Heterogeneously informed trading and the stock market efficiency during the COVID-19 pandemic

Abstract

This study investigates the U.S. stock market efficiency from the symmetric and asymmetric perspectives during the COVID-19 pandemic. We explore that the pandemic boosts (hurts) the information role of symmetrically (asymmetrically) informed trading. Specifically, we find that the epidemic outbreak and infection scale strengthen (weaken) the stock return reaction to symmetrically (asymmetrically) informed trading. Evidence also indicates that the effect of symmetrically (asymmetrically) informed trading on stocks' permanent price shocks and price informational efficiency is enhanced (impaired) during the pandemic. Moreover, all these effects are consistently more intensive to informed buys.

1. Introduction

Informed traders are selective in information collecting and processing by allocating their limited concentration across different types of information while investing in the stock market. Therefore, the stock market responsiveness to informed trading varies with traders' allocated concentration, which in turn affects market efficiency accordingly (Xu, Zhang, & Zhao, 2023). Market efficiency, which concerns how all information is timely revealed and then absorbed in markets, is a central issue in finance research. An information event about a stock can be either symmetric (i.e., public) or asymmetric (i.e., private). Existing studies of informed trading often focus on asymmetric information, but symmetrically informed trading has also attracted increasingly more attention in the literature (e.g., Bernile, Hu, & Tang, 2016; Xu et al., 2023; Xu, Yin, & Zhao, 2019). While both symmetric and asymmetric information attract informed investors, an exogenous shock of macro-uncertainty breeds public panic and in turn market sentiment, which probably leads to traders' concentration on (distraction from) symmetric (asymmetric) information when they invest. However, to our knowledge, no prior literature investigates this question in depth. Therefore, this study provides a novel contribution to the understanding of symmetric and asymmetric information roles by analyzing the heterogeneous market responsiveness to the informed trading initiated by these two types of information in the context of a macro-uncertainty shock.

The recent outbreak of the Corona Virus Disease 2019 (COVID-19) pandemic has badly affected the economy. The pandemic stems from a new strain of the corona virus from the severe acute respiratory syndrome species that outbroke in December 2019. The World Health Organization then declared it a Public Health Emergency of International Concern in January 2020 and soon a pandemic in March 2020. Such a pandemic is typically an exogenous shock of macro-uncertainty which has now deteriorated into a fatal crisis sweeping through the whole world. Globally, >2.8 billion people have been infected and approximately 5.4 million lives were lost as of December 2021. For the containment of its further diffusion, the movement of more than two billion people is strictly restricted. Not only the public health is under fierce attack of the pandemic, but the world economy is also brought to its knees, dealing a devastating blow to the financial markets. For instance, the slump of the U.S. stock market triggered four trading halts in just ten days in March 2020, which accounts for 80% of its total number of halts over its trading history since the introduction of its “circuit breaker” mechanism in 1988. Such explicit damage inflicted by the COVID-19 pandemic makes it imperative to comprehensively study into its impact on the stock market.

The U.S., in which the COVID-19 infection accounts for about 20% of the total worldwide cases, is now the country suffering the most from the pandemic. Focusing on all the stocks in the Center for Research in Security Prices (CRSP), we conduct a thorough investigation into the effects of the COVID-19 pandemic on the efficiency of the U.S. stock market induced by symmetrically and asymmetrically informed trading. To be specific, we firstly examine how the return reactions to symmetrically and asymmetrically informed trading are affected by the pandemic. Then, we move to the question of whether the impacts of symmetrically and asymmetrically informed trading on permanent shocks to stock prices are affected by the pandemic. Finally, we look into their corresponding effects on stocks' price informational efficiency.

Our investigation firstly concerns differential market performances in the pre-outbreak and post-outbreak periods of the pandemic, followed by a closer look into the effect of infection scale after its outbreak. The major findings of the study are summarized below. Firstly, we conduct the analysis that compares the stock return reactions to symmetrically and asymmetrically informed trading before and after the outbreak. It is explored that the outbreak on the one hand increases the stock return reaction to symmetrically informed trading but decreases the reaction to asymmetrically informed trading on the other hand. The analysis focusing on the infection scale in the post-outbreak period also generates such heterogeneous effects on the return reactions to these two types of informed trading. Moreover, further comparison between informed buy and sell trades suggests that the infection scale stimulates (dulls) the return reaction to symmetrically (asymmetrically) informed buys more than sells.

Secondly, we extract the permanent price shocks to a stock in an autoregressive system. Then, we investigate how the roles of symmetrically and asymmetrically informed trading in permanent price shocks are affected by the COVID-19 pandemic. We document that the effects of the pandemic in this regard are material and heterogeneous. Evidence shows that the effect of symmetrically informed trading on permanent price shocks is amplified by the epidemic outbreak and the scale of its infection, but the corresponding effect of asymmetrically informed trading is rather lessened. Moreover, a quicker (slower) increase in permanent price shocks during the pandemic is more likely to be driven by symmetrically (asymmetrically) informed buys compared with sells.

Finally, we analyze stocks' price informational efficiency. It is observed that the epidemic outbreak enhances the effect of symmetrically informed trading on efficiency, whereas the efficiency effect of asymmetrically informed trading is considerably impaired. Consistently, the efficiency effect of symmetrically (asymmetrically) informed trading increases (decreases) with a speedier scale of infection in the post-break period, and, again, the effect is more intensive to symmetrically (asymmetrically) informed buys. It therefore confirms the differential reactions of the stock market to symmetrically and asymmetrically informed trading under the disturbance of the pandemic, which consequently makes the information roles of the two types of informed trading distorted.

This paper contributes to a comprehensive understanding of the stock market efficiency in full insight from the symmetric and asymmetric perspectives. The information associated with the intrinsic value of a stock ranges between symmetric and asymmetric. While asymmetric information has been a long-lasting theme for efficiency studies, symmetric information is also an important force driving efficiency (e.g., Bernile et al., 2016; Duarte & Young, 2009; Xu et al., 2019). For instance, Xu et al. (2019) find that symmetrically informed trading is even more important than asymmetrically informed trading in explaining market efficiency. However, none of the prior research sheds light on the differential performances between the two types of informed trading in the context of a macro-uncertainty shock. Thus, our paper contributes to this strand of literature by examining the heterogeneous effects of symmetrically and asymmetrically informed trading in improving market efficiency during the COVID-19 pandemic. Our findings shed a novel light on the fact that the stock market is in more favor of efficiency due to symmetric information rather than asymmetric information during the pandemic.

On the other hand, our study also contributes to the growing literature relating the COVID-19 pandemic to the financial markets. Sharif, Aloui, and Yarovaya (2020) focus on geopolitical risks and economic policy uncertainty. Ji, Zhang, and Zhao (2020) search for safe-haven assets for investing after the outbreak. Cookson, Engelberg, and Mullins (2020) find that investors with different political identities hold dispersed beliefs during the pandemic. Smales (2020), Corbet, Hou, Hu, and Oxley (2020), and Gormsen and Koijen (2020) concern the epidemic influence on the global stock market returns, on the price discovery in the Chinese market, and on the aggregate stock and dividend futures markets, respectively. There is a closely related study, Xu et al. (2023), who only focus on symmetric information in their analysis and find that investors' attention to the macroeconomic and asset-specific news events is biased during the pandemic period. However, they do not shed any light on asymmetric information in the stock market. Therefore, this paper expands their empirical work by further considering asymmetric information and then comparing the differential performances between symmetrically and asymmetrically informed trading. In addition to the academic contribution, our study also practically assists practitioners and regulators in thoroughly comprehending the distinct efficiency roles of heterogeneously informed trading during the COVID-19 crisis and other similar systematic shocks, which enables them to invest in and regulate the stock market more smartly.

