Abnormal returns and idiosyncratic volatility puzzle: An empirical investigation in Vietnam stock market

Figures & data

Table 1. Description of variables

Variables	Description	Computation
Factors in capital asset pricing model
MKT	Market premium (value-weighted market return)	$\mathrm{M}\mathrm{K}\mathrm{T}=R_i-R_f$
SMB	Size premium (small minus big)	$SM{B}_t=\frac{\mathrm{S}/\mathrm{H}+S/M+S/L}{3}-\frac{B/H+B/M+B/L}{3}$
HML	Value premium (high minus low)	$HM{L}_t=\frac{\mathrm{S}/\mathrm{H}+B/H}{2}-\frac{S/L+B/L}{2}$
WML	Momentum premium (winner minus loser)	$WM{L}_t=\frac{\mathrm{S}/\mathrm{W}+B/W}{2}-\frac{S/L+B/L}{2}$
Control variables
IVOL	Idiosyncratic volatility	$IVO{L}_{i,t}=std\left({\epsilon }_{i,d}\right)$
Size	Market capitalization (in Vietnam Dong)	$\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}=\mathrm{l}\mathrm{n}\left(\mathrm{m}\mathrm{a}\mathrm{r}\mathrm{k}\mathrm{e}\mathrm{t}\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{i}\mathrm{t}\mathrm{a}\mathrm{l}\mathrm{i}\mathrm{z}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}\right)$
BM	Book-to-market ratio	$\mathrm{B}\mathrm{M}=\frac{Ownerequity}{marketcapitalization}$
TURN	Total trading volume to the share outstanding of equity	$\mathrm{T}\mathrm{U}\mathrm{R}\mathrm{N}=\frac{Totaltradingvolume}{Shareoutstandingofequity}$
LEV	Return in previous 1 month	$LE{V}_{i,t}=R_{i,t-1}$

Table 2. Statistic summary

Variable	Observation	Mean	Std. dev.	Min	Max
Rm	28421	0.0094	0.1396	−0.757	2.7101
AlphaCAPM	28421	0.0004	0.0061	−0.0623	0.0641
AlphaFF3	28421	0.0003	0.0063	−0.0647	0.0645
AlphaCH4	28421	0.0004	0.0066	−0.0645	0.0736
IVOLCAPM	28421	0.023	0.0097	0	0.1275
IVOLFF3	28421	0.021	0.0092	0	0.1246
IVOLCH4	28421	0.0202	0.0089	0	0.1243
LnSIZE	28421	13.1082	1.5289	8.4764	19.6433
BM	28421	1.2983	0.9546	0.0275	9.0973
MOM0212	28421	0.1252	0.6116	−0.9297	9.9028
REV	28421	0.0091	0.1423	−0.757	2.7101
TURN	28421	0.0812	0.1451	0	2.0715

Notes: Sample for stock traded on Vietnam Stock Exchange covering the period from February 2008 to December 2018. Size is computed as natural logarithm of the market capitalization (in Vietnam Dong) at the end of the month. MOM₀₂₁₂ is calculated as the cumulative return from month t-12 to month t-2. TURN is the ratio of total trading volume to the share outstanding of equity in a month. REV is the return in previous 1 month. The observation shows the number of trading observations in studied sample. All variables are noted in percent.

Table 3. Correlations

	Rm	AlphaCAPM	AlphaFF3	AlphaFF3	IVOLCAPM	IVOLFF3	IVOLCH4	Ln(SIZE)	BM	MOM0212	REV	TURN
Rm	1
AlphaCAPM	0.0211	1
AlphaFF3	0.0108	0.8555	1
AlphaCH4	0.0064	0.7956	0.9355	1
IVOLCAPM	0.0183	0.132	0.0812	0.0826	1
IVOLFF3	0.025	0.1337	0.0873	0.0889	0.9741	1
IVOLCH4	0.0228	0.1321	0.0854	0.0848	0.9633	0.9899	1
Ln(SIZE)	−0.0235	0.0429	0.0551	0.0454	−0.3697	−0.358	−0.3627	1
BM	0.0351	0.0212	0.0029	0.0056	0.2381	0.224	0.2296	−0.4084	1
MOM0212	0.0195	0.0518	0.0433	0.0231	−0.019	−0.0167	−0.0123	0.2155	0.1109	1
REV	0.0699	0.858	0.718	0.6544	0.1261	0.1254	0.1232	0.0579	0.0362	0.0366	1
TURN	−0.0431	0.11	0.0541	0.0452	0.1427	0.0971	0.0891	−0.0361	0.1428	0.1725	0.1328	1

