Global existence and stability of temporal periodic solution to non-isentropic compressible Euler equations with a source term

1.   Introduction

CEO turnover is a hot topic in corporate governance (Clayton et al., 2005). Dismissing the CEO is an effective way to rebuild the company's reputation and restore the shareholders confidence (Jensen & Meckling, 1976). This study was aimed to investigate the relationship between various risks and forced CEO turnover.

According to Andreou et al. (2017), crash risk is mainly derived from the managers hiding bad news for their own interest rather than releasing it in a timely manner. Once the accumulated bad news reaches the limit point, all of the bad news will flow to the market in a very short time, leading to stock price crashes (Hutton et al., 2009). The risk of stock price collapse not only directly leads to substantial damage to existing shareholders' wealth, but it also damages the company's performance due to the subsequent financial difficulties and the loss of customers and suppliers.

Risk management has been an important issue since the 2008 financial crisis. Bushman et al. (2010) found that idiosyncratic risk increases CEO turnover and systematic risk reduces the likelihood of CEO turnover in the United States of America. We evaluate the relationship under Chinese circumstances. The root of idiosyncratic risk is the uncertainty of information quality (Kapadia, 2007; Michael et al., 2010). Improving the information quality will decrease the idiosyncratic risk, which decreases information asymmetry and helps the board to evaluate the CEO's talent accurately.

We selected Chinese A-share listed companies from 2010 to 2019 as samples to investigate the impact of risks on CEO turnover. The results show that there is a positive relationship between crash risks and CEO turnover. The idiosyncratic risk will increase the likelihood of forced CEO turnover. In addition, the relationship is more significant in non-SOEs than in SOEs. The board of directors should consider the risk information when evaluating the CEO's talent.

1.1.   Contributions

This study analyzes the impact of different risks on forced CEO turnover under Chinese circumstances, so it has the following contributions. Firstly, existing studies focus on the determinants of the crash risk, and few studies are concerned with the consequences of stock price crash risk (Habib et al., 2018). This study investigates the impact of collapse risk on CEO turnover to provide a new perspective on the crash risks. Besides, crash risks are a non-performance indicator that can be used to evaluate CEOs' talent. Secondly, many studies analyze the factors influencing idiosyncratic risk, such as the capital market environment, investment efficiency and corporate performance. This study connects the CEO turnover, systematic risk and idiosyncratic risk together, thus connecting the internal and external economic factors of the company. Thirdly, because of the different governance mechanisms of SOEs and non-SOEs, this study investigates the relationship between CEO turnover and corporate risk under different ownerships. SOEs take up the largest part in the Chinese economy, and the goal is totally different from that of non-SOEs, which is necessary to distinguish them.

The remainder of the paper is organized as follows. Section 2 presents the literature review and the hypothesis development is described in Section 3. Section 4 describes the model, data and variables. We present the results and discuss the robustness tests in Sections 5 and 6. In Section 7, we present the conclusions.

2.   Literature review

2.1.   CEO turnover

The CEO is the core of the management team; they take responsibility for the decision-making on major issues, including organizational strategy, risk management and social responsibility. Effective corporate governance mechanisms can evaluate a CEO's talent properly and replace the ineffective one. Forced CEO turnover is a mechanism for punishing the CEO to solve agency problems (Chang & Wong, 2009). Previous studies have investigated the factors and impact of CEO turnover (Clayton et al., 2005; Wiersema & Zhang, 2013).

A large number of studies were aimed to discover that corporate performance is the key determinant of CEO turnover (Fisman et al., 2014; Jenter & Kanaan, 2015; Jenter & Lewellen, 2021; Kato & Long, 2006). CEOs are fired after bad firm performance relative to the industry average (Fee et al., 2018; Jenter & Kanaan, 2015). The main responsibility of the board is to employ, dismiss, supervise and compensate management to maximize the shareholders' value. The greater independence of the board tends to make discipline more rigorous for CEOs (Guo & Masulis, 2015). A CEO with higher power will reduce the likelihood of a turnover (Pi & Lowe, 2009). The legal system and economic environment will affect the corporate governance and further affect the stability of CEOs (Jenter & Kanaan, 2015). Lawsuits are followed by increased CEO turnover (Aharony et al., 2015). The media reports, especially the negative reports, will put pressure on the enterprise. In order to restore the company's reputation, the corporation usually replaces the CEO (Farrell & Whidbee, 2002). Wiersema and Zhang (2013) found that negative ratings from securities analysts accelerate the CEO dismissal decision. This is because the negative reports affect the board's judgment and evaluation of the CEO's ability.

