Does corporate governance have a differential effect on downside and upside risk?

Correspondence Searat Ali, School of Business, Faculty of Business and Law, University ofWollongong, Northfields Ave,WollongongNSW2522, Australia. Emails: searat@uow.edu.au Abstract We investigate whether corporate governance has differential effects on downside and upside risk. Intuitively, strong corporate governance should decrease the downside risk but increase the upside risk. However, using a large panel of 1164 non-financial Australian firms from 2001 to 2013, we find that strong corporate governance relates negatively not only to downside risk but also to upside risk. These findings are robust to alternative risk-taking and corporate governance proxies and alternative sample specifications.We also show that our main results are unaffected due to endogeneity bias by using firm and industry-year fixed effects, lagged independent variables, generalized method of moments and entropy balancing estimation techniques. In additional analyses, we document that our main results are homogeneous across different industries and for firms with varying levels of boardroom gender diversity. However, we find that our main results are driven by firms with lower ownership concentration aswell as by older andmoremature firms. Finally, we document that while reducing risk-taking (downside and upside risk), corporate governance reduces firm value. From a regulatory perspective, these findings raise questions on the design ofmonitoring-focused corporate governance recommendations and have implications for risk management.

role of corporate governance mechanisms in a firm's risk-taking, but the direction of the relationship (positive or negative) is unclear. Notably, the measure of corporate governance seems to drive the positive or negative relationship. On the one hand, governance strength measured through external mechanisms (e.g., anti-takeover provisions) produces a positive effect on risk-taking (e.g., Ferreira & Laux, 2007). The findings of these studies, however, are not generalizable to countries where anti-takeover provisions are non-existent. On the other hand, governance strength measured through internal mechanisms (e.g., board independence) reduces risk-taking (see e.g., Pathan, 2009). 1 However, the risk-taking proxies (i.e., total risk, idiosyncratic risk or systematic risk) used in this stream of literature do not differentiate downside and upside risk. Therefore, an important question is unexplored: Does firm-level monitoring-focused corporate governance reduce downside risk but increase upside potential?
Only recently, Wang et al. (2015), who use downside risk as a proxy for risk-taking, find that firms with strong corporate governance tend to have a lower level of downside risk in Taiwan. Our study differs from the study by Wang et al. (2015) in two important ways. First, we primarily focus on the independence of board and subcommittees; however, the prime focus of their study is on ownership structure. Unlike Taiwan, where ownership structure is an important governance mechanism, the board independence and subcommittees are more important for monitoring managerial behavior in Australia (Pham et al., 2011). Furthermore, the recommended percentage of independent directors is at least 50% in Australian firms, while the percentage of independent directors is 12% in Taiwanese sample firms (Wang et al., 2015). Given such a low percentage of independent directors in Taiwanese firms, the generalizability of their findings is critical to economies where board independence is high. Second, instead of merely focusing on downside risk, we also examine the corporate governance effect on upside risk. Overall, we augment the existing literature by examining the role of firm-level monitoring-focused corporate governance mechanisms (i.e., independence of board and subcommittees) in both downside and upside risk, with a focus on Australian firms.
The Australian Securities Exchange Corporate Governance Council, hereafter ASX CG Council, released the third edition of "Corporate governance principles and recommendations" in March 2014, to be effective on June 30, 2014.
The key changes made in the third edition are related to the recommendations on risk to reflect the lessons of the global financial crisis. 2 Given such changes relating to firm risk, it is timely to investigate the role of corporate gov-ernance mechanisms more important (Pham et al., 2011). Finally, we measure risk-taking by using three dimensions: total risk, downside risk and upside risk. Total risk is measured through the annualized standard deviation of daily stock reruns. Downside risk (upside risk) is measured using the left tail (right tail) of the return distribution. Specifically, downside risk (upside risk) measures potential losses (gains) over a specific time horizon at a given confidence level.
Our baseline empirical analysis reveals that strong corporate governance is associated with the reduction of total risk and downside risk, as well as upside risk. The association survives even after controlling for an industry effect, for a year effect and for firm characteristics. While showing that corporate governance reduces both downside and upside risk in Australia, we extend the prior literature (Ni & Purda, 2012;Pathan, 2009) that indicates a negative relationship between board independence and risk-taking in the United States. Our findings provide insight into the inconsistent influence of corporate governance on financial outcomes, as well as complement the study of Swan and Forsberg (2014) who document the value-destroying effects of independent governance structures for Australian firms.
We then perform a variety of checks, noting that the main findings are robust to alternative proxies of risk-taking (i.e., within-firm overtime operating performance variability, within and across firm operating performance variability and quantile regression-based risk metrics), individual governance mechanisms (i.e., independence of board and subcommittees), alternative proxies of corporate governance (i.e., Horwath corporate governance ranks and stars) and alternative sample specifications (i.e., excluding firms that do not have data throughout the sample period, excluding firm-year observations from global financial crises and excluding the largest and smallest 10% firms from the sample).
A methodological challenge for our study is the possibility that the negative effect of corporate governance on risktaking is driven by the endogeneity bias (i.e., omitted variables and reverse causality). For instance, the attitude of a firm toward corporate social responsibility (CSR) is arguably an unobservable factor that may affect firm risk and the board appointment process simultaneously. Prior studies suggest that CSR-compliant firms have low risk and at the same time have greater demand for independent directors, rendering our results spurious. Moreover, it is possible that corporate governance and risk-taking are determined simultaneously; that is, not only corporate governance may impact firm risk, but firm risk may also trigger changes in governance structure. For instance, Linck et al. (2008) and Monem (2013) show that firms with high risk may decide to adopt more independent governance mechanisms. If this is the case, current governance structure is likely to be influenced by past realization of risk-taking (i.e., reverse causality).
We use several identification strategies to alleviate these concerns and help establish causality. First, we apply a firm and industry-year fixed effects (FE) regression to overcome the issue of time un-varying omitted variable bias and to estimate the overtime influence of corporate governance on risk-taking. We also include the environmental, social and governance (ESG) score to control for the firm's attitude toward CSR. Second, we employ regressions based on 1 and 2 years lagged values of independent variables, which is less susceptible to reverse causality. Third, we employ a dynamic panel data estimation technique, that is, two-step system generalized method of moments (GMM). Finally, we implement an entropy balancing approach where each firm-year observation in the control group is reweighted in order to make the distribution of the covariates (i.e., mean, variance and skewness) similarly comparable in the treatment and control groups (i.e., firm-year observations with high and low corporate governance). Overall, the results from these identification tests confirm our main findings, that is, corporate governance reduces total risk, downside risk and upside risk.
We then explore when does corporate governance reduce risk-taking? To answer this question, we consider the role of industry membership, director gender, ownership concentration and firm life cycle in the relationship between corporate governance and a firm's risk-taking. First, we show that our main results exist in all the sectors except telecommunication services, information technology and utilities. Second, we find no apparent difference between firms with at least one woman director and those without any women directors. Third, we show that for high ownership firms, corporate governance reduces risk-taking but with less statistical significance. However, for firms with low ownership concentration, corporate governance is found to sharply reduce risk-taking with high statistical significance.
Finally, we find that for firms that are older and more mature, corporate governance significantly reduces risk-taking.
However, for firms that are younger, such an effect is not observed. Overall, we find that our main results of corporate governance reducing risk-taking are not dependent on the type of industry and the gender of directors. However, we find that ownership concentration and life cycle drive the inverse relation between governance and risk-taking. These results imply that ownership concentration and life cycle stages are important to consider while designing a firm's corporate governance (board structure) to adjust the risk-taking propensity of the firm.
So far, our main findings suggest that corporate governance reduces risk-taking (i.e., total risk, downside risk and upside risk). However, our understanding is limited if the inverse effect of corporate governance on risk-taking is value-relevant. Prior studies find mixed results between corporate governance and firm value (Christensen et al., 2010;Henry, 2008;Pham et al., 2011); some find evidence of beneficial effects, while others report no effects or even harmful effects. With no definitive conclusions, the question of whether corporate governance improves firm value remains inconclusive. To resolve this matter, we raise an additional question: Does reduction of risk-taking in response to strong corporate governance increase or decrease firm value? Following prior literature (Cheung, 2016;Harjoto & Laksmana, 2018), we use path analysis to examine the direct and indirect effects of corporate governance on firm value conditioned on risk-taking (i.e., total risk, downside risk and upside risk). Our results suggest that corporate governance reduces risk-taking (including total risk, downside risk and upside risk), and lower risk-taking leads to lower firm value.
Our study makes an important contribution to the literature while showing for the first time the inverse effect of corporate governance on risk-taking, including both downside and upside risks, in particular for firms with low ownership concentration and for firms in the mature and older stages of the life cycle. Since firm risk-taking is quite central to the value creation process, we also show that the inverse effect of corporate governance on risk-taking leads to reduction in firm value. These findings have implications for both regulators and shareholders who design regulations relating to the composition of board structure and who vote to elect directors as their representatives, respectively.
The role of independent boards in influencing corporate decisions must be clear to both parties. The findings of our study suggest that independent directors may act as devices to minimize unanticipated losses but may not improve the likelihood of unanticipated gains. From a wider regulatory perspective, these findings raise questions about the design of governance recommendations that are skewed toward monitoring mechanisms (i.e., the majority of independent directors on the board). Such governance recommendations are potentially limiting the upside potential by controlling the managerial entrepreneurial spirit to take on risky projects. Although excessive risk-taking behavior is clearly harmful to the firm and increases the risk of bankruptcy, overly conservative decisions may be equally detrimental, increasing the chance of missing the risky but value-enhancing projects. Hence, our study calls for a balance between monitoring by independent directors to curtail excessive risk and maintaining adequate exposure to opportunities with significant upside potential. In practice, this can be achieved through a balance between monitoring and reward structure.
The remainder of the paper is structured as follows. Section 2 presents the theoretical framework and hypotheses development. Section 3 describes the data, variables, estimation models and econometric methods and provides summary statistics. Section 4 discusses the empirical results on the relationship between corporate governance and risk-taking. Section 5 presents the results on the question: When does corporate governance reduce risk-taking? Section 6 reports the results on corporate governance, risk-taking and firm valuation. Section 7 concludes the paper.

