How successful Latin & North are in Integrating their Equity Markets? Evidence from Time-Varying Volatility Shock Analysis

Abstract

This study investigates time-dependent high dimensional intra- and inter-regional volatility spillover connectedness dynamics of equity markets of the North and Latin American economies for the sample period 2000-2016. A comparative study of the change in the level of connectedness, pre- and post-crisis, has been done concerning the 2008 crisis. For the same, static and rolling stands of generalized variance decompositions independent of Cholesky-factor ordering, and network theory applications is employed. The confluence is highly useful in finding the markets important to establish the spillover direction. It also assists in determining changes in spillover hierarchy, spillover patterns, and system-wide risk vulnerability of the nations covered in the study. The result shows that being the developed markets, the US and Canada dominate the region (both North and Latin) most. Due to NAFTA, Mexican economies are deeply linked with US and Canada. The Latin economies, Argentina, Colombia, Chile, and Peru are the receiver of shocks. The low system-wide total connectedness (41.59 percent) emphasize the requirement of a regional comprehensive economic partnership between North and Latin as a group.

Keywords: Diversification, Economic Integration, Financial Econometrics, International Financial Markets.

JEL Classification: C58, F15, F36, G15.

1. Introduction

The North, and Latin America region is a blend of developed, developing, and oil-rich economies. Canada, Venezuela, Mexico, Brazil, United States (US) and Colombia are the top crude oil exporters of the region1. In North America, the US and Canada have developed economies, whereas Mexico2 is categorized as an emerging economy embarking on economic reform programs. On the other hand, Latin America has set of most dynamic and open economies (Brazil, Colombia, Chile, and Peru) highly significant for global investors. Argentina which is the second largest country in the region is an exception. In the last two decades, considerable efforts have been made to integrate the economies of this region through trade and capital flows. In this regard, a noteworthy stride of the area is the creation of three crucial trading blocs. The North American Free Trade Agreement (NAFTA)3 between the US, Canada, and Mexico (formed in 1994). The Southern Common Market (Mercosur) among Argentina, Brazil, Paraguay, Uruguay, and Venezuela (formed in 1991), and the Pacific Alliance among Chile, Colombia, Mexico, and Peru (built recently in 2011). However, the existing trade blocs are limited to intra-regional connectedness only, i.e., between North-North and Latin-Latin. Although a bilateral free trade agreements between US-Chile (came into force on January 1, 2004), and the US-Peru (entered into force on February 1, 2009), is strengthening inter-regional connectedness of North and Latin, a comprehensive inter-regional economic partnership between Latin and North can boost the financial and economic connectedness of the entire America’s region significantly. In the last one decade, the GDP share of its rising stars, Brazil, Mexico, Colombia, Chile, and Peru has grown substantially. It is expected that they will continue to drive the growth of the region in the coming years. Further, to align their equity markets with the mature markets of North, they are liberalizing their stock markets since the early 90s. The efforts made in last two decades resulted in a significant increase in the interdependence of North and Latin American stock markets, but due to local and geopolitical factors, markets of Latin have been not equally benefited. In North, the stock market of USA is the largest followed by Canada & Mexico4. In Latin America, Brazil’s stock market is by far the most significant and most in-depth stock market followed by Chile, Colombia, and Peru. The stock markets of Chile, Colombia, and Peru are of medium to small size among emerging markets and are working towards a common securities market named MILA (Mercado Integrado Latinoamericano – The Latin American integrated market). With keen interest from Mexico to join, MILA holds the potential to become one of the world’s major trading venues. If implemented, this would inevitably increase the degree of interdependence between the Latin and North American markets.

1 Source: http://www.worldstopexports.com/worlds-top-oil-exports-country/ 2 Geographically, Canada, the United States, and Mexico make up the largest part of the continent of North America. Also, the geopolitical reality of Mexico is not consistent with its categorization as a Latin American country. 3 . NAFTA not only relaxed trade restrictions for virtually every good and service among them, but also, harmonized the commercial and legal framework, promoted cross country investment and foreign direct investment and liberalized their stock markets which led them to achieve stronger links among their stock markets.4 Source: http://www.visualcapitalist.com/all-of-the-worlds-stock-exchanges-by-size/

Owing to the increasing regionalization, the markets of Latin and North is now more exposed to idiosyncratic shocks. The cascading impact of idiosyncratic shocks may turn a regional crisis into a global crisis, as experienced during the 2008 financial crisis. The shock spillover from the distressed market transmits to other markets of the system through several transmission channels. The shock intensity and direction depends on the level of relative exposure to regional & bilateral trade &, and economic partnership. Against this background, it is essential to investigate the system-wide shock spillover dynamics and risk vulnerability of Latin and North American economies, highly relevant to portfolio managers in identifying the markets for asset allocation and controlling system-wide risk vulnerability.

The studies focusing pairwise connectedness among significant equity markets of the North & Latin America is plentiful (Pagan and Soydemir, 2000; Chen, Firth, and Rui, 2002; Tabak and Lima, 2002; Arouri, Bellalah, and Nguyen, 2010; Güloğlu et al. 2016; Gamba-Santamaria, 2017). The studies are mainly categorized as the US versus Latin and within Latin. However, the studies analyzing system-wide shock spillover connectedness of Latin and North American stock markets, including secondary markets like Bermuda, Costa Rica and Jamaica, is rare.

Empirical evidence suggests that in the time of fear, i.e., during the financial crisis, the effects of idiosyncratic shock spillovers increases the degree of system-wide fear connectedness. As implied volatility bears a direct relationship between the quantum of fear and markets' expectations of future volatility5, the connectedness between the equity market could be best captured by focusing on dynamic and directional linkages of local implied volatility indices accounting global fear sentiments ( Félix et al., 2017). However, due to non-availability of local implied volatility indices6, we have used a close substitute of the same. The nonparametric absolute volatility not only gives a reasonable estimate of the long-term memory effect of volatility spillover, but it also offers an excellent prediction of future market behavior (Forsberg, and Ghysels, 2007).

