Causal impact of stock price crash risk on cost of equity: Evidence from Chinese markets

Zonon, Babatounde Ifred Paterne; Wang, Xianzhi; Chen, Chuang; Bouraima, Mouhamed Bayane Article Causal impact of stock price crash risk on cost of equity: Evidence from Chinese markets Economies Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Zonon, Babatounde Ifred Paterne; Wang, Xianzhi; Chen, Chuang; Bouraima, Mouhamed Bayane (2025) : Causal impact of stock price crash risk on cost of equity: Evidence from Chinese markets, Economies, ISSN 2227-7099, MDPI, Basel, Vol. 13, Iss. 6, pp. 1-24, https://doi.org/10.3390/economies13060158 This Version is available at: https://hdl.handle.net/10419/329438 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ Academic Editor: Robert Czudaj Received: 1 May 2025 Revised: 27 May 2025 Accepted: 28 May 2025 Published: 2 June 2025 Citation: Zonon, B. I. P., Wang, X., Chen, C., & Bouraima, M. B. (2025). Causal Impact of Stock Price Crash Risk on Cost of Equity: Evidence from Chinese Markets. Economies,13(6), 158. https://doi.org/10.3390/ economies13060158 Copyright: © 2025 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/ licenses/by/4.0/). Article Causal Impact of Stock Price Crash Risk on Cost of Equity: Evidence from Chinese Markets Babatounde Ifred Paterne Zonon 1,* , Xianzhi Wang 2, Chuang Chen 3and Mouhamed Bayane Bouraima 4 1School of Economics and Management, Southwest Jiaotong University, Chengdu 610031, China 2Faculty of Arts and Social Sciences, Hong Kong Baptist University, Hong Kong SAR 999077, China; [email protected] 3School of Business, University of New South Wales, Sydney, NSW 2052, Australia; [email protected] 4 Sichuan College of Architectural Technology, Deyang 618000, China; [email protected] *Correspondence: [email protected] Abstract: This study investigates the causal impact of stock price crash risk on the cost of equity (COE) in China’s segmented Aand B-share markets with an emphasis on ownership structures and market regimes. Employing a bootstrap panel Granger causality framework, Markov-switching dynamic regression, and panel threshold regression models, the analysis reveals that heightened crash risk significantly increases COE, with the effects being more pronounced for A-shares because of domestic investors’ heightened risk sensitivity. This relationship further intensifies in bull markets, where investor optimism amplifies downside risk perceptions. Ownership segmentation plays a critical role, as foreign investors in B-shares exhibit weaker reliance on firm-level valuation metrics, favoring broader risk-diversification strategies. These findings offer actionable insights into corporate risk management, investor decision making, and policy formulation in segmented and emerging equity markets. Keywords: cost of equity; stock price crash risk; causality; bull market; bear market JEL Classification: G10; G15; G32 1. Introduction The relationship between stock price crash risk and the cost of equity (COE) has garnered substantial attention in the finance literature because of its significant implications for investment decisions, corporate governance, and market stability. Stock price crash risk, characterized by abrupt and significant declines in stock prices, typically arises from delayed disclosures and accumulation of negative information within firms. Recent studies highlight various determinants of crash risk, including managerial opportunism, opaque financial reporting, governance mechanisms, and external factors such as investor sentiment, carbon risks, operating leverage, and stock liquidity (Jin & Myers,2006;Hutton et al.,2009;Piotroski et al.,2014;An et al.,2020;Ren et al.,2023;Qian et al.,2025;Bose et al., 2024;Zhu & Zang,2024;Nguyen et al.,2025). Despite extensive research, most studies have utilized correlation-based methodologies, limiting their capacity to establish clear causal links between crash risks and COE. This critical gap motivates the current study, which rigorously investigates the causal relationships linking stock price crash risk to COE, explicitly differentiates between market-wide and firm-specific sources, and explores investor responses within segmented markets through advanced econometric techniques. Economies 2025,13, 158 https://doi.org/10.3390/economies13060158 Economies 2025,13, 158 2 of 24 Investor sensitivity to crash risk depends significantly on managerial transparency and the governance structure. In environments with high information asymmetry, investors face substantial uncertainty regarding firm-specific risks, leading to higher risk premiums and COE (Diamond & Verrecchia,1991;Chen & Chen,2024). Recent studies suggest that equity-based compensation for outside directors reduces crash risk by mitigating financial misreporting and bad news hoarding (Qian et al.,2025). Additionally, external factors, including irrational investor sentiment and emotional panic, exacerbate stock price volatility and crash risk (Fan & Gao,2024;Saleem et al.,2023). However, the literature rarely differentiates explicitly how these distinct types of crash risk influence investor behavior across different market structures or regimes. Recognizing these differences is crucial, as investors’ abilities to diversify or hedge such risks significantly influence their risk pricing and resultant financing costs. This study further distinguishes itself by examining these dynamics within China’s segmented Aand B-share markets, where domestic and foreign investors differ markedly in their sophistication, diversification capabilities, and risk-assessment strategies. Although the existing literature acknowledges the importance of investor sophistication and market segmentation, few studies have explicitly analyzed how these factors influence the causal relationship between crash risk and COE under varying market conditions. Domestic investors in A-shares, typically less globally diversified and more reliant on firm-specific information, may exhibit heightened sensitivity to firm-specific crash risks compared with foreign investors in B-shares, who generally benefit from global diversification (He et al.,2021). This study explicitly investigates these investor characteristics and market segmentation effects to provide novel insights into the conditions under which crash risk significantly affects investors’ expectations and firms’ financing costs. Methodologically, this study advances the literature by employing robust econometric techniques, specifically bootstrap panel Granger causality models and Markov-switching dynamic regressions. These methods explicitly address econometric challenges such as cross-sectional dependence, firm-specific heterogeneity, and regime-dependent investor behavior, which are inadequately captured by simpler methodologies. Additionally, a threshold regression was employed to reinforce the findings from the Markov-switching models by explicitly identifying the critical breakpoints. Thus, this study incorporates panel threshold regression analysis to enhance empirical robustness. By integrating explicit theoretical reasoning with rigorous methodologies, this study substantially enhances our understanding of the nuanced relationship between crash risk and COE. It moves beyond existing correlations, clarifies causal mechanisms, and demonstrates how distinct market regimes and investor sophistication shape financial outcomes. These findings offer actionable guidance for investors, policymakers, and corporate managers aiming to mitigate financial risks and optimize firm financing strategies in segmented markets. 