ON THE RELATIONSHIP BETWEEN FINANCIAL AND SUSTAINABLE VARIABLES: INSIGHTS FROM GRAPHICAL GAUSSIAN MODEL

1. Introduction

The last few years have been characterized by an exponential growth in the volumes of Socially Responsible Investments (SRI) due to several factors. As outlined in the Asset and Wealth Management Revolution 2022 report (PwC 2022), on a global scale, asset managers are expected to elevate their Environmental, Social and Governance (ESG)-related assets to reach US$33.9 trillion by 2026, marking a significant surge from the US$18.4 trillion recorded in 2021. Geographically, the growth rate of ESG assets in Europe shows a deceleration after the remarkable surge of $+$172% in 2021. In contrast, in the United States, the forecast is for a doubling of ESG assets by 2026, while the Asia/Pacific region distinguishes itself with the most pronounced percentage growth, expected to triple by the same year. This growth in SRI is in line with the increased attention of the public toward environmental risks which, according to a recent survey (World Economic Forum 2023), are perceived to be the most serious over a 10-year horizon. Furthermore, after the Paris Agreement in 2015, pressure from lawmakers started, particularly in Europe where, in 2018, the European Commission moved through its action plan (COM/2018/097) (European Commission 2018), with the aim to direct capital toward sustainable investments while increasing transparency. A fundamental step is the European Union (EU) Regulation 2019/2088 (European Union 2019), which contains a definition of “sustainable investment” and imposes common rules for different categories of financial operators on the disclosure of information on sustainability issues. Also, the EU Regulation 2021/1253 (European Union 2021) outlines the guidelines for the integration of sustainability factors, risks and preferences into certain organizational requirements and operating conditions for investment firms. A similar process has also started in other parts of the world, though it is still in the early stages. In the US, the Securities and Exchange Commission published only in March 2022 the Enhancement and Standardization of Climate-Related Disclosures, which would require registered public companies to disclose certain climate-related information in registration statements and periodic reports. Further elements reside in the COVID-19 pandemic, which drew attention to ESG investing strategies, as confirmed by Broadstock et al. (2021), followed by the recent war in Ukraine, that has dramatically shifted the focus on the energy issue and its impact on the costs of companies and their long-term sustainability.

Overall, as it emerges from a study by Simon Kucher & Partners (2021), the demand from consumers for “sustainable” products and services continues to grow, especially in the new generations, heavily affecting the economic results of companies and the relative investment flows. Therefore, the use of the ESG variables in the investment decision-making process has become a widespread practice, prompting interest from institutional and retail investors, companies, regulators and researchers on the possible relationships between financial performances and sustainable variables. In this regard, Starks (2023) discusses the trend in asset management, underlying the motivations for ESG investing, while Edmans (2023) titles his article “The end of ESG”, not to signal ESG’s death, but the ESG’s evolution from a niche subfield into a mainstream practice. However, mainly due to different regulations in various regions, the process is developing at different intensities and the relationships between variables may differ both temporally and geographically (Christensen et al. 2021, Pizzi et al. 2022, Cuomo et al. 2022). Using a differences-in-differences estimation for the period 2015–2020, based on a sample of EU firms as the treated group and a sample of US firms as the control group, Cicchiello et al. (2023) find that regulatory efforts are successful in improving disclosure commitment and effectiveness.

As a consequence of the widespread use of ESG information, in a context of increased nonfinancial disclosure, the number of ESG rating providers has also grown. As a result, there has been a proliferation of different rating methodologies each of which produces significantly different ESG ratings for the same company. This has started an interesting scientific debate on the relationships between ESG ratings, ESG disclosures and ESG divergences. Christensen et al. (2022) explain the degree of ESG disagreement in relation to the firm’s ESG disclosure and average ESG rating. Contrary to expectations, their findings suggest that greater ESG disclosure leads to greater disagreement across ESG rating agencies. Additionally, they observe that rating divergencies are more pronounced for firms with either high or low average ESG ratings, as opposed to those with medium average ESG ratings. Raters’ disagreement is also confirmed by Capizzi et al. (2021), who find that social and governance indicators are the main drivers of rating divergences. With reference to the US market, Kimbrough et al. (2022) point out that the disagreement among ESG rating agencies is lower for companies that voluntarily disclosure ESG information. Focusing on ESG disclosure rating, Eng et al. (2022) show that a company-tailored ESG disclosure provides incremental information and have a positive impact on the value/price of companies, suggesting that the harmonization could produce positive results on the value of companies. Finally, as highlighted in the EY Sustainable Finance Index 2022 (Ernst & Young 2022), based on 2021 data, financial firms have made considerable progress both in terms of ESG disclosures and performance on underlying ESG measure.

