Table 1 Summary statistics Panel A:...

Table 1

Summary statistics

Panel A: Descriptive statistics
	Mean	STD	25th Pctl	Median	75th Pctl	Min	Max	Skew	Kurt
VaR1	8.27	2.75	6.20	7.74	9.78	2.10	15.42	0.70	−0.17
VaR5	5.03	2.03	3.70	4.51	5.73	1.12	13.56	1.51	2.45
ES1	9.49	2.68	7.50	9.14	11.24	2.41	17.21	0.37	−0.56
ES5	6.88	2.39	5.22	6.41	8.06	1.70	14.69	0.98	0.61
SEMI-V	2.34	0.77	1.82	2.18	2.69	0.72	5.28	1.03	0.84
PC1	0.31	1.62	−0.84	0.14	1.28	−4.54	6.21	0.46	0.15
SIZE	11.97	1.73	10.74	11.70	13.02	6.35	18.49	0.54	0.32
BM	1.70	1.27	0.94	1.41	2.14	0.03	11.76	2.95	14.78
MOM	22.52	35.80	8.09	18.48	29.17	−56.97	481.54	5.17	47.86
STR	1.90	5.73	0.70	1.43	2.11	−11.60	140.35	15.26	337.32
ILLIQ	0.12	0.61	0.00	0.01	0.05	0.00	14.02	15.33	297.44
Coskew	−0.05	0.05	−0.07	−0.04	−0.02	−0.26	0.11	−0.83	2.05
BETA	0.76	0.26	0.57	0.73	0.92	0.06	1.60	0.48	0.08
Betadown	0.90	0.28	0.71	0.90	1.08	0.03	2.03	0.33	0.93
IVOL	2.64	1.13	1.92	2.31	3.01	0.52	9.40	1.73	3.80
MAX	4.17	1.69	3.08	3.75	4.73	0.74	14.33	1.56	3.21
VOLDU	−0.08	2.51	−0.13	−0.01	0.04	−23.67	52.09	9.70	227.29
GKMHI	0.13	0.05	0.10	0.12	0.15	0.00	0.50	0.99	6.77
GKMLO	0.18	0.06	0.14	0.18	0.21	0.00	0.50	0.13	1.80

Panel A: Descriptive statistics
	Mean	STD	25th Pctl	Median	75th Pctl	Min	Max	Skew	Kurt
VaR1	8.27	2.75	6.20	7.74	9.78	2.10	15.42	0.70	−0.17
VaR5	5.03	2.03	3.70	4.51	5.73	1.12	13.56	1.51	2.45
ES1	9.49	2.68	7.50	9.14	11.24	2.41	17.21	0.37	−0.56
ES5	6.88	2.39	5.22	6.41	8.06	1.70	14.69	0.98	0.61
SEMI-V	2.34	0.77	1.82	2.18	2.69	0.72	5.28	1.03	0.84
PC1	0.31	1.62	−0.84	0.14	1.28	−4.54	6.21	0.46	0.15
SIZE	11.97	1.73	10.74	11.70	13.02	6.35	18.49	0.54	0.32
BM	1.70	1.27	0.94	1.41	2.14	0.03	11.76	2.95	14.78
MOM	22.52	35.80	8.09	18.48	29.17	−56.97	481.54	5.17	47.86
STR	1.90	5.73	0.70	1.43	2.11	−11.60	140.35	15.26	337.32
ILLIQ	0.12	0.61	0.00	0.01	0.05	0.00	14.02	15.33	297.44
Coskew	−0.05	0.05	−0.07	−0.04	−0.02	−0.26	0.11	−0.83	2.05
BETA	0.76	0.26	0.57	0.73	0.92	0.06	1.60	0.48	0.08
Betadown	0.90	0.28	0.71	0.90	1.08	0.03	2.03	0.33	0.93
IVOL	2.64	1.13	1.92	2.31	3.01	0.52	9.40	1.73	3.80
MAX	4.17	1.69	3.08	3.75	4.73	0.74	14.33	1.56	3.21
VOLDU	−0.08	2.51	−0.13	−0.01	0.04	−23.67	52.09	9.70	227.29
GKMHI	0.13	0.05	0.10	0.12	0.15	0.00	0.50	0.99	6.77
GKMLO	0.18	0.06	0.14	0.18	0.21	0.00	0.50	0.13	1.80

