^{*}

^{**}

The aim of this paper is to analyze the contagion effect and the impact of the

global financial crisis in NAFTA bloc stock markets' volatility, using rolling window correlation and a GARCH approach. Once the contagion effect is established through an increasing correlation during the crisis period, volatility changes and leverage effects are tested with symmetric and asymmetric GARCH models with a dummy variable in the variance equation. Canada, the United States and Mexico's equity markets stock indexes daily yields, in US dollars, from January 2003 through February 2015 were studied. Results confirmed the presence of asymmetric volatility during the whole period and an increasing volatility since the Global Financial Crisis.

El objetivo de esta investigación es analizar el impacto de la crisis financiera global en la dinámica de la volatilidad de los mercados accionarios del bloque TLCAN, usando correlación medida a través de ventanas móviles y modelos GARCH simétricos (GARCH 1,1) y asimétricos (TARCH 1,1). Las variables financieras empleadas son los rendimientos de los precios de cierre diarios de los índices bursátiles: S&P 500 (Estados Unidos), IPC (México) y S&P TSE Composite (Canadá) en dólares de Estados Unidos, durante el periodo del primero de enero de 2003 al 27 de febrero de 2015. La evidencia confirma la existencia de volatilidad asimétrica en las series durante todo el periodo de estudio, así como incremento en la volatilidad a partir de la crisis bursátil presentada en 2007.

The global financial crisis (GFC) has been one of the most significant global events in history concerning economics and finance, due to the fast transmission of its profound impact around the world. The financial crisis first signs began to be evident through the subprime crisis in 2007 and lasted until the end of 2012. Second-round effects appeared until 2015, with the European sovereign debt crisis (

The North America Free Trade Agreement (NAFTA), integrated by Mexico, Canada and the United States, (U.S.), relates to one of the geographical zones undergoing important changes due to the GFC. The primary role played by the U.S. in the crisis and its strong relations with Mexico and Canada based on trade, foreign direct investment and, above all, foreign portfolio investments may explain the implications of the global financial crisis in the region.

To a large extent, profound and persistent global financial imbalances were caused by integration. In particular, countries with higher level of integration, as those belonging to the NAFTA bloc, have higher risk exposure to global turmoil. Therefore, to analyze the relation among the NAFTA stock markets is a key factor in order to establish the contagion effect by examining increasing correlation during the crisis. Once crisis transmission effects are determined, the presence of higher volatility and higher leverage effect, since the GFC, can be tested for by modeling NAFTA stock market's volatility through a GARCH approach.

It is of uttermost importance to study equity markets volatility and their relationships in an interconnected and deeply integrated financial backdrop, as is the NAFTA bloc case, since these markets have experienced an accelerated growth. Their rapid rise and development has allowed these stock markets to operate as a link between different economic and social agents (savers, pension funds, public and private investors and issuers), becoming an important investment channel. In this sense, an efficient performance of stock markets, as an investment channel, may enhance economic activity and reinforce economic growth and competitiveness of the NAFTA bloc economies.

On the other hand, this paper shows important implications for asset allocation, for portfolio diversification and, above all, for the construction of trilateral portfolios considering that higher correlation levels and similar responses to external financial shocks inhibit the traditional portfolio diversification techniques. Finally, to examine the volatility behavior of the NAFTA stock markets should shed some light about the integration process between these markets.^{1}

This paper is organized as follows. Section 1 presents a review of the literature. Section 2 unfolds the data and methodology used to estimate the contagion effect and the crisis effects stock market volatility. The following section discusses the empirical evidence. Finally, conclusions are presented.

Financial integration has increased investment options promoting higher levels of financial assets demand. However, it has also led to the instantaneous transmission of financial disequilibria among markets that, apparently, are not closely related. The growth of interconnections among stock markets and their relations with different economic agents have boosted the external shocks impact on economic activity, leading to the enormous devastation resulting from the recent global financial crisis and its effects. Given the importance of this phenomenon, extensive literature has been recently published about transmission effects and their impacts on the behavior of equity markets.

