**1. Introduction**

Although gender equality represents a fundamental human right, many studies show that today women are not treated equally with men in their households, local communities, or at their workplace.

Statistics show that, globally, women perform around 30%–35% of the total work hours, yet they receive only around 10% of the world's total net wages [1]. Women are underrepresented in power and in decision-making roles. They receive unequal pay for equal work and they continue to be targets of physical and mental abuse.

The UN's Sustainable Development Goals (SDGs) [2] underscore women's empowerment as an important development objective, in and of itself, and highlight the relevance of gender equality to addressing a wide range of global challenges. This report is based on the five main SDG objectives that the 2016 Sustainable Stock Exchanges (SSE) Report on Progress emphasized as being in the area that financial exchanges are capable to influence, and further analyses the contribution that these important entities can bring to the goals of sustainable development: enabling women to fully and effectively participate, and have similar opportunities with men for leadership, in all areas and at all levels where decisions are made, regarding politics, economy, or the public agenda, and other gender-equality targets related to the other sixteen SDGs.

Sustainability (sustainable development) is not a new concept. In Greek and Roman philosophy, there are reflections on the relationship between human activities and ecosystems. But the concept of sustainable development has been gradually built during the last three decades of the twentieth century. Thus, in 1987, the World Commission on Environment and Development (WCED) published the report "Our Common Future" [3], offering further details regarding what sustainable development includes, referring especially to the items related to people's relations with the environment and the responsibilities that present generations have to future generations. Knowledge sharing and capacity building are fundamental for the new ecosystem, in order to contribute to economic development. A strategic alignment, both at the macroeconomic and microeconomic level, will offer the convergence necessary for a strategic change.

Environmental, social, and governance (ESG) principles are increasingly used by investors when choosing their investments [4]. ESG criteria are also found to be helpful for investors that try to stay away from companies that, looking forward, could find themselves in significant financial risk because of a lack of preoccupation with their environmental, governmental, or social impact. Integrating climate, environmental, and social sustainability factors into financial markets and systems requires time, vision, and efforts. It also needs strong contributions from all stakeholders.

Gender diversity is an important part of ESG goals, is relevant for every community, and should be an imperative for each organization and business. For companies, a policy geared towards gender inclusion generates a positive and favorable work environment which facilitates increases in productivity due to better collaboration between employees and supports a climate more prone to innovation, one that fosters better business performance in general.

During the last few years, the public agenda has radically changed, and its main themes are more geared towards the ESG goals. Thus, it has become more relevant for a company to prove its dedication to alleviating gender inequality in the workplace. This reflects also on investors' agendas, which are increasingly adapted to the priorities of the communities and no longer only focused on optimizing the risk/return relationship. This is why not only employees, but also investors, stakeholders, and regulators, have become interested in how a listed company is performing in relation to global ESG goals, particularly in respect to gender equality aspiration.

In this context, our paper investigates the behavior of returns for three well-diversified gender equality indices in comparison with relevant overall market indices. Our study uses both cross-sectoral indices and financial sector indices, to see whether there are specific characteristics for the gender equality indices that sets them apart from the overall market. We focus mainly on the first two moments of the distribution of returns, namely mean and standard deviation, and on the correlations among indices. In order to do this, we model conditional volatilities and correlations using Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH) and Dynamic Conditional Correlation Multivariate Generalized Autoregressive Conditional Heteroskedasticity (DCC MV GARCH), respectively, and we identify the alternation of volatility regimes using a Markov switching

model. We also study correlations/slope coefficients among pairs of indices resulting from quantile regressions at different percentiles and a non-restricted vector autoregressive model.

According to the results that we have obtained from studying the behavior of daily returns for the period 1 January 2017 to 12 March 2020, there are no significant differences among the overall indices and the gender equality indices in what regards the average return and conditional volatility. Also, the dynamic conditional correlations and the slope coefficients at different quantiles are very close to 1, indicating practically a similar evolution for the daily returns of the gender equality indices and the overall indices.