Panel B: Correlation
	VaR1	VaR5	ES1	ES5	SEMI-V	Coskew	Beta down	BETA	SIZE	BM	MOM	STR	ILLIQ	IVOL	MAX	VOLDU	GKMHI
VaR5	0.87
ES1	0.95	0.81
ES5	0.96	0.96	0.93
SEMI-V	0.95	0.94	0.93	0.98
Coskew	0.00	0.03	−0.02	0.01	0.03
Betadown	0.25	0.21	0.28	0.25	0.21	−0.46
BETA	0.23	0.21	0.25	0.24	0.20	0.00	0.78
SIZE	−0.37	−0.34	−0.36	−0.37	−0.37	0.11	0.14	0.33
BM	0.12	0.13	0.10	0.13	0.16	0.03	−0.11	−0.16	−0.35
MOM	0.11	0.12	0.10	0.11	0.13	0.00	0.00	0.01	0.03	0.04
STR	−0.01	−0.01	−0.01	−0.01	0.01	0.00	−0.02	−0.02	0.01	0.04	−0.01
ILLIQ	0.03	0.03	0.02	0.03	0.06	0.02	−0.07	−0.08	−0.12	0.06	0.00	0.00
IVOL	0.56	0.58	0.54	0.59	0.59	0.00	0.04	0.02	−0.28	0.09	0.15	0.26	0.08
MAX	0.53	0.55	0.51	0.56	0.56	0.02	0.10	0.11	−0.20	0.08	0.14	0.47	0.05	0.90
VOLDU	0.00	0.01	0.00	0.01	0.00	0.00	0.01	0.01	−0.05	−0.01	−0.08	−0.12	0.00	−0.17	−0.18
GKMHI	−0.04	−0.04	−0.04	−0.04	−0.04	0.01	−0.02	−0.01	0.05	−0.02	−0.01	0.11	0.00	0.00	0.03	0.00
GKMLO	0.08	0.08	0.08	0.08	0.08	−0.02	0.03	0.02	−0.08	0.02	0.02	−0.13	−0.01	0.02	−0.02	0.00	−0.17

Panel B: Correlation
	VaR1	VaR5	ES1	ES5	SEMI-V	Coskew	Beta down	BETA	SIZE	BM	MOM	STR	ILLIQ	IVOL	MAX	VOLDU	GKMHI
VaR5	0.87
ES1	0.95	0.81
ES5	0.96	0.96	0.93
SEMI-V	0.95	0.94	0.93	0.98
Coskew	0.00	0.03	−0.02	0.01	0.03
Betadown	0.25	0.21	0.28	0.25	0.21	−0.46
BETA	0.23	0.21	0.25	0.24	0.20	0.00	0.78
SIZE	−0.37	−0.34	−0.36	−0.37	−0.37	0.11	0.14	0.33
BM	0.12	0.13	0.10	0.13	0.16	0.03	−0.11	−0.16	−0.35
MOM	0.11	0.12	0.10	0.11	0.13	0.00	0.00	0.01	0.03	0.04
STR	−0.01	−0.01	−0.01	−0.01	0.01	0.00	−0.02	−0.02	0.01	0.04	−0.01
ILLIQ	0.03	0.03	0.02	0.03	0.06	0.02	−0.07	−0.08	−0.12	0.06	0.00	0.00
IVOL	0.56	0.58	0.54	0.59	0.59	0.00	0.04	0.02	−0.28	0.09	0.15	0.26	0.08
MAX	0.53	0.55	0.51	0.56	0.56	0.02	0.10	0.11	−0.20	0.08	0.14	0.47	0.05	0.90
VOLDU	0.00	0.01	0.00	0.01	0.00	0.00	0.01	0.01	−0.05	−0.01	−0.08	−0.12	0.00	−0.17	−0.18
GKMHI	−0.04	−0.04	−0.04	−0.04	−0.04	0.01	−0.02	−0.01	0.05	−0.02	−0.01	0.11	0.00	0.00	0.03	0.00
GKMLO	0.08	0.08	0.08	0.08	0.08	−0.02	0.03	0.02	−0.08	0.02	0.02	−0.13	−0.01	0.02	−0.02	0.00	−0.17

Note(s): This table shows the descriptive statistics (Panel A) and the correlation matrix (Panel B) for the cross-section of the left-tail risk proxies and firm-specific characteristics. The time-series average was computed for each stock to obtain one representative value, and then cross-sectional statistics were calculated. The sample period covers January 1998 to May 2020, and 3,626,937 firm-day observations were used in the analysis. The definitions of all variables are given in Section 2

Source(s): Created by authors

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