Table 4. IVOL-stock returns relation on full-sample for both weighted methods

	Full-sample
	Equal-weighted method						Value-weighted method
	1	2	3	4	5	5_1	1	2	3	4	5	5_1
N	131	131	131	131	131	131	131	131	131	131	131	131
	IVOLCAPM
MEAN (%)	0.8363	0.8287	0.6816	0.5428	0.5592	−0.2771	0.0093	0.003	0.0045	−0.0025	−0.0026	−0.0119
T-statistic	(1.16)	(1.09)	(0.89)	(0.72)	(0.75)	(−0.71)	(0.32)	(0.11)	(0.17)	(−0.09)	(−0.09)	(−0.56)
	IVOLFF3
MEAN (%)	0.6934	0.8264	0.7652	0.4015	0.757	0.0636	0.0076	−0.0166	0.0034	0.0113	0.0036	−0.0040
T-statistic	(0.96)	(1.06)	(0.98)	(0.56)	(1.02)	(0.17)	(0.25)	(−0.59)	(0.12)	(0.47)	(0.12)	(−0.17)
	IVOLCH4
MEAN (%)	0.7177	0.8782	0.6268	0.5926	0.6286	−0.0891	−0.0018	−0.0038	0.0075	0.0048	0.0044	0.0062
T-statistic	(0.97)	(1.14)	(0.81)	(0.81)	(0.87)	(−0.23)	(−0.06)	(−0.13)	(0.29)	(0.19)	(0.15)	(0.28)

Notes: The equal-weighted and value-weighted raw returns that are computed based on sorting data with quantile portfolios of IVOL_CAPM, IVOL_FF3 and IVOL_CH4 under full-sample. Each month, stocks are ranked into quantile portfolios by IVOL of last month. Returns are in percentage form. The sample covers the period from January 2008 to December 2018. ***, ** and * denote the significance at the 1%, 5% and 10% levels, respectively. (5_1) column is the difference between return of highest fifth IVOL and return of lowest first IVOL. It shows the strategy of holding long position with the highest fifth IVOL and short position with the lowest first IVOL (also called IVOL strategy).

Table 5. IVOL-stock returns relation on positive alpha sub-samples

	Positive alpha sub-samples
	Equal-weighted method						Value-weighted method
	1	2	3	4	5	5_1	1	2	3	4	5	5_1
N	131	131	131	131	131	131	131	131	131	131	131	131
	IVOLCAPM
MEAN (%)	1.5665**	1.4895*	1.2946	0.2287	0.6519	−0.9146*	0.1296	0.0979	0.084	−0.0445	−0.0036	−0.1333*
T-statistic	(2.25)	(1.82)	(1.49)	(0.3)	(0.8)	(−1.84)	(1.24)	(1.32)	(0.67)	(−0.68)	(−0.05)	(−1.71)
	IVOLFF3
MEAN (%)	1.4668*	0.8691	0.8351	0.6052	0.4935	−0.9733*	0.099	0.0231	−0.0168	0.0108	0.031	−0.068
T-statistic	(1.97)	(1.08)	(1.05)	(0.8)	(0.61)	(−1.92)	(1.43)	(0.21)	(−0.26)	(0.18)	(0.43)	(−1.15)
	IVOLCH4
MEAN (%)	1.5642*	0.7312	0.5193	0.4255	0.5401	−1.0242**	0.104	0	−0.049	−0.0135	0.0263	−0.0777
T-statistic	(1.93)	(0.93)	(0.69)	(0.55)	(0.71)	(−1.98)	(1.06)	(0)	(−0.86)	(−0.19)	(0.38)	(−1.16)

Notes: The equal-weighted and value-weighted raw returns that are computed based on sorting data with quantile portfolios of IVOL_CAPM, IVOL_FF3 and IVOL_CH4 under positive alpha sub-samples. Each month, stocks are ranked into quantile portfolios by IVOL of last month. Returns are in percentage form. The sample covers the period from January 2008 to December 2018. ***, ** and * denote the significance at the 1%, 5% and 10% levels, respectively. (5_1) column is the difference between return of highest fifth IVOL and return of lowest first IVOL. It shows the strategy of holding long position with the highest fifth IVOL and short position with the lowest first IVOL (also called IVOL strategy).

