# Return and Volatility Transmission between World-Leading and Latin American Stock Markets: Portfolio Implications

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## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Data and Methodology

#### 3.1. Data

#### 3.2. Methodology

## 4. Empirical Results and Implications

#### 4.1. Descriptive Statistics

#### 4.2. Return and Volatility Spillover between the US and LA Stock Markets

#### 4.3. Return and Volatility Spillover between China and the LA Stock Markets

#### 4.4. Optimal Weights and Hedge Ratio Portfolio Implications

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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1 | Our study is different from the study of Gamba-Santamaria et al. (2017) in the following aspects. Gamba-Santamaria et al. (2017) examine the volatility spillover between the US and four Latin American markets (Brazil, Chile, Mexico, and Columbia) during the US financial crisis, whereas our study is examining the volatility as well as return spillover between the leading (US and China) markets and four Latin American markets (Brazil, Chile, Mexico, and Peru) during the US financial crisis and the crash of the Chinese stock market. More specifically, firstly our study examines the return as well as volatility spillovers, whereas Gamba-Santamaria et al. (2017) examine the directional volatility spillovers. Second, our study is examining the spillovers between two world-leading (the US and China) markets and four LA markets, whereas Gamba-Santamaria et al. (2017) examine the spillovers between US and four LA markets. Third, our study is focusing on the spillovers during the global financial crisis and the crash of the Chinese stock market in 2015, whereas Gamba-Santamaria et al. (2017) examine the spillovers during the US financial crisis. Fourth, our study is using the BEKK-GARCH model, whereas Gamba-Santamaria et al. (2017) employ the approach of Diebold and Yilmaz (2012). Lastly, our full data sample is from January 2001 to May 2020, whereas Gamba-Santamaria et al. (2017) use the sample period from January 2003 to January 2016. Apart from the differences, the study of Gamba-Santamaria et al. (2017) is very beneficial for understanding the linkages among the US and LA stock markets. |

2 | The number of lags is selected on the basis of the AIC and SIC criteria. |

3 | We apply the BEKK-GARCH model on the valuable suggestion of a respected reviewer. |

Markets | Mean | Std. Dev. | Skewness | Kurtosis | J-B Stat | Q-Stat | ARCH |
---|---|---|---|---|---|---|---|

US | 0.00016 | 0.0124 | −0.364 *** | 14.045 *** | 27181.3 *** | 56.584 *** | 548.40 *** |

CHN | 0.00040 | 0.0155 | −0.330 *** | 8.2116 *** | 6121.9 *** | 60.119 *** | 189.01 *** |

BRAZ | 0.00047 | 0.0183 | −0.403 *** | 9.6439 *** | 9937.1 *** | 24.957 *** | 686.82 *** |

CHIL | 0.00030 | 0.0105 | −0.878 *** | 19.883 *** | 37,432.8 *** | 148.49 *** | 180.34 *** |

MEXI | 0.00024 | 0.0128 | −0.086 * | 8.3698 *** | 6403.18 *** | 108.33 *** | 173.49 *** |

PERU | 0.00047 | 0.0133 | −0.549 *** | 15.441 *** | 34605.3 *** | 290.64 *** | 796.97 *** |

ADF (t-Test) | Phillips-Perron Test | |||||
---|---|---|---|---|---|---|

Markets | None | Constant | Constant and Trend | None | Constant | Constant and Trend |

US | −79.73 *** | −79.94 *** | −79.96 *** | −80.00 *** | −80.01 *** | −80.05 *** |

CHN | −32.44 *** | −32.48 *** | −32.49 *** | −69.97 *** | −69.89 *** | −69.88 *** |

BRAZ | −72.04 *** | −72.08 *** | −72.08 *** | −72.03 *** | −72.08 *** | −72.08 *** |

CHIL | −33.59 *** | −33.64 *** | −33.67 *** | −63.11 *** | −63.11 *** | −63.10 *** |

MEXI | −50.70 *** | −50.73 *** | −50.73 *** | −63.67 *** | −63.68 *** | −63.68 *** |

PERU | −31.06 *** | −31.12 *** | −31.15 *** | −61.82 *** | −61.75 *** | −61.64 *** |

**Table 3.**Estimates of BEKK-GARCH for the US and Latin American stock markets during the full sample period

Brazil and US | Chile and US | Mexico and US | Peru and US | |||||
---|---|---|---|---|---|---|---|---|

Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | |

Panel A. Mean Equation | ||||||||

${\mu}_{1}$ | 0.075 *** | 0.000 | 0.098 * | 0.062 | 0.058 *** | 0.000 | 0.047 *** | 0.000 |

${\varnothing}_{11}$ | −0.031 ** | 0.036 | 0.007 | 0.722 | 0.038 ** | 0.027 | 0.137 *** | 0.000 |

${\varnothing}_{12}$ | 0.023 *** | 0.005 | 0.000 | 0.938 | 0.021 | 0.109 | −0.019 | 0.185 |

${\mu}_{2}$ | 0.056 *** | 0.000 | 0.062 *** | 0.000 | 0.051 *** | 0.000 | 0.058 *** | 0.000 |

${\varnothing}_{21}$ | 0.055 ** | 0.028 | 0.111 *** | 0.000 | 0.050 *** | 0.005 | 0.081 *** | 0.000 |

${\varnothing}_{22}$ | −0.077 *** | 0.000 | −0.057 *** | 0.001 | −0.071 *** | 0.000 | −0.042 *** | 0.006 |

Panel B. Variance Equation | ||||||||

${c}_{11}$ | 0.219 *** | 0.000 | 2.496 *** | 0.000 | 0.117 *** | 0.000 | 0.161 *** | 0.000 |

${c}_{21}$ | 0.069 *** | 0.004 | 0.124 *** | 0.009 | 0.050 *** | 0.006 | 0.056 *** | 0.003 |

${c}_{22}$ | 0.118 *** | 0.000 | 0.042 | 0.571 | 0.124 *** | 0.000 | 0.122 *** | 0.000 |

${\alpha}_{11}$ | 0.225 *** | 0.000 | 0.003 | 0.562 | 0.264 *** | 0.000 | 0.309 *** | 0.000 |

${\alpha}_{12}$ | −0.014 | 0.319 | 0.001 | 0.611 | 0.008 | 0.609 | 0.004 | 0.836 |

${\alpha}_{21}$ | 0.036 | 0.421 | 0.151 ** | 0.026 | −0.026 | 0.390 | 0.010 | 0.541 |

${\alpha}_{22}$ | 0.338 *** | 0.000 | 0.341 *** | 0.000 | 0.314 *** | 0.000 | 0.300 *** | 0.000 |

${\beta}_{11}$ | 0.966 *** | 0.000 | 0.701 *** | 0.000 | 0.959 *** | 0.000 | 0.942 *** | 0.000 |

${\beta}_{12}$ | 0.005 | 0.158 | −0.003 | 0.400 | 0.005 | 0.349 | −0.002 | 0.789 |

${\beta}_{21}$ | −0.101 ** | 0.050 | 0.095 | 0.203 | 0.090 ** | 0.043 | −0.004 | 0.538 |

${\beta}_{22}$ | 0.933 *** | 0.000 | 0.944 *** | 0.000 | 0.938 *** | 0.000 | 0.947 *** | 0.000 |

Panel C. Diagnostic Tests | ||||||||

LogL | −16,174.1 | −21,397.4 | −13,816.1 | −14,378.1 | ||||

AIC | 6.789 | 8.588 | 5.970 | 6.370 | ||||

SIC | 6.799 | 8.635 | 6.017 | 6.417 | ||||

${Q}_{1}$[20] | 30.320 * | 0.065 | 1.791 | 0.720 | 19.075 | 0.517 | 328.759 * | 0.031 |

${Q}_{2}$[20] | 18.920 | 0.527 | 19.184 | 0.510 | 19.493 | 0.490 | 17.728 | 0.605 |

${Q}_{1}^{2}$[20] | 29.942 | 0.182 | 0.004 | 0.659 | 34.776 ** | 0.021 | 30.071 | 0.198 |

${Q}_{2}^{2}$[20] | 27.782 | 0.115 | 22.616 | 0.308 | 25.161 | 0.185 | 33.181 | 0.146 |

^{2}(20) indicate the empirical statistics of the Jarque–Bera test for normality, Ljung–Box Q statistics of order 20 for autocorrelation applied to the standardized residuals, and squared standardized residuals, respectively. Values in parentheses are the p-Value. ***, **, * indicate the statistical significance at 1%, 5%, and 10%, respectively.