Corporate governance and the firm's overall risk-taking
The implication of corporate governance on the firm's risk-taking can be viewed from the typical principal-agent relation. In the presence of separation between ownership and control, there will be some divergence between the agent's decisions and those decisions that would maximize the welfare of the principal (Jensen & Meckling, 1976). Excessive managerial risk aversion construes that firms will fail to maximize shareholder wealth by losing profitable investment opportunities. This sort of risk aversion may fail to entice potential investors, which may affect a firm's ability to compete, and eventually its survival. In contrast, an appetite for higher risk also results in massive bankruptcies, causing repercussion in destabilizing the financial and economic system. Two competing hypotheses predict either a positive or negative relationship between corporate governance and the firm's overall risk-taking: risk avoidance and riskseeking.
The proponents of risk avoidance hypothesis argue that managers may take less risks for at least two reasons.
First, K. John et al. (2008) suggest that managers are risk-averse because of their pursuit of personal benefits, including the corporate cash flows that they plan to divert to themselves at the expense of shareholders. This managerial cash flow diversion is expected to be lower if the firm has low cash flows because in this situation, there are few corporate resources to siphon, and hence siphoning behavior becomes readily detectable. To preserve their private benefits (i.e., cash flow diversion), managers may even forgo positive net present value risky projects. They only take risky projects if the expected outcome in the high cash flow state compensates for the lower level of diversion in low cash flow state.
Hence, if important private benefits are available to the managers, they are more likely to adopt conservative investment policies. Strong corporate governance should dampen the importance and the magnitude of private benefits to managers, resulting in less forgoing of firm value-enhancing risky projects. Second, the compensation structure also affects managerial risk choices. T. A. John and John (1993) suggest that in the presence of a simple compensation contract with no incentive feature {S, } (i.e., S denotes fixed salary of the managers in solvent states and ∅ denotes salary reduction for the managers in default states), the manager shows high levels of risk aversion and invests in riskless projects that have a zero net present value (no increment to value). Such a scenario is consistent with the overly conservative managerial behavior motivated by undiversified human capital and concentration of wealth in the firms they control (Wright et al., 1996). Risk-taking requires more effort to manage new ventures and a failure to manage risk may bring anxieties, putting managers out of their jobs. Baysinger and Hoskisson (1990) argue that managers are more concerned about their career (e.g., loss of reputation in the labor market) than the maximization of shareholder profit. Amihud and Lev (1981) show that powerful managers are motivated to be involved in risk reduction activities (e.g., diversifying conglomerate mergers). May (1995) argues that risk-averse managers may reject risky value-enhancing projects and accept safe value-reducing projects. Consistent with these arguments, Kim and Buchanan (2008), who investigate the association between chief executive officer (CEO) duality and risk-taking behavior in the US firms, find that firms with CEO duality take less risks. Likewise, Pathan (2009) finds a negative relation between CEO duality and bank risk-taking. He argues that powerful CEOs take less risks because their undiversifiable human capital leads them to develop a higher degree of risk aversion, resulting in less risky corporate strategies. Strong corporate governance, therefore, should impose more restrictions on managers, allowing managers less freedom in formulating corporate policies that reflect their own risk aversion. As a result, the propensity for risk-taking should be more in firms with strong corporate governance. Several empirical studies provide support for this hypothesis (see e.g., Ferreira & Laux, 2007;Li et al., 2013).
The proponents of a risk-seeking hypothesis argue that managers may take excessive risks for at least three reasons. First, managerial compensation is contingent on firm performance in most of the managerial compensation contracts. Given that managers are risk-averse, the nature of these incentive contracts encourages them to take more risks in order to obtain lucrative compensation. In pursuit of this, executives may take unnecessary risks and destroy the wealth of the shareholders as in the cases in the global financial crisis. In a similar vein, T. A. John and John (1993) suggest that in the presence of a simple compensation contract with incentive feature {S, ∅, α}that is, S denotes fixed salary of the manager in solvent states, ∅ denotes salary reduction for the managers in default states and α denotes to pay-to-shareholder sensitivity of the management compensation contract-the manager shows a high level of risk-taking and invests in high-risk projects that may have a negative net present value (destroy firm value). Therefore, strong corporate governance is expected to protect shareholders from excessive risk-taking. Second, powerful managers lack opinion diversification and compromise less with other executives, which increases the likelihood of "less balanced decisions" (either very good or very bad). Such extreme decisions result in more variability in firm performance, which reflects higher risk (Adams et al., 2005). Therefore, strong governance is less likely to prevent managers from taking too much risk. Third, Yixin Liu and Jiraporn (2010) argue that managerial dominance may increase information asymmetry in the firm, which makes it difficult for bondholders to monitor the actions of the managers, and thus bondholders require a higher yield (cost of debt). This suggests an increase in performance variability for firms that have a powerful CEO. These arguments suggest that strong corporate governance should lead to less risk-taking. The study by Jiraporn et al. (2015) provides support for this hypothesis.
The governance metrics in our study cover four dimensions of corporate governance (board, audit, nomination and remuneration), consisting of a total of 17 governance factors. The ASX CG Council (2003) recommends that firms' boards have a higher proportion of non-executive independent directors. The independent directors are effective in reducing agency problems by monitoring and controlling managerial opportunistic behavior (Fama & Jensen, 1983). Independent directors monitor managers more, making them cautious in their decision-making, which may reduce the firm's risk-taking. There are four reasons why the presence of independent directors may do so. First, the performance-based compensation encourages individual's risk-taking behavior (Fama, 1980;J. Wu & Tu, 2007) and in comparison to inside directors, the independent directors receive fewer performance-based compensations (Perry, 2000). Conclusively, independent directors may face lower motivation to take high risks in search of large positive returns. Second, managerial compensation contracts are designed by boards of directors that are acting on behalf of shareholders. Recently, Ongsakul and Jiraporn (2019) showed that risk-taking compensation incentives are viewed unfavorably by independent directors. Hence, independent directors are likely to design compensation contracts with less risk-taking incentives, which may promote managerial risk aversion, leading to rejection of value-enhancing risky projects. Third, to sustain their current directorship and to attain new ones, independent directors are more concerned about their reputation as an effective monitor (Fama & Jensen, 1983). As independent directors may lose significant reputation, in case of failed projects or any operating irregularity, independent directors may not take the high-risk projects. Fourth, there is a negative relation between independent directors and the cost of debt because independent directors bring improvement in the disclosure (R. C. Anderson et al., 2004), and there is an inverse relation between disclosure and firm-specific risk (Bartram et al., 2012). Therefore, independent directors may reduce the risk of the firm through the improved information disclosure. Consistent with these arguments, most of the empirical studies find a higher proportion of independent directors to be associated with reduced risk-taking in the US firms (Minton et al., 2011;Ni & Purda, 2012;Pathan, 2009).
The ASX CG Council (2003) recommends that firms separate the roles of CEO and chair of the board, and that an independent director should chair the board. These recommendations aim to make the board more independent and effective in monitoring the management. Moreover, the ASX CG Council (2003) suggests that firms should have a committed board that adequately discharges its responsibilities and duties. The frequency of board meetings can serve as a proxy for board commitment. With more frequent board meetings, the board is likely to have richer information about the firm's operating environment, which improves the board's ability to effectively exercise its independent monitoring role (Rutherford & Buchholtz, 2007).
Since many decisions taken by the board occur at the committee level, we examine if the existence and strength of board committees reduce firm risk or not. The ASX CG Council (2003) recommends that firms establish three board subcommittees: audit, nomination and remuneration. The audit committee is considered to be an important internal governance mechanism that assists in the reduction of information asymmetry between shareholders and management (Adams & Ferreira, 2007). Its interaction with external auditors assists the board to ensure that the financial statements represent a true and fair view of the firm's financial condition (Platt & Platt, 2012). Klein (2002) argues that an audit committee composed of independent directors improves board effectiveness in monitoring management, resulting in fewer earnings manipulations. Recently, Guo and Masulis (2015) found that the independence of the nomination committee leads to more rigorous CEO monitoring and discipline. Given this evidence, we argue that the existence and strength of the board subcommittees play an effective monitoring role, and so are likely to reduce the firm's overall risk-taking. Downside risk refers to the degree to which the asset value may decrease below a specific target, whereas upside risk denotes the extent to which the asset value may increase above the predetermined benchmark. Downside risk is undesirable because it is associated with investment underperformance and losses, whereas upside risk is desirable because it is linked with investment over performance and gains. The measures of the firm's overall risk, such as standard deviation of stock returns, treat the fluctuation above and below the mean in the same way; however, economists have long recognized that investors care differently about downside losses than they care about upside gains (Markowitz, 1952;Roy, 1952). In fact, investors require compensation for bearing downside risk (Ang et al., 2006).
Investors' loss aversion preferences can be explained by the behavioral framework of Kahneman and Tversky (1979). According to this framework, there is a reference point (such as the current level of wealth) relative to which investors evaluate outcomes, and there is a value function that investors use to evaluate probabilistic choices. The value function is convex below the reference point (risk-seeking) and concave above (risk-avoiding). The value function attaches greater weight to losses than to equivalent gains.
In this study, we apply the loss aversion model to the corporate board's risk management policies. One of the key functions of corporate boards is to review and guide the risk management policy of a firm. Although an independent board will prevent a firm from engaging in extremely risky investment and financial policies that threaten the future prospects of the firm, an overly active independent board may deter the entrepreneurial spirit of the management.
In the presence of regulatory pressure and the perception of proliferated liability, independent directors may offer excessively cautious or conservative strategic advice to protect their reputation (Korn/Ferry, 2005). If this is the case, such advice may curtail downside risk to the detriment of realizing upside potential.
As shown in Figure 1, more than 70% of surveyed Australian company directors felt that the governance regulations of 2003 caused board attention to focus on preventing downside risk (D. W. Anderson et al., 2007). Less than 5% felt that these governance regulations caused board attention to focus on maximizing upside potential (D. W. Ander-son et al., 2007). Considering these statistics, we argue that an internal governance mechanism (i.e., independent board and subcommittees) may be less effective in promoting managerial risk-taking behavior. Thus, these governance mechanisms may minimize downside risk arising from agency costs but may not increase upside risk. In fact, they may also decrease the upside risk.
Given the above arguments, we hypothesize the following: H2: All else being equal, the strength of corporate governance (as measured through board monitoring) reduces not only downside risk but also upside risk.