The rest of the paper proceeds as follows. Section 2 introduces our sample and variable construction. We demonstrate the heterogeneous effects of the COVID-19 pandemic on the stock return reactions to symmetrically and asymmetrically informed trading in Section 3 and confirm their corresponding effects in the analysis of stocks' permanent price shocks in Section 4. Section 5 examines price informational efficiency and presents consistent observations. Section 6 outlines robustness checks, and we conclude the paper in the last section.

2. Sample and regression variables

The empirical analysis of this paper considers all CRSP U.S. stocks. The current pandemic has seriously affected the U.S. since the end of January 2020. To examine the performances of the stock market before and after the epidemic outbreak, we select the sample period from January 2019 to December 2021. The constructions of our regression variables are detailed in the following subsections.

2.1. Dependent variables

Studying how the market responds to informed trading, we firstly analyze stock returns in two forms: the raw form of the return using closing prices Ret, and its variant adjusted by the return of the value-weighted basket of all CRSP stocks AdjRet.

Then, we compute stocks' permanent price shocks PPS by capturing the permanent component impounded into stock price variations through the approach developed by Beveridge and Nelson (1981).1 The approach is implemented in an autoregressive system. For each day, a stock's return is regressed at a fifteen-second frequency with sixty lags: r _τ = ∑_k=1 ⁶⁰ A _k r _τ−k + ε _τ, which yields $\mathrm{\Phi }\left(1\right)=1-{\sum }_{k=1}^{60}{\widehat{A}}_k$ and residuals ${\widehat{\epsilon }}_{\tau }$. The fifteen-second data here is available from the Thomson Reuters Tick History (TRTH). According to Beveridge and Nelson (1981), ${\mathrm{\Phi }}^{-2}\mathrm{Var}\left({\widehat{\mathrm{\epsilon }}}_{\tau }\right)$, which is the variance of $\mathrm{\Phi }{\left(1\right)}^{-1}{\widehat{\epsilon }}_{\tau }$, captures the permanent price shocks for a stock. We thus have: $\mathit{PPS}={\mathrm{\Phi }}^{-2}\mathrm{Var}\left({\widehat{\mathrm{\epsilon }}}_{\tau }\right)$.

Finally, we estimate stocks' price informational efficiency PIE for each day by its return variance ratio in the absolute value, which considers the variance at the one-minute and five-minute frequencies.2 The data source here is also the TRTH. Because variance ratio inversely gauges efficiency, PIE is defined as $-\left|\frac{{\sigma }_{5\mathit{min}}^2}{5\times {\sigma }_{1\mathit{min}}^2}-1\right|$.

We report the descriptive statistics of Ret, AdjRet, PPS and PIE in Panel A of Table 1 . We do not detrend these variables because their time-series are quite stationary over the sample period.

Table 1.

Summary statistics

Panel B: Dependent variables
	Reti, t	AdjReti, t	PPSi, t	PIEi, t
Mean	0.000	−0.000	0.005	−0.006
Median	0.000	−0.000	0.004	−0.005
Max	0.125	0.142	0.052	−0.000
Min	−0.219	−0.238	0.000	−0.014
Std. Dev.	0.017	0.023	0.006	0.004

Panel A: Explanatory variables
	InfoYZSym	InfoSSSym	InfoYZASym	InfoSSASym	dScalet
Mean	0.071	0.225	0.004	−0.034	2065.291
Median	0.046	0.169	0.002	−0.020	577.000
Max	1.080	0.968	0.049	−0.001	238,152.000
Min	0.000	0.002	0.000	−0.320	−78,657.000
Std. Dev.	0.108	0.327	0.005	0.087	23,063.980

Panel C: Control variables
	Capi, t	Amii, t	Voli, t
Mean	0.024	1.230	0.119
Median	0.013	0.875	0.073
Max	0.420	32.006	2.627
Min	0.000	0.001	0.003
Std. Dev.	0.056	2.095	0.196

The table reports the descriptive statistics of our main regression variables. Ret_{i, t}, AdjRet_{i, t}, PPS_{i, t} and PIE_{i, t} in Panel A are stock raw returns, adjusted returns, permanent price shocks and price informational efficiency, respectively. The explanatory variables in Panel B include symmetrically informed trading Info_YZ^Sym (Info_SS^Sym), asymmetrically informed trading Info_YZ^Asym (Info_SS^Asym), estimated via the approach of Yin and Zhao (2015) (Sarkar and Schwartz (2009)) respectively, and the detrended scale of COVID-19 infection dScale_t. Panel C is of control variables: capitalization Cap_{i, t}, Amihud's (2002) illiquidity Ami_{i, t}, and realized volatility Vol_{i, t}.

2.2. Explanatory variables

To measure the scale of COVID-19 infection, we obtain the number of new confirmed cases, which is the (daily) increase in the total number of infections, from the official site of the Centers for Disease Control and Prevention. Because the infection scale is of a significant trend, we eliminate the moving average of seven days from the raw data. We use dScale to denote the detrended scale.

To accurately gauge symmetrically and asymmetrically informed trading, we consider two approaches: (i) the hidden Markov model developed by Yin and Zhao (2015); and (ii) the sidedness measure proposed by Sarkar and Schwartz (2009). These two approaches are widely used for the estimation of informed trading in the financial markets. For example, Xu et al. (2019) closely compare between the two approaches in terms of the calculation, application, and the empirical results, and indicate that both approaches are quite reliable. More recently, Armstrong, Cardella, and Sabah (2021) and Brunetti, Harris, and Mankad (2022) focus on the approach of Sarkar and Schwartz (2009) to identify trading motives.

Yin and Zhao (2015) associate massive imbalanced trades with asymmetrically informed trading and relate massive balanced trades to symmetrically informed trading. Following them, we firstly conduct a hidden Markov model for each stock's trading, which generates the expected numbers of buys and sells, named λ _{b; i} and λ _{s; j}, for market state (i, j), and then we decompose λ _{b; i} and λ _{s; j} by the cluster analysis. Thus, we have: λ _{b; i} = μ _{b; i} + ν _{b; i} + ε _{b; i} and λ _{s; j} = μ _{s; j} + ν _{s; j} + ε _{s; j} for each day, where μ _{b; i} (μ _{s; j}) denotes asymmetrically informed buys (sells) with the market state (i,  j), and ν _{b; i} (ν _{s; j}) represents symmetrically informed buys (sells).3 Thus, we have the following definitions for the two types of informed trading for each stock:

$${\mathit{Info}}_{\mathit{YZ},t}^{\mathit{Asym}}=\sum _{i,j}\left({\mu }_{b;i}+{\mu }_{s;j}\right)\mathit{Pr}\left(\left(\mathit{State\; of}\mathit{day}t=\left(i,j\right)\right|\mathit{trading\; histroy}\right),$$

$${\mathit{Info}}_{\mathit{YZ},\mathrm{t}}^{\mathit{Sym}}=\sum _{i,j}\left({\nu }_{b;i}+{\nu }_{s;j}\right)\mathit{Pr}\left(\left(\mathit{State\; of}\mathit{day}t=\left(i,j\right)\right|\mathit{trading\; histroy}\right).$$

When separating informed buys from informed sells, we only consider μ _{b; i} (μ _{s; j}) and ν _{b; i} (ν _{s; j}) for asymmetrically and symmetrically informed buys (sells), respectively, in the definitions. That is, ${\mathit{Info}}_{\mathit{YZ},t}^{\mathit{Asym}+}=\sum _i\left({\mu }_{b;i}\right)$, ${\mathit{Info}}_{\mathit{YZ},t}^{\mathit{Asym}-}=\sum _j\left({\mu }_{s;j}\right)$, ${\mathit{Info}}_{\mathit{YZ},t}^{\mathit{Sym}+}=\sum _i\left({\nu }_{b;i}\right)$, and ${\mathit{Info}}_{\mathit{YZ},t}^{\mathit{Sym}-}=\sum _j\left({\nu }_{s;j}\right)$.

