# Determining the Difference in Predictive Capabilities of ESG Raw Scores
versus ESG Aggregated Scores on Annual Company Stock Returns And Volatility

Zhi Chen, Zachary Feinstein, Ionut Florescu, Papa Momar Ndiaye
School of Business, Stevens Institute of Technology
Hoboken, NJ, United States
{zchen100, zfeinste, ifloresc<EMAIL_ADDRESS>
###### Abstract

Investors are increasingly incorporating Environmental, Social, and Governance
(ESG) ratings into their investment strategies to evaluate and manage
potential risks and sustainability of companies. ESG ratings typically follow
a hierarchical structure, where raw data points are progressively aggregated,
leading to individual E, S, G scores and ultimately aggregating in a broad,
consolidated ESG score. While many studies have investigated the relationship
between stock performance and individual or overall ESG scores, few have used
raw ESG data into their analyses. Therefore, this paper aims to explore the
difference in predictive capabilities of ESG raw scores versus aggregated
scores on annual company stock returns and volatility. Our findings reveal a
trend where the predictive power is strongest at the raw data level, and it
gradually weakens through successive stages of aggregation, with the overall
scores exhibiting the weakest predictive capability. This result highlights
the effectiveness of raw ESG data in capturing the complex dynamics between
ESG factors and financial performance, making it the superior choice in
further study.

_K_ eywords ESG investing $\cdot$ Corporate social performance $\cdot$ ESG raw
variables $\cdot$ sustainable finance

##  1 Introduction

Non-financial performance, especially Corporate Social Performance (CSP), has
increasingly gained attention and importance among investors and firms. The
corporate social performance of companies is often characterized through
environmental, social, and governance (ESG) factors. Investors are
incorporating ESG factors, alongside traditional financial metrics into the
investment decision-making process. This integration is driven by the belief
that ESG information is crucial in identifying companies that are potentially
at risk of costly events linked to ESG issues, such as environmental damages
or lawsuits stemming from corporate misconduct or fraud. These types of risks,
which are not typically captured in traditional financial reports, can
significantly impact a company’s long-term financial stability and reputation.
Hence, by considering ESG factors, investors aim to gain a more comprehensive
understanding of a company’s overall risk profile and sustainability.
Therefore, ESG investing aligns with the growing demand among investors to
achieve a dual objective: to realize financial returns while also effectively
managing risks that may arise from environmental, social, or governance
shortcomings.

A company’s ESG factors is often evaluated by the ESG ratings, which are
developed by independent rating agencies. These agencies collect and assess a
numbers of variables relating to a company’s ESG practices. Subsequently,
these variables are integrated into their distinct methodologies. The outcome
is typically presented as a single score or rating. This score or rating acts
as a concise summary of the company’s ESG performance, offering investors a
rapid and comparative perspective.

However, the way the ESG ratings are calculated, by aggregating numbers of raw
data into single number, may be detrimental to the prediction power of the ESG
related variables collected. One possible explanation could be the
introduction of noise during the aggregation process. This noise could stem
from issues related to data quality and availability, where overlapping or
incomplete data sets impact the accuracy of the final score. Another possible
explanation could be the loss of important details. In the process of
aggregation, specific and significant information about various ESG aspects
could be overlooked or diluted, leading to a less precise reflection of a
company’s true ESG performance.

Additionally, there exists a notable divergence in the ratings issued for the
same firm by different ESG rating providers. [1] observed that the average
pairwise correlation for the overall ESG ratings from the seven data provides
is 45%. This divergence contrasts sharply with the higher average correlations
observed between credit ratings from Moody’s and S&P. According to [2], the
correlation between these two credit ratings has reached 99%. Discrepancies
between ESG scores and the low correlation can be accounted by the lack of
clear consensus around what should be measured when putting together an ESG
rating [3].

Therefore, recognizing the potential limitations and issues associated with
the use of aggregated ESG ratings, the object of this paper is to examine the
underlying raw variables, which are utilized in calculating the aggregated
scores. We aim to assess and compare the predictive capabilities of these raw
variables versus the aggregated ESG scores. This comparison will focus on
determining which approach (raw variables or aggregated scores) offers a more
accurate and reliable prediction of company stock returns and volatility.
Further, we aim to identify which specific raw variables are most significant
in the prediction.