Sample and data
The initial sample of 13,500 firm years consists of all Australian listed firms whose corporate governance data are available in the Securities Industry Research Centre of Asia-Pacific (SIRCA) during the period from 2001 to 2013. 4 We exclude financial firms because the optimal degree of risk-taking is different for financial firms (such as banks) than that of non-financial firms. If banks become financially distressed, they are supported by a financial safety net that provides incentive to banks to take excessive risk. Therefore, the association between governance and risk factors is expected to be different for financial firms (Laeven, 2013). We obtain data on firm characteristics and downside risk from the Morningstar DatAnalysis Premium and SIRCA, respectively. We condition the inclusion of each firm-year observation in the sample on the availability of data related to (1) corporate governance, (2) financial characteristic and (3) risk-taking. The final sample comprises 9412 observations on 1164 non-financial firms across all size groups (see Appendix A for the sample selection procedure). To eliminate the undue influence of extreme values in the data, possibly due to spurious outliers, all continuous variables are winsorized to the 5th and 95th percentiles.

Measures of corporate governance
The key independent variable in our study is corporate governance. We follow the Horwath report to capture the corporate governance standing for each of the considered firms. The Horwath report provides composite ratings based on six categories, namely, (1) board structure, (2) audit committee, (3) nomination committee, (4) remuneration committee, (5) external auditor independence and (6) code of conduct and other policy disclosures. 5 Multiple aspects may limit the generalizability of the findings obtained through the Horwath report. First, the Horwath report covers the top 250 firms each year; thus, the findings may not be generalizable to mid-cap and small-cap firms. Second, the Horwath report is available up to 2008; therefore, the findings do not consider the more recent market developments, particularly after Global Financial Crisis (GFC). Third, full details of the Horwath rating system are proprietary and confidential, so we are unable to make any comments on the assignment of ranking and stars beyond the information given in the reports. In addition, two of the six categories in the Horwath report are subjective. This may limit the implications of the findings for the investors, as they may not be able to replicate the entire Horwath 4 Why does our sample period end in 2013? The ASX CG Council released the third edition of Corporate governance principles and recommendations in March 2014, to be effective on June 30, 2014. Since the key changes made in the third edition are related to the recommendations on risk, we aim to test the relationship between governance and risk before the implementation to guide regulators about the potential impact. Moreover, the recommendation mainly focused on the internal audit and control functions (as opposed to incentive mechanisms), so we do not expect our main results of the negative effect of monitoring-focused corporate governance on overall risk-taking, including downside and upside risk, will change using an extended sample.
5 Categories 1-4 are based on objective criteria and Categories 5 and 6 are based on subjective criteria. ratings. Fourth, the Horwath report does not provide the category score/rating, so an important question is unexplored, that is, which governance category really influences risk-taking.
Following prior studies (Ali et al., 2017Nadarajah et al., 2018), we address these issues by collecting an extended corporate governance dataset across both cross-section (large, mid-cap and small firms) and time series (2001−2013) on the objective Horwath categories. These categories are based on 17 criteria. We assign the value "1" if a firm meets the particular criteria and "0" otherwise. For instance, if the majority of directors in a firm are independent, we assign 1 and otherwise 0. These individual values are then aggregated to construct a composite CG index ranging from 0 to 17, where 0 indicates the "worst" governance, and 17 indicates the "best" governance. Each gover-

Measures of risk-taking
The dependent variable of our study is risk-taking. We measure risk-taking by using the three proxies: total risk, downside risk and upside risk. The explanation of these risk-taking proxies is provided in the following section.

Measure of total risk
The first proxy of risk-taking is a total risk (TR). TR captures the overall variability in the stock returns of a firm and reflects the perception of the market about the risk inherent in the assets, liabilities and off-balance sheet positions of a firm. Following prior literature (see e.g., Minton et al., 2011;Pathan, 2009), we calculate the TR of a firm as the standard deviation of its daily stock returns for each financial year. We calculate daily stock returns as the natural logarithm of the ratio of equity return series as follows: where R it is daily stock returns for a firm i in a year t, In is natural logarithm and P it is the daily stock price.

Measures of downside risk
The second proxy of risk-taking is downside risk. We measure downside risk in two ways. The first is the value at risk (VaR), and the second is the conditional VaR (CVaR) or expected shortfall. Since its adoption by Basel, the VaR has become a popular technique to gauge downside risk. It measures potential losses over a specific time horizon at a given confidence level. There is an extensive coverage of VaR in the international literature. For instance, RiskMetrics introduced and popularized VaR (Longerstaey & Spencer, 1996), and more than 70 recognized authors comprehensively discussed VaR in the VaR Modeling and Implementation Handbooks (Gregoriou, 2009(Gregoriou, , 2010. We measure VaR by using two methods: the parametric VaR method (PVaR) and the historical VaR method (HVaR).
For the calculation of VaR, the PVaR method assumes a normal distribution of returns, whereas the HVaR method assumes history repeats itself and groups historical losses in best to worst categories. Since the parametric method assumes normal distribution of returns, we calculate the mean (x) and standard deviation (ơ) to obtain VaR for a single firm i. Given the normal curve assumption, and using the standard distribution table, the point of the worst 5% on the curve is: 95% confidence = −1.645ơx. To calculate VaR, as suggested by RiskMetrics, we use the logarithmic of the ratio of price relatives instead of the actual asset figure (see equation 1).
The HVaR method does not assume normal distribution; rather, it takes the 5 th percentile value as VaR at 95% confidence level. The daily stock returns are calculated in a same way as in the parametric method.
A key criticism of VaR is its inability to capture tail risk, that is, a risk beyond VaR (Allen & Powell, 2012). In addition, VaR has undesirable mathematical properties, such as lack of subadditivity. To overcome these drawbacks of VaR, we use CVaR, also known as expected shortfall, which considers losses beyond VaR (Artzner et al., 1999). CVaR does not contain the undesirable properties of VaR, and it is a coherent measure of downside risk (Pflug, 2000). A number of empirical studies in Australia have used CVaR for ranking risk among sectors (e.g., Allen & Powell, 2009, 2012. If we calculate VaR at the 95% confidence level, CVaR is the average of the 5% extreme returns, and if we calculate VaR at the 99% confidence level, CVaR is the average of the 1% extreme returns. In other words, CVaR is the average loss that incurs for the worst possible cases over a given time period. We calculate CVaR as follows: where R ij is the daily returns for firm i in year t, and n is the number of daily returns below VAR it . To facilitate interpretation, the values of VaR and CVaR are taken as positive in the empirical analysis.

Measures of upside risk
The third proxy of risk-taking is upside risk. It measures potential gains over a specific time horizon at a given confidence level. We measure upside risk in a similar fashion to the measurement of downside risk. The only difference is that downside risk is measured using the left tail (losses) of the stock returns, whereas upside risk is measured using the right tail (gains) of the stock returns. 6 Specifically, to measure upside risk using the historical method, the 5th percentile value is taken as upside risk (UP) at the 95% confidence level, and the average of 5% extreme returns is taken as the conditional upside risk (CuP). In other words, CuP is the average gain that incurs for the best possible cases over a given time period. We calculate CuP as follows: where R ij is the daily returns for firm i in year t, n is the number of daily returns above UP it .

Control variables
To isolate the effect of corporate governance on risk-taking, we include a number of control variables that have been found to influence the firm risk in prior literature (see e.g., Jiraporn et al., 2015;Koerniadi et al., 2014;Wang et al., 2015). They are profitability (ROA), leverage (TLTA), liquidity (CACL), firm size (LNMC), firm age, stock turnover (STO), price to earnings ratio (PER), product market competition (PMC), block holders (BLOCKS) and board size (BSize). Since firms in the same industry are relatively homogeneous (Alford, 1992), we also use industry membership ( Upside potential UP UP is based on the actual historical 95th percentile best return.

Conditional upside potential
CuP CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP).