The objective of this paper is two-fold. On the one hand, we aim to unveil the possible relationships between “sustainable variables” (ESG Score and ESG Disclosure) and “financial variables” (return and volatility) and gain knowledge of the underlying mechanism that ties these variables together. On the other hand, we want to assess whether the above relationships have a different pattern in regions/periods characterized by higher disclosure requirements and stricter sustainability regulations. To do so, we focus on data collected from 2017 to 2021 for specific geographic areas: Europe, America, Asia/Pacific.

We mainly focus on regulation because, although the geographic evolution on these issues may be caused by the efforts of different stakeholders, we believe that the most influential role is to be attributed to regulators, as pointed out by Cadez et al. (2019) among others. Other stakeholders, such as customers, suppliers, competitors and investors also have an important influence on company choices, but lack the coercive power that regulators have.

The main novelty of our paper is that we use a Graphical Gaussian Model to describe, through a graph, the conditional dependence structure of the joint distribution of the ESG variables and the financial ones, and to assess how it varies over different time periods and geographical areas. The advantage of such a modeling strategy is that it allows to consider all variables jointly and to look at their interdependencies. This approach is justified when the ordering between the variables may not be clear from a priori information. One of the key points is that the model provides measures on the conditional association between any couple of variables given all the other variables. This feature allows us to understand when the correlation between two variables is genuine or spurious, i.e. induced by the common correlation of these variables with a third one (or more). We highlight that, to the best of our knowledge, this is the first attempt in the literature to analyze the joint distribution of ESG and financial variables using a Graphical Gaussian Model.

Our analysis shows that more transparent companies (i.e. those that communicate more information about their sustainability to the market) are characterized by lower assets’ returns and lower or comparable volatilities. Companies with a higher level of compliance with sustainability factors (i.e. those that present a higher ESG Score) have lower assets’ volatility than companies achieving lower ESG Scores but are not penalized in terms of returns. Moreover, the increasing level of mandatory disclosure in the European area, induced by the current regulation, as expected, has reduced the strength of positive dependency between Disclosure Score and ESG Score, without affecting the negative relationship between the ESG Score and volatility.

The rest of this paper is organized as follows. Section 2 introduces the literature background and research hypotheses. Section 3 describes the variables used. Section 4 introduces the Graphical Gaussian Models and explains why these models offer a more accurate analysis than models based on simple correlation coefficients thus providing a more elaborate interpretation of the evidence. Section 5 illustrates the main findings examining the relationship between ESG-related variables, assets’ returns and volatility. Finally, Sec. 6 concludes.