This chapter is organized as follows. In ESG-related Risk, we identified ESG-
related risks and their impact on financial performance. In ESG Rating, we
introduce how the ESG rating are developed. In Are ESG Ratings Relevant to
Company Returns?, Are ESG Ratings Relevant to Company Volatility?, we
summarize the literature that connect the ESG rating with return and
volatility. In ESG Raw Data Analysis and Factor Construction, we summarize how
the people use raw data to construct factor. Building on these literature
review, in Question to be Addressed, we propose our idea and the question to
be addressed.

###  1.1 ESG-related Risk

ESG-related risks can manifest in various ways. Climate change has begun to
significantly impact a large number of firms, leading to direct financial
losses [4]. Utility sector companies will be increasingly exposed to threats
stemming from hurricanes, rising sea levels, and other climate-related events.
For example, in January 2019, Pacific Gas & Electric (PG&E) declared
bankruptcy. It was due to the massive financial liabilities from wildfires in
California that were linked to the company’s maintenance of power lines.
Energy sector companies, according to Intergovernmental Panel on Climate
Change (IPCC), is also vulnerable to climate change [5]. For example,
temperature variability is likely to influence energy demand via impacts on
heating and cooling requirements, thereby rendering energy enterprises
susceptible to price volatility and supply disruptions [6].

ESG regulations, while aimed at promoting sustainability and responsible
practices, may concurrently pose various risks to companies [7]. Failure to
comply with ESG regulations can result in fines, penalties and legal
liabilities. On the other hand, implementing the necessary changes to comply
with new or existing ESG regulations can be costly. This may include
investments in new technologies, infrastructure, or personnel training to meet
environmental standards or improve governance structures. ESG regulations may
also extend to a company’s supply chain, requiring not only the company but
also its suppliers to adhere to certain standards. This can create challenges
in managing supply chain relationships.

A company’s reputation is a crucial intangible asset that can significantly
impact its performance [8]. Investors and shareholders may lose confidence in
a company with a bad reputation, which can affect the share price negatively
and hinder the ability to raise capital. Take a look at a scandal from German
auto manufacturer Volkswagen [9]. In 2015-09 the U.S.’s Environmental
Protection Agency (EPA) accused the Volkswagen violating the Clean Air Act.
The company engineered its vehicles to circumvent government emissions testing
protocols. This resulted in an immediate drop in share price followed by
lawsuits. The Volkswagen scandal is evidence of the need for greater corporate
transparency. The scandal also highlights the failure of traditional valuation
models, such as discounted cash flow, to capture the full range of risk
companies face today. It shows the potential benefits of assessing companies
with non-financial data that reflect ESG risk.

There are a series of ESG-related risk that can influence company’s
performance. This give us a hint that ESG encompass a wealth of information
that can significantly aid in mitigating risks, which solely examining
traditional financial statements may not achieve. This is because ESG criteria
delve into a company’s broader contextual operations, shedding light on its
environmental impact, social relationships, and governance structures.
Analyzing ESG factors provides a holistic understanding of a company’s long-
term sustainability which is vital for investment decision-making.

###  1.2 ESG Rating

In order to provide the transparency of a company’s policies and efforts
concerning sustainability, rating agencies issue ESG rating. There are
multiple data providers such as (1) ASSET4 by Thomson Reuters, (2) Kinder
Lydenberg Domini & Co. (KLD) by MSCI and Sustainability Asset Management Group
(SAM), (3) S&P Global Ratings, and Bloomberg.

Typically, an ESG rating is presented as a single number or letter, serving as
a concise indicator of a company’s overall ESG management and performance.
This singular rating is aggregated hierarchically using numerous raw
variables, following a pyramid-like structure. At the base of this pyramid are
the raw data points. These data points, encompassing a wide range of factors
from carbon emissions and labor practices to board diversity and corporate
ethics, are synthesized at each ascending level of the pyramid-like rating
system.

In the aggregation process of determining an ESG rating, some ESG raters apply
a percentile ranking methodology. This approach involves comparing a company’s
ESG performance against that of its peers. For example, if a company receives
an ESG score of 80, it indicates that its ESG performance surpasses that of
80% of its peers. According to ASSET4 Professional Guide [10], all scores are
normalized by using z-scoring and benchmarked against the complete universe of
4000 companies. As per the Bloomberg ESG score documentation, the overall ESG
score of a company is determined based on its percentile ranking. E, S score
are industry-specific and governance scores is country-specific.

