to better assess cross-market dependence when stock return distributions are not Normal, have heavy tails, skewness or non-linearities. Our findings indicate that while in case of the emerging economies, the dynamic structure of volatility remained unchanged from the base period in the case of G5 economies the nature of the volatility processes was quite different in the crisis period. The non-parametric dependency estimate indicates that the strength of dependencies among the G5 economies is comparatively greater than for the emerging markets. However, as observed in prior research, the dependency

estimates increased in both the G5 and the emerging economies during GFC. Our tests employing copulas also find that the dependencies in the left tail (i.e., losses) are more pronounced in the emerging economies, whereas dependencies in both tails (i.e., losses and gains) with symmetric and asymmetric structures are found in case of the G5 economies. A noteworthy finding of the study is that not only the magnitude of bivariate dependency across all pairs increased in the crisis period, but the nature of volatility dynamics and the distribution of the innovations seem to be quite different from the base period. Similarly, the tail dependency estimates for the two periods across all emerging and the G5 economies portray a very different pattern of dependency. In addition, different copula models seem to best describe the joint bivariate distribution in the two periods. It is shown that if we employ the copula models found to be the best-fit in the base period to model the bivariate distributions in the crisis period, we would obtain vastly different estimates of the parameters. Hence, the volatility dynamics as well as the dependency structures appear to be both country- and period-specific. The implications of our findings are that the usefulness of the quantitative techniques to model risk may be limited particularly in times of financial crisis and turbulence. Since neither the bivariate distributions nor the associated parameters appear to be stable over time, the model risk would remain a challenge for applying the quantitative approaches to risk assessment and management. The study contributes to the literature on the insufficiencies of the quantitative models to capture the complexities of finance and highlights the unquantifiable uncertainty inherent in financial assets. The results complement the findings in earlier studies, Uppal (2013) and Uppal and Mangla (2013), evaluating Value at Risk models using Extreme Value Theory that underscore the inadequacies of the quantitative risk models in times of financial turbulence, and the need for prudential exercise of judgment in risk management. The acceptance and rationalization of the financialization phenomenon drives to a large extent from the mathematical models which inform the discourse termed as the financial logos. The quantitative models being performative, can frame financial decisions not only of individuals and the instructional entities but also of policy makers and regulators. Our results underscore that risk quantification may not be treated as an incontrovertible technique and the distinction between risk and uncertainty must be kept in the background. The study raises a note of skepticism in treating financial models dogmatically, and may serve as a cautionary note for the practitioners and policy makers in dealing with the financialization issues.

APPENDIX A: The Concept of Copulas Formally, “Copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform”. Following Fischer (2003) terminology, the Copula can be defined as follows: 1. Definition: A two-dimensional copula is a function C :[0, 1] 2→ [0, 1] which satisfies the following properties: 1. C is 2-increasing, i.e. for

0  u1  v1  1 and 0  u 2  v2  1 holds : C  v1, v2   C  v1, u 2   C  u1, v2   C  u1, u 2   0.

