“Firm-specific investor sentiment and stock price crash risk: The role of foreign investors in Korea’s stock market”

Building on a prior study that documents that stock price crashes are positively associated with firm-specific investor sentiment (hereafter, the sentiment), this study further investigates the moderating effect of foreign investors on Korea’s stock market. This study hypothesizes that foreign investors as sophisticated participants are indifferent of the significant relationship between the sentiment and the stock price crashes. For firms listed on the KSE over the period of 2011–2019, the analysis findings show that the high stock crash risk attributable to the high sentiment is attenuated for firms with high foreign ownership. However, such moderating effect of foreign ownership disap-pears when taking foreign investment horizon into consideration. This implies that future stock crash risk reduction under the high sentiment is due to the corporate monitoring role of foreign investors, who are targeting a long-term investment horizon. This study adds to the literature on the role of foreign investors by suggesting that foreign investors act as a rigorous monitor helpful for managing stock price, rather than a price maker who is rational under the high sentiment.


INTRODUCTION
Stock price crash is defined as the sudden and extreme fall of stock prices in firm-specific return dimension (Hutton et al., 2009), which is the most undesirous in the efficient stock market, but inevitable economic event in the practice field.While Jin and Myers (2006) have argued that the stock crash is attributed to the managerial problem such as incentives not to release bad news for their own benefits concerned with their compensation or reputation, many researchers have sought the causes and the stock crash predictors in the agency theory perspective.
Most studies that explain stock crashes as the agency cost incurred by the agency-principal conflicts of interest, commonly suggest information opacity in a certain context and emphasize the corporate governance mechanism in reducing the economic loss due to stock crashes (Kim et al., 2011a(Kim et al., , 2011b;;Boubaker et al., 2014;Andreou et al., 2016).Kim et al. (2011b) demonstrate that the likelihood of stock crashes increases by tax avoidance, which facilitates managerial opportunism, including the rent extraction and bad news accumulation, but is mitigated for firms with a strong monitoring system.Kim et al. (2014) document that socially responsible firms are likely to experience the crash, since managers engaged in CSR (corporate social responsibility) commit to more transparency.Boubaker et al. (2014) report controlling shareholders, especially those who have excessive control right to cashflow right, are not willing to provide firm-specific information to hide opportunistic practices, increasing the crash risk.
The studies above show that such a particular context of firm characteristics significantly influences the crash risk, and the effects are moderated by the effective corporate governance such as external or internal monitoring mechanisms (i.e., the high institutional ownership, the larger size of board of directors, the high analyst coverage, etc.).The similar strand of research is shown in Korea as well.Mostly, the effect of foreign ownership or foreigners' investment horizon as a proxy for the governance effectiveness on future stock crashes has been investigated (Jeong, 2020; Kim & Park, 2017;Lee, 2016).They show a consensus about foreign investors' monitoring role in restraining managerial inefficient decision and enhance the information transparency, which reduces future stock price crashes.
However, given that the crashes that eventually occur in the process of asset pricing, not only internal firm characteristics (i.e., corporate governance) but also external investors' behaviors, have an impact on the crash risk.The point is that the incongruent opinions among investors (Chen et al., 2001), high investor sentiment (Yin & Tian, 2017;Fu et al., 2021), or the lower retail investor attention (Wen et al., 2019) are also associated with future stock crashes, independent of internal firm characteristics.According to these studies, the trader types, including unsophisticated noise traders or rational arbitrageurs, play a crucial role as the external investors.This shows that valuation errors attributable to stock trading by such traders lead to current or future stock price crashes.Importantly, foreign investors play a monitoring role within the company and also act as external investors who can affect stock prices.