The percentile ranking system in ESG evaluations offers valuable insights into
a company’s position relative to its peers. However, they do not directly
reveal the absolute performance or the specific ESG metrics achieved. For a
more comprehensive understanding of a company’s ESG profile, examining the
actual values, such as specific emissions levels, diversity ratios, or
governance scores, is crucial.

Having discussed the structure and methodology of the ESG ratings, we now
begin to consider the sources and nature of the underlying data points. These
data points can be sourced from a variety of documents. Some common sources of
raw data for ESG ratings are: company disclosures, government and regulatory
filings, survey and questionnaires, non-governmental organization (NGO)
reports, media and news. Among of these sources, corporate disclosures,
principally in the form of Corporate Social Responsibility (CSR) reports,
serve as the primary resource. CSR reports provide detailed information on a
company’s ESG practices and performance, such as environmental stewardship,
labor and community relations, governance structures, and ethical conduct.
Many companies publish CSR reports on an annual basis. The issuance of CSR
reports can be at any time during the year. The EU Non-Financial Reporting
Directive (NFRD) mandates certain large companies to disclose non-financial
and diversity information [11].

Several organizations guide the publication of CSR reports for companies. For
example, Global Reporting Initiative (GRI) provides a comprehensive framework
to enable company to understand and report on their impacts on the economy,
environment and people in a comparable and credible way, thereby increasing
transparency on their contribution to sustainable development [12].

Despite these rating agencies take the similar resource, the ratings assigned
to companies by different rating agencies differ noticeably. [13] investigate
the convergence of the environmental rating provided by KLD, ASSET4 and Global
Engagement Services (GES) for US companies from the MSCI World universe
(2003-2011). The study shows that the correlations between ratings are 25% on
average. [14] examine correlations between overall ESG data of ASSET4 and KLD
as well as other rating agencies. The results shows the correlations range
from 13% to 52%, which indicates low convergence among raters.

[15] compares different rating approaches using ESG overall scores and
individuals E, S, G scores. The results suggests an evident lack in the
convergence of ESG measurement. The E,S,G scores of the ASSET4 and Bloomberg
exhibit positive correlations between 0.47 and 0.60. The correlation of
overall ESG score between these two raters is 0.62. In summary, the ratings
approaches lead to distinct results.

The divergence primarily stems from not only the differing emphases on the
underlying data but also variations in how these raw variables are aggregated
[2]. This lack of uniformity among data providers suggests that relying solely
on these aggregated ratings might not be the most appropriate approach for
assessing a company’s ESG performance. Instead, a more reliable method would
be to directly analyze the raw data. This approach not only circumvents the
biases and methodological discrepancies inherent in aggregated ratings but
also provides a more detailed understanding of a company’s ESG profile.

###  1.3 Are ESG Ratings Relevant to Company Returns?

In the investment world, two elements that investors typically focus on are
return and volatility. Therefore, understanding how ESG ratings interact with
these elements is crucial for making informed investment decisions. In this
chapter and the next chapter, we are reviewing research that explores the
relationship between ESG ratings and both return and volatility. This
exploration aims to shed light on whether and how ESG ratings impact financial
performance and risk profiles.

[16] investigate the association between ESG ratings and stock return during
the COVID-19 crisis. They perform regression analysis on cumulative stock
return and cumulative abnormal stock return, respectively, using Refinitiv ESG
overall score as the independent variable, with additional control variables,
over the period from 3 February 2020 to 23 March 2020. While no significant
coefficients on ESG score were observed for a firm’s cumulative stock return,
positive and significant coefficients on ESG score were found when analyzing
cumulative abnormal stock return. The adjusted R-squared for these two
regressions are 0.07 and 0.08, respectively, which may indicate that the
relationship between return and ESG ratings is weak.

[17] instead of using rating directly and associate them with returns, they
use changes in ESG ratings as independent variable. The authors regress change
of stock return on the change of ESG overall indexes for Eurostoxx50
companies. The parameter estimate was found to be significant. The adjusted
R-squared is 0.01.

In this paper [18], the authors change the dependent variable for company
performance. The authors explore the correlation between enterprise’s earnings
per share and ESG rating for Chinese companies. The author found that the ESG
indices signal is positively related to the stock market. The findings
demonstrate that the enterprise’s ESG indices have a significantly positive
impact on its EPS. The R-Squared is around 0.02.

