A panel study on the relationship between liquidity
shocks and stock price crash-risk on the European market
during the years 2000 until 2015
Amsterdam Business School
Name Melvin de Bruijn
Student number 10381627
Program Economics & Business Specialization Finance & Organization Number of ECTS 12
Supervisor Ilko Naaborg Target completion 31/01 /2017
Abstract
This thesis investigates the relationship between a liquidity shock in a firm’s stock and stock price crash-risk. Using Amihud’s (2002) measure of stock illiquidity to compute the liquidity shock, a positive (negative) shock has been found to increase (decrease) the likelihood of a price crash. An additional analysis is performed to research if the effect of a liquidity shock on crash-risk depends on the level of the stock’s liquidity. The analysis shows mixed results for this interaction effect. Furthermore, the effect of stock illiquidity on a crash-risk is non-significant when a variable for liquidity shock is included in the analysis.
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Statement of Originality
This document is written by Student Melvin de Bruijn who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.
The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
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Table of contents
i . Statement of Originality...1
ii. Table of contents...2
1. Introduction...3
2. Literature review ... 4
2.1. Literature review...4
2.2. Empirical findings in the literature...5
2.3. Conclusion on the literature...6
3. Hypothesis, methodology and data ... 7
3.1. Hypothesis and methodology... 7
3.2. Data and descriptive statistics ... 11
4. Empirical results ... 15
4.1. Empirical results ... 15
4.2 Robustness check ... 18
5. Conclusion and discussion ... 21
1. Introduction
In recent years research has been done to the mechanism of a stock price crash-risk. The liquidity of stocks is one of these mechanisms that can explain the behavior of a stock price crash-risk. The relationship between stock liquidity and a crash-risk was very recently researched by Chang, Chen and Zolotoy (2016). They found a positive relationship between stock liquidity and the onset of a crash-risk. This thesis will expand the research on this relationship by including a variable that measures the change in stock liquidity to measure the effect of a liquidity shock. This study researches the effect of a shock in stock liquidity, i.e. a sudden drop or rise in the stock’s liquidity, on the probability of a stock price crash-risk.
By answering the research question, this area of research will have more information about the changes in stock liquidity and its effect on a stock price crash-risk. With this study, information is available on the effect of a change in the stock liquidity of a firm’s stock on the stock price crash-risk. This information is of interest because it makes it possible to analyze if the effect of a liquidity shock depends on the level of liquidity of the stock itself. Another added value of this research is the use of European companies where previous studies mainly have focused on American companies.
This research provides useful information for investors and financial regulators as evidence on the working mechanism behind a stock price crash may let investors and financial regulators take precautionary measures. For example, investors can try to buy or sell their stock if the liquidity changes and the likelihood of a crash changes. Financial regulators could influence the stock liquidity by making use of the dealer- or auction market and changing the free float or tick size.
Weekly data on stock prices, the market index and the stock liquidity are
collected on the European market for the period 2000 until 2015. The liquidity of stocks is measured as the weekly average of the ratio of the daily return to the turnover value. The weekly stock prices and the market index are used to compute the firm-specific weekly returns. These weekly returns are used to
create a dummy variable for the dependent variable; the stock price crash-risk. A logit regression is performed, where the firm-specific stock price crash-risk is being regressed on the liquidity shock of stocks.
The thesis is outlined as follows. In section 2 an introduction of the available literature will be given. In section 3 the hypotheses are outlined and a
description of the data and methodology. The fourth section contains an analysis on the results and a robustness check. The final section will contain a conclusion and discussion.
2. Literature review
Section 2 contains a review of the literature on stock liquidity shocks and stock price crash-risk. Subsection 2.1 describes the theories available on stock
liquidity and crash-risk and the implications for the relationship between the two. Subsection 2.2 describes some of the empirical evidence for those theories. The last subsection 2.3 gives a conclusion on the literature and empirical
evidence.
2.1. Theories regarding stock liquidity, liquidity shocks and crashes
Recent studies that examine the mechanisms of stock price crash-risks claim that the accumulation of bad news is a key factor which leads to the onset of a stock price crash (Kim et al., 2011; Kim et al 2012; Hutton et al. 2009). These studies view withholding bad news from uniformed investors by firm management as the key factor in the onset of a stock price-crash. Bad news gets accumulated and when it reaches its upper limit, such news is made public and leads to a sudden decline in stock prices (i.e. a stock price-crash).
Governance theory explains the relationship between stock liquidity and stock price crash-risk. The theory predicts two different views on the relationship between stock liquidity and crash-risk. The first view of governance theory suggests that higher stock liquidity results in lower crash-risk (Maug, 1998; Edmans, 2009). The monitoring of firm management by blockholders reduces bad news accumulation since the firm’s managers will be less likely to make
inefficient decisions or undertake value-destroying investments. This happens when stock liquidity is higher because the value of information acquisition increases with stock liquidity as informed investors profit from private information (Holmstrom and Tirole, 1993). Therefore, higher stock liquidity increases information production and informed trading. This makes stock prices more indicative of the firm’s real value and weakens manager’s ability to
accumulate bad news.
