ESGM: ESG scores and the Missing pillar - Why doesmissing information matter?

Ozge Sahin∗,1, Karoline Bax2, Claudia Czado1, and Sandra Paterlini2

1Department of Mathematics, Technical University of Munich,Boltzmanstraße 3, Garching, 85748, Germany

2Department of Economics and Management, University of Trento, ViaInama 5, Trento, 38122, Italy

*Corresponding author: ozge.sahin@tum.de

Abstract

Environmental, Social, and Governance (ESG) scores measure companies’ per-formance concerning sustainability and societal impact and are organized on threepillars: Environmental (E), Social (S), and Governance (G). These complementarynon-financial ESG scores should provide information about the ESG performanceand risks of different companies. However, the extent of not yet published ESG in-formation makes the reliability of ESG scores questionable. To explicitly denote thenot yet published information on ESG category scores, a new pillar, the so-calledMissing (M) pillar, is formulated. Environmental, Social, Governance, and Missing(ESGM) scores are introduced to consider the potential release of new informationin the future. Furthermore, an optimization scheme is proposed to compute ESGMscores, linking them to the companies’ riskiness. By relying on the data provided byRefinitiv, we show that the ESGM scores strengthen the companies’ risk relation-ship. These new scores could benefit investors and practitioners as ESG exclusionstrategies using only ESG scores might exclude assets with a low score solely be-cause of their missing information and not necessarily because of a low ESG merit.Keywords: Disclosure; ESG methodology; ESG investment; sustainable finance;Value-at-Risk

1 Introduction

As sustainability concerns increase globally, sustainable finance and Environmental, So-cial, and Governance (ESG) investing strategies gained much interest. According toBloomberg, the “ESG ETF market had risen over 318% in 2020”, indicating the signifi-cant interest by investors (Bloomberg (2021)). To assess the companies’ ESG performance,investors can use their ESG scores which different data providers make available. Such

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scores use the publicly available data and voluntary disclosure to compute individual En-vironmental (E), Social (S), and Governance (G) pillar scores as well as an overall ESGaggregated score.

Until now, most works have focused on the link between ESG scores and corporate finan-cial performance (e.g., Friede et al. (2015); Cornett et al. (2016); Henke (2016); El Ghoulet al. (2017); Hou et al. (2019); Behl et al. (2021); Kalaitzoglou et al. (2021)). Recently,some studies have analyzed the link between ESG scores and risk measures (e.g., Shaferet al. (2020); Bax et al. (2021); Giese et al. (2021); Maiti (2021)).

In the last years, however, criticism of ESG scores has emerged. These include a largediscrepancy between ESG scores from different data providers (e.g., Berg et al. (2020);Billio et al. (2021); Gyonyorova et al. (2021)), as well as the possible update of ESGscores within five years from the data provider (e.g., Refinitiv scores are definitive afterfive years). Moreover, ESG scores might be subject to changes due to a release of newESG information (e.g., Berg et al. (2021)).

In this paper, we focus on considering the role and the amount of missing ESG informationas a potential source for a release of new ESG information with impacts on ESG scores inthe future. Thus, we introduce a new pillar, called the Missing (M) pillar, and define newscores: Environmental, Social, Governance, Missing (ESGM) scores by incorporatingthe M pillar into the three ESG pillars. The ESGM scores are easily interpretable asa convex combination of the E, S, G, and the newly introduced M pillar scores. Wepropose an optimization scheme to link ESGM scores and risk measures and run an in-sample and out-of-sample analysis to ensure robust results. We find that if the amountof missing information is explicitly considered, companies are encouraged to disclose newinformation by our ESGM score construction methodology as it positively impacts thescore. This assumption is reasonable considering the current ESG score constructionmethodology that positively rewards the disclosure of new information and the fact thatoften missing information is not due to the unwillingness to release such information butits unavailability.

Moreover, investors and practitioners can benefit from this research, as exclusion strategies(only including companies with a high ESG score in a portfolio and excluding companieswith a low ESG score (e.g., UNPRI (2021)) are well established. However, followingthis approach and using the widely available Refinitiv ESG data, which do not includethe potential of new information disclosure, would mean that possible companies withpotentially high scores after new ESG information adoption will be missed. Overall, thiscould lead to a more risky and less effective portfolio. Previously, the incorporation ofcorporate social responsibility, environmental and social considerations into investmentdecisions also have been studied from different angles by Calvo et al. (2016), Lamataet al. (2018), Qi (2018), Liagkouras et al. (2020), and De Spiegeleer et al. (2021).

The paper is structured as follows. We first introduce the methodology behind ESG scoreconstruction from Refinitiv in Section 2. Section 3 describes our methodology for M Pillarand ESGM scores, while Section 4 reports our empirical results. Section 5 concludes.

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2 Review of Refinitiv’s ESG score methodology

Among many data providers, Thomson Reuters (Refinitiv) is known as a reliable ESGdata source and is used in many studies (e.g., Dyck et al. (2019), Loof et al. (2021)). Itcollects publicly available ESG information of companies and aggregates such informa-tion to assign the companies with ten ESG category scores benchmarked against ThomsonReuters Business Classifications Industry Group or the respective Country Group (Re-finitiv (2021a); Refinitiv (2021b)). The ten categories are Environmental Innovation (EI),Resource Use (RU), Emissions (EM), Workforce (WF), Human Rights (HR), Community(CO), Product Responsibility (PR), Management (MG), Shareholders (SH), and Corpo-rate Social Responsibility (CS).

Then, the ESG category scores are aggregated to build the Environmental (E), Social (S),and Governance (G) pillar scores as illustrated in Figure 1. As a result, each pillar scoreis between zero and 100.

EI RU EM WF HR CO PR MG SH CS

E S G

ESG

Figure 1: Aggregation of ten ESG categories and three pillar scores in Refinitiv’s ESGscore construction methodology.

Next, an overall ESG aggregated score is the weighted sum of three pillar scores, i.e.,a convex combination of the E, S, and G pillar scores. The pillar score weights rangefrom zero to one, sum up to one, and can change for each pillar within industry groups(see Pages 9 and 10 in Refinitiv (2021a)). Hence, overall ESG aggregated scores alsorange from zero and 100. The higher the overall ESG aggregated scores are, the moreESG responsible the company is evaluated. In the following Example 1, we present anexemplary overall ESG aggregated score calculation of Refinitiv using the fictitious pillarscore weights of the industry group Household Goods and a generic name for the company.