Independent variable: Corporate governance (G-index)
Corporate G-index CG index CG index is a self-constructed index based on 17 objective criteria of the Horwath report, which ranges from 0 to 17 each year Board quality index BQI Board quality is a self-constructed BQI based on respective criteria, which ranges from 0 to 3 Audit quality index AQI Audit quality is a self-constructed audit quality index based on respective criteria, which ranges from 0 to 6 Nomination quality index NQI Nomination quality is a self-constructed governance category based on respective criteria, which ranges from 0 to 4

RQI
Remuneration quality is a self-constructed governance category based on respective criteria, which ranges from 0 to 4

Estimation model
To test the corporate governance and risk-taking hypotheses (H1 and H2), we specify regression equation (4) as follows: where subscript i denotes the individual firm (i = 1,2,. . . ,1164), t equals the time period (t = 2001, 2002,. . . ,2013), β is parameters to be estimated and ε i,t is the composite error including either industry- To test equation (4), we employ pooled ordinary least square (OLS) as a baseline method. The standard errors are clustered by firm to control for heteroskedasticity and within-firm correlation in the residuals (Petersen, 2009). Table 2 reports the descriptive statistics for the measures of risk-taking, corporate governance and firm characteristics in Panels A, B and C, respectively. The risk measures in Panel A of Table 2 indicate that, on average, the standard deviation of daily stock returns (TR) is 4.97. In terms of downside risk, the mean value at the 95% confidence levels of HvaR, PvaR and CvaR are 7.80%, 7.39% and 9.95%, respectively. These figures are higher than those of Wang et al. (2015) for Taiwanese firms (4.75% for VaR, and 5.86% for CvaR), suggesting higher downside risk in Australia, probably because of the large sample from the mining sector. In terms of upside risk, the mean value of UP is 9.03% and CuP is 12.90%.

Descriptive statistics
With regard to corporate governance variables in Panel B of Table 2, the mean value of the CG index is 8.47 (out of 17) and the range of CG index from 25th percentile to 75th percentile is 7 points. On average, the board quality is 2.08 (out of 3), the audit quality is 3.47 (out of 6), the nomination quality is 1.10 (out of 4) and remuneration quality is 1.85 (out of 4). The average number of directors on a board is six. The product market concentration (power) is 1%, which is lower than that of Taiwanese firms (4%). The percentage of shares held by blockholders is 33.18%, which is higher than that in Taiwanese firms (18.82%).
The escriptivee statistics of the firm characteristics in Panel C of Table 2 indicate that the sample firms have an average total market capitalization of AUD $390 million. On average, debt is 35% of the total capital structure, return on assets (ROA) is −11%, and asset liquidity is 4.66. The mean value of stock turnover is 50% of the total outstanding shares, and on average, the sample firms are 13.90 years old. Last, the average of PER is 2.13. indicates an issue of multicollinearity. The highest magnitude of the correlation coefficient of −0.58 appears between TLTA and CACL. Consequently, multicollinearity may not be an issue in further analyses. Moreover, we estimate the variance inflation factors (VIFs) for all the explanatory variables. The results from VIF (untabulated) are less than "5,"

Univariate analysis
further confirming non-multicollinearity among independent variables. Table 4 reports the results of the univariate analysis that we conducted to further clarify the relationship between corporate governance and risk variables. For this, we classified sample firms into high and low groups, based on corporate governance. The firms whose corporate governance score is higher or lower than the sample median are classified into the high group and low group. We observe a significant difference at the 1% level in all the measures of risk between high governance firms and the low governance firms. Specifically, the strongly governed firms have a signif-   icantly lower level of total, downside and upside risk. These findings provide initial support for the hypotheses that corporate governance reduces total risk (H1), as well as downside and upside risks (H2). Table 5 reports the results of pooled OLS estimates of equation (4), when CG index is the proxy for corporate governance and either TR, downside risk (PvaR, HvaR or CvaR) or upside risk (UP or CuP) is the dimension (proxy) for risktaking. The results for total risk, downside risk and upside risk as dependent variables are reported in Columns 1, 2−4 and 5 and 6, respectively. Industry FE, year FE, and robust standard errors are controlled for in all the regression analyses. The regression equation (4) is well-fitted with an adjusted R-square of 52.6%, 66.5%, 65.4%, 64.4%, 58.5% and 60.9% for TR, PVaR, HVaR, CVAR, UP and CuP, respectively, with statistically significant F-statistics.

Main results
The overall results suggest that corporate governance has a significant and negative impact on the firm's risk-taking.
Specifically, as predicted in H1, the coefficient on the CG index is negative and statistically significant at the 1% level for TR, implying that strong corporate governance reduces a firm's overall risk-taking. This finding is consistent with the finding of Jiraporn et al. (2015) in the United States. As anticipated in H2, the coefficient on the CG index is negative and statistically significant at the 1% level for downside risk, suggesting that firms with strong corporate governance have a lower downside risk. This finding is consistent with that of Wang et al. (2015) in Taiwan. Contrary to the intuition, and in line with H2, the coefficient on the CG index is negative and statistically significant at the 1% level for upside risk, implying that firms with strong corporate governance have a lower upside risk. This finding is novel in its kind because it shows that reduction in risk-taking through corporate governance relates not only to downside risk but also to upside risk. Notably, the reduction in upside risk is almost twice as much as that in downside risk.
Apart from the statistical significance, these results are economically significant as well. We can gauge the economic significance of the results by calculating the marginal effect of an increase in the CG index from the 25th to the 75th percentile, corresponding to an increase in the corporate governance from 5 to 12. Multiplying the change in CG index (7 points) by the coefficient on CG index (−0.068 in Column 1) gives a change in TR of approximately −9.58% of the mean TR. Similarly, downside risk, that is, PVaR, HVaR and CVaR change by −8.43%, −5.70% and −7.52%, respectively, in response to an increase in CG index by 7 points. Likewise, upside risk, as measured by UP and CuP, changes by −9.03% and −12.90%, respectively. Hence, these findings indicate that with an introduction of governance mechanisms that improve the CG index from the 25th to the 75th percentile, the reduction in upside risk is more economically Subscript i denotes individual firms and subscript t time period. The dependent variable, RISK, is either TR (Column 1) or PVaR (Column 2) or HVaR (Column 3) or CVaR (Column 4) or UP (Column 5) or CuP (Column 6). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (with a 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). The CG is a self-constructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). PMC is the annual sales by a firm divided by total industry sales. BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders. LNMC is the natural logarithm of number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets. CACL is the current assets divided by current liabilities. AGE is the natural logarithm of the number of years firm has been listed on the ASX at the end of its financial year. STO is the sum of daily shares traded divided by the number of shares outstanding in the financial year. PER is the market price per share divided by earnings per share. YEAR is the year dummies.  Wintoki et al. (2012) argue that a common problem in the area of empirical corporate governance research is endogeneity. Thus, it is challenging to establish a causal relationship between corporate governance and risk-taking. Prior literature suggests that governance mechanisms are endogenously chosen by firms to suit their operating and contracting environment (Adams & Ferreira, 2007;Coles et al., 2008). Two sources of endogeneity are particularly likely to bias our estimates of how corporate governance affects firm risk-taking.

Endogeneity bias
First, omitted variables (time-varying and time-unvarying; observable and unobservable) may simultaneously affect firm risk and corporate governance, including the director appointment process to the board and subcommittees. It is difficult, if not impossible, to capture all the determinants of risk-taking in the empirical models, which leads to the omitted variable bias. For instance, a firm's attitude toward CSR is an unobservable determinant of firm risk (Sila et al., 2016). On the one hand, CSR-compliant firms may have greater demand for independent directors because board independence is one of the aspects of CSR on which stakeholders evaluate the firm. On the other hand, CSR-compliant firms, through their engagement with stakeholders, have low risk (Godfrey, 2005;Waddock & Graves, 1997). Due to such omitted variables, governance structure may correlate with reduction in risk-taking but may not have a causal effect on risk-taking.
Second, the direction of causation between corporate governance and risk-taking is not clear. It is possible that corporate governance and risk-taking are determined simultaneously; that is, not only corporate governance may impact firm risk, but also firm risk may trigger changes in governance structure. For instance, Linck et al. (2008) and Monem (2013) show that firms with high risk may decide to adopt a more independent governance structure. Likewise, Hermalin and Weisbach (1998) suggest that firms appoint more outside directors on the board following poor performance.
Hence, firms with more uncertainty and that are less profitable may have more demand for independent governance structure. In such circumstances, the current governance structure is likely to be influenced by the past realization of risk-taking.
In order to solve these endogeneity problems, several empirical studies suggest natural experiment as a stateof-the-art solution (see e.g., Black et al., 2015;Chen et al., 2015;Gippel et al., 2015). However, such a methodology requires a purely exogenous natural event. In the context of our study, one may suggest considering ASX CG reforms in 2003 as a natural experiment; however, we are unable to use the reform as a natural experiment because the reform is not a mandate (i.e., quota law); rather, it is non-mandate (i.e., "comply or explain"). Therefore, the change in firm-level corporate governance is still at the discretion of the firm, and thus the impact of the reform is not credibly exogenous. Another common empirical strategy to deal with endogeneity is to identify an instrumental variable (IV) that is strongly correlated with corporate governance but does not have a direct influence on risk-taking. However, it is challenging to find a truly exogenous IV for corporate governance strength. For instance, industry average corporate governance is an IV commonly employed in the literature (Jiraporn et al., 2011;Yu Liu et al., 2014, 2015Yang & Zhao, 2014) as a source of exogenous variation in firm-level corporate governance but is often challenged because of its weak exclusion assumption. 8 Another way to address endogeneity bias due to possible covariate imbalance and selection bias is through multivariate matching methods such as propensity score matching (PSM; Rosenbaum & Rubin, 1983) and entropy balancing (Hainmueller, 2012). Although PSM and entropy balancing approaches both aim to balance the distribution of covariate across treatment and control groups, they differ in how the weights are assigned to the control group. PSM estimates a first-stage treatment model and then matches firm-year observations from the treatment group to the firm-year observations from the control group based on the resulting propensity score, assigning a weight of either those reported in Table 5; thus, we do not report them for brevity. Overall, we confirm that the main results related to H2 are not sensitive to alternative specifications for downside and upside risk. one (matched) or zero (excluded) to each control observation. Entropy balancing identifies continuous weights for all firm-year observations from the control group to equalize the distribution moments (e.g., means, variances and skewness) for all covariates in the treatment and control groups. While PSM is the most commonly used matching method, recent studies have cast doubt on its reliability due to issues including researcher discretion and statistical bias (see e.g., King & Nielsen, 2019). To address such issues, a new matching approach, entropy balancing, is suggested as a preferred approach because it requires fewer assumptions and eliminates the need for researcher adjustment of a propensity model (McMullin & Schonberger, 2020). Taking into account these endogeneity biases and the challenges around identifying a suitable instrument and matching method, our identification strategy includes firm and industry- year FE regression, lagged independent variables, GMM and entropy balancing techniques.