Conversely, the second view of governance theory suggests that higher stock liquidity results in higher crash risk. According to Edmans (2009), higher stock liquidity can make it easier for a blockholder to sell their stock in the case that bad news is made public. Heavy selling of stock from blockholders will lead to the decline of stock prices which is further magnified because other investors observe the decline. In turn, this makes them sell their stock which thereby, promotes an additional decline of prices.
2.2 Empirical findings in the literature
Governance theory predicts two competing viewpoints on the relationship between stock liquidity and stock price crash-risk. The first is that monitoring of management by blockholders reduces the likelihood of a price crash because it prevents bad news accumulation. For example, Maug (1998) concludes from his research that a liquid stock market leads to more monitoring because the
benefits of informed trading outweigh the monitoring costs.
Kim et al. (2012) also provides empirical evidence for the first prediction of governance theory. The authors find that higher corporate social responsibility performance of firms is negatively associated with a future chance of a price crash since firms who actively engage in corporate social responsibility are less likely to withhold bad news from investors. This effect is more pronounced when firms have less effective corporate governance mechanisms such as monitoring by boards or institutional investors.
The second prediction of governance theory is that higher liquidity increases the chance of a stock price crash-risk when bad news is made public, blockholders
can sell their stock and thereby, cause a decline in stock prices. Bharath et al. (2013) concludes that this threat of exit from blockholders is higher when stock liquidity is higher because they found that firms with larger blockholders
experience greater declines in firm value during crises, particularly when the manager’s wealth is sensitive to the stock price. Therefore higher stock liquidity leads to greater governance of firm management by blockholders.
Chang et al. (2016) provides empirical evidence on the direct relationship between stock liquidity and crash-risk. The sample in their study consists of 9,285 U.S. firms and is studied during the time period 1993-2010. In their study the relative effective spread is used as the stock liquidity measure and two variables are used to measure the price crash. The first measure for price crash is the amount of weeks in a year that a firm experiences weekly returns under 3.09 standard deviations below the mean of firm returns over the last year. The second is a measure of negative skewness. For both variables of stock price risk, stock liquidity is found to increase the chance of a stock price crash-risk. They reason that transient investors will sell their stock in the case of bad news release and when stock is more liquid this selling is done more easily. Managers are afraid that presenting bad news will lead to investors selling their stock. As such, they are inclined to withhold bad news of which an accumulation can lead to a sudden firm-specific stock crash.
2.3. Conclusion on the literature
The relationship between stock liquidity shocks and crash-risk is explained by governance theory. Two competing viewpoints based on governance theory are brought forward. The first view posits that stock liquidity results in higher crash risk because it causes bad news accumulation while the second view contends that stock liquidity results in lower crash risk because it prevents bad news accumulation. Both viewpoints have empirical findings that support them but a study that researched the relationship between stock liquidity and crash-risk directly found that higher stock liquidity increases crash-risk (Chang et al., 2016).
3. Methodology and Data
Section 3 contains information about the methodology and data used in this study. In subsection 3.1 a description is given of the independent variable,
dependent variable, control variables and the regression analyses. Subsection 3.2 contains an analysis on the data used in this study.
3.1. Hypotheses and methodology
The next section contains information on the variables and methodology used in this study. First, part a contains the hypotheses used in this study. Part b
describes the method for computing the independent variable stock liquidity shock. Next, part c describes the method for computing the dependent variable stock price crash-risk. Part d gives information on the control variables used in this study. The fifth and final part e describes the regression analyses.
a. Hypotheses
The predictions regarding the relationship the between liquidity shock and price crash-risk based on previous research contradict each other. As there is
empirical evidence for both competing viewpoints on the relationship between liquidity and crash-risk, the expectations in this study are based on Chang et al. (2016) research findings because they have studied this relationship directly. This thesis expects to find a positive (negative) relationship between a positive (negative) liquidity shock and a price crash because higher (lower) stock liquidity has been found to increase (decrease) the likelihood of a crash. Hypothesis 1. A positive (negative) liquidity shock increases (decreases) the likelihood of a future stock price crash.
The effect of the liquidity shock on crash-risk is explained by the resulting new level of liquidity after the shock. Therefore it is expected that the level of a liquidity shock depends on the current level of stock liquidity of the firm. For example, highly illiquid stock will be less influenced by a positive liquidity shock because the resulting stock remains highly illiquid. This expectation results in Hypothesis 2.
