Downside and upside risk spillovers from commercial banks into China’s financial system: a new copula quantile regression-based CoVaR model

Figures & data

Figure 1. The dynamics of NPLs in the banking sector (Data source: CBRC).

Table 1. Descriptive statistics of the stock returns.

Statistics	SOCBs	JSCBs	CCBs	Financial system
Basic statistics
Mean	0.0079	0.0171	0.0006	0.0106
Maximum	9.5529	9.5505	9.5414	9.5233
Minimum	−10.4863	−10.5186	−10.5065	−9.9386
Median	−0.0111	−0.0393	−0.0157	−0.0102
SD	1.6427	2.0308	2.0383	1.8646
Skewness	0.0623	0.0186	0.0417	−0.2450
Kurtosis	6.8893	4.3103	4.5182	4.3202
J-B	6266.5***	2453.2***	2696.2***	2496.0***
Downside VaR
1% quantile	−4.7485	−6.1860	−5.9846	−5.7907
2% quantile	−3.7337	−4.6846	−4.6570	−4.7658
3% quantile	−3.1956	−3.8782	−3.8100	−3.9014
4% quantile	−2.7501	−3.3519	−3.4084	−3.2236
5% quantile	−2.4037	−2.9656	−3.1221	−2.7847
6% quantile	−2.1721	−2.7488	−2.9001	−2.5617
7% quantile	−1.9876	−2.5284	−2.6672	−2.3549
8% quantile	−1.8300	−2.3461	−2.4286	−2.1285
9% quantile	−1.7061	−2.1586	−2.2802	−1.9734
10% quantile	−1.5685	−2.0178	−2.0760	−1.8577
Upside VaR
90% quantile	1.6133	2.1438	2.1150	1.9617
91% quantile	1.7609	2.3151	2.2881	2.0873
92% quantile	1.8709	2.4618	2.4140	2.3082
93% quantile	2.0562	2.7154	2.6086	2.5322
94% quantile	2.2809	2.9294	2.8264	2.7718
95% quantile	2.5648	3.1977	3.0393	2.9956
96% quantile	2.9232	3.6694	3.4813	3.3068
97% quantile	3.3674	4.3380	3.9928	3.6573
98% quantile	3.9218	5.0986	4.9033	4.1925
99% quantile	5.1695	6.2667	6.5782	5.0743

Note: J-B denotes the Jarque-Bera statistics. *** indicate rejection of the null hypothesis at the 1% significance level.

Source: Authors own estimations.

Figure 2. China’s stock price indices and financial risk events.

Source: Created by the authors.

Figure 3. Histograms and PDFs of the stock returns.

Source: Created by the authors.

Figure 4. QQ plots of the stock returns.

Source: Created by the authors.

Table 2. Estimates of parameters of the SKST distribution function.

Estimates	SOCBs	JSCBs	CCBs	Financial system
$\mu$	0.0036	0.0368	0.0031	0.0390
$\sigma$	4.3278	3.0381	2.5939	2.7199
$\vartheta$	2.0734	2.3182	2.5226	2.3428
$\gamma$	1.0195	1.0495	1.0139	1.0225

Note: This table provides the MLE of the SKST distribution for stock returns of SOCBs, JSCBs, CCBs and the financial system.

Source: Authors own estimations.

Figure 5. Fitted curves of the CQR models.

Source: Created by the authors.

Table 3. Estimates for the CQR models.

Banks	Estimates	Clayton CQR model	Gumbel CQR model
		$\tau$=0.05	$\tau$=0.95
SOCBs	$\widehat{\delta }$	5.15*** (1.78)	9.25** (3.99)
	$\widehat{\theta }$	−0.29 (0.20)	0.96*** (0.17)
	$\widehat{\eta }$	1.18*** (0.05)	1.01*** (0.04)
JSCBs	$\widehat{\delta }$	19.45*** (4.41)	16.27*** (3.95)
	$\widehat{\theta }$	−0.63*** (0.08)	0.83*** (0.07)
	$\widehat{\eta }$	1.21*** (0.04)	1.06*** (0.03)
CCBs	$\widehat{\delta }$	8.61*** (2.32)	5.89 *** (1.68)
	$\widehat{\theta }$	−0.53*** (0.13)	0.62*** (0.18)
	$\widehat{\eta }$	1.16*** (0.04)	1.03*** (0.04)

Note: Standard errors appear in parentheses. *** and ** indicate significance levels of 1% and 5%, respectively.

