Asymptotic Dependence Modelling of the BRICS Stock Markets
Abstract
:1. Introduction
1.1. Market Linkages and Extremal Dependence
1.1.1. Stock Markets Linkages
1.1.2. Extremal Dependence
1.2. Reviews of Studies on BRICS
1.3. Contributions and Research Highlights
- The 90th percentile is a more suitable choice in preference to the higher variance 95th and 99th percentiles;
- The pair of Brazilian IBOV and Chinese SHCOMP markets, which have a fairly strong dependence under the CMEV modelling, produced a nearly weak dependence under the point process;
- Bivariate point process results showed that the model best describes all the 10 paired markets is the Husler–Reiss, with the lowest AIC value in each pair;
- The entire findings were consistent with the results obtained from the CMEV modelling;
- The only likely exception to the consistency was between the pair of Brazilian IBOV and Chinese SHCOMP markets, which has a fairly strong dependence under the CMEV modelling but produced a nearly weak dependence under the point process;
- Weak extremal (asymptotic) dependence between each of the 7 (out of 10) paired markets from extremal dependence modelling outcomes gives beneficial risk reduction and high investment returns through international portfolio diversifications;
- A fairly good investment opportunity derivable from international portfolio diversifications can also be expected because the extremal dependence between the markets in these market pairs is “fairly strong” as compared to the “weak asymptotic” dependence.
2. Materials and Methods
2.1. Conditional Multivariate Extreme Value Modelling
2.1.1. Marginal Transformation
2.1.2. Regression Model Structure
2.1.3. Laplace Margins
2.1.4. Threshold Selection
2.1.5. Extreme Value Mixture Models
Bulk Model-Based Tail Fraction Approach
Parameterised Tail Fraction Approach
2.1.6. Estimation of Parameters
2.2. Multivariate Point Processes
2.2.1. Overview
2.2.2. Bivariate Point Process Model
2.3. Diagnostics: Model Checking
2.4. Data Description
3. Results
3.1. Multivariate Extreme Value Modelling
3.2. Conditional Multivariate Extreme Value Model
3.2.1. Multivariate Exploratory Plots
3.2.2. CMEV Model Fitting and Diagnostics
3.2.3. Dependence Modelling and Model Diagnostics
3.2.4. Extremal Dependence Results of the CMEV Model
- Conditioning on Brazilian IBOV market: From the table, it is clearly shown that the Russian IMOEX and Chinese SHCOMP markets have fairly strong positive extremal dependence on large values of the Brazilian IBOV market, with the Russian IMOEX market having stronger dependence than the Chinese SHCOMP market on the Brazilian IBOV market. The Indian NIFTY and South African JALSH markets, on the other hand, have a very weak negative extremal dependence on the conditioning the Brazilian IBOV market;
- Conditioning on Russian IMOEX market: The Brazilian IBOV, Indian NIFTY, Chinese SHCOMP and South African JALSH markets have a relatively weak positive extremal dependence on the Russian IMOEX market, with the strongest of this weak dependence being between the Russian IMOEX and Brazilian IBOV markets;
- Conditioning on Indian NIFTY market: Here, it is observed that the Brazilian IBOV and Russian IMOEX markets have varying levels of weak positive extremal dependencies on the Indian NIFTY market, while the asymptotic dependence between the Indian NIFTY and South African JALSH markets are moderately strong. The Chinese SHCOMP market, however has a weak negative dependence on the Indian NIFTY market;
- Conditioning on Chinese SHCOMP market: The values of this dependence parameter shows that the Brazilian IBOV is the most (fairly) strongly positively dependent on large values of the Chinese SHCOMP market, while the Russian IMOEX, Indian NIFTY, and South African JALSH markets have only weak extremal dependence on the Chinese SHCOMP market. More specifically, the Indian NIFTY and South African JALSH markets have weak negative levels of dependence while the Russian IMOEX market has a weak positive dependence on the Chinese SHCOMP market;
- Conditioning on South African JALSH market: The values of the dependence parameter estimates show that the Russian IMOEX, Indian NIFTY, and Chinese SHCOMP markets all have different weak positive extremal dependencies on the South African JALSH market. The strongest of these is between the South African JALSH and Indian NIFTY markets. The Brazilian IBOV market has a weak negative extremal dependence on the South African JALSH market.