When analyzing stock returns, we need a signed measure for informed trading. We therefore construct Info _YZ ^Asym+− by Info _YZ ^Asym+ − Info _YZ ^Asym−, and Info _YZ ^Sym+− by Info _YZ ^Sym+ − Info _YZ ^Sym−. The positive (negative) values of Info _YZ ^Asym+− and Info _YZ ^Sym+− indicate positive (negative) asymmetric and symmetric information, respectively.

For the reliability of our informed trading measures, we also implement the sidedness approach proposed by Sarkar and Schwartz (2009). The sidedness of trading a stock is measured by the correlation between standardized buy and sell trades. Following this measure, we construct the sidedness of trading for stock i on day t by: firstly, aggregating numbers of buys and sells for every fifteen minutes; then, generating SBUY (SSELL) by differencing between the number of buys (sells) in every fifteen minutes and the sample mean of the day scaled by the standard deviation; lastly, computing the correlation between SBUY and SSELL of the day and naming it SD _SS. Lee and Ready's (1991) approach is adopted for the classification of buys and sells, and the raw transaction data for the classification is from TRTH.

Sarkar and Schwartz (2009) use one-sidedness (two-sidedness), which is associated with the SD _SS around its small (large) end, to capture asymmetrically (symmetrically) informed trading. Following them, trading days are thus sorted into deciles according to SD _SS. Then, we define Info _SS ^Asym as −SD _SS in the three smallest deciles for asymmetrically informed trading (because SD _SS decreases with one-sidedness, this definition makes Info _SS ^Asym increases with one-sidedness), and Info _SS ^Sym as SD _SS in the three largest deciles for symmetrically informed trading (note that SD _SS increases with two-sidedness).

However, unlike Yin and Zhao's (2015) approach, the sidedness of Sarkar and Schwartz (2009) is founded upon buy-sell correlation and thus unable to indicate the signs of informed trading. Therefore, this approach is not appliable in the analysis of stock returns and buy-sell separation.

The summary statistics of the explanatory variables, i.e., the detrended scale of COVID-19 infection and the four informed trading variables, are displayed in Panel B of Table 1. Note that the time-series of the four informed trading variables are all unit-root-free and their trends are quite weak because our sample period is relatively short (i.e., three years), we do not detrend them in the analysis.4

2.3. Control variables

When analyzing permanent price shocks and price informational efficiency, we consider some important controls, which includes capitalization, Amihud's (2002) illiquidity, and realized volatility. They are widely used in the study concerning efficiency. For example, ample research includes volatility and capitalization when efficiency is analyzed (see e.g., Ben-David, Franzoni, & Moussawi, 2018; Comerton-Forde & Putniņš, 2015). There also exists a significant linkage between efficiency and liquidity (see, e.g., Chordia, Roll, & Subrahmanyam, 2008; Xu & Yin, 2017). The data for calculating capitalization and illiquidity are from CRSP. Realized volatility is calculated based on one-minute returns, and the data source for it is TRTH.

Their descriptive statistics are shown in Panel C of Table 1. Since the time-series of these control variables are largely stationarity, we do not detrend them.

3. Return reaction to informed trading during the pandemic

The sudden outbreak of the COVID-19 pandemic begets public panic, which is likely to distract the attention among panicky or sentimental investors to the asymmetric speculation but expedite the absorption of symmetric information in the market. To confirm this inference, we investigate how the stock return reactions to symmetrically and asymmetrically informed trading are influenced by the pandemic. To begin with, we want to compare between the market performances in the pre-outbreak and post-outbreak periods. To this end, we introduce the following regression:

$${\mathit{Return}}_{i,t}={\beta }_0+{\beta }_1{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+-}+{\beta }_2{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+-}+{\beta }_3{\mathit{Outb}}_t+{\beta }_4{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+-}\times {\mathit{Outb}}_t+{\beta }_5{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+-}\times {\mathit{Outb}}_t+{\beta }_6{\mathit{Return}}_{i,t-1}+{\epsilon }_{i,t}$$ (1)

where Return _{i, t} has two specifications: stock raw returns Ret _{i, t}, and adjusted returns AdjRet _{i, t}. Info _{YZ, i, t} ^Sym+− (Info _{YZ, i, t} ^Asym+−) denotes signed informed trading for stock i on day t due to symmetric (asymmetric) information, estimated by the approach of Yin and Zhao (2015). Because the Sarkar and Schwartz's (2009) approach is unable to indicate the signs of informed trading, we cannot apply it in the return analysis here. We construct a dummy variable Outb _t which indicates the occurrence of the epidemic outbreak, and it equals zero from January 1, 2019 to January 31, 2020 and unity from February 1, 2020 to December 31, 2021. We treat January 31, 2020 as the outbreak date in our analysis because the first case of COVID-19 infection was confirmed in late January 2020 in the U.S.

By including both symmetrically and asymmetrically informed trading, regression (1) explicitly separates stock return reactions to the two types of informed trading. Our key interest here is the two interaction variables Info _{YZ, i, t} ^Sym+− × Outb _t and Info _{YZ, i, t} ^Asym+− × Outb _t, since they respectively reflect the effects of the epidemic outbreak on the return reactions to symmetrically and asymmetrically informed trading. β ₄ > 0 (β ₄ < 0) implies that the stock price becomes more (less) efficient in revealing symmetric information after the outbreak of the pandemic, while β ₅ > 0 (β ₅ < 0) implies that the stock price is more (less) efficient in revealing asymmetric information. To explicitly compare the estimates between variables and highlight their economic significances, we standardize all regression variables. The estimation outcomes are tabulated in Table 2 , in which we apply the stock fixed effect and cluster standard errors at the stock level in even columns.

Table 2.

Epidemic outbreak, informed trading, and stock returns.

	Ret		AdjRet
	(1)	(2)	(3)	(4)
InfoYZ, i, tSym+−	0.107*** (3.82)	0.096*** (3.44)	0.085*** (3.01)	0.077*** (2.75)
InfoYZ, i, tASym+−	0.115*** (4.11)	0.103*** (3.69)	0.093*** (3.30)	0.083*** (2.94)
Outbt	−0.093*** (−3.34)	−0.085*** (−3.02)	−0.086*** (−3.07)	−0.079*** (−2.83)
InfoYZ, i, tSym+− × Outbt	0.110*** (3.96)	0.101*** (3.63)	0.097*** (3.49)	0.091*** (3.28)
InfoYZ, i, tASym+− × Outbt	−0.082*** (−2.93)	−0.076*** (−2.75)	−0.075*** (−2.72)	−0.070** (−2.52)
Reti, t−1 or AdjReti, t−1	YES	YES	YES	YES
Constant	YES	YES	YES	YES
Stock fixed effect		YES		YES
Adjusted R-squared	0.05	0.05	0.04	0.04

The table reports the estimation output of regression (1). The dependent variable is stock returns Ret_{i, t} or its adjusted variant AdjRet_{i, t}. Info_{YZ, i, t}^Sym+− and Info_{YZ, i, t}^ASym+− are signed informed trading due to symmetric and asymmetric information, respectively, estimated via the approach of Yin and Zhao (2015). The dummy indicator Out_t is zero from January 2019 to January 2020 and unity during February 2020 to December 2021. *** and ** indicate significance levels at the 1% and 5%, respectively, with t-statistics in parentheses.