2. For all u, v∈[0, 1]: . C  u, 0  C  0, v   0 and C  u, 1  u, C 1, v   v. The key hypothesis of Sklar (1959) states that any multivariate joint distribution could be recomposed as univariate marginal distribution functions and a copula which portrays the reliance structure between the variables. Further, the Copula is unique if the marginal distribution functions are continuous. Mathematically, Sklar Theorem in case of two variables, as explained in Fischer (2003), is stated as follows: 2. Theorem (Sklar) Let F1 and F2 be two univariate distribution functions. Then C(F1(x1), F2(x2)) defines a bivariate probability distribution with margins F1 und F2. On the other hand, let F be a 2-dimensional distribution function with margins F1 and F2. Then F has the copula representation F(x, y) = C(F1(X), F2(Y)). The copula C isunique if the margins are continuous. 3. Measure of Association: An imperative non-parametric statistic that measures the strength of association when the underlying variables are non-linear is the Kendall’s tau correlation. It is based on first ranking the data by each individual variable and then considering the similarity of the orderings of data. Embrechts et al. (2002) show that any copula can be used to measure Kendall’s tau in the following way: 𝜏𝑋,𝑌 = 4 ∬ 𝐶(𝑢1 , 𝑢2 )𝑑𝐶(𝑢1 , 𝑢2 ) − 1 where 𝑢1 , 𝑢2 ∈ [0,1] are the uniform variates drawn from the marginal distributions F1 and F2 respectively and the integration runs on the interval [0, 1]2. 4. Independence Test: The test explores the asymptotic independence of the two variables based on the Kendall’s tau, It considers the asymptotic normality of the test statistic 9𝑁(𝑁 − 1) 𝑇=√ × |𝜏𝑋,𝑌 | 2(2𝑁 + 5) where N is the number of observations 𝜏𝑋,𝑌 is the empirical Kendall’s tau. The p-value of the null hypothesis of bivariate independence asymptotically is:

𝑝. 𝑣𝑎𝑙𝑢𝑒 = 2 × (1 − Φ(𝑇)), where Φ is the standard normal distribution function. 5. Tail Dependence: Next the concept of tail dependence which measures the extreme comovements in the upper and lower tail of the bivariate distribution F(x, y) is introduced as follows: Definition : Let w be a threshold value. The upper tail coefficient𝜆𝑢 is then defined as 𝜆𝑢 = lim 𝑃(𝐹1(𝑌) > 𝑤|𝐹2(𝑋) > 𝑤) = lim ( 𝑢→1−

𝑢→1−

1 − 2𝑤 + 𝐶(𝑤, 𝑤) ) ∈ [0,1] 1−𝑤

Since 𝜆𝑢 ∈ [0,1], this indicates that the value of 𝜆𝑢 = 0 implies that X and Y are asymptotically independent whereas any other value indicates the asymptotic dependence of the two variables on the upper tail. Similarly, the lower tail dependence coefficient 𝜆𝐿 is defined as follows: 𝜆𝐿 = lim 𝑃(𝐹1(𝑌) < 𝑤|𝐹2(𝑋) < 𝑤) = lim ( 𝑢→0+

𝑢→0+

𝐶(𝑤, 𝑤) ) ∈ [0,1] , 𝑤

where the value of 𝜆𝐿 = 0 indicates that X and Y are asymptotically independent whereas the value closer to 1 indicates the strong asymptotic dependence of the variables on the lower tail. B: Families of Copula The major portion of this discussion is extracted from Embrechtset al. (2003). 1. Elliptical Copulas: Elliptical family indicates the copulas of elliptical distributions. The elliptical distributions mainly exhibit the properties of the multivariate normal distribution. However, few distributions can be used to model multivariate extremes and other forms of nonnormal dependences. Simulation as well as computation of Kendall’s tau rank correlation and tail dependence coefficients is comparatively simple from these distributions .The well known members of Elliptic Copula family are defined as follows: i) Gaussian Copula: The copula of the n-variate normal distribution with linear correlation matrix R is 𝐶𝑅𝐺𝐴 (𝒖) = 𝜑𝑅𝑛 (𝜑−1 (𝑢1 ), 𝜑−1 (𝑢2 ), … . . , 𝜑 −1 (𝑢𝑛 )) Where𝜑𝑅𝑛 denotes the multivariate distribution function of the n-standardized normal variates. The correlation structure is explained by the matrix Rand 𝜑 −1 denotes the quantile function of the standard normal distribution for each variable. Explicitly, in case of two random variables the copula expression can be written as

𝜑−1 (𝑢)𝜑−1 (𝑣)

𝐶𝑅𝐺𝐴 (𝑢, 𝑣) =

∬ −∞−∞

1 −(𝑠 2 − 2𝑅12 𝑠𝑡 + 𝑡 2 ) 𝑒𝑥𝑝 { } 𝑑𝑠 𝑑𝑡 2 1/2 2 2𝜋(1 − 𝑅12 ) 2(1 − 𝑅12 )