Example 1. (Overall ESG aggregated score calculation) The ESG pillar scores of Com-pany F in Household Goods in 2017 are 0.00 (E pillar), 63.01 (S pillar), and 54.77 (Gpillar) with weights 0.240, 0.294, and 0.466, respectively. Then its overall ESG aggregatedscore in 2017 is the weighted sum of all pillar scores:xESG,CompanyF,2017 = 0.240 · 0.00 + 0.294 · 63.01 + 0.466 · 54.77 = 44.05.

A drawback of the current ESG score methodology is that it does not explicitly considerthe potential disclosure of new ESG information. Indeed, Company F in Example 1 hasnot yet provided any ESG information for the E pillar score of 2017; therefore, its E pillarscore is zero. It also implies that the ESG category scores of 2017 building the E pillarscore (Resource Use, Emissions, and Environmental Innovation) are zero. Company F

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can disclose its ESG information regarding the E pillar’s categories until June 2022, giventhat ESG data of the last five years can be updated a posteriori (Refinitiv (2021a)).

To quantify the companies’ potential to disclose more ESG information in time and an-alyze the impact of the disclosure on the ESG scores and the risk of the portfolios, weconstruct our methodology in Section 3. Overall ESG aggregated scores will be calledESG scores in the rest of the paper.

3 Research methodology

In the following section, we formulate a Missing (M-) pillar score, which explicitly cap-tures the amount of not yet reported ESG information regarding the ten ESG categories.Later, we define Environmental, Social, Governance, and Missing (ESGM) scores andpropose an optimization approach for their computation, linking them to companies’riskiness. The optimization scheme aims to harvest the potential to strengthen the riskrelationship in disclosing missing ESG information. We report the notations of data andindices used in the paper in Appendix A.

3.1 Missing pillar (M pillar) score

Since a zero ESG category score denotes that the company has not yet reported any infor-mation regarding it as discussed in Example 1, we define a new pillar accounting for zerovalues, i.e., missing information, in the ten ESG category scores in a given business class:the Missing (M-) pillar score. A business class can be an industry group or an economicsector based on the business classification of Thomson Reuters (Refinitiv (2021a)). Forinstance, the selection of S&P 500 in Section 4.1 belongs to 61 industry groups from teneconomic sectors.

Definition 1. (The M pillar score) For company p in a given business class a and year t,first, we find the total number of zero values in its ESG categories, i.e., xazero,p,t. The setSazero,t contains these values for all a, p, t. Denoting the total number of companies with

same value as p in Sazero,t (including the company p itself) by eap,t, and the total number of

companies with a higher value than p in Sazero,t by lap,t, the M pillar score of company p in

a given business class a and year t is defined as:

xaM,p,t = 100 ·lap,t +

eap,t2

na

, p = 1, . . . , na, t = 1, . . . , T, a = 1, . . . , A, (1)

where na is the total number of companies in the given business class a, T is the to-tal number of years, and A is the total number of given business classes. The detailedcalculations and notations are given in Appendix A.

From the definition, when a company has more zero values in its ESG categories thanall other companies in its business class, its M pillar score will be the highest. This isbecause it has a higher extent of not yet published ESG information reflected in a high Mpillar score. Moreover, the M pillar score is continuous and between zero and 100, with amean value of 50 (proof in Appendix C). Such a formulation makes it robust to outliers

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and comparable with the three ESG pillar scores. Its formulation is similar to our dataprovider’s ESG category score methodology (Refinitiv (2021a)).

Since our data provider has ten ESG category scores, the highest total number of zerovalues a company can have in its ESG categories in our empirical analysis in Section 4is ten. Accordingly, Example 2 shows the M pillar score calculation steps using ten ESGcategory scores, where the business class is an economic sector, e.g., Consumer Cyclicals.

Example 2. (The M pillar score calculation) Let xap,t = (xaRU,p,t, . . . , x

aCS,p,t)

> containten ESG category scores of company p in business class a in year t. Suppose there arefour companies (na = 4) in the economic sector Consumer Cyclicals (a = 2), and theirfictitious ESG category scores in 2017 (t = 2017) are given as follows:x21,2017 = (99.3, 50.1, 12.3, 52.2, 0.00, 67.9, 0.00, 11.2, 20.4, 0.00)>,

x22,2017 = (63.5, 70.1, 52.3, 84.3, 10.2, 77.9, 88.9, 55.2, 80.4, 86.3)>,

x23,2017 = (36.3, 0.00, 12.3, 23.2, 0.00, 17.9, 0.00, 21.2, 50.5, 58.3)>,

x24,2017 = (85.2, 0.00, 12.3, 12.2, 0.00, 54.3, 52.5, 81.2, 75.6, 24.3)>.

For company p with p = 1, . . . , 4, we determine the total number of zero values in itsESG categories and have S2

zero,2017 = {3, 0, 3, 2}. Consider the fourth company: it holdsx2zero,4,2017 = 2, e24,2017 = 1, and l24,2017 = 1. Accordingly, we calculate its M pillar score as

given in Equation (1): x2M,4,2017 = 100 · 1+12

4= 37.5. For the second company without any

zero values in its ESG categories, the M pillar score is given by x2M,2,2017 = 100· 0+12

4= 12.5.

Since we also calculate x2M,1,2017 = 75 and x2M,3,2017 = 75, the M pillar score is betweenzero and 100; the average M pillar score of all companies is 50, as postulated.

3.2 Environmental, Social, Governance, and Missing (ESGM)scores

This section incorporates the M pillar into the three ESG pillars and builds new scores,the ESGM: Environmental, Social, Governance, and Missing scores.

Definition 2. (The ESGM score) The ESGM score of company p in a given businessclass a and year t is defined as a weighted sum:

xaESGM,p,t = xaE,p,t · waE + xaS,p,t · wa

S + xaG,p,t · waG + xaM,p,t · wa

M , ∀a, p, t. (2)

The ESGM scores have four weighted pillar scores, and a pillar score weight varies accord-ing to its business class. The next task is to estimate the pillar score weights. Since evenregulatory authorities, including the European Banking Authority (EBA), have acknowl-edged the role of ESG scores in quantifying the company riskiness and have identifieda need to incorporate ESG risks into overall business strategies and risk managementframeworks (EBA (2021)), we propose the following optimization scheme in Equation (3)

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to estimate them, connecting the companies’ ESGM scores with their risk performance.