Previous studies have indicated a positive effect after forced CEO turnover (Bernard et al., 2016). CEO turnovers improve corporation performance (Kato & Long, 2006). Firms experience increased return on assets (ROA) following CEO turnovers (Huson et al., 2004).

In China, the government plays an important role in resource allocation, which can significantly influence the firm (Li et al., 2008). A CEO with political connections is less likely to be fired (Pi & Lowe, 2009). There are great differences between SOEs and Non-SOEs (Chang & Wong, 2009).

2.2.   Crash risk

Many studies have analyzed the factors influencing stock price crashes (Kim & Zhang, 2016). Few studies have investigated the consequences of a stock price crash. Based on the agency theory, managers choose to hide bad news because of self-interest, and shareholders cannot capture the real situation of the company. Once bad news cannot be hidden, stock prices will face a significant drop. The nature of a crash risk is information asymmetry (Bleck, 2007). Overconfident CEOs are more likely to experience a stock price crash (Kim et al., 2016). Managers can use various approaches to hoard bad news, such as earnings manipulation and tax avoidance, which worsen the quality of information and increase the risk of stock price crashes (Chen et al., 2017). Corporate governance has a significant influence on crash risk (Chen et al., 2017). Andreou et al. (2016) showed that companies can reduce the likelihood of a crash by increasing the proportion of independent directors. External inspection also has a significant influence on crash risk. Auditors can find and prevent bad-news hoarding activities, thus reducing the risk of a collapse (Callen & Fang, 2015; Robin & Zhang, 2015). Companies can decrease the crash risk by improving social trust (Callen & Fang, 2015; Li et al., 2017).

The United States of America dominates the research on crash risk. In China, many references indicate that, if a firm has a connection with the government, it will face less crash risk (Li & Chan, 2016). Xu et al. (2014) reported that managers with excess rewards tend to hold bad news in SOEs. Executives fear penalties for releasing negative news related to politically sensitive events, which increases the crash risk (Lee & Wang, 2016).

2.3.   Idiosyncratic risk and systematic risk

Traditional financial theory differentiates risks into systematic risk and idiosyncratic risk, which requires the assumption that the capital market is efficient, investors are rational and information is complete (Bernile, 2018). The systematic risk is related to the whole market factors, which companies cannot control or eliminate from the market. It is also called "market risk" or "undiversifiable risk". Patton and Verardo (2012) discovered the impact of the earnings announcement effect on systematic risk. Unsystematic risk is controllable by the firm's internal factors. Investors can completely disperse the risk through the use of a diversified portfolio. It is also named as a "specific risk", "diversifiable risk" or "idiosyncratic risk". Idiosyncratic risk reflects microeconomic factors rather than macroeconomic factors. Idiosyncratic risks are important because the CEO can control and constrain them (Sassen et al., 2016). Besides, they represent 80% of the total risks (Bansal & Clelland, 2004). Idiosyncratic risks differ across firms and countries (Bartram et al., 2012; Bartram et al., 2011; Brown & Kapadia, 2007; Morck et al., 2000). Li (2004) showed that idiosyncratic risk has increased significantly in emerging markets.

A large number of studies have investigated the idiosyncratic risk based on the CEO's characteristics, earning management, information quality and expected return dimensions (Fu, 2009; Goyal & Santa-Clara, 2003). Few studies have investigated the causes of idiosyncratic volatility from the corporate governance perspective.

Upper echelons theory argues that a manager's risk attitude is affected by their own characteristics, including their experience (Mishra, 2020) and socioeconomic background (Gormley & Matsa, 2016). Dealing with the firm's specific risk is an important responsibility of management. Adams (2005) showed that CEOs with more power will lead to higher risks. Liu (2016) found a negative relationship between CEOs' ability and idiosyncratic risk.

Firm characteristics such as ownership (Panousi & Papanikolaou, 2012), firm age (Huang et al., 2014) and leverage level (Gerlach et al., 2015) can affect the idiosyncratic risk. Ownership concentration is positively associated with idiosyncratic risk (Abu-Ghunmi et al., 2015; Nguyen, 2011). A company's performance and size has a negative influence on idiosyncratic risk (Bali & Cakici, 2008; Irvine & Pontiff, 2009). Effective corporate governance also reduces the idiosyncratic risk (Ferreira & Laux, 2007).