NAFTA is one of the world’s largest free trade zones. Recently the number and depth of studies dealing with NAFTA's stock markets has increased. Among these publications stands out the article written by

Among the studies about contagion effect,

Related to the GFC impact on volatility performance,

In this paper, two studies were regarded as a starting point. First, the one presented by

The Daily closing price of Mexico (IPC), Canada (TSE) and the U.S. (S&P500) stock indexes, in US dollars, were used to test contagion effect and changes in the volatility behavior. The time period analyzed includes from January 1, 2003 to February 27, 2015. The pre-crisis period considered comprises January 2003 to August 8, 2007 and the crisis period August 9, 2007 to February 2015, according to the periods identified by

The analysis of empirical contagion aims to determine whether or not channels and intensities of shock propagation across countries change during certain crises periods. Particularly, the contagion effect is a phenomenon characterized by a significant increase in correlation levels among different markets as a consequence of a relevant shock from other markets (

Rolling window correlation shows contagion effects, but it does not give information about the crisis effects on volatility behavior. To overcome this limitation, this paper proposes a complementary methodology that includes a GARCH approach, using symmetric and asymmetric models with a dummy variable in the variance equation, proving whether or not the volatility and leverage effect increased since the GFC.

ARCH (Autoregressive Conditional Heteroscedasticity), GARCH models and all their extensions have been identified in the empirical literature as effective in modeling the volatility of financial series. This is because the GARCH models capture some features of the assets returns volatility flows. Among the stylized factors they capture are: thick tails, volatility clustering, leverage effects, cumulative information in non-trading periods, strong inverse relation between volatility and serial correlation and co-movements in volatilities (

Based on the effectiveness and good fit of the GARCH approach on modeling asset prices volatility, this paper used these models in order to prove that the GFC impacted the dynamic of the NAFTA countries stock markets, by increasing their volatility and their volatility asymmetry.

Another advantage of the GARCH models is their parsimony. This allows estimating and interpreting the results in a simple way.

Daily returns are identified as the closing index value natural logarithm difference for two consecutive trading days;

Unit root tests were applied to determine that an individual financial series is stationary. Therefore, Augmented Dickey Fuller and Phillips Perron Tests were used . The null hypothesis is _{
0
} : _{
1
} :

GARCH modeling (

With ^{0} > 0, ^{1}_{
t
}
_{
2
} ,... _{
q
} ≧ 0 and _{
1
}
_{
2
}
_{
3
}
_{
q
} ≧ _{
t
} represents the conditional variance estimated considering relevant past information; _{i}

Increasing volatility as a result of contagion effect is determined by introducing a dummy variable in the variance equation as follows:

D represents the dummy variable which takes value 0 before August 8, 2007 and one afterwards. If the dummy variable coefficient is positive and statistically significant, an increased volatility was caused by the GFC. Then, the model was tested for ARCH effect using an ARCH-LM test. If the coefficient is not statistically significant, the model will be adequate.

There is a wide range of asymmetric GARCH models: EGARCH de

The TARCH models proposed in this paper have the following generalized specification of the variance equation:

If _{
t
} = 1 if _{
t
} < 0

In this model if _{
t-i
} < 0 the possitive residual values are interpreted as positive shocks. If _{
t-i
} < 0, negative residual values represent negative shocks. Positive news has an _{1}_{1}_{
1
}
_{
1
} effect. Whether _{
1
} > 0, negative news increases volatility, this effect is known as asymetric volatility or leverage effect, in other words if _{
1
}

Here

Index
Level
Maximum variation
High
Low
Positive
Negative
IPC
Level/Change
3680.127
722.170
0.162
-0.115
Date
11/04/2013
24/11/2003
29/10/2008
06/10/2008
TSE
Level/Change
15323.764
5849.301
0.095
-0.105
Date
31/10/2007
18/05/2004
29/10/2008
01/12/2008
S&P 500
Level/Change
2115.480
676.530
0.104
-0.095
Date
24/02/2015
09/03/2009
14/10/2008
15/10/2008

Source: Prepared by author using Bloomberg and Economatica data.

Two lines can be observed in

Descriptive statistics of NAFTA countries equity markets indexes are presented in

S. D.
Mean
Kurtosis
Skewness
Jarque Bera
ARCH F-statistics Probability
US
0.0084
0.0005
4.3735
-0.0342
73.99635
5.81 (2)
0.00
Canadá
0.0098
0.0012
4.2862
-0.3532
84.2478
3.48 (3)
0.02
México
0.0145
0.0016
5.9237
-0.2688
345.745
9.78 (1)
0.00

Reported values are statistically representative at *1%,** 5% and ***10% significance levels.

