Crises and Contagion in Equity Portfolios

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Introduction
The international impact of the recent financial crises raises issues concerning the contagion (integration and comovements).Financial integration offers welfare gains; it may also carry substantial risks.This becomes more evident in crises (Devereux and Yu 2020).There is a transmission of crisis effects from one market to another (see, among others, Baele and Inghelbrecht 2010).Each crisis has different causes and consequences to financial markets.(Ehrmann et al. 2011) and (Gunay and Can 2022) researched the existence of contagion and spillovers in the global financial crisis.
The global financial crisis refers to the 2008 subprime crisis starting in the United States and having global consequences for a few years (Raddant and Kenett 2021).The 2010 EU sovereign debt crisis had similar international consequences (Shen et al. 2015).Contagion in the European Union during the global financial crisis and the European debt crisis were examined via ADCC-GJR-GARCH and Markov-switching models citepALEXAKIS2018222.The role of national governments (via the evolution of macroeconomics and policy making) in the EU debt crisis was also researched (Kosmidou et al. 2019).
In line with Corbet and Goodell (2022), we also opine that both financial contagion and systemic risk pose major considerations when it comes to financial market operations, while the investigation of interconnectedness dynamics has become one of major importance.Globalization dynamics and technological advancements have resulted in increased interconnectedness across financial markets and affect investments all over the world.In this paper, we consider cross-border investments and international portfolio contagion by looking into international equity markets (i.e., 4 regions/containments, 67 countries) and by further applying weights based on a set of macroeconomic variables that affect contagion dynamics.
The present paper makes a number of contributions to the literature.It extends the empirical findings provided by Cho et al. (2015) to the international stock markets.The augmented structural factor model of Cho et al. (2015) is employed to model shifts in integration and incorporate crisis dummies.It examines sixty international stock indices from sixty respective national stock exchanges instead of firm level data.The second contribution is whether certain portfolios based on national macroeconomic variables provide different contagion evidence than others.Moreover, the paper determines the value of the stock indices, either emerging or developed, and with different values of country characteristics (macroeconomic variables), on a regional and global level.
As far as the theoretical contributions of the paper are concerned, we add to the existing literature by considering various crises periods across the globe and by adopting different portfolio frameworks.For instance, we employ different weights for portfolio construction depending on the underlying macroeconomic variable.Moreover, we show that portfolio contagion is stronger in the global rather than the regional framework.In turn we find that market capitalization is the most appropriate macroeconomic variable to use in order to reveal contagion, compared to all other macroeconomic variables.We also show that Europe is the region mostly affected by crises and that the Argentinian crisis had a very pronounced effect across global economies.In this respect, we offer fresh insights regarding contagion in international equity portfolios, and we further provide fertile ground for future research on the relevant topic.
The remainder of the paper is organized as follows.Section 2 presents the literature review.Section 3 describes the dataset.In turn, Section 4 outlines methodology.Section 5 presents the empirical findings and the discussion, and Section 6 concludes.

