How fears index and liquidity affect returns of ivol puzzle before and during the Covid-19 pandemic

Figures & data

Table 1. Top 30 negative T-Statistic words

No.	Vietnamese Search Terms	English Search Terms	T-Statistic
1	SJC GIÁ VÀNG	SJC GOLD PRICE	−3.89
2	GIÁ VÀNG HÔM	GOLD PRICE IN	−3.11
3	LÃI GỬI TIẾT KIỆM	SAVING INTEREST RATE	−2.93
4	GỬI TIẾT KIỆM NGÂN HÀNG	DEPOSIT BANK	−2.86
5	VÀNG HÔM NAY	GOLD TODAY	−2.84
6	GIÁ VÀNG HÔM NAY	GOLD PRICE TODAY	−2.8
7	LÃI SUẤT GỬI TIẾT KIỆM	SAVING DEPOSIT RATE	−2.8
8	CHỨNG KHOÁN VIỆT NAM	VIETNAM SECURITIES	−2.52
9	MA CHUNG KHOAN	SECURITIES CODE	−2.51
10	VÀNG 9999	GOLD 9999	−2.49
11	SO TIET KIEM	SAVING	−2.21
12	BẢNG GIAO DỊCH CHỨNG KHOÁN	SECURITIES TRADING PANEL	−2.15
13	SAN GIAO DICH CHUNG KHOAN	STOCK EXCHANGE	−1.92
14	DAU TU CHUNG KHOAN	SECURITIES INVESTMENT	−1.9
15	GIÁ VÀNG	GOLD PRICE	−1.85
16	KINH TẾ VIỆT NAM	VIETNAM ECONOMY	−1.79
17	GIÁ VÀNG SJC	SJC GOLD PRICE	−1.78
18	LÃI TIẾT KIỆM	SAVING RATE	−1.73
19	VÀNG 9999 GIÁ	GOLD 9999 PRICE	−1.59
20	LAI SUAT NGAN HANG	BANK INTEREST RATE	−1.54
21	ĐỊNH GIÁ TÀI SẢN	ASSET PRICING	−1.36
22	NHẬN BẢO HIỂM THẤT NGHIỆP	RECEIVE UNEMPLOYMENT INSURANCE	−1.33
23	GIA CHUNG KHOAN	STOCK PRICES	−1.24
24	TÀI SẢN TÀI CHÍNH	FINANCIAL ASSETS	−1.2
25	BANG GIA TRUC TUYEN	ONLINE PRICE LIST	−1.18
26	LÀM BẢO HIỂM THẤT NGHIỆP	UNEMPLOYMENT INSURANCE	−1.14
27	LAI SUAT GUI TIET KIEM NGAN HANG	SAVING INTEREST RATE	−1.12
28	CHỨNG KHOÁN TRỰC TUYẾN	ONLINE SECURITIES	−1.11
29	KINH TẾ SUY THOÁI	ECONOMIC DEPRESSION	−1.06
30	LAI SUAT	INTEREST RATE	−1.05

Table 2. Estimation selection process

Procedure	Result
Hausman test	Chi-square = 7, P-value = 0.00. The selection test results between FEM and REM show that FEM is suitable.
Likelihood ratio test	F(512,360) = 1.27, P-value = 0.00. The selection test results between FEM and OLS show that FEM is suitable.
Heteroskedasticity test	F(513) = 4606.230, P-value = 0.00. The results show that the model has a heteroskedasticity problem.
2SLS method	We propose to use 2SLS regression to overcome heteroskedasticity and minimize endogeneity in the model.

Table 3. Variable definitions

RET	Monthly return of stock i is the last day returns d in month t Reti,t = (Close priced,t—Close priced-1,t)/Close priced-1,t
REV	Following Duong et al. (2021), the reversal in the month t is the stock returns over the month t-1.
TURN	Following Duong et al. (2021), to calculate the total number of shares outstanding divided by trading volume over the previous month. The formula is: Turnover = (Trading volume/Shares outstanding) * 1000
BM	Following FAMA and FRENCH (1992), the book to market ratio is the market value of stock in the previous calendar year and the book values of common stock.
SZ	Following Bali et al. (2011), the firm size is the logarithm of a stock’s market value at the end of month t.
IVOL	${\epsilon }_i^L$ We follow Ang et al. (2009) to compute the IVOL of stock i in month t, the standard deviation of daily residuals returns from the Fama–French three-factor model in month t. Is the idiosyncratic return on day d.
	$IVO{L}_{i,t}=\sqrt{var\left({\epsilon }_i^L\right)}$
DVOL	Following Bhushan (1994), trading volume VND (DVOL) is the stock price in VND multiplied by the number of shares traded.
FEARS	Following Da et al. (2015), FEARS is the top 30 $\mathrm{\Delta }\mathrm{A}\mathrm{S}\mathrm{V}\mathrm{I}$ of most significant negative t-statistic words in month t: $\mathrm{F}\mathrm{E}\mathrm{A}\mathrm{R}{\mathrm{S}}_{\mathrm{t}}=\sum _{\mathrm{i}=1}^{30}\frac{\mathrm{\Delta }\mathrm{A}\mathrm{S}\mathrm{V}{\mathrm{I}}_{\mathrm{t}}}{30}$

