The Role of Gender Diversity in Downside Risk: Empirical Evidence from Vietnamese Listed Firms

: Corporate governance has been marked as an important component of the fast-growing pace of the Vietnam economy recently. Aligning with the concern that gender plays a critical role in corporate management, this study aims to reveal the entire beneﬁts of the appearance of women on board to reduce downside risk in the frontier countries. By using a unique dataset from Vietnamese listed ﬁrms and appropriate econometric methods, we present tight results that the presentation of women at ﬁrm management level is more likely to lessen the downside risk. In particular, female non-senior reduces all risk attributes, whereas the presence of women in executive board decrease ﬁrm risk only. Furthermore, the decreasing of individual and systemic risk are additionally driven by female Chief Executive O ﬃ cer (CEO) and chairman. We found strong evidence that female leadership may decrease risk-taking in the low-risk ﬁrms at all managerial levels but not in the case of a female CEO. In summary, by examining data from speciﬁc frontier areas such as Vietnam, we conﬁrm that the role of female leadership in terms of reducing the downside risk depend on their power managerial levels and the ﬁrm-risk behavior.


Introduction
The twenty-first century has been marked as the most glorious period for the massive growth of Asian economics that implicates an increase in pressure on corporate governance for firm managers. Among them, gender equality in the boardroom has been raised as one of the concerns that impact corporate risk-taking [1]. Gender equality in the board is noticed as the main factor in corporate governance that improves firm performance [2]. Even though the proposition of women in management globally increased by 5% to 29% in 2019, it does not represent the scenario in Asian, where the role of women in business has still been underestimated (following the annual report of Grant Thornton, An Instinct for Growth, in 2019) [3].
Besides, as the weakness of internal corporate governance leads to the increase in agency cost, it is mentioned as the root of the recent financial crisis [4,5]. Indeed, the firm with good corporate governance is expected to perform better due to the lower cost capital and default risk [6]. In line with that viewpoint, the downside risk or excessive risk-taking behavior is highlighted as the main contribution to the cause of crisis due to the risk bearing of managers [7,8]. With the importance of corporate governance in protecting shareholders from undesirable downturn of stock market, the board verifying the impact of firm management on corporate risk-taking. Thus, these results have potential implications for other frontier markets that are poorly governed.
Overall, from the final results, we expect to find the profound significance of female managers on reducing downside risk. Herein, we distinguish the appearance of women in all aspects of managerial positions including senior and non-senior managers; chief executive officer, and chairman. In addition to deal with the endogeneity concern, we then divide women on board of directors into executive and non-executive levels. Thus, we proceed to investigate whether the downside risk is driven by their power that goes with the managerial levels or not [33]. Finally, we test whether it is different from gender diversity in determining risk-taking in high and low firm risks.
Eventually, the structure for the rest of this paper is organized into the following parts: the current literature of gender diversity in the boardroom is discussed in Section 2; data and methodology are shown in Section 3; empirical results and its implication are presented in Sections 4 and 5 concludes this study.

Literature Review
In the framework of the agency problem, the association of executive managers and risk-averse is normally explained by their reputation and employment [39,40]. However, the managers may ignore the principles of management function to take more risk due to the greater managerial incentives [41,42]. Thus, refs. [8,43] show that the financial crisis in 2008 is mainly caused by excessive risk-taking behavior from executive managers due to greater performance-based managerial incentives. Therefore, the tightly internal mechanisms play an essential role in monitoring and enhancing the quality of corporate governance as well as reducing the interest difference of stakeholders [40]. Moreover, ref. [31] recently mention the role of corporate governance in corporate firm's risk-taking in frontier equity markets characterized by high ownership concentration and poor governance mechanisms.
Although the tighter regulations help the governance mechanism effectively reduce the agency problems, they may cause negative effects such as moral hazard in the risk investment system. While shareholders are limited in assets, tighter regulations reduce their involvement in firm strategy decisions [44,45]. Following this, intensive government regulations may weaken external mechanisms [46]. Ref. [47] acknowledged that the cost of the hostile takeover was the important reason for the avoidance of firms, thus the internal mechanisms (e.g., the board of directors, managerial characteristics) become adapted factors in reducing agency problems. Ref. [48] explored this idea and found the negative impact of board size and power concentration of Chief Executive Officer (CEO) play on agency problems. Ref. [49] followed up on [48] research suggesting that the difference of board structure (e.g., more appearance of non-executive directors and more powerful CEO) reduces the agency cost and enhances the efficiency incorporate risk-taking. Recently, refs. [2,50] emphasized that the role of gender diversity in boardroom raises the confidence of investors due to the expectation that women would enhance internal mechanisms. In summary, by focusing on the role of women to improve firm internal mechanisms, the effect of gender diversity in the boardroom on corporate risk-taking is particularly discussed in the next following section.