Literature Review
Many scholars have recently been involved in research relating to the dynamics of contagion and financial interdependence.For instance, Corbet and Goodell (2022) stress the importance of investigating interconnectedness dynamics across firms, industries, and markets and provide evidence by considering reputational contagion.Furthermore, Corbet et al. (2022) offer valuable insights with regard to contagion dynamics by looking into the implications of the COVID-19 pandemic for stock market performance.In turn, Bouzzine and Lueg (2020) look into the impact of contagion dynamics stemming from environmental violations on the stock market performance.
Different methods have been employed to study contagion in financial crises.A part of the literature employed the DCC-GARCH methodology to quantify the impact of a global financial crisis in the interdependence of the markets (Nguyen et al. 2022).The literature has also employed a Markov-switching Bayesian vector autoregression (MSBVAR) model to research contagion for the global financial crisis (Troug and Murray 2021).It is expected that a trade-off emerges between the probability of crises and the severity of crises (Devereux and Yu 2020).The importance of national or regional exposures to contagion was evident and increased due to the global financial crisis, however.These effects have not been researched a lot in the literature.There was evidence for the banking sector, however (Park and Shin 2020), as well as in equity markets (Trihadmini and Falinaty 2020).
Another stream of the literature examined the role of macroeconomics in the international impact of the recent financial crises in contagion (Jiang et al. 2022).The Mexican and Asian crises, originating in emerging markets, were considered to have mostly a regional impact, whereas the recent US and EU debt crises had a global impact.The global impact of global financial crisis and the European sovereign debt crisis were examined in BenSaïda and Litimi (2021).They found an increased degree of dependence for each crisis, suggesting strong evidence of contagion for both the global financial crisis and EU sovereign debt crisis.The strong impacts depend on the role of macroeconomics.This is because controlling the impact of macro variables that capture real or financial linkages on stock correlations is crucial for determining market overreactions to shocks (Pineda et al. 2022).
The internationalization of the impact of the financial crises was expressed in both trading as well as asset allocation.The literature examined such impact for the recent global and EU financial crises in an asset allocation framework.Such regional and global impacts affect portfolio diversification and asset allocation.Financial crises create international portfolio diversification opportunities as the extent of the contagion increases (Akhtaruzzaman et al. 2014).Cho et al. (2015) examined whether crises have different effects on style portfolios.Others researched international contagion (the transmission of financial shocks internationally) for US downturns and the global financial crisis (Akhtaruzzaman and Shamsuddin 2016).The literature attempted to conceptualize this impact in a portfolio framework (e.g., Shen and Li 2020).
The methodology employed is a regime-switching GARCH model in accordance with a world-regional-local CAPM, similar to Cho et al. (2015) and Baele and Inghelbrecht (2010).More of the recent studies include Shruthi and Shijin (2020), Dua and Tuteja (2021), and Bouker and Mansouri (2022), among others.This is a joint hypothesis problem of an appropriate factor specification of comovements.Moreover, Baele and Inghelbrecht (2010) and Ehrmann et al. (2011) contagion tests are employed to discover whether international equity portfolios experienced contagion effects through increased comovements during periods of financial crises.Ehrmann et al. (2011) examined the additional impact on comovement represented by a multi-factor model with global, regional, and country factors.The US and EU financial crises are expected to have a high global impact in international equity portfolios.Cho et al. (2015) found signs of contagion with a global impact for the US crisis (also evident in Bekiros 2014; Dungey and Gajurel 2014).Cho et al. (2015) also found a regional impact for the Mexican and Asian crises (also evident in Ehrmann et al. 2011), and a limited impact for the EU debt crisis.Similar evidence is expected for the international equity portfolios in the present paper.

Dataset
The dataset begins on 3 January 2000 and ends on 31 December 2016, for a total of 4264 trading days.All of the data have been extracted from Datastream.We have employed data only up to 2016, because we targeted only the examination of financial crises.A wider dataset should have included data within the COVID-19 pandemic.This would have affected our results, as the literature provided evidence that COVID-19 affected contagion (Akhtaruzzaman et al. 2021).After cleaning the dataset for common trading days in an international setting; the trading days were reduced to 3906.All of the stock market data are in US dollars.Table 1 reveals the countries (split in regions/continents) and their respective stock exchanges and indices.The symbols, as well as the regional and global weights based on trade integration, GDP, and stock market capitalization, are also provided.In terms of trade integration, the Americas and Europe have the highest and lowest weightings, respectively.In terms of GDP, USA and Africa have the highest and lowest weightings, respectively.In terms of stock market capitalization, Europe and Africa have the highest and lowest weightings, respectively.We may conclude that USA and Europe are the regions with the highest portfolio weightings.The region with the lowest portfolio weightings is Africa.Sixty-seven countries are researched across four regions. 1  The countries selected are the countries with the most significant economies and stock markets in their regions/continents.The three financial crisis periods, following Cho et al. (2015), are: the Argentine debt crisis (1 December 2001-29 November 2002), the US financial crisis (18 July 2007-27 August 2009), and the EU debt crisis (8 December 2010-31 December 2011).Table 1 also reveals the regional (local) and the international significance of each country's trade integration, gross domestic product (GDP), inflation rate, interest rate, and stock market capitalization of each country.A quarterly or monthly macro data series is retrieved by the Economic Outlook Database of the International Monetary Fund.For quarterly data, a linear interpolation based on the monthly ones is implemented. 2 Notes: Table 1 describes the dataset.It includes the countries examined, their respective stock exchanges, main stock indices, and symbols.It also includes the average values of the international and regional significance of each country and region (for international significance) for different weighting schemes (e.g., trade integration, GDP, and stock market capitalization).
Table 2 presents the portfolio descriptive statistics.In terms of average portfolio values, the Americas and Europe have the highest values.In terms of portfolio standard deviations, Africa and Europe have the lowest values.In terms of portfolio Sharpe ratios, Europe and Asia have the highest values.In terms of cumulative return, the Americas with Europe second have the highest values, across all portfolio types.Regarding the overall portfolio performance by considering all portfolio descriptive estimates; Europe first and the Americas second are the best performers, with Africa last.By comparing portfolio types, the market capitalization seems to provide the best portfolio weighting scheme in terms of portfolio performance.