Note: the statistic test ARCH LM corresponds to the Lagrange multiplier used to detect the ARCH effect; the null hypothesis represents the absence of heteroscedasticity, distribution of that parameter is (^{
2
}

Country
S. D.
Mean
Kurtosis
Skewness
Jarque Bera
ARCH (1) F-statistics Probability
US
0.015
0.0002380
10.371
-0.454
3483.70*
172.03*
0.00
Canada
0.016
-0.0000319
9.703
-0.484
2897.44*
191.95*
0.00
Mexico
0.020
0.0000574
11.086
0.256
4146.74*
103.35*
0.00

Reported values are statistically representative at * 1%,** 5% and ***10% significance levels.

Note: As in ^{
2
}

It can be observed that volatility, measured by the increase in the standard deviation, is much higher after the crisis for all the markets. The returns distribution is negatively skewed during the pre-crisis period in all cases and negatively biased in the crisis period, except for the Mexican market that is positively biased, indicating the presence of asymmetry. The values concerning kurtosis suggest that, the distribution is leptokurtic with a high concentration on the central values and the presence of heavy tails. Additionally, LM ARCH results indicate the presence of ARCH effect for each and every one of the series under study. Since the GARCH model is suitable for modeling leptokurtic series, it is expected to correctly analyze equity markets indexes behavior. Finally, values of the ARCH (1,1) shown in

The condition of stationarity was tested applying the Phillips Perron and the Augmented Dickey Fuller tests. Results reported in

ADF
Phillips- Perron
Pre-crisis
Crisis
Pre-crisis
Crisis
Levels
FD
Levels
FD
Levels
FD
Levels
FD
-32.46
-16.59
-43.26
-21.41
-32.72
-307.81
-43.26
-376.45
(0.00)*
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
-29.98
-14.69
-35.25
-17.16
-29.99
-322.64
-35.21
-369.68
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
-29.48
-18.26
-35.19
-18.75
-29.34
-313.92
-38.02
-332.14
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)
(0.00)

Critical MacKinnon criteria at a significance level of 1% is -3.44. Null hypothesis, series has unit root

*Values within parentheses indicate probabilities

To confirm that the series are stationary, a regression equation for the average yield for each of the stock exchanges is performed by applying the Breusch-Godfrey test. The null hypothesis requires that the residuals are not serially correlated. The evidencia suggests that the probability value is greater than 0.05, rejecting the existence of autocorrelation.

For parameter estimation the Marquardt optimization logarithm was employed, in conjunction with the maximum likelihood method. Derived from maximum likelihood analysis a GARCH (1,1) model was chosen, since the other models presented negative coefficients _{
1
} y (_{1} y for all ( 0, or they were not significant at least at a 90% confidence level.

Results of the GARCH (1,1) dummy variable for the TLCAN financial series, are reported in

Coefficients
Mexico
u. S.
Canada
7.47E-06
2.52E-06
1.93E-06
(0.00)
(0.00)
(0.00)
0.0946
0.1027
0.0668
(0.00)
(0.00)
(0.00)
0.8782
0.8746
0.9236
(0.00)
(0.00)
(0.00)
0.9728
0.9701
0.9905
1.24E-06
7.20E-07
-3.17E-07
0.2198
0.0732
0.3007
0.0077
3.3911
0.1118
(0.9297)
(0.0657)
(0.7381)

*Values within parentheses indicate probabilities.

Furthermore, _{
1
} + (_{1} is smaller and very close to one, such condition insures that the ARCH process is stationary, i.e. the variance does not increase indefinitely. The fact that the lag coefficient of the conditional variance was larger than the error coefficient _{
1
} implies that there is a persistence of shocks with effects in the long run, that is, volatility does not decay rapidly but tends to remain and its effect dies off gradually.

The coefficients of the dummy variables introduced in the variance equation (GARCH dummy) are positive, except for the case of Canada; they are also statistically insignificant in the case of Mexico and Canada and in the U. S. case the coefficient is statistically significant at 10% significance level; this suggests that volatility increased in the U. S. market after the crisis. However, these results indicate the need to apply a TARCH model to examine the presence of asymmetric volatility and an increase in volatility following the financial crisis. The GARCH model is tested for its fitness and adequacy using ARCH-LM test. Results indicate that there was no ARCH effect after applying the GARCH models, since ARCH LM tests are not statistically significant as their probability value is higher than 0.05.