**Table 4.**Estimates of BEKK-GARCH for US and Latin American stock markets during the global financial crisis.

Brazil and US | Chile and US | Mexico and US | Peru and US | |||||
---|---|---|---|---|---|---|---|---|

Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | |

Panel A. Mean Equation | ||||||||

${\mu}_{1}$ | 0.101 * | 0.068 | 0.113 *** | 0.000 | 0.055 | 0.246 | −0.014 | 0.744 |

${\varnothing}_{11}$ | −0.044 | 0.450 | 0.118 *** | 0.001 | 0.023 | 0.680 | 0.138 *** | 0.000 |

${\varnothing}_{12}$ | 0.021 | 0.581 | 0.019 | 0.440 | 0.096 ** | 0.043 | −0.009 | 0.770 |

${\mu}_{2}$ | 0.019 | 0.665 | 0.046 | 0.361 | 0.064 | 0.144 | 0.029 | 0.518 |

${\varnothing}_{21}$ | 0.040 | 0.578 | 0.020 | 0.308 | 0.020 | 0.707 | 0.063 | 0.107 |

${\varnothing}_{22}$ | −0.128 *** | 0.007 | −0.164 *** | 0.000 | −0.188 *** | 0.000 | −0.100 *** | 0.003 |

Panel B. Variance Equation | ||||||||

${c}_{11}$ | 0.271 ** | 0.044 | 0.287 *** | 0.000 | 0.218 ** | 0.017 | 0.291 *** | 0.000 |

${c}_{21}$ | 0.098 | 0.546 | 0.040 | 0.417 | −0.035 | 0.730 | 0.173 *** | 0.000 |

${c}_{22}$ | 0.129 ** | 0.039 | 0.153 *** | 0.000 | 0.000 | 0.799 | 0.109 *** | 0.007 |

${\alpha}_{11}$ | 0.421 * | 0.069 | 0.483 *** | 0.000 | 0.117 | 0.220 | 0.453 *** | 0.000 |

${\alpha}_{12}$ | 0.139 ** | 0.022 | −0.055 | 0.333 | −0.104 * | 0.057 | 0.087 | 0.255 |

${\alpha}_{21}$ | −0.237 | 0.128 | −0.020 | 0.550 | 0.249 *** | 0.000 | −0.088 | 0.581 |

${\alpha}_{22}$ | 0.138 | 0.145 | 0.292 *** | 0.000 | 0.295 *** | 0.000 | 0.226 *** | 0.002 |

${\beta}_{11}$ | 0.902 *** | 0.000 | 0.841 *** | 0.000 | 1.063 *** | 0.000 | 0.896 *** | 0.000 |

${\beta}_{12}$ | -0.041 * | 0.082 | 0.051 ** | 0.034 | 0.218 *** | 0.001 | −0.034 | 0.197 |

${\beta}_{21}$ | 0.071 | 0.482 | 0.024 * | 0.083 | −0.183 *** | 0.000 | 0.014 | 0.687 |

${\beta}_{22}$ | 0.990 *** | 0.000 | 0.937 *** | 0.000 | 0.797 *** | 0.000 | 0.969 *** | 0.000 |

Panel C. Diagnostic Tests | ||||||||

LogL | −2766 | −2438.432 | −2514.181 | −2804.767 | ||||

AIC | 7.792 | 7.026 | 7.132 | 8.025 | ||||

SIC | 8.018 | 7.253 | 7.359 | 8.251 | ||||

${Q}_{1}$[20] | 15.405 | 0.753 | 15.396 | 0.753 | 15.749 | 0.732 | 18.138 | 0.578 |

${Q}_{2}$[20] | 19.980 | 0.459 | 22.469 | 0.316 | 25.023 | 0.201 | 19.998 | 0.458 |

${Q}_{1}^{2}$[20] | 23.671 | 0.257 | 17.388 | 0.628 | 15.064 | 0.773 | 13.734 | 0.844 |

${Q}_{2}^{2}$[20] | 37.237 ** | 0.011 | 45.203 *** | 0.001 | 33.878 ** | 0.027 | 37.570 *** | 0.010 |

^{2}(20) indicate the empirical statistics of the Jarque–Bera test for normality, Ljung–Box Q statistics of order 20 for autocorrelation applied to the standardized residuals, and squared standardized residuals, respectively. Values in parentheses are the p-Value. ***, **, * indicate the statistical significance at 1%, 5%, and 10%, respectively.