Previous literature all employs ESG overall ratings. [19] investigates each
ESG pillar individually, rather than considering them collectively as a single
aggregated ESG factor. The authors construct and incorporate three risk
factors based on E, S, G ratings into standard Fama-French 5-factors models.
The authors analyze if this addition improves the explanatory capabilities of
traditional asset pricing models. They found taking these factors into account
significantly enhances the explanatory power of standard asset pricing models.
All of the three factors are significantly related. The adjusted R-Squared
increase from 86.03 to 89.06 by adding three ESG factors.

In this paper [20] the author use different approach rather than linear
regression to explore the relationship between ESG rating and stock return.

The authors construct portfolios based on ESG ratings. They use ESG rating to
rank stocks. Then classified stocks into five quintiles (Q1 to Q5), where Q1
represents the companies with the lowest ESG rating and Q5 denotes those with
the highest ratings. The authors displayed the distribution of financial
variables across the five quintiles. The found that companies with higher ESG
ratings exhibited greater profitability and disbursed higher dividends in
comparison to companies with lower ESG ratings.

In summary, all of these paper with their empirical evidence suggests a weak
relationship between ESG ratings and stock return. Numerous studies have
demonstrated that the predictive power of utilizing ESG ratings is limited.

###  1.4 Are ESG Ratings Relevant to Company Volatility?

In the previous mentioned citation [16], the paper examine the relationship
between stock return and ESG rating. They also explore if firms with higher
corporate ESG ratings display lower stock volatility. They employ the same
independent variable and procedure, but this time they apply them with respect
to volatility. They found negative and statistically significant coefficient
on ESG score to volatility. The regression adjusted R-squared value is 0.18.
which is higher than that of return (0.08), this suggests a better explanation
of volatility.

[21] examine the influence of ESG performance on a company’s stock price
volatility by regressing volatility on the ESG ratings and several control
variables. They found that coefficient of ESG ratings is significantly
negatively associated with volatility, which conclude excellent ESG
performance of listed companies contributes to the stability of the company’s
stock price. The R-squared is 0.23.

[22] analyzes the connection between ESG ratings and tail risks by regressing
VaR on ESG overall ratings. The findings suggest that better ESG ratings are
associated with lower downside risk. The coefficient of ESG scores is
significant. The R-Squared is 0.378. This indicates that the relationship
between stock volatility and ESG is much stronger than return.

[23] present empirical evidence demonstrating the correlation between ESG
factors and risk-adjusted performance for stock indices. The paper compared
volatility of two indices. One index is the Dow Jones Sustainability Index
(DJSI) which pinpoint companies exhibiting strong ESG performance. Another
index comprise companies not listed on the DJSI, which is set as a reference
group. They found the ESG index portfolio showed lower volatility than
reference in the same industry, on average by 28.67% less. In the meantime,
the paper further showed that in most of industries, the ESG companies have
higher equity return than non-ESG companies, on average by 6.12%. We can find
out the distinction in volatility between portfolios with favorable ESG
ratings and those with unfavorable ESG ratings is found to be more significant
than the difference in returns between the two categories. This observations
indicate that ESG is more pronounced in risk management.

In the precious mentioned citation [20], the author show how well high ESG-
rated companies manage their operational risks, by comparing volatility for
each of five quintiles. The findings demonstrate a tendency for volatility to
diminish with the ascent of ESG rating of quantiles.

In summary, the predictive capacity of ESG metrics in relation to stock
volatility appears to exhibit a stronger relationship as compared to its
efficacy in forecasting stock returns. Various studies have highlighted that
portfolios with higher ESG ratings tend to exhibit lower volatility,
suggesting a potential risk-mitigating effect inherent in robust ESG
practices. Conversely, the relationship between ESG ratings and stock returns
is often found to be more tenuous, with the predictive power of ESG in this
domain being relatively weaker.

From analyzing the previous literature, we delved into the relationship
between stock returns and ESG metrics, and discerned a relatively weak
correlation. Furthermore, upon exploring the connection between stock
volatility and ESG metrics, a more robust relationship was observed.

Many researchers have analyzed the relationship between the ESG profile of
companies and their financial performance and risk characteristics.

###  1.5 ESG Raw Data Analysis and Factor Construction

It is noteworthy to mention that the aforementioned analysis relied on
aggregated data. In paper [24], the authors identified 285 studies that use
ASSET4 and find that the four pillars are more frequently used than the
overall, categories, and data points to capture corporate social performance.
There are 148 of the 285 studies use pillars.