1.1. Determinants of Stock Price Crash Risk and Cost of Equity (Brief Contextualization) Although this study primarily examines the economic consequences of stock price crash risk, a brief review of its determinants provides the necessary theoretical context. Prior research has extensively identified managerial behavior, institutional frameworks, and market conditions as pivotal determinants of crash risk. Jin and Myers (2006) and Hutton et al. (2009) emphasize managerial tendencies to withhold negative information, resulting in a higher crash risk. Recent studies have expanded on these determinants, highlighting the role of other aggregates such as operating leverage, liquidity, and carbon disclosure as critical factors influencing crash risk through increased information asymmetry, investors’ asymmetric responses, and managerial incentives to withhold negative information (Bose Economies 2025,13, 158 3 of 24 et al.,2024;Zhu & Zang,2024;Nguyen et al.,2025). Institutional investors may either mitigate crash risk effectively or unintentionally exacerbate it by aligning with managerial interests (Andreou et al.,2017). Moreover, heightened crash risk has implications for corporate control, reducing takeover premiums and lowering firm valuations (Carline et al.,2023). While the determinants are well documented, few studies have explicitly explored the causal impact of crash risk on COE. Transparency generally reduces information asymmetry and uncertainty, and lowers COE (Diamond & Verrecchia,1991). An increased crash risk reflects greater information asymmetry and increased financing costs (Botosan,1997;Liu & Ren,2019;Liang & Mao,2019). Crash risk indirectly increases COE through valuation adjustments, as manifested by higher book-to-market ratios (Chen et al.,2001). However, most studies rely on correlation-based methodologies that provide limited causal insights or explicit considerations of varying market conditions. This study contributes explicitly by investigating the causal relationships and differentiated impacts of market-wide and firm-specific crash risks on the COE. 1.2. Market Dynamics and Ownership Structures Market segmentation and ownership structures critically shape the relationship between crash risk and COE, influencing investor behavior, risk perceptions, and diversification opportunities. Previous studies recognize the moderating role of investor sophistication, yet few explicitly analyze how distinct market structures and investor behaviors under varying market regimes influence this relationship. Junxia and Qinsong (2019) indicate heightened investor sensitivity to crash risk in bull markets, although existing studies rarely employ methodologies that explicitly capture regime-dependent behavior. Recent findings suggest that internal (e.g., corporate governance) and external (e.g., institutional investors and analysts) monitoring significantly alleviate crash risk by reducing information asymmetry (Bose et al.,2024). Liang and Mao (2019) highlight domestic A-share investors’ greater sensitivity to crash risks due to limited diversification and reliance on firm-specific information compared to globally diversified foreign B-share investors. The existing literature has not explicitly tested how these differences manifest causally under varying market conditions. This study contributes explicitly through rigorous causality testing and regime-switching analyses, providing robust insights into the influence of market segmentation and investor behavior on the crash risk–COE nexus. Ownership structure also significantly impacts firm valuation and risk exposure. Carline et al. (2023) documented that firms with a higher crash risk experience reduced takeover premiums, which negatively influence their valuation and increase financing costs. Building explicitly on these findings, this study extends the prior literature by rigorously analyzing how market segmentation and ownership structure influence investor perceptions and risk pricing across distinct market regimes, thus providing novel and actionable insights beyond existing correlational findings. 1.3. Approach and Hypotheses Development Traditional studies examining the relationship between stock price crash risk and the cost of equity (COE) often rely on correlation-based or static panel regression models that do not adequately address causality, firm-level heterogeneity, or cross-sectional dependence. To overcome these limitations, this study adopts a multimethod econometric strategy that integrates causality testing and regime-sensitive modeling. First, we applied a bootstrap panel Granger causality model (Kónya,2006), which accounts for both cross-sectional dependence and slope heterogeneity, thus enhancing causal identification across firm panels. This technique is particularly suited for emerging Economies 2025,13, 158 4 of 24 markets, such as China, where structural interdependencies and firm-specific dynamics can bias conventional estimations. Second, to address the nonlinear behavior of financial markets, we incorporated a Markov-switching dynamic regression model (Ertugrul & Ozturk,2013). This framework identifies latent regimes, such as bull and bear markets, and estimates how the crash risk– COE relationship evolves across these states. This enables us to examine whether investors respond differently to crash risk depending on the prevailing market sentiment. Third, we complemented these models with a panel threshold regression (Hansen, 1999) that estimates observable breakpoints in crash risk measures (e.g., NCSKEW and DUVOL) that trigger distinct investor reactions. This model explicitly captures nonlinearity and structural shifts, offering further insights into how crash risk affects COE in segmented financial environments. This integrated framework was applied to China’s dual-share structure (A-shares for domestic investors and B-shares for foreign investors) to explore how investor sophistication and market segmentation influence the crash risk–COE relationship across regimes. Accordingly, this study tested the following hypotheses. H1: Stock price