Structural Regime-Switching Factor Model
The present paper employs the Cho et al. (2015) structural regime-switching factor model in an asset (non-portfolio) CAPM model.The present paper's model, as employed in Cho et al. (2015), concerns regional and international results and targets to capture key stylized facts like time varying betas, volatility clustering, volatility regimes, financial crises, and structural economic variables.
where r i,t is the excess return on country i with µ i,t its time-varying mean (expected return); r reg,t is the regional market return; e w,t is the global market shock (r w,t = µ w,t−1 + e w,t ); e i,t is the country specific idiosyncratic shock; e reg,t is the regional market shock (obtained from the regression r reg,t = µ reg,t−1 + β w reg,t e w,t + e reg,t ); Time varying betas are explained from both structural economics variables, a regime variable, and crisis dummies.
where β w i,t and β reg i,t are the time-varying exposures of country i to the world and regional shocks; S i,t is a latent regime variable different for each country; X w reg,t−1 are structural variables like trade integration (TI), gross domestic product (GDP), and stock market capitalization (MC) that are regionally or internationally aggregated; D j,t is a crisis dummy variable.
Following the specifications of Cho et al. (2015), the regional shocks e reg,t are estimated by an asymmetric GARCH(1,1) t-student model, and the world (global) shocks (e w,t ) by a regime-switching asymmetric GARCH(1,1) Normal model, respectively.
The model is estimated in three steps: First, the world shock is estimated; second, the regional shock is computed using the first step's world shock, and finally, the full model is estimated for each country.et al. (2011) consider contagion as the excess comovement beyond fundamental linkages and suggest the following test for contagion:

Ehrmann
where êi,t is the estimated idiosyncratic return shocks of portfolio i, D j,t is a crisis dummy variable, and v j captures the contagion crisis effect.

Empirical Findings and Discussion
Empirical findings concern (i) the portfolio performance (different measures); (ii) the stylized facts of volatility regimes, financial crises, and structural economics variables (in a structural regime-switching model); and (iii) the contagion test (following Ehrmann et al. 2011) results.

Portfolio Performance
In the present subsection, the results concern the portfolio time-varying betas.These are indicated by the implied global and implied regional betas (see Table 3).They are also reported for various portfolio weighting schemes (market capitalization, trade integration, GDP, inflation, and interest rates).In terms of implied global betas, the highest and lowest concern Botswana and the United Arab Emirates.An interesting result is that the countries in the Americas have low average values of implied global betas.It is also noticeable that most of the countries, even in Africa or Asia, that should have been expected to have exceptionally high global betas did not.All regions had average implied global betas compatible with most of the countries of other regions; with the single exception of Africa.Moreover, there is a lot of dispersion among countries of the same region.This is why we provided the average implied regional betas.Next, the average implied regional betas indicate the relative market risk of national stock indices within the region they belong to, and these are reported for various portfolio types (i.e., portfolio weighting schemes).Africa first with the Americas second are the regions where most of their regional countries have high implied regional betas.Europe has the lowest.The results are robust across most of the portfolio weighting schemes.A single exception is trade integration, for which the implied regional betas change a lot, with most of the countries having average implied regional betas higher than 1.

Stylized Facts
Tables 4-7, as well as, Table 8, report the estimated coefficients for all types of international equity portfolios.The results from such a model are retrieved regionally and internationally and concern the stylized facts of volatility regimes, financial crises, and structural macroeconomic variables.The differences between the portfolio types are signified via their differences in the magnitude and statistical significance of the coefficients in the structural regime-switching factor models.The magnitude and statistical significance results are not contradictory.This is why we mostly concentrate on statistical significance.
The statistical significance in the structural regime-switching factor model is high for both global and regional betas.This result concerns all regions and most of the portfolio weighting schemes.
The single exception was market capitalization, for which the results for most of regions were statistically significant only for regional betas.This exception concerns the statistical significance of all coefficients (regime variables, crises, and macroeconomic variables) and the overall model significance (adjusted R-squared and F-test).
The following results concern most portfolio weighting schemes.By considering the majority of the countries within a region with statistically significant latent regime variables.Regarding crisis-coefficients (ARG, US, and EU), Europe was affected by all crises, Africa was affected only by the US crisis, the Americas region was affected by the Argentinian and US crises, and Asia was affected mostly by the Argentinian and US crises (and in some weighting schemes, from the EU crisis as well).The macroeconomic variables indicated a significantly greater affect (where most of the countries had statistically significant macrocoefficients (MC, TI, GDP, INF, INT)) for all regions, as well as for all portfolio weighting schemes (the single exception is the market capitalization scheme for global betas).The overall significance (F-stat) was impressively high and was mostly concentrated on the Americas and Europe.The adjusted R-squared values are not impressively high, however.