LITERATURE REVIEW AND HYPOTHESIS
An indicator of investors' trading behavior that affects asset prices is the investor sentiment (Brown & Cliff, 2005; Lemmon & Portniaguina, 2006).
Investor sentiment is referred to as a degree of investor' optimistic mood in financial markets (Baker & Wurgler, 2006).Ryu et al. (2018) in Korea identify the sentiment, in terms of individual firm, which has an explanatory power for the asset price movement.Furthermore, Fu et al. (2021) document that the sentiment of an individual firm is positively related to the crash risk, confirming the role of noisy traders in high sentiment in limiting the rational arbitrageurs' position.Specifically, the risk in which arbitrage is not able to take away the effects of noise forms over-valued price and consequently leads to stock price crashes.
This study investigates how foreign investors influence the future stock price crashes attributable to such investor sentiment.Foreign investors act as not only the influential share trading participants but also external controllers following share ownership.Since foreign investors are engaged in the Korean stock market with enormous financial power, the impact of their trading activities on the market's condition depends on the position in which they engage in the stock market.
As share trading participants, foreign investors are considered to be sophisticated In summary, foreign investors can play both a monitoring role and a sentiment promoter role as a price setter.In this context, taking investors' behavior as an explanatory variable of stock price crashes attributable to the sentiment may make a difference in the existing findings, which concludes in terms of corporate governance.In other words, for stock crashes, the role of foreign investors as external investors, not internal monitors may depend on the sentiment level, meaning foreign investors may promote the high sentiment and contribute to the crash risk.
When foreign investors have an effect on forming firm-specific sentiment, the positive relation between the investor sentiment and stock crashes can be moderated or incremental.If foreign investors act as noisy traders/rational arbitrageurs to promote the sentiment, the crash risk due to the sentiment increases.But if they play a monitoring role as supervisors who are indifferent of hot money by short-term trading (i.e., corporate effective monitors), the sentiment related-crash decreases.That is, although the firm-specific investor sentiment is positively related to the future stock price crash risk, the effect of foreign investors on the relationship between the sentiment and future stock price crashes is unforeseeable.Thus, the null hypothesis is formed.Hence, this study aims to investigate the role of foreign investors in stock crashes attributable to investor sentiment.

H:
Foreign investors are indifferent of the positive relationship between firm-specific investor sentiment and future stock price crash risk.( )

METHODOLOGY
, where P t denotes the closing price of stocks of firm i in year t.The notation, (P t-i -P t-i-1 ) + in numerator of above equation corresponds to the equation of P t-i -P t-i-1 if the calculation of P t-i -P t-i-1 yields positive value, 0 otherwise.|P t-i -P t-i-1 | denotes the absolute value of the calculation of P t-i -P t-i-1 .While RSI i,t ranges between 0 and 100, representing the overbought market at RSI above 80 and the oversold market at RSI below 20 within 14-trading days.
Psychological Line Index (PLI) is also an indicator of investor sentiment, showing the market being either oversold or overbought.Similar to RSI measures, PLI above 75 implies overbuying market and that below 25 indicates an overselling market.
12 1 while measured on daily basis, the sentiment variable for the test needs to be modified into firm-year based one.The firm-specific investor sentiment for analysis, SENT t , is calculated as the yearly mean value of standardized -daily firm-specific investor sentiment (ε t ).This sentiment indicator is alleged to exhibit more robust explanatory power than existing sentiment measures do (Ryu et al., 2018).
According to Hutton et al. (2009), stock price crash is defined as the event that a firm's weekly returns belong to less than 0.1% of their distribution.Firm-specific weekly returns are measured as the residuals from estimating the following equation: , where r j,t = weekly returns for firm j and week t; r m,t = weekly returns for market of week t; r ind,t = weekly returns for industry to which firm i belongs of week t; where, weekly returns are calculated as market value weighted -average stock returns.
The estimation residual of the model represents the firm specific returns not explained by market and industry returns.The lagged returns are included to control for the effect of nonsynchronous trading by time periods on returns.Then, the residuals, or firm-specific weekly returns (ε j,t ), are transformed into linear function form (W j,t ) in equation ( 9).
By using W j,t in equation ( 9), stock price crash risk variables are measured in two ways, the negative skewness, NCSKEW, and the volatility, DUVOL.
The skewness (NCSKEW), presented in equation (10), is the negative of the third moment of firm-specific weekly returns form each year and normalized by the standard deviation ( ( ) ( )( ) The firm-specific weekly returns volatility (DUVOL) is calculated as the logarithm of the ratio of standard deviation of downward returns to that of upward returns.Where, upward/downward returns are measured as the abnormal returns adjusted by the average weekly returns for a year.Equation (11) represents the measurement of DUVOL, where n u and n d denote the frequency of upward/downward stock returns, respectively.The higher volatility indicates the higher likelihood of stock price crash.