Table 4. Descriptive statistics

Variable	N	Mean	Std.	Median	5th Pctl	95th Pctl
RET (%)	36,569	1.097	11.105	0.000	−16.168	21.583
LnBM	36,569	2.658	2.295	2.067	0.512	6.559
LnSZ	36,569	26.000	1.701	25.834	23.573	29.125
REV (%)	36,569	1.099	11.050	0.000	−16.071	21.429
LnTURN (%)	36,569	−3.076	2.399	−2.718	−7.698	0.256
LnDVOL	36,569	11.441	3.030	11.448	6.211	16.380
IVOL (%)	36,569	9.347	3.505	8.852	4.518	15.774
FEARS	36,569	−0.038	0.209	−0.063	−0.287	0.319

Notes: The table reports sample mean, standard deviation, median, the 5th percentile, 95th percentile. We take the natural logarithm of variables such as BM, SZ, TURN, and DVOL. The sample period is from December 2010 to December 2020.

Table 5. Pearson correlation matrix

Variables	FEARS	LnBM	LnSZ	REV	LnTURN	LnDVOL	IVOL
FEARS	1	−0.078***	0.080***	0.029***	−0.004	0.072***	−0.027***
LnBM		1	−0.622***	0.055***	0.067***	−0.282***	0.091***
LnSZ			1	−0.024***	0.038***	0.591***	−0.151***
REV				1	0.009*	0.111***	−0.007
LnTURN					1	0.515***	0.154***
LnDVOL						1	0.026***
IVOL							1

Notes: The table shows a Pearson correlation matrix for seven control variables. When using two-tailed tests, all correlate variables in this table are significantly different from zero at least at 1% level. The sample period is from December 2010 to December 2020. ***, **, * denote the p-value at 1%, 5%, 10%, respectively.

Table 6. Two-Stage Least Squares (2SLS) regression results before and during the pandemic

	(1)	(2)	(3)	(4)	(5)
Panel A: Before the COVID-19 period
IVOL	−0.058***	−0.057****	−0.078***	−0.059***	−0.056***
	(−3.39)	(−3.35)	(−4.57)	(−3.38)	(−3.24)
FEARS		0.944***	1.190***	1.099***	1.059***
		(3.13)	(3.95)	(3.65)	(3.51)
LnBM			0.990***	1.032***	1.019***
			(10.39)	(10.77)	(10.62)
LnSZ			−0.039	−0.198***	−0.177***
			(−0.87)	(−3.55)	(−3.15)
LnTURN				−0.349***	−0.337***
				(−11.22)	(−10.78)
LnDVOL				0.187***	0.168***
				(6.15)	(5.44)
REV					0.020***
					(3.48)
Constant	1.399***	1.442***	1.941	2.650**	2.321*
	(8.28)	(8.51)	(1.58)	(1.98)	(1.73)
Panel B: During the COVID-19 period
IVOL	0.199***	0.099*	0.064	0.054	0.073
	(3.44)	(1.73)	(1.10)	(0.91)	(1.24)
FEARS		−10.937***	−11.000***	−10.979***	−11.565***
		(−13.68)	(−13.79)	(−13.77)	(−14.64)
LnBM			1.555***	1.452***	1.545***
			(4.75)	(4.28)	(4.60)
LnSZ			0.27	0.037	−0.211
			(1.60)	(0.17)	(−0.99)
LnTURN				−0.089	−0.212**
				(−0.79)	(−1.89)
LnDVOL				0.185*	0.436***
				(1.65)	(3.84)
REV					−0.157***
					(−10.21)
Constant	0.922	2.63***	−4.726	−1.015	2.404
	(1.55)	(4.41)	(−1.02)	(−0.20)	(0.47)

Notes: We run a 2SLS regression of the returns in that month on seven variables, including IVOL, FEARS, and five control variables in Table 3. In detail, Model (1) tests the single impact of IVOL on stock returns. Model (2) add the impact of investor sentiment on stock returns. Model (3) investigates further the effect of fundamental variables such as a book to market ratio and firm size on stock return. Model (4) includes the liquidity variables such as trading turnover and DVOL (VND trading volume). Model (5) estimates all variables’ impact, including the reversal effect on stock returns. The table reports the time-series averages of the cross-sectional regression slope coefficients and their adjusted t-statistics (in parentheses) in each row. The sample period is from December 2010 to December 2020. ***, **, * denote the p-value at 1%, 5%, 10%, respectively.