Gender Diversity and Corporate Risk-Taking
The current literature frequently shows that the distinct gender stereotypes of men and women which are pointed as the main reasons to diversify risky behavior between them. Both risk aversion and risk-bearing are considered. Ref. [51] found that men tend to invest twice as less of their wealth in stocks and prepare their retirement plans in a less conservative way than women. Therefore, women are assumed to involve less in risk-taking behaviors than male counterparts [52]. In the context of a group, ref. [53] showed that women are less risky than a man in their willingness to lead the team decision. Particularly, ref. [54] detected that women are more conservative in risk attributes as well as ambiguity than their counterparts in the financial areas which attitude towards the risk of professional investors. Furthermore, the difference between compensation and incentives may be employed to the documented association between gender and risk-taking. Specifically, low-risk firms may be more likely to offer fixed pay contracts and more likely to attract female executives. Consistent with this argument, ref. [55] used the sample of Italian firms to reveal that more risk-averse and less talented managers tend to match with firms offering low-powered incentives. As [56] argued, with respect to firm performance and firm risk, the influence of female managers may indirectly result in firms having fewer returns (e.g., risk-averse) and fewer huge losses (having more stable performance). Such a risk-return paradox may be the result of differences in management capabilities brought on through the different gender characteristics. Ref. [1] contributed to that viewpoint as they found out that the appearance of women in the boardroom has a negative impact on risk in financial institutions in the European area. In contrast, ref. [12] showed that risk-taking behavior is increased by not only by younger executive teams but also the higher proportion of female executives in the German financial sector. Ref. [26] showed that the proportion of women onboard leads to an increase in risk-taking. In addition, the low proportion of women on board can be explained by their conservativeness and sensitivity that could be inefficient managers [57].
Despite the fact that the interest in gender difference in governance attributes has been amplified in recent years, these have not so many papers explored carefully the relation between women on executive positions and corporate risk-taking. Therefore, in line with the view that higher proportion of women in firm management increase firm financial performance and lower downside risk [1,58], we then expect to find the negative impact between gender diversity on corporate risk-taking in Vietnam. We propose our first hypothesizes following as: Hypothesis 1a (H1a). The proposition of women on firm management has a negative significant relationship with individual risk.
Hypothesis 1b (H1b). The proposition of women on firm management has a negative significant relationship with system risk.
Hypothesis 1c (H1c). The proposition of women on firm management has a negative significant relationship with system risk accumulation.

