Chinese stock market volatility and herding behavior asymmetry during the COVID-19 pandemic

Figures & data

Table 1. Descriptive statistics

Variable	Obs.	Mean	StdDev	Min	Max	Skewness	Kurtosis
$R_{CSI-300}$	676	0.0008	0.013	−0.079	0.059	−0.408	3.715
$CSA{D}^{CSI-300}$	676	0.0162	0.004	0.008	0.033	0.885	0.797
${\sigma }^{CSI-300}$	674	0.0100	0.009	0.001	0.090	3.639	21.553
$V_{CSI-300}$	674	37.3826	5.640	26.103	48.731	0.222	1.658
$R_B$	676	0.0003	0.111	−0.098	0.061	−1.120	11.823
$CSA{D}^B$	676	0.0101	0.003	0.005	0.027	1.591	4.262
${\sigma }^B$	674	0.0072	0.009	0.001	0.201	14.616	299.054
$V_B$	674	0.8937	0.110	0.653	1.103	0.005	1.759

The table reports descriptive statistics for the stock sample from 2 January 2019, to 15 October 2021, for the CSI-300, Shanghai/Shenzhen B-share individual stocks retrieved from the CSMAR database. The composite market return of the CSI-300 index and B-share index was obtained from WIND. The units of V_CSI-300 and V_B are in billions.

Table 2. Stationarity tests

Variable	ADF	1% level	5% level	10% level	p-value	Result
Panel A: ADF test statistic of CSI-300 index
$CSAD$	−5.684612	−3.978956	−3.420022	−3.132657	0.0000	Stationary
$\left|R_m\right|$	−12.29508	−3.978909	−3.419999	−3.132643	0.0000	Stationary
${R_m}^2$	−18.90171	−3.978861	−3.419976	−3.132629	0.0000	Stationary
Panel B: ADF test statistic of B-shares index
$CSAD$	−9.415624	−3.978909	−3.419999	−3.132643	0.0000	Stationary
$\left|R_m\right|$	−18.04540	−3.978861	−30419976	−3.132629	0.0000	Stationary
${R_m}^2$	−19.05791	−3.978861	−3.419976	−3.132629	0.0000	Stationary

This table reports the stationarity tests of CSI-300 and B-shares data from 2 January 2019, to 15 October 2021. This table uses EViews to analyze the ADF test statistic and also reports significance levels of different variables at 1%, 5%, and 10% and the p-values.

Figure 1. Scatter plot and fitting curve.

Table 3. Regression results of herding behavior before and during COVID-19

	CSI-indexed stocks		B-share stocks
Variable	Before COVID-19	During COVID-19	Before COVID-19	During COVID-19
$\alpha$	0.0127***	0.0156***	0.0073***	0.0086***
	(0.0127)	(0.0003)	(0.0002)	(0.0002)
${\beta }_1$	0.0926**	0.1898***	0.2133***	0.3454***
	(0.0411)	(0.0401)	(0.0386)	(0.0352)
${\beta }_2$	1.8260**	−0.3242**	−0.6380**	−3.2751***
	(0.7746)	(0.8877)	(1.0175)	(0.5492)

The table reports the results for the following regression equation:

$CSA{D}_t=\alpha +{\beta }_1\left|R_{m,t}\right|+{\beta }_2{\left(R_{m,t}\right)}^2+{\epsilon }_t,$

where CSAD is the cross-sectional absolute return deviation, R_m is the market return rate at time t, R_m² is the quadratic term added based on the non-linear characteristics of this study. Standard errors are in parentheses. ***, **, * represent statistical significance at the 10%, 5% and 1% levels, respectively.

Table 4. Impact of herding behavior on market volatility

Variable	CSI-300 index	B-share index
Panel A: Full sample period
${\gamma }_0$	0.0046**	0.0055**
	(2.0751)	(1.9917)
${\gamma }_1$	1.2261***	0.5697***
	(13.7367)	(5.4901)
${\gamma }_2$	−0.1762***	−0.2815***
	(−7.0653)	(−9.5738)
${\gamma }_3$	−3.83E–13***	−4.45E–12
	(−5.7563)	(−1.4826)
Panel B: Before COVID-19
${\gamma }_0$	0.0011	0.0010
	(0.2545)	(0.2147)
${\gamma }_1$	1.4386***	0.5640***
	(12.0760)	(4.2470)
${\gamma }_2$	−0.1814***	−0.3203***
	(−5.7201)	(−8.8324)
${\gamma }_3$	−3.69E–13***	1.17E–12
	(−2.9726)	(0.2072)
Panel C: During COVID-19
${\gamma }_0$	−0.0092	0.0209***
	(−0.6354)	(2.9680)
${\gamma }_1$	0.8011***	0.4577***
	(6.9961)	(4.2641)
${\gamma }_2$	−0.1888***	−0.0167
	(−5.2771)	(−0.4670)
${\gamma }_3$	1.03E–13	−1.90E–11***
	(0.3100)	(−2.8269)

The following regression equation measures the impact of herding behavior on stock market volatility:

${\sigma }_t^m={\gamma }_0+{\gamma }_{1}CSA{D}_{m,t-1}+{\gamma }_2{R}_{m,t-1}+{\gamma }_3{V}_{m,t}+{\epsilon }_t.$

t-statistics are in brackets. ***, **, * represent statistical significance at the 10%, 5% and 1% levels, respectively.

