Oil price shocks against stock return of oil- and gas-related firms in the economic depression: A new evidence from a copula approach

Figures & data

Table 1. Copula functions and its characteristics

Copula	$C\left(u,v\right)$	${\lambda }_L$	${\lambda }_U$
Gaussian	${\mathrm{\Phi }}_{\rho }\left({\mathrm{\Phi }}^{-1}\left(u\right),{\mathrm{\Phi }}^{-1}\left(v\right)\right)$, where ${\mathrm{\Phi }}_{\rho }$ is the bivariate standardized Gaussian cdf with Pearson’s correlation $\rho$ ${\mathrm{\Phi }}^{-1}$ is the inverse of the univariate standardized Gaussian cdf	0
Clayton	${\left(u^{-\alpha }+v^{-\alpha }-1\right)}^{-1/\alpha }$, $\alpha >0$	$2^{-1/\alpha }$	0
Rotated Clayton	$u+v-1+C\left(1-u,1-v\right)$, where C is Clayton copula	0	$2^{-1/\alpha }$
Plackett	$\begin{array}{rl}& \left\{\begin{array}{c}\left(\left(1+\left(\theta -1\right)\left(u+v\right)\right)-\frac{\sqrt{{\left(1+\left(\theta -1\right)\left(u+v\right)\right)}^2-4uv\theta \left(\theta -1\right)}}{2\left(\theta -1\right)}\right),for0<\theta \ne 1,\\ uvfor\theta =1\end{array}\right.\\ & \end{array}$	0
Frank	$\frac{1}{\alpha }ln\left(1+\frac{\left(e^{\alpha u}-1\right)\left(e^{\alpha v}-1\right)}{\left(e^{\alpha }-1\right)}\right)$, where $\alpha \ne 0$	0
Gumbel	$exp{\left(-{\left(-lnu\right)}^{\alpha }+{\left(-lnv\right)}^{\alpha }\right)}^{1/\alpha }$, $\alpha >1$	0	$2-2^{1/\alpha }$
Rotated Gumbel	$u+v-1+C\left(1-u,1-v\right)$, where C is Gumbel copula	$2-2^{1/\alpha }$	0
t-Student	$t_{v,r}\left(t_v^{-1}\left(u\right),t_v^{-1}\left(v\right)\right)$, where $t_{v,r}$ is the bivariate t-Student’s cdf with parameter r $\nu$ is degrees of freedom $t_v^{-1}$ is the inverse of the univariate t-Student’s cdf with $\nu$ degrees of freedom	$2t_{v+1}\left(-\sqrt{\frac{\left(v+1\right)\left(1-r\right)}{\left(1+r\right)}}\right)$
Symmetrized Joe-Clayton	$0.5\left(C_{{\tau }^U,{\tau }^L}\left(u,v\right)+u+v-1+C_{{\tau }^L,{\tau }^U}\left(1-u,1-v\right)\right)$, where$\begin{array}{rl}& C_{{\tau }^U,{\tau }^L}\left(u,v\right)=1-\\ & {\left\{{\left[{\left(1-{\left(1-u\right)}^{\kappa }\right)}^{-\gamma }+\left[{\left(1-{\left(1-v\right)}^{\kappa }\right)}^{-\gamma }-1\right]\right]}^{-1/\gamma }\right\}}^{1/\kappa }\end{array}$for $\kappa =1/{log}_2\left(2-{\tau }^U\right),\gamma =-1/{log}_2\left({\tau }^L\right)$, and ${\tau }^U,{\tau }^L\in \left(0,1\right)$	${\tau }^L$	${\tau }^U$

Source: Synthesis by the authors.