Hypothesis 2. The effect of a positive (negative) liquidity shock on future stock price crash-risk depends on the level of illiquidity of the firm. A positive
(negative) liquidity shock will have a higher (lower) effect on the likelihood of a crash for a company that already is less (more) illiquid.
b. Stock illiquidity and liquidity shock
The independent variable liquidity shock will be measured in two steps. First, a variable for stock illiquidity is created. Following a method of Amihud (2002) the illiquidity measure 𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡 is defined as:
(1) 𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡 = 𝐴𝑣𝑔 [ 𝑅𝑖 ,𝑑
𝑉𝑂𝐿𝐸𝑖 ,𝑑]
where 𝑅𝑖 ,𝑑 is the daily return on stock i and day d and 𝑉𝑂𝐿𝐸𝑖 ,𝑑 the trading volume in Euros of firm’s i stock on day d. In order to compute ILLIQ, a firm is required to have at least 3 days of daily return data available in a week. Data on daily stock return and stock volume to compute Amihud’s (2002) measure of illiquidity are easy to obtain and make it possible for many stock markets to construct time-series over a long period of time. This is advantageous because the effect of stock illiquidity and liquidity shocks is being studied over a long period.
In the next step the liquidity shock is calculated by following a method of Bali, Peng, Shen & Tang (2013). The authors define a liquidity shock as the difference between the stock’s illiquidity 𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡 and its past 52-weekly average:
(2) 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡 = −(𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡− 𝐴𝑉𝐺𝐼𝐿𝐿𝐼𝑄𝑖⎸𝑡−52 ,𝑡−1)
where 𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡 is the stock’s illiquidity of company i in week t and 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡 the difference between the stock’s liquidity of company i in week t and its past 52-weekly average. An increase in the value of 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡 indicates a higher
magnitude of a liquidity shock that results in higher stock liquidity.
A dummy variable for a positive liquidity shock 𝑃𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡 is created to test for an interaction effect, where a value of 1 indicates a positive increase in liquidity over its past 52-weekly average. In a second regression analysis the interaction
variable 𝑃𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡× 𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡 is included to test if the effect of a liquidity shock depends on the level of stock illiquidity of the firm.
c. Crash-risk
To construct a crash-risk measure, Jin and Myers (2006) measure of a stock price crash is used. The authors define stock price crash as a remote, negative outlier in a firm’s residual stock return. Following Hutton, Marcus, and Tehranian (2009), crash is an indicator which equals 1 if at least one week the firm-specific weekly stock return is 3.09 standard deviations below the mean of the firm’s weekly return over the last 52 weeks, and zero otherwise. In the robustness check the threshold of a crash will be changed to 3.5, 4 and 4.5. The firm-specific weekly return W is computed using the expanded market model as has been done before by Kim, Li & Zhang (2010):
(3) 𝑟𝑖 ,𝑡 = 𝛼 + 𝛽1𝑟𝑚𝑘𝑡 ,𝑡−2+ 𝛽2𝑟𝑚𝑘𝑡 ,𝑡−1+ 𝛽3𝑟𝑚𝑘𝑡 ,𝑡+ 𝛽4𝑟𝑚𝑘𝑡 ,𝑡+1+ 𝛽5𝑟𝑚𝑘𝑡 ,𝑡+2+ 𝜀𝑖
where 𝑟𝑖 ,𝑡 is firm’s i return in week t and 𝑟𝑚𝑘𝑡 ,𝑡 the value-weighted Euronext 100 market index return in week t. Lag and lead terms are incorporated in this model to allow for nonsynchronous trading (Dimson, 1979). In the robustness check two different market indexes are used for equation (3), namely the Euro Stoxx 50 and the Euro Stoxx 600. The residuals in equation (3) are skewed. Therefore the firm-specific return is calculated by transforming the residuals to a roughly symmetric distribution by taking the log of 1 plus the residual of equation (3): (4) 𝑊𝑖 ,𝑡 = ln(1 + 𝜀𝑖)
c. Control variables
The regression analysis includes three control variables that are expected to be correlated with forecasting crashes. Chen, Hong & Stein (2001) conclude in their study that crashes are more probable for stocks that are larger in terms of market capitalization that have experienced an increase in trading volume over the prior six months and have had positive returns over the prior 36 months. Therefore size, turnover volume and return index are incorporated in the
regression analysis as control variables and are expected to be positive correlated with CRASH.
The first control variable size (LSIZE) is represented by the market capital and is the share price multiplied by the number of ordinary shares issue. The second control variable turnover volume (LTURNV) is the number of shares traded for a stock on a particular day and is expressed in thousands. The third control variable the return index (RI) is the return index of individual equities and is constructed using the annualized dividend yield. All three control variables will be transformed into a log form because the distributions of the values are skewed.