Firm and industry-year FE
FE regression controls for unobserved heterogeneity due to time-unvarying omitted variables that differ across firms but are constant over time. While estimating the effects of independent variables on dependent variables, the FE method focuses on changes over time in the variables. Since this method focuses on the time-series variation between corporate governance and risk-taking, a causal relation between them can be examined using their time-series covariation, FE provides additional insight into the empirical linkage between corporate governance and risk-taking. 9 Table 6 reports the results of the regression equation (4) using firm and industry-year FE in Columns 1−6. The regression equation (4)  In Columns 7−12 of Table 6, we also present the FE results between corporate governance and risk-taking after controlling for the proxy of the firm's attitude toward CSR. As discussed earlier, CSR may simultaneously affect the director's appointment process and firm risk. To alleviate this concern, we collect ESG data from Bloomberg to be used as a proxy for the attitude of a firm toward CSR. The higher ESG score should reflect the positive attitude of the firms to engage with their stakeholders. Our results indicate that the firms with higher ESG disclosure have lower levels of risk-taking. Importantly, we find that even after controlling for ESG disclosure, firms with strong corporate governance have lower levels of risk-taking, including both downside and upside risk. 10

Lagged variables
In this model, we replace the contemporaneous values of corporate governance and other control variables with 1or 2-year lagged values. Regressions based on contemporaneous variables are susceptible to endogeneity bias due to reverse causality, whereas regressions based on lagged values of independent variables help to control for reverse causality and tend to be less susceptible to endogeneity effects. We re-estimate equation (4) Subscript i denotes individual firms and subscript t time period. The dependent variable, RISK, is either TR (Columns 1 and 7) or PVaR (Columns 2 and 8) or HVaR (Columns 3 and 9) or CVaR (Columns 4 and 10) or UP (Columns 5 and 11) or CuP (Columns 6 and 12). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (being 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). The CG is a selfconstructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). ESG is the environmental, social and governance score obtained from the Bloomberg database. PMC is the annual sales by a firm divided by total industry sales. BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders. LNMC is the natural logarithm of number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets. CACL is the current assets divided by current liabilities. AGE is the natural logarithm of the number of years firm has been listed on the ASX at the end of its financial year. STO is the sum of daily shares traded divided by the number of shares outstanding in the financial year. PER is the market price per share divided by earnings per share. YEAR is the year dummies.  Table 1 for variable definitions.
*** , ** and * indicate statistical significance at 1%, 5% and 10%, respectively. ables (i.e., years t − 1 and t − 2). The new estimates are virtually indistinguishable from the results reported in Table 5 and hence are unreported, for the interest of brevity.

GMM
In this section, we include a lagged risk-taking in the main regression and estimate the augmented regression using the Arellano and Bover (1995) and Blundell and Bond (1998) dynamic two-step system GMM. In the dynamic system GMM, first-differenced variables are used as internal instruments for the equations in levels and the estimates are robust to endogeneity bias, if any (Pathan, 2009). 11 Compared to the two-stage least square (2SLS) method, dynamic GMM has at least two benefits. First, it handles the endogeneity bias with internally generated instruments rather than external instruments or natural experiments that may not be readily available. Second, it explicitly models the dynamic nature of the governance-risk nexus by including prior year risk-taking as one of the regressors. The consistency of GMM estimation depends on two important conditions. The first condition is the serial independence of the residuals.
The residuals in the first difference should be serially correlated ) by way of construction, but the residuals in the second difference should not be serially correlated (AR2). The second condition is the validity of instruments, which is tested through the Hansen J-statistics of over-identifying restrictions. The Hansen J-statistics of over-identifying restrictions test the null hypothesis of instrument validity. Table 7 reports the results for total risk in Column 1, downside risk in Columns 2−4 and upside risk in Columns 5 and 6. The diagnostics tests show that all models are well-fitted with statistically insignificant test statistics for the secondorder autocorrelation in the second differences (AR2) and for the Hansen J-statistics of over-identifying restrictions.
The interpretation of the coefficients on the CG index remains qualitatively the same as in Table 5. Specifically, the statistically significant negative coefficients on the corporate governance for all the measures of risk-taking suggest that strong corporate governance inversely affects the firm's risk-taking. Similar to the previous findings, we find that corporate governance reduces total risk, as well as downside and upside risk. Overall, the system GMM estimates support the notion that, even after controlling for endogeneity, corporate governance is associated with a reduction in the firm's total risk, downside risk and upside risk. Therefore, we strongly support H1 and H2.

Entropy balancing
In this section, we discuss the results obtained through the entropy balancing method following recent corporate governance studies (e.g., Brodmann et al., 2021;Ongsakul et al., 2021;Sharma et al., 2021). We first divide our sample into two groups: treatment and control groups. The treatment group, HighCG, contains firm-year observations with corporate governance strength higher than the sample median, whereas the control group, LowCG, consists of firm-year observations with corporate governance strength lower than equal to the sample median. Then, we use entropy balancing Stata code provided by Hainmueller and Xu (2013) to converge the mean, variance and skewness of all covariates in the treatment and control groups, which was achieved as shown in Table 8, Panel A (before entropy balancing) and Panel B (after entropy balancing). Based on the treated balance, we then re-estimate the results of our regression reported in Table 5. Panel C of Table 8 presents the results for total risk in Column 1, downside risk in Columns 2−4 and upside risk in Columns 5 and 6. The interpretation of the coefficients on the CG index remains qualitatively the same as in Table 5. Specifically, the statistically significant negative coefficients on the CG index for all the measures of risk-taking suggest that strong corporate governance reduces total risk, as well as downside and upside risk. Hence, our findings are robust to potential endogeneity bias.  Note: This table presents the dynamic two-step system GMM estimates of equation (4) with year FE.

TA B L E 7
.
Subscript i denotes individual firms and subscript t time period. The dependent variable, RISK, is either TR (Column 1) or PVaR (Column 2) or HVaR (Column 3) or CVaR (Column 4) or UP (Column 5) or CuP (Column 6). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (with a 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). L.risk is a 1-year lagged risk measure. The CG is a selfconstructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). PMC is the annual sales by a firm divided by total industry sales. BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders.
LNMC is the natural logarithm of number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets. CACL is the current assets divided by current liabilities. AGE is the natural logarithm of the number of years a firm has been listed on the ASX at the end of its financial year. STO is the sum of daily shares traded divided by the number of shares outstanding in the financial year. PER is the market price per share divided by earnings per share.
YEAR is the year dummies. We use robust standard errors, incorporating the Windmeijer (2005) (4) with industry and year FE. Panels A and B report the means, variances and skewnesses for the covariates for the treatment group (i.e., governance score higher than sample median) and control groups (governance score lower than sample median) before and after balancing, respectively. We reach convergence or perfect balancing using Hainmueller's Stata code given that there is no mean, variance and skewness difference between the treatment and control groups after the balancing. Panel C presents the regression based on entropy balancing method.
Subscript i denotes individual firms and subscript t time period. The dependent variable, RISK, is either TR (Column 1) or PVaR (Column 2) or HVaR (Column 3) or CVaR (Column 4) or UP (Column 5) or CuP (Column 6). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (with a 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). The CG is a self-constructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). PMC is the annual sales by a firm divided by total industry sales.
BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders. LNMC is the natural logarithm of number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets. CACL is the current assets divided by current liabilities. AGE is the natural logarithm of the number of years a firm has been listed on the ASX at the end of its financial year.  Table 1 for variable definitions. *** , ** and * indicate statistical significance at 1%, 5% and 10%, respectively.

Alternative measures of risk-taking
So far, we have measured the risk-taking behavior of the firm using the riskiness of the firm stock. In doing so, we implicitly assume that a firm that takes a lot of risks in business is more likely to have volatile stock. In this section, we directly measure risk-taking behavior using variability in the earnings of the business.

Fundamental operating performance variability
First, we use fundamental operating performance variability as a proxy for risk-taking. We include two measures of firm performance: accounting performance (ROA) and firm value (Tobin's Q). ROA is the net income divided by total assets. Tobin's Q is the market value of assets divided by the book value of assets, where the market value of assets is equal to the market value of equity plus the difference between the book value of assets and the book value of equity.
Consistent with the prior studies on risk-taking (e.g., Adams et al., 2005;Cheng, 2008;Nakano & Nguyen, 2012), in using ROA and Tobin's Q, we measure performance variability in two ways: (1) within-firm over time performance variability and (2) within and across firm performance variability (i.e., absolute deviation from expected performance).
According to "within-firm over time performance variability," we use the standard deviation of ROA (variability of accounting performance) and Tobin's Q (variability of firm value) as a proxy for risk-taking, and we take the average of all the explanatory variables over the sample period. On the one hand, this procedure provides the benefit of eliminating the concern that the results are driven by the differences in cross-sectional variability in performance (Cheng, 2008); on the other hand, this procedure results in the collapse of panel data into cross-sectional data (Nakano & Nguyen, 2012). We estimate the association between corporate governance and risk-taking by OLS with standard errors corrected for heteroscedasticity: where RISK represents the standard deviation of either ROA or Tobin's Q. The definitions and details of the explanatory variables are outlined in Sections 3.2 and 3.4 and summarized in Table 1.
The "within and across firm performance variability" measures risk-taking through Glejser (1969) heteroscedasticity test. The estimates with the Glejser (1969) procedure are robust to both within and across firm correlations of residuals. The Glejser heteroscedasticity test is conducted in two steps. The first step deals with obtaining residuals by specifying the performance model. The dependent variable in the performance model is either ROA (equation 6) or Tobin's Q (equation 7). The independent variables are the same as in equation (4), except we drop ROA from equation (6). The residuals from the performance models indicate the "unexpected" performance, and thus the absolute value of these residuals serves as an appropriate measure for risk-taking. In the second step, the absolute values of the residuals obtained from the first step (performance models) are regressed on corporate governance and other control variables. We estimate the expected performance by using the following performance models: The error term ε i,t in the performance equations (7) and (8) represents the unexpected performance. We take the absolute value of ε i,t and use it as a proxy for risk-taking. We then use FE regression to regress the absolute value of ε i,t on all the variables appearing as explanatory variables in equation (4).  (5) and (8) are well-fitted with a reasonably welladjusted R-square and statistically significant F-statistics. The overall results suggest that corporate governance has a significant and negative impact on the firm's risk-taking. Specifically, the coefficient on corporate governance is negative and statistically significant for both ROA and Tobin's Q, regardless of whether the relationship is being measured using cross-sectional or panel data. These results are the same as in Column 1 of Table 5 for total risk. Therefore, we strongly support the hypothesis (H1); that is, strong corporate governance reduces the firm's overall risk-taking.