Model specification
This study investigates how foreign investors influence the future stock price crashes attributable to the investor sentiment.In line with the hypotheses on the role of foreign investors, the analysis aims to test the moderate effect of foreign investors on the future stock price crashes positively related to the sentiment.Since stock price reflects a value-weighted average consensus of all investors who estimate corporate value, this study takes foreign investor ownership as a proxy for foreign investors' trading behavior, which affects their valuation process.Foreign ownership is simply measured as the percentage of the share numbers that foreigners own out of total outstanding shares of a firm at the end of year.Then, by regression analysis, whether the higher foreign ownership enables the magnitude of stock crash risk, which responds to the sentiment, to be reduced is examined.The test models are specified as follows: ( ) Own : Foreign ownership of firm i at year t-1; SENT t-1 Mkt : Marketwide sentiment at year t-1.Control variables are illustrated as below.
Equation ( 12) is the regression model to test the effect of foreign investors on the stock price crash risk positively related to the firm sentiment.The interesting main variables are SENT t-1 Firm (firm-specific investor sentiment) and FOR t-1 Own (foreign ownership).If the firm sentiment has a positive relationship with future stock crashes even in the Korean stock market, the coefficient of SENT t-1 Firm , β 1 , would show significantly positive sign.Further, if foreign investors as the sophisticate participants play a crucial role in mitigating such relationship, the interaction term of SENT t-1 Firm •FOR t-1 Own would show the significantly negative sign.This means that foreign investors serve as the rational price maker or as a rigorous monitor not as the noisy traders who promote the investor sentiment in which valuation error is incorporated.

SENT t-1
Mkt (market-wide sentiment) is included to control the impact of the common sentiment that is pervasive but not observable in the stock market (Yin & Tian, 2017).It is measured as the yearly average of all firm-specific investor sentiments according to Guo et 12).Given that stock price crash is likely to occur in firms in which infor-mation is not transferred efficiently, stock crashes may rely on firm size (SIZE) in which the information transmission speed or market's reaction depending on the information transparency may be different (Hutton et al., 2009).Since stock price crash risk is closely associated with firm performance and financial health (Kim & Jeong, 2017;Hutton et al., 2009;DeFond et al., 2015), return on assets (ROA), firm leverage (LEV), changes in sales (∆SALES), cash flows from operation (CFO), and financial loss (LOSS) are included in the estimation.Firms with high market-to-book value is susceptible to stock crashes which are likely to arise in the over-valued in the short run.
Given that Chen et al. ( 2001) document that high-yielding firms are prone to facing future stock crashes, equation (12) needs to include stock returns (RET) measured as the yearly average based on a firm's weekly returns.Since investors' incongruence in regard with stock price forecasting may increase the future stock crash risk, the regression is implemented with both the detrended share turnover (TURN) and the standard deviation of firm's weekly returns (SIGMA) controlled.To control extremely negative skewness with time-serially consistence that affects future stock price crashes, the model includes the lagged NCSKEW (Bae et al., 2016).Lastly, the information quality (|DA|), measured as the accumulation of value of accruals (absolute) over prior three consecutive years, is included in the model because it is deeply related to information opacity, which is responsible for stock crashes.
All regressions consider industry and year dummies to control for the fixed effects.Also, a oneyear lag between the dependent and independent variables is imposed to capture the effect of the sentiment and the prior role of foreign investor followed by stock price crash.The test statistical significance of all estimates by regression analysis is calculated based on firm-clustered standard error (Petersen, 2009).