(waE, w

aS, w

aG, w

aM) = arg max

waE ,wa

S ,waG,wa

M

t2∑t=t1

τrisk

(xaESGM,t, xa

risk,t

)(3a)

subject to waE + wa

S + waG + wa

M = 1, ∀a, (3b)

waE, w

aS, w

aG ≥ 0.100, ∀a, (3c)

waM ≥ 0, ∀a, (3d)

waE, w

aS, w

aG ≥ wa

M , ∀a. (3e)

We analyze the ESGM scores’ influence on their risk performance by focusing on theirdependence in Equation (3a). We choose Kendall’s tau (τ) as our dependence measuresince it is robust to outliers. Given the growing literature linking the ESG scores with arisk measure, such as the VaR (e.g., Verheyden et al. (2016)) or volatility (e.g., Zhang etal. (2021)), we can specify a generic risk function in Equation (4). More complex objectivefunctions aiming to find optimal ESG portfolios for investors, such as proposed in Ahmedet al. (2021) and Pedersen et al. (2021), are subject to future research. Nevertheless, wepropose a flexible framework that can take only VaR and volatility or their joint interactionwith the artificially introduced risk measure as the product of the VaR and volatility, i.e.,vvrisk. High ESGM scores should be linked to the strong VaR (e.g., Diemont et al. (2016))and vvrisk, as well as the low volatility (e.g., Kumar et al. (2016)). Moreover, the pillarscore weights can be estimated using data from the period [t1, t2]. In Section 4.3, wewill be using the two recent years of the ESG data for an in-sample estimation, i.e.,t1 = 2017, t2 = 2018, while t3 = 2019 will be used for an out-of-sample evaluation inSection 4.4.

τrisk

(xaESGM,t, xa

risk,t

)=

τ(xaESGM,t, xa

vv,t

), if risk = vvrisk,

τ(xaESGM,t, xa

V aR,t

), if risk = V aR,

−τ(xaESGM,t, xa

vol,t

), if risk = vol.

(4)

The constraint in Equation (3b) ensures that the ESGM scores are between zero and 100,similar to the ESG scores. To exclude unrealistic scenarios, Equation (3c) ensures thateach pillar score except the M pillar score has a positive lower bound, which is motivatedby the lowest weight ever given to one of the E, S, and G pillar scores in one of theindustry groups by our data provider. To account for cases with no impacts of disclosingnew ESG information on the risk performance, we set a lower bound of zero for the Mpillar score weight in Equation (3d). In Equation (3e), we assume that the E, S, and Gpillar score weights are larger than or equal to the M pillar score weight. It considers therelative importance of already disclosed ESG information in the E, S, and G pillar scorescompared to the potential disclosure represented by the M pillar score.

Moreover, disclosing reduces the companies’ weighted M pillar score due to a decrease inthe number of zero values entering the computation of the M pillar score. By assigninghigher weights to the E, S, and G pillar scores, our scheme encourages companies to

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disclose new ESG information, which usually positively impacts both their ESGM andESG scores. Additionally, such an optimization scheme allows us to see which businessclasses with not yet disclosed ESG information might play a role and for which businessclasses a re-weighting scheme for the E, S, and G pillar scores matters to strengthen therisk dependence. An empirical analysis is provided in Section 4.

Overall, in Equation (3), the constraints are linear, and the objective function is non-linear in terms of the parameters with unknown derivatives. Thus, such a scheme can besolved by a derivative-free optimization algorithm dealing with linear constraints. Larsonet al. (2019) provide a recent review of derivative-free optimization methods.

When our ESGM pillar score weights are estimated, we compute a company’s ESGMscore as follows in Example 3.

Example 3. (The ESGM score calculation)Suppose the estimated pillar weights of the companies in the economic sector ConsumerCyclicals (a = 2) are given by w2

E = 0.258, w2S = 0.122, w2

G = 0.498, w2M = 0.122. Then,

a company’s ESGM score (p = 1) in Consumer Cyclicals with the following pillar scoresin 2017, xaE,1,2017 = 40.0, xaS,1,2017 = 60.0, xaG,1,2017 = 20.0, xaM,1,2017 = 50.0, is calculatedas follows:x2ESGM,1,2017 = 0.258 · 40.0 + 0.122 · 60.0 + 0.498 · 20.0 + 0.122 · 50.0 = 33.70.

4 Empirical results

Before reporting our empirical results, we first explore the data in this section. The dataset consists of the constituents of the S&P 500 from ten economic sectors, i.e., the topmarket capitalization companies around the world. We calculate the M pillar score andestimate the ESGM pillar weights by solving the optimization scheme in Equation (3),using the derivative-free optimization solver, LINCOA (Linearly Constrained Optimiza-tion Algorithm) 1. Later, we compute the ESGM scores for each of the ten sectors. Webase our four pillar score weights estimation on training (in-sample) data to avoid overfit-ting the data. Finally, we compare the relationship between risk, ESGM scores and ESGscores using test (out-of-sample) data.

4.1 Data

Using the non-definitive ESG data, for which companies can still disclose the ESG in-formation, our data consists of yearly ESG, E, S, and G pillar composed from the tenESG categories Resource Use, Emissions, Environmental Innovation, Workforce, Human

1LINCOA solves linearly constrained optimization problems without using derivatives of the objectivefunction and uses a trust region method (Powell (2015)). As Powell (2015) mentioned, we transformthe linear equality in Equation (3b) into two inequalities. After running sensitivity analyses, the initialand final trust-region radii are set to 10−1 and 10−3, respectively. The maximum number of functionevaluations allowed is 10,000. As the numerical optimization problems are sensitive to initial parametervalues, we use ten different starting values and choose the optimal weights in correspondence with thebest objective function value of ten runs. We do not observe multiple optimal solutions. All results areavailable from the authors upon request.

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Rights, Community, Product Responsibility, Management, Shareholders, and CorporateSocial Responsibility scores (extracted on February 4, 2021) of the constituents of theS&P 500 over the period 2017 to 2019.

We use the companies’ daily price data from January 2, 2017, to December 30, 2019, tocompute their daily log returns. Since 17 companies do not report either ESG data orprice data in 2017-2018 in the database, we excluded them from our analysis, workingwith a total of 483 companies. To have as many companies as possible in the sample,we argue that investors use the latest score available in the market to make their riskassessment. Hence, the ESG data of the companies, which do not have any values in2019, are imputed by their ESG data in 2018, assuming their score has not yet beenupdated, and investors would still consider these scores in their decision making. In total,we imputed the ESG data of 66 companies in 2019. The dependence estimated usingPearson correlation (Kendall’s τ) between the ESG scores in 2017 and 2018 is equal to0.94 (0.79), between the scores in 2018 and 2019 to 0.93 (0.78), while between the ESGscores in 2017 and 2019 to 0.89 (0.71).