2. Background and Hypotheses Development

The relationship between financial profitability and the level of compliance with ESG factors is at the center of a great debate both among practitioners and in the academic literature. Results may be affected by how ESG ratings are measured, as pointed out by Dorfleitner et al. (2015), due to the strong disagreements between different rating systems. Further than works already mentioned in the introduction (Christensen et al. 2022, Kimbrough et al. 2022, Eng et al. 2022, Capizzi et al. 2021), for a systematic analysis of this issue see also Billio et al. (2021), Avramov et al. (2022) and Berg et al. (2022). Moreover, results on the impact of ESG ratings on financial performance may depend on the period analyzed and the kind of financial performance/risk measures that are used. Hence, there is not a consensus about the nature of the relationship between financial profitability and sustainability. For example, Bauer et al. (2005, 2006) and Renneboog et al. (2008) found no statistical differences in the risk-adjusted returns of ethical and conventional funds. On the other hand, removing from portfolios the assets involved in some controversial business activities (as for example, producing alcohol or tobacco, and gaming) provides lower expected returns, consistently with the lower risk obtained by screening such kind of stocks (see Hong & Kacperczyk (2009) and Luo & Balvers (2017)). The effect of negative screening on portfolios is also analyzed in Herzel et al. (2011) who found that the efficient frontier of the opportunity set is significantly affected by negative screening only when the screening is based on the environmental dimension. Finally, many studies are in favor of a positive relationship between financial performances and ESG compliance. Among them, Deng et al. (2023) find that corporations’ high ESG Scores are related to lower stock price crash risk. D’Amato et al. (2022), using explainable machine learning techniques, find that the ESG Score is a good predictor of the Earnings Before Interest and Taxes (EBIT). Nicolosi et al. (2014) implement a latent variable model to measure the level of ESG compliance of firms that take industry into account and show that, if accurately measured, compliance is not negatively associated with returns. Huang (2021) reviews different studies on the relationship between ESG performance and corporate financial performance finding a positive, statistically significant link. However, the economic results of this relationship are modest, suggesting that ESG activity is not primarily motivated by corporate financial performances. Lins et al. (2017), Becchetti et al. (2015a), Nofsinger & Varma (2014) and Nakai et al. (2016) find that ethical funds outperformed conventional ones during periods of financial crisis. Such a pattern has been observed even in the most recent pandemic-related crisis as reported in Broadstock et al. (2021), Omura et al. (2021) and Alfalih (2023).

We engage in this debate by analyzing the relationship between two financial variables, namely, Return and Volatility, and the ESG rating and ESG Disclosure Score for different cross sections of stocks (see Sec. 3 for a description of the dataset and the variables used). We use a Graphical Gaussian Model to identify the conditional correlation between the variables at hand (see Sec. 4 for the description of the model).

2.1. Volatility versus ESG-related variables

In our initial analysis, we investigate the relation between assets’ volatility and ESG rating (or Disclosure Score). The following hypotheses are tested against the null hypothesis that the two variables at hand are not correlated conditionally to the remaining two variables.

Research Hypothesis 1. Volatility is negatively correlated to ESG rating conditionally to Return and ESG Disclosure Score.

Research Hypothesis 2. Volatility is negatively correlated to ESG Disclosure Score conditionally to Return and ESG rating.

Hypotheses 1 and 2 are supported by many papers highlighting that a higher level of ESG compliance makes the stocks more able to absorb external negative shocks either because they are exposed to lower stakeholder risk, that is the risk of litigation with stakeholders (see Becchetti et al. (2015b)) or because responsible investors rely on longer investment horizons thus reducing fire-sales in case of financial turmoil. Indeed, the real wage of SRI is a general risk reduction. In line with this evidence, Boubaker et al. (2020) and Kim et al. (2014) find that firms that are high ranked in the ESG dimensions are less likely to default. Results in Atif & Ali (2021) confirm that an active ESG disclosure significantly reduces the default risk, through increased profitability and reduced performance variability and cost of debt. Also, Shakil (2021), studying oil and gas firms, shows a significant relation between good ESG performance and lower financial risks. Cerqueti et al. (2021) study ESG investing from a systemic point of view finding that funds that are high ranked in the ESG dimensions are also less exposed to contagion risk in case of financial distress. Moreover, Cerqueti et al. (2022) find that a network of funds is more resilient to external shocks when funds are high-ranked in the ESG dimensions than a corresponding system of low-ranked funds. A positive effect of high ESG Scores on systemic risk is also found in Bax et al. (2023). Cardillo et al. (2023) investigate the implications of COVID-19 pandemic shock on the financial markets and show that firms with higher ESG Scores perform better than other firms, particularly when they dispose higher cash holdings and liquid assets essential to absorb the pandemic externalities. With reference to Chinese companies, Xu (2023) analyzed the impact of corporate ESG performance on stock price volatility in the years 2011–2021, finding that corporate ESG performance significantly reduces stock price volatility. Sabbaghi’s (2022, 2023) studies confirm the hypothesis that the influence of news on volatility in high ESG-rated firms is more pronounced for negative news than positive news, both in developed and emerging markets. Additionally, the research reveals a slow reaction to news within the ESG framework among small-sized firms and those in emerging markets.

2.2. Return versus ESG-related variables

Here, we assess the relation between assets’ return and ESG rating (or Disclosure Score). The following hypotheses are tested against the null hypothesis that the two variables at hand are not correlated conditionally to the remaining two variables:

Research Hypothesis 3. Return is correlated to ESG rating conditionally to Volatility and ESG Disclosure Score.