Contagion Test
Tables 9-12, as well as Table 13, report the Ehrmann et al. (2011) contagion test results of all international equity portfolios while splitting them between the implied global and implied regional betas.The differences between the portfolio types are signified via their differences in the magnitude and statistical significance of the coefficients in the structural regime switching factor models.The magnitude and statistical significance results are not contradictory.This is why we mostly concentrate on statistical significance.The contagion effect is assessed by the v 0 coefficient, whereas the contagion from each crisis is indicated by the (Arg cr., US cr., and EU cr.) coefficients.They are all reported in Table 5A-E.
The most important result of the Ehrmann et al. (2011) contagion test was the indication of strong contagion.There were 3-4 regions with most of their countries having statistically significant contagion.This result holds for all portfolio weighting schemes.Specifically, across the portfolio weighting schemes, the presence of contagion was evident in all regions (in descending order): Europe (7 cases), Asia (5 cases), the Americas (3 cases), and Africa (2 cases).Furthermore, across all regions, the presence of contagion was evident in all portfolio weighting schemes (in a descending order): MC, GDP, and INT first with 4 cases per each scheme and TI and INF with 3 cases per each scheme.Moreover, across all regions and portfolio weighting schemes, the implied global betas had stronger indications of contagion compared to the implied regional betas (11 compared to 7 cases).Notes: Table 5 reports the estimated coefficients for all types of international equity international-trade-based portfolios from the structural regime-switching factor model.Coefficients are retrieved regionally and internationally and concern the stylized facts of volatility regimes, financial crises, and structural economics variables.β w 0 and β w 1 are the estimates of the latent regime variables.The three crises concern the coefficients of the three respective dummy variables.MC, IT, GDP, INF, and INT concern the coefficients of the respective structural macroeconomic variables (i.e., changes in market capitalization, trade integration , GDP growth, inflation rate, and interest rate).Then, the adjusted R 2 (adj.R 2 ) and the joint significance hypothesis F test (F − stat) are reported.** and * indicate statistical significance in 5% and 10%, respectively.Notes: Table 7 reports the estimated coefficients for all types of international equity inflation-rate-based portfolios from the structural regime-switching factor model.Coefficients are retrieved regionally and internationally and concern the stylized facts of volatility regimes, financial crises, and structural economic variables.β w 0 and β w 1 are the estimates of the latent regime variables.The three crises concern the coefficients of the three respective dummy variables.MC, IT, GDP, INF, and INT concern the coefficients of the respective structural macroeconomic variables (i.e., changes in market capitalization, trade integration , GDP growth, inflation rate, and interest rate).Then, the adjusted R 2 (adj.R 2 ) and the joint significance hypothesis F test (F − stat) are reported.** and * indicate statistical significance in 5% and 10%, respectively.Overall, there was no strong evidence in favor of crises causing contagion on a regional level with either global or regional implied betas.There were many countries from all regions with statistically significant crisis-coefficients, however, on a country level.The Argentinian crisis was the crisis that affected mostly contagion, with EU second and US third.The Argentinian crisis caused contagion in three cases: in Africa (on trade-integrationand GDP-based portfolios for implied global betas) and Asia (on trade-integration-based portfolios for implied regional betas).The EU crisis was responsible for contagion in a few cases only: in Africa (on inflation-rate-and interest-rate-based portfolios for the implied global betas) and the Americas (on trade-integration-based portfolios for implied regional betas).The US crisis was responsible for contagion in a single case only: in the Americas on GDP-based portfolios for implied global betas.

Table 1 .
Description of the dataset.
Notes: Table2presents the portfolio performance measures (average, standard deviation, Sharpe ratio, and cumulative return) of the different types of international equity portfolios.

Table 3 .
Average implied global and regional betas.

Table 4 .
Structural regime-switching factor model on market-capitalization-based portfolios.