"The idiosyncratic volatility puzzle" refers to the positive, negative and uncorrelated relationships between expected return and idiosyncratic risk. Some scholars believe that it is irrelevant because investors can eliminate idiosyncratic risk through the use of investment portfolios. Only the systematic risk affects the expected return in a perfect capital market (Bali & Cakici, 2008). Some scholars who hold the positive relationship believe that investors expect higher return compensation for the idiosyncratic risk. However, it is impossible to achieve a completely diversified portfolio due to the restrictions on the investors' age, income level, education level and other factors (Malkiel, 2002; Xu & Malkiel, 2003). Other studies revealed a negative relationship between idiosyncratic risks and expect return (Ang et al., 2008; Hodrick, 2008; Huang, 2010).

A stream of research revealed that idiosyncratic risk has informational effects (Campbell et al., 2001; Campbell & Taksler, 2003; Ferreira & Laux, 2007). Many researchers have documented that a high information quality reduces the idiosyncratic risk (Bartram et al., 2011; Rajgopal & Venkatachalam, 2011).

3.   Hypothesis development

3.1.   Analyzing the impact of crash risk on forced CEO turnover

CEOs are agents who have relative information advantages based on agency theory (Jensen & Meckling, 1976). The existence of information asymmetries between managers and stakeholders results in crash risk (Benmelech et al., 2010; Hutton et al., 2009). In order to seek private interests, CEOs cover up bad news by using various approaches, such as the implementation of earnings management, tax evasion, related party transactions, and non-robust accounting policies (Chen et al., 2017). Directors obtain less information than CEOs, and the cost of evaluating the reliability of information is very high, which reduces the directors' supervision efficiency (Masulis & Mobbs, 2011; Raheja, 2005).When the hidden bad news accumulates to a certain point, a stock price crash occurs. The occurrence of a stock price crash is an indicator of the CEO's opportunistic behavior (Hutton et al., 2009).

A stock price crash is a major negative event that seriously damages the company's reputation. Reputation is an asset that can generate future cash flow, especially in a market with incomplete information (Kreps & Wilson, 1982). Reputation can reduce the cost of capital (Beatty & Ritter, 1986) and help companies attract long-term investors (Milgrom & Roberts, 1986) and obtain excess returns. Besides, the damage to a company's reputation leads to stock price decline and a significant increase in the cost of financing (Kravet & Shevlin, 2010). Therefore, once a company's reputation is damaged, the board will take various measures to restore its reputation (Suchman, 1995). The company will give an explanation after the scandal is exposed in order to repair the relationship with investors (Westphal & Deephouse, 2011). Dismissing the CEO is the most effective way to rebuild investors' confidence (Karpoff, 2008).

Given the extensive damage to the firm value brought about by stock price crashes, the low ability of executives should be terminated in order to protect the shareholders. Crash risk can serve as an indicator of the executives' inability. To sum up, after the collapse of a company's stock price, the board of directors is likely to make a decision to dismiss the CEO. Therefore, the author puts forward the first research hypothesis.

Hypothesis 1 (H1): the higher the crash risk, the higher the possibility of a CEO turnover in the future.

3.2.   Analyzing the impact of risks on forced CEO turnover

Risk management has been an important issue since the 2008 financial crisis. Bushman et al. (2010) find that, in the United States of America, idiosyncratic risk increases the likelihood of a CEO turnover and systematic risk reduces the CEO turnover. This study evaluated the relationships under Chinese circumstances.

We believe that idiosyncratic risk can capture factors of return variability, which is related to the CEO's talent and is under the CEO's control. Systematic risk reflects information that is unrelated to the CEO's talent and outside of the CEO's control. One of the important roles of the board is to properly evaluate the CEO's ability and make decisions regarding firing and retaining. Firing the inability CEO is a mechanism to protect the interests of shareholders (Jensen & Meckling, 1976). Firm performance is an important indicator for evaluating the CEO's talent, which is significantly affected by volatility. If volatility is driven primarily by factors within the firm, which we call the idiosyncratic risk, the board will replace low-talent incumbents. If the volatility is unrelated to the CEO's talent and outside of the CEO's control, which is systematic risk, the board will find it difficult to assess the CEO's talent and make a decision regarding whether to fire. Extensive studies have shown that poor performance leads to forced CEO turnover. This study complements existing literature by investigating the impact of risks on forced CEO turnover.