Research Hypothesis 4. Return is correlated to ESG Disclosure Score conditionally to Volatility and ESG rating.

We highlight that Hypotheses 3 and 4 are neutral with respect to the sign (either positive or negative) of the conditional correlation between Return and ESG rating (or Disclosure). We just test whether a correlation is statistically significant and a posteriori we verify its sign. We prefer not to assume any direction for the relationship involving Return and ESG variables since the literature provides evidence either of a positive, negative, or neutral relationship. Some examples of such conflicting results have been provided at the beginning of this section. From a theoretical point of view, the possibility of such opposite behaviors is conciliated by Pedersen et al. (2021) who construct an ESG-efficient frontier where equilibrium asset prices are computed within an ESG-adjusted capital asset pricing model (CAPM). They show that a positive relationship of return and ESG Scores is obtained when the value of ESG information is not fully priced by the market. Such a relation becomes neutral when most investors recognize the value of ESG and it becomes negative when investors, pushed by their personal ESG preferences, are willing to accept lower returns for more ethical stocks. The whole analysis is carried on considering different time periods and geographical areas and a comparison of results is performed to assess differences between geographic areas.

3. Data

In this section, we describe the four variables used in the Graphical Gaussian Model and the data sample.

3.1. ESG-related variables

We use two ESG-related variables. The first, the ESG Score provided by MSCI, represents a weighted average score of the underlying pillar scores. Scores range from 10 (best) to zero (worst). MSCI ESG Scoring aims to measure a company’s management of financially relevant ESG risks and opportunities (see MSCI ESG Methodology (2022)). Using the MSCI ESG Scoring we cover all the geographical areas. The second one, the ESG Disclosure Score provided by Bloomberg, quantifies the transparency of a company in reporting ESG data (Tamimi & Sebastianelli 2017, McBrayer 2018, Bolognesi & Burchi 2023). This weighted score is normalized to range from zero, for companies that do not disclose ESG data, to 100 for those which disclose every data point collected. Bloomberg accounts for industry-specific disclosures by normalizing the final score based only on a selected set of fields applicable to the industry type (Yoo & Managi 2022, Khan 2022).

3.2. Financial market variables

We use two “Financial Market” variables: the first, Return, measures the mean of daily returns (expressed as a percentage) of a stock on a specific period; the second, Volatility, is the standard deviation of the daily returns of a stock on the same specific period (a logarithmic transformation of this variable is performed to achieve normality). The use of a market-based return variable, rather than a model-based return measure (within the CAPM or Fama and French model), is justified by the need to avoid statistical errors in the input variables of the Graphical Gaussian Model.

3.3. Estimation sample

We collect data for the constituents of the STOXX${}^{\text{®}}$ Global 1800 Index. The index contains 600 European, 600 American and 600 Asia/Pacific stocks. We reduce the number of observations from 1800 to about 1400 after selecting from the investment universe only those stocks for which complete data are available. Table 1 shows the sample size for different years and geographical areas. Table 2 describes the main statistics of the four variables at hand for the entire dataset. In Tables A.1–A.4 report the same statistics for the geographical subsamples.

With the aim to compare different periods and geographical areas, we also consider different subsets corresponding to the calendar years from 2017 to 2021 and, for each year, we implement the analysis (a) over the entire dataset and (b) over three subsets corresponding to the following geographical areas: Europe, America and Asia/Pacific.

With reference to each reporting period analyzed, sustainability data refer to the beginning of the reporting period while return and volatility data refer to the end of the reporting period. Our preliminary data analysis indicates that the variables exhibit approximate normality, but with varying degrees of departure from the normal distribution.

4. The Model

Graphical Gaussian Models are a particular class of undirected graphical models for a vector of random variables with a multivariate Gaussian joint distribution. The model postulates the existence of a conditional independence structure between variables that can be visualized by mean of a graph.