The process of condensing raw data into a singular aggregated figure may
potentially incorporate noise, thereby possibly decrease the predictive
accuracy of the ESG metrics. The noise may arise from the fact that these
ratings are computed using a percentile-based methodology. The percentile-
based methodology, often used in calculating ESG ratings, can potentially lead
to inconsistencies in the ratings for several reasons:

  * •

Relative Performance
The percentile-based methodology measures a company’s performance relative to
a peer group rather than against fixed criteria. Therefore, a company’s ESG
rating can change not just because of its own performance, but also due to
changes in the performance of its peers.

  * •

Dynamic Peer Groups
The composition of peer groups may change over time, which can lead to
inconsistencies in ESG ratings. A company might fall into a different
percentile merely because of changes in the peer group rather than any change
in its own ESG performance.

  * •

Lack of Absolute Benchmarks
The absence of absolute benchmarks may result in companies with weaker
sustainability performances receiving favorable ratings merely due to the
comparative weakness of their peer group.

This observation propels us towards a deeper investigation, hinting at the
prospect of establishing a more discerning linkage between raw ESG data and
stock return/volatility. In currently paper we are looking at, there are few
papers employing raw ESG data for analysis.

[25] explore whether incorporating ESG information into portfolio construction
brings benefits.

Specifically, the authors categorized companies into ’good’ and ’bad’ ESG
groups, using both all ESG raw data and ESG material data derived from the
SASB material map. Financial materiality refers to the relevance of ESG
factors, both positive or negative, on a company’s financial performance. The
sustainability-related risks and opportunities that are most likely to affect
cash flows, stock return and volatility, and cost of capital vary by industry.

They then compare the performance of these two portfolios and find out the
difference between good and bad for using raw data is falling into expectation
comparing with using all data.

[26] aim to link carbon raw data to financial valuation. The authors construct
three carbon factors based on carbon emission and intensity. The authors want
to capture the actual value of carbon emission generated by companies and how
well a company performs, in terms of market capitalization or sales, relative
to the carbon emissions it produces.

They then add these factors into Fama-French 3-factors model. The regression
analysis shows that all models have high explanatory power. Further, adding
the carbon factors will improve the predictive ability slightly.

###  1.6 Question to be Addressed

Stock market investors prioritize identifying leading indicators that could
provide insights into the future direction of stock returns and volatility.
Beyond solely relying on financial indicators, incorporating ESG factors can
serve as an alternative and potentially robust method to measure and evaluate
risk. Therefore, we aim to explore the correlation between ESG indicators and
return/volatility.

Numerous studies have employed aggregated ESG ratings to predict returns or
volatility while very few papers tried to connect the ESG raw data with
company performance. Further, the results have been inconclusive. Given this
motivation we seek to explore the following research questions (RQs):

  * •

(RQ1) Is ESG raw data preferable and better proxy of ESG performance for a
company than ESG aggregating data?

  * •

(RQ2) Does ESG data hold greater relevance for predicting volatility compared
to return?

  * •

(RQ3) Is there a specific subset of raw data that is particularly well-suited
for each distinct predictive goal?

##  2 Data

###  2.1 ASSET4 Data and Its Structure

The ASSET4 data initiated in 2002 and now provided ESG scores of over 4300
companies worldwide. The coverage universe comprises listed companies ranging
from the S&P 500, Russell 1000, MSCI Europe, FTSE 250, ASX 300 to the MSCI
World Index and the 250 MSCI Emerging Markets companies [15].

The ASSET4 data has received endorsements from several reputable
organizations, reflecting its reliability and significance in the field.
ASSET4 is signatory of the UN’s Principles for Responsible Investment and a
contributing member to organizations and initiatives like: UNEP-FI, Eurosif,
UKSIF, USSIF, and the Veres Coalition [27].

ASSET4 uses a hierarchical, four-level rating system for evaluating each
company’s ESG performance. See the figure 1. On the left-hand side, it
presents an overview of the structure, labeling each layer with its respective
name. On the right-hand side of the diagram it displayed the specific items
contained within each of these layers.

Figure 1: Data Structure of ASSET4

  * •

Overall ESG Score (Fifth Level)
This is the apex of the pyramid, where a composite ESG score is calculated for
each company, providing a single number (between 0 and 100). A high (low)
score indicates a strong (poor) company performance.

The overall score is based on scores in four key pillars: Environmental,
Social, Corporate Governance, and Economic Performance.