d. Regression analysis
The regression analysis that will be performed examines the relation between stock liquidity shocks and crash-risks. The regression is specified as follows: (5) 𝐶𝑅𝐴𝑆𝐻𝑖 ,𝑡= 𝛼 + 𝛽1𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1+ 𝛽2𝐿𝑆𝐼𝑍𝐸𝑖 ,𝑡−1 + 𝛽3𝐿𝑇𝑈𝑅𝑁𝑉𝑖 ,𝑡−1+ 𝛽4𝐿𝑅𝐼𝑖 ,𝑡−1+ 𝜀𝑖
In this regression equation, i denotes the firm and t the week. Because the dependent variable represents the probability of a future crash, 𝐶𝑅𝐴𝑆𝐻𝑖 ,𝑡 is measured in week t and the independent and control variables in week t-1. A logit regression is used because 𝐶𝑅𝐴𝑆𝐻𝑖 ,𝑡 is defined as a dummy variable. In this regression 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 is the independent variable. Hypothesis 1 predicts that if the level of liquidity of the firm’s stock is higher, the likelihood of a stock price crash increases. The variable 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 is a continuous variable where higher
levels of 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 indicate an increase in stock liquidity. The coefficient on
variable 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 is therefore expected to be positive. At last, all three control
variables are included in the regression.
A second regression will be performed in order to test for the interaction effect specified in Hypothesis 2:
(6) C𝑅𝐴𝑆𝐻𝑖 ,𝑡 = 𝛼 + 𝛽1𝑃𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1+ 𝛽2𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡−1+ 𝛽3𝑃𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡−1+ 𝛽4𝐿𝑇𝑈𝑅𝑁𝑉𝑖 ,𝑡−1+ 𝛽5𝐿𝑅𝐼𝑖 ,𝑡−1+ 𝜀𝑖
Hypothesis 2 predicts the coefficient of the interaction variable 𝑃𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1× 𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡−1 to be significantly negative because a positive liquidity shock is expected to have less effect on stock price crash-risk as the level of the stock’s illiquidity increases. According to Hypothesis 1 the coefficient on dummy variable 𝑃𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 is expected to be significantly positive in regression equation (6) because an increase in a company’s stock liquidity from a positive liquidity shock will decrease the likelihood of a stock price crash. The inclusion of the level of stock illiquidity of the firm 𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡−1 means that when testing the effect of a positive liquidity shock on stock price crash-risk, the level of illiquidity of the firm’s stock is held as a control variable. This makes it possible to test if the effect of a liquidity shock is independent from the level of illiquidity of the firm’s stock. Previous research has found a positive relationship between the level of liquidity of a firm’s stock and stock price crash-risk (Chang, Chen & Zolotoy, 2016). Therefore it is expected to find a negative coefficient for 𝐼𝐿𝐿𝐼𝑄𝑖 ,𝑡−1, a higher level of stock illiquidity means a lower level of stock
liquidity. Due to the problem of multicollinearity the control variable LSIZE is left out in regression equation (6). This will be further explained in part b of section 3.2. Both in regression equation (5) and (6) the z-statistics are computed using standard errors adjusted for heteroscedasticity.
3.2. Data and descriptive statistics
The next section contains information about data collection and summary statistics of the main variables. Part a contains information on the sample and data collection. Part b contains summary statistics and a correlation matrix of the variables used in this study.
a. Sample selection
The sample of companies consists of enlisted companies on four European stock exchange lists; the Euro Stoxx 50, the Euro Stoxx 600, Euronext 100 and the Alternext Allshare. For each company weekly data has been collected on a firm’s closing stock price, market capital, stock return index and turnover volume. Daily data on the firm’s closing stock price and turnover value has also been retrieved. All the data originates from Worldscope via Datastream. Alternext Allshare and the Stoxx 600 have companies enlisted on them that are smaller in size (as measured by their market capital). Including small companies was done because smaller companies are more likely to be less liquid and by incorporating them into the sample the independent variable will contain companies with high and low levels of stock liquidity.
Data is collected for nearly 16 years, namely from the 3rd of January 2000 until
the 25th of December 2015. For some companies data couldn’t be retrieved
because of errors and they were removed from the dataset. Values on the original data at the 1st and 99th percentile are removed because they are
considered to be outliers. The final sample contains 9,265 firm-specific years of data for 818 companies on multiple variables, which means a panel data set is being used. Finally, for the main regression weekly data on the Euronext 100 index is collected for the same time-period as it represents the value-weighted market index. For the robustness check weekly data on the Euro Stoxx 50 and Euro Stoxx 600 is collected.
b. Summary statistics
For the dependent variable CRASH the frequency of crashes during the sample period is relatively small. In Table 1 the mean of the crash is 0.008 and in Table 2 the percentage of crashes during the sample period is 0.79 percent. These
frequencies are relatively lower than the frequency of crashes that have been found in previous research (Hutton, Marcus & 2009; Chang, Chen & Zolotoy 2016). A possible explanation is the difference of the sample being studied, namely European companies in this study and American companies in their
studies. Also, the size of the sample being studied in this study is lower than in their studies.
There are two kinds of variables to represent the liquidity shock of the firm’s stock. The first one LIQSH seems to be approximately normally distributed. The second variable for a liquidity shock in Table 1, dummy variable PLIQSH, has a mean of 0.638. Because PLIQSH is equal to 1 when there is a positive liquidity shock, this indicates that during the sample period the frequency of positive crashes was higher than that of negative crashes.