Women in Top Executive and Corporate Risk-Taking
There is a vast evidence which shows that female leadership can improve both internal mechanisms and the firm's external performance [59][60][61]. Therefore, the attendance of women in board of directors could help the firm reduce coordination and communication problems in the boardroom. By employing the dataset of 638 firms listed from American Fortune 1000, ref. [60] showed the significant connection between the proportion of women on board and firm performance illustrated by Tobin's Q ratio. Ref. [62] found that a higher percentage of women on board increases firm performance which presents by both accountant and market-based ratios. Supporting the perspective that women should be encouraged to participate in a leadership function, ref. [59] argued that female leadership increases firm performance at both accountant and market-based aspects. Furthermore, ref. [63] showed interesting evidence that the proportion of women on board could make a negative effect on firm performance if it reaches the particular number of 30 percent.
We also emphasize that even though the growth of relevant literature in board structure has increased quickly, it is not in the case of gender and corporate risk-taking. In the context of gender equality encouragement in the boardroom, it shows that women leaders are more disciplined, particularistic, and democratic than men in executive function [64]. Aligning with that view, ref. [65] indicated that the unique characteristics of women such as a slight edge over men support firm strategy. Developing from these findings, ref. [61] argued that women should be on board due to their flexibility in internal communication and being less hierarchical. Later, refs. [66,67] agreed that women have enough capabilities to make the difference in executive positions with their unique characteristics. Hence, female leadership has the ability to fulfill the board's strategic role.
Regarding market assessment to the female executives, ref. [68] showed the underrated evaluation of market to female CEOs. Furthermore, they also found consistent results that firms with female leadership decrease idiosyncratic risk. The uniqueness of women's characteristics in leadership positions is also clearly clarified in the study of [69] that companies with female leaders us less leverage, less volatile earnings, and higher opportunity for survival.
Although female employees have been encouraged to participate more in executives, the empirical evidence on the relationship between female executive managers and corporate risk-taking has not made such distinction. We, therefore, expect the negative relationship between female manager and all risk attributes of downside risk in Vietnam and propose our second hypothesis as follow: Hypothesis 2a (H2a). The representation of women as top executive manager has a negative significant relationship with individual risk.
Hypothesis 2b (H2b). The representation of women as top executive manager has a negative significant relationship with system risk.
Hypothesis 2c (H2c). The representation of women as top executive manager has a negative significant relationship with system risk accumulation.

Data
Osiris is a confident database for this study because it comprises the massive data of corporate governance from most of the firms listed in the stock market, including the firm's statement for data validity. Therefore, we use Osiris to collect governance mechanism variables, whereas Datastream is a confidential source for the equity data of listed companies. Although Osiris is well-known as a strong database on corporate governance structure, not all values are summarized. For example, we need to handle the missing values manually by including several important variables such as the gender of managers. Specifically, we counted the number of female directors who are still attending on board, and then they are cross-checked through companies' official websites.
This study uses 178 Vietnamese listed companies including 1424 observations that represent seven essential product and manufacturing sectors (especially excepting finance and real estate). The Vietnamese government's massive privatization scheme since 1986 has changed significantly ownership structure in Vietnamese enterprises. Therefore, the listed equity market of Vietnam, which has been available since 2000, constitutes an interesting venue for governance research [31].
Besides, the research period runs from 2010 to 2017, which is relevant to two remarkable events: (1) the period is marked as Vietnamese economic recovery since the happening of the financial crisis in 2009 [70]; and (2) the "law on enterprises" was revised in 2014. The new regulations highlight the important role of internal governance mechanisms in firm performance improvement [31], and the essential role of privatizing state-owned enterprises [71].

Variables and Econometric Models
Since Morgan proposed their RiskMetrics in 1996 (see RiskMetrics Group in 1994) (as stressed in [72], this sort of risk method was proposed in early of 1963 by Baumol and was referred to as the expected gain-confidence limit criterion [73]), value at risk (VaR) (See an internal model-based approach to market risk capital requirements (Bank for International Settlements in 1995)) has widely recognized as a compelling tool in monitoring financial risk that goes beyond the financial sector [4]. It is defined as the possibility of maximum loss in a confidence level following as: where F X is the distribution function of the loss.
In this study, we use the generalize hyperbolic distribution (GHD) to calculate VaR and expected shortfall (ES). That distribution is acknowledged to be the comprehensive of downside risk measurement [1,24]. According to [25], GHD can be presented as: where, and 0 ≤ β ≤ α; µ and λ ∈ R, and δ > 0. The parameters µ and δ representing the location and scale, respectively. The shape parameters, α and β, correspond to tail heaviness and asymmetry of the density, respectively. K λ is a modified Bessel function of the third kind and x ∈ R. By considering excessive risk-taking as the main reason contributing to the unsustainability of the market and directly affecting firm's competitiveness, our paper will focus on exploring the role of gender diversity on excessive risk-taking behavior as follow: where Risktaking is classified by the risk attributes of downside risk. Gender defines gender diversity. Board and Firm represent for board characteristics and firm characteristics respectively. All variable definitions are presented in Table 1.
The model is basically estimated by two-stage least squares (2SLS) with robust standard errors clustered by firm. Potential problems of endogeneity are considered in model estimation. Following [26], we test and confirm that the own variable is truly instrumented by lnage and fbpower (represent for the female senior managers on average of all firms in the same sector) with the null hypothesis of Wooldridge test indicating exogeneity. Further, we apply the Sargan test for over-identifying restrictions to check for instrument exogeneity, where insignificant test statistics indicate that the instruments may be valid. Additionally, we highlight that the proportions of female managers could also be endogenous because of a reverse causality of firm risk and the appointment of the executive managers [14,74]. The variables of gender diversity, therefore, have been lagged to alleviate that concern. We further robust our results, even overcome these limitations by applying generalized method of moments (GMM). It is addressed to control for simultaneity concerns, omitted variable bias and the dynamic relationship of current appointed female executive managers and previous realizations of risk [75].