crash risk significantly increases equity costs because of heightened investor uncertainty and compensation required for perceived risks. H2: The impact of crash risk on COE is more pronounced for A-shares than for B-shares because of the differences in investor behavior, sophistication, and diversification strategies stemming from market segmentation. H3: The relationship between crash risk and COE varies across market regimes, and is stronger in bull markets because of amplified investor optimism and increased sensitivity to potential downside risks. By testing these hypotheses through robust empirical analyses, this study reaffirms key theoretical expectations and refines them through the lens of causality and dynamic market behavior. It provides actionable insights for investors, regulators, and corporate managers seeking to better understand and manage financing costs in segmented and behaviorally complex financial markets. The remainder of this paper is organized as follows. Section 2outlines the materials and methods, Section 3presents the empirical results, and Section 4concludes the study with key findings, implications, and recommendations for future research. 2. Materials and Methods 2.1. Sample Selection This study uses weekly data from firms listed on the Shanghai and Shenzhen Stock Exchanges, sourced from the China Stock Market and Accounting Research (CSMAR) database, covering the period 2010 to 2023. The starting point of 2010 ensured the exclusion of the effects of the 2008 global financial crisis, focusing on the periods of relative market stability. While the COVID-19 pandemic influenced markets in 2020–2021, these years were retained to capture the full market dynamics. The sample includes A-shares (domestic investors) and B-shares (foreign investors), facilitating an examination of how the ownership structure influences the COE–crash risk relationship. Weekly data are used for the COE estimation because they capture the short-term market dynamics that affect investor risk perceptions. Although COE is less volatile than stock market indicators, it remains sensitive to changes in crash risks, macroeconomic variables, Economies 2025,13, 158 5 of 24 and investor sentiment. Weekly intervals offer a granular view of these relationships and improve causal inference. Return on equity (ROE), a key COE input, is generally stable over short periods but may vary due to earnings forecasts, market revaluations, or economic shocks. Capturing these nuances through weekly data ensures robust analysis of firm fundamentals and market conditions. The study excludes financially distressed firms marked as “ST” or “PT” due to illiquidity and delisting risks (Allen et al.,2015) and omits financial sector firms because of their distinct leverage structures and reporting practices (Fama & French,1992). Firms with positive book values and consistent data for at least eight years were included, whereas cross-listed firms were excluded to control for the global market influence. This approach ensures a high-quality dataset, minimizing biases while aligning with prior research on capturing granular market responses to risk factors (Vorst,2017;Liu & Ren,2019). 2.2. Measures of Stock Price Crash Risk The four models measure firm-specific crash risk. The first measure, CRASHit, is a proxy that equals one if during the fiscal year, there is a one-week minimum at which a firm faces a stock price crash, and zero otherwise (Vorst,2017). A stock price crash week can be defined as the week in which a firm’s specific weekly return is at least 3.2 standard deviations below the mean specific return. Thus, under a normal distribution, 0.1 percent of all weeks were defined as crash weeks (Hutton et al.,2009). Firm-specific weekly returns (Equation (2)) are computed as the natural logarithm of one, which is added to the residual of the model below (Equation (1)): rit =αi+βrmt+εit (1) wit =ln(1+εit)(2) where r it is firm i’s stock return during week t, rm t is the market return, and εit represents the proportion of firm i’s weekly stock returns that the aggregate market movements fail to explain. The second measure of crash risk is NCSKEWit, also referred to as negative conditional return skewness, which is derived from the third moment of firm-specific weekly returns standardized by their volatility (Chen et al.,2001;Kim et al.,2016). Higher NCSKEW values correspond to an increased negative skewness, indicating a higher probability of extreme negative returns. This measure has been validated in studies examining information asymmetry and managerial behavior (Jin & Myers,2006;Hutton et al.,2009). This theoretical foundation is based on the aggregation of undisclosed negative information that ultimately results in a sharp decline. .NCSKEWit =−[n(n−1)3/2Σw3 it]/[(n−1)(n−2)(∑w2 it)3/2]. (3) NCSKEWit is computed as the negative of the third moment of firm-specific weekly returns divided by the standard deviation of firm-specific weekly returns raised to third power. In full respect to the prior literature, this study selects the negative of the third moment so that higher values of NCSKEWit correspond to increased negative NCSKEW, and hence, increased crash risk. The third measure of crash risk is down-to-up volatility DUVOLit. It evaluates the asymmetry in volatility between weeks with below-average (down) and above-average (up) returns (Chen et al.,2001). By taking the natural logarithm of the ratio of the standard deviation of down-week returns to that of up-week returns, DUVOLit captures the likeli- Economies 2025,13, 158 6 of 24 hood of more extreme losses than gains. This metric has been widely used to examine crash risk in the context of market transparency and investor sentiment (Piotroski et al.,2014; Saleem & Usman,2021). Studies have confirmed its sensitivity to abrupt changes, which makes it particularly suitable for this study. A higher DUVOLit value indicates increased crash risk. This equation is expressed as follows: DUVOLit =log{(nu−1)∑ down w2 it/"(nd−1)∑ up w2 it#}(4) where the number of “down/up” weeks (n d (n u )) minus one will scale the standard deviation of “down” (“up” up’ up’ up’)-week firm-specific weekly returns. A “down/up” week is a week during which the firm-specific weekly stock return is below/above the mean weekly return for the fiscal year. The fourth measure is implied volatility smirk (IV_SKEW), introduced by Kim et al. (2011). This is an options-based measure that equates the option pricing formula with the option market price. This can be expressed as follows: IV −SKEW =IVOTMP −IVATMC (5) where IV stands for implied volatility, and OTM puts are put options with a delta value between − 0.375 and − 0.125. ATM is a call option with delta values ranging from 0.375 to 0.625. To obtain the annual measure of the volatility smirk, the daily IV-SKEW over the 12 months ending 3 months after the fiscal year-end should be averaged. Although implied volatility smirks (IV_SKEW) can provide additional insights, their use was precluded because of the lack of available options data within the scope of this study. Consequently, the fourth measure (IV_SKEW) was excluded from the analysis. Additionally, the first measure (CRASHit) was not utilized separately because it conceptually overlaps with and is embedded in the calculations of NCSKEW and DUVOL, both of which provide richer theoretical and empirical grounding for capturing crash risk (Chen et al., 2001;Kim et al.,2016). Although NCSKEW and DUVOL specifically focus on sudden declines, aligning closely with theoretical models connecting crash risk to delayed disclosures and investor reactions (Diamond & Verrecchia,1991), their widespread acceptance and use in the literature ensure robust comparability and methodological validity. 