In a high dimensional spillover connectedness system, controlling the optimal inference of coefficients and degree of parameter variations is highly cumbersome (Granger, 2008; Tse and Tsui, 2002; Engle and Kelly, 2012). Recently, utilizing the generalized variance decomposition (GVD) approach of Koop et al. (1996), and Peshran and Shin (1998), Diebold, and Yilmaz derived GVD connectedness measures found very helpful in capturing the system-wide connectedness of financial assets like equity, bond, and currency (Diebold and Yilmaz, 2012, 2014, 2016). Eventually, they also suggested the usefulness of the same in creating sensible network maps for exploring the system-wide connectedness dynamics of large-scale financial systems. Surprisingly, so far, the network studies in empirical finance is mostly limited to exploring bivariate connectedness only (Tse et al., 2010; Greenwood-Nimmo et al., 2016; Baumöhl et al. 2018). The existing network studies are mostly based on the concept of a threshold, either fixed arbitrarily or

5 In a high fear market, a risk premium charged by the options writer, thus, options are priced with higher volatilities than the volatilities used in low fear. This implies that the implied volatility indexes track the investors' fear sentiment.6 VIX is not available for all countries covered in the analysis. Available only for US, Canada, and Mexico.

through some statistical validation, primarily used to explore the connectedness of high significance only (Curme et al., 2014). In the late 1950s, Erdős–Rényi has introduced two random graph models (Erdős, and Rényi, 1959).

Whereas the first is limited to exploring connectedness of high significance picking a fixed number of edges based on a threshold, the second is more intuitive selecting each of the independently present possible edges between the nodes/vertices. For this reason, the second has led to the emergence of more sensible network graphs highly useful for risk vulnerability analysis. This paper uses the same along with time-dependent static and rolling connectedness GVD measures for the full sample and sub-sample periods of pre- and post-crisis. Since crude oil plays a critical role in the geopolitics of the region, the impact of the same is analyzed from the perspective of oil crisis 2008-09 and 2014-2016. Cumulative assessment of these three would help in system-wide risk assessment, risk mitigation and forecasting the connectedness pattern. This would also help policymakers undertake measures that can potentially make the equity markets more resilient to the cross-border volatility overspills. This study is expected to provide better insight on the equity market connectedness of the Latin and North American markets for three prominent reasons. First, as absolute volatility is obtained non-parametrically, they are more precise measures of the underlying volatility process than either ARCH, GARCH or SV models ( Forsberg, and Ghysels, 2007). Second, the inference in this paper is based on a more accurate measure of system-wide rolling variance decomposition independent of Cholesky-factor ordering. Third, the study deepens the application of network measures. Other than Canada, USA, Mexico, Brazil, Argentina, Chile, Colombia, Peru, and Venezuela, the markets of Costa Rica and Jamaica is also included in the study to make it more comprehensive.

The remainder of the paper is organized as follows. Section 2 provides an overview of the previous academic literature on the stock market return spillovers and contagion of Latin and North American markets within the region as well as globally. Section 3 describes the data and its descriptive analysis. Section 4 provides brief of the generalized variance decomposition methodology and the network theory applications. Section 5 discusses the results and conclusions of static, rolling and network dynamics of system-wide connectedness. Section 6 concludes the study.

2. Literature Review

In the academic discourse, the quest of a pairwise and system-wide dynamic and directional connectedness model which can support policymakers and portfolio managers to take curative measures to curb the shock spillover from the mature or conventional markets of the region/globe is not new. The literature on pairwise intra- and inter-regional connectedness of Latin and North American stock markets is extensive too. Choudry (1997) employed the error-correction model and concluded that the long-run correlation exists between the United States and Latin American stock markets. A similar study was carried out by Tabak and Lima (2002). They included the US and Peru in their research

along with the stock markets mentioned in Choudry (1997). They found no significant connectedness among the United States and Latin American stock markets from 1995 to 2001; however, shocks originating from the US do impact Latin American stock markets. Christofi and Pericli (1999) used a VAR model and a multivariate exponential GARCH process to study the intra-regional connectedness of Latin American stock markets and found significant intra-regional connectedness among stock markets of Mexico, Brazil, Colombia, Argentina, and Chile. Pagan and Soydemir (2000) employed impulse response functions to analyze the interdependence of the Latin American markets. They concluded that because of the geographical location, any financial shock originating from Brazil seems to have more impact on Chile and Argentina as compared to the shock origination from Mexican stock markets. Using multivariate cointegration analysis, Chen, Firth, and Rui (2002) analyzed the connectedness among Latin American stock markets of Argentina, Brazil, Chile, Colombia, Mexico and Venezuela from 1995 to 2000. The study suggested one long-term equilibrium relationship between the stock price indexes of Latin American stock market. They also find that Argentina is profoundly influenced by Brazil, whereas Mexico influenced all stock markets considered under this study, except Colombia in the short-term. Moreover, the connectedness among them increases abruptly after every crisis (1987 stock market crash, 1994 Mexico Peso Crisis, 1997-98 Asian financial crisis and the 2001-02 Argentine Economic Crisis). Their study also confirmed that the connectedness among these markets is significantly more during the crisis than the period before and after the crisis. Boschi (2005) investigated the contagion impact of the Argentine crisis on a set of American and non-American developing countries: Brazil, Mexico, Russia, Turkey, Uruguay, and Venezuela. The result showed that there is no evidence of contagion during the crisis. Thus, ruled out the non-crisis-contingent theories of international financial contagion. In contrast, Collins, and Gavron (2005) showed that the Argentine Crisis of 2001 caused the most incidents of contagion. They analyzed the contagion impact across 42 countries during nine financial events commonly tested as well as those that are more recent.