The two left-hand (right-hand) columns present the estimation outcome for the regression of raw returns (adjusted returns). As can be seen in the table, the estimated coefficients of Info _{YZ, i, t} ^Sym+− and Info _{YZ, i, t} ^Asym+− are positive and significant in all specifications, which are in line with the prevailing perception that informed trades vary returns. More specifically, the estimated coefficient of Info _{YZ, i, t} ^Sym+− (Info _{YZ, i, t} ^Asym+−) is 0.096 (0.103) in the second column, exploring that the one-standard-deviation increase of Info _{YZ, i, t} ^Sym+− (Info _{YZ, i, t} ^Asym+−) is related to the standard-deviation increase by 9.60% (10.30%) of stock returns. Additionally, the estimated coefficients of Outb _t are negative and significant, confirming a sizable hit by the pandemic to the stock market. We can see that the estimated coefficient of Outb _t is −0.085 in the second column, indicating a decrease by 8.50% of return standard deviation after the pandemic outbreaks. For the interaction variables Info _{YZ, i, t} ^Sym+− × Outb _t and Info _{YZ, i, t} ^Asym+− × Outb _t, their estimated coefficients are significant but opposite in directions. We can see that stock returns are more responsive to symmetrically informed trading after the pandemic outbreaks, in the sense of significantly positive estimates of Info _{YZ, i, t} ^Sym+− × Outb _t. On the other hand, the pandemic slows down the return response to asymmetrically informed trading, indicated by the significantly negative estimates of Info _{YZ, i, t} ^Asym+− × Outb _t. These findings provide a strong support to our inference that the pandemic makes the U.S. stock market react timelier to symmetrically informed trading at the cost of a slower response to asymmetrically informed trading.

Next, we want to confirm whether the infection scale in the post-outbreak period could also lead to the heterogeneous return reactions to symmetrically and asymmetrically informed trading. We therefore focus on the period of February 2020 to December 2021 and introduce dScale which captures the (detrended) scale of COVID-19 infection. Then, we replicate regression (1) by replacing Outb _t by dScale _t in the post-outbreak period:

$${\mathit{Return}}_{i,t}={\beta }_0+{\beta }_1{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+-}+{\beta }_2{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+-}+{\beta }_3{\mathit{dScale}}_t+{\beta }_4{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+-}\times {\mathit{dScale}}_t+{\beta }_5{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+-}\times {\mathit{dScale}}_t+{\beta }_6{\mathit{Return}}_{i,t-1}+{\epsilon }_{i,t}$$ (2)

As in regression (1), all variables are converted into their standardized variants. Other regression variables and settings remain unchanged. The estimation output is tabulated in Table 3 below.

Table 3.

Epidemic infection scale, informed trading, and stock returns.

	Ret		AdjRet
	(1)	(2)	(3)	(4)
InfoYZ, i, tSym+−	0.092*** (3.29)	0.081*** (2.86)	0.075*** (2.69)	0.067** (2.37)
InfoYZ, i, tASym+−	0.086*** (3.10)	0.077*** (2.75)	0.069** (2.47)	0.064** (2.28)
dScalet	−0.081*** (−2.90)	−0.074*** (−2.67)	−0.073*** (−2.63)	−0.069** (−2.44)
InfoYZ, i, tSym+− × dScalet	0.087*** (3.12)	0.082*** (2.92)	0.077*** (2.76)	0.072*** (2.60)
InfoYZ, i, tASym+− × dScalet	−0.064** (−2.29)	−0.059** (−2.14)	−0.059** (−2.12)	−0.055** (−1.96)
Reti, t−1 or AdjReti, t−1	YES	YES	YES	YES
Constant	YES	YES	YES	YES
Stock fixed effect		YES		YES
Adjusted R-squared	0.04	0.04	0.03	0.03

The table reports the estimation output of regression (2). The dependent variable is stock returns Ret_{i, t} or its adjusted variant AdjRet_{i, t}. Info_{YZ, i, t}^Sym+− and Info_{YZ, i, t}^ASym+− are signed informed trading due to symmetric and asymmetric information, respectively, estimated via the approach of Yin and Zhao (2015). dScale_t is detrended scale of infection. *** and ** indicate significance levels at the 1% and 5%, respectively, with t-statistics in parentheses.

We summarize the major observations as follows. Firstly, it is confirmed that both symmetrically and asymmetrically informed trading have a positive effect on stock returns as their positive and significant estimated coefficients can also be observed here. Moreover, the effect of symmetrically informed trading on returns is slightly stronger (smaller) than that of asymmetrically informed trading in Table 3 (Table 2), implying that symmetric information becomes more important after the outbreak of the pandemic whereas asymmetric information seems losing its advantage in speculative investment. Secondly, we can also see a significantly negative effect of the infection scale on stock returns after the outbreak, indicated by the negative and significant coefficients of dScale _t. It suggests that as the disease spreads more speedily, the market is subject to more slump in returns. Thirdly, we find significantly positive (negative) coefficients of Info _{YZ, i, t} ^Sym+− × dScale _t (Info _{YZ, i, t} ^Asym+− × dScale _t), suggesting that, although the infection scale significantly increases the effect of symmetrically informed trading on stock returns, it considerably decreases such return effect of asymmetrically informed trading, consistent with the role of Outb _t in Table 2.

Finally, one may be interested in the question as to whether informed buys (triggered by positive information) perform differentially from informed sells (induced by negative information) for the above effects. To find the answer, we investigate into the impacts of dScale _t by separating informed buys from informed sells. Therefore, we modify regression (2) as follows:

$${\mathit{Return}}_{i,t}={\beta }_0+{\beta }_1{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+}+{\beta }_2{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}-}+{\beta }_3{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+}+{\beta }_4{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}-}+{\beta }_5{\mathit{dScale}}_t+{\beta }_6{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+}\times {\mathit{dScale}}_t+{\beta }_7{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}-}\times {\mathit{dScale}}_t+{\beta }_8{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+}\times {\mathit{dScale}}_t+{\beta }_9{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}-}\times {\mathit{dScale}}_t+{\beta }_{10}{\mathit{Return}}_{i,t-1}+{\epsilon }_{i,t}$$ (3)

where + (−) in the superscripts of the variables represent informed buys (sells).

We report the estimation result in Table 4 and summarize the major findings below. Firstly, it confirms that the symmetrically or asymmetrically informed buys (sells) are associated with the return increase (decrease). A closer comparison indicates that symmetrically informed buys outweigh symmetrically informed sells in the magnitude and significance of the effect on returns, evidenced by greater values of the estimated coefficients and the t-statistics of Info _{YZ, i, t} ^Sym+ than those of Info _{YZ, i, t} ^Sym−, whereas such case turns opposite for the asymmetric counterparts. This implies that stock returns respond more quickly (slowly) to symmetrically (asymmetrically) informed buys than to sells after the pandemic outbreaks. Next, we confirm the negative effect of dScale _t on returns. Turning to the four interaction variables, while the estimated coefficients of Info _{YZ, i, t} ^Sym+ × dScale _t and Info _{YZ, i, t} ^Sym− × dScale _t are all positive and significant, the magnitude and significance of the former are far greater than the latter. For the effects of Info _{YZ, i, t} ^Asym+ × dScale _t and Info _{YZ, i, t} ^Asym− × dScale _t, the statistical disparity is even greater in the sense that the estimated coefficients of the former are significantly negative, whereas those of the latter are largely insignificant. This observation is quite interesting and it suggests that the scale of COVID-19 infection stimulates (dulls) stock return reaction to symmetrically (asymmetrically) informed buys more than sells, which implies a quicker (slower) reflection of positive symmetric (asymmetric) information than negative ones in market prices. It is consistent with Mian and Sankaraguruswamy (2012) who document higher stock price sensitivity to good earnings news (i.e., positive symmetric information) during high sentiment periods. Investors in the pandemic period can be sentimental (Wang, Xu, & Sharma, 2021). It is likely that they become eager for positive symmetric information but doubtful of the positive asymmetric information, which leads to the differential reflection between good and bad information in the market.