2.3. Measure of Cost of Equity This study follows Ashbaugh et al. (2004) in estimating the cost of equity as the discount rate applied to future cash flows to determine a firm’s current stock price. We used a variation of the residual income valuation model (Ohlson,1995), which is equivalent to the dividend discount model. This approach is mathematically the same as the wellknown dividend discount model, and has been used by numerous authors, including Botosan (1997) and Gebhardt et al. (2001). In their methodology, R is defined as the implied cost of equity and the internal rate of return, which equates the intrinsic value of the stock to the current stock price by simply summing the discounted future abnormal earnings and current book value of equity (BE): Pt=Bt+ ∞ ∑ i=1 Et(ROEt+1−R)Bt+i−1 (1+R)i(6) where P t represents the stock price at time t, B t is the BE at time t, R is the forecasted cost of equity, ROE t+i is the return on equity in period t + i, and Et is the expectation considering Economies 2025,13, 158 7 of 24 the information available at time t. Since Equation (6) needs earnings forecasts of future periods, it is further developed into a new version: finite horizon. Pt=Bt+ T ∑ i=1 (FROEt+i−R)Bt+i−1 (1+R)i+(FROEt+T−R)Bt+T−1 (1+T)tR(7) where FROE is the forecast return on equity. To calculate the ex ante cost of equity, this study used Gebhardt et al.’s (2001) industry method and Easton’s (2004) PEG ratio. The industry method assumes that a firm’s ROE automatically reverts to industry-level ROE when it exceeds the forecast horizon. The use of the PEG ratio implies that abnormal earnings do not increase when they exceed the forecast horizon: Lu and Ye (2004) proved that the industry approach is better for analyzing the Chinese market. However, Botosan and Plumlee (2005) concluded that in the American capital market, the PEG ratio measure is a better approach because it is consistently and predictably related to various risk measures, and therefore, proves to be more reliable than other alternatives. Brav et al. (2003), Botosan and Plumlee (2002a,2002b), and Francis et al. (2004) use dividend forecasts and target prices to derive a measure of expected returns for firms based on models that consider these forecasts. Using the CSMAR database, the averages of the high and low expected returns for 2010–2023 are used to calculate the COE. This approach aligns with previous studies (Brav et al.,2003;Botosan & Plumlee,2002a). 2.4. Control Variables Following established practices in the finance literature, this study incorporates the market beta (BETA), book-to-market ratio (BM), and book value of equity (BE) as control variables to account for key factors influencing the cost of equity (COE). These variables have been widely validated as critical determinants of financing costs, investor risk perceptions, and firm valuation. BETA captures a firm’s sensitivity to market movements and systematic risk, where higher values reflect greater exposure to market volatility, leading investors to demand higher expected returns (Fama & French,1992,1993). Including BETA ensures that marketwide risks, a foundational determinant of equity pricing, are properly controlled for. BM, defined as the ratio of book value to the market value of equity, serves as a proxy for both valuation risk and growth opportunity. Higher BM ratios often signal undervaluation or financial distress, prompting investors to require higher returns (Chen et al.,2001). Additionally, BM correlates with stock price crash risk (Hutton et al.,2009), reinforcing its relevance in capturing firms’ underlying vulnerability to asymmetric information and valuation shifts. The BE reflects a firm’s financial strength and stability. Firms with larger book equity tend to face lower perceived risk from investors, resulting in reduced COE (Botosan,1997; Liang & Mao,2019). In the Chinese context, where financial reporting standards and government interventions can amplify the signaling role of financial strength, controlling for BE is particularly important for isolating firm-specific effects on COE. Together, these control variables address systematic risk, firm valuation risk, and financial health, and are commonly emphasized in the cost of equity and crash risk research (Francis et al.,2004;Liu & Ren,2019). Moreover, by incorporating firm-level fixed effects and clustering standard errors at the firm level, the analysis accounts for additional variable bias and within-firm correlations over time. This ensures that unobserved firm characteristics or structural differences across firms do not confound the estimated impact of crash risk on the COE. Economies 2025,13, 158 8 of 24 2.5. Cross-Sectional Dependence Tests Given the nature of our panel, with a large N and small T, the Friedman, Frees, and Pesaran tests (Friedman,1937;Frees,1995,2004;Pesaran,2020) are well suited. The Lagrange Multiplier (LM) test was developed by Breusch and Pagan (1980) and is presented in Equation (8): LMBP =TN−1 ∑ i=1 N ∑ j=i+1 ˆ P2 i(8) where ˆ P2 i is the correlation coefficient between the residuals derived from panel model estimates. Under the null hypothesis (Ho), there is an asymptotic chi-square distribution (chi2) concerning the LM statistic, with degrees of freedom of N (N − 1)/2. i, j, and T are derived from the panel model equation with t = 1, 2, . . . , T. Following this equation, Pesaran (2020) proposed another alternative: CD =s2T N(N−1)∑N−1 i=1∑N j=i+1ˆ pij(9) Unlike the LM statistic, CD has a mean of exactly zero for fixed values of T and N under an extensive range of panel data models such as nonstationary, dynamic, homogeneous, and heterogeneous models. Friedman’s statistic is derived from the average Spearman’s correlation, and is expressed as follows: Rave =2 N(N−1)∑ i+1 N ∑ j=i+1 ˆ rij (10) where ˆ rij is the sample estimate of the rank correlation coefficient of residuals. A large value of R_ave indicates the presence of non-zero cross-sectional correlations. The present model and the CD statistic involve the sum of pairwise correlation coefficients rather than the sum of squared correlations used in the LM test. However, if a check of whether any cross-sectional dependence is left out in the disturbance is to be conducted, CD and R_ave lack the power to detect it. However, this drawback does not affect the Frees statistic. This method is based on the sum of the squared rank correlation coefficients. R2 ave =2 N(N−1) N−1 ∑ i=1 N ∑ j=i+1 ˆ r2 ij (11) A function of this statistic follows a joint distribution of two independently drawn x2variables. 