Quantile regression-based risk metrics
Second, we measure risk-taking (or performance variability) using the quantile regression forecasts of the interquartile range (IQR) of the distribution of profitability, that is, ROA (Konstantinidi & Pope, 2016). This approach relies only on cross-sectional fundamental characteristics and requires time series data for computation. We forecast performance in different quantiles using the following equation: Our model resembles that of Hou et al. (2012), with the exception that we forecast ROA instead of earnings. SIZE is the natural logarithm of the total assets. PAYOUT is the ratio of the dividend paid divided by total assets. PAYER is the dummy variable that is equal to 1 if PAYOUT > 0 and 0 otherwise. LOSS is the dummy variable that equals 1 if ROA < 0 and 0 otherwise. ACC is the difference between net income and operating cash flow, scaled by total assets.
All of these variables are winsorized in the top and bottom percentiles to mitigate the effects of outliers. To estimate the forecasting equation and to avoid the effect of small firms, we only consider firms with full data and with total assets in excess of $100 million (Konstantinidi & Pope, 2016). Our requirements result in a sample of 4080 firm-year observations.
First, we capture conditional dispersion in the future earnings distribution using the predicted IQR = Q i75 − Q i75 , which is a commonly used measure of earnings dispersion. The higher the IQR, the higher the uncertainty in future earnings. Second, we estimate conditional skewness in the future earnings distribution as SKEW = which captures the balance between upside risk relative to downside risk in future earnings within the two middle quartiles. Third, we estimate conditional kurtosis in the future earnings distribution as   Note: This table presents the regression estimates of equations (6) and (9) using alternative proxies of risk-taking, that is, fundamental operating performance variability.
Subscript i denotes individual firms and subscript t time period. Panel A presents the cross-sectional regression estimates of equation (6) where the dependent variable, RISK, is a standard deviation of ROA or Tobin's Q. Panel B presents the panel regression estimates of equation (9) where the dependent variable, | |, is the absolute value of residuals derived from the performance models as specified in equations (7) and (8). The CG is a self-constructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). PMC is the annual sales by a firm divided by total industry sales. BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders. LNMC is the natural logarithm of number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets. CACL is the current assets divided by current liabilities. AGE is the natural logarithm of the number of years a firm has been listed on the ASX at the end of its financial year. STO is the sum of daily shares traded divided by the number of shares outstanding in the financial year. PER is the market price per share divided by earnings per share. YEAR is the year dummies.  Table 1 (4) with firm and industry year FE using alternative proxies of risktaking, that is, quantile regression-based risk matrices.
Subscript i denotes individual firms and subscript t time period. The dependent variable, RISK, is either dispersion (IQR in Column 1), or skewness (SKEW in Column 2), or kurtosis (KURT in Column 3), or UP (Column 4) or downside risk (DOWN in Column 5) in future earnings as derived from equation (10) in Section 4.3.2. The CG is a self-constructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). PMC is the annual sales by a firm divided by total industry sales. BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders. LNMC is the natural logarithm of number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets.  Table 1 for variable definitions. *** , ** and * indicate statistical significance at 1%, 5% and 10%, respectively.

Alternative proxies of corporate governance
The empirical evidence so far demonstrates a strong negative impact of overall corporate governance on risk-taking, including both downside and upside risk. In this section, we aim to understand which specific governance categories and variables drive the negative relationship.
Panel A of Table 11 presents the results relating to the BQI and the subcommittee quality index (SCQI). As can be seen, BQI and SCQI negatively affect the firm's risk-taking. Specifically, BQI and SCQI negatively affect total risk, downside risk and upside risk. This evidence suggests that both governance categories drive the relationship between corporate governance and risk-taking. However, we note larger coefficients on BQI than on SCQI. Given such a difference, in Panel B of Table 11, we report the results related to BQI variables on risk-taking. The BQI variables include the percentage of independent directors (%_Independent), CEO duality (DUAL) and board meetings (Meeting). The results reveal that %_Independent and Meeting are significantly related to a reduction in total, downside and upside risks. However, CEO duality positively and significantly influences total, downside and upside risks. These findings corroborate prior risk-taking literature that shows the inverse relationship between independent directors and risk-taking (Ni & Purda, 2012;Pathan, 2009) and the positive relationship between powerful CEOs and risk-taking (Adams et al., 2005).
In other words, independent directors and independent chairpersons reduce the firm's risk-taking, including both downside and upside risk.
We then check the effect of SCQI individual categories (AQI, NQI and RQI) on risk-taking and report the results in Panel C of Finally, we investigate the effect of BQI and AQI on risk-taking and report the results in Panel D of Table 11. The results show that both BQI and AQI have a negative and statistically significant impact on total, downside and upside risk. However, we note that the BQI's reduction in downside and upside risk is not substantially different. However, the AQI's reduction in upside risk is much larger than that of downside risk. These findings raise concerns about overmonitoring the management through the independent board and the independent audit committees, making the management extra cautious in their decision-making, resulting in the reduction of not only downside risk but also upside risk.
To check the robustness of our results, we use governance rankings and ratings from the Horwath reports available from 2001 to 2008. Each report covers the top 250 Australian listed firms based on the market capitalization on 30 June of the previous year. The top 250 firms represent over 80% of market capitalization and have a major influence on the capital market of Australia. The report provides a measure of corporate governance in two formats: (1) Corporate governance "rank" (CG rank) and (2) Corporate governance "stars" (CG stars). The CG rank ranges from 1 to 250 each year, where the firm with the best governance receives the rank of 1, based on its overall governance standing relative to other firms in the same year. We follow Beekes and Brown (2006) and Ali et al. (2016) in order to refine the CG rank.
First, we reverse the CG rank so that a higher CG rank indicates "best" governance, while a lower CG rank indicates "worse" governance. Second, we adjust CG rank for ties. Finally, we take the natural logarithm of the reversed CG rank.
The CG stars range from 1 to 5. The firms with "outstanding" corporate governance structure receive 5 stars, and the firms with "poor" governance structure receive 1 star. 12 We report the results in Panels E and F of Table 11. The results show that both CG rank and CG stars are negatively and significantly related to total, downside and upside risk. Hence, our results are robust to the use of the governance score from the original Horwath report.
12 See Appendix D: Horwath CG Report 2008 for the criteria used in the determinants of CG rank and stars. Full details of the Horwath rating system are proprietary and confidential, so we are unable to make any comments on the assignment of ranking and stars beyond the information given in the reports.  (4) with firm and industry-year FE using alternative governance measures, that is, individual governance mechanisms and Horwath governance score.
Subscript i denotes individual firms and subscript t time period. The dependent variable, RISK, is either TR (Column 1) or PVaR (Column 2) or HVaR (Column 3) or CVaR (Column 4) or UP (Column 5) or CuP (Column 6). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (with a 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). BQI and SCQI in Panel A; percentage of independent directors on board (%_Independent), CEO chairperson duality (DUAL) and number of board meetings held during the fiscal year (Meeting) in Panel B; AQI, NQI and RQI in Panel C; BQI and AQI in Panel D (see Appendix B); Horwath CG Stars in Panel E; and Horwath CG Ranks in Panel F (see Appendix D). PMC is the annual sales by a firm divided by total industry sales. BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders. LNMC is the natural logarithm of number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets. CACL is the current assets divided by current liabilities. AGE is the natural logarithm of the number of years a firm has been listed on the ASX at the end of its financial year. STO is the sum of daily shares traded divided by the number of shares outstanding in the financial year. PER is the market price per share divided by earnings per share. YEAR is the year dummies. ε is the composite error including industry-FE (IND) and idiosyncratic error (V). The industry classification is based on Standard & Poor's two-digit GICS. Figures in parentheses are the robust t-statistics. See Table 1 for variable definitions. *** , ** and * indicate statistical significance at 1%, 5% and 10%, respectively.

