Can google search volume index predict the returns and trading volumes of stocks in a retail investor dominant market

Figures & data

Table 1. Descriptive statistics

	Mean	Standard deviation	Max	Min	Median	Skewness	Kurtosis
$\mathrm{E}\mathrm{R}$	0.177	5.411	47.483	−28.445	0.000	0.622	8.138
LnSVI	2.877	1.306	4.605	0	3.258	−1.309	3.601
AVol	0.099	1.004	16.005	−1.000	−0.162	5.001	44.941

Note: This table repots descriptive statistics, including mean, standard deviation, maximum, minimum, median, skewness, and kurtosis for each variable. ER, LnSVI, and AVol denote weekly excess return, log of google search volume, and abnormal trading volume, respectively.

Table 2. Correlation matrix

Correlation	$\mathrm{E}{\mathrm{R}}_{\mathrm{t}}$	AVolt	LnSVIt	LnSVIt-1
$\mathrm{E}{\mathrm{R}}_{\mathrm{t}}$	1.000
AVolt	0.314*** (<0.001)	1.000
LnSVIt	0.032*** (0.006)	0.107*** (<0.001)	1.000
LnSVIt-1	−0.022* (0.058)	0.030** (0.013)	0.297*** (<0.001)	1.000

Note: This table reports the correlation matrix among used variables. ER, LnSVI, and AVol denote weekly excess return, log of google search volume, and abnormal trading volume, respectively. *^, **, and *** refer to significance levels of 10%, 5%, and 1%, respectively; p-values are in parentheses.

Table 3. Regression results for GSVI prediction of weekly excess returns

Independent variable	Dependent variable: $\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}$
	(1)	(2)	(3)	(4)^#	(5)^$	(6)^$
Constant	−0.121 (−0.88)	−0.126 (−0.91)	0.416*** (2.98)	0.660*** (3.34)	0.890** (2.53)	0.277* (1.90)
$\mathrm{M}\mathrm{R}{\mathrm{P}}_{\mathrm{t}}$	1.386*** (34.39)	1.388*** (34.41)	1.388*** (34.39)	1.470*** (29.09)	1.459*** (24.21)	1.316*** (24.61)
$5\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}$	0.670*** (7.51)	0.689*** (7.66)	0.692*** (7.70)	0.579*** (5.14)	0.476*** (3.55)	0.909*** (7.63)
$\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}$	−0.533*** (−4.83)	−0.522*** (−4.71)	−0.519*** (−4.69)	−0.596*** (−4.29)	−0.607*** (−3.67)	−0.430*** (−2.93)
$\mathrm{R}\mathrm{M}{\mathrm{W}}_{\mathrm{t}}$	−0.653*** (−6.12)	−0.657*** (−6.09)	−0.648*** (−6.01)	−0.788*** (−5.84)	−0.911*** (−5.67)	−0.382*** (−2.68)
$\mathrm{C}\mathrm{M}{\mathrm{A}}_{\mathrm{t}}$	−0.314*** (−3.45)	−0.320*** (−3.50)	−0.325*** (−3.56)	−0.542*** (−4.74)	−0.644*** (−4.73)	−0.010 (−0.08)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}}$	0.127*** (2.96)	0.132*** (3.07)
$\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}-1}$		−0.028*** (−2.71)	−0.027** (−2.59)	−0.042*** (−3.31)	−0.021 (−1.44)	−0.031** (−2.09)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$			−0.057 (−1.32)	−0.077 (−1.29)	−0.137 (−1.34)	−0.085* (−1.75)
F test	1.14	1.23	1.27	0.95	1.17	1.09
LM test	0.33	0.00	0.00	0.00	0.00	0.00
Adj R^2	0.2028	0.2043	0.2024	0.2223	0.2210	0.1899
Number of observations	7,440	7,392	7,392	5,082	3,696	3,696