Diamandis (2009) employed vector auto-regression and cointegration analysis to study international financial correlation and a stochastic trend among stock markets of the US and the Latin America region. He concludes that there exists only partial connectedness among the US and the Latin American stock markets. Later, Lahrech and Sylwester (2011) studied the US and Latin American stock markets for the period 1988 to 2004, and show that there exists strong inter-dependency among them post liberalization of Argentina and Brazil markets. In a similar study, Arouri, Bellalah, and Nguyen (2010) explored the connectedness of six stock markets in Latin America (Brazil, Argentina, Colombia, Chile, Mexico, and Venezuela) with World stock markets from 1985 to 2005 by using a DCC-GARCH model. They found a positive correlation between them because of increasing globalization, the removal of barriers to international trade, universal standardization, and technological integration.

Barba and Ceretta (2010) employed the Engle-Granger methodology to study the connectedness among the United States and Latin America region before, during and after

the Global Financial Crisis of 2007-2008. Argentina, Mexico, Chile, and Brazil were considered from Latin America. They found that individual Latin American country responds differently to the crisis. While Brazil and Argentina have become more integrated with the US and their relationship has changed over time, the relationship between Chile and Mexico did not change significantly with the US. They show that shocks originated from the US impacts Latin American countries heterogeneously. To add further, Dufrenot, Mignon, and Péguin-Feissolle (2011) conducted a study on the dynamic financial correlation of the US, Peru, Colombia, Brazil, Mexico, and Chile with the 2007-2008 global financial crisis by using a time-varying transition probability Markov switching model (TVPMS). They found that US financial crisis has the highest influence on Mexico, whereas other Latin American countries (Peru, Colombia, and Brazil) are more affected by the shocks originated within the region rather than US financial. Weber (2013) proposed a stochastic volatility model for determining contemporaneous causality-in-variance effects across four major American equity markets, US, Canada, Brazil, and Mexico. The stochastic volatility transmission of variances is featured by an appropriately specified state space setup. Recently, Bolaños et al. (2015) determined the impact of the proposed Latin American Integrated Market (MILA) start-up on the profitability, risk, correlation, and trading volume of stock markets of Chile, Colombia, and Peru (the countries that confirm it).

In the context of growing interdependence of financial markets, applications of network theory have increased vigorously to explain the system-wide connectedness dynamics of large financial systems. Recently, Baumöhl et al. (2018) depicted the network volatility spillovers among 40 developed, emerging and frontier stock markets during the 2006–2014, by fitting a spatial model incorporating several exogenous characteristics.  Shahzad et al. (2018) studied the spillover structure of 58 nations using bivariate cross-quantilogram approach.  Among the system-wide network studies, the work of Diebold and Yilmaz (2014, 2016) is the most popular one.

3. Data & its Descriptive Statistics

This study uses the daily closing price of stock indices of 12 stock exchanges of the North and Latin America region. From North America, other than Canada, USA, and Mexico, Bermuda is also included in the study. From Latin, other than Brazil, Argentina, Chile, Colombia, Peru, and Venezuela, Costa Rica and Jamaica is also included in the study to make it more comprehensive. Bloomberg financial database is the source or all the data. The Bloomberg codes of the equity indices for each selected country are: BSX (Bermuda), SPTX (Canada), MEXBOL (Mexico), SPX (United States of America), MERVAL (Argentina), IBOV (Brazil), IPSA (Chile), CRSMBCT (Costa Rica), COLCAP (Colombia), JMSMX (Jamaica), SPBLPGPT (Peru), and IBVC (Venezuela). The sample period of the study is from 15th July 2002 to 22nd Dec 2016, a total of 3769 daily observations. As the study involves countries from the same time zone, the end-of-the-day closing price would not create any problem for the study. The maximum time lag between

the openings of stock markets Brazil and Mexico, falling on the last time zones of the region is not more than 4 Hours. However, as our approach to volatility connectedness is based on rolling medium-term volatility connectedness, instead of instant or end-of-the-day, time-zone is not a problem.

Figure 1 displays the time series plot of the equity indices over the sample period for the selected countries of North America and Latin America. It exhibits that in the north the USA, Canada, Mexico and in south Brazil, Chile, Colombia are showing a similar trend. The spikes are very similar. For instance, in the mid of 2008 during the global financial turmoil, the peak could be seen indicating a sudden fall in business sentiments. Similarly, in most of the countries, the downward spiral due to global financial crises 2008 is followed by a change in the trend and a phase of recovery between 2009 and 2010. However, the developing economies such as Mexico, Chile, Brazil, and Colombia are much faster in recovery due to increased domestic demand and influx of funds as part of debt restructuring in many developed economies. Another important reason is a massive flight of capital from the developed world to the developing nations during this period. After recovery, most of the economies reached pre-crisis levels, as evident from Figure 1. Interestingly, the US index has shown considerable positivism in comparison to other countries during this period. Canada too seems to have made from the recession troubles. The similar trend found in US and Canadian market can be explained by the higher level of connectedness of these two economies. It would also be correct to assume the similarity in the business sentiments of the two countries. The rest of the economies are developing; hence their indices seem to face stagnation concerning growth experiencing slight bullish phase followed by corrections.

