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Stock Liquidity and Stock Price Crash Risk:

U.S. Banks

Final version: Menno Schaaf, Msc Finance

a,s

Faculty of Economics and Business, Research Paper, University of Groningen, Nettelbosje 2, Groningen

P A P E R I N F O

A B S T R A C T

Paper history:

Final version 11 January 2018

Keywords:

Stock Liquidity Stock Price Crash Risk U.S. Banks

Down-to-up volatility

Negative conditional skewness

Words:

12717

1. Introduction Research Topic

Banks determine the sentiment of the market. In the eyes of many people, financial institutions have a leading role in the financial landscape. If they can crash easily, how about the other firms? We all know what happened with the Lehman Brothers bank back in 2007. It was the beginning of the credit crisis. Banks suddenly did not trust each other anymore and

I am very grateful for the helpful comments from prof. dr. L.H. Hoogduin (supervisor). a Corresponding author. E-mail address: m.schaaf@student.rug.nl (M. Schaaf).

s Corresponding student number: M. Schaaf (S3018555).

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took each other almost down to the bottom. The key factor here is transparency, because it reduces information asymmetry among investors and it secures market efficiency. Efficient markets reflect information into stock prices fast and precisely. Opacity was the reason of many recent scandals such as Enron, WorldCom, and Fannie Mae (Bleck and Liu, 2007). In these examples, market participants were too late discovering negative information. Hence, they were not able to anticipate the market reaction. This triggered researchers to investigate the mechanisms of stock price crash risk. Stock price crash risk is the likelihood of occurrence of negative stock returns. For investors, this is a relevant and practical indicator to base their investment allocations on (DeFond, Hung, Li, and Li, 2015). To be more precisely, according to Jin and Myers (2006), a stock price crash risk is the chance of having a large, negative, firm-specific return outlier in the residual return of a firm. They state that crashes release bad news about firms. The accumulation of bad news, as part of transparency, can explain a lot of variation. Managers with a short-term horizon or career ambitions can choose to hide bad news from the market to increase stock prices (Ball, 2009). When bad information accumulates, Chang, Chen, and Zolotoy (2017) state that it eventually will hit its maximum capacity. Once revealed, it will lead to large price declines. Especially for financial institutions like banks, large price declines could hurt investor’s trust and confidence of the financial climate (DeFond, Hung, Li, and Li, 2015). Perhaps stock liquidity plays a role somewhere in this complicated process. Stock liquidity is the ability to trade a large quantity of stocks at low costs within a short framework of time, and with minimal or no price impact (Chang, Chen, and Zolotoy, 2017). Stock liquidity is an important mechanism to monitor the management of a company (Chauhan, Kumar, and Pathak, 2017). The relationship between stock liquidity and stock price crash risk is undetermined yet. In sum, stock liquidity can affect stock price crash risk via the chance of bad news accumulation, the degree of bad news hoarding by managers, and the power of the market reaction by investors. The literature contradicts itself on the stock liquidity topic, whether it mitigates or increases stock price crash risk. Chauhan, Kumar, and Pathak (2017) find a negative relationship between stock liquidity and stock price crash risk. They state that stock liquidity is a governance tool for disciplining managers for not releasing bad news, because blockholders put pressure on managers not to hide the bad news and price informativeness restricts managers to manipulate stock prices. Chang, Chen, and Zolotoy (2017) find a positive relationship between stock liquidity and stock price crash risk. They state that stock liquidity increases the short-term pressure on managers and gives them incentives to hide bad news. Moreover, stock liquidity increases the exit of transient institutions leadings to ex-post stock reactions following bad news releases. Conclusions point into different directions, which prevailing effect causes the relationship.

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but excluded financial institutions. This thesis adds new insights, because it focusses solely on U.S. banks. Chang, Chen, and Zolotoy (2017) included financial institutions as well, so their research results are not isolated and perhaps too much diversified. Using the framework of Chauhan, Kumar, and Pathak (2017) and applying it to U.S. banks creates a unique outcome by isolating the effect of stock liquidity on stock price crash risk.

Using a large sample of U.S. banks for 2001-2012, this thesis investigates the relationship between stock liquidity and stock price crash risk. Using different measurements of stock price crash risk variables (negative conditional skewness, and down-to-up volatility), different proxies of stock liquidity (illiquidity, zero-day volume, and stock turnover), different errors to correct for heteroskedasticity and serial correlation (HAC, and WHITE), and a correction for potential market volatility driven by the financial crisis (dummy variable). Furthermore, this thesis uses fixed time effects to deal with endogeneity and causality. This research finds that stock liquidity has a positive relationship with stock price crash risk. The mechanism of the transient investor channel explains the causality. Transient investors have a short investment horizon and an excessive focus on short-term performance. U.S. banks managers have an equity-based compensation structure. Combining the aggressive investment style of transient investors with the equity-based compensation structure for U.S. banks strengthens the need for short-term achievements even more. A bad performance not only affects the transient investors, but also the manager’s own payment. This behavior pressures managers to perform according the expectations or to hide bad news and let it eventually accumulate until it crashes. The barrier to sell stocks is low when stock liquidity is high. Stock liquidity becomes a leverage tool for panicking transient investors. This panicking reaction is driven by bad news accumulation, bad news hiding, and the power of the market investors to strengthen the decrease of the stock price with their selling.

This thesis does not help to avoid a (possible) next stock price crash. I would probably get the Nobel Prize for that if I could come up with such an indicator. Focusing on stock price crash instead of stock price crash risk does not provide enough data since there is only one recent stock crash in 2007/2008. What this thesis brings to the table is that it presents stock liquidity as a useful indicator of potential stock price crash risk. Investors take a risk by investing their money into a company. The return they get is the compensation for the risk that they are willing to bear. Therefore, this thesis helps investors who have difficulties allocating their investments. Investors are often more under-diversified with their portfolios than professional institutions are. Investors can use this indicator in risk management applications and option pricing (Berkowitz and O’Brien, 2002).