Risk measurement
• Individual risk IR Generalized hyperbolic distribution-based value at risk (VaR) at 99% confidence level, derived from the firm's market price • Systemic risk (SR) SR Generalized hyperbolic distribution-based conditional value at risk (CVaR) at 99% confidence level, derived from the firm's market price

Firm characteristics
• Size of firm Size Size of the firm is equal to the natural logarithm of total assets • Cash flow ratio Cash The ratio of cash flow to total assets • Book equity ratio Bea The ratio of total book equity to total assets • Tangible assets ratio Tang The ratio of tangible assets to total assets • Firm leverage ratio Lev The ratio of total debt to total assets • Firm market ratio MB The ratio of the market capability to book value • Ownership ratio Own The ratio of firm ownership to total equity

Dependent Variable
We conceptualize downside risk that is proxy into three risk attributes including individual risk (IR) and two its sub-components, namely, systemic risk (SR) and systemic contribution risk (CSR). First, we estimated the IR, which is defined as the maximum possible loss of each firm's market value asset at a given confidence level (99%) (e.g., the GHD-based value at risk/VaR). Second, we calculate SR, which is defined as the maximum possible loss of the system's market assets at a given confidence level (99%), conditional on each firm's IR (i.e., the GHD-based conditional value at Risk/Expected shortfall). Finally, the CSR of each firm is determined by the difference between IR and SR. The accuracy of the risk calculation is carefully validated by the percentage of violations from [76].

Key Explanatory Variables
To explore the impact of female managers on downside risk, we consider the proportion of all women on (1) senior and (2) non-senior management and their position as the firm's representation in law such as (3) chairman and (4) the CEO. In addition to further our findings and test for the validity of regression results, we measure the proportion of executive and non-executive female directors to board size (exe and non-exe, respectively), which estimate whether the impact of female directors on risk-taking is a result of management responsibilities.

Control Variables
According to prior literature, we then select a set of control variables and devices into two groups: (1) board characteristic and (2) firm characteristic.
Board characteristics: We used both ages of the chairman (Achair) and CEO (Aceo) to control for the working experience. With regards to the structure of the executive managers, we considered senior and non-senior size (illustrated by Board and Manager respectively), measured by the natural logarithm of the number of women on board and lower-level managers. Furthermore, duality controls for the different from power between chairman and CEO in firm final decision making.
Firm characteristic: It indeed had been found that the existing inconclusive evidence of the female leadership is inadequate for other factors explaining financial performance [77,78]. We thus controlled the size of firms, cash flow, shareholder fund, tangible asset, leverage, growth opportunities, and ownership structure. However, other firm-specific characteristics that are unobservable or unmeasured in our model (e.g., the appointment of a new CEO) could result in an estimation bias [48]. Table 2 shows the descriptive statistics of all the variables. The percentage of observations (firms) with at least one women on the management board is 22%, which are increased to 26.97% when it refers to non-senior managing level. The proportion of women at the chief executive officer (CEO) position is quite low (9.55%), even as chairman of firms (10.67%). These numbers are consistent with the report of Thornton (2019). It indicates that the joining of women at the executive level is no more than 30% compared to their counterparts. The average size of the board of directors (management) is approximately nine directors (six managers). On average, the women hold the executive position lower than their counterparts, even the total number of senior managers is higher than non-senior managers. Moreover, the sample contains the average percentage of major shareholders (own) is 59%.  Table 3 presents the correlation matrix between independent variables. All coefficients are generally low, being the highest relevant coefficient between the age of Chairman and CEO (0.437).