There is no tail dependence for Gaussian Copulas. ii)Student’s t-Copula:If any stochastic variable X has the form √ν 𝐗=𝛍+ 𝐙, √𝐒 Where𝝁 = (𝑢1 , 𝑢2 , … . , 𝜇𝑛 ) ,S ∼ χ2 υ and 𝐙is multivariate standard normal variable with mean vector0 and covariance matrix∑. Then, X has a multivariate t-distribution with υ degrees of 𝜐 freedom, mean vector 𝝁 (for υ>1) and covariance matrix ∑ (for 𝜈 > 2 ). 𝜈−2 The Copula of X can be expressed as: 𝑡 (𝒖) 𝑛 𝐶𝜈,𝑅 = 𝑡𝜈,𝑅 (𝑡𝜈−1 (𝑢1 ), 𝑡𝜈−1 (𝑢2 ), … . . , 𝑡𝜈−1 (𝑢𝑛 ))

Explicitly the Copula expression, in case of two random variables can be written as: 𝑡𝜈−1 (𝑢)𝑡𝜈−1 (𝑣) 𝑡 (𝑢, 𝐶𝜈,𝑅 𝑣) =

∬ −∞−∞

1 (𝑠 2 − 2𝑅12 𝑠𝑡 + 𝑡 2 ) 𝑒𝑥𝑝 {1 + } 2 1/2 2 2𝜋(1 − 𝑅12 ) 𝜈(1 − 𝑅12 )

−(𝜈+2) 2

𝑑𝑠 𝑑𝑡

The tail dependence coefficients (because of symmetry) in case of two random variables can be expressed as: 1 − 𝑅12 𝜆𝑢 = 𝜆𝑙 = 2𝑡𝜈+1 (−√𝜈 + 1 (√ )) 1 + 𝑅12 2. Archimedean Copulas: Mathematically Archimedean Copulas can be defined as follows (see Rachev, 2003): Definition: Let 𝜑be a continuous, strictly decreasing function from [0, 1] to [0,∞]such that 𝜑(1) = 0, and let 𝜑[−1] be the pseudo-inverse of 𝜑. Let C be the function from [0, 1]2to [0, 1] given by C(u, v) = 𝜑[−1]( 𝜑(u) + 𝜑(v)) (1) Then C is a copula if and only if 𝜑is convex.The function 𝜑 is called agenerator of the copula. If 𝜑 (0) = ∞, we say that 𝜑 is a strict generator. In this case,𝜑 [−1] = 𝜑-1and C(u, v) = 𝜑-1(𝜑 (u) + 𝜑 (v)) is said to be a strict Archimedean copula. The two well-known members of this family are Gumbel copula that is appropriate to model upper tail dependence and the Clayton copula when the lower tail dependence is of interest. Mathematically, Gumbel and Clayton copulas can be defined as: i) Gumbel Copula: Let𝜑 (t)=(− ln 𝑡)𝜃 , where 𝜃 ≥ 1. Then eq. (1) can be expressed as:

1

𝐶𝜃 (𝑢, 𝑣) = exp(−[(− ln 𝑢)𝜃 + (− ln 𝑣)𝜃 ]𝜃 ) This Copula family is called Gumbel copula with upper tail dependence coefficient given by 𝜆𝑢 = 2 − 21/𝜃 ii) Clayton Copula: Let𝜑 (t) =(𝑡 −𝜃 − 1)/𝜃 , where 𝜃 ∈ [−1, ∞) − {0}. This gives the Clayton Copula as 1