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2. Literature Review

2.1. Stock price crash risk and stock liquidity

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Stock liquidity is the ability to trade a large quantity of stocks at low costs within a short framework of time, and with minimal or no price impact (Chang, Chen, and Zolotoy, 2017). Prior research states that stock price crash risk can occur by publishing bad news all at once. Stock liquidity can play an important role in this, because it can affect crash risk in one or more of the following items: the chance of bad news accumulation (i.e. bad news arises due to managerial failure or a negative shock), the degree of bad news hoarding by the managers (once managers know that there is bad news, it is released or hoarded), and the power of the market reaction when the bad news is being revealed (how much will the company’s stock price be punished by the market). Managers often have a higher level of private information about firms than their stockholders have. Regulations and statutes require managers to release that information, but their incentives are not always aligned with the investors’ (Chang, Chen, and Zolotoy, 2017).

Chang, Chen, and Zolotoy (2017) notice that prior research offers competing perspectives on the question whether stock liquidity increases or decreases stock price crash risk. The question is, which effect dominates? Stock price crash risk can decrease investors’ welfare and confidence, so it is important to know whether stock liquidity mitigates or exacerbates stock price crash risk. Chang, Chen, and Zolotoy (2017) use a large sample of U.S. firms for 1993-2010, and find strong support that stock liquidity strengthens stock price crash risk. This conclusion is based on using relative effective spread as their primary measure of stock liquidity, while this thesis uses illiquidity as a proxy to measure stock liquidity. The relative effective spread is the ratio of the absolute value of the difference between the trade price and the midpoint of the bid-ask quote over the trade price (Chang, Chen, and Zolotoy, 2017). Stocks with higher liquidity (lower relative effective spreads) are more vulnerable to stock price crash risk. Increasing stock liquidity by one standard deviation increases stock price crash risk by 0.027 and increases negative skewness of stock returns by 0.047 (Chang, Chen, and Zolotoy, 2017). They also compare their results with non-U.S. markets as a benchmark. It turns out that the change in stock price crash risk is significantly more positive for the U.S. market as a total. Emerging markets have a relatively lower level of transparency to reflect information compared to U.S. markets (Chauhan, Kumar, and Pathak, 2017). This strengthens the correlation between stock liquidity and crash risk, due to the accumulation of bad news being released all at once. High stock liquidity increases short-term pressure and gives managers incentives to hide bad news. Moreover, more stock liquidity increases the exit of transient institutions, which leads to ex post stock reactions following bad news releases (Chang, Chen, and Zolotoy, 2017).

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Kumar, and Pathak (2017) use a large sample of Indian firms listed on the National Stock Exchange during 2001-2012, and find strong support that stock liquidity is negatively correlated with stock price crash risk. In their sample, they exclude financial firms and utility firms. According to them, stock liquidity decreases stock price crash risk, because blockholders may put pressure on managers to not hide the bad news and price informativeness restricts managers to manipulate stock prices (Chauhan, Kumar, and Pathak, 2017). The dominance of controlling ownership restricts the influence of internal governance to mitigate stock price crash risk. Change in financial market regulations is needed, because stock liquidity can complement internal governance. In their research, they also tackle identification concerns about the causality. Using the difference-in-difference approach, the two-stage least square method and average stock liquidity, they confirm that their main finding is robust, and that stock liquidity reduces stock price crash risk.

2.2 The relationship between stock liquidity and stock price crash risk

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positively correlated with the degree of unexpected bad earnings releases. Given that liquidity increases short-term pressure, stimulates managers to hide bad news and weakens market stability, are not the only reasons why stock liquidity is positively correlated to stock price crash risk. Higher liquidity firms also have a higher chance of bad future earnings news, which lead to more selling by transient investors but not by blockholders. This leads to price reactions when bad news releases (Chang, Chen, and Zolotoy, 2017). Chang, Chen, and Zolotoy (2017) do not state that stock liquidity is always negative, but they do find a negative side via the transient investor channel. Regulators determine the financial landscape and need to determine the optimal level of stock liquidity. A way to do this is by implementing new corporate governance rules to increase transparency. Increased transparency will lead to more informed and efficient trading (Brogaard, Li, and Xia, 2017). The optimal level is obviously different for each firm, because it depends on a trade-off between gains and losses. Such a trade-off could, for example, be between the marginal value-at-risk and stockholders’ value. The optimal point, when it comes to mitigating stock price crash risk, is reached when stockholders’ value decreases more than the value-at-risk decreases (Brogaard, Li, and Xia, 2017). Another field in which new corporate governance rules could be implied is the accounting culture (optimistic vs. conservative). Optimistic accounting means higher returns, but also higher risks. Conservative accounting means lower returns, but also lower risks. New corporate governance rules should convert the corporate accounting culture from optimistic to conservative. Conservative accounting is related to a lower chance of stock price crash risk, because it restricts managers’ incentive and ability to overstate firm performances and to withhold bad news from investors (Kim and Zhang, 2016).