Notes: This table reports the results for Equation (1)(1) $\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}=\alpha +{\beta }_1\mathrm{M}\mathrm{R}{\mathrm{P}}_{\mathrm{t}}+{\beta }_{2}5\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_3\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_4\mathrm{R}\mathrm{M}{\mathrm{W}}_{\mathrm{t}}+{\beta }_5\mathrm{C}\mathrm{M}{\mathrm{A}}_{\mathrm{t}}+{\beta }_6\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}-1}+\gamma \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\epsilon }_{\mathrm{i}\mathrm{t}},$(1) : $\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}=\alpha +{\beta }_1\mathrm{M}\mathrm{R}{\mathrm{P}}_{\mathrm{t}}+{\beta }_{2}5\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_3\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_4\mathrm{R}\mathrm{M}{\mathrm{W}}_{\mathrm{t}}+{\beta }_5\mathrm{C}\mathrm{M}{\mathrm{A}}_{\mathrm{t}}+{\beta }_6\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}-1}+\gamma \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\epsilon }_{\mathrm{i}\mathrm{t}}$ with different specifications. $\mathrm{M}\mathrm{R}{\mathrm{P}}_{\mathrm{t}}$ is the market risk premium factor; $5\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}$ and $\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}$ are the size effect and value premium factors, respectively; and $\mathrm{R}\mathrm{M}{\mathrm{W}}_{\mathrm{t}}$ and $\mathrm{C}\mathrm{M}{\mathrm{A}}_{\mathrm{t}}$ are the profitability and investment factors for week t in the five-factor model, respectively. *^, **, and *** refer to significance levels of 10%, 5%, and 1%, respectively; t values are in parentheses. The F-test is used to verify whether the fixed effects model outperforms OLS, and the LM test is used to verify whether the random effects model outperforms OLS. # refers to the 33 stocks in the TPEx 50 Index at the end of August 2019. $ is to distinguish stocks with high attention (low coefficient of variation) and low attention (high coefficient of variation) according to the coefficient of variation of the Google Search Volume Index.

Table 4. The longer effect of GSVI on excess returns

Independent variable	Dependent variable: $\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}$
	Full sample	High attention group	Low attention group
Constant	0.450*** (2.75)	2.242** (2.23)	0.541** (2.64)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	−0.067 (−1.41)	−0.034 (−0.32)	−0.094* (−1.73)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-2}$	0.005 (0.13)	0.029 (0.28)	−0.035 (−0.72)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-3}$	0.070 (1.25)	0.017 (0.14)	0.057 (0.90)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-4}$	−0.169*** (−2.90)	−0.314** (−2.26)	−0.152** (−2.36)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-5}$	−0.031 (−0.59)	−0.061 (−0.87)	−0.050 (−0.77)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-6}$	0.098* (1.76)	0.023 (0.21)	0.101 (1.50)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-7}$	0.074 (1.34)	−0.228* (−1.72)	0.145** (2.56)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-8}$	−0.037 (−0.76)	−0.188 (−1.61)	−0.016 (−0.32)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-9}$	0.053 (0.93)	0.105 (0.93)	0.020 (0.31)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-10}$	0.057 (1.22)	0.091 (0.78)	0.028 (0.52)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-11}$	−0.053 (−1.19)	0.052 (0.47)	−0.100* (−2.02)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-12}$	−0.066 (−1.33)	−0.028 (−0.24)	−0.102* (−1.88)
Control variable	Yes	Yes	Yes
F test	1.24	1.27	0.86
LM test	0.00	0.00	0.00
Adj R^2	0.2065	0.2286	0.1961
Wald test: $\sum _{h=1}^{4}LnSV{I}_{it-h}=0$
F statistics	4.04*	3.44*	4.30**
Wald test: $\sum _{h=1}^{8}LnSV{I}_{it-h}=0$
F statistics	0.41	5.07**	0.17
Wald test: $\sum _{h=1}^{12}LnSV{I}_{it-h}=0$
F statistics	1.71	3.65*	4.31**