The distribution of the interaction variable 𝑃𝐿𝐼𝑄𝑆𝐻 × 𝐼𝐿𝐿𝐼𝑄 seems skewed because the difference between its means and maximum value in Table 1 is large. However, outliers are already been deleted at the 1st and 99th percentile of the
original data. Further deleting of outliers on this variable will produce biased results. Therefore, nothing is done with this variable. The other control variables
LSIZE, LTURNV and LRI seem from Table 1 to be approximately normally
distributed.
Table 1
Descriptive statistics
This table presents summary statistics for all variables used in this study.
Source: Datastream and worldscope.
Variable Observations Mean Standard
deviation Minimum value Maximum value CRASH 481793 0.008 0.088 0 1 PLIQSH 457019 0.638 0.480 0 1 LIQSH 457019 0.0004 0.059 -8.207 5.148 ILLIQ 497087 0.005 0.078 0 17.27 𝑃𝐿𝐼𝑄𝑆𝐻 × 𝐼𝐿𝐿𝐼𝑄 457019 0.001 0.005 0 0.657 LSIZE 525041 7.503 2.522 -3.507 14.175 LTURNV 513326 7.126 3.155 -2.303 14.964 LRI 525064 6.541 2.199 -2.813 13.841
Table 2
Frequency dependent variable
This table shows the frequency as of weekly crashes for 9,265 firm-years in the sample period 2000 – 2015. Crashes are defined based on residuals. These residuals come from an expanded index model with lag and lead variables for the market index as independent variables.
Source: Datastream and worldscope.
Table 3 shows the correlation matrix for the key variables of interest. Both independent variables LIQSH and PLIQSH have significant negative correlations with dependent variable CRASH. Hypothesis 1 predicted the coefficients on these variables to be positive because higher level of stock liquidity increases the likelihood of a crash. These correlations contradict Hypothesis 1. The correlation between CRASH and variable ILLIQ is significantly positive, which contradicts previous research that found a positive relationship between stock liquidity and stock price crash-risk (Chang, Chen & Zolotoy, 2016). Other contradicting
correlations are those of the control variables LSIZE, LTURNV and LRI with
CRASH. Chen, Hong & Stein (2001) found that the size, turnover volume and
return have a positive effect on the onset of a stock price crash. The use of slightly different indicators for these three variables may explain the
contradicting negative correlation coefficients with CRASH found in Table 3. The correlation coefficient matrix shows possible multicollinearity problems. First, the variable LIQSH shows a high correlation with the variable ILLIQ. However, this is not a problem since they are not together included in the regression. Second, the control variable LSIZE shows a significant correlation of 0.77 with LTURNV and one of 0.53 with LRI. To test if this multicollinearity influences the results, a second regression of equation (6) is performed without the control variable LSIZE. In this second regression the coefficient on ILLIQ had significantly changed, which means that the inclusion of LSIZE in regression
𝐶𝑅𝐴𝑆𝐻𝑡 Number of Observations Percent of Sample
0 478,041 99.22
1 3,752 0.78
equation (6) causes multicollinearity problems. Therefore the variable LSIZE was excluded from regression equation (6).
Table 3
Correlation coefficient matrix
This table presents the correlations matrix. Correlations between the variables are computed from 8,382.86 firm-years in the sample period 2000-2015. *, **, *** indicate statistical significance at the 10% and 5% and 1% levels.
CRASH PLIQSH LIQSH ILLIQ 𝑃𝐿𝐼𝑄𝑆𝐻 × 𝐼𝐿𝐿𝐼𝑄 LSIZE LTURN V LRI CRASH 1.00 PLIQSH -0.04 *** 1.00 LIQSH -0.05 *** 0.06*** 1.00 ILLIQ 0.02*** -0.06 *** -0.56 *** 1.00 𝑃𝐿𝐼𝑄𝑆𝐻 × 𝐼𝐿𝐿𝐼𝑄 -0.001 0.08*** 0.24*** 0.12*** 1.00 LSIZE - 0.005 *** -0.05 *** -0.01 *** -0.14 *** -0.22’ *** 1.00 LTURN V -0.005 *** -0.04 *** -0.01 *** -0.14 *** -0.20 *** 0.77*** 1.00 LRI -0.005 *** -0.02 *** -0.01 *** -0.09 -0.14 *** 0.53*** 0.42*** 1.00 Source: Datastream and worldscope.
4. Analysis
Section 4 contains the results of the regression analyses and is divided in two subsections. Subsection 4.1 describes the empirical results for the two main regression analyses used in this study. Subsection 4.2 describes the results of the robustness check.