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(Norli, Ostergaard, and Schindele, 2015). When a manager’s compensation is related to stock prices, blockholders can threaten the management to sell their stocks to put a downward pressure on the stock prices. When stock prices decrease, the equity compensation for the managers will be less. Either by exit threats or intervention threats, stock liquidity can discipline managers. Knowing this, managers might be willing to release bad news on time and decrease stock price crash risk. The second reason, provided by Chauhan, Kumar, and Pathak (2017), why stock liquidity can decrease crash risk is stock price informativeness. Informed investors base their trading activity on the amount of stock liquidity. The higher the liquidity, the more it will reduce the costs (Grossman and Stiglitz, 1980). The more liquid the stocks are, the more the investors will trade, which eventually leads to more stock price informativeness (Chauhan, Kumar, and Pathak, 2017). Chance of mispricing-errors will also be lower for liquid stocks, because the market will correct them (Chordia, Goyal, Sadka, Sadka, and Shivakumar, 2009). Increases in stock price informativeness also decrease the incentives of managers to hide bad news. Managers are restricted in hiding bad news to increase earnings (Chauhan, Kumar, and Pathak, 2017). Taken together, Chauhan, Kumar, and Pathak (2017) state that the (negative) relationship between stock liquidity and crash risk increases when firms have a higher level of stock price informativeness (Chauhan, Kumar, and Pathak, 2017). The effect exit threats plays a bigger role when managerial wealth is sensitive to stock prices (Chauhan, Kumar, and Pathak, 2017). This is not the case for India, but it might be the case for U.S. banks. Stock-option-based compensation in India is not yet a common way to reward managers for their performances. This means for this thesis that the threat of exits can also play a role explaining the results. The effect of stock liquidity decreases stock price crash risk for firms with a higher level of blockholder ownership (Chauhan, Kumar, and Pathak, 2017). This means that the threat of intervention, if stock liquidity is high, disciplines managers. Price informativeness also discourages managers’ intention to hide bad news from the market, because stock liquidity encourages traders to sell and buy at lower costs.

2.3. Other factors influencing stock price crash risk

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the firms. When this happens, it increases the possibility of hidden, bigger issues at the firm (Graham, Harvey, and Rajgopal, 2005). An increased stock price crash risk is an example of such an issue. After the earnings announcement, managers spend lots of time to figure out what went wrong. What they should do, to mitigate future stock price crash risk however, is to present their view of the firm’s future prospective (Graham, Harvey, and Rajgopal, 2005). Hoarding bad news also links to stock price crash risk via the agency theory framework, due to the weak alignment of goals between the principal and the agent. This disturbed relationship may reflect an important reason that explains lack of complete disclosure. When a firm is not completely transparent, their managers can benefit themselves at the expense of stockholders and gain a part of the cash flows in ways not realized by investors. An example of this is managers keeping a bad project for private benefits. The bad news is that, to protect their jobs, managers may absorb downside risk and losses caused by their performances due to hiding bad news until the stock price crash eventually occurs. Investors can always use the exit option, but this is costly. Exercise of this option can lead to a stock price crash (Jin and Myers, 2006). As literature suggests, bad news hiding, and stock price crash risk are driven by conflicts between principals and agents (Chang, Chen, and Zolotoy, 2017).

Religiosity can also be associated with future stock price crash risk. Callen and Fang (2015) find robust evidence that firms, headquartered in countries where the level of religion is higher, have lower levels of future stock price crash risk. For their research, they use data from the Association of Religion Data Archives (ARDA) and combine this with data from the Center for Research in Security Prices (CRSP). Using a sample of 80,404 firm-year observations from 1971-2000, they not only use the same expanded market and industry regression model as this thesis, but also the same proxies for stock price crash risk. The mechanism behind their results is that religion provides a set of morals and values in those countries. These morals and values help to avoid that managers hide bad news. The negative relationship between religiosity and future stock price crash risk is even stronger when firms are riskier and have weaker governance mechanisms, measured by stockholder takeover rights and dedicated institutional ownership (Callen and Fang, 2015).

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traditional governance mechanisms that should align the interests of the principals and the agents, are less effective when the CEO is overconfident (Kim, Wang, and Zhang, 2016). Digging deeper into the perks of managers, Xu, Li, Yuan, and Chan (2014) investigated the relationship between excessive perk consumption and stock price crash risk for state-owned Chinese companies. If managers want to enjoy their excessive perks, it creates an incentive for them to hide bad news for some periods. This leads to a higher future stock price crash risk. In their study, they use a sample of Chinese SEOs from 2003-2010. Collecting data from the China Stock market and Accounting Research (CSMAR) database and institutional ownership data from the Wind Financial database (WindDB), they use the expanded market regression model to calculate firm-specific weekly returns (Xu, Li, Yuan, and Chan,2014). In their research, they also use the same proxies for risk as this thesis. They find a positive relationship between excess perks and stock price crash risk. This relationship is even stronger for firms whose executives are approaching their retirement, because it encourages them to focus on short-term results and neglect long-term issues. Using perks simply reducing the value of the company, because it lowers the cash flow. The solution for this problem would be a strong external monitoring to hide bad news (Xu, Li, Yuan, and Chan,2014).

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with a lower market development, and less conservative accounting (Chen, Chan, Dong, and Zhang, 2016). Internal control can decrease the amount of bad news that executives withhold from investors. The negative correlation between internal control and stock price crash risk is driven by firms with good internal control and strong corporate governance.

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fair view of the firm. Li, Wang, and Wang (2017) investigate the effect of social trust on stock price crash risk. Social trust is a proxy for the level of collective trust within a community. Selecting all Chinese A-stock listed companies for the period 2001-2015 and using the CSMAR database, they also use the same expanded market model and proxies. The final sample consists of 964 firm-year observations in 2001 and 1925 observations in 2014. The conclusion of their research is that firms headquartered in regions with higher social trust have a smaller risk of stock price crashes. Higher social trusts areas have higher levels of accounting conservatism and less restatements.

2.4. Research Questions

Based on the two main papers of Chauhan, Kumar, and Pathak (2017) and Chang, Chen, and Zolotoy (2017), it is not clear what the exact relationship between stock liquidity and stock price crash risk can be for U.S. banks. The evidence from both papers conflicts with each other. Higher stock liquidity can decrease the chances of bad news accumulation through either intervention or the threat of exit. Furthermore, it can mitigate the trading reactions of investors by increasing the stock price informativeness. On the other hand, higher stock liquidity can also create more short-term pressure on the managers’ performances by attracting more transient institutional investors. More pressure on managers means more accumulation of bad news, which when eventually gets released, increases the stock price crash risk. This is due to the selling of transient investors who demand excellent short-term performances (Chang, Chen, and Zolotoy, 2017).