Table 2. Copula Parameters

Name	Parameters	Copulas
Gaussian	$\rho$	$C\left({\mu }_x,{\mu }_y,\rho \right)={\phi }_{\rho }\left({\phi }^{-1}\left({\mu }_x\right),{\phi }^{-1}\left({\mu }_y\right)\right)$
Student	$\rho ,k$	$C\left({\mu }_x,{\mu }_y,\rho ,k\right)=T_{\rho ,k}\left(T_k^{-1}\left({\mu }_x\right),T_k^{-1}\left({\mu }_y\right)\right)$
Plackett	$\theta >0$	$C\left(\mu ,\upsilon \right)=\frac{1+\left(\theta -1\right)\left(\mu +\upsilon \right)-{\left\{{\left[1+\left(\theta -1\right)\left(\mu +\upsilon \right)\right]}^2-4\theta \left(\theta -1\right)\mu \upsilon \right\}}^{\frac{1}{2}}}{2\left(\theta -1\right)}$
Clayton	$\theta >0$	$C\left(\mu ,\upsilon ,\theta \right)={\left({\mu }^{-\theta }+{\upsilon }^{-\theta }-1\right)}^{\frac{-1}{\theta }}$
Rotated Clayton	$\theta >0$	$C\left(\mu ,\upsilon ,\theta \right)=\mu -{\left({\mu }^{\theta }+{\left(1-\upsilon \right)}^{\theta }-1\right)}^{\frac{1}{\theta }}$
Gumbel	$\theta \ge 1$	$C\left(\mu ,\upsilon ,\theta \right)=exp{\left[-\left[Ln{\left(\mu \right)}^{\theta }+{\left(-Ln\left(\upsilon \right)\right)}^{\theta }\right]\right]}^{\frac{1}{\theta }}$
Rotated Gumbel	$\theta \ge 1$	$C\left(\mu ,\upsilon ,\theta \right)=\mu -exp{\left[-\left[Ln{\left(\mu \right)}^{-\theta }+{\left(-Ln\left(1-\upsilon \right)\right)}^{-\theta }\right]\right]}^{\frac{-1}{\theta }}$
Frank	$\theta \ne 0$	$C\left(\mu ,\upsilon ,\theta \right)=\frac{-1}{\theta }Ln\left[1+\frac{\left(exp{\left(-{\theta }_{\mu }\right)}^{-1}\right)\left(exp{\left(-{\theta }_{\upsilon }\right)}^{-1}\right)}{exp\left(-\theta \right)-1}\right]$
Symmetrized-Joe-Clayton (SJC)	u, v	$C\left(u,v\left|{\tau }^U,\right.{\tau }^L\right)=1-{\left({\left[1-{\left(1-u\right)}^k\right]}^{-\gamma }+{\left[1-v^k\right]}^{-\gamma }-1^{-1/\gamma }\right)}^{1/k}$

Source: Synthesis by the authors.