The sample contains companies from ten different Thomson Reuters Business Classifica-tions Economic Sectors (Refinitiv (2021b)): Basic Materials (23 companies), ConsumerCyclicals (77 companies), Consumer Non-Cyclicals (39 companies), Energy (24 compa-nies), Financial (60 companies), Healthcare (56 companies), Industrials (65 companies),Real Estate (28 companies), Technology (82 companies), and Utilities (29 companies).Even though the data provider determines the ESG, pillar, and category scores for 47industry groups within the S&P 500 as the business class, we work with ten economicsectors to have a larger sample size within each sector to optimize the ESGM pillar scoreweights. Since using industry groups is a more granular approach than using sectorsdue to a larger number of convex pillar score weight combinations, it implies a trade-offin favor of the data provider’s weighting scheme. Still, the ESGM scores show a riskstrengthening effect in Sections 4.3 and 4.4 compared to the data provider’s ESG scores.

Table 1 shows that the percentage of the companies with not yet disclosed ESG infor-mation regarding at least one of the ten ESG categories ranges from a minimum of 15%in Consumer Non-Cyclicals in 2019 to a maximum of 71% in Healthcare in 2017 with anaverage of 47% across ten sectors and three years. More than half of the companies inConsumer Cyclicals, Energy, and Healthcare have at least one of the ten ESG categorieswith not yet released ESG information in each year. Moreover, we observe that the per-centage of such companies tends to decrease in time in Table 1. Such a result might implythat the companies disclose more information as it becomes available, which could providenew insights into their ESG performance and risk characteristics. Furthermore, since theESG scores have had a strong impact on the company’s value (e.g., Fatemi et al. (2018)),one can expect the companies to publish more ESG information in the future.

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Sector 2017 2018 2019Basic Materials 35% 30% 30%Consumer Cycl. 56% 55% 53%Consumer N-Cycl. 23% 18% 15%Energy 67% 67% 58%Financials 61% 53% 47%Healthcare 71% 64% 59%Industrials 47% 47% 44%Real Estate 68% 54% 46%Technology 48% 44% 34%Utilities 45% 41% 34%

Table 1: Percentage of the companies with not yet disclosed ESG information at leastone of the ten ESG categories across ten sectors and three years.

Figure 2 shows that companies with lower ESG scores tend to have more ESG categorieswith not yet published ESG information. It could be due to the lack of infrastructureallowing them to collect and then release such information. However, it would still implythat a company with a lower ESG score could have a large potential to upgrade its ESGscore when not yet recorded information is disclosed.

Figure 2: Scatter plot of the companies’ ESG scores and their number of ESG categorieswith undisclosed ESG information in Consumer Cyclicals in 2017, where a diamond de-notes the median ESG score of the respective column.

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Figure 3 shows the variability in the companies’ E, S, and G pillar scores in 2017 across tensectors. We observe similar findings for the years 2018 and 2019 (available upon request).

Figure 3: E, S, and G pillar scores in 2017 across ten sectors.

For the risk measures, we estimate the companies’ annual 95% VaR as the empiricalquantile and the annual volatility as the market risk measure using the daily logarithmicreturns. Then, we calculate the companies’ vvrisk. Figure 6 in Appendix B gives thepairwise scatter plots with the empirical Kendall’s τ of the VaR, volatility, vvrisk for ourdata. We remark that less negative VaR tends to be associated with smaller volatilitylevels, and the vvrisk is highly negatively/positively dependent on the volatility/VaR.Moreover, we can observe the variability in the VaR of the companies in each of the tensectors in Figure 7 in Appendix B, showing that Utilities has the smallest variation. Wepresent here the results using VaR as the risk measure in Equation (4). However, theresults similarly hold when considering the volatility or vvrisk in Equation (4) (availableupon request).

Next, we report the descriptive statistics of the companies’ M pillar scores in Section4.2. Since we have three years (t ∈ [2017, 2019]) in our data, we use 2017 and 2018 asthe in-sample data to estimate the pillar weights in Section 4.3. Later, in Section 4.4,we apply our estimated pillar weights to the out-of-sample data, i.e., E, S, G, and Mpillar scores of 2019, to calculate the ESGM scores for 2019. Then, we compare their riskperformance with the ESG scores for 2019 as an out-of-sample analysis. We discuss ourresults in Section 4.5.

4.2 M pillar scores

Since the companies in the data set contain the ESG categories with not yet reported ESGinformation as shown in Table 1, we account for their information disclosure, assigning aM pillar score as in Equation (1) in each of the ten sectors. The range of the number ofESG categories with unclosed ESG information is zero to six.

After computing the companies’ M pillar scores across ten sectors and three years, weobserve that the mean M pillar score within each sector and year is 50, as constructed.The M pillar score shows variation among ten sectors, and the standard deviation of theM pillar score changes from 18.31 for Consumer Non-Cyclicals in 2019 to 28.16 for RealEstate in 2017. Consumer Non-Cyclicals has the lowest percentage of the companies withundisclosed ESG information regarding an ESG category in Table 1, and its M pillar score

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has the lowest standard deviation.

Table 2 reports the empirical Kendall’s τ values between the ESG scores, E, S, G, andM pillar scores in Consumer Cyclicals in 2017. We see that the E, S, and G pillar scoreshave positive medium-sized dependence with the ESG scores, while the M pillar scorenegatively depends on the ESG scores and the other pillars as expected. When more ESGinformation is available for a company, the number of ESG categories with undisclosedESG information decreases. Accordingly, its ESG category scores increase, assumingnothing changes in the other available information. Then, since an ESG pillar scoreaggregates the underlying ESG category scores, the respective E, S, and G pillar scoresincrease, thereby increasing its ESG score. However, since the number of zero values usedfor the computation of the M pillar score decreases, its M pillar score goes down. Ourfindings are characteristically similar when considering other years and sectors.

ESG E S G MESG 1.00E 0.66 1.00S 0.76 0.54 1.00G 0.46 0.25 0.31 1.00M -0.52 -0.57 -0.44 -0.20 1.00

Table 2: Empirical Kendall’s τ matrix of the ESG scores, E, S, G, and M pillar scores inConsumer Cyclicals in 2017.