The research question of this thesis is to determine the sign of causality. Chang, Chen, and Zolotoy (2017) find strong support that stock liquidity strengthens stock price crash risk through the mechanism of demanding short-term orientated transient investors. This support applies to U.S. firms for 1993-2010. Chauhan, Kumar, and Pathak (2017) find a strong support that stock liquidity is negatively correlated with stock price crash risk, because of the price informativeness and treat of exit and intervention. This support applies to Indian firms listed on the National Stock Exchange during 2001-2012. However, they exclude financial firms and utility firms. Chang, Chen, and Zolotoy (2017) use relative effective spread as their proxy to measure stock liquidity, while Chauhan, Kumar, and Pathak (2017) use illiquidity as their proxy. This leads into the following research question:

• What is the relationship between stock liquidity and stock price crash risk for U.S. banks

during 2001-2012?

2.5. Hypothesis

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pressure from investors (transient investors or blockholders) must be significant to affect the prices of liquid stocks (Chang, Chen, and Zolotoy, 2017). Although Chang, Chen, and Zolotoy (2017) use a different proxy to measure stock liquidity, their research focusses on the same market as this thesis does. This thesis only examines the U.S. banks, while their research consists of the whole U.S. market. Next to this, they also compare their results with non-U.S. markets as a benchmark. Although Chauhan, Kumar, and Pathak (2017) use the same period of interest and proxy as this thesis, the fact that they use it for the Indian market makes their sign of causality less trustworthy for the U.S. banks. It turns out that the change in stock price crash risk is significantly more positive for the U.S. market as a total. This strengthens the correlation between stock liquidity and stock price crash risk.

This thesis prefers country of interests over the same proxy and period, because the Indian market is less equity-based-compensation, while the U.S. market is. Equity-based compensated markets increase short-term pressure on managers and therefore the incentives to hide bad news. Therefore, this thesis uses the causality sign from Chang, Chen, and Zolotoy (2017) and predicts this positive correlation. This gives the following hypothesis:

• 𝐻1: U.S. banks with higher levels of stock liquidity have higher levels of stock price crash risk.

To use the best of both worlds, this thesis does use the methodology from Chauhan, Kumar, and Pathak (2017), because they exclude banks from their sample. Although the countries of interest are different, it still creates a unique opportunity to compare a sample of banks with a sample of listed companies excluding financial institutions. Eventually, this thesis will compare its results with the results of Chang, Chen, and Zolotoy (2017) to see if the banking sector has the same overall results as the whole U.S. market.

3. Data and variables

3.1 Sample selection

To get a clear view about the financial institutions from the U.S., this thesis focuses on U.S. banks. This research measures the relationship between stock liquidity and stock price crash risk for listened U.S. banks. The period of interest is equal to the period from 2001-2012. This makes the research comparable with the research of Chauhan, Kumar, and Pathak (2017). They excluded financial firms and utility firms from their research.

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Datastream, a database maintained by Thomson Reuters. This database has all the data to calculate the dependent and independent variables. Each bank needs to have at least 26 weeks of stock return data and a year-end stock price larger than $1. After doing this, I winsorize the top and bottom 1% values to mitigate for outliers (Chauhan, Kumar, and Pathak, 2017). The final sample contains 84,820 unique quarterly variable observations for 179 U.S. banks for 2001-2012. The complete descriptions of the variables are in table 1.

3.2. Crash risk measures

Based on the framework of Kim, Li, and Zhang (2011) and Chauhan, Wadhwa, Syamala, and Goyal (2015), this thesis uses two proxies of stock price crash risk to measure idiosyncratic risk. First, the negative conditional skewness of daily stock returns (NCSKEW). Negative conditional skewness is important to look at, because stock price crash risk is the chance of having a large, negative, outlier in the residual return of a firm. We measure negative outliers by measuring negative conditional skewness. Secondly, the log of down-to-up volatility of daily stock returns (DUV). Volatility is the fluctuation of the stock returns. The volatility is captured by calculating the ratio of standard deviations of down-day-returns to up-day-returns. The daily returns are calculated as the natural log of (1 + residual returns). This is denoted by W, from the extended market model (Chauhan, Kumar, and Pathak, 2017): 𝑟𝑖,𝑡 = 𝛼𝑗 + 𝛽1,𝑖𝑟𝑚,𝑡−2+ 𝛽2,𝑖𝑟𝑚,𝑡−1+ 𝛽3,𝑖𝑟𝑚,𝑡+ 𝛽4,𝑖𝑟𝑚,𝑡+1+ 𝛽5,𝑖𝑟𝑚,𝑡+2+ 𝜀𝑖,𝑡 (1)

The daily stock i return 𝑟𝑖,𝑡 on trading day t, and 𝑟𝑚,𝑡is the daily market return on day t. To

anticipate for non-synchronous effects, there are two lead and lag terms (Dimson, 1979). The crash risk proxy 𝑁𝐶𝑆𝐾𝐸𝑊𝑖,𝑞 is estimated for every quarter q. The negative third

moment of skewness of bank-specific daily returns (W) is divided by the standard deviation of the daily returns for bank i in quarter q to normalize it (Chauhan, Kumar, and Pathak, 2017):

𝑁𝐶𝑆𝐾𝐸𝑊𝑖,𝑞 = − [𝑛(𝑛 − 1) 3

2(∑ 𝑊1,𝑞3 )/(𝑛 − 1)(𝑛 − 2)(∑ 𝑊1,𝑞2 ) 3

2 ] (2)

The negative sign in front makes sure that a higher value of negative conditional skewness shows higher crash risk.