Table 3. Descriptive Statistics of Returns of Daily Stocks and World Crude Oil

	RWTI	RPET	RPGD	RPGS	RPVC	RPVD	RPVE	RPVG	RPVS
Period 1: 25 November 2009–31 December 2010
Mean	0.000597	−0.001012	−0.000398	0.001720	0.001245	−0.001531	1.87E-06	−0.002586	−0.000444
Median	0.000000	−0.003335	0.000000	0.000000	0.000000	0.000000	4.98E-08	−0.004181	0.000000
Maximum	0.078204	0.056761	0.048998	0.093925	0.093889	0.048790	0.000442	0.095361	0.079512
Minimum	−0.051170	−0.051545	−0.051570	−0.098086	−0.094599	−0.035207	4.97E-08	−0.085599	−0.071974
Std. Dev.	0.017800	0.027439	0.024982	0.040541	0.043228	0.029255	2.69E-05	0.039153	0.027268
Skewness	0.138632	0.124731	0.091320	0.072165	0.125006	−5.452727	16.29173	0.192499	0.211143
Kurtosis	3.748668	2.334457	2.687811	2.529309	2.132871	64.27353	266.6143	2.387617	3.338095
Jarque-Bera	7.143956	5.662209	1.466264	2.716691	9.128280	43414.07	790795.0	5.864609	3.279936
Probability	0.028100	0.058948	0.480402	0.257086	0.010419	0.000000	0.000000	0.053274	0.193986
Sum	0.160689	−0.272337	−0.106958	0.462685	0.334878	−0.411735	0.000503	−0.695583	−0.119318
Sum Sq. Dev.	0.084916	0.201772	0.167257	0.440470	0.500798	0.229375	1.94E-07	0.410841	0.199267
Observations	269	269	269	269	269	269	269	269	269
Period 2: 4 January 2011—31 December 2012
Mean	−0.000113	−0.000174	−3.39E-05	−0.000604	−0.001095	−0.000854	2.09E-06	−0.000717	−0.000164
Median	0.001034	0.000000	0.000000	−0.003973	0.000000	0.000000	4.97E-08	0.000000	0.000000
Maximum	0.089454	0.055620	0.062907	0.091073	0.071705	0.066129	0.000441	0.079947	0.092849
Minimum	−0.090379	−0.062606	−0.051728	−0.091603	−0.083228	−0.063949	4.97E-08	−0.091989	−0.082779
Std. Dev.	0.019818	0.022814	0.021596	0.029706	0.029812	0.022283	2.86E-05	0.033380	0.026502
Skewness	−0.137570	−0.017233	−0.042724	0.174491	0.102050	0.014093	15.31434	0.112896	0.578123
Kurtosis	5.633333	3.295877	3.500641	3.265921	2.920162	3.563616	235.6871	2.778974	6.231984
Jarque-Bera	139.0346	1.759829	5.115870	3.817980	0.952617	6.316082	1092448.	1.980045	233.6887
Probability	0.000000	0.414818	0.077465	0.148230	0.621072	0.042509	0.000000	0.371568	0.000000
Sum	−0.053624	−0.082867	−0.016113	−0.287332	−0.521297	−0.406409	0.000994	−0.341117	−0.077837
Sum Sq.Dev	0.186559	0.247226	0.221525	0.419156	0.422173	0.235861	3.88E-07	0.529256	0.333621
Observations	476	476	476	476	476	476	476	476	476
Period 3: 2 January 2013–4 October 2019
Mean	−0.000338	0.000185	0.000819	0.000836	−0.000199	−0.000494	2.00E-06	6.76E-06	0.000456
Median	0.000409	0.000000	0.000000	0.000000	0.000000	0.000000	4.96E-08	0.000000	0.000000
Maximum	0.136944	0.067345	0.067587	0.092246	0.096481	0.067659	0.000441	0.095210	0.095126
Minimum	−0.090703	−0.071900	−0.062395	−0.095326	−0.099578	−0.060500	4.96E-08	−0.091999	−0.095662
Std. Dev.	0.021390	0.017471	0.021084	0.023117	0.028343	0.026221	2.77E-05	0.022606	0.025404
Skewness	0.096992	0.116488	0.163670	0.046225	0.128602	−0.135497	15.75649	0.253933	−0.226266
Kurtosis	6.053914	6.476200	5.124990	7.528805	5.338476	4.605091	249.4568	8.482072	6.040764
Jarque-Bera	655.4816	849.6772	323.5915	1436.303	387.4237	185.4828	3886672.	2121.773	661.5722
Probability	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000	0.000000
Sum	−0.567188	0.310753	1.376663	1.403780	−0.334338	−0.830348	0.003016	0.011355	0.765547
Sum Sq.Dev	0.768181	0.512515	0.746355	0.897266	1.348782	1.154413	1.16E-06	0.857990	1.083525
Observations	1680	1680	1680	1680	1680	1680	1511	1680	1680

Source: Calculation of the authors from collected data.

Note: RPET, RPGD, RPGS, RPVC, RPVD, RPVE, RPVG, and RPVS are the return of the stock of PET, PGD, PGS, PVC, PVD, PVE, PVG, and PVS. In addition, PET, PGD, and PVD are in Ho Chi Minh City Stock Exchange (HOSE); PGS, PVC, PVE, PVG, and PVS are in Hanoi Stock Exchange (HNX).

RWTI is the return of world oil.

Figure 1. Normal q-q plots of returns of stock indices for period 1.

Source: Drawing of the authors from collected data.

Figure 2. Normal q-q plots of returns of stock indices for period 2.

Source: Drawing of the authors from collected data.

Figure 3. Normal q-q plots of returns of stock indices for period 3.

Source: Drawing of the authors from collected data.