Table 6. IVOL-stock returns relation on negative alpha sub-samples

	Negative alpha sub-samples
	Equal-weighted method						Value-weighted method
	1	2	3	4	5	5_1	1	2	3	4	5	5_1
N	131	131	131	131	131	131	131	131	131	131	131	131
	IVOLCAPM
MEAN (%)	0.4321	0.0179	0.5478	0.5595	0.7962	0.3641	−0.0445	−0.0503	−0.0231	−0.0114	−0.0216	0.0229
T-statistic	(0.57)	(0.02)	(0.68)	(0.74)	(1.13)	(0.85)	(−0.65)	(−0.9)	(−0.33)	(−0.21)	(−0.4)	(0.46)
	IVOLFF3
MEAN (%)	0.3415	0.4604	0.6021	0.3721	0.9644	0.6229	−0.0706	−0.0483	0.0107	−0.023	0.0227	0.0933*
T-statistic	(0.45)	(0.59)	(0.73)	(0.5)	(1.37)	(1.56)	(−0.93)	(−0.71)	(0.18)	(−0.41)	(0.41)	(1.76)
	IVOLCH4
MEAN (%)	0.4491	0.6574	0.4879	0.5762	0.9564	0.5074	−0.0204	−0.0684	0.0029	0.0325	0.0026	0.023
T-statistic	(0.58)	(0.8)	(0.65)	(0.76)	(1.29)	(1.32)	(−0.28)	(−0.9)	(0.05)	(0.55)	(0.04)	(0.49)

Notes: The equal-weighted and value-weighted raw returns that are computed based on sorting data with quantile portfolios of IVOL_CAPM, IVOL_FF3 and IVOL_CH4 under negative alpha sub-samples. Each month, stocks are ranked into quantile portfolios by IVOL of last month. Returns are in percentage form. The sample covers the period from January 2008 to December 2018. ***, ** and * denote the significance at the 1%, 5% and 10% levels, respectively. (5_1) column is the difference between return of highest fifth IVOL and return of lowest first IVOL. It shows the strategy of holding long position with the highest fifth IVOL and short position with the lowest first IVOL (also called IVOL strategy).

Table 7. IVOL_CAPM and stock returns

	Full-sample				Positive alpha sub-samples				Negative alpha sub-samples
Variables	(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)	(12)
IVOLCAPM	−0.1392	−0.2781*	−0.2703*	−0.2531*	−0.5295**	−0.6725*	−0.6021**	−0.4447*	0.179	−0.0778	−0.0924	0.0044
	(−0.83)	(−1.8)	(−1.86)	(−1.72)	(−2.19)	(−2.7)	(−2.48)	(−1.78)	(0.8)	(−0.32)	(−0.4)	(0.02)
Ln(SIZE)		−0.0016	−0.0023**	−0.0017*		−0.0008	−0.0021	−0.0007		−0.0031**	−0.0033*	−0.0023**
		(−1.53)	(−2.27)	(−1.74)		(−0.55)	(−1.56)	(−0.55)		(−2.55)	(−2.79)	(−1.99)
BM		−0.0068	−0.0064	−0.0024		−0.0174	−0.0166*	−0.0105		−0.0017	−0.0008	0.0058
		(−1.11)	(−1.1)	(−0.55)		(−1.54)	(−1.67)	(−1.49)		(−0.35)	(−0.16)	(1.37)
MOM0212			0.003	0.0059			0.0069	0.0063			−0.0009	0.0041
			(0.41)	(0.97)			(0.97)	(0.86)			(−0.11)	(0.57)
REV				0.0187				0.0242				−0.0387
				(1.32)				(1.19)				(−1.4)
TURN				0.0121				0.0566				0.0004
				(0.3)				(1.26)				(0.01)
_cons	0.0105	0.0363*	0.0419**	0.0345**	0.023**	0.0372	0.0507**	0.0271	0.0014	0.0496**	0.0478**	0.0277
	(1.05)	(1.75)	(2.34)	(2.08)	(2.29)	(1.48)	(2.26)	(1.28)	(0.13)	(2.09)	(2.29)	(1.41)
N	28,421	28,421	28,421	28,421	14,311	14,311	14,311	14,311	14,110	14,110	14,110	14,110
R-sq	0.0185	0.0457	0.071	0.1163	0.0318	0.0776	0.1086	0.1709	0.0261	0.0669	0.1	0.1561
F-Statistic	0.69	2.27	2.5	1.51	4.8	3.32	3.08	1.57	0.63	2.24	2	1.35
P value	0.4093	0.0834	0.046	0.1786	0.0302	0.022	0.0184	0.1606	0.4275	0.0864	0.0984	0.2388