4.3 In-sample analysis

After having the companies’ E, S, G, and M pillar scores, now, we focus on estimating theE, S, G, and M pillar score weights using the data in 2017 and 2018 across ten sectors,linking the resulting ESGM scores to their risk measures as formulated in Equation (3).Precisely, we find (wa

E, waS, w

aG, w

aM) for all a and aim to analyze for which sectors there is

a risk strengthening effect using the M pillar, i.e., potential disclosure of ESG information.

Table 3 reports the sectors’ estimated four pillar score weights, where the M pillar weightis not close to zero. For the remaining six sectors, where the M pillar weight is almostzero, the re-weighting scheme for the E, S, and G pillar scores usually leads to strongerrisk dependence than the original ESG scores (available upon request). According toTable 3, as postulated in Equation (3), the pillar score weights sum up to one; the E, S,and G pillar score weights are at least 0.100; the M pillar score is non-negative, and theE, S, and G pillar score weights are larger than or equal to the M pillar score weight. Wealso see that ESGM scores are built on the M pillar for Consumer Cyclicals, Real Estate,Technology, and Utilities. We can see in Table 4 that the ESGM scores provide strongerVaR dependence for these sectors, except for Real Estate in 2017. The minimal decreasecan be explained since we aim to maximize the dependence between the resulting ESGMscores and VaR over two years. Hence, a reduction in the dependence for a year might beobserved; however, overall dependence in the two years is stronger with the ESGM scores.

A company is assigned to a rating class (i.e., A, B, C, or D) based on its ESG score using

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Sector E S G MConsumer Cycl. 0.258 0.122 0.498 0.122Real Estate 0.700 0.100 0.100 0.100Technology 0.247 0.247 0.259 0.247Utilities 0.327 0.226 0.223 0.224

Table 3: New E, S, G, M pillar score weights, resulting in the ESGM scores in Table 4across four sectors for which we have a non-zero M pillar score weight.

Panel A: ESG and VaRSector 2017 2018Consumer Cycl. 0.161 ** 0.144 **Real Estate -0.138 -0.312Technology 0.154 ** 0.028Utilities -0.079 -0.030

Panel B: ESGM and VaR2017 2018

0.198 *** 0.212 ***-0.153 -0.2650.186 *** 0.0960.000 0.163

Table 4: Kendall’s τ between ESG, ESGM scores, and 95% VaR in 2017, 2018 across foursectors (in-sample) for which we have a non-zero M pillar score weight. The hypothesistesting is H0 : τ = 0 versus HA : τ > 0 (Hollander et al. (2013)). *, **, and *** denotestatistical significance at 10%, 5%, and 1% levels, respectively.

thresholds or quartiles (e.g., Refinitiv (2021a)). Thus, we group the companies with thehighest to lowest ESG and ESGM scores in the first/second/third/fourth quartile as ESGand ESGM rating class A/B/C/D in each of four sectors, respectively. Class D containsthe companies, which have low scores and might be excluded in ESG portfolios. Wewitness that low ESGM scores (class D) are associated with higher median risks than lowESG scores (class D), as demonstrated in Figure 4. The sole exception is Real Estate,where the dependence sign is opposite of the desired one in Table 4, consistent with theliterature from the return aspect (e.g., Dıaz et al. (2021)).

Additionally, since the VaR variation is low in Utilities, dividing the companies into classeswith different VaR characteristics is hard. Thus, we can argue that the companies whichhave not yet released ESG information as much as their peers do, thereby having lowerESG scores than them, in these sectors, might result in risk underestimation in the ESGportfolios using exclusion strategies. It means that the excluded companies, e.g., ESGclass D, might have strong risk performances similar to others. Instead, the ESGM scoresquantify better the companies that can be excluded, e.g., ESGM class D, and providestronger risk performances for such portfolios than the ESG scores as seen for ConsumerCyclicals in 2017.

Comparing the ESG and ESGM rating classes in Consumer Cyclicals in 2017 presentsthat ESGM scores move three/one companies from the ESG class D to the ESGM classC/B in 2017. Such a result reveals that the companies with low ESG scores might notnecessarily provide the worst risk performances. Rather, their ESG scores could be lowdue to not yet disclosed ESG information the data provider does not explicitly pointout. Still, these companies might publish more ESG information in the future, increasing

12

Figure 4: Empirical 95% VaR of rating class D for ESG and ESGM in 2017, 2018.

their ESG scores, as modeled by their ESGM scores. Similar results hold for Real Estate,Utilities, and Technology (available upon request).

4.4 Out-of-sample analysis

ESGM scores provide stronger risk dependence and identify more reliably the companiesfor exclusion strategies in ESG portfolios than the ESG scores as discussed in Section 4.3.Nevertheless, we estimate the ESGM pillar score weights to strengthen the link betweenthe resulting ESGM scores and risk. Therefore, we use the estimated E, S, G, and M pillarscore weights for another year to calculate ESGM scores, where the ESG data is still non-definitive, and companies can publish their ESG information in time. Accordingly, weperform an out-of-sample analysis using the data for 2019.

First, we calculate the companies’ ESGM scores for 2019 in each sector as follows:

xaESGM,p,2019 = xa

E,p,2019 · waE + xa

S,p,2019 · waS + xa

G,p,2019 · waG + xa

M,p,2019 · waM ,∀a, p,

where waE, wa

S, waG, and wa

M are the estimated weights using the training data in 2017and 2018 in Section 4.3.

Second, we analyze the dependence between the ESG scores, ESGM scores and VaR in2019 in Table 5, again focusing on four sectors analyzed in our in-sample-analysis inSection 4.3. As can be seen, the out-of-sample analysis also confirms the higher risk

13

dependence for the ESGM scores than the ESG scores in all cases but Real Estate.

Panel A: ESG and VaRSector 2019Consumer Cycl. 0.036Real Estate -0.310Technology 0.051Utilities -0.099

Panel B: ESGM and VaR2019

0.095-0.3390.070

-0.010

Table 5: Kendall’s τ between ESG, ESGM scores, and 95% VaR in 2019 across foursectors (out-of-sample).

Finally, Figure 5 suggests that the ESGM class D presents higher median risks than theESG class D in Consumer Cyclicals and Technology. However, the performance of theESG and ESGM scores seems to be similar in Real Estate and Utilities. Hence, the ESGportfolios using exclusion strategies could benefit from the ESGM scores in terms of therisk performance, supporting our findings using the in-sample data in Section 4.3.

Figure 5: Empirical 95% VaR of rating class D for ESG and ESGM in 2019.