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𝐷𝑈𝑉𝑖,𝑞 = log {(𝑛𝑢− 1) ∑ 𝑊1,𝑞

2 𝑑𝑜𝑤𝑛

(𝑛𝑑− 1) ∑𝑢𝑝𝑊1,𝑞2 } (3)

In equation 3, 𝑛𝑢and 𝑛𝑑 are the numbers of up- and down-days in quarter t. Higher

down-to-up volatility means higher stock price crash risk (Chauhan, Kumar, and Pathak, 2017). It does not involve third moments, so it is less affected by volatile returns (Kim, Li, and Li, 2014).

3.3. Stock liquidity measure

Liquidity measures the cost involved in trading. Buyers and sellers take opposite positions of each other and make the trade happen. Illiquid stocks cost more to buy and to sell, because of the higher difference between the bid and ask price. This thesis uses daily trading information to calculate liquidity. The cost of liquidity is measured by either trading volume, the spread, or the stock price. Liquidity is extremely hard to measure (Kyle, 1985). Therefore, this thesis uses the method of Amihud (2002) to calculate a volume-based illiquidity measure. This is a precise measure of price impact, compared to other measures (Goyenko, Holden, and Trzcinka 2009). Fong, Holden, and Trzcinka (2017) state in their research that illiquidity is a trustful cost-per-dollar-volume proxy. Illiquidity is the absolute daily return divided by the daily dollar trading volume, averaged over bank i and quarter q (Chauhan, Kumar, and Pathak, 2017). The daily dollar trading volume is the adjusted closing price of the stock multiplied with the daily trading volume in dollars. Liquid stocks are easier to sell than illiquid stocks, so they have a higher trading volume. The higher the volume, the bigger the number, the lower the illiquidity and higher the liquidity. A higher trading volume also decreases the average commission fees per stock, which makes the stock more liquid:

𝐼𝑙𝑙𝑖𝑞𝑢𝑖𝑑𝑖𝑡𝑦𝑖,𝑞 = 1 𝐷𝑖,𝑡𝑋 ∑ |𝑟𝑒𝑡𝑖,𝑑| 𝑉𝑜𝑙𝑢𝑚𝑒𝑖,𝑑 𝐷 𝑑=1 (4)

In equation 4, ret are daily stock returns and volume is the dollar trading volume on day d of bank i. D is the number of trading days in quarter q. After calculating illiquidity, this thesis rescales it, multiplying by 10^6, to get a readable value. To reduce the range into more manageable values, this thesis uses the logarithm. Illiquidity does not contain units of measurements (i.e. Kg, liter, etc.), so this method is justified (Danyliv, Bland, and Nicholass, 2014) The Illiquidity variable measures illiquidity of stocks, so lower Illiquidity means a higher liquidity (Chauhan, Kumar, and Pathak, 2017).

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3.4. Stock liquidity and stock price crash risk

Crash risk is always measured for the next quarter, while the independent variables are measured one quarter before that.

𝐶𝑟𝑎𝑠ℎ𝑅𝑖𝑠𝑘𝑞+1,𝑖 = 𝛼 + 𝛽1𝑆𝑡𝑜𝑐𝑘𝑙𝑖𝑞𝑞,𝑖+ ∑ 𝛽𝑛 𝑛

𝐶𝑜𝑛𝑡𝑟𝑜𝑙𝑞,𝑖𝑛 + Time + 𝜀𝑞,𝑖 (5)

The letters i and q refer to bank and quarter, n refers to the same set of control variables from the previous section. The regression model also includes fixed effects for time to mitigate for time-invariant factors. This helps to contain the omitted variable biased. There is, however, no control for industry fixed effects, because the sample only consists of banks. It makes no difference to distinguish them with fixed industry effects, because this thesis already includes firm-specific control variables (Chauhan, Kumar, and Pathak, 2017).

3.5. Control variables

To get an isolated effect of liquidity on crash risk, this thesis uses some control variables to make sure that they do not affect the dependent variables. The control variables follow the prior literature of Chauhan, Kumar, and Pathak (2017) and Chang, Chen, and Zolotoy (2017), because of the degree of comparability. These variables include the following: change in turnover (DTURN), which captures the heterogeneity in investor opinion (Chen, Hong, and Stein, 2001), quarterly skewness (NCSKEW) of the daily returns to adjust for potential serial correlation, the quarterly standard deviation of returns (STD), because the higher the volatility the more likely there is a crash (Chen, Hong, and Stein, 2001),

Table 1

Description of the control and robustness variables used in the regression models. Using the framework of Chauhan, Kumar, and Pathak (2017).

Variable Definition

Stock Turnover – TURN The ratio of quarterly trading volume of stocks to outstanding stocks. Zero-day volume – ZDV The number of days when there is no trading divided by the total

trading days, over a quarter.

Turnover – DTURN The % change in stock-level turnover over two successive

quarters. Quarterly firm-level turnover is dividing the difference in firm-specific quarterly trading volume by the total outstanding stocks. Negative skewness – NCSKEW Negative of the third moment of return distribution divided by the

standard deviation of firm returns for each quarter.

Standard deviation – Std Quarterly standard deviation of stock returns using estimated daily returns.

Stock return – RET Quarterly cumulative stock return using estimated daily returns. Price to book value – PB Quarter equity market value divided by the quarter equity book value. Firm size – Size Natural logarithm of the quarterly market value of equity, in million

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the cumulative quarterly equity-return (RET), because banks that recently have experienced higher returns have a higher chance of crashes (Chen, Hong, and Stein, 2001), the ratio of price to book value (PB), because overpriced glamour stocks are vulnerable to crashes when you compare them to value stocks, size of the bank (SIZE), assuming that different sizes are prone to different levels of crash risk (Chauhan, Kumar, and Pathak, 2017).