Sample criteria
For companies listed on the Korea Stock Exchange's securities market from 2011 to 2019, the analyses are implemented.The sample meets the following requirements for analysis for the period.1) KSE-listed firms with December-year end excluding the financial industry.
3) Firm-years available for financial and stock price data from the Fn-Guide database.
The sample excludes the financial and insurance industry, which is a little different in accounts of financial statements from the other industry.By excluding firms with non-December year-end, the analysis ensures consistent test period.As main variables for the analysis, the stock crash risk and the firm sentiment are measured mainly using returns and/or trading volume of stocks on a daily basis.The data in which the continuity in stock transaction does not exist due to the trading suspension or designation as issues for administration are excluded from the samples.This procedure yields 5,308 of firm-years observations in final samples.Note: * While the measurement for the firm sentiment requires daily returns and trading volume, some of the data do not show the continuity in stock transaction due to the trading suspension or designation as issues for administration.) is calculated as the average of firm-specific investor sentiments over one year, showing lower variance in distribution.The main independent variable is foreign ownership (FOR t-1

Own
).Foreign investor ownership, FOR t-1 Own , has the mean value of 0.102, indicating about 10.2% of total shares is owned by foreign investors on average.This statistic is based on the samples that include even firms in which foreign investors do not engage.It ranges from 0% to 60.8%.), but also foreign investor ownership (i.e., FOR t-1 Own .Specifically, the coefficient (ρ) on correlation of NCSKEW t and SENT t-1 Firm is 0.122 and significant at the 1% level.This is in line with a prior study that documents stock price crash occurrence, which is attributable to firm-specific in-vestor sentiment.
However, the positive coefficient of 0.128 on the correlation of NCSKEW t and FOR t-1 Own is rather unexpected result, given prior evidence by Kim and Park (2017) who document that the foreign ownership or foreign investment period do not have an influence on stock crash risk as a single factor.These results are consistent with the other stock crash measure in this study, DUVOL t .
While foreign ownership is taken as the proxy of sophisticated participants in the stock market, the coefficient of FOR t-1 Own is 0.147 and significantly positive, implying that foreign investors may act sentiment promoters.However, simple analysis without controlling other factors that affect future stock price crashes is limited to test the hypotheses in the statistically unbiased manner.Thus, the regressions are implemented only to elaborate the analysis for the hypotheses in section 4.3.This study builds on the evidence that the future stock price crash risk is positively affected by the firm-specific investor sentiment (Fu et al., 2021).However, the evidence from the Korean stock market does not exist, it is necessary to revisit the relationship between the investor sentiment and future stock crashes prior to looking into the role foreign investors.Table 3 provides the analysis results that show the significant positive effect of firm-specific investor sentiment on future stock price crashes.
For NCSKEW t , the coefficient of SENT t-1 Firm is 0.499 (t-statistics = 9.50) in the case of the simple equation without other control variables but for ).Such positive relationship is robust to the regressions of both the equation with other control variables and the equations in which the dependent variable is substituted by DUVOL t .The coefficients of market wide sentiment (SENT t-1

Mkt
) are not statistically significant in any regressions, which implies market-wide sentiment does not have an incremental explanatory power exceeding firm-specific investors sentiment.Owing to results consistent with prior study, further research that investigates the role of foreign investors can proceed in sequence.
Table 5 presents the regression results on the main models, i.e. equation (12) and baseline models, which exclude other control variables but for market-wide sentiment.Equation ( 12) includes the interaction term of firm sentiment and foreign ownership to examine the moderate effect of foreign investors on the future stock price crashes attributable to firm-specific investor sentiment.If foreign investors who are considered as sophisticated participants play a role in reducing the future stock price crashes due to firm-specific investor sentiment, the coefficient of (SENT t-1 Firm •FOR t-1