Gender diversity represents a new trend, influencing the literature, research studies, financial markets, investor behavior, and the real economy.

In order to be able to accurately assess how different organizations perform in relation to gender equality, investors should have good access to relevant data. Stock exchanges have the ability to enhance investors' access to information by improving the reporting requirements for issuers both in terms of quality and quantity, and including more in these requirements data on topics related to gender equality. By enhancing disclosure, the exchanges and the issuers allow investors of all kind, and especially large institutional investors, to manager risk more efficiently and effectively and to be better informed when making decisions regarding their portfolio composition [1].

Prior to the last 15–20 years, very few authors considered ESG-related information and variables when assessing factors that contribute to the performance and resilience of companies. The classic approach was to rely mainly on financial indicators related to a company's balance sheet and profit and loss accounts. Such approaches are still valid and useful today, as recent studies show. Valaskova et al. [5] concluded that such indicators (i.e., return ratios, liquidity ratios, indebtedness, turnover etc.) still represent the most significant predictors of profitability and prosperity for Slovak companies. Also, Kovacova et al. [6] analyzed the effectiveness of over 100 bankruptcy models developed in Visegrad countries using cluster and correspondence analysis, and argued that such variables continue to have significant explanatory power with regard to the performance of companies (in this case, more specifically, their capacity to avoid failure), despite the fact that the set of most relevant variables might be different from one country to another. In accordance with these findings, Kliestik et al. [7] propose a new bankruptcy model that takes into account the legal and business particularities of the Slovak economy, arguing that this approach outperforms the conventional tools, having a higher sensitivity to the deterioration of the financial solidity of companies.

During the last couple of decades, many authors have argued that companies' stances related to gender diversity are relevant for their profitability and, indirectly, for the results of those investing in the securities that they issue, thus significantly expanding the set of variables used in assessing the performance of the companies. As an example, Morgan Stanley have collected data related to this topic from many public companies in different markets, creating a proprietary database and framework that includes more than 1600 listed equities. The results of their research argue that companies that are more gender diverse perform at similar levels with others but show lower volatility, a finding which has important implications for portfolio managers and corporate boards of directors. [8].

The results from a study using a sample of French firms between 2002 and 2012, listed on the Paris Stock Exchange, show that stock market liquidity is positively and significantly associated with the presence of women directors. It was found that investors' decisions vary according to their positions in the board: women independent members decrease illiquidity costs, while the presence of female inside directors increases daily trading volume. In addition, inside women increases the firm's ability to implement better strategies that cope with economic, social, and environmental constraints, which leads investors to react positively. Surprisingly, the presence of female independent directors reduces company involvement in sustainable development projects [9].

Increasing the representation of women in boardrooms could enhance corporate reputation and increase both financial and social performance [10,11]. For instance, Boulouta [10] and Bear et al. [12] found a significant and positive effect of women directors on corporate social responsibility (CSR) and CSR ratings. Díaz-García et al. [13], Galia and Zenou [14], and Nielsen et al. [15] also show the positive effect of gender diversity on innovation, even on radical innovations, which are usually perceived as a male-controlled arena.

Gender diversity on boards could be considered as a substitute mechanism for governance in poorly governed firms. One plausible reason is that women directors are tough controllers: they are tempted to set up better monitoring and increase public and private disclosure [16].

According to some studies, the presence of women in boardrooms could be viewed as a signal made by the firm to investors of better competence, financial and social performance, and career evolution [17]. Furthermore, women directors most often bring new resources to the firm which may enhance the corporate public image and reputation in the stock market [18].

Kirkpatrick [19] emphasizes that the "failures and weaknesses in corporate governance arrangements which did not serve their purpose to safeguard against excessive risk taking in a number of financial services companies were significantly contributing to the financial crisis".

Taking as a starting point previous studies in governance (e.g., Caprio, Laeven and Levine [20]), the analysis performed by Adams and Mehran [21] employ a sample of banking data over 34 years to examine the relationship between banks' board structure and performance. The results indicate that board independence has no influence on bank performance. Other studies on bank performance (e.g., Hermalin and Weisbach [22]) emphasize that "board composition does not seem to predict corporate performance, while board size has a negative relationship to performance."