Data Analysis
To check whether a problem of multicollinearity might be present, we perform a variance inflation factor (VIF) test. There are no serious problems of multicollinearity and all the condition indices are below 10 [79]. Furthermore, the mean VIF of all variables is 1.42, which confirms the validity of variables using in this study. Table 4 shows the results of 2SLS estimations with robust standard errors clustered by the firm for the three measures of downside risk: individual risk (IR, columns 1-4), systemic risk (SR, columns 5-8), and systemic contribution risk (CSR, columns 9-10). To test H2a and H2b, we distinguish women as chairman is the head of the board of directors while the CEO is the top senior executive. We found that both IR and SR are increased by both female CEO and chairman, but have no significant impact on CSR. Thus, these findings support both H2a and H2b, but reject H2c. The significant and negative effect of CEO and chairman to IR and SR regards to the assumption of agency theory with the special characteristics of women on their employment risk consideration [80]. In support of H1a, we provide evidence that the presence of women in firm senior management is negative and significant in determining individual risk, but it does not show a significantly negative relation to SR and CSR. Thus, the results do not support H1b and H1c. According to [2], women are more efficient to improve internal mechanisms. Thus, their appearance of firm management in reducing excessive risk-taking behavior is strongly supported [1].

Two-Stage Least Squares (2SLS) Testing
Among the control variables, the increase in firm size causes a decrease in all risk attributes. However, the positive impact of Bea and Tang shows the logical evidence that firms that have more financial capabilities tend to take more risks than the others.      Table 5 shows whether the impact of female managers on corporate risk-taking is robust to the application of the generalized method of moments (GMM) model. The outcomes are still remained as 2SLS's results and corroborate our main findings to support H2a and H2b. These results confirm that the representation of women as the firm's CEO and Chairman reduce both individual risk (IR) and systemic risk (SR). In particular, women are mentioned as less risky [53], and more conservative than male counterparts [52,69]. Thus, the negative relationship between top female leaders infirm and corporate risk-taking is established. Furthermore, we found no significant effect of female CEO to CSR, which reject H2c.

Generalized Method of Moments (GMM)
In addition, to test H1a, H1b, and H1c, we conjecture that the risk orientation of a firm is heterogeneous and differs depending on the managing levels. We find that by distinguishing senior and non-senior managers, all risk attributes (including IR, SR, and CSR) mainly decrease by the increase in the female non-senior managers, whereas senior managers reduce only individual risk (IR). Thus, these findings only support H1a. These findings are consistent with [1,11], which encourage the high proportion of women in managerial levels to reduce downside risk. In another hand, the linkage between the number of female managers and executives is probably from the outside pressure to create greater diversity, instead of firm value enhancing [81]. In that context, if women are not required to increase the firm's benefits, female managers and executives are more associated with less aggressive investment policies and better acquisition. Therefore, the role of women in firm management is more consistent with institutional ownership rather than their interest in maximizing the managerial incentives. Thus, that characteristic reduces excessive risk-taking behavior which decreases the firm's downside risk, especially in the manufacturing sector [82].

Further Analysis
To further our analysis, we continue running the 2SLS and GMM to estimate whether the female executive or non-executive makes the impact to firm's downside risk. After running the robustness tests for endogeneity concern, the outcomes from Table 6 indicate that the women make the significant effect on individual risk only in the case of executive director. That finding acknowledge that the women benefit firms in higher power position such as executive directors or managers [33]. In addition, we find no significant relationship between female non-executive directors and risk attributes. That result clarifies the findings above that the proportion of female senior managers reduces firm risk-taking only if they hold a more powerful position in board of directors. In another meaning, it confirms that women need to face a "second glass ceiling" since their power is limited by non-executive even after attending to the board level [32]. In line with that view, the role of a non-executive director is commonly mentioned as a board supervisor that scrutinizes executive director's performance, information asymmetries and dysfunctional working relation rather than involvement to a firm's strategy planning [83].
In the context of gender diversity in high or low-risk firms, Table 7 shows the quantile regression to consider heterogeneous responses to gender diversity in executive management. Intuitively, high and low-risk firms (Q25: 25th percentile and Q75: 75th percentile) might respond differently from the women on alternative management levels. This viewpoint implies that it is possible to represent the relationship between gender diversity and risk with different estimation according to the firms' riskiness. We justify the use of quantile regressions with the Breusch-Pagan/Cool Weisberg tests which reject the null hypothesis if homoscedastic errors for all models. We find that in high-risk firms (Q75), the appearance of women in non-senior management levels and female chairman decreases all risk attributes. Furthermore, in low-risk firms (Q25), the outcomes indicate that the appearance of women in both senior and non-senior management plays a critical role in reducing firm risk-taking. In addition, the firm ownership increases the risk-taking in case of high-risk firms which explained the role of power concentration incorporates the risk.   This table presents one-step GMM estimations by firms where ownership is instrumented with the female on board concentration of other companies of the same year and with the logarithm of the firm's age. Hansen' J presents the p-value for the test of over-identifying restrictions with the null of the validity of the instruments. ** p < 0.05; *** p < 0.01. Table 6. The impact of female executive and non-executive directors onboard and downside risk.