**Table 5.**Estimates of BEKK-GARCH for the US and Latin American stock markets during the crash of the Chinese stock market.

Brazil and US | Chile and US | Mexico and US | Peru and US | |||||
---|---|---|---|---|---|---|---|---|

Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | |

Panel A. Mean Equation | ||||||||

${\mu}_{1}$ | 0.090 | 0.105 | 0.030 | 0.210 | 0.013 | 0.585 | 0.088 ** | 0.029 |

${\varnothing}_{11}$ | −0.047 | 0.172 | 0.077 * | 0.082 | −0.032 | 0.469 | 0.076 * | 0.089 |

${\varnothing}_{12}$ | 0.016 | 0.302 | −0.035 | 0.134 | 0.002 | 0.937 | −0.025 | 0.550 |

${\mu}_{2}$ | 0.064 *** | 0.004 | 0.075 *** | 0.001 | 0.072 *** | 0.001 | 0.061 | 0.158 |

${\varnothing}_{21}$ | 0.129 * | 0.064 | 0.120 *** | 0.001 | 0.137 *** | 0.000 | 0.086 * | 0.093 |

${\varnothing}_{22}$ | −0.066 ** | 0.040 | −0.052 | 0.112 | −0.059 * | 0.083 | −0.050 * | 0.085 |

Panel B. Variance Equation | ||||||||

${c}_{11}$ | 0.268 *** | 0.005 | 0.361 *** | 0.004 | 0.599 *** | 0.000 | 0.159 * | 0.066 |

${c}_{21}$ | 0.151 ** | 0.017 | 0.011 | 0.720 | 0.164 *** | 0.000 | 0.117 | 0.122 |

${c}_{22}$ | 0.124 * | 0.076 | 0.186 *** | 0.000 | 0.124 | 0.150 | 0.089 | 0.790 |

${\alpha}_{11}$ | 0.196 *** | 0.001 | 0.522 *** | 0.001 | 0.434 *** | 0.000 | 0.278 ** | 0.011 |

${\alpha}_{12}$ | 0.008 | 0.821 | −0.024 | 0.326 | 0.033 | 0.298 | 0.142 | 0.331 |

${\alpha}_{21}$ | 0.023 | 0.744 | −0.028 | 0.648 | −0.115 * | 0.052 | 0.019 | 0.850 |

${\alpha}_{22}$ | 0.430 *** | 0.000 | 0.421 *** | 0.000 | 0.381 *** | 0.000 | 0.313 | 0.416 |

${\beta}_{11}$ | 0.958 *** | 0.000 | 0.686 *** | 0.001 | −0.359* | 0.077 | 0.949 *** | 0.000 |

${\beta}_{12}$ | −0.008 | 0.571 | 0.018 | 0.411 | −0.068 *** | 0.000 | −0.042 | 0.464 |

${\beta}_{21}$ | 0.013 | 0.697 | 0.076 | 0.227 | 0.528 *** | 0.000 | −0.014 | 0.766 |

${\beta}_{22}$ | 0.880 *** | 0.000 | 0.879 *** | 0.000 | 0.915 *** | 0.000 | 0.917 *** | 0.000 |