An inverted relation between bank performance and board size and between the proportion of non-executive directors and performance is found by De Andres and Vallelado [23]. Their results show that a "bank's board composition and size are related to directors' ability to monitor and advise management and that a larger and not excessively independent board might prove more efficient in monitoring and advising functions, and create more value". The authors also point out that in an environment characterized by limited competition, tight regulation, and higher informational asymmetries, banks' boards become an important mechanism for corporate governance, as their specialized knowledge of the banking business and specific risks enables them to better design banking business conduct and monitor executive managers.

Pathan and Faff [24] studied whether specific features of board structure (in terms of the total number of members, the number of independent members, and gender equality) exhibited by large US banks and/or their holding companies are able to determine bank performance. The study concludes that both the total number of board members and the number of independent members are negatively related with bank performance, while better gender diversity is linked with improved financial performance.

Another research paper by Pathan and Skully [25] that examines the trends of boards of directors (board size, composition, and CEO duality) for a sample of 212 US bank holding companies emphasizes that board size recorded a decreasing trend over the time period considered for large and medium-sized banks, while it remained relatively stable for small banks.

Empirical studies of investors' reactions to the appointment of women directors are still rare. Lee and James [26] test stock price reactions to the announcements of female and male CEOs. They conclude that investors' reactions are significantly more negative to the announcements of female CEOs than those of male CEOs. However, they are more significant and positive when women CEOs have been promoted from within the firm than from outside the firm. Similarly, Bharath et al. [27] focus on the insider trading behavior of senior corporate executives. Despite both female and male executives making positive profits, female members earn less than their male counterparts. In fact, market responses, in the short term, are driven by the stereotype that female executives are less informed about future corporate performance than males. In addition, gender bias may exist among institutional shareholders and could lead to a decrease in stock price even when gender diversity on boards has no effect on profits. One explanation is that non-block institutional investors may sell stocks of firms with gender-diverse boards (Dobbin and Jung [28]).

Post-2008 financial crisis research studies are trying to identify the influence of banks' governance structures on the main indicators related to the capital of the bank, and their contribution to systemic risk through individual risk-taking. Angeloni [29] mentions that "the relations between capital levels, risk and governance become more complex". This approach allows for a dynamic analysis of other prudential standards (on liquidity, credit allocation and provisioning, and distribution of resources) whose accomplishment is subordinated to supporting and preserving banks' solvency, capital being considered a core measure of a bank's solvency.

By conducting a first panel regression analysis, Boitan and Ni¸tescu [30] document that larger boards and increased gender diversity negatively contribute to increases in managerial efficiency, although the influence exerted is small. The effect of increasing the number of independent directors appointed to the board and the bank size is positively associated with the managerial efficiency of large banks. The authors challenge the general perception that increased gender diversity contribute to increased managerial efficiency.

As per IFM studies [31], "just 18 percent of firms globally are led by women, and on average, only 22 percent of board members in OECD countries are women. There is even lower representation in emerging economies, such as India at 13 percent or 8 percent in Brazil. Progress has been slow to say the least".

Another study conducted by IMF staff analyzes a sample of two million firms geographically dispersed over 34 European countries, and the results show that, in general, a higher level of gender diversity at the level of senior management is linked with better financial performance. More specifically, the IMF study concludes that replacing one male senior management position with a woman at the same level of management is linked with an increase of 8–13 basis points for the return on assets of the company.

Although progress on improving the gender diversity at the workplace is being made, the pace appears to be still very slow, and large gender gaps are still present when analyzing employment and income data. For example, data shows that the participation rate of woman in the workforce is on average 20% lower than the similar rate for men, at a global level. Also, quantitative research on legal systems across countries shows that woman only hold around three quarters of the legal rights that are afforded to men on matters related to, for example, property, inheritance, and access to financial services [32,33].