3.2.5. Prediction under the CMEV Model
3.3. Bivariate Point Process Modelling
Point Process and CMEV Models Compared
4. Discussion
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
BRICS | Brazil, Russia, India, China, and South Africa |
GARCH | Generalised Autoregressive Conditional Heteroscedasticity |
CMEV | Conditional Multivariate Extreme Value |
GAS | Generalised Autoregressive Score |
GFC | Global Financial Crisis |
EVT | Extreme Value Theory |
GEVD | Generalised Extreme Value Distribution |
GPD | Generalised Pareto Distribution |
MLE | Maximum Likelihood Estimation |
Appendix A
Appendix A.1. Box Plots of the Markets Returns Data
Appendix A.2. Dependence Model Diagnostics
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REF | Data | Models | Main Findings |
---|---|---|---|
Chan-Lau et al. (2004) | Stock returns of some emerging and some mature stock markets | Extremal dependence and correlation approaches | Results show that the measures of contagion are not highly correlated |
Ji et al. (2020b) | Oil demand and stock returns of BRICS countries | Time-varying copula-GARCH CoVAR approach | The results show that there is a large risk spillover from some oil demand to the stock returns in all the BRICS countries |
Samuel (2018) | Daily stock returns for South Africa, Egypt, Nigeria, and Kenya | Bivariate-threshold-excess model and point process approach | The markets displayed asymptotic independence or (very) weak asymptotic dependence and negative dependence |
Ijumba (2013) | BRICS’s stock returns | Vector Autoregressive (VAR), univariate GARCH (1,1) and multivariate GARCH models | The Multivariate GARCH showed volatility persistence among BRICS stock markets |
Afuecheta et al. (2020) | BRICS’s stock returns | Generalised extreme value distribution, the generalised logistic distribution, the generalised Pareto distribution, the Student’s t-one exponential parameter distribution and the Student’s t-two parameter Weibull distribution; Galambos, Hsler–Reiss, Gumbel, normal, and Student’s t | The results indicated that the GEVD gave the best fit to the tails of the returns distributions of the BRICS stock markets. Using the copulas in modelling the tail dependence, the Gumbel copula gave the best fit |
Fullana et al. (2021) | Stock market returns and monetary policy | Structural vector autoregressive and regression models | Results suggest no significant monetary policy shocks on the stock market returns under certain circumstances |
BenSaida et al. (2018) | G7 stock market indices | Regime-switching copula models | Results showed evidence of regime shifts in the dependence structure during crisis periods |
Model | Independence | Dependence |
---|---|---|
Logistic | → 1 | → 0 |
Negative logistic | → 0 | →∞ |
Husler–Reiss | → 0 | →∞ |
Bilogistic | = → 1 | = → 0 |
Negative bilogistic | = → ∞ | = → 0 |
Coles–Tawn (or Dirichlet) | = → 0 | = → ∞ |
Dependence Parameters | IMOEX | NIFTY | SHCOMP | JALSH | |
---|---|---|---|---|---|
Conditioning on: IBOV | a | 0.3888 | −0.0194 | 0.3157 | −0.0408 |