  * •

4 Pillars (Fourth Level)
Each pillar score is calculated from its own several category scores. For
example, environmental pillar has three category: resource reduction, emission
reduction, product innovation. Therefore environmental pillar scores is based
on these three category scores.

  * •

18 Category Scores (Third Level)
Each category is comprehensively defined by its corresponding indicators and
data points. For instance, the ’Resource Reduction’ category is computed
through approximately 60 data points. These data points collectively offer a
multifaceted view and capture various aspects of a company’s efforts and
performance in resource reduction. Importantly, these data points are
exclusive to their respective categories, ensuring that each data point is
unique to a single category and there is no overlap. The relationship is
depicted in the figure 1 through a black arrow line.

  * •

Key Performance Indicator (KPI) (Second Level)
These indicators are computed from combination of data points. The ASSET4
define the rules of how to determine the KPI using a group of data points. For
example, to determine an indicator ’resource reduction/Monitoring’, it need to
check 4 data points. The rule for this indicator might be formulated as
follows: if data point 1 and data point 5 both equal ’yes’, or if data point 3
equals ’yes’, or data point 4 equals ’no’, then the indicator is assigned a
’yes’. Otherwise, it is assigned a ’no’.

  * •

Raw Data Points (First Level)
At the base of the ASSET4 data structure, there are around 700 data points.
One of the reasons we use this dataset is they supply raw ESG data that could
be used by us to devise our own measurement.

It is important to note that the ASSET4’s methodology and data structure
partially changed in 2017 [28]. Before 2017, ASSET4 comprised four pillars:
(1) environmental pillar, (2) social pillar, (3) corporate governance pillar
and (4) economic pillar. In 2017, the economic pillar was removed, leaving
three pillars. To maintain consistency in data structure and ensure
comparability of data over time, we have chosen to focus solely on the three
remaining pillars in our analysis.

Our sample consists of stocks that are constituents of S&P500 and Russell
2000. The S&P500 includes 500 of the largest U.S. companies. The Russell 2000,
on the other hand, focuses on 2000 smaller business. Together, these indexes
provide a comprehensive view of the U.S. stock market, representing both
large-cap and small-cap segments.

Among this stock universe, we specifically focus on the energy-related
companies. The reasons are as follows:

  * •

ESG sensitivity
The energy sector has a strong environmental impact, primarily due to
greenhouse gas emissions, resource extraction processes, and waste management.
Further, as the world moves towards sustainable energy solutions to combat
climate change, energy companies are at the forefront of this transition.
Thus, ESG scores are more relevant to energy sector.

  * •

Regulatory and policy scrutiny
Energy companies often face stringent regulations due to their environmental
impact. Focusing on them can help understand how these companies are managing
regulatory risks and complying with evolving environmental laws.

We determined the energy-related companies based on an industry
classfification system operated by Refinitiv: The Refinitiv Business
Classification (TRBC). According to TRBC, there are 51 energy-related
companies in the combined stock universe comprised by S&P500 and Russell 2000.

For each company in energy sector, we collect different levels of data: ESG
overall score, pillar score, category score, raw data point with data ranging
from 2002-2020.

##  3 Determining the Difference in Predictive Capabilities of ESG Raw Scores
versus ESG Aggregated Scores on Annual Company Stock Returns and Volatility

###  3.1 Statement of problem

Often investors use the ASSET4 dataset by primarily relying on aggregated
scores, such as overall scores, pillar scores, and category scores. This
aligns with the findings and discussions presented in our literature review.
Our review of the existing literature reveals a relatively scant usage of
ESG’s raw data. As previously discussed, aggregating these data into a single
numerical score can potentially lead to loss of detailed information and the
introduction of noise, which may obscure crucial insights. In light of this,
our research aims to determine the difference in predictive capabilities of
ESG raw scores versus ESG aggregated scores on annual company stock returns
and volatility. We expect to see that using the raw data, as opposed to
aggregated scores, could have a more significant impact on predicting
financial returns and volatility.

###  3.2 Which ESG Raw Variables are Impacting Return and Volatility

When examining the usage of ESG raw data as independent variables in
statistical analysis, it’s important to note that the available pool of
potential explanatory variables contains close to 500 variables. However, the
number of available observations is approximately 400 in the energy sector.
This discrepancy between the number of variables and observations means that
we cannot directly use the entirety of the ESG raw data in our regression
analyses.