To compare the statistical properties of the data under study, we computed a variety of summary statistics. Table 1 depicts the descriptive statistics of return. Noteworthy, Venezuela shows the highest mean return. On the other hand, Bermuda shows the lowest mean return. Argentina stock exchange shows maximum fluctuations across the mean, whereas Jamaica shows minimum. Jarque-Bera test indicates that the return does not follow a normal distribution. Test statistics of LM ARCH, Robust Ljung-Box (Q-Statistics on raw data) and Box-Pierce (Q-Statistics on squared data) is indicating the presence of ARCH (conditional heteroscedasticity) and strong autocorrelation in the squared return series’ of the equity indices. This supports our decision of using absolute volatility as a proxy of market volatility instead of deterministic ARCH & GARCH models and non-deterministic SV models. Table 2 reports the correlation matrix for the equity returns. Table 2 exhibits that the major economies of the region Canada, US, Mexico, Brazil, Peru, Argentina, Colombia, and Chile are the one showing strong to moderate positive correlation. The effect of North-North and Latin-Latin is visible from Table 2. The markets of North America countries (except Bermuda) exhibits a strong positive correlation with each other. Correlation of US-Canada is the highest followed by Canada-Mexico. Markets of Argentina, Brazil, Chile, and Peru have a significant correlation with the US. This hints towards the possibility of higher directional connectedness from the countries like US and Canada towards Brazil, Chile, Mexico, Peru, and Argentina.

Figure 1: Time Series Graphs of Price and Return of North & Latin American Markets

Table 1: Descriptive Statistics of Returns of North & Latin American Markets

Mean Median

Maximum

Minimum

Std. Dev.

Skewness

Kurtosis Jarque-Bera

LM ARCH (Lag 10)

Ljung-Box Q-(20)

Box-Pierce Q2-(50)

Bermuda -0.007 0.000 15.244 -12.938 1.206 0.020 28.957 105782.800 ** 25.36 ** 30.69 403.09**

Canada 0.022 0.052 9.370 -9.788 1.072 -0.682 14.348 20511.310 ** 184.72 ** 16.65 11776.2**

Mexico 0.052 0.047 10.441 -7.266 1.213 0.043 9.470 6573.783 ** 79.14 ** 24.95 4574.85**

Us 0.024 0.035 10.957 -9.470 1.204 -0.247 13.329 16789.070 ** 146.08 ** 22.49 9171.85**

Argentina 0.101 0.038 10.432 -12.952 1.943 -0.481 6.858 2482.548 ** 49.86 ** 32.79* 1857.41**

Brazil 0.045 0.000 13.678 -12.096 1.735 -0.044 7.783 3592.246 ** 127.44 ** 29.00 5809.58**

Chile 0.039 0.014 11.803 -7.173 0.974 0.000 13.447 17135.620 ** 82.386** 59.09** 1922.44**

Colombia 0.060 0.004 18.126 -13.254 1.265 -0.098 25.451 79142.470 ** 164.48 ** 41.92** 3435.00**

Costa Rica 0.026 0.000 57.175 -57.398 1.621 -0.454 835.052109000000.0

** 281.69 ** 13.75 927.444**

Jamaica 0.042 0.000 7.958 -6.319 0.782 0.598 16.278 27904.890 ** 16.307** 56.16** 289.131**

Peru 0.069 0.025 12.816 -13.291 1.437 -0.464 14.394 20516.120 ** 134.97** 30.33 4814.15**

Venezuela 0.220 0.000 19.811 -20.651 1.661 0.857 26.250 85332.130 ** 72.479** 40.67** 1086.65**LM ARCH Test H0: No ARCH effect.Robust Ljung-Box Q-Statistics on raw data H0: No serial correlation ==> Accept H0 when the probability is High [Q < Chisq(lag)]Box-Pierce Q-Statistics on Squared data H0: No serial correlation ==> Accept H0 when the probability is High [Q < Chisq(lag)]**: Reject the H0 hypothesis at 5% level of significance in all three cases*: Reject the H0 hypothesis at 10% level of significance in all three casesNo of Observations: 3768

Table 2: Unconditional Correlation Statistics of Latin and North American Stock Market Returns

Bermuda Canada Mexico US Argentina Brazil Chile Colombia

Costa Rica Jamaica Peru Venezuela

Bermuda 1Canada -0.001 1Mexico 0.002 0.614 1US 0.004 0.734 0.692 1Argentina 0.019 0.523 0.481 0.485 1Brazil 0.018 0.595 0.653 0.618 0.534 1Chile 0.013 0.484 0.547 0.495 0.421 0.523 1Colombia 0.003 0.350 0.367 0.277 0.329 0.332 0.348 1

Costa Rica -0.012 0.000 0.008 -0.014 0.000 0.008-

0.004 0.011 1Jamaica 0.009 0.042 0.032 0.012 0.017 0.031 0.033 0.059 0.006 1Peru 0.009 0.480 0.422 0.391 0.389 0.430 0.424 0.329 0.000 0.037 1Venezuela 0.032 0.022 0.006 0.006 0.007 0.019 0.023 0.044 -0.019 0.012 0.025 1

4. Methodology

In an increasing era of regionalization and globalization, the financial crisis of one nation/region can have a significant impact on stock markets returns of other markets/region. Therefore, in empirical finance, it is often of interest to know the response of one variable to another variable in a system that involves some further variables. In the high dimensional VAR system, impulse response function (IRF) and forecast error variance decomposition (FEVD) are the prominent tools in interpreting shock spillovers (Pesaran, Schuermann, and Weiner, 2004; Lanne, and Nyberg, 2016). In FEVD, which is an improved version of IRF, the connectedness arises not only through the cross-variable dependence captured in VAR coefficients but also through the shock dependence caught in the VAR disturbance covariance matrix. Correlation of the error terms indicates that a shock in one variable is likely to be accompanied by a shock in another variable of the system, thus more helpful for system-wide connectedness analysis. However, similar to IRF, the FEVD results are found to be sensitive to Cholesky ordering (Diebold and Yilmaz, 2009). In such case, the generalized approach of Koop et al. (1996), and Pesaran, and Shin (1998), in short KPPS, is highly useful. The generalized method of KPPS, not only allow for correlated shocks but also appropriately accounts for uncorrelated structural shocks (arising elsewhere) from correlated reduced-form shocks that too by producing variance decompositions invariant of ordering (Diebold and Yilmaz, 2012). Utilizing the same, Diebold, and Yilmaz derived a set of connectedness measures found highly useful for explaining the pairwise and system-wide directional connectedness of a financial system (Diebold and Yilmaz, 2012, 2014, 2016). This paper uses the same. Next section explains the same in brief.