b | 0.1019 | 0.0257 | 0.2452 | 0.0633 | |
Dependence Parameters | IBOV | NIFTY | SHCOMP | JALSH | |
Conditioning on: IMOEX | a | 0.1655 | 0.0151 | 0.0314 | 0.0184 |
b | 0.1386 | 0.0669 | −0.1024 | 0.1650 | |
Conditioning on: NIFTY | a | 0.1116 | 0.0059 | −0.1110 | 0.2531 |
b | 0.0066 | 0.0140 | −0.1518 | 0.2034 | |
Dependence Parameters | IBOV | IMOEX | NIFTY | JALSH | |
Conditioning on: SHCOMP | a | 0.3159 | 0.0717 | −0.0957 | −0.1235 |
b | 0.2081 | −0.0055 | −0.0352 | 0.1015 | |
Dependence Parameters | IBOV | IMOEX | NIFTY | SHCOMP | |
Conditioning on: JALSH | a | −0.0606 | 0.1018 | 0.2011 | 0.0311 |
b | 0.0642 | −0.0138 | 0.2315 | 0.1255 |
Conditioning on IBOV | IMOEX | NIFTY | SHCOMP | JALSH |
0.510 | 0.305 | 0.454 | 0.302 | |
Conditioning on IMOEX | IBOV | NIFTY | SHCOMP | JALSH |
0.433 | 0.346 | 0.358 | 0.351 | |
Conditioning on NIFTY | IBOV | IMOEX | SHCOMP | JALSH |
0.323 | 0.363 | 0.315 | 0.402 | |
Conditioning on SHCOMP | IBOV | IMOEX | NIFTY | JALSH |
0.425 | 0.347 | 0.342 | 0.278 | |
Conditioning on JALSH | IBOV | IMOEX | NIFTY | SHCOMP |
0.280 | 0.337 | 0.408 | 0.318 |
AIC | |||
Logistic | 0.5994 (0.0117) | Nil | 3762.38 |
Negative logistic | 0.9055 (0.0314) | Nil | 3711.77 |
Husler–Reiss | 1.3413 (0.0345) | Nil | 3669.11 |
Bilogistic | 0.5829 (0.0258) | 0.6155 (0.0247) | 3763.84 |
Negative bilogistic | 1.1938 (0.1134) | 1.0210 (0.0978) | 3712.99 |
ct (or Dirichlet) | 0.8195 (0.1010) | 1.0172 (0.1369) | 3718.47 |
AIC | |||
Logistic | 0.6066 (0.0114) | Nil | 3756.67 |
Negative logistic | 0.8854 (0.0300) | Nil | 3701.53 |
Husler–Reiss | 1.3174 (0.0330) | Nil | 3656.31 |
Bilogistic | 0.6209 (0.0244) | 0.5909 (0.0267) | 3758.23 |
Negative bilogistic | 1.0470 (0.1029) | 1.2140 (0.1141) | 3702.85 |
ct (or Dirichlet) | 0.9829 (0.1364) | 0.7940 (0.0959) | 3710.40 |
AIC | |||
Logistic | 0.6086 (0.0114) | Nil | 3788.63 |
Negative logistic | 0.8779 (0.0296) | Nil | 3733.10 |
Husler–Reiss | 1.3100 (0.0326) | Nil | 3683.98 |
Bilogistic | 0.6264 (0.0235) | 0.5901 (0.0250) | 3789.91 |
Negative bilogistic | 1.0629 (0.0988) | 1.2186 (0.1111) | 3734.46 |
ct (or Dirichlet) | 0.9515 (0.1229) | 0.7931 (0.0949) | 3742.99 |
AIC | |||
Logistic | 0.6132 (0.0114) | Nil | 3817.37 |
Negative logistic | 0.8646 (0.0292) | Nil | 3761.19 |
Husler–Reiss | 1.2906 (0.0321) | Nil | 3715.79 |
Bilogistic | 0.6137 (0.0246) | 0.6125 (0.0254) | 3819.37 |
Negative bilogistic | 1.1414 (0.1098) | 1.1707 (0.1096) | 3763.17 |
ct (or Dirichlet) | 0.8591 (0.1121) | 0.8303 (0.1027) | 3772.86 |
AIC | |||
Logistic | 0.6073 (0.0116) | Nil | 3873.50 |
Negative logistic | 0.8818 (0.0302) | Nil | 3821.21 |
Husler–Reiss | 1.3110 (0.0332) | Nil | 3780.47 |
Bilogistic | 0.6185 (0.0240) | 0.5955 (0.0254) | 3875.22 |
Negative bilogistic | 1.0850 (0.1033) | 1.1839 (0.1100) | 3822.96 |
ct (or Dirichlet) | 0.9256 (0.1208) | 0.8203 (0.0997) | 3830.56 |
AIC | |||
Logistic | 0.6072 (0.0116) | Nil | 3941.75 |
Negative logistic | 0.8806 (0.0303) | Nil | 3887.51 |
Husler–Reiss | 1.3145 (0.0334) | Nil | 3838.94 |
Bilogistic | 0.6140 (0.0244) | 0.6003 (0.0252) | 3943.65 |