4.1. Empirical results
Table 4 shows the regressions of crash on a liquidity shock where liquidity shock is measured as a continuous variable. An increase in the absolute level of
𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 means a higher magnitude of a liquidity shock and results in higher
that the effect of a stock liquidity shock on crash is negatively significant at the 1% level. The negative coefficient of 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 indicates a positive effect of
liquidity shock on crash-risk because a negative log value between 0 and 1 is a positive value. This means that an increase in the magnitude of a positive (negative) liquidity shock increases (decreases) the likelihood of a stock price crash.
In the second regression three control variables are included. The coefficient of 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 in the second regression is again negative and significant at the 1%
level. For the average company used in this sample, the likelihood of a stock price crash goes up by e-0.601 = 0.548 percentage points when 𝐿𝐼𝑄𝑆𝐻
𝑖 ,𝑡−1 goes up
by 1. Now the control variables are included, the coefficient of 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 is higher in magnitude than the one found in regression 1. All three control
variables are significant at the 1% or 5% level. However, it was expected that all the three control variables would have a positive effect on the likelihood of a crash. However, the effect of 𝐿𝑆𝐼𝑍𝐸𝑡−1 has been found to be negative while those on 𝐿𝑇𝑈𝑅𝑁𝑉 𝑡−1 and 𝑅𝐼𝑡−1 are positive.
The results for testing the interaction effect can be found in Table 5. A Liquidity shock is now measured as the dummy 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1, where 1 indicates that the liquidity shock is positive. Because 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 is a dummy, it is unwise to test for the magnitude of the effect of a positive liquidity shock. This has already been done in the regressions of Table 4. But the inclusion of 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 in the
regression makes it possible to test the direction of the effect and for interaction effects, and to control for the level of stock illiquidity of the firm.
All three regressions in Table 5 show a negative coefficient between 0 and 1 of 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 and are significant at the 1% level. This confirms the same results for
the positive direction of the effect of a liquidity shock in previous regressions. This indicates that the effect of a positive liquidity shock increases the likelihood of a price crash.
Regression number 2 and 3 in Table 5 include two additional variables; the variable for stock illiquidity I𝐿𝐿𝐼𝑄𝑡−1 and the interaction between the dummy for
a positive shock and stock illiquidity 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1. Regression number 3 also includes the control variables. The coefficients on the variable
I𝐿𝐿𝐼𝑄𝑡−1 are in regression 2 and 3 insignificant. This means that the effect of the
stock illiquidity on the likelihood of a crash does not exist when the variable for a liquidity shock is included in the regression.
Table 4
Main regression results (1)
This table shows the regression results for regression equation (5) and reports the coefficients for all variables. The dependent variable is dummy variable (𝐶𝑅𝐴𝑆𝐻𝑡), which equals to 1 if the firm experiences
one or more weeks where the mean of the firm’s return is 3.09 standard deviations below the past yearly mean of the firm’s return. The independent dummy variable liquidity shock is defined as the continuous variable 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1.. The control variables LTURNV and LRI are included in all regressions. Regression
results for regression equation (6). Standard errors are reported in parentheses below the coefficients. *, **, *** indicate statistical significance at the 10% and 5% and 1% levels.
(1) (2) Constant -4.872*** (0.017) -4.868*** (0.065) 𝐿𝐼𝑄𝑆𝐻𝑖 ,𝑡−1 -0.481*** (0.101) -0.601*** (0.157) 𝐿𝑆𝐼𝑍𝐸𝑡−1 0.052*** (0.012) 𝐿𝑇𝑈𝑅𝑁𝑉 𝑡−1 -0.040*** (0.009) 𝐿𝑅𝐼𝑡−1 -0.020** (0.009) Observations 448,225 435,909 Pseudo R2 0.0001 0.0007
Source: Datastream and worldscope.
The last two regressions in Table 5 show significant results for the interaction effect. In regression number 2, the interaction effect 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1 is
found to be significantly positive at the 5% level. This indicates that the effect of a positive liquidity shock increases the likelihood of a crash when a firm’s stock becomes more liquid. When the control variables are included in the regression, the interaction effect is significant at the 1% level.
Table 5
Main Regression Results (2)
This table shows the regression results for regression equation (6) and reports the coefficients for all variables. The dependent variable is dummy (𝐶𝑅𝐴𝑆𝐻𝑡), which equals to 1 if the firm experiences one or
more weeks where the mean of the firm’s return is 3.09 standard deviations below the past yearly mean of the firm’s return. The independent dummy variable liquidity shock is defined as the positive liquidity shock (𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1), which is equal to one if the liquidity shock is positive, and zero otherwise. Coefficients on the
level of stock illiquidity I𝐿𝐿𝐼𝑄𝑡−1 and the interaction variable 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1 are also reported. The
control variables LTURNV and LRI are included in all regressions. Regression results for regression equation (6). Standard errors are reported in parentheses below the coefficients. *, **, *** indicate statistical
significance at the 10% and 5% and 1% levels.