Notes: Dependent variable: Stock returns. FMB regression: 02/2008–12/2018. The result of Fama-Macbeth regression for IVOL estimated by CAPM. In detail, model (1)–model (4) are estimated for full-sample, model (5)–model (8) are computed for sub-samples with positive abnormal returns and model (9)–model (12) are regressed for sub-samples with negative abnormal returns.

Table 8. IVOL_FF3 and stock returns

	Full-sample				Positive alpha sub-samples				Negative alpha sub-samples
Variables	(13)	(14)	(15)	(16)	(17)	(18)	(19)	(20)	(21)	(22)	(23)	(24)
IVOLFF3	−0.0414	−0.1855	−0.1975	−0.2225	−0.4724*	−0.5632**	−0.569**	−0.5655**	0.281	0.0861	0.0653	0.1769
	(−0.24)	(−1.15)	(−1.31)	(−1.48)	(−1.77)	(−2.03)	(−2.11)	(−2.23)	(1.06)	(0.31)	(0.25)	(0.64)
Ln(SIZE)		−0.0014	−0.0022**	−0.0017*		−0.0014	−0.0027*	−0.0021*		−0.0023*	−0.0028**	−0.0018*
		(−1.33)	(−2.13)	(−1.68)		(−0.98)	(−1.96)	(−1.78)		(−1.97)	(−2.49)	(−1.68)
BM		−0.0069	−0.0066	−0.0024		−0.0158	−0.0163	−0.0108		−0.0016	−0.0019	0.0031
		(−1.11)	(−1.11)	(−0.55)		(−1.35)	(−1.47)	(−1.32)		(−0.38)	(−0.48)	(0.82)
MOM0212			0.0031	0.006			0.0111*	0.0121**			−0.0006	0.0028
			(0.43)	(0.98)			(1.91)	(2.3)			(−0.08)	(0.39)
REV				0.019				0.0381*				−0.0111
				(1.36)				(1.97)				(−0.43)
TURN				0.0114				0.0487				0.0006
				(0.28)				(1.09)				(0.01)
_cons	0.0084	0.0313	0.0382**	0.0323**	0.0176*	0.0399	0.0572**	0.0479**	0.0008	0.0356	0.0385*	0.022
	(0.83)	(1.51)	(2.16)	(1.99)	(1.69)	(1.57)	(2.38)	(2.44)	(0.06)	(1.58)	(1.91)	(1.16)
N	28421	28421	28421	28421	14272	14272	14272	14272	14149	14149	14149	14149
R-sq	0.016	0.0446	0.0702	0.1161	0.0289	0.0755	0.1072	0.1669	0.0242	0.0655	0.0996	0.153
F-Statistic	0.06	1.45	1.93	1.36	3.14	2.3	3.52	3.37	1.12	1.38	1.63	0.71
p value	0.8132	0.2317	0.1099	0.234	0.079	0.0801	0.0092	0.0041	0.2928	0.2522	0.1707	0.6445

Notes: Dependent variable: Stock returns. FMB regression: 02/2008–12/2018. The result of Fama-Macbeth regression for IVOL estimated by FF3 model. More details, model (13)–model (16) are estimated for full-sample, model (17)–model (20) are computed for sub-samples with positive abnormal returns and model (21)–model (24) are regressed for sub-samples with negative abnormal returns.

