The impact of BRICS formation on portfolio diversification: Empirical evidence from pre- and post-formation eras

Figures & data

Table 1. Johansen-Juselius cointegration test results for pre- and post-BRICS Formation sub-periods

	Pre-BRICS Formation				Post-BRICS Formation
Null Hypotheses	${\lambda }_{\mathbf{t}\mathbf{r}\mathbf{a}\mathbf{c}\mathbf{e}}$	Critical Values (trace)	${\lambda }_{\mathbf{m}\mathbf{a}\mathbf{x}}$	Critical Values (max)	${\lambda }_{\mathbf{t}\mathbf{r}\mathbf{a}\mathbf{c}\mathbf{e}}$	Critical Values (trace)	${\lambda }_{\mathbf{m}\mathbf{a}\mathbf{x}}$	Critical Values (max)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)
r = 0	151.36***	84.37	91.34***	35.58	86.08*	84.37	34.38	35.58
r$\le 1$	60.02	60.08	31.78*	29.54	51.69	60.08	20.92	29.54
r$\le 2$	28.23	39.75	14.39	23.44	30.76	39.75	14.40	23.44
r$\le 3$	13.83	23.34	12.03	17.23	16.36	27.34	11.54	17.23
r$\le 4$	1.80	10.66	1.80	10.66	4.81	21.12	4.81	7.66

Note: r represents the number of cointegrated vectors. Columns (2) to (5) illustrate results for pre-BRICS formation sub-period. Columns (6) to (9) illustrate results for post-BRICS formation sub-period. Null hypothesis is there is no cointegration among variables. ***, **, * indicate rejection of the null hypotheses under 1%, 5% and 10% levels of confidence, respectively.

Table 2. Exclusion test results for pre- and post-BRICS Formation

	Pre-BRICS Formation		Post-BRICS Formation
Country	Null Hypotheses	${\chi }^2$	Null Hypotheses	${\chi }^2$
(1)	(2)	(3)	(4)	(5)
Brazil	${\beta }_{Brazil}$= 0	0.885	${\beta }_{Brazil}$= 0	13.132***
China	${\beta }_{China}$= 0	16.290***	${\beta }_{China}$= 0	0.027
India	${\beta }_{India}$= 0	2.361	${\beta }_{India}$= 0	3.135*
Russia	${\beta }_{Russia}$= 0	56.111***	${\beta }_{Russia}$= 0	11.082***
South Africa	${\beta }_{South.A}$= 0	42.713***	${\beta }_{South.A}$= 0	9.987***

Note: Column (1) illustrates the stock markets. Columns (2) and (3) illustrate results for pre-BRICS formation sub-period. Columns (4) and (5) illustrate results for post-BRICS formation sub-period. Null hypothesis is $\beta =0$ which implies that the variable (market) is excluded from cointegrating vector. ${\chi }^2$indicates for Chi-square test statistics for 1 degree of freedom. ***, **, * indicate rejection of the null hypotheses under 1%, 5% and 10% levels of confidence, respectively.

Table 3. Weak Exogeneity test results for pre- and post-BRICS Formation

	Pre-Crisis		Post-Crisis
Country	Null Hypotheses	${\chi }^2$	Null Hypotheses	${\chi }^2$
(1)	(2)	(3)	(4)	(5)
Brazil	${\alpha }_{Brazil}$= 0	-	${\alpha }_{Brazil}$= 0	9.117***
China	${\alpha }_{China}$= 0	0.018	${\alpha }_{China}$= 0	-
India	${\alpha }_{India}$= 0	-	${\alpha }_{India}$= 0	0.003
Russia	${\alpha }_{Russia}$= 0	0.672	${\alpha }_{Russia}$= 0	1.874
South Africa	${\alpha }_{South.A}$= 0	59.481***	${\alpha }_{South.A}$= 0	9.250***

Note: Column (1) illustrates the stock markets. Columns (2) and (3) illustrate results for pre-BRICS formation sub-period. Columns (4) and (5) illustrate results for post-BRICS formation sub-period. Null hypothesis is $\alpha =0$ which implies that the variable (market) is weakly exogenous. ${\chi }^2$indicates for Chi-square test statistics for 1 degree of freedom. ***, **, * indicate rejection of the null hypotheses under 1%, 5% and 10% levels of confidence, respectively.

Table 4. Ganger Causality Results Based on Vector-Error Correction Model (VECM) for pre- BRICS Formation

	∆Brazil	∆China	∆India	∆Russia	∆South.A	ECT
Dependent variable	F-Statistics				t-Statistics
(1)	(2)	(3)	(4)	(5)	(6)	(7)
∆Brazil	-	4.358***	1.883	9.820***	3.066**	-
∆China	1.262	-	0.974	3.993**	0.987	−1.347
∆India	0.113	4.645**	-	2.831*	3.115**	-
∆Russia	1.891	0.349	0.860	-	0.116	0.128
∆South.A	0.510	2.986*	0.490	6.306***	-	3.714**

Note: Column (1) illustrates stock markets under consideration as dependent variables. Columns (2) to (6) indicate asymptotic Granger F statistics for short-term causality. Column (7) shows the t statistics which tests the null hypothesis and indicates if each lagged ECT is statistically insignificant. ***, **, * indicate rejection of the null hypotheses under 1%, 5% and 10% levels of confidence, respectively.