2.6. Slope Homogeneity Test Pesaran and Yamagata (2008) developed a standardized dispersion statistic that covers a larger spectrum of analysis. Unlike Swamy’s (1970) model, which is limited to models in which N is smaller than T, the Pesaran and Yamagata models consider this and extend it to wider panels. The model can be represented as follows: ∼ ∆=√N N−1∼ s−k √2k !(12) Economies 2025,13, 158 15 of 24 The dynamic regression results presented in Table A6 confirm and extend the static analysis findings, reinforcing the significant influence of stock price crash risk (measured by NCSKEW and DUVOL) on the cost of equity (COE) across different market conditions. Consistent with Ertugrul and Ozturk (2013), who stress the importance of regime-dependent dynamics in financial risk studies, this analysis illustrates that the crash risk–COE relationship is sensitive to shifts between bull and bear markets. Crash risk measures significantly raise COE under both regimes, with notably stronger effects for A-shares, reflecting domestic investors’ heightened vulnerability to market volatility (Piotroski et al.,2014). Fan and Gao (2024) further corroborate this finding, highlighting that Chinese domestic investors exhibit disproportionate risk sensitivity in response to asymmetric information shocks, particularly during periods of market turbulence. The persistent divergence between Aand B-shares across regimes emphasizes the enduring impact of market segmentation on China’s capital markets. Moreover, the results reveal that COE increases more sharply in bull markets, which is consistent with Junxia and Qinsong (2019), who find that heightened investor optimism amplifies downside risk concerns. This regime asymmetry is particularly pronounced among A-shares, where transitions from bull to bear markets are less frequent (p21 = 39.74%) than those among B-shares (p21 = 89%), suggesting greater volatility and faster sentiment shifts among foreign investors. These transition probabilities align with Liang and Mao (2019), who observed that foreign investors adjust more rapidly to changing market conditions, driven by global risk considerations. These findings collectively validate H3, confirming that heightened investor optimism in bull markets intensifies the relationship between crash risk and financing costs. This aligns with the theoretical perspectives proposed by Jin and Myers (2006) and is empirically consistent with the evidence presented by Qian et al. (2025), who document stronger risk–price relationships during optimistic market phases in emerging economies. Systematic risk, proxied by BETA, also plays a crucial role in determining COE, especially in bull markets. Its positive and significant effect across regimes supports earlier findings by Gode et al. (2005), and is consistent with those of Zhao et al. (2024), who emphasize that investors’ sensitivity to systematic factors strengthens during periods of elevated market optimism. The behavior of valuation metrics reveals regime-dependent patterns. BM positively impacts COE in bear markets for both share classes, reflecting investors’ heightened risk aversion during downturns (Chen et al.,2001). However, for A-shares, the BM’s effect turns negative in bull markets, suggesting that domestic investors interpret undervaluation as a favorable signal during optimistic periods. This differentiated behavior is consistent with Fan and Gao (2024), who show that A-share investors exhibit stronger valuation focus under positive market sentiment. In contrast, B-share investors’ valuation responses remain relatively muted, consistent with their broader international diversification strategies. The book value of equity (BE) also demonstrates segmented effects. For A-shares, the BE consistently lowers the COE across regimes, underscoring the stabilizing influence of financial strength and the role of implicit government protection in the domestic market (Chen et al.,2023). Conversely, for B-shares, BE positively impacts COE in bear markets, suggesting that foreign investors may interpret increases in book equity as signals of hidden risks or inefficiencies (Saleem & Usman,2021). Overall, the Markov-switching dynamic regression results indicate that the relationship between crash risk and COE is not static, but highly regime-dependent. Investor behavior, ownership structure, and market segmentation significantly influence how crash risk is priced in bull-and-bear markets. This confirms that firms must adopt regime-specific Economies 2025,13, 158 16 of 24 risk management strategies to mitigate the financial consequences of crash risks, especially during periods of elevated optimism when downside risks are often underpriced. Unlike traditional studies that focus solely on static relationships, this analysis highlights the necessity of dynamic modeling approaches to fully capture the nuances of financing costs under market segmentation (Liang & Mao,2019;Qian et al.,2025). By integrating crash risk exposure, investor behavior, and market regime dynamics, this study offers actionable insights into capital management strategies for firms operating in segmented and volatile financial environments. 3.3.2. Threshold Model Given the panel structure of our dataset and the likelihood of firm-specific heterogeneity, we employed the panel threshold regression (PTR) model developed by Hansen (1999), which is specifically designed for shortand large-N panels. This approach allows us to estimate the threshold level of stock price crash risk proxied by NCSKEW and DUVOL at which the marginal effect on the cost of equity (COE) shifts significantly. The model accounts for firm-level fixed effects to control for unobserved heterogeneity, and allows regime-dependent slope coefficients. To ensure robustness, standard errors are heteroscedasticity-consistent and clustered at the firm level to address within-firm autocorrelation over time. Panel threshold regression (PTR) analysis further validates the nonlinear relationship between stock price crash risk and cost of equity (COE), complementing the regimedependent dynamics identified by the Markov-switching model. Tables A7 and A8 present the PTR results, with NCSKEW and DUVOL serving