Source: Authors own estimations.

Table 4. Estimates of downside and upside tail dependence coefficients.

Banks	Clayton copula	Gumbel copula
SOCBs	0.8740	0.9221
JSCBs	0.9650	0.9565
CCBs	0.9227	0.8751

Note: The downside and upside tail dependence coefficients for Clayton and Gumbel copulas are computed based on $\widehat{\delta }$ in Table 3.

Source: Authors own estimations.

Table 5. Static risk spillovers of downside risk.

Banks	Estimates	$\alpha$=1%	$\alpha$=2%	$\alpha$=3%	$\alpha$=4%	$\alpha$=5%	$\alpha$=6%	$\alpha$=7%	$\alpha$=8%	$\alpha$=9%	$\alpha$=10%
SOCBs	${\mathit{DCoVaR}}_{0.05}^{s|{\mathit{VaR}}_{0.5}^i}$	−0.95	−0.95	−0.95	−0.95	−0.95	−0.95	−0.95	−0.95	−0.95	−0.95
	$D{\mathit{CoVaR}}_{0.05}^{s|{\mathit{VaR}}_{\alpha }^i}$	−7.93	−6.46	−5.67	−5.00	−4.48	−4.13	−3.84	−3.60	−3.41	−3.20
	$\Delta \mathit{DCoVaR}$	−6.98	−5.51	−4.72	−4.05	−3.52	−3.17	−2.89	−2.65	−2.45	−2.24
	$\mathrm{\%}\mathit{DCoVaR}$	731.79%	577.76%	494.45%	424.53%	369.55%	332.49%	302.82%	277.37%	257.32%	235.02%
JSCBs	${\mathit{DCoVaR}}_{0.05}^{s|{\mathit{VaR}}_{0.5}^i}$	−0.86	−0.86	−0.86	−0.86	−0.86	−0.86	−0.86	−0.86	−0.86	−0.86
	$D{\mathit{CoVaR}}_{0.05}^{s|{\mathit{VaR}}_{\alpha }^i}$	−8.13	−6.31	−5.34	−4.70	−4.24	−3.98	−3.71	−3.49	−3.27	−3.10
	$\Delta \mathit{DCoVaR}$	−7.27	−5.45	−4.48	−3.84	−3.37	−3.11	−2.85	−2.63	−2.40	−2.24
	$\mathrm{\%}\mathit{DCoVaR}$	840.63%	630.60%	517.79%	444.23%	390.32%	360.10%	329.44%	304.12%	278.13%	258.67%
CCBs	${\mathit{DCoVaR}}_{0.05}^{s|{\mathit{VaR}}_{0.5}^i}$	−0.97	−0.97	−0.97	−0.97	−0.97	−0.97	−0.97	−0.97	−0.97	−0.97
	$D{\mathit{CoVaR}}_{0.05}^{s|{\mathit{VaR}}_{\alpha }^i}$	−7.96	−6.25	−5.18	−4.68	−4.33	−4.06	−3.78	−3.50	−3.33	−3.09
	$\Delta \mathit{DCoVaR}$	−7.00	−5.29	−4.22	−3.72	−3.37	−3.10	−2.82	−2.54	−2.36	−2.12
	$\mathrm{\%}\mathit{DCoVaR}$	725.12%	547.60%	436.95%	385.36%	349.01%	321.09%	292.08%	262.68%	244.57%	219.92%