𝐶𝜃 (𝑢, 𝑣) = max([𝑢−θ + 𝑣 −θ − 1]−θ , 0), where the lower tail dependence coefficient is given by 𝜆𝐿 = 2−1/𝜃 Another class of Archimedean copulas which is gaining popularity during past few years is the 2-parameter Archimedean copulas. This class is different from the one parameter Archimedean copulas (discussed before) in a sense that it discriminate the dependence of the upper tail from the lower tail. This indicates that under this family two different parameter coefficients are estimated; one is used to describe the lower tail dependence and the other explains upper tail dependence. This class of Copulas can be considered when tail dependence is found on both upper and lower tails with asymmetry behavior. We’re going to include two members from this family of copulas i.e. BB7 (Joe-Clayton) and BB1 (Gumbel-Clayton) copula. iii) BB7 (Joe-Clayton) Copula: Mathematically BB7 Copula can have the following functional form (1 − (1 − 𝑢)𝜃 )−𝛿 + 𝐶𝐵𝐵7 (𝑢, 𝑣) = 1 − (1 − [ ] (1 − (1 − 𝑣)𝜃 )−𝛿 − 1

−1/𝛿 1/𝜃

)

,

where𝜃 ∈ (0, ∈ ∞) and 𝛿 ∈ [1, ∞)could be utilized to gauge tail reliance coefficients for upper and lower tails. The upper and lower tail dependence coefficients are given by 𝜆𝐿 = 2−1/𝛿 and𝜆𝑈 = 2 − 21/𝜃 However, the BB7 Copula cannot accommodate negative dependence of the variables. iv) BB1 Copula: The BB1 Copula is a two parameter copula having the following functional form 1

𝐶𝐵𝐵1 (𝑢, 𝑣) = (1 + [(𝑢−𝜃 − 1)𝛿 + (𝑣 −𝜃 − 1)𝛿 ]𝛿 )

−1/𝜃

where 𝜃 ∈ (0, ∈ ∞) and 𝛿 ∈ [1, ∞) can be used to estimate tail dependence coefficients for upper and lower tails. The upper and lower tail dependence coefficients are given by 𝜆𝐿 = 2−1/𝛿𝜃 and𝜆𝑈 = 2 − 21/𝛿

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Table 1a: Descriptive Statistics of Emerging Economies Economies Brazil South Africa India China Emerging Economies Base Period

Mexico

Mean Median Std. Dev. Skewness Kurtosis Jarque-Bera Mean Median Std. Dev. Skewness Kurtosis Jarque-Bera

0.0014 0.0010 0.0011 0.0014 0.0155 0.0111 -0.2726 -0.4897 4.1111 6.2515 66.6*** 501.1*** Global Financial Crisis Period 0.0001 0.0001 0.0004 0.0000 0.0211 0.0148 0.0661 -0.0611 9.4278 5.3804 1796.3*** 246.9***

0.0013 0.0017 0.0141 -0.8727 10.4541 2547.1***

0.0009 0.0001 0.0144 -0.3977 7.7193 995.4***

0.0014 0.0018 0.0111 -0.2104 6.1845 448.4***

0.0002 0.0000 0.0196 0.2388 9.7507 1990.4***

-0.0003 0.0000 0.0198 -0.2045 5.4405 266.1***

0.0001 0.0004 0.0159 0.2764 8.7405 1445.4***

Japan

FTSE 100

S&P 500

0.0007 0.0004 0.0105 -0.4536 4.8705 187.8***

0.0005 0.0005 0.0068 -0.3158 4.4719 111.5***

0.0004 0.0006 0.0067 -0.1842 3.9985 49.2***

-0.0007 0.0000 0.0181 -0.3020 9.7985 2024.5***

-0.0001 0.0000 0.0158 -0.0535 8.9858 1557.6***

-0.0001 0.0005 0.0171 -0.1957 10.0768 2183.1***

Table 1b: Descriptive Statistics of G5 Economies France Germany Base Period Mean 0.0007 0.0008 Median 0.0007 0.0009 Std. Dev. 0.0085 0.0096 Skewness -0.2510 -0.3020 Kurtosis 4.3173 4.2173 Jarque-Bera 86.4*** 80.2*** Global Financial Crisis Period Mean -0.0004 -0.0002 Median 0.0000 0.0002 Std. Dev. 0.0173 0.0165 Skewness 0.1661 0.2389 Kurtosis 8.7737 9.6570 Jarque-Bera 1453.5*** 1935.8*** *** indicates significance at 1% level of significance