Notes: This table reports the results for equation, $\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}=\alpha +{\beta }_1\mathrm{M}\mathrm{R}{\mathrm{P}}_{\mathrm{t}}+{\beta }_{2}5\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_3\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_4\mathrm{R}\mathrm{M}{\mathrm{W}}_{\mathrm{t}}+{\beta }_5\mathrm{C}\mathrm{M}{\mathrm{A}}_{\mathrm{t}}+{\beta }_6\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}-1}+\sum _{k=1}^{12}{\gamma }_k\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-\mathrm{k}}+{\epsilon }_{\mathrm{i}\mathrm{t}}$, in order to examine the longer effect of GSVI. *^, **, and *** refer to significance levels of 10%, 5%, and 1%, respectively; t values are stated in parentheses. Control variables include the five factors proposed by Fama and French (2015) and the excess return of the previous period. The F-test is used to verify whether the fixed effects model outperforms OLS, and the LM test is used to verify whether the random effects model outperforms OLS.

Table 5. Distinguishing the effect of GSVI on excess returns under positive and negative shocks

Independent variable	Dependent variable: $\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}$
	Full sample	High attention group	Low attention group
Constant	0.524*** (3.43)	0.924*** (2.61)	0.279* (1.91)
$\mathrm{M}\mathrm{R}{\mathrm{P}}_{\mathrm{t}}$	1.389*** (34.44)	1.460*** (24.22)	1.316*** (24.63)
$5\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}$	0.698*** (7.77)	0.477*** (3.55)	0.909*** (7.64)
$\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}$	−0.510*** (−4.61)	−0.602*** (−3.64)	−0.422*** (−2.88)
$\mathrm{R}\mathrm{M}{\mathrm{W}}_{\mathrm{t}}$	−0.644*** (−5.98)	−0.909*** (−5.65)	−0.381*** (−2.67)
$\mathrm{C}\mathrm{M}{\mathrm{A}}_{\mathrm{t}}$	−0.330*** (−3.61)	−0.647*** (−4.75)	−0.013 (−0.11)
$\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}-1}$	−0.049*** (−2.99)	−0.015 (−0.61)	−0.058*** (−2.70)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	−0.111** (−2.21)	−0.161 (−1.54)	−0.105** (−2.04)
$\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	0.131* (1.90)	0.025 (0.25)	0.186** (2.00)
$\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	0.001 (0.02)	0.081 (0.86)	−0.053 (−0.57)
F test	1.30*	1.17	1.13
LM test	0.00	0.00	0.00
Adj R^2	0.2043	0.2208	0.1904
Wald test: $\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ = $\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$
F statistics	1.43	0.12	2.74*
Wald test: $\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ + $\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ = 0
F statistics	0.07	0.97	0.70
Wald test: $\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ + $\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ = 0
F statistics	2.07	0.39	2.46

Notes: This table reports the results for Equation (2)(2) $\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}=\alpha +{\beta }_1\mathrm{M}\mathrm{R}{\mathrm{P}}_{\mathrm{t}}+{\beta }_{2}5\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_3\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_4\mathrm{R}\mathrm{M}{\mathrm{W}}_{\mathrm{t}}+{\beta }_5\mathrm{C}\mathrm{M}{\mathrm{A}}_{\mathrm{t}}+{\beta }_6\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_1\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_2\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_3\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\epsilon }_{\mathrm{i}\mathrm{t}}$(2) : $\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}=\alpha +{\beta }_1\mathrm{M}\mathrm{R}{\mathrm{P}}_{\mathrm{t}}+{\beta }_{2}5\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_3\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_4\mathrm{R}\mathrm{M}{\mathrm{W}}_{\mathrm{t}}+{\beta }_5\mathrm{C}\mathrm{M}{\mathrm{A}}_{\mathrm{t}}+{\beta }_6\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_1\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_2\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_3\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\epsilon }_{\mathrm{i}\mathrm{t}}$, to examine the effects of positive and negative shocks. *^, **, and *** refer to the significance level of 10%, 5%, and 1%, respectively; t values are in parentheses. The F-test is used to verify whether the fixed effects model outperforms OLS, and the LM test is used to verify whether the random effects model outperforms OLS.