3.6 Descriptive statistics

In table 2 are the descriptive statistics. The mean and median values of the stock price crash risk in a quarter are: negative conditional skewness -2.035 and -0.601, down-to-up volatility -0.017 and -0.015, respectively. Compared to the paper of Chauhan, Kumar, and Pathak (2017), the down-to-up volatility is much lower compared to theirs. The negative conditional skewness on the other hand, is much higher compared to theirs, this is probably due to scaling. The higher values of the negative conditional skewness do not influence the results of the tests, because the scaling is still consistent across the sample. If there is a misestimation in the scaling, the effect cancels itself out. Taken together, scaling is not a problem for this paper. Focusing on the down-to-up volatility, this comparison clearly shows that U.S. banks are less sensitive to stock price crash risk than Indian firms are. A reason for this could be that U.S. banks are more transparent in their reporting and that they have a more equity-based compensation structure for managers. The illiquidity in the sample is different than in the sample of Chauhan, Kumar, and Pathak (2017). This is due to the logarithm to make the values more manageable. The mean and median of illiquidity are 1.997 and 1.948. For robustness, this thesis also includes illiquidity measured without logarithm.

Table 2

Descriptive statistics.

Variable N Mean Median Std Maximum Minimum

DUV 8413 -0.017 -0.015 0.151 0.402 -0.439 NCSKEW 8413 -2.035 -0.601 53.827 177.723 -243.370 Log_Illiquidity 8413 1.997 1.948 1.171 4.362 0.036 ZDV 8592 0.094 0.000 0.193 0.869 0.000 TURN 8592 0.191 0.103 0.250 1.139 0.004 DTURN 8424 0.005 0.000 0.095 0.449 -0.350 RET 8249 -0.006 0.002 0.166 0.485 -0.675 Std 8592 0.024 0.022 0.017 0.144 0.007 Size 8592 5.945 5.659 1.816 11.815 2.248 PB 8540 1.577 1.490 0.689 3.790 0.320

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stock turnover is higher for U.S. banks. The mean and median for stock turnover and zero-day volume are: 0.191 and 0.103, 0.094 and 0.000, respectively. On an average day 19% of the total outstanding stocks is traded. For zero-day volume there is no trading on 9.4% of the days. In table 3 is the correlation matrix. What is surprising, is the nonsignificant positive correlation between down-to-up volatility and negative conditional skewness. Although the nonsignificant positive correlation is weak, these two proxies should measure the same thing. This is apparently not the case, therefore there are additional proxies for robustness.

Table 3

Correlation matrix. The bold values mark a significant level at 5%.

Variable DUV NCSK. Illiq. ZDV TURN DTURN RET Std Size PB

DUV 1 NCSK. 0.016 1 LogIlliq. -0.044 -0.128 1 ZDV -0.055 -0.172 0.560 1 TURN 0.017 0.163 -0.526 -0.317 1 DTURN -0.037 0.011 -0.031 -0.020 0.196 1 RET 0.022 -0.006 -0.134 -0.047 0.028 0.022 1 Std -0.022 0.036 0.198 0.055 -0.136 -0.009 -0.178 1 Size 0.058 0.171 -0.704 -0.426 0.5 0.018 0.051 -0.322 1 PB 0.009 -0.010 -0.213 -0.093 -0.115 0.032 -0.037 -0.119 0.328 1

Conflicting with Chauhan, Kumar, and Pathak (2017), but in line with Chang, Chen, and Zolotoy (2017), are the correlations between the proxies and the liquidity measures. Consistent with the hypothesis, illiquidity and zero-day volume are significantly negatively correlated with the stock price crash risk proxies. More illiquidity decreases the down-to-up volatility and negative conditional skewness, which means that more liquidity increases the down-to-up volatility and negative conditional skewness. More zero-day volume decreases the down-to-up volatility and negative conditional skewness, which means that the higher the number of days when there is no trading (higher illiquidity), the lower is the stock price crash risk. Higher stock turnover (high liquidity) leads to higher stock price crash risk, but is only significant for negative conditional skewness. Based on the three measures of illiquidity, the conclusion is that stock liquidity is positively correlated with stock price crash risk

4. Results

4.1 Stock liquidity and stock price crash risk

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The coefficients of the liquidity measures to capture stock price crash risk are half of the time consistent and significant. The other half of the time, they are not significant, but do have the right sign in front of the coefficient. Illiquidity is significantly negatively correlated with stock price crash risk, but only for negative conditional skewness (0.003) and not for down-to-up volatility (0.857). The reason for this is that negative conditional skewness and down-to-up volatility are not significantly positively correlated in the correlation matrix. Stock turnover is 2.526 and positively correlated with negative conditional skewness, but only significant at (0.125). For down-to-up volatility it is -0.009, so it is not consistent with the expectations. However, it is far from significant (0.318). Zero-day volume is -3.556 and is negatively significantly correlated with negative conditional skewness at a 10% significance level (0.079). For down-to-up volatility, zero-day volume is -0.033 and negatively significantly correlated too (0.002). Taken together, these results support the expectations that stock liquidity is positively correlated with stock price crash risk. This is in line with the conclusion of Chang, Chen, and Zolotoy (2017).

Table 4

Stock liquidity and stock price crash risk. Panel A shows results for NCSKEW and Panel B for DUV. Equation 5 is estimated using panel least squares (PLS). The errors are normal standard errors.