Own
) would be significantly negative, with the coefficient of SENT t-1 Firm positive.
The results show the negative coefficient of (SENT t- 1 Firm •FOR t-1

Own
) and the positive one of SENT t-1 Firm , supporting the role of foreign investors as sophisticated participants (i.e., a rational price market or a rigorous monitor).For NCSKEW t as a dependent variable, the coefficients of SENT t-1 Firm and (SENT t-

Own
) are 0.405 (t-statistics = 4.34) and -0.994 (t-statistics = -2.79),respectively.These results are similar even in the case of DUVOL t as a dependent variable and to those from the regression of Baseline equation that excludes other control variables.
Overall, the findings suggest that foreign investors moderate the future crash risk attributable to the firm sentiment.This means that foreign investors act as rational price makers or as corporate monitors not as the noisy traders who promote the investor sentiment in which valuation error is incorporated.This clearly rejects the hypothesis that foreign investors are indifferent of the positive relationship between firm-specific investor sentiment and future stock price crash risk.
However, the analysis result can be weak evidence to argue for the monitoring role of foreign investors in reducing crash risk.Thus, a series of tests with a variety of proxy for foreign investors' behavior (i.e., foreign ownership change, long-term horizon investment) are further conducted in the next section.

Additional tests
Several additional tests to examine more closely whether foreign investors serve as rational price setters or strict supervisors of management are conducted in this section.When considering only foreign investor ownership as a proxy for foreign investors' trading behavior, foreign investors' ownership itself does not reflect their investment propensity, so it is explained in terms of both short-term profit pursuers and corporate monitors (Shleifer & Vishny, 1986;Maug, 1998).This means that foreign ownership, by which the sentiment is affected, cannot distinct a rational price maker from a corporate monitor.Hence, by considering the yearly growth in foreign ownership, which denotes the existence of foreign investors engaging in stock price movement in the model, the analysis tries to capture the effect of foreign investors as a price maker.
If foreign investors who acquire stocks act as rational participants not as noisy traders in the purpose of their own interests in the short run, the changes in foreign investor ownership would mitigate positive relations between the investor sentiment and the stock crash risk.However, Table 4 provides the opposite, showing the insignificant coefficient of the interaction term, (SENT t-1 Firm •∆FOR t-1

Own
).The coefficients are 0.502 (t-statistics = 0.45) for NCSKEW t and 0.512 (t-statistics = 0.50) for DUVOL t as a dependent variable.This indicates that foreign investors who currently acquire stocks are indifferent of stock crashes attributable to the sentiment.In other words, foreign investor may play as a price maker who promotes sentiment.However, this interpretation is also disputable because the changes in foreign ownership do not reflect the characteristics of foreign investors regarding the investing horizon, which has an influence on the level of corporate monitoring or short-term arbitrage by foreign investor.Considering that the noisy traders in foreign investors largely correspond to those who are in shortterm investment horizon, it is necessary to take investment horizon into consideration to examine the role of foreign investors (Chen et al., 2007;Callen & Fang, 2013).As previously mentioned, foreign ownership, as a proxy for foreign investors' trading behavior by which the sentiment is affected, cannot distinct a rational price maker from a corporate monitor.This is the case that foreign investors who own the large ownership may serve as a noisy trader for short-term performance, as well as a monitor (Shleifer & Vishny, 1986;Maug, 1998).Hence, the analysis uses foreign investment horizon as a proxy for foreign investors' trading behavior to capture the role of foreign investors dedicated to a monitoring role.
The investment horizon (i.e., short-term or longterm investment period) even given the same level of the ownership makes a difference in the role of foreign investors in stock valuation or corporate governance.To distinguish long-term investors from short-term ones, Kim and Jang (2012) utilize the daily turnover, which indicates the level of foreign investors' buy-sell trading amount compared to market values of their holding shares at day t.
The equation above represents the foreigners' share turnover; where N i,f,d S and N i,f,d B denote the number of shares sold and bought by foreigners, respectively.P i,f,d S and P i,f,d B denote the price of shares sold and bought by foreigners, respectively.N i,f,d denotes the number of shares that foreigners hold, and P i,d denotes the stock price.Thus, the denominator (N i,f,d • P i,d + N i,f,d-1 • P i,f,d-1 )/2 indicates the daily average of market value shares that foreigners own.The numerator (N i,f,d • P i,d + N i,f,d-1 • P i,f,d-1 )/2 indicates the average trading amount by foreigners at day t.TURN t is, as a test variable, the firm-yearly summation of such daily turnover.
A higher (lower) value of TURN t which means higher turnover, indicates foreigners' short-term (long-term) investing tendency.Foreigners' investment horizon (FOR t-1