Table 9. IVOL_CH4 and stock returns

	Full-sample				Positive alpha sub-samples				Negative alpha sub-samples
Variables	(25)	(26)	(27)	(28)	(29)	(30)	(31)	(32)	(33)	(34)	(35)	(36)
IVOLCH4	−0.0644	−0.2119	−0.2202	−0.2309	−0.4298	−0.5116*	−0.5267*	−0.5109**	0.148	−0.0643	−0.0975	−0.0139
	(−0.36)	(−1.23)	(−1.44)	(−1.59)	(−1.52)	(−1.71)	(−1.81)	(−1.99)	(0.57)	(−0.26)	(−0.39)	(−0.05)
Ln(SIZE)		−0.0015	−0.0022**	−0.0017*		−0.0014	−0.0026*	−0.0022*		−0.0018	−0.0023**	−0.0014
		(−1.34)	(−2.16)	(−1.72)		(−0.91)	(−1.84)	(−1.73)		(−1.6)	(−2.12)	(−1.31)
BM		−0.007	−0.0065	−0.0025		−0.0157	−0.0159	−0.0108		−0.0022	−0.0016	0.0034
		(−1.12)	(−1.11)	(−0.57)		(−1.36)	(−1.48)	(−1.33)		(−0.5)	(−0.39)	(0.92)
MOM0212			0.0032	0.0061			0.009	0.0089			−0.0009	0.0047
			(0.45)	(1)			(1.3)	(1.36)			(−0.1)	(0.67)
REV				0.0186				0.0364*				0.0025
				(1.33)				(1.85)				(0.1)
TURN				0.0102				0.0308				0.0042
				(0.25)				(0.89)				(0.07)
_cons	0.0086	0.0318	0.0385**	0.0326**	0.0148	0.0373	0.0528**	0.0463**	0.0049	0.0329	0.036*	0.0226
	(0.84)	(1.49)	(2.17)	(2.05)	(1.45)	(1.32)	(2.14)	(2.29)	(0.43)	(1.56)	(1.87)	(1.2)
N	28421	28421	28421	28421	14438	14438	14438	14438	13983	13983	13983	13983
R-sq	0.0158	0.0444	0.07	0.1159	0.0281	0.072	0.1049	0.1639	0.0212	0.0612	0.0957	0.153
F-Statistic	0.13	1.52	2.04	1.44	2.32	1.86	2.63	2.46	0.32	0.96	1.2	0.5
p value	0.7216	0.2126	0.0921	0.203	0.1306	0.1391	0.0371	0.0275	0.571	0.4133	0.315	0.8043

Notes: Dependent variable: Stock returns. FMB regression: 02/2008–12/2018. The result of Fama-Macbeth regression for IVOL estimated by CH4 model. More details, model (25)–model (28) are estimated for full-sample, model (29)–model (32) are computed for sub-samples with positive abnormal returns and model (33)–model (36) are regressed for sub-samples with negative abnormal returns.

Table 10. The explanatory power of asset pricing model for stock returns based on IVOL-sorted portfolio with equal-weighted method and IVOL strategy return

	1	2	3	4	5	5_1	Mean alpha	GRS F test	p value
	CAPM
Alpha	0.0036	0.0051	0.0045	0.0003	0.0037	0.0001	0.0034	0.92	0.47
	(1.13)	(1.36)	(1.16)	(0.07)	(0.76)	(0.04)
MKT	0.9447***	0.9953***	0.9909***	0.851***	0.8152***	−0.1295***
	(23.59)	(20.93)	(20.17)	(15.97)	(13.08)	(−2.81)
R-sq	0.812	0.773	0.759	0.664	0.57	0.058
	Fama-French three-factor model
Alpha	0.0033	0.005*	0.0044	0.0003	0.0037	0.0004	0.0033	1.12	0.35
	(1.28)	(1.67)	(1.55)	(0.08)	(1.07)	(0.13)
MKT	0.9606***	1.0361***	1.0492***	0.9112***	0.901***	−0.0595
	(25.9)	(24.38)	(25.83)	(19.48)	(18.15)	(−1.3)
SMB	17.4954***	22.3718***	25.6761***	25.7939***	33.8222***	16.3268***
	(7.92)	(8.83)	(10.61)	(9.25)	(11.44)	(6)
HML	10.1877***	14.0446***	16.6818***	16.8381***	22.4146***	12.2269***
	(6.26)	(7.53)	(9.36)	(8.2)	(10.29)	(6.1)
R-sq	0.875	0.859	0.872	0.799	0.789	0.28
	Carhart four-factor model
Alpha	0.0037	0.0056*	0.005*	0.0005	0.004	0.0003	0.0038	1.41	0.22
	(1.47)	(1.94)	(1.77)	(0.16)	(1.13)	(0.08)
MKT	0.8954***	0.9388***	0.9603***	0.8554***	0.8417***	−0.0536
	(22.54)	(20.7)	(21.82)	(16.59)	(15.28)	(−1.06)
SMB	13.4159***	15.9782***	19.3538***	21.0519***	28.0819***	14.6659***
	(6.84)	(7.13)	(8.9)	(8.26)	(10.32)	(5.88)
HML	4.8033***	6.844***	8.5666***	8.9509***	12.1049***	7.3016***
	(4.46)	(5.56)	(7.17)	(6.39)	(8.09)	(5.33)
WML	−3.5695***	−5.3861***	−4.7431***	−2.6589*	−2.5872*	0.9823
	(−3.28)	(−4.33)	(−3.93)	(−1.88)	(−1.71)	(0.71)
R-sq	0.882	0.868	0.877	0.8	0.786	0.278