(1) (2) (3) Constant -4.402*** (0.023) -4.403*** (0.023) -4.215*** (0.062) 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 -0.881*** (0.035) -0.885*** (0.035) -0.902*** (0.036) I𝐿𝐿𝐼𝑄𝑡−1 0.206 (0.135) -0.562 (0.461) 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1 5.620** (1.406) 3.946* (2.010) 𝐿𝑇𝑈𝑅𝑁𝑉 𝑡−1 -0.019*** (0.006) 𝐿𝑅𝐼𝑡−1 -0.007 (0.009) Observations 448,225 448,225 437,272 Pseudo R2 0.0162 0.0163 0.0169
Source: Datastream and worldscope.
4.2 Robustness check
Section 4.2 contains the results for the robustness check. Part a contains the results for the robustness check when the dependent variable price-crash risk is differently defined. Part b contains the results for the robustness check with the use of a different the market index.
a. Alternative definitions of stock price crash-risk
For the robustness check two changes are introduced to the two main
regressions in equation (5) and (6). The first change is an adjustment for the dependent dummy variable CRASH. Three new thresholds for the definition of a crash are being tested. In the robustness check a crash is equal to 1 when the weekly return is respectively 3.5, 4 and 4.5 standard deviations below the mean weekly returns over the past year, and zero otherwise. Panel A shows the regression results for regression equation (5). Panel A in Table 6 shows that the effect of 𝐿𝐼𝑄𝑆𝐻𝑡−1 on 𝐶𝑅𝐴𝑆𝐻𝑡 is significantly positive at the 1% level for all alternative specifications for the dummy variable 𝐶𝑅𝐴𝑆𝐻𝑡. These results confirm
the main results in Table 3 that also show a significant and negative coefficient between 0 and 1 on 𝐿𝐼𝑄𝑆𝐻𝑡−1. Panel B represents the results for regression equation (6). Panel B in Table 6 shows that for all three regressions the coefficients on 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1are negatively significant at the 1% level and also confirm previous findings. Also, the level of illiquidity 𝐼𝐿𝐿𝐼𝑄𝑡−1 is again found to be insignificant. However, the results for the interaction effect 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 ×
𝐼𝐿𝐿𝐼𝑄𝑡−1 contradict previous findings because the coefficients in all three regressions are found to be insignificant in the robustness check. This may be explained by the low frequency of crashes in the sample being studied in comparison to other research. When the definitions of a crash are stricter, the frequencies of crashes become lower and this makes it harder to find a
significant relationship between crash and the interaction variable.
b. Alternative use of market index
The second change in the robustness check is the use of a different market index in the expanded market model to compute the firm-specific weekly return. Table 7 shows that using Euro Stoxx 50 or Euro Stoxx 600 as the market index does not change the findings of main regression (1) and (2). In all regressions and for both regression equations, the coefficients on the variables 𝐿𝐼𝑄𝑆𝐻𝑡−1, 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 and
𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1 are found to be significant at the 1% level, negative and between 0 and 1. The coefficient on 𝐼𝐿𝐿𝐼𝑄𝑡−1 is again found to be insignificant.
In short, all previous research findings of the main regression are found to be robust when an alternative market index is used but not when an alternative definition for the variable for crash-risk is used. The coefficient on the
interaction variable 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1 in regression equation (6) is found to be insignificant in the robustness check for all alternative definitions of crash-risk. However, the results for the coefficients on the other variables in regression equation (6) are robust against alternative definitions of crash-risk.
Table 6
Additional analysis (1): Alternative definitions of crash-risk
This table represents the results for the robustness tests with different definitions of crash-risk. The dependent variable is the crash-risk (𝐶𝑅𝐴𝑆𝐻𝑡). Regression (1), (2), and (3) define a crash (𝐶𝑅𝐴𝑆𝐻𝑡) as
equal to 1 when the weekly return is respectively 3.5, 4 and 4.5 standard deviations below the mean weekly returns over the past year, and zero otherwise. Panel A reports the results for regression equation (5) with 𝐿𝐼𝑄𝑆𝐻𝑡−1 as the main independent variable. Panel B reports the results for regression equation (6) with the
positive liquidity shock (𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1) as the independent variable. Coefficients on the level of stock
illiquidity I𝐿𝐿𝐼𝑄𝑡−1 and the interaction variable 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1 are also reported. Other control
variables are included as in table 4 and 5 but not reported. Standard errors are reported in parentheses below the coefficients. *, **, *** indicate statistical significance at the 10% and 5% and 1% levels.
Source: Datastream and worldscope.