Table 4.

Extended return analysis: informed buys versus informed sells.

	Ret		AdjRet
	(1)	(2)	(3)	(4)
InfoYZ, i, tSym+	0.099*** (3.54)	0.088*** (3.15)	0.082*** (2.91)	0.077*** (2.73)
InfoYZ, i, tSym−	0.056** (2.01)	0.052* (1.85)	0.051* (1.80)	0.048* (1.71)
InfoYZ, i, tAsym+	0.067** (2.41)	0.060** (2.13)	0.059** (2.10)	0.056** (1.98)
InfoYZ, i, tAsym−	0.088*** (3.16)	0.084*** (3.01)	0.077*** (2.75)	0.073*** (2.58)
dScalet	−0.073*** (−2.62)	−0.069** (−2.47)	−0.069** (−2.46)	−0.063** (−2.22)
InfoYZ, i, tSym+ × dScalet	0.109*** (3.93)	0.105*** (3.75)	0.102*** (3.66)	0.095*** (3.41)
InfoYZ, i, tSym− × dScalet	0.058** (2.10)	0.55** (1.98)	0.054* (1.93)	0.051* (1.84)
InfoYZ, i, tAsym+ × dScalet	−0.087*** (−3.10)	−0.084*** (−3.00)	−0.080*** (−2.85)	−0.073*** (−2.62)
InfoYZ, i, tAsym− × dScalet	−0.049* (−1.76)	−0.045 (−1.63)	−0.044 (−1.56)	−0.041 (−1.47)
Reti, t−1 or AdjReti, t−1	YES	YES	YES	YES
Constant	YES	YES	YES	YES
Stock fixed effect		YES		YES
Adjusted R-squared	0.04	0.04	0.03	0.03

The table reports the estimation output of regression (3). The dependent variable is stock returns Ret_{i, t} or its adjusted variant AdjRet_{i, t}. Info_{YZ, i, t}^Sym and Info_{YZ, i, t}^Asym are symmetrically and asymmetrically informed trading respectively, estimated via the approach of Yin and Zhao (2015), and + (−) in the superscripts represents informed buys (sells). dScale_t is detrended scale of infection. ***, ** and * indicate significance levels at the 1%, 5% and 10%, respectively, with t-statistics in parentheses.

To sum up, this section provides the empirical evidence that the epidemic outbreak and its spread not only inflict an explicit damage on the stock market returns but also distort the market responsiveness to heterogeneously informed trading. Evidence reveals that the stock market reactions to symmetrically and asymmetrically informed trading are heterogeneous during the COVID-19 pandemic: There is the enhanced attention to symmetrically informed trading during the pandemic, whereas the attention to asymmetrically informed trading is rather weakened. Moreover, further classifying informed trades into buys and sells, we show that the positive (negative) effect of the pandemic on the market reactions to symmetrically (asymmetrically) informed trading is more intensive to informed buys than to sells.

4. Permanent price shocks and informed trading during the pandemic

We have demonstrated that the stock market performs differentially in the return reactions to symmetrically and asymmetrically informed trading during the pandemic. The information-induced return variation of a stock is closely associated with a sizable permanent price shock to it. Therefore, in this section, we want to confirm such heterogeneous market responses to informed trading by analyzing permanent price shocks.

We firstly focus on the effect of epidemic outbreak Outb _t over the full period and thus estimate the following regression:

$${\mathit{PPS}}_{i,t}={\beta }_0+{\beta }_1{\mathit{Info}}_{i,t}^{\mathit{Sym}}+{\beta }_2{\mathit{Info}}_{i,t}^{\mathit{Asym}}+{\beta }_3{\mathit{Outb}}_t+{\beta }_4{\mathit{Info}}_{i,t}^{\mathit{Sym}}\times {\mathit{Outb}}_t+{\beta }_5{\mathit{Info}}_{i,t}^{\mathit{Asym}}\times {\mathit{Outb}}_t+{\beta }_6{\mathit{PPS}}_{i,t-1}+\mathit{Controls}+{\epsilon }_{i,t}$$ (4)

The dependent variable is stocks' permanent price shocks PPS, and its construction was detailed in Section 2.1. Here, we focus on the unsigned measure of informed trading Info _{i, t} ^Sym and Info _{i, t} ^Asym, and they are estimated via the approach of Yin and Zhao (2015) or Sarkar and Schwartz (2009). We use PPS _{i, t−1} to capture the persistence or decay of PPS _{i, t} in case of a potential omittance of the shock from the previous day. Control variables include capitalization, Amihud's (2002) illiquidity, and realized volatility. The construction of the control variables was introduced in Section 2.3. Other regression variables and settings follow previous exercises. The regression results are in Table 5 below.

Table 5.

Epidemic outbreak, informed trading, and permanent price shocks.

	YZ		SS
	(1)	(2)	(3)	(4)
Infoi, tSym	0.155*** (5.52)	0.140*** (5.00)	0.127*** (4.54)	0.115*** (4.08)
Infoi, tAsym	0.172*** (6.12)	0.157*** (5.61)	0.143*** (5.09)	0.127*** (4.52)
Outbt	0.0078*** (2.76)	0.072** (2.56)	0.070** (2.46)	0.065** (2.29)
Infoi, tSym × Outbt	0.171*** (6.08)	0.160*** (5.72)	0.150*** (5.42)	0.143*** (5.13)
Infoi, tAsym × Outbt	−0.132*** (−4.71)	−0.122*** (−4.43)	−0.119*** (−4.32)	−0.112*** (−4.07)
PPSi, t−1	YES	YES	YES	YES
Controls	YES	YES	YES	YES
Constant	YES	YES	YES	YES
Stock fixed effect		YES		YES
Adjusted R-squared	0.19	0.19	0.14	0.14

The table reports the estimation output of regression (4). The dependent variable is permanent price shocks PPS_{i, t}. Info_{i, t}^Sym and Info_{i, t}^Asym are symmetrically and asymmetrically informed trading respectively, and they are estimated via the approach of Yin and Zhao (2015) in the YZ columns and via Sarkar and Schwartz (2009) in the SS columns. The dummy indicator Out_t is zero from January 2019 to January 2020 and unity during February 2020 to December 2021. Control variables include capitalization, illiquidity, and realized volatility. *** and ** indicate significance levels at the 1% and 5%, respectively, with t-statistics in parentheses.

We can see from the table that the estimations for all specifications generate significantly positive coefficients of Info _{i, t} ^Sym and Info _{i, t} ^Asym which confirm the informational effect of symmetrically and asymmetrically informed trading. Turning to the effect of epidemic outbreak, we show that the estimated coefficients of Outb _t are significantly positive throughout the four columns. It implies that although the epidemic outbreak hits stock market returns, it expedites the information incorporation into market prices. Moreover, we show that the estimated coefficients of the interaction variable Info _{i, t} ^Sym × Outb _t (Info _{i, t} ^Asym × Outb _t) are positive (negative) and quite significant, indicating an amplified (lessened) effect of symmetrically (asymmetrically) informed trading on stocks' permanent price shocks during the pandemic. It reveals that the epidemic outbreak improves the informativeness of symmetrically informed trading but hurts that of asymmetrically informed trading, closely consistent with our findings in Section 3.