Table 5. Regression results in bear and bull markets

Variables	Coefficient	Std.Error	t-Statistic	Prob.
Panel A: Regression analysis of CSI-300 index
$\alpha$	0.0156	0.0003	49.69	0.000
${\beta }_1$	−0.1631	0.0472	−3.45	0.001
${\beta }_2$	0.1982	0.0396	5.00	0.006
${\beta }_3$	−0.0155	0.9023	−0.02	0.986
Panel B: Regression analysis of B-shares index
$\alpha$	0.0086	0.0002	41.77	0.000
${\beta }_1$	−0.3451	0.0453	−7.63	0.000
${\beta }_2$	0.3455	0.0351	9.85	0.000
${\beta }_3$	−3.2727	0.6068	−5.39	0.000

The table reports the regression results equation:

$CSA{D}_t=\alpha +{\beta }_1(1-D)R_{m,t}+{\beta }_{2}D{R}_{m,t}+{\beta }_3{\left(R_{m,t}\right)}^2+{\epsilon }_t,$

where D is a dummy variable that equals one on bear days (negative R_m) and zero on bull days (positive R_m). The sample period covers from 12 December 2019, to 15 October 2021; the period begins with the first case of COVID-19.

Table 6. Order of autoregressive model—information criterion

Lag	LL	LR	df	P	FPE	AIC	HQIC	SBIC
Panel A: CSI-300 index information Criteria
0	1773.43				0.000	−8.15	−8.15	−8.14
1	1883.32	219.770	1	0.000	0.000	−8.650	−8.642	−8.631
2	1898.84	31.049	1	0.000	0.000	−8.717	−8.705	−8.688
3	1905.79	13.908	1	0.000	0.000	−8.744	−8.729	−8.706*
4	1906.18	0.771	1	0.380	0.000	−8.741	−8.723	−8.694
5	1907.93	3.491	1	0.062	0.000	−8.744	−8.722	−8.688
6	1910.55	5.247	1	0.022	0.000	−8.752	−8.726	−8.686
7	1912.92	4.745	1	0.029	0.000	−8.758	−8.729	−8.683
8	1913.01	0.172	1	0.679	0.000	−8.754	−8.721	−8.670
9	1913.92	1.819	1	0.177	0.000	−8.754	−8.717	−8.660
10	1918.90	9.956*	1	0.002	9.1e-06*	−8.771*	−8.731*	−8.669
Panel A: B-share index information Criteria
0	1875.76				0.000	−8.620	−8.616	−8.610
1	1916.36	81.189	1	0.000	0.000	−8.802	−8.794	−8.783
2	1926.56	20.399	1	0.000	0.000	−8.844	−8.833	−8.816
3	1928.22	3.324	1	0.068	0.000	−8.847	−8.832	−8.810
4	1933.46	10.473	1	0.001	0.000	−8.866	−8.848	−8.820*
5	1936.42	5.933*	1	0.015	8.2e-06*	−8.876*	−8.853*	−8.819
6	1937.17	1.485	1	0.223	0.000	−8.874	−8.848	−8.809
7	1937.78	1.226	1	0.268	0.000	−8.873	−8.843	−8.798
8	1937.83	0.107	1	0.743	0.000	−8.868	−8.835	−8.784
9	1939.30	2.936	1	0.087	0.000	−8.870	−8.833	−8.777
10	1940.27	1.936	1	0.164	0.000	−8.870	−8.830	−8.767

The table shows the information criterion used to determine the order of the autoregressive model.

Figure 2. Time trends of CSAD.

Table 8. Threshold GARCH model

Variable	CSI-300 Index	B-share Index
CSAD
Rm	0.021**	0.034***
Rm^2	3.427***	2.105***
Constant	0.014***	0.009***
ARCH
Arch L1.	0.264***	0.144
Tarch L1.	0.215**	0.296***
Garch L1.	0.457***	0.387***
Constant	2.27e-06***	2.88e-06***

The table shows the results of the Threshold GARCH model.

Table 7. OLS vs. E-GARCH models

Variable	AR(10)-OLS	E-GARCH
Panel A: CSI-300 Index E-GARCH
CSAD
L1.	0.419***	0.411***
L2.	0.141***	0.111**
L3.	0.155***	0.175***
L4.	0.022	0.038
L5.	0.101**	0.134***
L6.	−0.159***	−0.159***
L7.	0.076**	0.037**
L8.	−0.067	−0.079
L9.	−0.002	0.006**
L10.	0.152***	0.174***
Constant	0.003***	0.003***
ARCH
Earch L1.		0.153***
Earch_a L1.		−0.006
Egarch L1		0.896***
Constant		−1.221***
Panel B: B-share Index E-GARCH
CSAD
L1.	0.294***	0.260***
L2.	0.148***	0.147***
L3.	0.037	0.037**
L4.	0.165***	0.187***
Constant	0.004***	0.004***
ARCH
Earch L1.		0.137***
Earch_a L1.		−0.084**
Egarch L1		0.855***
Constant		−1.710***

The table compares the lag term least-squares method and the E-GARCH model. The 10-order lag is adopted for CSI-300, and the 4-order lag is adopted for B-shares.