From the perspective of investment, there are two dimensions to investigate.

Firm investment decisions are related to the idiosyncratic risk rather than systematic risk (Datta et al., 2017). A large number of studies revealed that CEOs are reluctant to take on risky projects due to reputation costs and turnover threat (Goel & Thakor, 2008; Panousi & Papanikolaou, 2012). This is especially true for CEOs who have a risk-aversion attitude regarding idiosyncratic volatility and investment (Angeletos, 2007; Panousi & Papanikolaou, 2012). Therefore, CEOs tend to reduce firm risk to decrease the probability of being fired (Chakraborty, 2007; Peters & Wagner, 2014). Other scholars believe that boards might constantly encourage excessive risk-taking to maximize the value if a company has poor performance (Boyd & De Nicolo, 2005). The pressure from the board encourages CEOs to seek higher returns and risky projects to improve performance and secure their position (Zwiebel, 1995). CEOs have to change their risk-aversion attitude to risk seek to improve performance (John et al., 2008).

3.2.1.   Information quality

The root of idiosyncratic risk is the uncertainty of information quality (Brandt et al., 2010; Brown & Kapadia, 2007). Jin and Myers (2006) found that firms possessing less information transparency exhibit high idiosyncratic risks. The relationship between information quality and idiosyncratic risk is negative, especially in emerging markets. Chen and Petkova (2010) discovered that higher information quality benefits shareholders because it decreases uncertainty and reduces information asymmetry, which allows the board to evaluate the CEO's talent accurately (Zhang, 2016).

Based on the above analysis, we put forward the second and third hypothesis:

Hypothesis 2 (H2): Idiosyncratic risk increases the likelihood of forced CEO turnover.

As previously said, systematic risk is the type of risk that the CEO cannot control; therefore, we put forward the third hypothesis:

Hypothesis 3 (H3): The relationship between systematic risk and CEO turnover is unrelated.

3.3.   Relationship between CEO turnover and risks in SOE and non-SOE

Different ownerships have different governance mechanisms, and thus different attitudes regarding risks. In China, the government plays an important role in economic affairs and resource allocation, and state-owned enterprises occupy a dominant position in the market (Child & Tse, 2001).

They have the following differences. First, due to lack of owners of the SOEs, SOEs face less litigation risk. Besides, SOEs have strong political connections. Luo et al. (2016) discovered that, in China, political connections can reduce crash risk. CEOs in SOEs tend to pursue future official careers. They have the incentives to release bad news at normal times and avoid crash events in the near future, thereby safeguarding the official careers of politicians. Second, the government controls the governance of SOEs rather than markets. The government assesses business performance, supervises business behavior and issues governance policies. The executives are appointed and dismissed by the government, which is a political promotion tactic; they are unlikely to be dismissed. Non-SOEs are willing to provide liability insurance for senior managers so as to enhance the attractiveness of the company and win the battle for talent. Third, SOEs are supported by the government and enjoy various preferential policies, such as government assistance, bank credits and market access policies (Chung & Wynn, 2008; Dewatripont & Maskin, 1995; Preuss & Königsgruber, 2021).

The goals of SOEs are to provide public service and fiscal stability, and to perform sector regulation and employment creation rather than value maximization (Wang et al., 2008). In addition, SOEs have a political connection with the government, meaning that there is less risk compared with non-SOEs. They have information advantages that can help them to make proper strategies and thus reduce policy uncertainty (Alon et al., 2014). SOEs can obtain favorable loans and subsidies easily to reduce the risk of capital shortage (Haß et al., 2017). Therefore, managers in SOEs face fewer risks than those in non-SOEs. We put forward the following fourth and the fifth hypotheses:

Hypothesis 4(H4): The relationship between crash risk and CEO turnover is more significant in non-SOEs than in SOEs.

Hypothesis 5(H5): The relationship between idiosyncratic risk and CEO turnover is more significant in non-SOEs than in SOEs.