Alternative sample specifications
We check the robustness of the main results to alternative sample specifications. First, we suspect that the GFC period in the analysis may affect the main results. During the GFC period, the corporate governance of the sample firms is not much affected, but the risk-taking of the sample firms is highly affected. To preclude the possibility that data from the GFC period affect the results, we check the sensitivity of the results by excluding GFC observations (2008 and 2009) from the dataset. The results in Panel A of Table 12 show that corporate governance significantly reduces total risk and both the downside risk and upside risk. These results are qualitatively similar to those reported in Table 5; therefore, the data from the GFC period do not alter such a relationship.
Second, we suspect that the unbalanced part of the sample may affect the main results. To eliminate this concern, we create a strictly balanced dataset (of 5530 firm-year observations) containing firms that survive throughout the sample period (n = 13). It is evident from the results presented in Panel B of Table 12 that the relationship between corporate governance and risk-taking remains the same, implying that such a relationship is not driven by an unbalanced part of the sample.
Finally, we investigate the sensitivity of the results to potential firm-size effects. For this purpose, we re-estimate the regression equation (4) by eliminating the largest 10% and the smallest 10% of the firms. The estimation results reported in Panel C of Table 12 show that even after excluding the smallest and largest firms from the sample, the results are similar to those reported in Table 5. This suggests that the findings are altered by neither small firms nor large firms.

WHEN DOES CORPORATE GOVERNANCE REDUCE RISK-TAKING?
In this section, we consider the role of industry membership, director gender, ownership concentration and firm life cycle in the relationship between corporate governance and a firm's risk-taking. Such an analysis is important to draw policy implications. 13

Role of industry membership
In this section, we examine the relationship between corporate governance and risk-taking within each industry, given that different industries may have different risk exposures and corporate governance needs. Table 13 presents the sample distribution and the cross-sectional average of corporate governance and risk measures across industries. The number of observations in each industry shows the level of development of the Australian economy. For instance, the material sector comprises 34% of the sample firms. It is the most visible industry and plays a dominant role in the Australian stock market. By contrast, utilities and telecommunication services comprise only 1% and 2% of the sample firms, respectively. The statistics show that material, which is the largest industry, has the lowest CG index and the highest downside and upside risk. Consumer staples, the third smallest, has the highest CG index and the lowest downside and upside risk. Notably, corporate governance and levels of risk vary from industry to industry, thus it is worthy to conduct industry-wise regression. The results are reported in Table 14, which shows that corporate governance is negatively and significantly associated with risk-taking in consumer discretionary, consumer staples, health care, industrial, energy and materials. However, such a relationship is insignificant for information technology, telecommunication services and utilities. 13 We thank the anonymous reviewer for recommending these additional analyses.  (4) with firm and industry-year FE using alternative sample specifications. Panel A presents the estimates using the sample that excludes firm-year observations from GFC. Panel B reports the estimates using the firms that survive throughout the sample period (i.e., balanced data). Panel C presents the estimates using the sample that excludes the largest 10% and smallest 10% of the firm-year observations.
Subscript i denotes individual firms and subscript t time period. The dependent variable, RISK, is either TR (Column 1) or PVaR (Column 2) or HVaR (Column 3) or CVaR (Column 4) or UP (Column 5) or CuP (Column 6). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (with a 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). The CG is a self-constructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). PMC is the annual sales by a firm divided by total industry sales. BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders. LNMC is the natural logarithm of number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets. CACL is the current assets divided by current liabilities.  Table  1 for variable definitions. *** , ** and * indicate statistical significance at 1%, 5% and 10%, respectively.

Role of boardroom gender diversity
The undeniable case for gender diversity on boards. It is not only the right thing to do but the smart thing to do" (AICD, 2015). Given this proliferating attention, it is interesting to explore the implications of boardroom gender diversity in relation to the effect of corporate governance on risk-taking.
Women directors are generally less overconfident than male directors due to the perceived precision of beliefs about future uncertain events (Barber & Odean, 2001) or the level of expectations of what will happen in a less favorable future event (Malmendier & Tate, 2008). Consequently, women's choices can be less risky than men's. Levi et al. (2014) find that greater women representation on a corporate board is negatively associated with corporate investments (i.e., mergers and acquisitions). However, Sila et al. (2016) show that the inverse effect of women directors on equity risk is spurious and driven by unobserved between-firm heterogeneous factors. In this section, we examine whether boardroom gender diversity plays a significant role in the relationship between corporate governance and risk-taking. There are 2310 firm-year observations with at least one women director and 7608 firm-year observations without any women directors. The firm and industry-year FE regression results reported in Panel A of Table 15 indicate no apparent difference between firms with at least one women director and those without any women directors.
Hence, our main results are not driven by the gender of directors.

Role of ownership concentration
The equity ownership of large shareholders in a firm has the potential to influence its risk-taking, which may not only affect the ability of a firm to compete but also the survival of the firm (Wright et al., 1996). Shleifer and Vishny (1986) argue that large shareholders have the resources to gather information, monitor managers and direct firms toward  (4) for a sub-sample of each industry separately. The industry classification is based on two-digit GICS.
Subscript i denotes individual firms and subscript t time period. The dependent variable, RISK, is either TR (Column 1) or PVaR (Column 2) or HVaR (Column 3) or CVaR (Column 4) or UP (Column 5) or CuP (Column 6). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (with a 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). The CG is a self-constructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). Other control variables and firm-year FE are included in all regressions. Figures in parentheses are the robust t-statistics. See Table  1 for variable definitions. *** , ** and * indicate statistical significance at 1%, 5% and 10%, respectively.
projects that are high risk and high return. Likewise, Amihud and Lev (1981) state that although managers, due to risk aversion attitude, are inclined toward risk reduction activities, they will not be able to do so in owner-controlled firms.
Consistent with this, Saunders et al. (1990) document higher risk-taking behavior in banks that are owner-controlled than in banks that are manager controlled. In a cross-country analysis, Paligorova (2010) Subscript i denotes individual firms and subscript t time period. The dependent variable, RISK, is either TR (Column 1) or PVaR (Column 2) or HVaR (Column 3) or CVaR (Column 4) or UP (Column 5) or CuP (Column 6). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (with a 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). The CG is a self-constructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B relationship between equity ownership and risk-taking in banks. In a similar vein, Nguyen (2011) in Japan andGürsoy andAydogan (2002) in Turkey find a positive relation between concentrated ownership and firm performance by relating the governance structure to the risk-taking strategies of firms. More recently, Koerniadi et al. (2013) found a strong positive influence of outside block holdings on the risk-taking propensity of New Zealand firms. Based on this evidence, the firms with concentrated shareholdings should have more risk-taking than firms with dispersed share ownership. If such is the case, we argue that shared ownership may weaken the inverse relationship between corporate governance and the firm's risk-taking by overcoming excessive managerial conservatism.
We consider four ownership concentration variables, namely, the percentage of shares held by the top 20 shareholders (Top20), by substantial shareholders (block) and by the CEO, as well as the presence of directors with substantial shareholdings (Directors). We collect these data from SIRCA. Based on these four variables, we construct an ownership concentration index (OC index). We assign 1 if the Top20, block and CEO shareholdings are higher than the sample median and 0 otherwise, and we assign 1 if one or more of the directors is the substantial shareholders of the firm and 0 otherwise. The OC index ranges from 0 to 4, where 0 indicates the lowest concentration and 4 the highest concentration. We split the sample into two groups. The first group contains the firms with high ownership concentration (OC index > 2); the second group has the firms with low ownership concentration (OC index < = 2). Table 15 presents the firm and industry-year FE regression results between corporate governance and risk-taking for firms with high ownership concentration (Columns 1, 3, 5, 7, 9, 11) and low ownership concentration (Columns 2,4,6,8,10,12). For high ownership firms, corporate governance reduces total risk, downside risk and upside risk but with less statistical significance. However, for firms with low ownership concentration, corporate governance is found to sharply reduce total risk, downside risk and upside risk with strong statistical significance. These findings confirm that the negative effect of corporate governance on risk-taking is weaker for firms with high ownership concentration than for firms with low ownership concentration. 14 Hence, our main results are driven by the level of ownership concentration.

Role of the firm life cycle
According to the corporate life cycle theory, a firm has different resources, capabilities, strategies, structures and functions in different development stages (Miller & Friesen, 1984;Quinn & Cameron, 1983). In particular, extant empirical studies suggest that managerial risk-taking propensity varies with a change in the life cycle stage of a firm. For instance, Adams et al. (2005) document that risky-taking incentive is higher for younger firms, whereas performance variability is lower for older firms. This is because a firm is more likely to pursue growth-oriented investment strategy during the initial stage, whereas the maintenance of assets in place is a more likely investment strategy for firms in the mature stage (Richardson, 2006). Consistent with this, Hasan and Habib (2017) and Habib and Hasan (2017) find that risk-taking is higher in the introduction stage of the life cycle but lower in the mature stage. They argue that an early phase firm has a more fluid resource base and requires more risky investments for expansion than that of a mature phase firm. Given this evidence, we expect that the inverse relationship between corporate governance and the firm's risk-taking should be stronger (weaker) for older (younger) firms.
As life cycle stages are naturally related to firm age, we use firm age as a simple and natural proxy of the life cycle.
We measure firm age as the difference between the current fiscal year and the year of incorporation. We consider a firm as old if its age is higher than the sample median and young if its age is lower than the sample median. Panel C of Table 15 presents the firm and industry-year FE regression results between corporate governance and risk-taking for younger firms in Columns 1, 3, 5, 7, 9 and 11 and older firms in columns 2, 4, 6, 8, 10 and 12. As expected, we find that corporate governance reduces total risk, downside risk and upside risk but with less statistical significance and magnitude for younger firms. However, for older firms, corporate governance is found to sharply reduce total risk, 14 We also perform analysis based on individual ownership variables and find similar results.
downside risk and upside risk with high statistical significance and magnitude. These findings confirm that the negative effect of corporate governance on risk-taking is weaker for younger firms and stronger for mature firms. Hence, our main results are driven by the life cycle stage of the firm.