Panel C. Diagnostic Tests | ||||||||

LogL | −2078 | −1582.556 | −1545.033 | −1733.842 | ||||

AIC | 5.759 | 4.585 | 4.429 | 4.891 | ||||

SIC | 5.986 | 4.812 | 4.655 | 5.118 | ||||

${Q}_{1}$[20] | 21.413 | 0.373 | 33.001 ** | 0.034 | 21.955 | 0.343 | 31.804 ** | 0.045 |

${Q}_{2}$[20] | 24.907 | 0.205 | 24.713 | 0.213 | 24.601 | 0.217 | 25.783 | 0.173 |

${Q}_{1}^{2}$[20] | 6.942 | 0.897 | 85.117 *** | 0.000 | 29.827 * | 0.073 | 16.276 | 0.699 |

${Q}_{2}^{2}$[20] | 8.249 | 0.890 | 9.945 | 0.969 | 10.383 | 0.961 | 8.909 | 0.984 |

^{2}(20) indicate the empirical statistics of the Jarque–Bera test for normality, Ljung–Box Q statistics of order 20 for autocorrelation applied to the standardized residuals, and squared standardized residuals, respectively. Values in parentheses are the p-Value. ***, **, * indicate the statistical significance at 1%, 5%, and 10%, respectively.

**Table 6.**Estimates of BEKK-GARCH for the China and Latin American stock markets during the full sample period.

Brazil and China | Chile and China | Mexico and China | Peru and China | |||||
---|---|---|---|---|---|---|---|---|

Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | |

Panel A. Mean Equation | ||||||||

${\mu}_{1}$ | 0.076 *** | 0.001 | 0.047 *** | 0.000 | 0.038 *** | 0.004 | 0.050 *** | 0.000 |

${\varnothing}_{11}$ | 0.033 ** | 0.050 | 0.205 *** | 0.000 | 0.101 *** | 0.000 | 0.234 *** | 0.000 |

${\varnothing}_{12}$ | 0.013 | 0.208 | 0.020 | 0.190 | 0.014 | 0.213 | 0.015 | 0.287 |

${\mu}_{2}$ | 0.044 *** | 0.008 | 0.042 ** | 0.026 | 0.050 *** | 0.000 | 0.039 ** | 0.045 |

${\varnothing}_{21}$ | 0.132 *** | 0.000 | 0.036 *** | 0.000 | 0.075 *** | 0.000 | 0.053 *** | 0.000 |

${\varnothing}_{22}$ | 0.037 *** | 0.005 | 0.041 ** | 0.019 | 0.036 ** | 0.011 | 0.042 *** | 0.009 |

Panel B. Variance Equation | ||||||||

${c}_{11}$ | 0.283 *** | 0.000 | 0.186 *** | 0.000 | 0.138 *** | 0.000 | 0.219 *** | 0.000 |

${c}_{21}$ | 0.009 | 0.699 | −0.001 | 0.956 | 0.009 | 0.721 | −0.013 | 0.500 |

${c}_{22}$ | 0.118 *** | 0.000 | 0.121 *** | 0.000 | 0.115 *** | 0.000 | 0.108 *** | 0.000 |

${\alpha}_{11}$ | 0.273 *** | 0.000 | 0.347 *** | 0.000 | 0.279 *** | 0.000 | 0.394 *** | 0.000 |

${\alpha}_{12}$ | −0.023 * | 0.059 | 0.013 | 0.490 | −0.037 *** | 0.002 | −0.024 * | 0.057 |

${\alpha}_{21}$ | 0.000 | 0.899 | 0.001 | 0.950 | 0.021 * | 0.087 | −0.002 | 0.920 |

${\alpha}_{22}$ | 0.250 *** | 0.000 | 0.243 *** | 0.000 | 0.240 *** | 0.000 | 0.237 *** | 0.000 |

${\beta}_{11}$ | 0.948 *** | 0.000 | 0.919 *** | 0.000 | 0.954 *** | 0.000 | 0.904 *** | 0.000 |

${\beta}_{12}$ | 0.015 ** | 0.040 | −0.002 | 0.741 | 0.009 *** | 0.003 | 0.015 *** | 0.007 |

${\beta}_{21}$ | 0.002 | 0.814 | 0.002 | 0.726 | −0.004 | 0.283 | 0.001 | 0.840 |

${\beta}_{22}$ | 0.966 *** | 0.000 | 0.968 *** | 0.000 | 0.969 *** | 0.000 | 0.970 *** | 0.000 |