4.   Sample, variables, and descriptive statistics

4.1.   Data sources and sample selection

In this study, Chinese enterprises listed in the Shanghai Stock Exchange and Shenzhen Stock Exchange from 2010 to 2019 were applied as initial samples. The sample period began in 2010 because of the financial crisis that occurred in 2008, which had a significant influence on the stock market. All the data are from the China Stock Market and Accounting Research (CSMAR) database, except for the forced CEO turnover data, which were manually screened from their resumes. According to the following criteria, we excluded (1) firms flagged a Special Treatment (ST) or *ST, (2) financial services firms, because of their industry uniqueness, (3) firms with fewer than 30 trading weeks and (4) the companies whose CEO's tenure was less than one year and there was incomplete information on the key variables. To avoid outliers, we winsorized at the 1% level in both tails. In addition, we controlled for years and industries' fixed effects. Finally, we obtained 15,293 firm-year observations.

4.2.   Model

We examined whether various risks affect the likelihood of forced CEO turnover by using the linear probability model (LPM). LPM simplifies the interpretation of coefficients, although it may produce fitted values outside of the 0 to 1 range (Wooldridge, 2002). According to Chyz and Gaertner (2017), the LPM is suitable for test. In the robustness tests, we used the logit model shown in Table 9.

All of the above variables are explained in Table 3. Industry (I) and year (T) fixed effects (industry and year dummies) were included in order to remove the effects of macroeconomic and cross-sectional effects. If the coefficient of β1 is positive and significant, Hypotheses 1 and 2 are supported, showing the probability of forced CEO turnover increase with the crash risk and idiosyncratic risk.

4.3.   Key variables

4.3.1.   CEO turnover

The dummy variable TO_FORCE was equal to 1 for turnover events in the year t, and 0 otherwise (Cao et al., 2017). TO_FORCE was measured during the t period, while all other variables were measured during the t−1 period (Cao et al., 2017).

China Securities Regulatory Commission has required that enterprises should disclose the reasons for the CEO turnover in detail since 2000. Previous studies generally divided CEO turnover into normal and forced turnover (Chang & Wong, 2009). A normal CEO turnover refers to the reasons that are not related to management behavior, such as retirement, health condition and expiration term. There is no consistent definition of forced turnover, so we mainly followed Cao et al. (2017) to evaluate forced CEO turnover.

There were 3,137 CEO turnover events during the sample period. In Table 1, there are 12 reasons for CEO turnover, which were provided by the CSMAR database. Change of job takes up the highest percentage, accounting for 31.94% of the total turnover. The second one is the contract expiration, which represented 28.91%; the third reason comprises personal reasons (13.01%). Only 0.92% of CEO turnovers fell in the dismissal category. We reclassified the reasons for job changes, resignations, personal reasons and reasons not given (Firth et al., 2006). Other turnovers were classified as normal, with one exception: if the CEO is less than 60 years old and the stated reason is retirement, we classified this turnover as forced.

We tracked the destinations of departing CEOs using the resume information provided by the CSMAR database. For example, the reason for a job change can be divided into force or voluntary turnover. If a departing CEO moved to a position that was better than their previous position, then we classified it as non-forced (Huson et al., 2004). Table 2 summarizes the reasons for CEO turnovers and the corresponding frequency. After reexamining 1,836 cases by searching through CEO resumes, 649 cases were determined to be not forced. We can see that 417 cases resulted in the CEO remaining as chairman or vice chairman, and 232 cases resulted in promotion (210 CEOs promoted as chairman or vice chairman; 22 CEOs became government officials). We classified the remaining 385 cases as forced turnover. These included 243 CEOs who accepted new positions ranked lower than CEO positions; there were 944 cases without any traceable information. In conclusion, there were 1,898 normal turnover events, which accounted for 60.50% of the total, and 417 cases of forced turnover (13.29%). Because we investigated the impact of risks on forced CEO turnover, we ignored voluntary turnovers (Chakraborty et al., 2007).

4.3.2.   Idiosyncratic risk and systematic risk

According to the capital asset pricing model (CAPM), we get the coefficient $\left(\beta |i\right)$ and residual standard deviation $\left(\varepsilon |i, t\right)$. Following Bernile et al. (2018), idiosyncratic risk can be calculated as the square root of 252 multiplied by the standard deviation of daily excess stock returns. The total risk equals the square root of 252 multiplied by the standard deviation of daily stock returns.

where ${R}_{i, d}$ is the daily return of the firm i and ${R}_{m, d}$ is the daily value-weighted market return.