Lti
) is represented as the indicator of either short-term investment or longterm investment, which are determined based on the yearly median value of TURN t .
Although not tabulated, the correlation coefficients of the foreign ownership and foreign investment horizon indicator with firm-specific investor sentiment are qualitatively different from each other.The coefficient of FOR t-1 Own is 0.147 and significantly positive, while that of FOR t-1 Lti is not statistically significant (0.000, p-values = 0.988).This implies that foreign investment horizon may have different implication from foreign ownership in explaining the relationship between the firm sentiment and future stock crash risk.
Equation ( 15) is the test model with respect to the foreign investment horizon.
( ) where CRASH t (NCSKEW t or DUVOL t ); Stock price crash of firm i in year t; SENT t-1 Firm Investor sentiment of firm i in year t-1; FOR t-1 Lti : Foreign investment tendency of firm i in year t-1; SENT t- 1 Mkt : Market-wide sentiment in year t-1.Control variables are identical to the equation (12).
As expected, if there exists a moderate effect of foreign investors who are dedicated to the role of a corporate monitor with long-term investment horizon, the interaction term of (SENT t-1 Firm •FOR t-1

Lti
) is expected to show the significantly negative sign.Other control variables except for SENT t-1 Mkt (market-wide sentiment) in the equations are illustrated as follows.Detailed variable definitions are giv-en in Appendix A.
Table 4 provides the analysis results of equation (15), which includes the interaction term of foreign investment horizon with firm-specific investor sentiment.If foreign investors who are regarded dedicated to a corporate monitor with longterm investment horizon play a role in reducing future stock crashes due to firm-specific investor sentiment, the coefficient of (SENT t-1 Firm •FOR t-1

Fti
) would be significantly negative, with the coefficient of SENT t-1 Firm positive.
The results show the negative coefficient of (SENT t- ) and the positive one of SENT t-1 Firm .For NCSKEW t as a dependent variable, the coefficients of SENT t-1 Firm and (SENT t-1 Firm •FOR t-1

Fti
) are 0.704 (t-statistics = 8.67) and -0.412 (t-statistics = -3.83),respectively.These results are similar even in the case of DUVOL t as a dependent variable and to those from the regression of Baseline equation that excludes other control variables.
Additionally, the analysis results presented in Table 5 and Table 6 confirm the significant effect of foreign investors in a long-term investment horizon.As shown in the estimation results of the interaction terms in the tables, the moderate effect ) (0.1080, t-statistics = 0.10), while the coefficients of (SENT t- 1 Firm •FOR t-1

Lti
) are still significantly negative.
The results from Table 4 to Table 6 show consistently that foreign investors are effective in future stock crash reduction as a corporate monitor ded-icated in the long-term investment horizon.While foreign investors have been regarded as a corporate monitor internally and as a price setter externally, this study reveals the foreign investors' dominant role as a corporate monitor under the market sentiment state.Especially, it suggests that foreign investors as sophisticated investors act as a monitor when investing in the long term, moderating stock crash risk due to the investor sentiment.