4.5 Discussion

As a result, our findings support the proposed methodology and provide evidence of theneed for considering the disclosure of new ESG information that can be linked to thecompanies’ riskiness as seen, especially for Consumer Cyclicals and Technology. Even

14

though our empirical analyses are based on the Refinitiv ESG data, Lopez et al. (2020)find that the divergence of the ESG scores of Consumer Cyclicals and Technology amongdifferent data providers is less than others. Likewise, the divergence appears to be lower forcompanies whose scores are away from the mean, e.g., ESG class D, than others. Hence,we conjecture that our findings might also hold for Consumer Cyclicals and Technologywhen using different ESG data providers.

On the other hand, our estimated M pillar weight is zero for some sectors despite hav-ing many companies with not yet disclosed ESG information regarding at least one ofthe ten ESG categories like Healthcare. This result suggests investigating determinantsof the occurrence and distribution of the companies’ missing ESG information amongESG categories and exploring alternative optimization schemes. Such an analysis couldalso provide insights into how ESG information should be disclosed to have an accuratemeasure of the companies’ ESG performance and responsible investing.

5 Conclusion

We propose a new pillar score, the so-called Missing (M-) pillar score, to explicitly considerthe companies’ potential of disclosing new ESG information. By doing so, we introducea new Environmental, Social, Governance, and Missing (ESGM) score. In addition, ourstudy formulates an optimization scheme to link the companies’ ESGM scores and riski-ness. Such a scheme encourages companies to publish more ESG information and evaluatethe impact of disclosing on the risk.

We evaluate the risk performance of the proposed ESGM scores and ESG scores usingin-sample and out-of-sample data. The in-sample data analysis allows us to estimate theESGM scores’ pillar weights, which are used to compute the ESGM scores. The out-of-sample data analysis tests the power of the ESGM scores regarding their risk dependence.Using the S&P 500 companies’ non-definitive ESG data provided by Refinitiv, we showthat the ESGM scores provide stronger risk dependence than the ESG scores in somesectors using both the in-sample and out-of-sample data. We argue that a potentialdisclosure of new ESG information impacts the risk in these sectors. This approachpotentially supports the investment decisions as an ESG exclusion strategy depends on theESG rating class, which is affected by missing information. Furthermore, incorporatingthe potential of possible disclosure allows to include companies in the portfolio that wouldotherwise be excluded as too much data is missing at the time of the investment decision.

Our study is limited by a small number of companies within each sector. Future studiesshould consider applying our M pillar score and ESGM scores formulations to data witha larger number of companies. The second limitation of our research is that it does notaccount for common risk factors. Considering these points and performing an empiricalanalysis with European companies are left for future research. Moreover, necessary mod-ifications for the M pillar score can be considered in the future to evaluate the ESGMscores also from other ESG data providers. Lastly, exploring optimization schemes withdifferent objective functions and constraints can be considered in the future.

15

A Indices, data, notation

Index&Data NotationSector (Business class) a = 1, . . . , 10Total number of companies nCompany z z = 1, . . . , nTotal number of companies in sector a na

Company p in sector a p = 1, . . . , na

Year t = 2017, . . . , 2019Value-at-Risk of company z in year t xV aR,z,t

Value-at-Risk values of companies in year t xV aR,t = (xV aR,1,t, . . . , xV aR,n,t)>

Value-at-Risk of company p in sector a and year t xaV aR,p,t

Value-at-Risk values of companies in sector a and year t xaV aR,t = (xaV aR,1,t, . . . , x

aV aR,na,t

)>

Volatility of company z in year t xvol,z,tVolatility values of companies in year t xvol,t = (xvol,1,t, . . . , xvol,n,t)

>

Volatility of company p in sector a and year t xavol,p,tVolatility values of companies in sector a and year t xa

vol,t = (xavol,1,t, . . . , xavol,na,t

)>

vvrisk of company z in year t xvv,z,tvvrisk values of all companies in year t xvv,t = (xvv,1,t, . . . , xvv,n,t)

>

vvrisk of company p in sector a and year t xavv,p,tvvrisk values of companies in sector a and year t xa

vv,t = (xavv,1,t, . . . , xavv,na,t)

>

ESG score of company z in year t xESG,z,t

ESG scores of companies in year t xESG,t = (xESG,1,t, . . . , xESG,n,t)>

ESG score of company p in sector a and year t xaESG,p,t

ESG scores of companies in sector a and year t xaESG,t = (xaESG,1,t, . . . , x

aESG,na,t

)>

ESGM score of company z in year t xESGM,z,t

ESGM scores of companies in year t xESGM,t = (xESGM,1,t, . . . , xESGM,n,t)>

ESGM score of company p in sector a and year t xaESGM,p,t

ESGM scores of companies in sector a and year t xaESGM,t = (xaESGM,1,t, . . . , x

aESGM,na,t

)>

E pillar score of company p in sector a and year t xaE,p,t

E pillar scores of companies in sector a and year t xaE,t = (xaE,1,t, . . . , x

aE,na,t

)>

S pillar score of company p in sector a and year t xaS,p,tS pillar scores of companies in sector a and year t xa

S,t = (xaS,1,t, . . . , xaS,na,t

)>

G pillar score of company p in sector a and year t xaG,p,t

G pillar scores of companies in sector a and year t xaG,t = (xaG,1,t, . . . , x

aG,na,t

)>

M pillar score of company p in sector a and year t xaM,p,t

M pillar scores of companies in sector a and year t xaM,t = (xaM,1,t, . . . , x

aM,na,t

)>

Resource use score of company p in sector a and year t xaRU,p,t

Emissions score of company p in sector a and year t xaEM,p,t

Environmental innovation score of company p xaEI,p,t

in sector a and year tWorkforce score of company p in sector a and year t xaWF,p,t

Human rights score of company p in sector a and year t xaHR,p,t

Community score of company p in sector a and year t xaCO,p,t

Product Responsibility score of company p xaPR,p,t

in sector a and year tManagement score of company p in sector a and year t xaMG,p,t

Shareholders score of company p in sector a and year t xaSH,p,t

CSR strategy score of company p in sector a and year t xaCS,p,t

Total number of zero values in ESG categories xazero,p,tof company p in sector a and year tSet of ESG category indices SCAT = {RU,EM,EI,WF,HR,CO, PR,MG,SH,CS}Set of total number of zero values in ESG categories Sa

zero,t = {xazero,1,t, . . . , xazero,na,t}of companies in sector a and year tTotal number of companies that company p has eap,tthe same total number of zerovalues in ESG categories in sector a and year tTotal number of companies that company p has lap,ta higher total number of zerovalues in ESG categories in sector a and year t

Table 6: Mathematical indices, data, and their notation used in the paper.