Table 2: GARCH Modeling of Stock Returns Base Period Country

GFC Period

Innovation Innovation Volatility Dynamics Distribution F-Stat Prob Volatility Dynamics Distribution F-Stat Prob

a) Emerging Economies Brazil GARCH(1,1) South Africa AR(1)-GARCH(1,1) India AR(1)-GARCH(1,1) China GARCH(1,1) Mexico GARCH(1,1)

Normal Normal Normal Normal Normal

0.2591 0.6109 GARCH(1,1) 0.8088 0.3687 GARCH(1,1) 1.8950 0.1689 GARCH(1,1) 0.0608 0.8054 GARCH(1,1) 0.0413 0.8390 GARCH(1,1)

Normal Normal Normal Normal Normal

0.8597 0.3540 0.0413 0.8389 0.4328 0.5108 0.0571 0.8111 0.3075 0.5794

b) G5 Countries France GARCH(1,1) Germany GARCH(1,1) Japan GARCH(1,1) FTSE 100 GARCH(1,1) S&P 500 GARCH(1,1)

Normal Normal Normal Normal Normal

0.9299 0.3351 GARCH(1,1) 0.4083 0.5230 GARCH(1,1) 0.2429 0.6222 GARCH(1,1) 0.1002 0.7516 GARCH(1,1) 1.3299 0.2491 AR(1)-GARCH(2,2)

Student’s t Student’s t Normal Student’s t Student’s t

1.3938 0.2380 2.2065 0.1377 1.3700 0.2421 2.7802 0.0957 0.0798 0.7777

Table 3 : Kendall’s Tau (Bivariate Dependency) Country Pairs Base Period a) Emerging Economies Brazil India 0.0820 Brazil South Africa0.1690 Brazil China 0.0621 Brazil Mexico 0.3863 India South Africa0.1831 India China 0.0502 India Mexico 0.0946 South Africa China 0.0119 South Africa Mexico 0.2097 China Mexico 0.0424 b) G5 Countries Pairs France Germany 0.7387 France Japan 0.1965 France FTSE 100 0.6349 France S&P 500 0.2708 Germany Japan 0.1920 Germany FTSE 100 0.5835 Germany S&P 500 0.2907 Japan FTSE 100 0.1749 Japan S&P 500 0.0700 FTSE 100 S&P 500 0.2643 c) US and Emerging Markets S&P 500 Brazil 0.3855 S&P 500 India 0.0486 S&P 500 South Africa0.1296 S&P 500 China 0.0271 S&P 500 Mexico 0.3984

GFC Period

Z-Score

0.1816 0.2397 0.0974 0.4858 0.2939 0.1994 0.2019 0.1323 0.2901 0.0890

2.30 1.68 0.81 2.81 2.68 3.46 2.50 2.76 1.96 1.07

** *

0.8010 0.1928 0.7256 0.4579 0.1676 0.6814 0.4476 0.1727 0.0980 0.4121

3.50 0.09 3.87 4.94 0.57 3.74 4.15 0.05 0.64 3.82

***

2.77 2.86 2.82 0.39 3.29

*** *** ***

0.4839 0.1725 0.2489 0.0442 0.5125

*** *** *** ** *** **

*** *** *** ***

***

***

Note: The z-test statistic tests whether the estimated correlations are significantly different across the two periods. The rejection of the null hypothesis against the onesided alternative that the turmoil correlation is greater at the 10%, 5%, 1% significance levels, is denoted by *, **, ***, respectively.