4.1 GVD Connectedness - Independent of Cholesky Ordering

We build volatility connectedness measures from the variance decomposition matrix of a

vector autoregressive approximating model, written as V i =∑i=1

pΦ V t−1+ε t , where Φ is a

N×N matrix of parameters to be estimated, and ε t ~ (0 , Σ ) . The moving average

representation is V t =∑i=1

∞Ai εt−i , where the N×N coefficient matrices

Ai obey the

recursion Ai=Φ0+Φ1 A i−1+Φ2 A i−2+. . .. .+Φ p A i−p with A0 and N×N identity matrix and Ai=0 for i<0 . All aspects of connectedness are contained in this very general representation. In particular, contemporaneous aspects of connectedness are summarized inΦ0 , and dynamic aspects in ....,, 21 Nevertheless, attempting to understand

connectedness via the potentially many hundreds of coefficients in { Φ0 , Φ1 , Φ2 , . . .} is

typically fruitless. One needs a transformation of { Φ0 , Φ1 , Φ2 , . . .} that better reveals and more compactly summarizes connectedness. Generalized variance decompositions achieve this. Table 3, which we call a connectedness table/matrix [D], is central to our understanding the system-wide and pairwise connectedness measures of North & Latin American countries.

Table 3: Connectedness Matrix Schematic

_____________________________________________________________________x1 x2 … xN From Others

_____________________________________________________________________

x1 d1 1 d1 2 … d1 N ∑j=1

N

d1 j , j≠1

x2 d2 1 d2 2 … d2 N ∑j=1

N

d2 j , j≠2

⋮ ⋮ ⋮ ⋱ ⋮

xN d N 1 dN 2 … d N N ∑j=1

N

d N j , j≠N

_____________________________________________________________________

To Others ∑i=1

N

d i 1 ∑i=1

N

d i 2 … ∑i=1

N

d i N1N ∑

i , j=1

N

d i j

i≠1 i≠2 i≠N i≠ j_____________________________________________________________________

Table 3 upper-left block contains the pairwise variance decompositions including self, and we denote it byD= [d ij ] . The off-diagonal entries of D are the parts of the N forecast-error variance decompositions of relevance from a connectedness perspective; in particular, they measure pairwise directional connectedness. Hence we denote the pairwise directional connectedness from j to i as

C i ← j=d i j

It is important to note that in generalC i ← j≠C j ← i . It means there are N2−N separate

pairwise directional connectedness measures in matrix D (Table 3). This implies the net pairwise directional connectedness should be defined as

C i , j=C j ← i − Ci ← j

Table 3 exhibits that there would be 2N total directional connectedness measures, N to others or transmitted, and N from others or received. The pairwise connectedness, i.e., country j's contribution to country i's H-step-ahead error variance is measured as (Diebold and Yilmaz, 2012)

θijg(H) =

σ jj−1 ∑

h=0

H−1

(e i' Ah∑ e j)

2

∑h=0

H−1

(e i' Ah∑ Ah

' e i)

Where is the covariance matrix for the error vector ε , σ i j is the standard deviation of the

error term for the ith equation and e i is the selection vector with one as the ith element and

zeros otherwise.

The current approach of system-wide connectedness splits the forecast error variance of the variable i into parts attributed to the various variables in the system only. Thus, contrary to the linear and non-linear advance regression models like ordinary VAR, GARCH, etc., the overall fit (in our case it is degree of connectedness) doesn’t increase directly with the increase in the number of variables. For effective connectedness measures, choice of rolling window is analogous to bandwidth choice in density estimation. In this paper, we use a VAR (2) approximating model with rolling estimation window of 100 trading days, i.e., five months average. The 10-step-ahead error variance (H=10 days) is used to measure five specific variety of connectedness metrics “From, To, Net, Total and Pairwise.” (for details, please see Diebold and Yilmaz, 2012, 2015). This not only helps in managing the issue of time zone but also helps in controlling the outliers resulted from the use of daily squared returns as a proxy of absolute volatility, which causes a big problem in VAR estimation. The piecewise rolling variance decompositions primarily help in constructing network graphs for specific sample periods which further helps in capturing and forecasting the changes in directional connectedness during those particular periods. Next section explains the same in brief.

4.2 Network Graphs

According to the first model of Erdős-Rényi (1959), a network can only be represented as a symmetric adjacency matrix A=[ A ij ] , having elements as either 1 or 0, where Aij=1 if nodes i and j are connected, and Aij=0 otherwise. Erdős-Rényi shows that the matrix A has all network properties. Subsequently, they used the same to form sensible network maps.

Interestingly, it turns out that the variance decomposition matrix D, which defines connectedness table and all associated connectedness measures (From, To, Net, Total, and Pairwise), is an extended advance version of the network adjacency matrix A (Diebold and Yilmaz, 2014, 2015). The networks defined by the matrix D are more sophisticated than the classical network structures for three main reasons. First, the matrix D does not contain only zero and one value; instead, the entries are weights, with some potentially strong and others potentially weak. Second, the links are directed; i.e., the strength of the ij link is not necessarily the same as that of the ji link and hence the GVD matrix D ends up being asymmetric. Third, it has constraints on sums of rows of D. Each row must sum up to 100, implies that the total system-wide “From all others” variance decomposition cannot exceed 100. However, as some of Latin and North American markets are more vulnerable to external shocks than others, they are likely to transmit strong intensity shocks received from its one counterpart to the next counterpart sharing close economic & financial tie-ups in the form of idiosyncratic shocks. This generates a higher degree of connectedness among a group of such dependent nations. Therefore, no such restriction on the column

sum of matrix D. This implies that the “To” connectedness values can be more or less than 100 in some specific cases. As a result, unlike matrix A, the diagonal elements of matrix D would not be zero, represented as

Dii=1−∑j=1j≠ i

N

d ij

The “To” and “From” degrees which represent the row sums and column sums are expressed as:

δ i¿=∑

j=1j ≠i

N

d ij

δ j¿=∑

i=1i ≠ j

N

d ij

Compared to adjacency matrix A, the matrix D can be used to create more sensible network maps.