as threshold variables to define lowand high-risk regimes. The threshold regression results based on NCSKEW (Table A7) reveal a clear regime shift in the impact of crash risk on COE for both A-shares and B-shares. For A-shares, the coefficient of NCSKEW increases sharply from 1.1232 (State 1, low crash risk) to 0.1021 (State 2, high crash risk), and both are statistically significant. This significant reduction in sensitivity under high-crash-risk conditions suggests that once crash risk exceeds a critical threshold, investors adjust their pricing expectations more conservatively, consistent with risk-pricing theories (Jin & Myers,2006). It also echoes the findings of Fan and Gao (2024), who argue that, in high-risk environments, investors in emerging markets become relatively less responsive to marginal increases in negative signals, reflecting risk-saturation behavior. Similarly, for B-shares, although both coefficients are significant, the sensitivity is reversed: NCSKEW has a larger effect in the high-crash-risk regime (0.2419) than in the low-risk regime (0.101), suggesting that foreign investors react more strongly when the crash risk surpasses a critical point. This pattern aligns with Qian et al. (2025), who show that foreign investors in segmented markets adjust more aggressively to extreme downside signals than domestic investors do. DUVOL-based thresholds (Table A8) further confirmed these dynamics. For A-shares, DUVOL’s effect on COE is stronger in the low-risk regime (coefficient = 10.5824) than in the high-risk regime (coefficient = 0.2063), again consistent with domestic investors showing risk saturation once crash risk becomes excessive. By contrast, for B-shares, although the coefficients remain positive across regimes, their relative magnitudes are less pronounced (0.7013 and 0.2663, respectively), suggesting more measured responses from foreign investors. Importantly, the threshold regressions also reveal structural heterogeneity in how the control variables affect COE across regimes. For example, BETA exhibits significantly stronger effects on COE in low-risk regimes for A-shares (0.2291 for the NCSKEW model; 0.4181 for the DUVOL model), supporting the notion that systematic risk pricing is more Economies 2025,13, 158 17 of 24 prominent when market sentiment is optimistic (Gode et al.,2005;Zhao et al.,2024), which increases COE in bear markets but shows regime-dependent reversals for A-shares. This reinforces Fan and Gao’s (2024) finding that valuation concerns fluctuate with market sentiment, and BE consistently exhibits insignificant or weak effects across regimes for A-shares but shows differentiated signs for B-shares, underscoring that foreign investors interpret financial strength signals differently depending on crash risk regimes (Saleem & Usman,2021;Chen et al.,2023). Thus, the PTR analysis strongly supports H3, confirming that the impact of crash risk on financing costs is nonlinear and regime-dependent and shaped by both market segmentation and investor heterogeneity. Moreover, compared with baseline panel regressions and Granger causality tests, the PTR approach offers richer insights by explicitly identifying the threshold levels at which investor behavior fundamentally shifts. This refinement addresses the call for models capable of capturing nonlinearities and discontinuous investor responses to crash risk (Bose et al.,2024). Overall, the PTR results robustly validate the central proposition that crash risk significantly and causally increases the cost of equity in segmented markets, with the effect varying depending on investor type, ownership structure, and market regime. 3.4. Implications of the Findings The empirical findings from this study offer important implications for corporate managers, investors, and policymakers operating in segmented and behaviorally diverse capital markets such as China’s Aand B-share structures. For corporate managers, evidence that crash risk significantly increases the cost of equity, especially in A-shares dominated by domestic investors, underscores the necessity of improving corporate transparency, financial disclosures, and governance mechanisms. Enhanced disclosure practices can reduce information asymmetry, mitigate investor uncertainty, and lower financing costs. In bull markets, where investor optimism can exaggerate sensitivity to downside risk, firms should be especially proactive in stabilizing expectations and managing narrative control. For investors, this study highlights that the pricing of crash risk is highly sensitive to both market regimes and investor types. Domestic investors in A-shares appear more sensitive to firm-specific crash signals under bullish conditions, whereas foreign investors in B-shares react more strongly when risk thresholds are surpassed. These patterns suggest the need for investors to calibrate their risk assessment models by incorporating regime switches and threshold effects when pricing securities, particularly in emerging markets, where behavioral biases may be more pronounced. For policymakers and regulators, the results support the need for nuanced regulatory frameworks that consider behavioral segmentation. Measures such as promoting information transparency, encouraging the diversification of domestic portfolios, and ensuring the consistent enforcement of disclosure rules can help reduce systemic vulnerability. Additionally, understanding how investor sentiment and information flow influence pricing under different regimes can lead to more responsive and market-stabilizing interventions. Finally, the regimeand threshold-dependent nature of the crash risk–COE relationship implies that traditional linear policy and investment models may overlook important dynamics. Future policy designs should integrate the nonlinear behavior of market participants, particularly during optimistic phases when risk mispricing is more likely to occur. This underscores the importance of adopting dynamic, behaviorally grounded approaches to risk regulation and capital market development. Economies 2025,13, 158 18 of 24 4. Conclusions This study rigorously examines the causal relationship between stock price crash risk and cost of equity (COE) in China’s segmented Aand B-share markets by applying a combination of static and dynamic methodologies. The findings consistently reveal that heightened crash risk leads to a significantly elevated COE, with the effect being particularly pronounced in the A-share market, where less globally diversified and domestically focused investors dominate. The application of Markov-switching dynamic regression models and panel threshold regression (PTR) further reveals that this relationship is regimedependent, intensifying in bull markets when heightened investor optimism amplifies sensitivity to downside risks. These results underscore