Table 4 : Independence Test (on Bivariate Pseudo-Copulas) Country Pairs a) Emerging Economies Brazil Brazil Brazil Brazil India India India South Africa South Africa China

India South Africa China Mexico South Africa China Mexico China Mexico Mexico

b) G5 countries France Germany France Japan France FTSE 100 France S&P 500 Germany Japan Germany FTSE 100 Germany S&P 500 Japan FTSE 100 Japan S&P 500 FTSE 100 S&P 500 c) US with Emerging Markets Brazil S&P 500 India S&P 500 South Africa S&P 500 China S&P 500 Mexico S&P 500

Base Period Stat p-value

GFC Period Stat p-value

3.9616 8.1696 3.0012 18.6734 8.8509 2.4290 4.5735 0.5728 10.1349 2.0498

0.0001 0.0000

0.0000 0.0000

0.0000 0.5668 0.0000 0.0404

8.7844 11.5913 4.7127 23.4941 14.2128 9.6418 9.7634 6.3964 14.0298 4.3026

35.7238 9.5044 30.7041 13.0978 9.2846 28.2191 14.0592 8.4582 3.3872 12.7817

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0007 0.0000

38.7173 9.3217 35.0741 22.1338 8.1015 32.9404 21.6342 8.3484 4.7388 19.9225

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

18.6347 2.3480 6.2655 1.3117 19.2598

0.0001 0.0188 0.0000 0.1896 0.0000

23.39389 8.3375 12.0300 2.1396 24.7759

0.0000 0.0000 0.0000 0.0324 0.0000

0.0027 0.0000 0.0000 0.0151

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Table 5: Copula Selection and Goodness-of-Fit Test Results Country Pairs

Copula Model Base Period

GFC Period

Base Period GFC Period Stat p-value Stat p-value

a) Emerging Economies Brazil India

Clayton

BB7

1.8522

0.1735

0.0608

0.4600

Brazil Brazil Brazil

South Africa China Mexico

Clayton Clayton Student’s t

BB1 Gaussian BB7

0.2468 0.9028 0.0011

0.6193 0.3420 0.9999

0.0506 0.1328 0.0692

0.6100 0.7156

India India India South Africa

South Africa China Mexico China

Student’s t Clayton Gaussian Independence

Student’s t Gaussian Student’s t Gaussian

0.0014 4.0831 1.3528 n.a.

0.9999 0.0433 0.2448

0.0061 0.3661 0.0002 0.4125

South Africa

Mexico

Clayton

Student’s t

2.5907

0.1075

0.0025

0.9999

China

Mexico

Clayton

Gaussian

2.0190

0.0687

0.7932

0.1553

0.4000 0.9999 0.5452 0.9999 0.5207

b) G5 Economies France

Germany

BB1

Student’s t

0.5748

0.4400

0.0008

0.9999

France

Japan

Clayton

Clayton

0.0377

0.8461

0.6247

France

FTSE100

BB1

Student’s t

0.8020

0.1100

0.0198

0.4293 0.9999

France

S&P 500

Student’s t

Student’s t

0.0006

0.9999

0.0122

Germany

Japan

Student’s t

Clayton

0.0052

0.9999

3.8332

0.9999 0.0502

Germany

FTSE100

Student’s t

Student’s t

0.0038

0.9999

0.0246

0.9989

Germany

S&P 500

Student’s t

Student’s t

0.0025

0.9999

0.0065

0.9998

Japan

FTSE100

Clayton

Clayton

1.6963

0.1928

0.3934

0.5305

Japan FTSE100

S&P 500 S&P 500

Gaussian BB7

Clayton Student’s t

4.1191 0.6120

0.0424 0.5400

1.5251 0.0218

0.2168 0.9999

Clayton Clayton Student-t Independence Clayton

0.0009 0.0143 1.3085 n.a. 0.0010

0.9999 0.9047 0.2527

0.0586 1.4966 0.0004 n.a. 0.4856

0.8087 0.2212 0.9999

c) US with Emerging Markets S&P 500 S&P 500 S&P 500 S&P 500 S&P 500

Brazil India South Africa China Mexico

Student- t Clayton Gaussian Independence Student-t

0.9999

0.4859

Table 6: Parameter Estimates of Selected Copulas Country Pairs

Base Period Pram 1 Pram 2

GFC Period Pram 1 Pram 2

Clayton Clayton Clayton Student’s t Student’s t Clayton Gaussian Independence Clayton Clayton