5. Results and Analysis

5.1 Static Connectedness

Table 4 exhibits the full-sample static connectedness matrix defined as [D] in section 4.1. In Table 4, the inner 12x12 submatrix gives the estimated i-jth pairwise directional connectedness between the North and Latin American countries. The off-diagonal column sum gives the “To” connectedness. The off-diagonal row sum gives the “From” connectedness. The bottom-most row gives the “Net” connectedness (the difference between To and From connectedness). The largest value within the row is represented by the diagonal elements, i.e., connectedness with the self. The highest “From” connectedness is shown for US (69.24%), followed by Canada (68.44%) and Mexico (68.17%). Brazil (67.33%), Argentina (60.00%) and Chile (61.31%) have also high “From” connectedness in the Latin American region. The highest “To” connectedness is from the US (83.21%) followed by Mexico (80.64%) and then by Canada (78.73%). Also, Brazil (76.92%), Chile (56.26%) and Argentina (52.92%) are other countries that have high “To” connectedness in the Latin American region. The highest positive “Net” connectedness is shown by America (13.97%) followed by Mexico (12.46%) and Canada (10.30%). Colombia shows the highest negative “Net” connectedness (-18.63%) followed by Peru (-12.82%). The system-wide “Total” connectedness for all countries is 41.89%, which shows moderate connectedness for the Americas region. Pairwise, highest connectedness is between US-Canada (17.55%), followed by US-Mexico (15.09%). Except for these two pairs only Brazil (12.07%) contribute to a two figure pairwise connectedness. The difference between ij & ji pairwise connectedness help in knowing the direction of spillover.

Noteworthy, the countries showing high connectedness with self-implies that their economy relies heavily on internal factors and the market is not much liberalized. The onus of opening the domestic markets lies solely with the policymakers and regulatory authorities of that nation if they foresee the benefits of free trade rather than having a conservative approach of a closed economy. In our study, it is quite clear that countries such as Bermuda, Costa Rica, Jamaica, and Venezuela show very high self-connectedness signifying that these nations rely more on internal factors.

Table 4: Static Connectedness Matrix (for Full Sample Period)

To market i

From market jBermuda

Canada

Mexico US

Argentina

Brazil

Chile

Colombia

Costa Rica

Jamaica Peru

Venezuela

Connectedness from others

Bermuda 99.28 0.05 0.06 0.09 0.07 0.04 0.04 0.01 0.07 0.11 0.03 0.14 0.72

Canada 0.02 31.56 12.0117.77 8.59 11.36 7.49 3.68 0.02 0.10 7.37 0.01 68.44

Mexico return 0.02 11.97 31.8315.74 7.34 13.52 9.59 4.15 0.01 0.04 5.77 0.02 68.17

US 0.02 17.55 15.0930.76 7.85 12.07 8.33 2.68 0.01 0.02 5.58 0.03 69.24

Argentina 0.02 10.92 9.5710.41 40.00 11.71 7.09 4.13 0.04 0.14 5.95 0.01 60.00

Brazil 0.05 11.70 13.9512.81 9.47 32.67 9.19 3.68 0.00 0.08 6.37 0.02 67.33

Chile 0.06 9.22 12.0011.07 6.83 11.16

38.69 4.28 0.01 0.03 6.62 0.02 61.31

Colombia 0.01 6.57 8.63 6.02 5.61 7.19 6.38 53.83 0.02 0.18 5.33 0.22 46.17Costa Rica 0.07 0.05 0.17 0.13 0.05 0.07 0.09 0.05 98.75 0.10 0.12 0.35 1.25Jamaica return 0.13 0.43 0.30 0.37 0.40 0.21 0.13 0.28 0.35 97.13 0.18 0.08 2.87

Peru 0.02 10.22 8.82 8.74 6.68 9.53 7.87 4.27 0.00 0.0443.76 0.03 56.24

Venezuela 0.20 0.04 0.04 0.05 0.03 0.05 0.05 0.30 0.09 0.03 0.09 99.03 0.97Connectedness to others 0.62 78.73 80.64

83.21 52.92 76.92

56.26 27.53 0.62 0.88

43.42 0.93 41.89 Total Connectedness

Net Connectedness -0.10 10.30 12.46 13.97

-7.08 9.59 -5.05 -18.63 -0.63 -1.98 -12.8

-0.04

2

5.2 Dynamic Rolling Connectedness

The Static connectedness is indicative of connectedness for the full sample period. It does not throw any light on the change of connectedness concerning time. This calls for a new measure which would give insight to the time variation of connectedness. Rolling connectedness does the same.

Figure 2 shows the plot of rolling “Net” connectedness over the full sample period. The pattern of rolling graphs indicates the impact of financial, economic and geopolitical events throughout the sample period. US, Canada, Mexico, and Brazil are the net transmitters throughout the full sample, and Peru shows similar trends in the “To” and “From” and “Net” connectedness. Except for the US, no other country can be said to have high instances of net connectedness in their favor. It is because of the critical position the US has in the equity markets across the world and in the Americas region. The neighbors of US are no different and have attached their fortunes with that of US. Other than US, Canada, Mexico, and Brazil are the net transmitters throughout the full sample. Bermuda, Costa Rica, Colombia, Jamaica, and Venezuela remained the net receivers throughout. Chile, Peru, and Argentina show variations between receivers and transmitters.