4.3.3.   Crash risk

According to extensive literature, two methods are used to measure crash risk (Dumitrescu & Zakriya, 2021; Habib et al., 2018; Li & Zeng, 2019). We obtained the following measures from the CSMAR database.

Firstly, we used the weekly return in the following expanded market model regression:

where ${R}_{i, j}$ is the return that includes the reinvestment with cash dividends for the firm i in the week j. ${R}_{m, j}$ is the average return of all A-shares weighted by the market value in the week j. The firm-specific weekly return can be obtained by using Equation (7) (Hutton et al., 2009).

Then, the negative conditional return skewness (NCSKEW) and down-to-up volatility measure (DUVOL) are constructed based on ${w}_{i, j}$.

n represents the number of weekly returns during the year t.

The "up" weeks $\left(n|u\right)$ and "down" weeks $\left(n|d\right)$ represent the number of weeks that the idiosyncratic return ${w}_{i, j}$ is respectively larger or smaller than the average annual return ${w}_{i, t}$.

A higher value of NCSKEW and DUVOL indicates a greater crash risk. DUVOL is better, as it is less likely to be overly influenced by extreme weekly returns (An et al., 2015).

4.3.4.   Control variables

We added the set of control variables included in the model used by Chyz and Gaertner (2017), which captures the variables shown in existing literature (Cao et al., 2017; Chyz & Gaertner, 2017; Deng et al., 2019; Guo & Masulis, 2015; Tran et al., 2016; Zhang, 2016). We controlled the following variables in the model: SIGMA, RET, MB, LEV, ROA, SIZE, DTURN, TENURE, STATE, FIRMAGE, DUAL and MA_SCORE. In addition, we also controlled the industries' and years' dummy variables. Details of the variable definitions are shown in Table 3.

5.   Empirical results

5.1.   Descriptive statistics

Table 4 presents the descriptive results, including the mean, standard deviation, minimum, median and maximum dimensions. The means of TOTAL_RISK, IDIOSYNCTRIC_RISK and SYSTEMATIC_RISK were 1.929, 1.707 and 5.684, respectively. The average values of NCSKEW and DUVOL were -0.293 and -0.2, respectively, which are generally consistent with previous studies.

This table reports descriptive statistics for full samples. TO_FORCE is a dummy variable that equals 1 when a CEO is fired, and 0 otherwise. The crash risk was measured by using NCSKEW and DUVOL. Details of the variable definitions are provided in Table 3.

5.2.   Correlations

Table 5 presents the Pearson correlations of the main variables. Consistent with H1, we found that the crash risk indicators (both NCSKEW and DUVOL) were positive and significantly correlated with forced CEO turnover. It is suggested that crash risk is an important indicator that needs to be considered in the CEO's evaluation. Total risk and idiosyncratic risk were positively and significantly correlated with forced CEO turnover, which is consistent with H2. Systematic risk had a negative and insignificant relationship with forced CEO turnover.

This table reports the Pearson correlation coefficients for the full sample, with p-values reported below each correlation. Details of the variables definitions are shown in Table 3.

5.3.   Regression results

Columns (1) and (2) in Table 6 show that the coefficients were positive and significant at 1%, which supports H1. The results for TOTAL_RISK and IDIOSYNCRATIC_RISK shown in Columns (3) and (4) are positive and significant at 1%, which is consistent with H2. The systematic risk presented in Column (5) had no impact on forced CEO turnover, which supports H3.

This table presents the results for the main tests, which examined the effects of risks on forced CEO turnover. The regression coefficients are reported above, while the standard errors are reported below. Note that the single, double and triple asterisks denote statistical significance at the 10%, 5% and 1% levels, respectively, for examining H1, H2 and H3. The results in this table were obtained by applying an LPM with robust standard errors to control firm-level clustering. Details of the variable definitions are shown in Table 3.

Table 7 presents the results for non-SOEs, and Table 8 describes the relationships between forced CEO turnover and various risks in SOEs. We can see that crash risk, total risk and idiosyncratic risk have a more significant and positive relationship with forced CEO turnover in non-SOEs than SOEs, which supports H4 and H5.