Another potential challenge needs to be consider is the raw data are
correlated within each category, due to the inherent characteristics of the
ASSET4 dataset. For example, consider resource reduction category, which is
aggregated from around 50 raw data point. These 50 raw data points measured
the same category are therefore correlated to each other. When
multicollinearity occurs, it can significantly distort the results and weaken
the model’s reliability.

Our solution to handle the above problems is stepwise regression. The stepwise
regression systematically adds or removes variables in the regression model
based on specific statistical criteria, ultimately selecting an optimal subset
of variables that most effectively explains the response variable. Therefore,
this method can also help us circumvent the problems of large number of
variables and multicollinearity.

By comparison, Principal Component Analysis (PCA) is another tool used for
dimensionality reduction. However, when PCA projects the raw data into a new
dimensional space, it transforms the original variables into a new components.
This transformation, while useful for reducing complexity, means that it is
difficult to directly trace back to the raw data. In our case, we would like
to identify which raw variables are essential in predicting the return and
volatility. This requires a meticulous examination of the individual data
points, as opposed to relying on aggregated or transformed data.

We start from running a stepwise regression on raw data within each category
to predict return and volatility. The results are in the table 1. The green
highlights indicate the top five adjusted R-squared values for predicting
annual return, while the blue highlights represent the top five for
forecasting annual volatility. For predicting annual return, the most relevant
subset of raw data comes from the following categories: Shareholder Rights
(0.1383), Community (0.1515), Product Responsibility (0.0984), Diversity and
Opportunity (0.0837) and Compensation Policy (0.0785). On the other hand, the
categories most significant for predicting annual volatility include: Health
and Safety (0.4520), Community (0.4169), Product Responsibility (0.2916),
Shareholder Rights (0.2584), Training and Development (0.1808). This analysis
reveals a difference in performance between the prediction of annual
volatility and annual return. The models for predicting volatility exhibit
considerably better performance. This suggests that the variables are more
closely related to volatility than those related to annual return.

Table 1: Stepwise Regression on ESG raw data

Pillar Category Where Raw Data From Target adj.r.squared f.statistics p.value
E Resource Reduction [rgb] .906, .902, .902Annual Volatility [rgb] .906, .902,
.9020.1011 [rgb] .906, .902, .90214.0960 [rgb] .906, .902, .9020.0000 Annual
Return 0.0552 5.5370 0.0000 Emission reduction [rgb] .906, .902, .902Annual
Volatility [rgb] .906, .902, .9020.0723 [rgb] .906, .902, .9027.0505 [rgb]
.906, .902, .9020.0000 Annual Return 0.0781 5.9313 0.0000 Product
Responsibility [rgb] .906, .902, .902Annual Volatility [rgb] .906, .902,
.9020.2917 [rgb] .906, .902, .90216.9890 [rgb] .906, .902, .9020.0000 Annual
Return 0.0984 6.6512 0.0000 S Community [rgb] .906, .902, .902Annual
Volatility [rgb] .906, .902, .9020.4169 [rgb] .906, .902, .90214.8846 [rgb]
.906, .902, .9020.0000 Annual Return 0.1515 7.9324 0.0000 Employment Quality
[rgb] .906, .902, .902Annual Volatility [rgb] .906, .902, .9020.1699 [rgb]
.906, .902, .90220.0805 [rgb] .906, .902, .9020.0000 Annual Return 0.0291
3.7961 0.0022 Health and Safety [rgb] .906, .902, .902Annual Volatility [rgb]
.906, .902, .9020.4520 [rgb] .906, .902, .90222.3571 [rgb] .906, .902,
.9020.0000 Annual Return 0.0698 6.8249 0.0000 Training and Development [rgb]
.906, .902, .902Annual Volatility [rgb] .906, .902, .9020.1809 [rgb] .906,
.902, .90213.8632 [rgb] .906, .902, .9020.0000 Annual Return 0.0655 9.1631
0.0000 Diversity and Opportunity [rgb] .906, .902, .902Annual Volatility [rgb]
.906, .902, .9020.0631 [rgb] .906, .902, .9028.8487 [rgb] .906, .902,
.9020.0000 Annual Return 0.0837 8.0960 0.0000 Human Right [rgb] .906, .902,
.902Annual Volatility [rgb] .906, .902, .9020.0138 [rgb] .906, .902,
.9027.5352 [rgb] .906, .902, .9020.0063 Annual Return 0.0503 5.9337 0.0000
Product Innovation [rgb] .906, .902, .902Annual Volatility [rgb] .906, .902,
.9020.0100 [rgb] .906, .902, .9025.7295 [rgb] .906, .902, .9020.0171 Annual
Return 0.0089 3.0921 0.0463 G Compensation Policy [rgb] .906, .902, .902Annual
Volatility [rgb] .906, .902, .9020.0640 [rgb] .906, .902, .9028.9647 [rgb]
.906, .902, .9020.0000 Annual Return 0.0785 8.9391 0.0000 Board Function [rgb]
.906, .902, .902Annual Volatility [rgb] .906, .902, .9020.0659 [rgb] .906,
.902, .9025.1091 [rgb] .906, .902, .9020.0000 Annual Return 0.0757 10.5387
0.0000 Board Structure [rgb] .906, .902, .902Annual Volatility [rgb] .906,
.902, .9020.0936 [rgb] .906, .902, .9027.0129 [rgb] .906, .902, .9020.0000
Annual Return 0.0682 9.5222 0.0000 Shareholder Rights [rgb] .906, .902,
.902Annual Volatility [rgb] .906, .902, .9020.2585 [rgb] .906, .902,
.90210.5544 [rgb] .906, .902, .9020.0000 Annual Return 0.1384 8.4834 0.0000
Vision and Strategy [rgb] .906, .902, .902Annual Volatility [rgb] .906, .902,
.9020.0432 [rgb] .906, .902, .9025.2034 [rgb] .906, .902, .9020.0001 Annual
Return 0.0490 5.7985 0.0000