Table 4. Dependence coefficient of WCOR and SR in pre-depression period

Indices	Correlation	Indices	Correlation
Rworld crude oil and Rpvd	0.088956	Rworld crude oil and Rpvg	0.052599
Rworld crude oil and Rpvs	0.021793	Rworld crude oil and Rpgd	0.053884
Rworld crude oil and Rpvc	0.050118	Rworld crude oil and Rpet	0.039832
Rworld crude oil and Rpgs	−0.010565	Rworld crude oil and Rpve	0.088794

Source: Calculation of the authors.

Table 5. Dependence coefficient of WCOR and SR in depression period

Indices	Correlation	Indices	Correlation
Rworld crude oil and Rpvd	0.118301	Rworld crude oil and Rpvg	0.062655
Rworld crude oil and Rpvs	0.026647	Rworld crude oil and Rpgd	0.026301
Rworld crude oil and Rpvc	0.048821	Rworld crude oil and Rpet	0.002757
Rworld crude oil and Rpgs	0.036629	Rworld crude oil and Rpve	0.036521

Source: Calculation of the authors.

Table 6. Dependence coefficient of WCOR and SR in post- depression period

Indices	Correlation	Indices	Correlation
Rworld crude oil and Rpvd	0.106004	Rworld crude oil and Rpvg	0.0009066
Rworld crude oil and Rpvs	0.086365	Rworld crude oil and Rpgd	0.026845
Rworld crude oil and Rpvc	0.096750	Rworld crude oil and Rpet	0.030799
Rworld crude oil and Rpgs	0.044071	Rworld crude oil and Rpve	0.067405

Source: Calculation of the authors.

Figure 4. DCs between WCOR and SR in three periods.

Source: Drawing of the authors.

Table 7. Estimation of copula parameters for WCOR and PVD in pre-depression period and best copula

Copula	Para 1	Para 2	Para 3	Para 4	Para 5	Para 6	LL	AIC	BIC	R
Normal	0.0889						−1.0685	−2.1297	−2.1163	7
Clayton	0.1804						−2.6857	−5.3641	−5.3507	2
Rotated Clayton	0.0233						−0.0449	−0.0824	−0.0691	8
Plackett	1.4791						−2.0538	−4.1003	−4.0869	5
Frank	0.7423						−1.9347	−3.8620	−3.8487	6
Gumbel	1.1						0.3024	0.6123	0.6257	9
Rotated Gumbel	1.1						−2.4935	−4.9796	−4.96626	4
Student	0.1184	7.1896					−2.7271	−5.4393	−5.4126	1
Symmetrized Joe-Clayton	1.75E-09	0.0890					−2.6343	−5.2537	−5.2269	3

Note: Para and R denote for parameter, and ranking.

Source: Calculation of the authors from collected data.

Table 8. Estimation of copula parameters for WCOR and PVD in depression period and best copula

Copula	Para 1	Para 2	Para 3	Para 4	Para 5	Para 6	LL	AIC	BIC	R
Normal	0.1183						−3.4530	−6.9020	−6.8935	4
Clayton	0.1317						−2.5910	−5.1780	−5.1694	6
Rotated Clayton	0.1017						−1.6701	−3.3361	−3.3275	8
Plackett	1.5588						−5.4101	−10.816	−10.8076	2
Frank	0.9043						−5.4866	−10.969	−10.9606	1
Gumbel	1.1						−0.6393	−1.2745	−1.2659	9
Rotated Gumbel	1.1						−2.2196	−4.4352	−4.4266	7
Student	0.1249	66.08					−3.5279	−7.0477	−7.0306	3
Symmetrized Joe-Clayton	0.0002	0.020					−2.6903	−5.3725	−5.3554	5

Note: Para and R denote for parameter, and ranking.