Note: ${\mathit{DCoVaR}}_{0.05}^{s|{\mathit{VaR}}_{0.5}^i}$ and $D{\mathit{CoVaR}}_{0.05}^{s|{\mathit{VaR}}_{\alpha }^i}$ denote the downside CoVaR of financial system condition on the normal state and financial distress with different risk levels. Financial distress is measured as the return of banking taking values equal to its VaR. $\alpha$ denotes the risk level of financial event. For example, $\alpha =1\%$ means a financial event once in 100 years. $\Delta \mathit{DCoVaR}$ and$\%\mathit{DCoVaR}$ are downside risk spillovers and risk-spillover intensity computed according to Equations (16)(16) $${\Delta \mathit{DCoVaR}}_{\beta }^{s|i}{=\mathit{DCoVaR}}_{\beta }^{s|X^i={\mathit{VaR}}_{\alpha }^i}-{\mathit{DCoVaR}}_{\beta }^{s|X^i={\mathit{VaR}}_{0.5}^i},\mathrm{ }$$(16) and (18)(18) $$\mathrm{\%}{\mathit{DCoVaR}}_{\beta }^{s|i}=({\Delta \mathit{DCoVaR}}_{\beta }^{s|i}/{\mathit{DCoVaR}}_{\beta }^{s|X^i={\mathit{VaR}}_{0.5}^i})\mathrm{*}100\mathrm{\%},$$(18) .

Source: Authors own estimations.

Table 6. Static risk spillovers of upside risk.

	Estimates	$\alpha$=90%	$\alpha$=91%	$\alpha$=92%	$\alpha$=93%	$\alpha$=94%	$\alpha$=95%	$\alpha$=96%	$\alpha$=97%	$\alpha$=98%	$\alpha$=99%
SOCBs	${\mathit{UCoVaR}}_{0.95}^{s|{\mathit{VaR}}_{0.5}^i}$	1.28	1.28	1.28	1.28	1.28	1.28	1.28	1.28	1.28	1.28
	$U{\mathit{CoVaR}}_{0.95}^{s|{\mathit{VaR}}_{\alpha }^i}$	3.30	3.49	3.62	3.85	4.12	4.47	4.89	5.42	6.06	7.48
	$\Delta \mathit{UCoVaR}$	2.02	2.20	2.34	2.57	2.84	3.18	3.61	4.13	4.78	6.20
	$\mathrm{\%}\mathit{UCoVaR}$	157.07%	171.32%	181.86%	199.65%	221.00%	247.68%	280.95%	321.74%	371.94%	482.47%
JSCBs	${\mathit{UCoVaR}}_{0.95}^{s|{\mathit{VaR}}_{0.5}^i}$	1.01	1.01	1.01	1.01	1.01	1.01	1.01	1.01	1.01	1.01
	$U{\mathit{CoVaR}}_{0.95}^{s|{\mathit{VaR}}_{\alpha }^i}$	3.14	3.31	3.46	3.71	3.92	4.19	4.66	5.33	6.09	7.25
	$\Delta \mathit{UCoVaR}$	2.13	2.30	2.44	2.70	2.91	3.18	3.65	4.32	5.08	6.24
	$\mathrm{\%}\mathit{UCoVaR}$	210.02%	226.87%	241.32%	266.20%	287.31%	313.73%	360.21%	426.25%	501.14%	615.84%
CCBs	${\mathit{UCoVaR}}_{0.95}^{s|{\mathit{VaR}}_{0.5}^i}$	1.11	1.11	1.11	1.11	1.11	1.11	1.11	1.11	1.11	1.11
	$U{\mathit{CoVaR}}_{0.95}^{s|{\mathit{VaR}}_{\alpha }^i}$	3.24	3.43	3.58	3.80	4.05	4.30	4.83	5.44	6.56	8.67
	$\Delta \mathit{UCoVaR}$	2.13	2.32	2.47	2.69	2.94	3.19	3.72	4.33	5.45	7.56
	$\mathrm{\%}\mathit{UCoVaR}$	191.59%	209.16%	222.03%	242.14%	264.95%	287.21%	334.59%	389.87%	490.54%	680.53%