Discussion and Implications
The occurrence of the financial crisis has made risk management become the important element in business [24]. It is clearly mentioned that good corporate governance alleviates the downside risk of firms and even financial market [4,6]. By considering women in alternative managerial levels incorporate risk-taking, this study aims to consolidate and extend the results of [1]. We consider compositing of three risk attributes (i.e., individual risk, systemic risk, and contribution risk) which are measured by parametric-based value at risk (VaR) and expected shortfall.
To answer the research question on the role of corporate governance in risk management, especially in Vietnam as a frontier market, our main argument is that women could reduce the agency problem in firm management, which enhances their impact on executive decision-making even in reducing downside risk [12,56]. Similarly, ref. [84] showed that female managers improve effective collaboration among all board members that lead to an increase in accounting return [85]. In such a context of gender diversity and downside risk, our empirical results indicate that the risk attributes reduction is mainly driven by female non-senior managers who provide more specific expertise with their conservative characteristics for board's decisions as they are appointed [65]. Besides, we provide the evidence for the female CEO and chairman to increase the IR and SR It explains that the female top executives do the business orientation in manufacturing firms with fewer risk strategies. Therefore, their experience and education will influence the board in identifying effective risk-considering actions [86]. In addition, we also found that women are limited their involvement to a firm's strategy if they are appointed as non-executive directors [32]. Otherwise, the female executive director has a negative impact on firm risk (IR). In this process, the stand IR is important because the risk is the main component to achieve a successful investment strategy that defines the firm's industrial competitiveness [14]. On the other hand, the SR and CSR were marked as the critical factors that lead to the financial crisis [5]. The relationship between gender diversity and downside risk is also determined whether firms are high or low risk-takers. We find that women have more impact on reducing excessive risk-taking at both senior and non-senior management in low-risk firms, but it does not support the case of female CEO. This is probably due to the fact that they are less prone to engage in activities as CEO with uncertain economic results or against the desires of the firm.
Consequently, our study successfully links gender diversity with the firm's risk management, especially downside risk. We apply the comprehensive proxy measure of gender diversity that involves female managers and executives. Our results demonstrate that a high proportion of women in alternative firm managerial levels lowers risk attributes, which are proxies for downside risk. In a context such as developing Asian countries, the proportion of women is slightly lower firm management level, our study is very important, once it shows the vital role of women in reducing the firm's downside risk [3]. Therefore, the policymakers, specifically in countries that are similar to Vietnam, should control the proportion of women in firm managerial levels to ensure gender equality and systematic risks. However, this study does not mention the quotas to achieve gender equality in the management structure. On the other hand, the appearance of women may not relevant to a firm's value-enhancing strategy [81]. In such a case, women tend to take less risk strategy rather than maximize managerial incentives from increase firm risk. Therefore, high-risk firms may consider increasing the number of women in management to lower the risk.
From this study, we provide the most important findings on the role of gender diversity, not only onboard but also on firm management in reducing downside risk. As with most research, we mention several limitations for future studies. First, we restrict the data from only Vietnamese listed companies which represent for frontier markets. Future studies may include different industrial sectors or countries. Second, we restrict women only on executive and management levels. Future work may consider clarifying their role in alternative positions (e.g., institutional ownership).