Negative bilogistic | 1.1083 (0.1068) | 1.1628 (0.1106) | 3889.43 |
ct (or Dirichlet) | 0.9066 (0.1206) | 0.8415 (0.1072) | 3897.57 |
AIC | |||
Logistic | 0.6126 (0.0114) | Nil | 3935.83 |
Negative logistic | 0.8653 (0.0293) | Nil | 3883.64 |
Husler–Reiss | 1.2908 (0.0321) | Nil | 3839.97 |
Bilogistic | 0.6068 (0.0232) | 0.6184 (0.0231) | 3937.75 |
Negative bilogistic | 1.1356 (0.1036) | 1.1759 (0.1065) | 3885.60 |
ct (or Dirichlet) | 0.8727 (0.1101) | 0.8151 (0.0967) | 3894.70 |
AIC | |||
Logistic | 0.6063 (0.0117) | Nil | 3805.05 |
Negative logistic | 0.8826 (0.0305) | Nil | 3758.71 |
Husler–Reiss | 1.3070 (0.0332) | Nil | 3719.32 |
Bilogistic | 0.6142 (0.0231) | 0.5980 (0.0245) | 3806.90 |
Negative bilogistic | 1.1027 (0.1029) | 1.1632 (0.1055) | 3760.61 |
ct (or Dirichlet) | 0.8996 (0.1146) | 0.8365 (0.1005) | 3767.56 |
AIC | |||
Logistic | 0.6040 (0.0115) | Nil | 3745.97 |
Negative logistic | 0.8924 (0.0304) | Nil | 3699.66 |
Husler–Reiss | 1.3200 (0.0332) | Nil | 3664.18 |
Bilogistic | 0.6054 (0.0229) | 0.6026 (0.0229) | 3747.97 |
Negative bilogistic | 1.1070 (0.0979) | 1.1343 (0.1005) | 3701.64 |
ct (or Dirichlet) | 0.8946 (0.1064) | 0.8649 (0.1018) | 3707.80 |
AIC | |||
Logistic | 0.6149 (0.0114) | Nil | 3869.14 |
Negative logistic | 0.8605 (0.0290) | Nil | 3810.94 |
Husler–Reiss | 1.2883 (0.0320) | Nil | 3764.18 |
Bilogistic | 0.6283 (0.0242) | 0.6006 (0.0260) | 3870.76 |
Negative bilogistic | 1.1129 (0.1076) | 1.2121 (0.1143) | 3812.71 |
ct (or Dirichlet) | 0.8926 (0.1183) | 0.7915 (0.0977) | 3823.01 |
Brazilian IBOV and Indian NIFTY | Weak | Weak |
Brazilian IBOV and S/African JALSH | Weak | Weak |
Russian IMOEX and Indian NIFTY | Weak | Weak |
Russian IMOEX and Chinese SHCOMP | Weak | Weak |
Russian IMOEX and S/African JALSH | Weak | Weak |
Indian NIFTY and Chinese SHCOMP | Weak | Weak |
Chinese SHCOMP and S/African JALSH | Weak | Weak |
Panel B | ||
Brazilian IBOV and Russian IMOEX | Fairly strong | Fairly strong |
Indian NIFTY and S/African JALSH | Fairly strong | Fairly strong |
Panel C | ||
Brazilian IBOV and Chinese SHCOMP | Fairly strong | Nearly weak |
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Sigauke, C.; Mukhodobwane, R.; Chagwiza, W.; Garira, W. Asymptotic Dependence Modelling of the BRICS Stock Markets. Int. J. Financial Stud. 2022, 10, 58. https://doi.org/10.3390/ijfs10030058
Sigauke C, Mukhodobwane R, Chagwiza W, Garira W. Asymptotic Dependence Modelling of the BRICS Stock Markets. International Journal of Financial Studies. 2022; 10(3):58. https://doi.org/10.3390/ijfs10030058
Chicago/Turabian StyleSigauke, Caston, Rosinah Mukhodobwane, Wilbert Chagwiza, and Winston Garira. 2022. "Asymptotic Dependence Modelling of the BRICS Stock Markets" International Journal of Financial Studies 10, no. 3: 58. https://doi.org/10.3390/ijfs10030058
APA StyleSigauke, C., Mukhodobwane, R., Chagwiza, W., & Garira, W. (2022). Asymptotic Dependence Modelling of the BRICS Stock Markets. International Journal of Financial Studies, 10(3), 58. https://doi.org/10.3390/ijfs10030058