Figure 3 depicts the rolling plot of the system-wide “Total” connectedness. It illustrates that the “Total” connectedness remained within the range of 50 to 60. Post-crisis there is an upshot in the connectedness graph, and it reaches an all-time high of 65. The Eurozone debt crisis again hikes the graph, depicting the level of connectedness to go up during the crisis for a short while. Figure 3 exhibits three strong cycles of connectedness. First starting in the early 2000s and ending in 2007. Second, beginning with the Subprime crises 2008 and continued till 2012, sometimes eased in between, coinciding with the development of the global financial crisis and Eurozone debt crisis. This phase, the total return connectedness index touched its all-time high and rose above 65%. Third, starting with the slowdown in crude oil prices in 2014 continued until the end of 2016.

Figure 2: Rolling Net Connectedness

Figure 3: Rolling Total Connectedness

5.2 Network Connectedness (during Pre and Post Crisis)

The static and rolling connectedness measures explained previously provides very raw information about the system-wide and pairwise spillover dynamics. Understanding of time-varying spillover paths, patterns, clusters, hierarchy, exposure to shocks, etc. is still incomplete. This section explores the same with the help of network maps. A comparative study is undertaken by analyzing the change in the dynamics of network linkage during pre and post-crisis period.

For the same, this section plots “Bidirectional Connectedness Layout,” and “Directional Spillover with Vulnerability (Degree) Arrangement.” The bidirectional spillover layout provides information on volatility asymmetry existing between any two pairs, i.e., the shock intensity, nodes are passing to each other. The directional degree spillover measures the pairwise net shock intensity, direction, and vulnerability of nodes spillover. Cumulative assessment of these two will provide a comprehensive structure of system-wide and pairwise spillover connectedness dynamics of the Latin & North nations. This section explores the same in detail.

Figure 4 (Panel A1, and A2) displays the bidirectional network plot for the pre-crisis, during-crisis, and post-crisis. The time frame for pre-crisis is from January 2001 to December 2007. Post Crisis ranges from April 2009 to December 2016. The subprime crisis period covers the whole year of 2008. The period is extended till March 2009 to include the impact of the crude oil crisis of 2008-09 started mid of the crisis year. Each node represents the chosen country of the North America and Latin America region. The color of each node indicates the degree of the total “Net” connectedness, i.e., the net

difference of “To all others” minus “From all others.” A detailed analysis of these helps us in knowing the net quantum of shocks, receives and transmits by respective nodes/countries. Node colors Red, and Blue indicate they are the net transmitter of the shocks with color Red being strongest and Blue the moderate. Node Color Pink indicates strongest receiver of shocks and color Green indicates a moderate receiver. Additionally, the color of edges shows the intensity of connectedness, as an example Red color edge is of strongest intensity, Blue being the moderate and Green the weakest. To impart intensity of the same color, we have taken the thickness of edges. The color codes are based on a set of threshold values inferred from the GVD connectedness matrix (Table 4) derived for the full sample and periods of high volatilities (calculated separate GVD connectedness matrix, but not shown in the paper due to space constraints). In each case, the threshold values remain same, fixed arbitrarily for the first.

Figure 4 depicts the counter-clockwise arrangement of North American and Latin American nation regarding net transmission, from the highest transmitter to lowest transmitter, and from lowest receiver to highest receiver. As an example, in the pre-crisis window, surprisingly, Mexico is the highest net transmitter instead of US, and Brazil is the lowest transmitter. Bermuda is the lowest receiver and Peru is the highest net receiver. The thick bold edges and arrows signify the bidirectional shock intensity. Panel A1 evident that in the pre-crisis window the three big economies of the North (US, Canada, and Mexico) are the most significant transmitter of shocks, with Brazil being only a Latin American country.

Panel A1 and A2 show that the developed economies of the north reciprocate high level of connectedness, as evident from thick bold red edges and arrows. In fact, US-Canada, US-Mexico, and Canada-Mexico pairs show very strong symmetric bidirectional connectedness throughout. In the pre-crisis, Brazil is the only Latin American nation to have a strong bidirectional connectedness with the US, Canada, and Mexico. Interestingly, the big four transmitters rank high on GDP size. However, in the case of nations such as Jamaica, Costa Rica, and Bermuda even the bidirectional connectedness was weak (Panel A1 and A2). Chile, Argentina, Peru, and Colombia show a moderate level of connectedness with big four, i.e., the US, Canada, Mexico, and Brazil.

Post-crisis (Panel A2), the level of connectedness remains marginally high in comparison to the pre-crisis period. During the crisis, the bidirectional level of connectedness increased from member countries such as the US, Mexico, Brazil, etc. Hence the net effect is a strong spillover. During 2008-09 crude oil crisis, for exporting Latin American countries (Venezuela, Brazil, and Colombia), falling energy prices posed a significant threat to their financial sustainability. This has also intensified the shock spillover intensity among the oil exporting nations of Latin and North. However, the impact of the crude oil crisis is not distinguishable due to overlap with the Subprime crisis. Apparently, regional vicinity coupled with trade agreements like NAFTA has increased the economic interlinkages among the member nations of North America. On the other side, the Caribbean island nation Jamaica and Costa Rica show a moderate level of connectedness

with rest of the nations under study. A cumulative assessment of bi-directional network connectedness graph from pre to post reveals that not much of regional integration has happened in past decade. The countries which were initially strongly interconnected continue to do so. However, there is no new inclusion. The countries that seem to be left out are Bermuda, Costa Rica, Jamaica. The question that arises is how much important is regional integration from the perspective of a nation and region perspective. What could be the pitfalls if in a region certain nations are flourishing while the rest are left behind? The question finds its way in benefits of cross-country trade. The local governments of Bermuda, Jamaica and Costa Rica has to move away from the conservative approach of closed markets to liberalized market and free trade.