Table 6. Effect of GSVI on abnormal trading volume

Dependent variable: AVolit	Full sample		High attention group		Low attention group
Independent variable	(1)	(2)	(3)	(4)	(5)	(6)
Constant	0.003 (0.11)	0.019 (0.68)	−0.097 (−1.47)	−0.047 (−0.73)	0.019 (0.57)	0.028 (0.88)
$\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}$	0.058*** (27.52)	0.059*** (28.36)	0.049*** (18.86)	0.050*** (19.81)	0.070*** (20.60)	0.070*** (20.83)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	0.028*** (3.21)	0.001 (0.14)	0.053*** (2.78)	0.017 (0.90)	0.030*** (2.65)	0.004 (0.30)
$\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$		0.177*** (17.03)		0.181*** (14.14)		0.168*** (9.98)
$\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$		−0.015 (−1.36)		−0.018 (−1.43)		−0.008 (−0.42)
F test	0.88	0.97	1.19	1.26	0.59	0.75
LM test	0.00	0.00	0.19	0.49	0.00	0.00
Adj R^2	0.0999	0.1382	0.0943	0.1470	0.1106	0.1362
Wald test: $\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ = $\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$
F statistics		68.99***		38.85***		25.61***

Notes: This table reports the results for Equations (3)(3) $\mathrm{A}\mathrm{V}\mathrm{o}{\mathrm{l}}_{\mathrm{i}\mathrm{t}}=\alpha +\beta \mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}+\gamma \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\epsilon }_{\mathrm{i}\mathrm{t}}$(3) and (4(4) $\mathrm{A}\mathrm{V}\mathrm{o}\mathrm{l}{}_{\mathrm{i}\mathrm{t}}=\alpha +\beta \mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}+{\gamma }_1\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_2\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_3\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\epsilon }_{\mathrm{i}\mathrm{t}}$(4) ) in order to examine the effects of GSVI and shocks on abnormal trading volume. *^, **, and *** denote significance levels of 10%, 5%, and 1%, respectively; the t value is in parentheses. The F-test is used to verify whether the fixed effects model outperforms OLS, and the LM test is used to verify whether the random effects model outperforms OLS.

Table 7. Robustness analysis of shock thresholds and excess returns

	Full sample		High attention group		Low attention group
Independent variable	0.5 times	2 times	0.5 times	2 times	0.5 times	2 times
Constant	0.510*** (3.34)	0.540*** (3.54)	0.869** (2.46)	0.973*** (2.76)	0.280** (2.15)	0.288** (1.98)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	−0.086* (−1.66)	−0.117** (−2.39)	−0.106* (−1.81)	−0.179* (−1.74)	−0.115** (−2.28)	−0.104** (−2.09)
$\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	0.063 (1.16)	0.360*** (3.44)	0.029 (0.37)	0.234 (1.57)	0.064 (0.99)	0.459*** (3.16)
$\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	−0.066 (−1.27)	0.125 (1.08)	−0.110 (−1.49)	0.311* (1.91)	0.044 (0.59)	−0.101 (−0.62)
Control variable	Yes	Yes	Yes	Yes	Yes	Yes
F test	1.31*	1.32*	1.24	1.21	1.10	1.12
LM test	0.00	0.00	0.00	0.00	0.00	0.00
Adj R^2	0.2042	0.2055	0.2210	0.2222	0.1897	0.1917
Wald test: $\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ = $\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$
F statistics	2.71*	1.91	1.27	0.10	0.04	5.71**
Wald test: $\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ + $\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ = 0
F statistics	0.13	4.80**	0.49	0.10	0.45	5.81**
Wald test: $\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ + $\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ = 0
F statistics	5.94**	0.01	2.15	0.51	1.02	1.54