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Total number of zero values in ESG categories of company p in sector a and year t(xazero,p,t):

xazero,p,t =∑

j′∈SCATj′:xa

j′,p,t=0

1, ∀a, p, t. (5)

Total number of companies that company p has the same total number of zero values inESG categories in sector a and year t (eap,t):

eap,t =∑

j′∈[1,na]j′:xa

zero,j′,t=xazero,p,t

1, ∀a, p, t. (6)

Total number of companies that company p has a higher total number of zero values inESG categories in sector a and year t (lap,t):

lap,t =∑

j′∈[1,na]j′:xa

zero,j′,t<xazero,p,t

1, ∀a, p, t. (7)

B 95% VaR, volatility, vvrisk

(a) in 2017 (b) in 2018 (c) in 2019

Figure 6: Pairwise scatter plots of volatility, VaR, and vvrisk in a year, where upperdiagonal shows the empirical Kendall’s τ .

Figure 7: 95% VaR across ten sectors.

17

C Proof of the M pillar score bounds and average

Let S = {x1, . . . , xN} be a set with N elements such that x1 ≤ . . . ≤ xN . For the dthelement, xd, assume the number of elements whose value is smaller/larger than xd in Sare denoted by nd

s/ndl . Also, nd

e corresponds to the number of elements xd has the samevalue in S (including itself). It holds that nd

s + ndl + nd

e = N for d = 1, . . . N . Then its Mpillar score is given by:

xdM = 100 ·nds + nd

e

2

Nfor d = 1, . . . , N.

Lower bound on M pillar score: Since it holds nds ≥ 0, nd

e ≥ 0, N ≥ 0, we have xdM ≥ 0 for∀d,

Upper bound on M pillar score: Since it holds xdM = 100· nds+

nde2

N≤ 100· n

ds+

nde2

nds+nd

e≤ 100· n

ds+nd

e

nds+nd

e,

we have xdM ≤ 100 for ∀d.Average value of M pillar score: Denoting the average value of the M pillar score for theelements in S by xM , we can write:

xM = 100 ·(n1

s + . . .+ nNs ) + (n1

e+...+nNe )

2

N ·N.

In the first scenario, assume x1 < . . . < xN . Then, it holds

xM = 100 ·(0 + . . .+N − 1) + (1+...+1)

2

N ·N= 100 ·

N ·(N−1)2

+ N2

N ·N= 50.

In the second scenario, assume x1 = . . . = xj < xj+1 < . . . < xN . Then, we have

xM = 100 ·(0 + . . .+ 0 + J + (J + 1) + . . .+N − 1) + (J+...+J+1+...+1)

2

N ·N

= 100 ·(N−1+J)·(N−J)

2+ J ·J+(N−J)

2

N ·N= 50.

The second scenario can be easily adopted for the equal elements, which exist more thanonce in the set, and it can be proven that the average M pillar score is 50.

References

Ahmed, Muhammad Farid, Yang Gao, and Stephen Satchell (2021). “Modeling demandfor ESG”. In: The European Journal of Finance, pp. 1–15.

Bax, Karoline, Ozge Sahin, Claudia Czado, and Sandra Paterlini (2021). “ESG, Risk, and(Tail) Dependence”. In: Available at SSRN 3846739. doi: 10.2139/ssrn.3846739.

Behl, Abhishek, PS Kumari, Harnesh Makhija, and Dipasha Sharma (2021). “Exploringthe relationship of ESG score and firm value using cross-lagged panel analyses: Caseof the Indian energy sector”. In: Annals of Operations Research, pp. 1–26.

Berg, Florian, Julian F Kolbel, and Roberto Rigobon (2020). “Aggregate Confusion: TheDivergence of ESG Ratings”. In: Available at SSRN 3438533. doi: 10.2139/ssrn.3438533.

18

Berg, Florian, Kornelia Fabisik, and Zacharias Sautner (2021). “Is History RepeatingItself? The (Un)Predictable Past of ESG Ratings”. In: Available at SSRN 3722087.doi: 110.2139/ssrn.3722087.

Billio, Monica, Michele Costola, Iva Hristova, Carmelo Latino, and Loriana Pelizzon(2021). “Inside the ESG ratings: (Dis)agreement and performance”. In: CorporateSocial Responsibility and Environmental Management 28(5), pp. 1426–1445.

Bloomberg (2021). ESG assets may hit 53 trillion dollars by 2025, a third of global AUM.https://www.bloomberg.com/professional/blog/esg-assets-may-hit-53-

trillion-by-2025-a-third-of-global-aum/. visited on 2021-11-22.Calvo, Clara, Carlos Ivorra, and Vicente Liern (2016). “Fuzzy portfolio selection with

non-financial goals: exploring the efficient frontier”. In: Annals of Operations Research245(1), pp. 31–46. doi: 10.1007/s10479-014-1561-2.

Cornett, Marcia Millon, Otgontsetseg Erhemjamts, and Hassan Tehranian (2016). “Greedor good deeds: An examination of the relation between corporate social responsibilityand the financial performance of U.S. commercial banks around the financial crisis”.In: Journal of Banking & Finance 70, pp. 137–159. issn: 0378-4266.

De Spiegeleer, Jan, Stephan Hocht, Daniel Jakubowski, Sofie Reyners, and Wim Schoutens(2021). “ESG: a new dimension in portfolio allocation”. In: Journal of SustainableFinance & Investment 0(0), pp. 1–41. doi: 10.1080/20430795.2021.1923336.

Dıaz, Violeta, Denada Ibrushi, and Jialin Zhao (2021). “Reconsidering systematic factorsduring the Covid-19 pandemic–The rising importance of ESG”. In: Finance ResearchLetters 38, p. 101870. doi: 10.1016/j.frl.2020.101870.

Diemont, Dolf, Kyle Moore, and Aloy Soppe (2016). “The downside of being responsible:Corporate social responsibility and tail risk”. In: Journal of Business Ethics 137(2),pp. 213–229. doi: 10.1007/s10551-015-2549-9.

Dyck, Alexander, Karl V Lins, Lukas Roth, and Hannes F Wagner (2019). “Do insti-tutional investors drive corporate social responsibility? International evidence”. In:Journal of Financial Economics 131(3), pp. 693–714.