The financial literature, provides ample evidence proving that changes in the conditional volatility of stock returns not only depends on the magnitude of the shocks, but also on its signs; namely, good and bad news leads to different results. Bad news yields greater changes in volatility than good news which can be tested applying a TARCH (1,1) model with a dummy variable in the variance equation. Results of its implementation are shown in

Coefficients
Mexico
u. S.
Canada
6.70E-06
1.17E-05
2.29E-06
(0.00)*
(0.00)
(0.00)
0.003568
0.17777
0.035707
0.5261
(0.00)
(0.00)
0.130937
0.199725
0.052788
(0.00)
(0.00)
(0.00)
0.90793
0.703279
0.924504
(0.00)
(0.00)
(0.00)
0.911498
0.881049
0.960211
-1.09E-06
5.01E-07
-6.24E-07
(0.1346)
(0.7707)
(0.0381)
0.4542
0.7475
0.2126
(0.5004)
(0.4548)
(0.6447)

*Values within parentheses indicate probabilities.

In _{
v
} while bad news’ impact is a_{x}+ y, therefore, the impact of bad news is larger than that of good news in all financial markets analyzed. In this regard, the Canadian market shows a more pronounced effect on the asymmetry of volatility, followed by the Mexican and the U.S. markets. Therefore, the evidence confirms that negative impacts produced a leverage effect.

Results reported for the dummy variable indicate that the financial crisis did not increase the magnitude of the leverage effect on the NAFTA financial markets, where the probability associated with the dummy variable is not statistically significant and, in the case of Mexico and Canada, the dummy coefficient is negative. Meanwhile, the values of the one lag ARCH- LM values are statistically insignificant, with a probability value higher than 0.05.

As previously mentioned, the Canadian market presented higher volatility and leverage effect, followed by the Mexican market. It could be because of the size of the Canadian market and its recent merger process that started in 2011 and officially finished in 2014. This merger process has given place to the second higher transatlantic market, combining the London Stock Exchange Group pic (LSEG) with the TMX Group. These types of international operations could increase the global risk exposure.

This paper analyzes the contagion effect and volatility changes of the stock market indexes for the countries comprising the NAFTA bloc: Mexico, Canada and the U. S. Its aim was to unveil whether or not those markets were characterized by asymmetric volatility as well as if such effect became accentuated due to the global financial crisis, which began in 2007 with disequilibria in the U. S. market. Data examined included January 1, 2003 to February 27, 2015. The methodology employed to prove the contagion effect was rolling window correlation, and to capture the dynamics of the volatility returns of the IPC, TSE and S&P500 indexes, GARCH (1,1) and TARCH (1,1) models were used.

The rolling window correlation analysis offers evidence about contagion effect among the NAFTA countries stock markets. The equity indexes more closely related are IPC and S&P followed by TSE and S&P. This evidence has important implications on asset allocation and risk diversification concerning tri-national portfolios among these equity markets. Portfolio weights should be carefully optimized to benefit from higher risk returns from the Mexican market and lower risk-return performance from the other two bloc members, particularly the low correlation between the Canadian and Mexican stock markets.

Empirically, the stationarity of the series, the presence of ARCH effect and normality were first verified. Then, relevant models were chosen applying maximum likelihood analysis identifying a GARCH (1,1) model as the most suitable. The empirical evidence suggests the persistence of shocks with long run effects. Results associated with the dummy variable indicated that volatility in the Mexican and Canadian markets were not very large following the crisis, nevertheless in the case of the U. S., equity markets indexes increasing volatility since the global financial crisis, was confirmed.

Finally, a TARCH (1,1) model was applied to determine the presence of asymmetric volatility impacts on the returns of the NAFTA markets and, likewise, if such asymmetry increased following the financial crisis. Findings show that for the three stock exchanges there was a leverage effect in their return series; that is, negative news have a larger impact than positive ones on volatility. The Canadian market shows the largest asymmetry in volatility, followed by the stock markets from Mexico and the U. S., respectively. With regard to the effects of the financial crisis on volatility behavior, results about the dummy variable indicate that the financial crisis did not accentuate the asymmetrical behavior of volatility. These latter results may be indicative of a greater integration among the Mexican, Canadian and the U.S. markets due to their similar reaction to exogenous shocks.

The importance of this type of analysis consists in emphasizing that long memory and leverage effect inhibit investment operations, and higher market yields imply higher costs for corporations issuing shares and bonds, which affect the real economy, generates more expensive funding, increases prices and discourages investment. As a corollary, for policy makers, findings imply the need to enhance their stock markets to further economic integration and development.

f the price of a security, commodity or asset is different in two different markets, then an arbitrageur will purchase the asset in the cheaper market and sell it the most expensive. Otherwise, the markets are integrated.