Let $Y=(Y_1,Y_2,\dots ,Y_p)$ be a vector of jointly distributed Gaussian random variables, with expected value $E(Y)=\mu$ and covariance matrix $\sum =({\sigma }_{ij})$. Let ${\sum }^{-1}=({\sigma }^{ij})$ be the concentration matrix of Y. Let V be a set of nodes associated with Y and $E\subseteq (V\times V)$ a set of undirected edges. The following results hold (Wermuth 1976) :

where ${\rho }_{ij}$ is the marginal correlation coefficient between $Y_i$ and $Y_j$ and ${\rho }_{ij|V\setminus \{i,j\}}$ is the partial correlation coefficient between $Y_i$ and $Y_j$ given all other variables. Note that the partial correlation coefficient can be seen as the correlation between the residuals of two linear regressions: one of $Y_i$ against the variables in $V\setminus \{i,j\}$ the other of $Y_j$ against the same set of variables. As it is well known, in the Gaussian distribution, correlation coefficients are constant with respect to the value of the conditioning variables.

It follows from (1) that, if Y has a joint Gaussian distribution, then ${\sigma }_{ij}=0$ if and only if $Y_i$ is independent of $Y_j$. Furthermore, ${\sigma }^{ij}=0$ if and only if $Y_i$ is conditionally independent of $Y_j$ given all the remaining variables in $V\setminus \{i,j\}$. Moreover, if two variables are (marginally/conditionally) independent, they are also (marginally/partially) uncorrelated and vice versa.

A relationship between the partial correlation coefficient ${\rho }_{ij|V\setminus \{i,j\}}$ and the marginal correlation coefficient ${\rho }_{ij}$ is induced by (1). For instance, with just three variables, we have

The above relationship points out that even if ${\rho }_{12|3}=0$, ${\rho }_{12}$ can be different from 0 if $Y_1$ and $Y_2$ both share an association with $Y_3$. This situation gives rise to the so-called spurious correlation.

A concentration graph $G_{\mathrm{\text{con}}}^V=(V,E_{\mathrm{\text{con}}}^V)$ is the pair of a set V of nodes associated with Y and a set $E_{\mathrm{\text{con}}}^V$ of undirected edges such that there is no edge joining nodes i and j whenever $Y_i$ and $Y_j$ are uncorrelated given all other variables. A covariance graph $G_{\mathrm{\text{cov}}}^V=(V,E_{\mathrm{\text{cov}}}^V)$ is the pair of a set V of nodes associated with Y and a set $E_{\mathrm{\text{cov}}}^V$ of undirected edges such that there is no edge joining nodes i and j whenever $Y_i$ and $Y_j$ are marginally uncorrelated. In this paper, we first fit the concentration graph $G_{\mathrm{\text{con}}}^V$ to our data and then derive the implied covariance graph $G_{\mathrm{\text{cov}}}^V$.

To give an idea of a Graphical Gaussian Model and its visual representation through the concentration and covariance graphs, we start from the simplest example which involves three jointly Gaussian random variables, say X, W and Z. We assume that X is independent from Z given W. Therefore, the partial correlation coefficient ${\rho }_{xz|w}$ between X and Z, after conditioning on W, is zero. The conditional independence structure may be visualized by mean of the concentration graph as in Fig. 1(a), which exhibits a missing edge between the vertices (Z, X).

Figure 1(b) represents the covariance graph with the induced marginal correlation structure between the three random variables X, Z and W, when the underlying conditional independence is as in Fig. 1(a). It follows from (1) that the marginal correlation coefficients ${\rho }_{xw}$ and ${\rho }_{wz}$ are different from zero and the marginal correlation coefficient ${\rho }_{xz}$ is also nonzero, as a marginal correlation is induced by the common correlation of both variables, X and Z, with W.

In Fig. 2, a second example is presented. The graph is obtained from the previous one after removing the edge between X and W. This second graph encodes the notion that X is marginally independent from W and Z. In this case, both partial correlation ${\rho }_{xz|w}$ and ${\rho }_{xw|z}$ are zero (Fig. 2(a)). These two conditions together imply that marginal correlations ${\rho }_{xz}$ and ${\rho }_{xw}$ (Fig. 2(b)) are also zero.