Panel A1: Pre-Crisis Panel A2: Post Crisis

Note: Node Threshold Level: Red > 10, 0≤Blue≤10, -5≤Green<0, Pink < -5 Edge Threshold Level (Bidirectional): Red > 5.75, 5.75≤Blue≤3.5, Green < 3.5

Figure 4: Bidirectional Network Connectedness Latin and North Economies

Figure 5 (Panel B1, and B2) depicts the Net pairwise directional spillover with degree arrangement of Latin and North America markets. The edge between any two nodes has only one-way (equal to the net pairwise connectedness measures between the two respective nodes). Due to the offsetting of shocks the net directional transmission between node pairs transmitting similar intensity of shocks to each other could be low. A directional spillover graph can give a fair idea of the group of nations that affect the stock market of a country strongly. A unidirectional transmission exhibits which nations affect the domestic market of a nation under study. In pre-crisis (Panel B1), Colombia is receiving strong shocks from Brazil and Mexico while moderate shocks from US, Canada, Argentina, and Chile. Panel B1 shows that in the pre-crisis window none of the nations under study send strong shocks to Bermuda, Costa Rica, Jamaica, and Venezuela. Noteworthy, the level of connectedness analyzed from bidirectional spillover layout reveals that these nations show low bidirectional connectedness with rest of the nations under study, throughout. However, the position of Bermuda and Jamaica on the vulnerability map makes them most exposed to incoming shocks transmissions. The only positivity in favor of them is their low to moderate level of connectedness with the rest of the nations of Latin and North.

The arrangement of nodes in Panel B1 and B2 reflects an arrangement of the number of transmissions decreasing in a counter-clockwise manner. Panel B1 exhibits that in the pre-crisis window Mexico is sending most number of shocks across the region, whereas Colombia is receiving the most number of shocks. This arrangement is useful to assess the vulnerability to shocks on a system-wide scale and should be seen as the downside of regional integration. A careful assessment of degree arrangement helps to figure out that which nations have become more vulnerable to external shocks with the pace of regional integrations. Any association that champions and promotes the merits of regional integration of North America and Latin America should weigh the need of regional integration via-a-vis the downside of it. The assessment would help to target the risk arising due to regional integration, and to take proper risk mitigation measure. Thus the degree arrangement serves as a checkbox for the regional integration. Any effort put in to strengthen cross-country ties should not only be examined from the gains made but also from the losses that may happen with a particular stock market by making it more vulnerable. The vulnerability (degree) arrangement may help the policymakers to focus more on stabilizing internal economic situations, whereas for the nations on the receiving side focus should be on external interlinkages.

Figure 4 and Figure 5 serve the investors and policymakers to assess the system-wide risk and act accordingly. From the North American region, the significant economies regarding the size of GDP and crude oil outputs as well as developed stock markets are transmitters. However, for the Latin American nation, this does not hold true. Among the Latin American countries, except Brazil, economies are either the strong net receiver or moderate receiver of shocks. The possible reason for this could be the relative less openness and illiquidity of stock market compared to the market of Brazil. The Directional Spillover assessment proves useful for the policymakers and regulatory authorities, Central banks to assess the countries on a pairwise basis. As an example, a Stock Exchange

Regulatory body of Colombia would watch carefully the markets of Mexico, Brazil, US and Canada for any kind of economic distress to affect the Colombian stock market. It is quite visible that in the post-crisis period moderate transmission from Canada and US turned strong post-crisis. Similar reasoning holds true for each node receiving strong spillover as depicted by network diagram. The study of Directional Spillover is on the pairwise basis to identify the nation which is currently affecting the stock market by sending shocks or which may affect in future. The assessment would help the policymakers to precisely take precautionary measures as their ambit of sources of shocks has expanded across the country borders.

Panel B1: Pre-Crisis Panel B2: Post Crisis

Note: Edge Threshold Level (Directional): Red > 2, 0.2≤Blue≤2, Green < 0.2

Figure 5: Directional Network Connectedness and Vulnerability (Exposure to shocks) of Latin and North Economies

6. Conclusion

In this paper, we applied the system-wide time-dependent connectedness concept to reveal insight into the way of financial spillovers and connectedness of the twelve equity markets of North America and Latin America thus reflecting the level of financial integration among these nations. The methods of generalized variance decomposition and network graph are used to explore the time-varying connectedness, the direction of spillovers, and exposure to shocks. The approach allows us to quantify system-wide and pairwise volatility spillover robust to ordering in VAR and capturing asymmetries in volatilities. The study mainly emphasized the comparative investigation of volatility transmission during pre- and post-crisis centering global financial crisis 2008, and crude-oil crisis 2008-09. The research aligns with the macroeconomic events and impact has been captured through static, rolling and directional network maps. For the full sample, we found system-wide connectedness of 41.59% between the nations under review. This shows that more efforts are required to increase the overall connectedness of North and Latin America. In addition to existing trade blocks, a regional comprehensive economic partnership between North and Latin as a group can integrate the markets more. The study reveals that developed economies of the region, i.e., US and Canada are more strongly connected, transmits strong bidirectional connectedness to each other, and are primarily responsible for transmission of shocks into the region. Being the developed markets, the US and Canada dominate the region (North and Latin both) most. Moreover, due to geographical proximity and NAFTA, Mexican economies are deeply linked with US and Canada. Thus deepening regional ties with free flow of capital and goods across America will add a new dimension in regional stability and economic reforms will be more focused and directed.

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