Table 5. Ganger Causality Results Based on Vector-Error Correction Model (VECM) for post-BRICS Formation

	∆Brazil	∆China	∆India	∆Russia	∆South.A	ECT
Dependent variable	F-Statistics					t-Statistics
(1)	(2)	(3)	(4)	(5)	(6)	(7)
∆Brazil	-	0.354	5.582***	5.999***	0.373	−1.760*
∆China	1.243	-	7.283***	3.441**	0.507	-
∆India	2.989*	1.874	-	7.937***	0.726	2.641**
∆Russia	0.474	0.680	1.178	-	0.407	1.998**
∆South.A	2.248	0.040	0.383	6.215***	-	−1.513

Note: Column (1) illustrates stock markets under consideration as dependent variables. Columns (2) to (6) indicate asymptotic Granger F statistics for short-term causality. Column (7) shows the t statistics which tests the null hypothesis and indicates if each lagged ECT is statistically insignificant. ***, **, * indicate rejection of the null hypotheses under 1%, 5% and 10% levels of confidence, respectively.

Table 6. Decomposition of forecast error variances for all stock markets in pre-BRICS Formation sub-period

		Innovation in Markets
Dependent Variables	Weeks	Brazil	China	India	Russia	South.A
Brazil	2	99.198	0.023	0.131	0.353	0.292
	6	97.592	0.363	0.161	1.746	0.135
	10	94.944	1.180	0.251	3.381	0.240
China	2	1.991	97.443	0.023	0.146	0.394
	6	1.840	94.652	0.050	0.154	3.301
	10	1.339	89.967	0.243	0.746	7.703
India	2	36.552	0.029	63.009	0.067	0.341
	6	42.985	0.210	55.556	1.076	0.171
	10	46.046	0.999	49.930	2.812	0.210
Russia	2	0.189	0.133	0.199	99.401	0.075
	6	0.125	0.253	0.158	99.311	0.150
	10	0.089	0.689	0.732	98.228	0.259
South.A	2	55.082	0.463	0.158	0.507	43.788
	6	56.441	0.840	0.269	3.102	39.346
	10	55.767	1.415	0.658	6.920	35.237

Note: Table illustrates variance decomposition of forecast error variances for stock markets (Brazil, China, India, Russia and South Africa) in pre-BRICS formation sub-period. Forecast error variances are for 2, 6 and 10 weeks.

Table 7. Decomposition of forecast error variances for all stock markets in post-BRICS Formation sub-period

		Innovation in Markets
Dependent Variables	Weeks	Brazil	China	India	Russia	South.A
Brazil	2	94.872	0.012	0.825	4.253	0.036
	6	90.706	0.016	0.508	8.439	0.328
	10	89.111	0.102	0.401	9.787	0.596
China	2	1.684	98.024	0.218	0.007	0.065
	6	1.020	98.677	0.176	0.069	0.055
	10	0.713	98.334	0.683	0.075	0.192
India	2	14.126	0.792	83.919	1.047	0.114
	6	19.369	1.145	77.378	1.274	0.832
	10	23.884	0.882	72.428	1.017	1.785
Russia	2	0.042	0.598	0.648	98.649	0.060
	6	0.603	0.642	1.163	97.350	0.240
	10	1.558	0.489	2.406	94.965	0.579
South.A	2	18.624	0.655	15.614	1.065	64.040
	6	15.536	0.502	20.269	1.591	62.099
	10	13.363	0.352	24.040	1.358	60.883

Note: Table illustrates variance decomposition of forecast error variances for stock markets (Brazil, China, India, Russia and South Africa) in post-BRICS formation sub-period. Forecast error variances are for 2, 6 and 10 weeks.

Table 8. Generalized Impulse Response by country to one standard deviation innovation in each stock market (pre-BRICS Formation)

		To One SD Impulse In
Market Responding	Weeks	Brazil	China	India	Russia	South.A
Brazil	1	16.414	1.514	9.140	3.982	1.197
	5	14.076	2.473	8.395	2.738	1.380
	10	12.672	3.794	7.938	3.859	0.870
China	1	1.004	10.887	0.803	−0.560	0.142
	5	1.402	10.886	0.126	−0.941	0.349
	10	0.664	10.161	0.142	−0.232	0.440
India	1	0.720	0.954	12.939	−0.195	0.583
	5	0.800	0.146	11.98	0.155	0.639
	10	0.762	0.277	9.483	0.282	0.565
Russia	1	1.434	−3.044	−0.894	69.130	3.242
	5	1.419	3.927	2.566	60.792	0.585
	10	−1.418	7.884	7.146	52.474	5.180
South.A	1	4.668	8.368	2.885	3.510	64.11
	5	3.900	9.222	2.458	1.285	50.128
	10	3.381	1.163	2.456	2.030	41.920

Note: Table illustrates generalized impulse response by country to one standard deviation innovation in each stock market (pre-BRICS Formation). There is one, five and ten week horizon.

Table 9. Generalized Impulse Response by country to one standard deviation innovation in each stock market (post-BRICS Formation)

		To One SD Impulse In
Market Responding	Weeks	Brazil	China	India	Russia	South.A
Brazil	1	16.706	1.950	6.613	−2.104	0.742
	5	15.156	1.553	5.066	5.193	0.540
	10	13.950	0.666	6.097	4.913	0.506
China	1	0.110	94.865	0.649	0.584	0.126
	5	0.523	93.228	0.615	0.885	0.904
	10	−0.418	77.713	1.304	0.557	0.441
India	1	5.552	10.103	15.050	−1.474	0.794
	5	7.248	4.246	14.525	0.359	0.968
	10	8.504	7.142	13.893	−0.266	1.071
Russia	1	−0.589	2.882	−4.580	46.768	−2.915
	5	0.444	3.471	−3.380	39.468	−2.881
	10	7.363	1.144	−5.280	29.707	−4.360
South.A	1	3.930	1.176	4.665	5.510	8.840
	5	2.872	8.032	4.727	6.455	7.811
	10	2.090	3.345	4.714	1.181	7.051

Note: Table illustrates generalized impulse response by country to one standard deviation innovation in each stock market (post-BRICS Formation). There are one, five and ten week horizons.