(1) (2) (3)
Panel A: Results for regression equation (5)
Constant -5.344*** (0.082) -5.768*** (0.102) -6.142*** (0.123) 𝐿𝐼𝑄𝑆𝐻𝑡−1 -0.628*** (0.160) -0.580*** (0.153) -0.670*** (0.161) Observations 435,909 435,909 435,909 Pseudo R2 0.0008 0.0008 0.0008
Panel B: Results for regression equation (6)
Constant -4.691*** (0.078) -5.089*** (0.098) -5.471*** (0.121) 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 -0.868*** (0.447) -0.910*** (0.056) -0.910*** (0.069) I𝐿𝐿𝐼𝑄𝑡−1 -0.474 (0.708) -0.825 (1.003) -0.467 (1.047) 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1 4.070 (3.987) 3.832 (5.288) -2.034 (9.664) Observations 437,272 437,272 437,272 Pseudo R2 0.0146 0.0150 0.0144
Table 7
Additional analysis (2): Alternative market index
This table represents the results for the robustness tests with the use of different alternative market index. Regression (1) and (2) in Panel A and B contain an alternative market index when calculating the stock’s illiquidity I𝐿𝐿𝐼𝑄𝑡−1, respectively the Euro Stoxx 50 and Euro Stoxx 600. The dependent variable is the
crash-risk (𝐶𝑅𝐴𝑆𝐻𝑡). Panel A reports the results for regression equation (5) with 𝐿𝐼𝑄𝑆𝐻𝑡−1 as the main
independent variable. Panel B reports the results for regression equation (6) with the positive liquidity shock (𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1) as the independent variable. Coefficients on the level of stock illiquidity I𝐿𝐿𝐼𝑄𝑡−1 and
the interaction variable 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1 are also reported. Other control variables are included as in
table 4 and 5 but not reported. Standard errors are reported in parentheses below the coefficients. *, **, *** indicate statistical significance at the 10% and 5% and 1% levels.
Source: Datastream and worldscope.
5. Conclusion and discussion
The effect of a liquidity shock on a firm’s stock is tested against the likelihood of a stock price crash. First, a regression is performed on crash with liquidity shock as a continuous independent variable. The results show a significant and positive (negative) effect of a positive (negative) liquidity shock on the likelihood of a crash. Next, an additional regression is performed with a dummy variable for a positive liquidity shock to test for the direction of the effect and a possible interaction effect with the level of illiquidity of the firm’s stock. The direction of the effect of a positive liquidity shock on stock price crash is found to be
(1) (2)
Panel A: Results for regression equation (5)
Constant -4.891*** (0.158) -4.901*** (0.066) 𝐿𝐼𝑄𝑆𝐻𝑡−1 -0.610*** (0.158) -0.694*** (0.193) Observations 435,909 435,909 Pseudo R2 0.0009 0.0008
Panel B: Results for regression equation (6)
Constant -4.211*** (0.061) -4.263*** (0.062) 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 -0.933*** (0.035) -0.899*** (0.357) I𝐿𝐿𝐼𝑄𝑡−1 -0.543 (0.462) -0.099 (0.407) 𝑃𝐿𝐼𝑄𝑆𝐻𝑡−1 × 𝐼𝐿𝐿𝐼𝑄𝑡−1 5.318*** (1.842) 5.410*** (1.724) Observations 437,272 437,272 Pseudo R2 0.0181 0.0168
significantly positive. This means that a positive (negative) liquidity shock increases (decreases) the likelihood of a crash and confirms the results from the first regression. Furthermore, the effect of the liquidity shock on a price crash is found to depend on the level of illiquidity of the firm’s stock. A positive (negative) liquidity shock increases (decreases) the likelihood of a crash when a firm’s
stock becomes more (less) liquid. However, when alternative variables of a crash risk are included in the regression this interaction effect disappears. Governance theory predicts two contradicting views on the relationship between stock liquidity shocks and stock price crash-risk. This thesis gives empirical evidence for the view that higher (lower) stock liquidity, due to a positive (negative) liquidity shock, increases (decreases) the likelihood of a crash
because managers are less likely to withhold bad news. This causes bad news to pile up and to cause a price crash when the news becomes public. This confirms the research findings of Chang. et al. (2016).
This thesis has several limitations. The first is regarding the data. Data on the variables for the European companies are not always consistently available which makes it hard to compute unbiased variables. However, this problem was dealt with by setting a baseline for a minimum amount of observations during a certain period. The second limitation is the choice of the independent variable. This study uses Amihud’s (2002) illiquidity measure to compute the stock
illiquidity and liquidity shock. However, as Amihud argues in his paper, there are better measures of stock liquidity available that are finer and more precise. However, these require a lot of data that are not available in many stock markets. The main results in this thesis show that a positive (negative) liquidity shock increases (decreases) the onset of a future price crash. These results have some implications and recommendations for managers and financial regulators. First, managers can undertake actions that could prevent the onset of a positive liquidity shock because it increases the likelihood of a crash. At the same time, firms should be cautious in the event of a positive liquidity shock; at higher levels of stock liquidity, a positive liquidity shock can increase the likelihood of a crash.
This thesis found that when controlling for a liquidity shock, the effect of stock illiquidity on stock price crash risk disappears. However this effect was not always present during the robustness check. It is interesting to research further if stock prices react to changes in the level of stock liquidity, stock liquidity shocks or maybe both.
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