CORPORATE GOVERNANCE, RISK-TAKING AND FIRM VALUATION
Despite the ASX CG Council's emphasis on firm risk, prior studies investigate the role of corporate governance with the level of firm performance but not with the variability of firm performance, that is, risk-taking (Christensen et al., 2010;Henry, 2008;Pham et al., 2011). Interestingly, these studies find mixed results; some find evidence of beneficial effects, while others report no effects or even harmful effects. For instance, Henry (2008) finds a positive relationship between corporate governance and firm value, while Christensen et al. (2010) and Swan and Forsberg (2014) document that independent directors have a negative association with firm value. Pham et al. (2011) find that the relationship between corporate governance variables and firm value is spurious. The underlying assumption in these governance-value studies is one of the important reasons for these inconsistent findings. These studies assume a composition-conduct-value relationship, that is, certain corporate governance mechanisms lead to certain behaviors in the boardroom, which ultimately influence the corporate outcomes, such as firm value (Adams et al., 2010).
This suggests the indirect governance-value linkage. Therefore, instead of directly linking corporate governance with firm value, there is a need to study the role of corporate governance mechanisms in shaping risk-taking behavior of top management, which in turn influences the firm value (Balachandran & Faff, 2015;Johnson et al., 2012). Thus far, we have established the first-order relationship between corporate governance and risk-taking by showing higher corporate governance (as measured using the independence of board and subcommittees) leads to lower risk-taking, including downside and upside risks. Now, we explore the effect of corporate governance on firm value via risk-taking.
Such analysis is important to understand the mixed findings in the governance-value literature.
Following prior accounting and finance literature (Cheung, 2016;Harjoto & Laksmana, 2018), we use path analysis to examine the direct and indirect effects of corporate governance on firm value conditioned on risk-taking (i.e., total, downside and upside risks). Equation (10) specifies the path model as follows: δ 1 represents the direct effect of corporate governance on firm value. The multiplication of β 1 from equation (4) and β 2 from equation (10) denotes the indirect effect of corporate governance on firm value via risk-taking.
We report path regression results in Table 16. Panel A reports the direct effect of corporate governance on firm value and Panel B reports the indirect effect of corporate governance on firm value through corporate risk-taking. As reported in Panel A, we find a negative and significant direct effect of corporate governance on firm value. This finding is consistent with our theoretical argument and that of some existing studies (Christensen et al., 2010;Swan & Forsberg, 2014). Importantly, we also find a positive and significant effect of risk-taking on firm value, which is consistent with the existing studies (Nguyen, 2011

Indirect (TR) I n d i r e c t( PVaR) I n d i r e c t( HVaR) I n d i r e c t( CVaR) I n d i r e c t( UP) I n d i r e c t( CuP)
Subscript i denotes individual firms and subscript t time period. The dependent variable is firm value (Tobin's Q). RISK is either TR (Column 1) or PVaR (Column 2) or HVaR (Column 3) or CVaR (Column 4) or UP (Column 5) or CuP (Column 6). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (being 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). The CG is a self-constructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). PMC is the annual sales by a firm divided by total industry sales. BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders. LNMC is the natural logarithm of the number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets. CACL is the current assets divided by current liabilities. AGE is the natural logarithm of the number of years firm has been listed on the ASX at the end of its financial year. STO is the sum of daily shares traded divided by the number of shares outstanding in the financial year. PER is the market price per share divided by earnings per share.  Table 1 for variable definitions. *** , ** and * indicate statistical significance at 1%, 5% and 10%, respectively. nance on risk-taking. Corporate governance reduces risk-taking (including total, downside and upside risks), and lower risk-taking leads to lower firm value. The economic significance (magnitude) of the indirect impact of corporate governance on firm value, relative to the direct impact of corporate governance on firm value, varies from 4.50% (CVaR) to 13.65% (UP). 15 Thus, our path regression results in Table 16 suggest that a reduction in risk-taking in response to strong corporate governance reduces firm value, and such an effect is stronger in the case of upside risk, compared to downside risk.

CONCLUSION
We investigate the effect of corporate governance on risk-taking. In particular, we examine whether corporate governance has a differential effect on downside and upside risk. Intuitively, corporate governance should reduce downside risk but increase upside risk. However, we argue that the overemphasis on controlling risk by the ASX CG Council, while defining corporate governance, may make managers more risk-averse, leading to conservative decisions and ultimately reducing not only downside risk but also upside risk. To the best of our knowledge, we are the first to investigate the risk-taking perspective of corporate governance recommendations in Australia and to disentangle the impact of corporate governance on the downside and upside risk. Using a sample of 1164 Australian non-financial firms over the 2001−2013 period, that is, 9412 firm-year observations, we find that strong corporate governance reduces risktaking, including total risk as well as both downside and upside risk.
Our main findings are robust to alternative proxies of risk-taking, to alternative sample specifications and to individual/alternative proxies of corporate governance. In terms of individual governance mechanisms, we find that the inverse effect of corporate governance on risk-taking is driven by both the independence of the board and the subcommittees. Among the board subcommittees, only the audit committee significantly reduces risk-taking, where magnitude is larger for upside risk than for downside risk. These findings raise concern about the over-monitoring of the management through the independent board and the independent audit committee, making the management extra cautious in their decision-making, resulting in the reduction of not only downside risk but also upside risk. We employ firm and industry-year FE, lagged independent variables, GMM and entropy balancing estimation techniques to show that our main results are unaffected due to endogeneity bias originating from omitted variables and reverse causality.
In further analyses, we show that the inverse effect of corporate governance on risk-taking is homogeneous across different industries and for firms with varying levels of boardroom gender diversity. However, we find that the inverse effect of corporate governance on risk-taking is weaker for firms with high levels of equity concentration and for firms that are younger. Finally, we explore whether the reduction of risk-taking in response to strong corporate governance increases or decreases firm value. Our path analysis suggests that corporate governance reduces risk-taking (including total, downside and upside risks), and lower risk-taking leads to lower firm value.
The findings in our study imply that corporate governance is an important determinant of a firm's risk-taking. Given that corporate governance reduces both downside and upside risk as well as firm valuation, regulators should redefine corporate governance recommendations. The appropriate balance is required between monitoring and incentive mechanisms to create the differential effect of corporate governance on downside and upside risks, and thus enhance firm valuation. Future research may examine the interaction effect of monitoring and incentive mechanism on downside and upside risks.

Two-stage least squares (2SLS) approach
We also use a 2SLS approach to further address the reverse causality issue. This 2SLS requires an IV that is strongly correlated with corporate governance but does not have a direct influence on risk-taking. Following Jiraporn et al.
(2011), Yu Liu et al. (2014), Yang and Zhao (2014) and Yu Liu et al. (2015), we use the average corporate governance of all the firms in firm i's industry (excluding firm i's score) as an IV. The intuition behind using industry-average corporate governance (Industry_CG) as an IV is that a firm's governance arrangements (such as a board and its subcommittees) might be highly related with the industry peers due to similar business mix and investment opportunities, but such industry average is unlikely to directly affect a firm's risk-taking (Yang & Zhao, 2014). Further to this, managers may influence governance choices of their own firm but should have little or no influence on the governance choices of other firms. Given these arguments, Industry_CG should be a valid instrument: It is unrelated to firm-level risk-taking but related to firm-level corporate governance.  (4).
RISK i,t = o + 1 CG i,t + 2 PMC i,t + 3 BSize i,t + 4 BLOCK i,t + 5 LNMC i,t + 6 ROA i,t + 7 TLTA i,t + 8 CACL i,t + 9 AGE i,t + 10 STO i,t + 11 PER i,t + YEAR t + i,t . (4) Subscript i denotes individual firms and subscript t time period. The dependent variable, CG, in first stage is a self-constructed corporate G-index based on 17 objective criteria of the Horwath report, which ranges from a minimum score of 0 to a maximum of 17 each year (see Appendix B). Industry_CG is an IV measured as (industry CG minus firm-level CG) divided by (total observations in an industry minus one). The industry classification is based on Standard & Poor's two-digit GICS. The dependent variable, RISK, in second stage is either TR (Column 1) or PVaR (Column 2) or HVaR (Column 3) or CVaR (Column 4) or UP (Column 5) or CuP (Column 6). TR is the standard deviation of daily stock returns in a financial year. PVar is 1.645σ (with a 95% confidence level based on a normal distribution). HVaR is based on the actual historical 95th percentile worst return. CVaR is calculated as the average of the worst 5% of actual returns (those beyond the 95% VaR). UP is based on the actual historical 95th percentile best return. CuP is calculated as the average of the best 5% of actual returns (those beyond the 95% UP). PMC is the annual sales by a firm divided by total industry sales. BSize is the number of directors on the board. BLOCK is the percentage of outstanding shares held by the substantial shareholders. LNMC is the natural logarithm of number of shares outstanding multiplied by market price per share at the end of its financial year. ROA is the net income divided by total assets. TLTA is the total liabilities divided by total assets. CACL is the current assets divided by current liabilities. AGE is the natural logarithm of the number of years a firm has been listed on the ASX at the end of its financial year. STO is the sum of daily shares traded divided by the number of shares outstanding in the financial year. PER is the market price per share divided by earnings per share. YEAR is the year dummies. ε is the idiosyncratic error. Figures in parentheses are the robust t-statistics. See Table 1 for variable definitions. *** , ** and * indicate statistical significance at 1%, 5% and 10%, respectively.
test as the F-statistic is 292.46, which is well above 10 and is significant at the 1% level. Columns 2−7 present the second-stage regression results, where either total risk, downside risk or upside risk is the dependent variable (risktaking). We replace corporate governance with the fitted corporate governance (Fitted_CG) from the first-stage regression. The coefficients on the Fitted_CG are statistically significant and negative for all the measures of risk-taking. These findings confirm the earlier findings, that is, strong corporate governance reduces risk-taking including upside and downside (H1 and H2). The 2SLS results remain unaffected when we use alternative methods, that is, information maximum likelihood and GMM. Thus, we conclude that the main results are robust to the use of the 2SLS approach.