the complex interplay between market segmentation, ownership structures, investor behavior, and market regimes, which are particularly salient in several market contexts. This study makes three key contributions to the literature. First, it moves beyond traditional correlation-based studies by providing rigorous causal evidence that links crash risk to COE, utilizing bootstrap panel Granger causality and threshold modeling to establish directionality and robustness. Second, it demonstrates that the crash risk–COE relationship is nonlinear and varies systematically with market regime, a dimension largely overlooked in prior research. The combined use of Markov-switching dynamic regression and panel threshold regression frameworks more comprehensively captures these nonlinearities and structural shifts. Third, it highlights the critical importance of ownership segmentation and investor sophistication in financial decision making and risk pricing. The findings illustrate that domestic and foreign investors exhibit asymmetric responses to crash risk across different market conditions, thus providing deeper insight into how structural factors shape capital costs. The practical implications of this study are multi-faceted. For corporate managers, particularly those operating in the A-share segment, the results emphasize the need to strengthen corporate transparency, disclosure practices, and governance frameworks to mitigate domestic investors’ heightened crash risk sensitivity. In bull markets, particular attention should be paid to stabilizing investor expectations to prevent disproportionate increases in financing costs. For policymakers, evidence advocates refined regulatory strategies that consider segmented market behavior. Initiatives promoting greater information transparency, broadening domestic investor participation, and managing foreign investor sentiment during market upswings can significantly enhance market resilience and reduce systemic vulnerability. For investors, the results highlight the need to adapt risk-assessment frameworks to account for both ownership structures and market regimes. Domestic investors must remain vigilant during bullish periods, when optimism can obscure accumulating risks, whereas foreign investors should intensify their monitoring of firm fundamentals during downturns, when hidden financial fragilities are likely to surface. However, this study had several limitations. Focusing exclusively on China’s Aand B-share markets may constrain the generalizability of our findings to other institutional and regulatory contexts. Moreover, although NCSKEW and DUVOL are well-established proxies for crash risk, they may not fully capture slow-building or extended low-return scenarios. Other dimensions, such as governance-related indicators, sentiment indices, and implied volatility skewness measures, were not included because of data constraints. Furthermore, the exclusion of financial firms due to their unique regulatory and leverage characteristics limits the sectoral breadth of conclusions. Future research could broaden the scope by incorporating alternative crash risk measures such as managerial opacity indices (Hutton et al.,2009) or implied volatility skewness metrics to better capture the different dimensions of crash risk. Examining mechanisms Economies 2025,13, 158 19 of 24 such as insider trading could deepen the understanding of how information asymmetry channels influence the crash risk–COE nexus. Simulation-based approaches can be used in parallel with empirical models to illustrate the dynamic mechanisms under controlled conditions. Integrating direct sentiment measures (e.g., survey-based or media tone indices) would allow a more explicit behavioral interpretation of regime-dependent effects. Methodologically, future studies could also consider smooth transition or multiplethreshold models (e.g., STR and LSTR) to capture complex nonlinear dynamics more finely, particularly in smaller panels or macro-level applications. Furthermore, integrating alternative COE estimation models (e.g., Claus & Thomas, 2001) could enhance robustness, while comparative cross-country studies could illuminate how institutional maturity and regulatory quality shape the crash risk–COE relationship. Finally, incorporating behavioral finance perspectives could enrich future research by exploring how investor sentiment, cognitive biases, and psychological factors interact with market regimes to shape capital costs. Author Contributions: Conceptualization, B.I.P.Z. and X.W.; Methodology, B.I.P.Z. and X.W.; Software, X.W. and C.C.; Validation, B.I.P.Z., X.W., C.C. and M.B.B.; Formal analysis B.I.P.Z., X.W. and M.B.B.; Investigation, C.C.; Data curation, X.W. and C.C.; Writing—original draft, B.I.P.Z., X.W., C.C. and M.B.B.; Writing—review & editing, B.I.P.Z. and X.W.; Supervision, B.I.P.Z.; Project administration, M.B.B. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: The data presented in this study are available upon request from the corresponding author due to ongoing research. Conflicts of Interest: The authors declare no conflicts of interest. Appendix A Variables’ Definitions Variables Definition COE This is the measure of the cost of equity, which is calculated using dividend forecasts and target prices to derive an estimate of expected return for firms, using models for valuation that integrate these forecasts. The method is close to the ones used by Brav et al. (2003), Botosan and Plumlee (2002a,2002b), and Francis et al. (2004). NCSKEW Short for Negative Coefficient Skewness, it is the negative of the third moment of firm-specific weekly returns for each firm and year divided by the standard deviation of firm-specific weekly returns raised to the third power. DUVOL Short for down-to-up volatility, it is the log of the ratio of the standard deviation of the “down-weeks” over the standard deviation of the “up-weeks”. BETA BETA is the market beta estimated from CSMAR data over 60 months before a firm-year fiscal year-end observation. BM Book-to-market value of securities published by the Shanghai Exchange and the Shenzhen Stock Exchange, covering fourteen years and calculated as the ratio of total assets/market value. BE Book value of equity of securities published by the Shanghai Exchange and the Shenzhen Stock Exchange, covering fourteen years. Economies 2025,13, 158 20 of 24 Table A1. Descriptive statistics. Variable No of Firm-Years No of Unique Firms Mean Std. Dev. Min Max Median A-shares COE 29,582 2113 0.3038 0.6839 0.0095 2.6127 0.1650 NCSKEW 29,582 2113 −0.5450 1.4560 −3.4825 2.8606 −0.5074 DUVOL 29,582 2113 −0.0735 0.3050 −0.7917 0.6691 −0.0538 BETA 29,582 2113 0.6776 0.8898 0.4629 1.4410 0.9832 BM 29,582 2113 0.5513 1.2618 0.0000 1.0802 0.5523 BE 29,582 2113 3.7238 4.7973 0.0000 26.4776 2.2487 B-shares COE 1512 108 0.0629 0.2713 0.0006 