This table reports the results for the effects of risks on forced CEO turnover in non-SOEs. The regression coefficients are reported above, while the standard errors are reported below. The single, double and triple asterisks denote statistical significance at the 10%, 5% and 1% levels, respectively, for examining H4 and H5. The results in this table were obtained by applying an LPM (OLS) with robust standard errors to control for firm-level clustering. Details of the variable definitions are shown in Table 3.

This table reports the results for the effects of risks on forced CEO turnover in SOEs. The regression coefficients are reported above, while the standard errors are reported below. The single, double and triple asterisks denote statistical significance at the 10%, 5% and 1% levels, respectively, for examining H4 and H5. The results in this table were obtained by applying an LPM (OLS) with robust standard errors to control for firm-level clustering. Details of the variable definitions are shown in Table 3.

The R-squared realizations are low in Table 6, suggesting limited explanatory power. However, according to Brickley (2003), a low R is very common in the CEO turnover literature.

6.   Robustness

In this section, we describe a series of additional tests that were performed to ensure the robustness of the results in Table 6.

6.1.   Falsification tests

In accordance with Chyz and Gaertner (2017), Table 9 reports the falsification tests to support the primary results in Table 6. We reassessed the main test by replacing the forced CEO replacement with normal CEO turnover (L_UNFORCE). Table 2 shows the 1989 normal CEO turnover events. Normal CEO departures are unrelated to the deliberate action of the board (Fee et al., 2013). The coefficient between risks and turnover is negative and insignificant, which supports the H1, H2 and H3. This is because risks are not positively related to non-forced turnover.

6.2.   Logit model

We also tested the relationship between various risks and forced CEO turnover by using a logit model for robustness, which is consistent with the LPM. This paper findings are in line with Bushman et al. (2010), who believes that idiosyncratic risk increases the probability of CEO turnover.

This table shows the results of applying the Logit model for robustness tests.

6.3.   Changes in risks following forced turnover

In accordance with Chyz and Gaertner (2017), we also conducted an analysis of the impact of forced CEO turnover on future risks (Table 11). If high risks played an important role in the CEOs firing, we expected these trends to be reversed after turnover, corresponding to a negative relationship between forced CEO turnover and future risks. Table 11 shows the results, the negative relationship between forced CEO turnover and future crash risks, although the results are not significant. Total risks and idiosyncratic risks also have negative influences after CEO turnover, suggesting that these firms that have experienced a CEO turnover appeared to decrease risks.

This table describes the impact of forced CEO turnover on future risks.

6.4.   Pay-for-performance sensitivity and CEO turnover

In accordance with Bushman (2010), we also conducted an analysis of the pay-for-performance sensitivity (PPS) and CEO turnover (Table 12). The results show that the PPS increased for idiosyncratic risk and had no impact on systematic risk, which is consistent with the information content on the performance with respect to the CEO's talent.

6.5.   Adding other control variables

Because the director's responsibility is to appoint and evaluate the CEO's talent (Bushman et al., 2010), we also controlled the Board (i.e., natural logarithm of the total number of directors on the board) and Indep variables (i.e., ratio of the number of independent directors to the total number of directors on the board). The results shown in Table 13 are still consistent.

6.6.   CEO turnover and risk-taking

As was done by Chakraborty et al. (2007), we determined the negative relationship between termination risk and risk-taking. We also evaluated it (Table 14). In accordance with (Zhou et al., 2022), Risk 1 is defined as the volatility of a firm's ROA over 3-year overlapping periods. Risk 2 is the difference between maximum and minimum ROAs over 3-year overlapping periods. Columns (1) and (2) show the full sample results, Columns (3) and (4) represent the relationship in SOEs and Columns (5) and (6) present the relationship in non-SOEs. The results show that the firms that experienced CEO turnover tended to reduce risk-taking, which is also significant in non-SOEs.

7.   Conclusions

Previous studies have extensively investigated the factors that lead to CEO turnover. Few studies analyzed the impact of risks on forced CEO turnover. This work fills this gap and investigated the relationship using Chinese data. We found that the crash risk significantly increases the likelihood of forced CEO turnover. We also discovered that the total risk and idiosyncratic risk increase the possibility of forced CEO turnover, while the systematic risk has no effect on forced CEO turnover. The impact of risks on forced CEO turnover is more significant in non-SOEs than in SOEs. These findings can practically influence the boards, which can help them to evaluate the top managers' ability and competence.

Conflict of interest

The author declares no conflicts of interest in this research.