Panel C. Diagnostic Tests | ||||||||

LogL | −19,187.432 | −15,839.650 | −17,037.161 | −16,739.334 | ||||

AIC | 7.720 | 6.599 | 7.002 | 7.045 | ||||

SIC | 7.767 | 6.646 | 7.049 | 7.092 | ||||

${Q}_{1}$[20] | 21.935 | 0.344 | 19.993 | 0.458 | 17.078 | 0.648 | 72.725 *** | 0.000 |

${Q}_{2}$[20] | 82.861 *** | 0.000 | 78.794 *** | 0.000 | 83.815 *** | 0.000 | 80.555 *** | 0.000 |

${Q}_{1}^{2}$[20] | 26.742 | 0.133 | 8.890 | 0.984 | 26.056 | 0.187 | 18.240 | 0.572 |

${Q}_{2}^{2}$[20] | 22.787 | 0.299 | 22.412 | 0.319 | 25.134 | 0.196 | 25.146 | 0.196 |

^{2}(20) indicate the empirical statistics of the Jarque–Bera test for normality, Ljung–Box Q statistics of order 20 for autocorrelation applied to the standardized residuals, and squared standardized residuals, respectively. Values in parentheses are the p-Value. ***, **, * indicate the statistical significance at 1%, 5%, and 10%, respectively.

**Table 7.**Estimates of BEKK-GARCH for the China and Latin American stock markets during the global financial crisis.

BRAZIL and China | Chile and China | Mexico and China | Peru and China | |||||
---|---|---|---|---|---|---|---|---|

Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | |

Panel A. Mean Equation | ||||||||

${\mu}_{1}$ | 0.106 * | 0.081 | 0.116 *** | 0.001 | 0.035 | 0.476 | 0.014 | 0.773 |

${\varnothing}_{11}$ | 0.029 | 0.465 | 0.195 *** | 0.000 | 0.034 | 0.340 | 0.211 *** | 0.000 |

${\varnothing}_{12}$ | −0.003 | 0.938 | −0.073 | 0.189 | −0.034 | 0.424 | −0.023 | 0.554 |

${\mu}_{2}$ | 0.044 | 0.590 | 0.001 | 0.987 | 0.090 | 0.285 | 0.030 | 0.731 |

${\varnothing}_{21}$ | 0.186 *** | 0.000 | 0.030 * | 0.083 | 0.101 *** | 0.000 | 0.103 *** | 0.000 |

${\varnothing}_{22}$ | 0.032 | 0.422 | 0.022 | 0.572 | 0.033 | 0.431 | 0.027 | 0.488 |

Panel B. Variance Equation | ||||||||

${c}_{11}$ | −0.201 | 0.105 | 0.142 ** | 0.025 | 0.127 *** | 0.008 | 0.344 *** | 0.000 |

${c}_{21}$ | 0.134 | 0.577 | 1.932 *** | 0.000 | 0.134 | 0.479 | 0.081 | 0.250 |

${c}_{22}$ | 0.143 | 0.385 | 0.000 | 0.920 | 0.195 ** | 0.037 | 0.163 * | 0.098 |

${\alpha}_{11}$ | 0.297 *** | 0.000 | 0.408 *** | 0.000 | 0.253 *** | 0.000 | 0.477 *** | 0.000 |

${\alpha}_{12}$ | −0.041 | 0.409 | −0.108 | 0.124 | −0.041 | 0.392 | −0.005 | 0.902 |

${\alpha}_{21}$ | −0.069 * | 0.089 | 0.007 | 0.686 | 0.060 ** | 0.020 | −0.031 | 0.215 |

${\alpha}_{22}$ | 0.188 *** | 0.001 | 0.316 *** | 0.000 | 0.209 *** | 0.000 | 0.181 *** | 0.000 |

${\beta}_{11}$ | 0.947 *** | 0.000 | 0.893 *** | 0.000 | 0.960 *** | 0.000 | 0.870 *** | 0.000 |

${\beta}_{12}$ | 0.006 | 0.580 | 0.021 | 0.130 | 0.003 | 0.820 | 0.005 | 0.777 |

${\beta}_{21}$ | 0.028 * | 0.085 | 0.047 | 0.260 | −0.009 | 0.292 | 0.005 | 0.515 |

${\beta}_{22}$ | 0.977 *** | 0.000 | −0.259 | 0.143 | 0.972 *** | 0.000 | 0.979 *** | 0.000 |