Table 7. Two-Stage Least Squares (2SLS) regression results in subsamples

Constant	FEARS	LnBM	LnSZ	REV	LnTURN	LnDVOL	IVOL
Panel A: Low FEARS before COVID-19
0.750	2.262***	1.102***	−0.094	0.007	−0.278***	0.144***	−0.056***
(0.47)	(3.43)	(9.84)	(−1.43)	(1.01)	(−7.48)	(3.94)	(−2.73)
Panel B: Low FEARS during COVID-19
13.473**	72.898***	1.088***	−0.120	0.029	−0.101	0.102	0.087
(2.11)	(15.54)	(2.63)	(−0.45)	(1.16)	(−0.70)	(0.70)	(1.23)
Panel C: High FEARS before COVID-19
6.513***	−0.186	0.729***	−0.364***	0.050***	−0.479***	0.225***	−0.061*
(2.56)	(−0.31)	(3.90)	(−3.43)	(4.70)	(−8.31)	(3.85)	(−1.85)
Panel D: High FEARS during COVID-19
1.265	−36.913***	2.148***	0.352	−0.262***	0.188	0.144	0.084
(0.19)	(−31.12)	(4.96)	(1.30)	(−15.25)	(1.33)	(1.01)	(1.08)
Panel E: Low turnover stocks before COVID-19
5.470**	1.516***	0.986***	−0.341***	−0.052***	−0.180***	0.280***	0.031
(2.24)	(2.99)	(5.70)	(−3.59)	(−5.20)	(−3.02)	(6.03)	(1.04)
Panel F: Low turnover stocks during COVID-19
−3.382	−9.878***	1.631***	0.040	−0.160***	−0.090	0.413***	0.030
(−0.41)	(−8.35)	(2.92)	(0.13)	(−5.78)	(−0.50)	(2.93)	(0.32)
Panel G: High turnover stocks before COVID-19
1.105	0.903	1.115***	−0.079	0.010	−0.429***	0.116*	−0.130***
(0.41)	(1.48)	(6.42)	(−0.71)	(1.07)	(−6.73)	(1.84)	(−2.65)
Panel H: High turnover stocks during COVID-19
−11.770	−11.658***	1.550**	0.296	−0.175***	−0.158	0.235	0.287*
(−1.08)	(−7.28)	(2.42)	(0.67)	(−6.55)	(−0.73)	(1.06)	(1.75)

Notes: We run 2SLS regressions of the returns in that month on seven variables, including IVOL, FEARS, and five control variables in Table 3. In detail, the model is estimated for the period before and during COVID-19. The table reports the time-series averages of the regression slope coefficients and their adjusted t-statistics (in parentheses) in each row. The sample period is from December 2010 to December 2020. ***, **, * denote the p-value at 1%, 5%, 10%, respectively.

Table 8. Equal-weighted and value-weighted portfolios are sorted by IVOL

Tercile	Low FEARS	High FEARS	Before COVID-19	During COVID-19	Low Turn	High Turn
Panel A: Equal-weight (EW) portfolio:
Low IVOL	1.115	1.521	1.075	2.599	1.256	1.233
Medium IVOL	0.842	1.550	0.850	2.793	1.189	0.717
High IVOL	0.593	1.302	0.589	2.643	1.399	0.470
Returns difference	−0.522**	−0.219	−0.486**	0.044	0.143	−0.763***
	(−2.06)	(−0.48)	(−2.14)	(0.05)	(0.55)	(−2.96)
Alpha difference	−0.481***	−0.070*	−0.556***	1.835***	0.004	−0.890***
	(−27.49)	(−1.94)	(−34.09)	(44.89)	(0.23)	(−48.66)
Panel B: Value-weight (VW) portfolio:
Low IVOL	0.842	0.916	0.770	1.647	0.746	0.927
Medium IVOL	0.127	1.782	0.574	1.121	0.428	0.583
High IVOL	0.200	0.924	0.239	1.934	1.179	−0.315
Returns difference	−0.642	0.008	−0.531	0.287	0.433	−1.243**
	(−1.11)	(0.01)	(−1.07)	(0.23)	(0.79)	(−2.28)
Alpha difference	−0.766***	0.136***	−0.708***	2.291***	0.486***	−1.482***
	(−22.60)	(3.01)	(−24.44)	(67.73)	(15.46)	(−44.50)

Notes: This table reports the equal-weight (EW) and value-weight (VW) based on IVOL. Each month, we sort stocks into tercile based on the IVOL. With 33.33% highest, 33.33% medium, and 33.33% lowest IVOL group, respectively. The monthly return difference is the arbitrary returns between high IVOL and low IVOL stocks. Adjusted t-statistics is the value in parentheses. The study spans the months of December 2010 through December 2020. ***, **, * denote the p-value at 1%, 5%, 10%, respectively.

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