We focus on the Graphical Gaussian Models of the joint distribution of four random variables, namely, Volatility, ESG Score, Disclosure Score and Return. The modeling strategy aims to identify, via appropriate inferential procedures based on maximum likelihood (ML) estimation, the set of conditional independencies implicit in a joint distribution fitted on the data at hand. The best fitting model is selected through a stepwise selection procedure based on the likelihood ratio test. The chosen graphical model is therefore a well-fitting model that is the outcome of a model selection procedure that starts from the saturated one and at each step removes the edge corresponding to a partial correlation coefficient with the highest p-value of the likelihood ratio test (see Edwards (2000, Chap. 3) for details). Understanding the conditional independence structure can enhance our comprehension of a particular phenomenon. This knowledge not only may be of scientific importance per se, but also it may help in taking the best investment decision.

An instance is provided by the following example, taken from the data at hand (full sample, year 2020). The best fitting conditional independence graph for the four variables of interest is reported in Fig. 3(a) with the indication of the actual value of the partial correlation coefficients significantly different from zero (p-value lower than 0.05). Figure 3(b) displays the induced marginal correlation structure along with the corresponding correlation coefficient values. To aid interpretation, the values of positive partial and marginal correlation coefficients are in black, while the negative ones are in red. The graph in Fig. 3(b) shows a negative marginal correlation between ESG Score and Return, implying that companies with a higher ESG Score tend to present lower returns. However, Fig. 3(a) conveys the important information that there is a positive conditional dependence between Return and ESG Score, given Volatility and Disclosure Score. This means that in an investment decision process, it is possible to maximize the return and at the same time the portfolio ESG Score by fixing the level of volatility and disclosure, whatever they are. Moreover, the graph in Fig. 3(b) shows a negative marginal correlation between Volatility and Disclosure Score. However, Volatility and Disclosure Score are conditional independent given Return and ESG Score (Fig. 3(a)). Hence the negative marginal correlation between these two variables in Fig. 3(b) is spurious and it is induced by their partial correlations with the conditioning variables, Return and ESG Score.

It is worth noticing that, in our analysis, based on the full dataset (see Table A.5), we found that in six situations (20% of the occurrences) the marginal correlation is spurious, i.e. induced by correlation with other variables. In two extreme cases (years 2017 and 2020), we found a change of sign moving from marginal correlation to partial correlation. The methodology proposed allows us to sharpen our understanding of the relationship between the variables, permitting to distinguish which ones are induced by the common association with other variables. Of course, knowledge is limited to the variables used to construct the model.

5. Findings

This section presents the results of our analysis. Figure 4 shows graphs obtained by implementing the model over the entire estimation sample. The number next to each edge is the partial correlation between the two variables. In the following, we summarize the main findings from the model in response to the first objective of the paper.

Research Hypothesis 1. For all periods, the edge [B D] between Volatility and ESG Score shows a significant negative partial correlation, therefore a higher ESG Score is associated with a lower volatility after conditioning on Disclosure and Return. This result could be explained by the fact that more sustainable companies are less vulnerable (in terms of reputation, regulatory or political risk), and therefore present a lower volatility of market price, as discussed by Cornell (2021). This finding is consistent with those in Giese & Lee (2019) and those released by the Morgan Stanley Institute for Sustainable Investing (2019) that, in the Sustainable Reality white paper, analyzed the performance returns and risks of nearly 11000 mutual funds from 2004 to 2018 and found a statistically significant difference in terms of risk: sustainable funds experienced a 20% smaller downside risk than traditional funds. Other studies, such as Managi et al. (2012) and Górka & Kuziak (2022), report no statistical difference in terms of risk.

Research Hypothesis 2. The relationship that emerges in edge [B C] between Volatility and Disclosure Score also ties in well with the previous finding. In years 2017, 2019 and 2020, the model estimates a conditional independence between these two variables, while in years 2018 and 2021, there is negative association. This denotes that companies with higher Disclosure Score do not tend to be more volatile than those with low Disclosure Score, confirming that being more transparent is not leading to higher volatility. In this context, Krueger et al. (2021) found that one of the effects of mandatory ESG disclosure is to reduce the risk of stock price crash suggesting that ESG disclosure reduces volatility. In the same manner, Lopez-de-Silanes et al. (2019) found a statistically significant negative relationship between volatility and Bloomberg ESG Disclosure Score for US, while the coefficient loses statistical significance in other countries.