Notes: This table reports the robustness results for Equation (2)(2) $\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}=\alpha +{\beta }_1\mathrm{M}\mathrm{R}{\mathrm{P}}_{\mathrm{t}}+{\beta }_{2}5\mathrm{S}\mathrm{M}{\mathrm{B}}_{\mathrm{t}}+{\beta }_3\mathrm{H}\mathrm{M}{\mathrm{L}}_{\mathrm{t}}+{\beta }_4\mathrm{R}\mathrm{M}{\mathrm{W}}_{\mathrm{t}}+{\beta }_5\mathrm{C}\mathrm{M}{\mathrm{A}}_{\mathrm{t}}+{\beta }_6\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_1\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_2\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_3\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\epsilon }_{\mathrm{i}\mathrm{t}}$(2) , in which we modify the thresholds for identifying positive/negative shocks. *^, **, and *** denote significance levels of 10%, 5%, and 1%, respectively; t values are in parentheses; “0.5 times” means the average return plus or minus 0.5 times the standard deviation as the threshold for positive and negative shocks; “2 times” means the average return plus or minus two standard deviations as the threshold for positive and negative shocks. The F-test is used to verify whether the fixed effects model outperforms OLS, and the LM test is used to verify whether the random effects model outperforms OLS.

Table 8. Robustness analysis of shock thresholds and abnormal volumes

	Full sample		High attention group		Low attention group
Independent variable	0.5 times	2 times	0.5 times	2 times	0.5 times	2 times
Constant	0.014 (0.51)	0.024 (0.87)	−0.071 (−1.11)	−0.033 (−0.52)	0.027 (0.86)	0.032 (0.99)
$\mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}$	0.059*** (28.27)	0.058*** (28.03)	0.050*** (19.49)	0.050*** (19.50)	0.071*** (20.99)	0.069*** (20.65)
$\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	0.000 (0.05)	0.007 (0.85)	0.026 (1.33)	0.022 (1.16)	−0.003 (−0.25)	0.009 (0.80)
$\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	0.115*** (13.20)	0.334*** (19.17)	0.104*** (9.72)	0.323*** (14.96)	0.128*** (8.96)	0.345*** (12.21)
$\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$	−0.019** (−2.25)	0.026 (1.26)	−0.025** (−2.40)	0.006 (0.23)	−0.013 (−0.93)	0.053 (1.61)
F test	0.98	0.84	1.28	1.11	0.73	0.62
LM test	0.00	0.00	0.00	0.04	0.00	0.00
Adj R^2	0.1289	0.1455	0.1280	0.1494	0.1354	0.1474
Wald test: $\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$ = $\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}$
F statistics	66.43***	44.38***	33.28***	27.46***	32.74***	14.61***

Notes: This table reports the robustness results for Equation (4)(4) $\mathrm{A}\mathrm{V}\mathrm{o}\mathrm{l}{}_{\mathrm{i}\mathrm{t}}=\alpha +\beta \mathrm{E}{\mathrm{R}}_{\mathrm{i}\mathrm{t}}+{\gamma }_1\mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_2\mathrm{P}\mathrm{O}{\mathrm{S}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\gamma }_3\mathrm{N}\mathrm{E}{\mathrm{G}}_{\mathrm{i}\mathrm{t}-1}\cdot \mathrm{L}\mathrm{n}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{i}\mathrm{t}-1}+{\epsilon }_{\mathrm{i}\mathrm{t}}$(4) , in which we modify the thresholds for identifying positive/negative shocks. *^, **, and *** denote significance levels of 10%, 5%, and 1%, respectively; t values are in parentheses; “0.5 times” means the average return plus or minus 0.5 times the standard deviation as the threshold for positive and negative shocks; “2 times” means the average return plus or minus two standard deviations as the threshold for positive and negative shocks. The F-test is used to verify whether the fixed effects model outperforms OLS, and the LM test is used to verify whether the random effects model outperforms OLS.

Fama, E. F., & French, K. R. (2015). A five-factor asset pricing model. Journal of Financial Economics, 116(1), 1–22. https://doi.org/10.1016/j.jfineco.2014.10.010

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