Table 9. Estimation of copula parameters for WCOR and PVD in post- depression period and best copula

Copula	Para 1	Para 2	Para 3	Para 4	Para 5	Para 6	LL	AIC	BIC	R
Normal	0.1060						−9.49251	−18.983	−18.9806	3
Clayton	0.1144						−8.95725	−17.913	−17.9101	4
Rotated Clayton	0.1018						−7.04297	−14.084	−14.0815	8
Plackett	1.3439						−7.85307	−15.704	−15.7017	5
Frank	0.5798						−7.66982	−15.338	−15.3352	6
Gumbel	1.1						−4.62413	−9.2470	−9.24383	9
Rotated Gumbel	1.1						−7.17954	−14.357	−14.3546	7
Student	0.1043	20.253					−11.2367	−22.471	−22.4645	1
Symmetrized Joe-Clayton	0.0028	0.0127					−11.0138	−22.025	−22.0187	2

Note: Para and R denote for parameter, and ranking.

Source: Calculation of the authors from collected data.

Table 10. The choice of the best copula for WCOR and Vietnam’s oil and gas stock returns, and tail dependence coefficients in each period

Indices	Pre-depression period			In depression period			Post- depression period
	Best copula	UTDC	LTDC	Best copula	UTDC	LTDC	Best copula	UTDC	LTDC
Rworld crude oil and Rpvd	Student	0.034045	0.034045	Frank	0	0	Student	0.000443	0.000443
Rworld crude oil and Rpvs	Clayton	1.15E-05	0	Clayton	4.07E-05	0	Student	0.001976	0.001976
Rworld crude oil and Rpvc	Plackett	0	0	Clayton	0.0001461	0	Symmetrized Joe-Clayton	0.009956	0.000453
Rworld crude oil and Rpgs	Student	1.95E-07	1.95E-07	Student	0.0021422	0.0021422	Clayton	9.36E-06	0
Rworld crude oil and Rpvg	Student	0.006131	0.006131	Student	3.99E-05	3.99E-05	Clayton	5.86E-32	0
Rworld crude oil and Rpgd	Frank	0	0	Clayton	5.44E-05	0	Normal	0	0
Rworld crude oil and Rpet	Student	0.019254	0.019254	Student	0.001072	0.0010728	Frank	0	0
Rworld crude oil and Rpve	Plackett	0	0	Student	0.000624	6.25E-04	Symmetrized Joe-Clayton	0.002785	7.74E-06

Note: UTDC: upper tail dependence coefficient, LTDC: lower tail dependence coefficient.

Source: Calculation of the authors.

Table 11. Granger Causality Test

Period	Variables	F-statistics	p value
Pre-depression	RWTI does not Granger Cause RPVD	1.38392	0.1883
	RWTI does not Granger Cause RPVS	1.90321	0.0455**
	RWTI does not Granger Cause RPVC	1.32493	0.2177
	RWTI does not Granger Cause RPGS	1.36167	0.1990
	RWTI does not Granger Cause RPVG	2.43081	0.0090***
	RWTI does not Granger Cause RPGD	2.55723	0.0060***
	RWTI does not Granger Cause RPET	1.74764	0.0712*
	RWTI does not Granger Cause RPVE	0.63805	0.7805
In depression	RWTI does not Granger Cause RPVD	1.70480	0.0771*
	RWTI does not Granger Cause RPVS	0.72881	0.6974
	RWTI does not Granger Cause RPVC	0.88680	0.5455
	RWTI does not Granger Cause RPGS	0.58356	0.8277
	RWTI does not Granger Cause RPVG	1.31314	0.2205
	RWTI does not Granger Cause RPGD	0.55182	0.8528
	RWTI does not Granger Cause RPET	1.05639	0.3950
	RWTI does not Granger Cause RPVE	0.55735	0.8486
Post-depression	RWTI does not Granger Cause RPVD	14.5977	4.E-25***
	RWTI does not Granger Cause RPVS	10.9588	3.E-18***
	RWTI does not Granger Cause RPVC	10.8859	4.E-18***
	RWTI does not Granger Cause RPGS	1.72414	0.0702*
	RWTI does not Granger Cause RPVG	1.89527	0.0417**
	RWTI does not Granger Cause RPGD	0.89638	0.5358
	RWTI does not Granger Cause RPET	2.60665	0.0038***
	RWTI does not Granger Cause RPVE	0.78522	0.6432

Source: Authors’ calculations.

Notes: ***, **, * significance at 1%, 5%, and 10% level.