0.1629 0.3376 0.1209 0.5668 0.2900 0.1127 0.1601

0.3524 0.4744 0.1792 0.1706 0.4438 0.3756 0.3130

BB1 Clayton BB1 Student’s t Student’s t Student’s t Student’s t Clayton Gaussian BB7

0.9495 0.4222 0.8568 0.6994 0.4438 0.7933 0.4490 0.3712 0.1117 1.3458

2.5203

0.5734 0.1048 0.2024 0.5889

Copula Model

a) Emerging Economies Brazil Brazil Brazil Brazil India India India South Africa South Africa China

India South Africa China Mexico South Africa China Mexico China Mexico Mexico

10.2785 18.577

0.4295 0.0823

33.1905 19.167

0.5727 0.1711

b) G5 Economies France France France France Germany Germany Germany Japan Japan FTSE100

Germany Japan FTSE100 S&P 500 Japan FTSE100 S&P 500 FTSE100 S&P 500 S&P 500

0.8373 0.4059 0.5199 0.6615 0.2718 0.8640 0.6518 0.3821 0.1608 1.5052

3.3708

5.6764

0.6948 0.2811 0.3795

5.0703

10.4674

0.7281

5.3563

1.8603 4.1999 19.167 6.6937 5.7904

0.3404

2.582 5.8792 30.0000 10.5501 7.5478

0.6876

c) US with Emerging Markets S&P 500 S&P 500 S&P 500 S&P 500 S&P 500

Brazil India South Africa China Mexico

Student- t Clayton Gaussian Independence Student-t

Table 7: Upper and Lower Tail Dependency Country Pairs

Upper Tail Base Period

Lower Tail Base Period

* GFC Period GFC Period a) Emerging Economies Brazil India 0.0000 0.0000 0.0142 0.1399 Brazil South Africa 0.0000 0.0000 0.1284 0.2320 Brazil China 0.0000 0.0000 0.0032 0.0209 Brazil Mexico T 0.1044 0.0000 0.1044 0.0000 India South Africa T 0.0038 0.0113 0.0038 0.0113 India China 0.0000 0.0000 0.0021 0.1595 India Mexico N n.a. n.a. n.a. n.a. South Africa China I n.a. n.a. n.a. n.a. South Africa Mexico 0.0000 0.0000 0.1991 0.2981 China Mexico 0.0000 0.0000 0.0002 0.0174 b) G5 Economies France Germany 0.6834 0.7717 0.7485 0.7823 France Japan 0.0000 0.0000 0.1936 0.1813 France FTSE100 0.5485 0.6921 0.6473 0.5967 France S&P500 T 0.1164 0.2757 0.1164 0.2757 Germany Japan T 0.0036 0.0002 0.0036 0.0002 Germany FTSE100 T 0.3750 0.3774 0.3750 0.3774 Germany S&P500 T 0.1534 0.2141 0.1534 0.2141 Japan FTSE100 0.0000 0.0000 0.1546 0.1630 Japan S&P500 0.0000 0.0000 0.0000 0.0000 FTSE100 S&P500 0.3263 0.4151 0.1305 0.3649 c) US with Emerging Markets S&P500 Brazil T 0.2221 0.3358 0.2221 0.3358 S&P500 India 0.0000 0.0000 0.0013 0.0849 S&P500 South Africa N n.a. n.a. n.a. n.a. S&P500 China I n.a. n.a. n.a. n.a. S&P500 Mexico T 0.1118 0.3538 0.1118 0.3538 * Note: letters denote the type of copula family; N=Gaussian, T= student’s-t and I= independent