EBA (2021). Management and supervision of ESG risks for credit institutions and in-vestment firms. https://www.eba.europa.eu/eba- publishes- its- report-

management-and-supervision-esg-risks-credit-institutions-and-investment.visited on 2021-04-26.

El Ghoul, Sadok and Aymen Karoui (2017). “Does corporate social responsibility affectmutual fund performance and flows?” In: Journal of Banking & Finance 77, pp. 53–63.issn: 0378-4266. doi: https://doi.org/10.1016/j.jbankfin.2016.10.009.

Fatemi, Ali, Martin Glaum, and Stefanie Kaiser (2018). “ESG performance and firm value:The moderating role of disclosure”. In: Global Finance Journal 38, pp. 45–64.

Friede, Gunnar, Timo Busch, and Alexander Bassen (2015). “ESG and financial perfor-mance: aggregated evidence from more than 2000 empirical studies”. In: Journal ofSustainable Finance & Investment 5(4), pp. 210–233.

Giese, Guido, Zoltan Nagy, and Linda-Eling Lee (2021). “Deconstructing ESG RatingsPerformance: Risk and Return for E, S, and G by Time Horizon, Sector, and Weight-ing”. In: The Journal of Portfolio Management 47(3), pp. 94–111. issn: 0095-4918.doi: 10.3905/jpm.2020.1.198.

19

Gyonyorova, Lucie, Martin Stachon, and Daniel Stasek (2021). “ESG ratings: relevantinformation or misleading clue? Evidence from the S&P Global 1200”. In: Journal ofSustainable Finance & Investment, pp. 1–35. doi: 10.1080/20430795.2021.1922062.

Henke, Hans-Martin (2016). “The effect of social screening on bond mutual fund perfor-mance”. In: Journal of Banking & Finance 67, pp. 69–84. issn: 0378-4266.

Hollander, Myles, Douglas A Wolfe, and Eric Chicken (2013). Nonparametric statisticalmethods. Vol. 751. John Wiley & Sons. doi: 10.1002/9781119196037.

Hou, Chen-En, Wen-Min Lu, and Shiu-Wan Hung (2019). “Does CSR matter? Influenceof corporate social responsibility on corporate performance in the creative industry”.In: Annals of Operations Research 278(1), pp. 255–279.

Kalaitzoglou, Iordanis, Hui Pan, and Jacek Niklewski (2021). “Corporate social respon-sibility: How much is enough? A higher dimension perspective of the relationshipbetween financial and social performance”. In: Annals of Operations Research 306(1),pp. 209–245. doi: 10.1007/s10479-020-03834-y.

Kumar, N. C. Ashwin, Camille Smith, Leıla Badis, Nan Wang, Paz Ambrosy, and Ro-drigo Tavares (2016). “ESG factors and risk-adjusted performance: a new quantitativemodel”. In: Journal of Sustainable Finance & Investment 6(4), pp. 292–300. doi:10.1080/20430795.2016.1234909.

Lamata, Maria Teresa, Vicente Liern, and Blanca Perez-Gladish (2018). “Doing good bydoing well: A MCDM framework for evaluating corporate social responsibility attrac-tiveness”. In: Annals of Operations Research 267(1), pp. 249–266.

Larson, Jeffrey, Matt Menickelly, and Stefan M. Wild (2019). “Derivative-free optimiza-tion methods”. In: Acta Numerica 28, 287–404. doi: 10.1017/S0962492919000060.

Liagkouras, K, K Metaxiotis, and G Tsihrintzis (2020). “Incorporating environmental andsocial considerations into the portfolio optimization process”. In: Annals of OperationsResearch, pp. 1–26. doi: s10479-020-03554-3.

Loof, Hans, Maziar Sahamkhadam, and Andreas Stephan (2021). “Is Corporate SocialResponsibility investing a free lunch? The relationship between ESG, tail risk, and up-side potential of stocks before and during the COVID-19 crisis”. In: Finance ResearchLetters. issn: 1544-6123. doi: https://doi.org/10.1016/j.frl.2021.102499.

Lopez, Claude, Oscar Contreras, and Joseph Bendix (2020). “ESG Ratings: The RoadAhead”. In: Available at SSRN 3706440.

Maiti, Moinak (2021). “Is ESG the succeeding risk factor?” In: Journal of SustainableFinance & Investment 11(3), pp. 199–213. doi: 10.1080/20430795.2020.1723380.

Pedersen, Lasse Heje, Shaun Fitzgibbons, and Lukasz Pomorski (2021). “Responsibleinvesting: The ESG-efficient frontier”. In: Journal of Financial Economics 142(2),pp. 572–597. doi: 10.1016/j.jfineco.2020.11.001.

Powell, M. J. D. (2015). “On fast trust region methods for quadratic models with linearconstraints”. In: Mathematical Programming Computation 7, pp. 237–267. doi: 10.1007/s12532-015-0084-4.

Qi, Yue (2018). “On outperforming social-screening-indexing by multiple-objective port-folio selection”. In: Annals of Operations Research 267(1), pp. 493–513. doi: 10.1007/s10479-018-2921-0.

Refinitiv (2021a). Environmental, Social and Governance (ESG) scores from Refinitiv.https : / / www . refinitiv . com / content / dam / marketing / en _ us / documents /

methodology/refinitiv-esg-scores-methodology.pdf. visited on 2021-10-26.

20

Refinitiv (2021b). The Refinitiv Business Classification. https://www.refinitiv.com/content/dam/marketing/en_us/documents/quick- reference- guides/trbc-

business-classification-quick-guide.pdf. visited on 2021-10-26.Shafer, Michael and Edward Szado (2020). “Environmental, social, and governance prac-

tices and perceived tail risk”. In: Accounting & Finance 60(4), pp. 4195–4224.UNPRI (2021). A PRACTICAL GUIDE TO ESG INTEGRATION FOR EQUITY IN-

VESTING. https://www.unpri.org/download?ac=10. visited on 2021-11-22.Verheyden, Tim, Robert G. Eccles, and Andreas Feiner (2016). “ESG for All? The Im-

pact of ESG Screening on Return, Risk, and Diversification”. In: Journal of AppliedCorporate Finance 28(2), pp. 47–55. doi: https://doi.org/10.1111/jacf.12174.

Zhang, Jingyan, Jan De Spiegeleer, and Wim Schoutens (2021). “Implied Tail Risk andESG Ratings”. In: Mathematics 9(14), p. 1611. doi: 10.3390/math9141611.

21