As what we did in the return analysis, we next focus on the post-outbreak period and confirm whether the above findings can still be observed with the scale of epidemic infection. We then conduct the following regression over February 2020 to December 2021:

$${\mathit{PPS}}_{i,t}={\beta }_0+{\beta }_1{\mathit{Info}}_{i,t}^{\mathit{Sym}}+{\beta }_2{\mathit{Info}}_{i,t}^{\mathit{Asym}}+{\beta }_3{\mathit{dScale}}_t+{\beta }_4{\mathit{Info}}_{i,t}^{\mathit{Sym}}\times {\mathit{dScale}}_t+{\beta }_5{\mathit{Info}}_{i,t}^{\mathit{Asym}}\times {\mathit{dScale}}_t+{\beta }_6{\mathit{PPS}}_{i,t-1}+\mathit{Controls}+{\epsilon }_{i,t}$$ (5)

We report the regression outcome in Table 6 .

Table 6.

Epidemic infection scale, informed trading, and permanent price shocks.

	YZ		SS
	(1)	(2)	(3)	(4)
Infoi, tSym	0.137*** (4.90)	0.124*** (4.41)	0.112*** (4.02)	0.100*** (3.56)
Infoi, tAsym	0.119*** (4.25)	0.108*** (3.89)	0.097*** (3.47)	0.088** (3.15)
dScalet	0.061** (2.17)	0.057** (2.03)	0.055** (1.98)	0.052* (1.89)
Infoi, tSym × dScalet	0.143*** (5.17)	0.137*** (4.86)	0.129*** (4.58)	0.120*** (4.32)
Infoi, tAsym × dScalet	−0.110*** (−3.93)	−0.103*** (−3.71)	−0.100*** (−3.60)	−0.095*** (−3.93)
PPSi, t−1	YES	YES	YES	YES
Controls	YES	YES	YES	YES
Constant	YES	YES	YES	YES
Stock fixed effect		YES		YES
Adjusted R-squared	0.15	0.15	0.11	0.11

The table reports the estimation output of regression (5). The dependent variable is permanent price shocks PPS_{i, t}. Info_{i, t}^Sym and Info_{i, t}^Asym are symmetrically and asymmetrically informed trading respectively, and they are estimated via the approach of Yin and Zhao (2015) in the YZ columns and via Sarkar and Schwartz (2009) in the SS columns. dScale_t is detrended scale of infection. Control variables include capitalization, illiquidity, and realized volatility. ***, ** and * indicate significance levels at the 1%, 5% and 10%, respectively, with t-statistics in parentheses.

From the table, we can also see positive and significant coefficients of Info _{i, t} ^Sym and Info _{i, t} ^Asym, confirming their impacts on permanent price shocks. Comparing between their estimates in Table 5, Table 6, we show that the permanent effect of symmetrically informed trading is slightly weaker (greater) than that of asymmetrically informed trading in the full (post-outbreak) period, suggesting the increasing importance of symmetric information compared to asymmetric information over time in explaining permanent price shocks. Also, the estimation output in the table exhibits a considerable effect of infection scale on permanent price shocks, evidenced by the positive and significant coefficients of dScale _t. More importantly, the heterogeneous performances of symmetrically and asymmetrically informed trading in delivering the information are also evident here as the disease worsens, in the sense of significantly positive (negative) coefficients of Info _{i, t} ^Sym × dScale _t (Info _{i, t} ^Asym × dScale _t), which are in line with our previous observations.

Finally, we like to examine whether the above effects are subject to different intensiveness between informed buys and sells. Because the Sarkar and Schwartz's (2009) measure is not applicable to buy-sell separation, we can only use the approach of Yin and Zhao (2015) to estimate informed buys and sells here. Thus, we conduct the following regression:

$${\mathit{PPS}}_{i,t}={\beta }_0+{\beta }_1{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+}+{\beta }_2{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}-}+{\beta }_3{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+}+{\beta }_4{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}-}+{\beta }_5{\mathit{dScale}}_t+{\beta }_6{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+}\times {\mathit{dScale}}_t+{\beta }_7{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}-}\times {\mathit{dScale}}_t+{\beta }_8{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+}\times {\mathit{dScale}}_t+{\beta }_9{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}-}\times {\mathit{dScale}}_t+{\beta }_{10}{\mathit{PPS}}_{i,t-1}+\mathit{Controls}+{\epsilon }_{i,t}$$ (6)

The results are tabulated in Table 7 and a summary of key observations is given as follows. We firstly confirm the positive effects of informed trading on permanent price shocks regardless of the information types, as we show that all the four types of informed trades have significantly positive coefficients in all specifications. When looking into the magnitude and significance of their effects, we explore that symmetrically informed buys are more important than symmetrically informed sells in explaining permanent price shocks, whereas the opposite case applies for the asymmetric counterparts. This is consistent with the corresponding observations in the return analysis in Section 3, implying that the stock market might enjoy positive symmetric information but overlook positive asymmetric information during the pandemic. Also, the positive effect of epidemic infection scale on permanent price shocks is corroborated here. Turning to the interaction variables, the magnitude and significance of the estimated coefficients of Info _{YZ, i, t} ^Sym+ × dScale _t (Info _{YZ, i, t} ^Asym+ × dScale _t) are unambiguously greater than those of Info _{YZ, i, t} ^Sym− × dScale _t (Info _{YZ, i, t} ^Asym− × dScale _t), suggesting a quicker (slower) increase in PPS _{i, t} driven by Info _{YZ, i, t} ^Sym+ (Info _{YZ, i, t} ^Asym+) under the disturbance of dScale _t. This observation confirms that the symmetrically (asymmetrically) informed buys are more (less) informative during the pandemic.

Table 7.

Extended analysis of permanent price shocks: informed buys versus informed sells.

	(1)	(2)
InfoYZ, i, tSym+	0.131*** (4.69)	0.118*** (4.20)
InfoYZ, i, tSym−	0.086*** (3.05)	0.080*** (2.84)
InfoYZ, i, tAsym+	0.087*** (3.10)	0.081*** (2.89)
InfoYZ, i, tAsym−	0.114*** (4.08)	0.103*** (3.67)
dScalet	0.055** (1.97)	0.051* (1.84)
InfoYZ, i, tSym+ × dScalet	0.192*** (6.91)	0.181*** (6.50)
InfoYZ, i, tSym− × dScalet	0.098*** (3.47)	0.091*** (3.20)
InfoYZ, i, tAsym+ × dScalet	−0.154*** (−5.49)	−0.146*** (−5.23)
InfoYZ, i, tAsym− × dScalet	−0.075*** (−2.68)	−0.069** (−2.49)
PPSi, t−1	YES	YES
Controls	YES	YES
Constant	YES	YES
Stock fixed effect		YES
Adjusted R-squared	0.16	0.16

The table reports the estimation output of regression (6). The dependent variable is permanent price shocks PPS_{i, t}. Info_{YZ, i, t}^Sym and Info_{YZ, i, t}^Asym are symmetrically and asymmetrically informed trading respectively, estimated via the approach of Yin and Zhao (2015), and + (−) in the superscripts represents informed buys (sells). dScale_t is detrended scale of infection. Control variables include capitalization, illiquidity, and realized volatility. ***, ** and * indicate significance levels at the 1%, 5% and 10%, respectively, with t-statistics in parentheses.