1.0649 0.0315 NCSKEW 1512 108 −0.2971 1.4501 −3.3712 3.0085 −0.2886 DUVOL 1512 108 −0.0474 0.2911 −0.8573 0.6133 −0.0390 BETA 1512 108 0.5020 0.7989 0.2800 1.2901 0.8075 BM 1512 108 0.5524 1.3015 0.0000 1.1128 0.5847 BE 1512 108 2.3432 3.7094 0.0000 24.3875 1.3092 Notes: Table of descriptive statistics for all variables. The sample contains 29,582 firm-year observations for firms trading A-shares and 1512 firm-year observations for B-shares from 2010 to 2023. Table A2. Pairwise correlation table of the selected variables for firms trading Aand B-shares. Variables COE NCSKEW DUVOL BETA BM BE A-shares COE 1.0000 NCSKEW 0.1622 ** 1.0000 DUVOL 0.0639 ** 0.7525 *** 1.0000 BETA 0.6216 ** 0.1065 *** 0.0872 *** 1.0000 BM 0.0495 *** −0.0349 *** −0.0189 *** 0.0263 *** 1.0000 BE −0.0104 * −0.0468 *** −0.0232 *** −0.0499 *** 0.1837 *** 1.0000 B-shares COE 1.0000 NCSKEW 0.1133 ** 1.0000 DUVOL 0.0404 * 0.7328 *** 1.0000 BETA 0.5544 ** 0.0307 * 0.0031 * 1.0000 BM 0.0277 * −0.0096 * −0.0147 * 0.0027 * 1.0000 BE −0.0338 * 0.0287 * 0.0380 * 0.0417 * −0.0642 ** 1.0000 Note: ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. Table A3. Panel regression. Stock A Stock B Variables COE COE COE COE NCSKEW 0.0455 *** - 0.0243 *** - (17.5) - (14.92) - DUVOL - 0.0271 ** - 0.0355 * - (7.13) - (11.42) BETA 0.0197 *** 0.0200 *** 0.0192 *** 0.0190 *** (19.13) (11.14) (12.10) (12.72) BM 0.1912 *** 0.1997 *** 0.0249 * 0.0254 * (12.82) (13.30) (2.04) (2.05) BE −0.0106 *** −0.0101 *** −0.0003 * −0.0004 * (−10.35) (−9.72) (−0.19) (−0.27) Intercept 0.1224 *** 0.1229 *** −0.0301 * −0.0213 * (5.63) (5.61) (−0.84) (−0.59) Observations 25356 25356 1296 1296 Adj. R-square 0.4030 0.5325 0.3224 0.2259 Note: Table of panel regression results of (1) COE on NCSKEW, BETA, BM, and BE; (2) COE on DUVOL, BETA, BM, and BE, for Aand B-shares. The z-values are shown in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. Firm fixed effects included. Standard errors are heteroscedasticity-robust and clustered at the firm level. Economies 2025,13, 158 21 of 24 Table A4. Cross-sectional dependence and slope homogeneity tests. Stock A Stock B Equation (1) Equation (2) Equation (1) Equation (2) Form Test p-Value (a) Test p-Value (b) Test p-Value (a) Test p-Value (b) Cross-sectional dependence Pesaran’s test 273.4790 0.0000 290.6810 0.0000 91.3960 0.0000 158.6100 0.0000 Friedman’s test 1013.4030 0.0000 1132.4870 0.0000 278.5600 0.0000 471.7530 0.0000 Frees’ test 65.9960 0.5811 *** 83.9210 0.5811 *** 10.6680 0.5811 *** 25.3400 0.5811 *** Slope homogeneity ∆~4.0380 0.0000 3.2280 0.0010 −4.8150 0.0000 −4.3190 0.0000 ∆~adj. 6.9930 0.0000 5.5910 0.0000 −8.3400 0.0000 −7.4810 0.0000 Note: For stocks A and B, Equation (1) represents the first equation as per Table A3 (NCSKEW is the independent variable), and Equation (2) represents the second equation as per Table A3 (DUVOL is the dependent variable). The null hypothesis (Ho) for the cross-sectional dependence test indicates no cross-sectional dependence. (a,b) The value presented in Frees’ test is the alpha from a Q distribution; *** indicates significance at the 1% level. For the slope homogeneity test, the null hypothesis is that the coefficients are homogeneous. Table A5. Bootstrap panel Granger causality test for H1 and H2. Share Type Causal Relationship Wald Statistic 10% Critical Value 5% Critical Value 1% Critical Value Panel A: H1—Effect of Crash Risk on Cost of Equity (COE) A-shares NCSKEW → COE 15.0160 ** 9.7890 13.1170 16.1560 A-shares DUVOL →COE 24.4910 ** 14.4290 16.4210 31.2350 B-shares NCSKEW → COE 14.4010 * 13.7000 15.9010 22.1170 B-shares DUVOL →COE 14.1470 ** 9.2670 10.4320 15.6910 Panel B: H2—Effect of Segmentation-Related Variables on COE (by Market Type) A-shares BM →COE 20.3410 ** 11.1080 14.8820 27.7310 B-shares BM →COE 10.9670 11.0070 13.1180 17.8400 Note: ** and * indicate the rejection of the null hypothesis at the 5% and 10% levels, respectively. Table A6. Markov-switching dynamic regression. Stock A Stock B Variables Bear Bull Bear Bull NCSKEW 0.0652 *** 0.1324 *** 0.0283 *** 0.0305 ** (13.68) (16.77) (17.29) (11.31) DUVOL 0.1353 *** 0.3441 *** 0.0947 *** 0.1080 *** (10.11) (16.22) (4.92) (11.04) BETA 0.0027 *** 0.0401 *** 0.0063 *** 0.0606 *** (12.03) (17.03) (12.05) (16.88) BM 0.1322 *** −0.0980 *** 0.0223 * 0.0114 (13.07) (−5.76) (1.76) (0.24) BE −0.0039 *** −0.0034 *** 0.0004 * −0.0001 (−5.20) (−3.57) (1.84) (−0.01) Intercept 0.0981 *** 0.0975 *** 0.0082 −0.0273 (6.16) (4.97) (0.43) (−0.39) Sigma 0.2730 ** 0.1121 ** p11 0.8106 ** 0.9215 ** p21 0.3974 ** 0.8900 ** Note: z-values are given in parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respectively. Firm fixed effects are captured through regime-dependent intercepts. Standard errors are heteroscedasticityconsistent. Sigma is the standard deviation for the entire process, and p11 and p21 are the transition probabilities from one state to another. Bears represent State 1 and bulls represent State 2. Economies 2025,13, 158 22 of 24 Table A7. Threshold regression (NCSKEW). Stock A Stock B Variable State 1 State 2 Variable State 1 State 2 NCSKEW 1.1232 ** 0.1021 *** NCSKEW 0.101 * 0.2419 * 2.37 3.31 1.94 1.74 DUVOL 4.2282 ** 1.2391 *** DUVOL 0.6687 * 0.6145 * 2.54 3.58 1.75 1.82 BETA 0.2291 *** 0.008 BETA 0.0257 *** 0.0236 * −4.23 0.45 −2.63 1.86 BM 4.2823 *** 0.7945 BM 0.5478 *** 1.2591 *** 3.1 1.58 2.62 2.81 BE −0.1061 0.0132 BE 0.0091 −0.0074 −1.02 0.44 0.9 −0.41 Intercept 0.4496 −0.2731 Intercept −0.0906 −0.3937 0.19 −0.31 −0.49 −0.92 Threshold −0.4515 Threshold 0.2991 Note: Firm fixed effects are included. Standard errors are heteroscedasticity-consistent and are clustered at the firm level. The z-values are given in the parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. The threshold value represents crash risk (measured by the NCSKEW), separating the lowand high-risk regimes. Table A8. Threshold regression (DUVOL). Stock A Stock B Variable State 1 State 2 Variable State 1 State 2 NCSKEW 0.3101 * 0.996 * NCSKEW 0.1029 ** 0.2065 *** 1.8 1.73 2.46 3.96 DUVOL 10.5824 * 0.2063 * DUVOL 0.7013 * 0.2663 * 1.95 1.83 1.84 1.71 BETA 0.4181 *** 0.0036 ** BETA 0.0197 * 0.0432 * 13.99 2.24 1.86 1.93 BM 5.0598 −1.3912 *** BM 0.5516 *** 1.1591 *** 3.97 −2.83 2.66 2.91 BE −0.0929 0.0042 BE 0.0109 −0.0105 * −1.07 0.12 1.09 −1.88 Intercept 4.528 0.1336 Intercept −0.0665 −0.2906 2.29 0.24 −0.36 −0.75 Threshold −0.0907 Threshold 0.1235 Note: Firm fixed effects are included. Standard errors are heteroscedasticity-consistent and are clustered at the firm level. The z-values are given in the parentheses. ***, **, and * denote significance at the 1%, 5%, and 10% levels, respectively. The threshold value represents crash risk (measured by the DUVOL), separating the lowand high-risk regimes. References Allen, F., Carletti, E., & Marquez, R. (2015). 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