Research Hypothesis 3. The missing [D A] edge in 2018 and 2021 shows that, given the other variables, the ESG Score and Return are conditionally independent, differently from what happens in the other years, when the correlation is positive. The results show that investing in companies with a higher ESG Score generally does not penalize in terms of profitability, and in some cases, it also produces higher expected returns. The meta-analysis by Hornuf & Yüksel (2022) comes to the same conclusion after reviewing 153 empirical studies containing 1047 observations on SRI performance. They found that, on average, SRI neither outperforms nor underperforms the market portfolio. Furthermore, they observed that studies published in reputable journals, particularly financial ones, or authored by individuals with a frequent focus on sustainable investments, tend to be more supportive of the notion that SRI lacks the capacity to generate outperformance. Another meta-analysis by Friede et al. (2015) combines the findings of about 2200 individual studies and shows that roughly 90% of studies find a nonnegative ESG–corporate financial performance relation. Verheyden et al. (2016) get stronger results reporting “an unequivocally positive” contribution to risk-adjusted returns when using a best-in-class ESG screening approach (one that effectively selects companies with the highest 90% of ESG rankings), both on a global and a developed market.

Research Hypothesis 4. The edge [A C], expressing the relationship between Return and Disclosure Score, presents a negative sign, with the only exception of 2021. This indicates that companies with a higher degree of disclosure tend to have a lower expected return. The correlation remains significant also after conditioning on the ESG Score and the Volatility. This result is confirmed among others by Grewal et al. (2019), who found a negative equity market reaction to events associated with the passage of EU Directive 2014/95 on disclosure of nonfinancial information and by Blomqvist & Stradi (2022), who focused on the abnormal returns depending on preferences toward responsible assets in the US equity market. The reason for such a relation may be due to the higher costs expected by the market for companies to be more transparent, with a consequent penalization in terms of expected returns. The reversal of the sign of the partial correlation in 2021 could mean the beginning (but subsequent analyses are necessary) of a different attitude from investors, which may present a larger appreciation to transparency, with more focus on the benefits rather than the costs associated with it.

To show the coherence between Graphical Gaussian Models and standard linear regression methods, in Table A.6, the results of two linear regressions are reported. The first one concerns the regression of Return against Disclosure Score, ESG Score and Volatility. With the only exception of 2021, the sign of the regression coefficient of the Disclosure Score is negative and significant, in full coherence with the above findings. The second one concerns Volatility against Return, ESG Score and Disclosure Score. The regression coefficient of Disclosure Score is either negative (2018 and 2021) or not significant, in full coherence with the above findings.

Unlike standard linear regression models, Graphical Gaussian Models encompass the joint distribution of all considered variables, eliminating the need to choose a response variable. When no clear ordering among the variables is available from a priori information, this model is more appropriate. Furthermore, when research hypotheses concern relationships between different variables, one has to resort to the fitting of several different linear regression models, one for each response variable, with the issues of multiple testing, lack of efficiency and, possibly, lack of coherence between the findings. The modeling strategy here proposed permits to assess several research questions with just one model. This modeling strategy may also provide interesting insights on aspects that may be outside the focus of the research.

A further result of the analysis, not listed formally in the set of our research hypotheses, is that for all periods there is a significant positive partial correlation for the edge [C D] implying that, also after conditioning on Volatility and Return, companies that know they have low ESG Scores make less disclosure. This may be attributed to the tendency of companies with higher ESG Scores to make more disclosures, while those aware of their low ESG Scores often provide less information to the market. This finding is confirmed by Lopez-de-Silanes et al. (2019) who analyzed the relationship between ESG disclosure and the quality of a firm’s ESG criteria using Sustainalytics ESG rankings on firms of six different countries from year 2015 to year 2018.

Overall, our model shows a quite stable relationship between market variables and the ESG variables, with only one sign inversion in 2021 of the partial correlation between Return and Disclosure Score. However, a remarkably interesting result concerns the evolution, from 2017 to 2021, of the actual value of the partial correlation between Disclosure and ESG Score, which decreases almost constantly over time.