Table 4 .
Cont.Table4reports the estimated coefficients for all types of international equity market-capitalization-based portfolios from the structural regime-switching factor model.Coefficients are retrieved regionally and internationally and concern the stylized facts of volatility regimes, financial crises, and structural economic variables.β w 0 and β w 1 are the estimates of the latent regime variables.The three crises concern the coefficients of the three respective dummy variables.MC, IT, GDP, INF, and INT concern the coefficients of the respective structural macroeconomic variables (i.e., changes in market capitalization, trade integration , GDP growth, inflation rate, and interest rate).Then, the adjusted R 2 (adj.R 2 ) and the joint significance hypothesis F test (F − stat) are reported.** and * indicate statistical significance in 5% and 10%, respectively.

Table 5 .
Structural regime-switching factor model on trade-integration-based portfolios.

Table 6 .
Structural regime-switching factor model on GDP-based portfolios.

Table 6 .
Cont.Table6reports the estimated coefficients for all types of international equity GDP-based portfolios from the structural regime-switching factor model.Coefficients are retrieved regionally and internationally and concern the stylized facts of volatility regimes, financial crises, and structural economic variables.β w 0 and β w 1 are the estimates of the latent regime variables.The three crises concern the coefficients of the three respective dummy variables.MC, IT, GDP, INF, and INT concern the coefficients of the respective structural macroeconomic variables (i.e., changes in market capitalization, trade integration , GDP growth, inflation rate, and interest rate).Then, the adjusted R 2 (adj.R 2 ) and the joint significance hypothesis F test (F − stat) are reported.** and * indicate statistical significance in 5% and 10%, respectively.

Table 7 .
Structural regime-switching factor model on inflation-rate-based portfolios.

Table 8 .
Structural regime-switching factor model on interest-rate-based portfolios.

Table 8 .
Cont.Table8reports the estimated coefficients for all types of international equity interest-rate-based portfolios from the structural regime-switching factor model.Coefficients are retrieved regionally and internationally and concern the stylized facts of volatility regimes, financial crises, and structural economic variables.β w 0 and β w 1 are the estimates of the latent regime variables.The three crises concern the coefficients of the three respective dummy variables.MC, IT, GDP, INF, and INT concern the coefficients of the respective structural macroeconomic variables (i.e., changes in market capitalization, trade integration , GDP growth, inflation rate, and interest rate).Then, the adjusted R 2 (adj.R 2 ) and the joint significance hypothesis F test (F − stat) are reported.** and * indicate statistical significance in 5% and 10%, respectively.

Table 9 .
Ehrmann et al. (2011)he results of theEhrmann et al. (2011)contagion test depending on market-capitalizationbased portfolios.The v 0 and v j coefficients (j concerns the crises) are reported with an indication of statistical significance as well.** and * indicate statistical significance in 5% and 10%, respectively.Results came from either internationally or regionally constructed portfolios.Portfolios are market capitalization weighted portfolios; specifically, the weighting scheme is based upon changes in stock market capitalization.

Table 10 .
Ehrmann et al. (2011)the results of theEhrmann et al. (2011)contagion test depending on trade-integrationbased portfolios.The v 0 and v j coefficients (j concerns the crises) are reported with an indication of statistical significance as well.** and * indicate statistical significance in 5% and 10%, respectively.Results came from either internationally or regionally constructed portfolios.Portfolios are trade integration weighted portfolios; specifically, the weighting scheme is based upon changes in trade integration.

Table 11 .
Ehrmann et al. (2011)the results of theEhrmann et al. (2011)contagion test depending on GDP-based portfolios.The v 0 and v j coefficients (j concerns the crises) are reported with an indication of statistical significance as well.** and * indicate statistical significance in 5% and 10%, respectively.Results came from either internationally or regionally constructed portfolios.Portfolios are GDP weighted portfolios; specifically, the weighting scheme is based upon changes in GDP growth rate.

Table 12 .
Ehrmann et al. (2011)the results of theEhrmann et al. (2011)contagion test depending on inflation-ratebased portfolios.The v 0 and v j coefficients (j concerns the crises) are reported with an indication of statistical significance as well.** and * indicate statistical significance in 5% and 10%, respectively.Results came from either internationally or regionally constructed portfolios.Portfolios are inflation rate weighted portfolios; specifically, the weighting scheme is based upon changes in inflation rates.

Table 13 .
Ehrmann et al. (2011)the results of theEhrmann et al. (2011)contagion test.The v 0 and v j coefficients (j concerns the crises) are reported with an indication of statistical significance as well.** and * indicate statistical significance in 5% and 10%, respectively.Results came from either internationally or regionally constructed portfolios.Portfolios are interest rate weighted portfolios; specifically, the weighting scheme is based upon changes in interest rates.