In sum, we conduct the analysis of permanent price shocks in this section. Evidence indicates that the pandemic not only affects stocks' permanent price shocks directly, but also distort the information roles of heterogeneously informed trading. We document that the pandemic leads to differential performances of symmetrically and asymmetrically informed trading in information delivery. While the pandemic increases the effect of symmetrically informed trading on permanent price shocks, such an effect of asymmetrically informed trading is however reduced. Finally, we document that the enhanced (impaired) effect of symmetrically (asymmetrically) informed trading on permanent price shocks, exerted by the pandemic, is more intensive to informed buys than to sells.

5. Price informational efficiency and informed trading during the pandemic

The result of information dissemination is ultimately the improvement of price informational efficiency. We have evidenced in the previous sections that the COVID-19 pandemic hits the stock market by varying the effects of informed trading on returns and permanent price shocks, and the effects between symmetrically and asymmetrically informed trading are heterogeneous. Now we want to explicitly examine price informational efficiency to verify these findings. The detail of our efficiency measures was in Section 2.1. Like the prior sections, we firstly estimate the following regression over the full period:

$${\mathit{PIE}}_{i,t}={\beta }_0+{\beta }_1{\mathit{Info}}_{i,t}^{\mathit{Sym}}+{\beta }_2{\mathit{Info}}_{i,t}^{\mathit{Asym}}+{\beta }_3{\mathit{Outb}}_t+{\beta }_4{\mathit{Info}}_{i,t}^{\mathit{Sym}}\times {\mathit{Outb}}_t+{\beta }_5{\mathit{Info}}_{i,t}^{\mathit{Asym}}\times {\mathit{Outb}}_t+{\beta }_6{\mathit{PIE}}_{i,t-1}+\mathit{Controls}+{\epsilon }_{i,t}$$ (7)

The regression corresponds to regression (4) but using efficiency as the dependent variable instead. The results are in Table 8 below.

Table 8.

Epidemic outbreak, informed trading, and price informational efficiency.

	YZ		SS
	(1)	(2)	(3)	(4)
Infoi, tSym	0.136*** (4.86)	0.125*** (4.44)	0.110*** (3.91)	0.102*** (3.62)
Infoi, tAsym	0.149*** (5.32)	0.135*** (4.81)	0.124*** (4.39)	0.109*** (3.86)
Outbt	0.065** (2.30)	0.061** (2.16)	0.058** (2.06)	0.054* (1.93)
Infoi, tSym × Outbt	0.149*** (5.32)	0.140*** (5.03)	0.133*** (4.78)	0.126*** (4.51)
Infoi, tAsym × Outbt	−0.116*** (−4.16)	−0.108*** (−3.90)	−0.105*** (−3.82)	−0.099*** (−3.58)
PIEi, t−1	YES	YES	YES	YES
Controls	YES	YES	YES	YES
Constant	YES	YES	YES	YES
Stock fixed effect		YES		YES
Adjusted R-squared	0.13	0.13	0.10	0.10

The table reports the estimation output of regression (7). The dependent variable is price informational efficiency PIE_{i, t}. Info_{i, t}^Sym and Info_{i, t}^Asym are symmetrically and asymmetrically informed trading respectively, and they are estimated via the approach of Yin and Zhao (2015) in the YZ columns and via Sarkar and Schwartz (2009) in the SS columns. The dummy indicator Out_t is zero from January 2019 to January 2020 and unity during February 2020 to December 2021. Control variables include capitalization, illiquidity, and realized volatility. ***, ** and * indicate significance levels at the 1%, 5% and 10%, respectively, with t-statistics in parentheses.

Comparing the estimation output here with those in Table 2, Table 5, the observations are quite consistent. We not only show the direct impacts of heterogeneously informed trading on price informational efficiency, but also explore the heterogeneous effects of the pandemic on the efficiency roles of symmetrically and asymmetrically informed trading. It thus reconfirms our inference that the market responds more quickly to symmetrically informed trading than to asymmetrically informed trading after the outbreak.

Then, we focus on the post-break period and specify the regression as follows:

$${\mathit{PIE}}_{i,t}={\beta }_0+{\beta }_1{\mathit{Info}}_{i,t}^{\mathit{Sym}}+{\beta }_2{\mathit{Info}}_{i,t}^{\mathit{Asym}}+{\beta }_3{\mathit{dScale}}_t+{\beta }_4{\mathit{Info}}_{i,t}^{\mathit{Sym}}\times {\mathit{dScale}}_t+{\beta }_5{\mathit{Info}}_{i,t}^{\mathit{Asym}}\times {\mathit{dScale}}_t+{\beta }_6{\mathit{PIE}}_{i,t-1}+\mathit{Controls}+{\epsilon }_{i,t}$$ (8)

The estimation output is in Table 9 . Again, the observations are similar as previously. We confirm not only the explicit effects of the two types of informed trading on price informational efficiency but also the slightly greater efficiency effect of symmetrically informed trading over asymmetrically informed trading in the post-outbreak period. More importantly, the significant and opposite impacts of infection scale on the efficiency effects of symmetrically and asymmetrically informed trading are also evident. It thus confirms a speedier efficiency improvement by symmetrically informed trading but tardier by asymmetrically informed trading, along with an increase in epidemic infection.

Table 9.

Epidemic infection scale, informed trading, and price informational efficiency.

	YZ		SS
	(1)	(2)	(3)	(4)
Infoi, tSym	0.116*** (4.18)	0.106*** (3.79)	0.097*** (3.46)	0.085*** (3.06)
Infoi, tAsym	0.108*** (3.84)	0.098*** (3.48)	0.088*** (3.15)	0.081** (2.91)
dScalet	0.056** (1.99)	0.052* (1.87)	0.050* (1.81)	0.048* (1.70)
Infoi, tSym × dScalet	0.123*** (4.42)	0.117*** (4.15)	0.110*** (3.93)	0.104*** (3.74)
Infoi, tAsym × dScalet	−0.096*** (−3.41)	0.090*** (−3.24)	−0.089*** (−3.21)	−0.084*** (−3.00)
PIEi, t−1	YES	YES	YES	YES
Controls	YES	YES	YES	YES
Constant	YES	YES	YES	YES
Stock fixed effect		YES		YES
Adjusted R-squared	0.10	0.10	0.08	0.08

The table reports the estimation output of regression (8). The dependent variable is price informational efficiency PIE_{i, t}. Info_{i, t}^Sym and Info_{i, t}^Asym are symmetrically and asymmetrically informed trading respectively, and they are estimated via the approach of Yin and Zhao (2015) in the YZ columns and via Sarkar and Schwartz (2009) in the SS columns. dScale_t is detrended scale of infection. Control variables include capitalization, illiquidity, and realized volatility. ***, ** and * indicate significance levels at the 1%, 5% and 10%, respectively, with t-statistics in parentheses.

Finally, we split informed trades into informed buys and sells and estimate the regression below, with the estimation results in Table 10 . Again, we can only use the approach of Yin and Zhao (2015) to estimate informed buys and sells.

$${\mathit{PIE}}_{i,t}={\beta }_0+{\beta }_1{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+}+{\beta }_2{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}-}+{\beta }_3{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+}+{\beta }_4{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}-}+{\beta }_5{\mathit{dScale}}_t+{\beta }_6{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}+}\times {\mathit{dScale}}_t+{\beta }_7{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Sym}-}\times \mathrm{d}{\mathit{Scale}}_t+{\beta }_8{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}+}\times {\mathit{dScale}}_t+{\beta }_9{\mathit{Info}}_{\mathit{YZ},i,t}^{\mathit{Asym}-}\times {\mathit{dScale}}_t+{\beta }_{10}{\mathit{PIE}}_{i,t-1}+\mathit{Controls}+{\epsilon }_{i,t}$$ (9)

Table 10.