In response to the second objective of the paper to assess differences between geographic areas, we apply our methodology to each dataset separately. The resulting graphical models are represented in Fig. 5. An interesting feature is that, though the conditional independence structure varies slightly across areas, the direction of nonzero associations between financial variables and ESG variables remains stable in almost all areas and years considered. We observe only two exceptions: (a) in the year 2018 within the Asia/Pacific region, a negative correlation between Returns and ESG Scores, in contrast to the consistently positive or null correlations observed in all other cases and (b), in the year 2020 within the America area, a positive association between Volatility and Disclosure Score, zero or negative in all the other areas. The consistent results over time in the European area may be attributed to the robust regulatory framework on sustainability. Another interesting aspect concerns the evolution of the partial correlation between Disclosure Score and ESG Score for all the areas considered, see Table 3. As well as for the full sample, also for the European area our model shows a conditional dependence with a partial correlation always positive, but with a strong reduction (−35.3%) from 2017 to 2021. The same trend is in America and Asia/Pacific, but with less intensity, with a reduction of about 8% and 16% in the US and Asia/Pacific, respectively.

In our opinion, one of the reasons for these differences lies in the approach taken in the different geographical areas. While Europe has adopted a regulatory-driven approach, US and Asia/Pacific areas are more self-driven by the market, and it is only recently that governments in these areas are taking steps to regulate these aspects more closely. In Europe, the reduction in the strength of the conditional association reflects the important steps toward sustainability regulation for both companies and market participants. The more companies are forced to increase their level of disclosure, the more the Disclosure Score will not depend on the ESG Score level. Indirectly, the same conclusion is reached by Krueger et al. (2021) who demonstrate that companies with low ESG ratings are the ones that most increase the amount of disclosure on sustainability issues once mandatory.

It is interesting to note that, also in Europe, the negative association between Volatility and ESG is confirmed, thereby showing that the underlying process that makes companies with high ESG Score less vulnerable is not affected by the regulation. In the long term, however, when disclosure will be effectively mandatory, we expect the partial correlation coefficient between Disclosure Score and the other financial variable to vanish, with the ESG Score carrying the relevant information for the financial markets.

6. Conclusion

Our research confirms that companies with low ESG Scores make less disclosure in all the geographical areas and for all periods analyzed. Further, there is a stable partial negative correlation between ESG Score and Volatility, which suggests that investing in high ESG-rated companies is less risky: more sustainable companies are less vulnerable, a process which reflects in a lower volatility of returns. Our findings also suggest that investing in companies with higher ESG Scores generally does not penalize in terms of returns.

Specifically, looking at the European area, analyses show that the more companies are forced by the regulation to increase their level of disclosure, the more the Disclosure Score will not depend on the ESG Score level. This is expected, as the disclosure is no longer an exclusive strategy done by companies with high ESG Scores, but a mandatory and public signal that companies have to send. The progressive implementation of the comprehensive European policy agenda on sustainable finance, improving information quality and comparability, should reinforce this trend in Europe. However, the negative link between ESG Score and volatility is stable and does not seem to be influenced by different regulations.

Looking at the evolution over time of the relationships between the financial market variables and the ESG variables, overall, our model shows quite stable results with one sign inversion in 2021 of the partial correlation between Return and Disclosure Score. In this context, it is relevant to note that results confirm the stability of the relationships even in a context of more than doubled volatility during the pandemic crisis in the transition from 2019 to 2020. It could be interesting to carry out the research in order to verify our results in times of higher volatility impressed by higher inflation in 2022.

Finally, the applied methodology, besides being useful in investment strategies, can also be used by regulators to verify the effectiveness of sustainability disclosure policies. Our analysis seems to indicate that the enforcement does bring companies with a low ESG Score to disclose, without altering the underlying mechanism that relates the ESG Score to the other financial variables, such as volatility of returns.

The findings of this study should also be viewed in light of some potential limitations. The use of a single ESG data provider in a context of strong rating disagreement among rating companies does not permit a full generalization of the results obtained. This is mitigated, however, by the fact that MSCI is recognized as a market leader in this field, and it is therefore widely used by financial practitioners. Furthermore, different measures of financial risk and return variables may be considered. Future research could address these issues. Finally, in this paper, we emphasize the role of regulation in generating possible temporal and geographical discrepancies. Future analysis could investigate the ability of other stakeholders to influence these patterns.

ORCID

Paola Musile Tanzi  https://orcid.org/0000-0002-4496-3146

Marco Nicolosi  https://orcid.org/0000-0001-8082-8876

Elena Stanghellini  https://orcid.org/0000-0002-2503-8342