Panel C. Diagnostic Tests | ||||||||

LogL | −3318.981 | −2879.180 | −3090.113 | −3166.538 | ||||

AIC | 8.973 | 7.826 | 8.388 | 8.689 | ||||

SIC | 9.200 | 8.052 | 8.614 | 8.915 | ||||

${Q}_{1}$[20] | 14.730 | 0.792 | 11.805 | 0.923 | 17.935 | 0.592 | 17.407 | 0.626 |

${Q}_{2}$[20] | 30.922 * | 0.056 | 32.099 ** | 0.042 | 30.614 * | 0.060 | 31.335 * | 0.051 |

${Q}_{1}^{2}$[20] | 22.021 | 0.339 | 12.016 | 0.916 | 14.074 | 0.827 | 9.990 | 0.968 |

${Q}_{2}^{2}$[20] | 28.559 | 0.127 | 37.567 | 0.161 | 26.806 | 0.141 | 28.213 | 0.104 |

^{2}(20) indicate the empirical statistics of the Jarque–Bera test for normality, Ljung–Box Q statistics of order 20 for autocorrelation applied to the standardized residuals, and squared standardized residuals, respectively. Values in parentheses are the p-Value. ***, **, * indicate the statistical significance at 1%, 5%, and 10%, respectively.

**Table 8.**Estimates of BEKK-GARCH for the China and Latin American stock markets during the crash of the Chinese stock market.

BRAZIL and China | Chile and China | Mexico and China | Peru and China | |||||
---|---|---|---|---|---|---|---|---|

Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | Coefficient | p-Value | |

Panel A. Mean Equation | ||||||||

${\mu}_{1}$ | 0.055 | 0.282 | 0.039 * | 0.063 | 0.008 | 0.765 | 0.059 * | 0.087 |

${\varnothing}_{11}$ | 0.036 | 0.292 | 0.181 *** | 0.000 | 0.077 ** | 0.017 | 0.229 *** | 0.000 |

${\varnothing}_{12}$ | 0.043 ** | 0.048 | 0.026 | 0.350 | 0.012 | 0.791 | 0.033 | 0.333 |

${\mu}_{2}$ | 0.022 | 0.495 | 0.020 | 0.474 | 0.020 | 0.420 | 0.022 | 0.410 |

${\varnothing}_{21}$ | 0.105 *** | 0.001 | 0.057 *** | 0.001 | 0.074 *** | 0.000 | 0.062 *** | 0.003 |

${\varnothing}_{22}$ | 0.032 | 0.360 | 0.040 | 0.228 | 0.039 | 0.255 | 0.026 | 0.470 |

Panel B. Variance Equation | ||||||||

${c}_{11}$ | 0.915 *** | 0.000 | 0.232 * | 0.057 | 0.390 *** | 0.000 | 0.259 *** | 0.009 |

${c}_{21}$ | 0.126 *** | 0.001 | 0.049 | 0.132 | 0.033 | 0.553 | 0.089 ** | 0.045 |

${c}_{22}$ | 0.000 | 0.865 | 0.000 | 0.799 | 0.058 | 0.237 | 0.051 | 0.320 |

${\alpha}_{11}$ | 0.334 *** | 0.000 | 0.452 *** | 0.004 | 0.405 *** | 0.000 | 0.345 *** | 0.004 |

${\alpha}_{12}$ | −0.043 | 0.159 | 0.096 ** | 0.021 | −0.017 | 0.778 | 0.006 | 0.934 |

${\alpha}_{21}$ | 0.051 | 0.336 | 0.005 | 0.845 | −0.069 | 0.394 | 0.054 | 0.182 |

${\alpha}_{22}$ | 0.236 *** | 0.000 | 0.208 *** | 0.000 | 0.229 *** | 0.000 | 0.256 *** | 0.000 |

${\beta}_{11}$ | 0.691 *** | 0.000 | 0.844 *** | 0.000 | 0.751 *** | 0.000 | 0.890 *** | 0.000 |

${\beta}_{12}$ | −0.069 * | 0.071 | −0.065 | 0.109 | −0.032 | 0.662 | −0.032 | 0.410 |