CONCLUSION
The aim of this study is to investigate whether foreign investors as sophisticated participants in the Korean stock market moderate the future stock crash risk attributable to the firm sentiment.This study hypothesizes that the foreign investors as sophisticated participants are indifferent of the significant relationship between the sentiment and stock price crashes.For firms listed on the KSE for the period of 2011-2019, the main results show that the increased future stock price crash risk, which is attributable to the high sentiment, is attenuated for firms with high foreign ownership.However, such moderate effect disappears in the estimation, which takes foreign investment horizon into consideration.This implies that the effect of foreign investors in reducing future stock crashes is due to foreign investors dedicated to a corporate monitoring with long-term investment horizon.
This study conveys some implications to the academics and practice field.This study adds to the literature on the characteristics of foreign investors by examining the role of foreign investors under a certain market condition (i.e., the sentiment state).In particular, by resolving the limitation of previous studies that confine research setting to overlooking the role of foreign investors as external pricing setters, this study helps in a broader understanding of the role of foreign investors in the capital market.However, while this study assumes foreign investors as external price makers or as controllers for sustainable cor- Chen et al., 2001; Kim et al., 2014; Kim & Zhang, 2016).The higher negative skewness indicates the higher likelihood of stock price crash.
(NCSKEW t or DUVOL t ): Stock price crash of firm i in year t; SENT t-1 Firm : Investor sentiment of firm i at year t-1; FOR t-1 al. (2019) and Fu et al. (2021).

Table 1 .
Sample selection criteria

Table 3 .
Correlation analysis results for the main test variables

Variables DUVOL t SENT t-1 Firm SENT t-1 Mkt FOR t-1
Note: This table presents the Pearson correlation coefficients.The figures in parentheses are p-values.The notations * and † denote the statistical significance at 1% and 5% level, respectively.Please refer to Appendix A for variable definitions, and Appendix B for correlation coefficients of all test variables.

Table 4 .
Additional test: The role of foreign investor (foreign ownership growth) Note: t-statistics are calculated based on firm-clustered standard errors.***, **, and * indicate statistical significance at the 1%, 5% and 10% level, respectively.Please refer to Appendix A for the definitions of test variables.

Table 5 .
Additional test: The effect of foreign ownership and foreign investment horizon

Table 6 .
Additional test: The effect of foreign ownership growth and foreign investment horizon Note: t-statistics are calculated based on firm-clustered standard errors.***, **, and * indicate statistical significance at the 1%, 5% and 10% level, respectively.Please refer to Appendix A for the definitions of test variables.
This table presents the results of Pearson correlation analysis.The figures in parentheses are p-values.Please refer to Appendix A for variable definitions. 25)e:http://dx.doi.org/10.21511/imfi.19(4).2022.25

Table B2 .
The effect of firm-specific investor sentiment on stock price crash risk Note: t-statistics are calculated based on firm-clustered standard errors.***, **, and * indicate statistical significance at the 1%, 5% and 10% level, respectively.Please refer to Appendix A for definitions of test variables.

Table B3 .
The effect of firm-specific investor sentiment on stock price crash risk: The role of foreign investors Note: t-statistics are calculated based on firm-clustered standard errors.***, **, and * indicate statistical significance at the 1%, 5% and 10% level, respectively.Please refer to Appendix A for definitions of test variables.Investment Management and Financial Innovations, Volume 19, Issue 4, 2022 25)p://dx.doi.org/10.21511/imfi.19(4).2022.25

Table B4 .
Additional test: The role of foreign investors (foreign investment horizon) Note: t-statistics are calculated based on firm-clustered standard errors.***, **, and * indicate statistical significance at the 1%, 5% and 10% level, respectively.Please refer to Appendix A for definitions of test variables.