**4. Conclusions**

In this paper, we aimed to study the relative stock market performance of companies recognized for supporting gender equality policies and practices. In order to do this, we selected three well-diversified equity indices published by Bloomberg that are composed of companies committed to supporting gender equality through policy development, representation, and transparency: one cross-sectoral index, one financial sector index, and one index composed exclusively of non-financial companies. The cross-sectoral gender equality index is a combination of the other two, and gathers 325 companies across 11 sectors, headquarter in 42 countries and regions, with a minimum individual market capitalization of USD 1 billion and a total market capitalization of USD 12 trillion. We compare several performance metrics for these indices with similar ones computed for selected MSCI overall market indices, and especially for the MSCI World and MSCI World Financial Sector indices.

We conducted our research over a sample of 834 daily logarithmic returns from a period of more than three years (1 January 2017—12 March 2020), using several statistical methods to characterize the properties of the distribution of historical returns (mean, standard deviation, skewness, kurtosis) and correlations. We also used several econometric models to study the characteristics of dynamic conditional mean, standard deviation (volatility), correlation, causality, and spill-over effects. Namely we calibrated EGARCH (1,1) models to examine the evolution of conditional volatility, Markov switching models to investigate the synchronization of volatility regimes, DCC MV GARCH (1,1) models to describe the evolution of dynamic conditional correlations, simple linear quantile regression to analyze the values of the slope coefficients in the relations between gender equality indices and overall indices, and, finally, VAR (2) models to test for causality and spill-over effects.

Using the statistical methods described, we could not confirm any particularities for the gender equality indices in comparison with the overall indices. For our sample, the mean values of the distributions were similar and not statistically different from zero, the standard deviation was larger in comparison with the mean, all the series presented significant negative skewness and excess kurtosis, and the values of the fifth percentile of the distributions of daily returns (left tail) were quite similar. Thus, the daily returns of the gender equality indices confirmed the usual stylized facts for general equity returns described by most studies.

When comparing the distributions of daily conditional volatilities estimated using the EGARCH (1,1) model, we observed, however, some relevant differences: mean and median daily conditional volatility were, in general, higher for the gender equality indices in comparison with their correspondent overall MSCI indices. This also held true for the values of the 0.95 quantile. Also, the gender equality indices exhibited lower skewness and excess kurtosis of the daily conditional volatilities in comparison with their correspondent MSCI indices.

Overall, we found in our sample a strong link between the evolution of the gender equality indices in comparison with the overall indices. The values of daily conditional volatility were highly synchronized between the gender equality indices and their correspondent overall MSCI indices, but the gender equality indices exhibited, in general, higher daily conditional volatility.

Thus, the results obtained from our sample point in an opposite direction to the conclusions of the research conducted by Morgan Stanley [8], a situation which could be explained by the difference in sample size (ours was significantly reduced and composed of aggregated indices, not of individual issuers), sample period, and methods.

The synchronized reaction of the indices to the risk events was confirmed, including during the burst of market risk aversion at the beginning of the Covid-19 pandemic towards the end of our sample. The volatility regimes of BGEI vs. MXWO and BGEIF vs. MXWO0FN, respectively, identified using a Markov switching model, were synchronized more than 94% of the time. Furthermore, the results from the DCC MV GARCH (1,1) model showed that, during the entire period investigated by us, the conditional correlations between the gender equality indices and the overall MSCI indices were very high, with the correlations among the financial indices appearing to be more stable over time in comparison with the correlations among cross-sectoral indices.

We tested these findings using another, different, method: we calibrated simple linear quantile regressions among the equity indices included in our sample. The results obtained showed that, in the case of the regressions between the gender equality indices and the overall MSCI indices, the values of the slope coefficients are close to 1 and relatively stable in relation with the value of the quantile.

Using separate VAR (2) models for the cross-sectoral indices and for the financial sector indices, we found only very little evidence of causality and spill-over effects.

Based on the results of our analysis from several different approaches and using different econometric and statistical methods, we argue that the daily returns of the gender equality indices that we have investigated over the period 1 January 2017—12 March 2020 exhibited very similar characteristics with the daily returns of the overall market indices. Thus, we were not able to confirm the hypotheses proposed by Sanders and Boivia [17] or Singh and Vinnicombe [18] that the presence of women in boardrooms brings better perception in the stock market or is more favourably viewed by investors, inducing a different (better) share price performance in comparison with the other companies.

In our interpretation, this could mean that, limited to our sample and methods of investigation, there were no significant differences in investors' behaviour towards the equity issued by public companies committed to supporting gender equality in comparison with their approach towards listed equity in general. Accordingly, if a large selection of equity issued by companies committed to gender equality would have been included in already large diversified portfolios, it would probably not have modified their overall characteristics and performance. This is somewhat similar to presuming that, in relation with our sample and period investigated, investors were almost neutral towards large diversified portfolio of gender equality listed companies in comparison with their approach towards the overall market. It could also mean that investors do not yet manifest a specific approach in relation to this category of listed equity, or that they do not yet anticipate a significantly different financial performance of companies stemming from their approach towards gender equality.

We consider our results to be relevant for asset managers, market regulators, and supervisors, in an integrated risk based assessment framework, in order to examine how the institutional investors' strategies oriented towards gender equality ESG objectives might impact the individual and sectoral resilience to market risk.

In our research, we were limited to only a short-term approach using daily returns, because the data that we collected for the gender equality indices was only available from the beginning of 2017. As longer time series will gradually become available, our methods can also be adapted to analyze data at a lower frequency, such as weekly or monthly time series; thus enabling the inclusion of a medium-term approach into the analysis. Future studies using the same methodology could also consider dividends and other relevant corporate events, using total returns indices if available.

**Author Contributions:** Conceptualization, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; methodology, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; software, L.B., D. ¸S.A. and I.P.; validation, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; formal analysis, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; investigation, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; resources, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; data curation, L.B., D. ¸S.A., and I.P.; writing—original draft preparation, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; writing—review and editing, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; visualization, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; supervision, L.B., D. ¸S.A., D.C.N., V.M., I.P. and B.K.; All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