Panel A NCSKEW q+1 Panel B DUV q+1

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The previous paragraph focused more on statistical significance, while this paragraph will focus on the economic significance of the coefficients. There is a difference between statistical and economic significance. A coefficient might be statistically significant; however, the effect might be small in the regression due to the weak economic significance. The difference is that statistical significance focuses on t-tests and p-values whether to reject the null-hypothesis or not with a certain probability, while economic significance looks at the impact and sign of the coefficient. Unfortunately, there is no certain threshold to state which value is economically significant and which is not. It depends on how large the value of the coefficient is compared to the mean of the dependent variable. For illiquidity, the value -1.152 for negative conditional skewness is both statistically and economically significant. The mean of negative conditional skewness is -2.035, hence the value of illiquidity of -1.152 is large enough to have an economically significant impact on it. Also, comparing the value of illiquidity with the rest of the regression, illiquidity turns out to have a big impact on the total regression. For stock turnover, the values for both stock price crash risk proxies are not statistically significant. Although, the value 2.526 would economically affect the mean of negative conditional skewness if it was statistically significant. For zero-day volume, the value -3.556 for negative conditional skewness is more economically significant than the value of -0.033 for down-to-up volatility. The mean of down-to-up volatility is -0.017, hence the value of zero-day volume of -3.556 is large enough to have an economically significant impact on it. However, both values are statistically significant.

The control variables are partially consistent with prior literature. Stock turnover change (DTURN) is significantly negative for down-to-up volatility, which is surprising because it should capture the heterogeneity in investor’s opinion. Stock return (RET) is positively for both proxies, but not significantly. The volatility (STD) is positively associated with stock price crash risk, but only for negative conditional skewness. The control variable negative conditional skewness (NCSKEW) is positive as expected and adjusts for serial correlation from one quarter to another. Just as Chen, Chang, and Zolotoy (2017), firm size (SIZE) is positively correlated with stock price crash risk. Large firms are more monitored by regulators and may have more incentives to hide bad news from investors. Lastly, price-to-book value (PB) is negatively correlated with negative conditional skewness. This can happen when firms offer a high return on assets, which shows stability of firms.

4.2 Robustness tests

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Table 5

Stock liquidity and stock price crash risk. Panel A shows results for NCSKEW and Panel B for DUV. This time, the illiquidity is calculated without logarithm for robustness purposes.

Panel A NCSKEW q+1 Panel B DUV q+1

Illiquidity 0.000*** 0.000* (0.003) (0.054) TURN 2.526 (0.125 -0.009 (0.318) ZDV -3.556* (0.079) -0.033*** (0.002) Time Fixed Effects No No No No No No Adjusted R2 0.716 0.716 0.716 0.006 0.006 0.006

Table 5 shows the results of the regression model without logarithm for illiquidity. Comparing these results with the original equation with logarithm for illiquidity results into quite similar results. However, there are two differences between the equations. The first difference is that illiquidity is for down-to-up volatility, (0.054) against (0.857). The second difference is that the coefficients are smaller than in the original equation. In the equation without a logarithm for illiquidity, the results are economically less significant. The signs in front of the coefficients are still the same, this makes the results quite similar.

To make sure the sample is more robust, this thesis tests the sample for potential heteroskedasticity and serial correlation. To test for heteroskedasticity, I use the Breusch-Pagan-Godfrey test for both risk proxies. This test shows F-statistics of 35.805 and 38.260 with probabilities of (0.000) and (0.000), hence the sample shows signs of heteroskedasticity. Heteroskedasticity means that the variance of the variable changes over time. This makes it hard to calculate accurate estimates with a certain probability. To test for serial correlation, I use the Breusch-Godfrey LM test. This tests shows F-statistics of 874.536 and 3.542 with probabilities of (0.000) and (0.029). Hence, the data shows signs of serial correlation. This means that the current value of variables effects its future value. Therefore, this thesis tests the sample again with HAC-errors and WHITE-errors to mitigate the effects of heteroskedasticity and serial correlation.

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Table 6

Stock liquidity and stock price crash risk. Panel A shows results for NCSKEW and Panel B for DUV. This time, the liquidity measures are calculated using HAC-errors. This error corrects for the heteroskedasticity and serial correlation in the sample.

Panel A NCSKEW q+1 Panel B DUV q+1

Log_Illiquidity -1.268*** 0.000 (0.001) (0.838) TURN -0.144 (0.923) -0.008 (0.394) ZDV -3.654 (0.308) -0.031** (0.037) Time Fixed Effects No No No No No No Adjusted R2 0.694 0.694 0.694 0.006 0.006 0.007

Table 7 shows the results of the regression model with WHITE-errors. Comparing these results with the original regression with normal standard errors results into comparable results. However, there are two differences between the equations. The first difference is that stock turnover has a negative coefficient for negative conditional skewness, 2.526 against -0.144. Both are still not significant. The second difference is that zero-day volume is not significant at 10% anymore for NCSKEW, (0.079) against (0.315). The other coefficients are no different than the original equation with normal errors.

Table 7

Stock liquidity and stock price crash risk. Panel A shows results for NCSKEW and Panel B for DUV. This time, the liquidity measures are calculated using WHITE-errors This error corrects for the heteroskedasticity in the sample.

Panel A NCSKEW q+1 Panel B DUV q+1

Log_Illiquidity -1.268*** 0.000 (0.001) (0.839) TURN -0.144 (0.925) -0.008 (0.378) ZDV -3.654 (0.315) -0.031** (0.025) Time Fixed Effects No No No No No No Adjusted R2 0.694 0.694 0.694 0.006 0.006 0.007

The financial crisis during 2007-2008 could also influence the results. We mitigate this concern by including a dummy for all the quarterly observations during 2007-2008. If there is a financial crisis during a given quarter, the dummy takes the value of 1, and value of 0 if there is no financial crisis during a given quarter. Anticipating for the financial crisis controls for abnormal market volatility that could drive the results.

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including a financial crisis dummy results into the same results for all the stock price crash risk proxies. Looking at the dummy variables, none of them is statistically significant. Another thing to look at is the Adjusted R2, which turns out to be the exact same as in the original model.

Table 8

Stock liquidity and stock price crash risk. Panel A shows results for NCSKEW and Panel B for DUV. This time, the equation includes a dummy for the quarterly observations during 2007-2008.