${\beta}_{21}$ | −0.072 * | 0.056 | 0.005 | 0.525 | 0.031 | 0.260 | −0.012 | 0.404 |

${\beta}_{22}$ | 0.968 *** | 0.000 | 0.978 *** | 0.000 | 0.974 *** | 0.000 | 0.965 *** | 0.000 |

Panel C. Diagnostic Tests | ||||||||

LogL | −2506.043 | −1947.155 | −2014.255 | −2107.485 | ||||

AIC | 7.227 | 5.934 | 5.989 | 6.295 | ||||

SIC | 7.454 | 6.160 | 6.216 | 6.521 | ||||

${Q}_{1}$[20] | 21.462 | 0.370 | 29.255 * | 0.083 | 24.444 | 0.224 | 23.882 | 0.248 |

${Q}_{2}$[20] | 23.562 | 0.262 | 27.467 | 0.123 | 24.664 | 0.215 | 26.564 | 0.148 |

${Q}_{1}^{2}$[20] | 10.480 | 0.959 | 61.006 *** | 0.000 | 15.298 | 0.759 | 14.951 | 0.779 |

${Q}_{2}^{2}$[20] | 21.376 | 0.375 | 27.907 | 0.112 | 25.661 | 0.177 | 20.186 | 0.446 |

^{2}(20) indicate the empirical statistics of the Jarque–Bera test for normality, Ljung–Box Q statistics of order 20 for autocorrelation applied to the standardized residuals, and squared standardized residuals, respectively. Values in parentheses are the p-Value. ***, **, * indicate the statistical significance at 1%, 5%, and 10%, respectively.

BRAZ/US | CHIL/US | MEXI/US | Peru/US | |
---|---|---|---|---|

Full Sample Period | ||||

${w}_{t}^{LU}$ | 0.11 | 0.51 | 0.29 | 0.27 |

${\beta}_{t}^{LU}$ | 0.93 | 0.63 | 0.25 | 0.28 |

US Financial Crisis | ||||

${w}_{t}^{LU}$ | 0.17 | 0.77 | 0.49 | 0.41 |

${\beta}_{t}^{LU}$ | 0.94 | 0.42 | 0.77 | 0.56 |

Chinese Stock Market Crash | ||||

${w}_{t}^{LU}$ | 0.09 | 0.54 | 0.46 | 0.39 |

${\beta}_{t}^{LU}$ | 0.98 | 0.34 | 0.59 | 0.43 |

Header | BRAZ/CHN | CHIL/CHN | MEXI/CHN | Peru/CHN |
---|---|---|---|---|

Full Sample Period | ||||

${w}_{t}^{LC}$ | 0.41 | 0.70 | 0.61 | 0.63 |

${\beta}_{t}^{LC}$ | 0.14 | 0.07 | 0.07 | 0.08 |

US Financial Crisis | ||||

${w}_{t}^{LC}$ | 0.53 | 0.81 | 0.68 | 0.63 |

${\beta}_{t}^{LC}$ | 0.21 | 0.09 | 0.15 | 0.13 |

Chinese Stock Market Crash | ||||

${w}_{t}^{LC}$ | 0.43 | 0.68 | 0.64 | 0.64 |

${\beta}_{t}^{LC}$ | 0.23 | 0.11 | 0.07 | 0.11 |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Yousaf, I.; Ali, S.; Wong, W.-K.
Return and Volatility Transmission between World-Leading and Latin American Stock Markets: Portfolio Implications. *J. Risk Financial Manag.* **2020**, *13*, 148.
https://doi.org/10.3390/jrfm13070148

**AMA Style**

Yousaf I, Ali S, Wong W-K.
Return and Volatility Transmission between World-Leading and Latin American Stock Markets: Portfolio Implications. *Journal of Risk and Financial Management*. 2020; 13(7):148.
https://doi.org/10.3390/jrfm13070148

**Chicago/Turabian Style**

Yousaf, Imran, Shoaib Ali, and Wing-Keung Wong.
2020. "Return and Volatility Transmission between World-Leading and Latin American Stock Markets: Portfolio Implications" *Journal of Risk and Financial Management* 13, no. 7: 148.
https://doi.org/10.3390/jrfm13070148