Extended analysis of price informational efficiency: informed buys versus informed sells.

	(1)	(2)
InfoYZ, i, tSym+	0.107*** (3.84)	0.099*** (3.57)
InfoYZ, i, tSym−	0.078*** (2.81)	0.073*** (2.60)
InfoYZ, i, tAsym+	0.081*** (2.89)	0.075*** (2.68)
InfoYZ, i, tAsym−	0.101*** (3.60)	0.090*** (3.22)
dScalet	0.051* (1.83)	0.047* (1.65)
InfoYZ, i, tSym+ × dScalet	0.159*** (5.71)	0.152*** (5.39)
InfoYZ, i, tSym− × dScalet	0.087*** (3.12)	0.082*** (2.92)
InfoYZ, i, tAsym+ × dScalet	−0.129*** (−4.61)	−0.123*** (−4.43)
InfoYZ, i, tAsym− × dScalet	−0.068** (−2.45)	−0.063** (−2.28)
PIEi, t−1	YES	YES
Controls	YES	YES
Constant	YES	YES
Stock fixed effect		YES
Adjusted R-squared	0.11	0.11

The table reports the estimation output of regression (9). The dependent variable is price informational efficiency PIE_{i, t}. Info_{YZ, i, t}^Sym and Info_{YZ, i, t}^Asym are symmetrically and asymmetrically informed trading respectively, estimated via the approach of Yin and Zhao (2015), and + (−) in the superscripts represents informed buys (sells). dScale_t is detrended scale of infection. Control variables include capitalization, illiquidity, and realized volatility. ***, ** and * indicate significance levels at the 1%, 5% and 10%, respectively, with t-statistics in parentheses.

In short, the positive impacts of all informed trades on efficiency, the greater efficiency effect of symmetrically (compared with asymmetrically) informed trading, and the heterogeneous epidemic impacts on the efficiency effects of symmetrically and asymmetrically informed trading, are all evident in the table. Moreover, comparing between the efficiency effects of informed buys and sells, we also confirm that as the disease spreads, the increased (reduced) efficiency effect of symmetrically (asymmetrically) informed trading is more intensive to informed buys.

Collectively, all the consistent findings so far are well consolidated. Here becomes the full picture: The pandemic causes a widespread damage on numerous industries, which brings a sudden and fundamental shock to the stock market. On the other hand, the pandemic also generates public panic, which distracts the market attention and in turn leads to the distortion of information reflection. Under the pressure of the pandemic, investors become keen on collecting/processing (positive) symmetric information but overlook those (positive) asymmetric ones, leading to a faster permanent price shocks from symmetrically informed trading but slower from asymmetrically informed trading (with buy trades in particular), and in turn varying stock returns accordingly. Consequently, the pandemic stimulates the improvement of price informational efficiency by symmetrically informed trading at the cost of weakened efficiency improvement by asymmetrically informed trading.

6. Robustness checks

We have provided consistent evidence from the U.S. stock market that the COVID-19 pandemic improves the information role of symmetrically informed trading at the expense of the diminished informativeness of asymmetrically informed trading. For the reliability of these empirical results, we perform various robustness checks in this section. They are detailed below.

Firstly, we adjust the variables concerning the pandemic. The cut-off date of the COVID-19 outbreak is January 31, 2020 in the empirical exercises. Nevertheless, the precise time of the outbreak is still a big puzzle, which requires us to consider all possible outbreak dates for the analysis. Therefore, we set the alternative date of COVID-19 outbreak to each day in the period of January–February in 2020. Then, we replicate the regressions (1), (4) and (7), and adjust the sample period for the regressions (2), (3), (5), (6), (8) and (9) accordingly as well. Besides the reconsideration of all possible outbreak dates, we also remeasure the scale of COVID-19 infection by adding suspected and/or subtracting recovered cases. Moreover, as an alternative detrending approach for the scale of COVID-19 infection, we eliminate the linear time-trend over the period instead of eliminating the moving average of seven days. All these experiments yield qualitatively consistent observations as those reported in Table 2, Table 3, Table 4, Table 5, Table 6, Table 7, Table 8, Table 9, Table 10.

For dependent variables, besides the raw and adjusted close-to-close returns, we also apply the two forms of open-to-close returns in the analysis. For robustness on the measure of permanent price shocks, we use an alternative sampling resolution and number of lags in the construction: PPS is re-estimated by the autoregressive model at the one-minute frequency with ten or thirty lags. Turning to the efficiency measure, in addition to the reconstruction of variance ratio by the new combination of fifteen-second and one-minute return variances, we also implement a new proxy for efficiency: return autocorrelation in the absolute value, which is constructed by the estimated coefficient of the first-order lag of one-minute returns over the day. Finally, we replicate all experiments using these newly constructed variables, and they result in highly consistent findings.

Finally, except the scale of COVID-19 infection which is subject to a significant trend, we do not detrend our regression variables due to their stationarity over the sample period. For robustness, we also apply the detrended series of all variables (except returns) to the regressions (1)–(9) and find qualitatively similar results.

In sum, none of these exercises leads to a qualitatively different observation. We therefore confirm that our empirical findings in the paper are quite solid and robust. While the estimation outputs of the above robustness checks are not tabulated here, they are available upon request from the authors.

7. Concluding remarks

This paper studies the efficiency of the U.S. stock market in terms of the information roles of symmetrically and asymmetrically informed trading during the COVID-19 pandemic. We firstly analyze how the stock return reactions to symmetrically and asymmetrically informed trading are affected by the pandemic, followed by a thorough investigation into the effects of these two types of informed trading on permanent price shocks to the stock market under the disturbance of the pandemic, and then we examine the corresponding effects on stocks' price informational efficiency. Finally, we conduct a range of robustness tests to make our findings and conclusions more solid and convincing.

We explore that the pandemic on the one hand increases the stock return reaction to symmetrically informed trading but decreases the reaction to asymmetrically informed trading on the other hand. Studying into the nature of information dissemination, we confirm that the effect of symmetrically informed trading on stocks' permanent price shocks is strengthened by the pandemic whereas such effect of asymmetrically informed trading is weakened. As a consequence of permanent price shocks, we observe that the pandemic enhances the effect of symmetrically informed trading on stocks' price informational efficiency but the efficiency effect of asymmetrically informed trading is profoundly impaired by the pandemic. Moreover, there is consistent evidence that all the above effects are more intensive to informed buys, suggesting increased attention to (distraction from) positive symmetric (asymmetric) information.

The invasion of the COVID-19 pandemic on a global scale has attracted increasing attention to its impact on the financial markets. Our investigation focuses on the market efficiency of the U.S. stock market from both symmetric and asymmetric perspectives. The current pandemic introduces new mechanisms of information propagation and thus complicates the information environment of the market. By separately gauging the effects of symmetrically and asymmetrically informed trading and taking the role of the current pandemic into account, we offer a new understanding of the function of the stock markets, aiming for an answer to the question as to how symmetric and asymmetric information are reflected in asset prices in the context of a major and sudden macro-uncertainty event. Given the implication of our paper, market players and policymakers are advised for a smart use of the information during the period of such a systematic disaster in the future.

Data availability

Data will be made available on request.