Panel A NCSKEW q+1 Panel B DUV q+1

Log_Illiquidity -1.140*** 0.000 (0.003) (0.845) TURN 2.529 (0.125) -0.009 (0.318) ZDV -3.506* (0.083) -0.033*** (0.002) Crisis dummy -1.219 (0.143) -1.279 (0.124) -1.251 (0.133) 0.003 (0.510) 0.003 (0.517) 0.003 (0.481) Time Fixed Effects No No No No No No Adjusted R2 0.716 0.716 0.716 0.005 0.005 0.007

Based on all the robustness tests, I can conclude that overall the results are consistent with the hypothesis. Stock liquidity is positively statistically significant for stock price crash risk. These results are consistent with the robustness findings of Chang, Chen, and Zolotoy (2017), who also find a positive relationship between stock liquidity and stock price crash risk after implementing multiple robustness tests.

4.3 Endogeneity

This section tests for potential endogeneity from potential firm-specific time-invariant omitted factors. Although there is a positive relationship between stock liquidity and stock price crash risk, reverse causality can be a driver of this. This means that equation 5 will be estimated with time fixed effects to anticipate both issues.

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Table 9

Stock liquidity and stock price crash risk. Panel A shows results for NCSKEW and Panel B for DUV. We estimate equation 5 using panel least squares (PLS). The coefficients and probabilities are calculated using normal standard errors. This time, they also include fixed time effects to address endogeneity from potential firm-specific time-invariant omitted factors.

Panel A NCSKEW q+1 Panel B DUV q+1

Log_Illiquidity -0.767 0.000 (0.102) (0.892) TURN 8.513*** (0.000) -0.014 (0.235) ZDV -4.873 (0.162) -0.102*** (0.000) Time Fixed Effects

Yes Yes Yes Yes Yes Yes

Adjusted R2 0.794 0.794 0.794 0.004 0.026 0.029

Summarizing the above results shows that the relationship between stock liquidity and stock price crash risk is a positive one. The results are robust, because this thesis corrects for the spread of liquidity via a logarithm, heteroskedasticity via WHITE- and HAC-errors, and the financial crisis via a dummy variable. Using fixed time effects to anticipate for potential endogeneity and reverse causality, confirms the positive relationship again.

4.4 Empirical analysis: which channel matters?

This section will discuss the causes of the positive relationship between stock liquidity and stock price crash risk in an empirical way.

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compensation increase stock price crash risk. Equity-based compensation should lead to more alignment between principals and agents, but instead it leads to more stock price crash risk. Especially in the U.S., where managers’ compensation is equity based, they also have an incentive to hide bad news for their own benefit. Firms with a higher level of transient institutional ownership experience a stronger effect of stock liquidity on stock price crash risk, because crash weeks are characterized by more bad earnings releases than non-crash weeks (Chang, Cheng, and Zolotoy, 2017). Higher liquidity is positively correlated with the degree of unexpected bad earnings release. This is in line with the transient investor channel, because bad news accumulates until it is realized all together and stock price crash risk increases.

As already stating in the literature section, stock liquidity is the ability to trade a large quantity of stocks at low costs within a short framework of time, and with minimal or no price impact (Chang, Chen, and Zolotoy, 2017). The ability to trade a large quantity of stocks at low costs within a short-framework of time transforms stock liquidity into a dangerous leverage tool for the U.S. banks during 2001-2012, because of the positive relationship. Where blockholders seem to stay calm during a downturn of the market, transient investors panic more. This panicking reaction leads to an enormous selling of their stocks. Combining this irrational investor behavior with the easiness and low costs of selling their stocks (high stock liquidity), makes them sell their stocks faster than they would do when it would be harder and more expensive to sell their stocks (low stock liquidity). This extreme selling of their stocks is consistent with the positive relationship of stock liquidity and abnormal institutional selling during periods of crash (Chang, Cheng, and Zolotoy, 2017).

5. Conclusion and limitations

This thesis examines the relationship between stock liquidity and stock price crash risk for U.S. banks during 2001-2012. After analyzing the results, this research finds a positive relationship between stock liquidity and stock price crash risk. The results are robust to different measurements of stock price crash risk variables, different proxies of stock liquidity, different errors to correct for heteroskedasticity and serial correlation, and market volatility driven by the financial crisis. Furthermore, this research uses fixed time effects to deal with endogeneity and causality.

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to the expectations or to hide bad news and let it eventually accumulate until it crashes. The barrier to sell stocks is low when stock liquidity is high. Stock liquidity becomes a leverage tool for panicking transient investors. This panicking is driven by bad news accumulation, bad news hiding, and the power of the market investors to strengthen the decrease of the stock price with their selling. Investors take a risk by investing their money into a company. The return they get is the compensation for the risk that they are willing to bear. Stock liquidity as an indicator for stock price crash risk might help them with making better allocation decisions. A limitation of this research is the fact that it uses the empirical results of Chang, Chen, and Zolotoy (2017) to determine which channel matters. Interesting would be to deeper investigate the different types of investors and their relationship with stock price crash risk. Another limitation is that this thesis only uses fixed time effects to correct for the reverse causality. There are probably more ways to test this.

Despite the above stated limitations, stock liquidity seems to be a promising indicator of stock price crash risk. However, more research is needed before completely relying on stock liquidity as an indicator of stock price crash risk. More control variables should be included in regression models of future research, i.e. CEO compensation structure, CEO age, number of analysts following, transitional ownership, and blockholder ownership. Besides all the numbers, the role of using common sense should also not be underestimated. Deviations from market fundamental values are evidence of irrational behavior. For example, sentiment, driven by information asymmetry. A combination of stock liquidity as an indicator for stock price crash risk and using common sense about the stock market would benefit investors.

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