Note: ${\mathit{UCoVaR}}_{0.95}^{s|{\mathit{VaR}}_{0.5}^i}$ and $U{\mathit{CoVaR}}_{0.95}^{s|{\mathit{VaR}}_{\alpha }^i}$ denote the upside CoVaR of financial system condition on the normal state and financial distress with different risk levels. Financial distress is measured as the return of banking taking values equal to its VaR. $\alpha$ denotes the risk level of financial event. For example, $\alpha =95\%$ means a financial event once in 20 years. $\Delta \mathit{UCoVaR}$ and $\%\mathit{UCoVaR}$ are upside risk spillovers and risk-spillover intensity computed according to Equations (17)(17) $${\Delta \mathit{UCoVaR}}_{1-\beta }^{s|i}{=\mathit{UCoVaR}}_{1-\beta }^{s|X^i={\mathit{VaR}}_{1-\alpha }^i}-{\mathit{UCoVaR}}_{1-\beta }^{s|X^i={\mathit{VaR}}_{0.5}^i},$$(17) and (19)(19) $$\mathrm{\%}{\mathit{UCoVaR}}_{1-\beta }^{s|i}=({\Delta \mathit{UCoVaR}}_{1-\beta }^{s|i}/{\mathit{UCoVaR}}_{1-\beta }^{s|X^i={\mathit{VaR}}_{0.5}^i})\mathrm{*}100\mathrm{\%}.$$(19) .

Source: Authors own estimations.

Figure 6. The dynamics of downside risk spillovers from the three kinds of banks to financial system in China over period from 2 December 2014 to 31 July 2020.

Source: Created by the authors.

Figure 7. The dynamics of upside risk spillovers from the three kinds of banks to financial system in China from 2 December 2014 to 31 July 2020.

Source: Created by the authors.

Table 7. Dominance tests for the risk spillovers.

	Null hypothesis	Statistics	p-Value
Downside	$H_0:\mathrm{SOCBs }\mathrm{\ge }\mathrm{JSCBs}$	0.508	0.000***
	$H_0:C\mathrm{CBs}\ge JS\mathrm{CBs}$	0.503	0.000***
	$H_0:C\mathrm{CBs}\ge SO\mathrm{CBs}$	1	0.000***
Upside	$H_0:\mathrm{SOCBs }\mathrm{\ge }\mathrm{JSCBs}$	0.473	0.000***
	$H_0:C\mathrm{CBs}\ge JS\mathrm{CBs}$	0.508	0.000***
	$H_0:\mathrm{SOCBs}\ge \mathit{CCBs}$	0.503	0.000***

Note: The null hypothesis ‘SOCBs ≥ JSCBs’ means that the SOCBs are more or equally risky than the JSCBs when financial events with the same risk levels occur in these two kinds of commercial banks. Three asterisks indicate significance at the 1% level.

Source: Authors own estimations.

Table 8. Significance tests for the risk spillovers.

	Null hypothesis	Statistics	p-Value
Downside	$H_0:\Delta \mathit{DCoVaR}\mathit{\text{ of }}\mathrm{SOCBs}=0$	1	0.000***
	$H_0:\Delta \mathit{DCoVaR}\mathit{\text{ of }}\mathrm{JSCBs}=0$	1	0.000***
	$H_0:\Delta \mathit{DCoVaR}\mathit{\text{ of }}\mathrm{CCBs}=0$	1	0.000***
Upside	$H_0:\Delta \mathit{UCoVaR}\mathit{\text{ of }}\mathrm{SOCBs}=0$	1	0.000***
	$H_0:\Delta \mathit{UCoVaR}\mathit{\text{ of }}\mathrm{JSCBs}=0$	1	0.000***
	$H_0:\Delta \mathit{UCoVaR}\mathit{\text{ of }}\mathrm{CCBs}=0$	1	0.000***

Note: Three asterisks indicate significance at the 1% level.

Source: Authors own estimations.

Table 9. Asymmetry tests for the risk spillovers from banks to China’s financial system.

Banks	Null hypothesis	Statistics	p-Value
SOCBs	$H_0:\%\mathit{UCoVaR}\ge \%\mathit{DCoVaR}$	1	0.000***
JSCBs	$H_0:\%\mathit{UCoVaR}\ge \%\mathit{DCoVaR}$	0.707	0.000***
CCBs	$H_0:\%\mathit{UCoVaR}\ge \%\mathit{DCoVaR}$	0.868	0.000***

Note: Three asterisks indicate significance at the 1% level.

Source: Authors own estimations.

Figure A1. Clayton and Gumbel CQR curves.

Source: Created by the authors.