Notes: The result of GRS test to evaluate the explanatory power of CAPM, FF3 model and CH4 model for IVOL-sorted portfolios and IVOL strategy return. Columns (1)–(5) report the result regression for monthly excess returns of IVOL quantile portfolios. Returns in IVOL portfolio are calculated in equal-weighted method. Column (5_1) shows the monthly IVOL strategy. The results of GRS test include mean alpha, GRS F test and p value. **, * and * denote the significance at the 1%, 5% and 10% levels, respectively.

Table 11. The explanatory power of asset pricing model for stock returns based on IVOL-sorted portfolio with value-weighted method and IVOL strategy return

	1	2	3	4	5	5_1	Mean alpha	GRS F test	p value
	CAPM
Alpha	−0.0068***	−0.007***	−0.0068***	−0.0068***	−0.0068***	−0.0001	−0.0068	217.48	0
	(−29.44)	(−28.63)	(−28.77)	(−29.73)	(−26.64)	(−0.28)
MKT	0.0411***	0.0386***	0.0362***	0.0315***	0.0345***	−0.0066**
	(14.08)	(12.4)	(12.01)	(10.88)	(10.58)	(−2.27)
R-sq	0.606	0.544	0.528	0.479	0.465	0.038
	Fama-French three-factor model
Alpha	−0.0068***	−0.007***	−0.0068***	−0.0068***	−0.0068***	0	−0.0069	218.85	0
	(−30.38)	(−28.36)	(−28.63)	(−29.52)	(−27.97)	(−0.14)
MKT	0.0369***	0.0388***	0.0358***	0.0323***	0.0361***	−0.0008
	(11.52)	(10.97)	(10.49)	(9.86)	(10.33)	(−0.26)
SMB	0.045	−0.0568	0.1657	0.1612	0.8207***	0.7757***
	(0.24)	(−0.27)	(0.81)	(0.83)	(3.94)	(4.33)
HML	−0.1841	−0.0232	0.0686	0.1265	0.5215***	0.7055***
	(−1.31)	(−0.15)	(0.46)	(0.88)	(3.4)	(5.35)
R-sq	0.633	0.544	0.531	0.482	0.523	0.217
	Carhart four-factor model
Alpha	−0.0068***	−0.007***	−0.0068***	−0.0068***	−0.0068***	0	−0.0069	219	0
	(−30.23)	(−28.46)	(−28.52)	(−30.85)	(−27.94)	(−0.19)
MKT	0.0357***	0.041***	0.0368***	0.037***	0.0356***	−0.0001
	(10.12)	(10.58)	(9.77)	(10.71)	(9.28)	(−0.02)
SMB	−0.0402	0.0543	0.107	0.363**	0.7457***	0.7859***
	(−0.23)	(0.28)	(0.58)	(2.12)	(3.93)	(4.89)
HML	−0.2166**	0.0106	−0.0093	0.112	0.2861***	0.5027***
	(−2.26)	(0.1)	(−0.09)	(1.19)	(2.75)	(5.69)
WML	−0.0694	0.1388	0.0798	0.3061***	−0.0033	0.0661
	(−0.72)	(1.31)	(0.77)	(3.23)	(−0.03)	(0.74)
R-sq	0.634	0.55	0.532	0.525	0.527	0.246

Notes: The result of GRS test to evaluate the explanatory power of CAPM, FF3 model and CH4 model for IVOL-sorted portfolios and IVOL strategy return. Columns (1)–(5) report the result regression for monthly excess returns of IVOL quantile portfolios. Returns in IVOL portfolio are calculated in value-weighted method. Column (5_1) shows the monthly IVOL strategy. The results of GRS test include mean alpha, GRS F test and p value. **, * and * denote the significance at the 1%, 5% and 10% levels, respectively.