###  3.3 What are the Difference in Predictive Capabilities of ESG Raw Scores
versus ESG Aggregated Scores on Annual Company Stock Returns and Volatility

####  3.3.1 Preliminary Comparison

From the previous analysis, we successfully identified the top five
categories, whose subsets of raw data that are most effective in predicting
return. Likewise, we also determined the top five categories, whose subsets of
raw data that best predict the volatility. However, we only use raw data from
one category in each prediction, whether to return or volatility. This means
that we haven’t fully used the information available across the entire
spectrum of raw data. We are curious that could the predictive power be
enhanced by incorporating variables from multiple categories? We aim to
capture a more holistic view of the factors influencing return and volatility.

Therefore, we plan to group raw data from the combined top five categories
with subset that demonstrate the highest performance in predicting return, and
use this group of raw data to predict return. likewise, we group raw data from
the combined top five categories with subset that best predict the volatility,
and use the group of raw data to predict volatility.

Due to the potential correlation among data points from different categories,
we face the risk of multicollinearity again. To mitigate this issue, we plan
to use stepwise regression again. In this way, we aim to determine the
predicted ability of using ESG raw data.

Next, we are going to compare the prediction ability using ESG raw data versus
using ESG aggregated data. Specifically, ESG aggregated data include four
tiers: the indicator level, the category level, encompassing 15 different
categories; the pillar level, which consolidates these categories into 3
broader pillars; and the overall level, representing a singular, comprehensive
ESG score.

In summary, the experiments for comparison are as follows:

  1. 1.

Run stepwise regression on ESG raw data from some combined categories to
predict return and volatility.

  2. 2.

Run stepwise regression on ESG indicator data
In the indicator level, we examined the correlation among variables and
discovered that some of them are highly correlated. This significant
correlation could potentially lead to issues of multicollinearity. Therefore,
to mitigate this, we have decided to use stepwise regression for data in the
indicator level.

  3. 3.

Run linear regression to investigate the relationship between return and
volatility across 15 category scores.

  4. 4.

Run linear regression to investigate the relationship between return and
volatility across 3 pillar scores.

  5. 5.

Run linear regression to investigate the relationship between return and
volatility across 1 ESG overall score.

In this analysis, we are inputting different layers of ESG data, from raw data
to more aggregated scores. We aim to explore how this transition will impact
the prediction ability, providing a clearer understanding at each level of
data aggregation.

The comparing results of ESG raw data scores and aggregated scores are
displayed in the table 2. To confirm the validity of our results, we examined
the Variance Inflation Factors (VIF) of the coefficients and found that all
VIF values are below 10, with the majority being under 5. This indicates a low
level of multicollinearity among the predictors in regression models.

Table 2: Compare Difference in predictive capbilities of ESG raw scores versus
aggregated scores

Independent Variable Response Variable adj.r.squared f.statistics p.value Raw
Data [rgb] .906, .902, .902Annual Volatility [rgb] .906, .902, .9020.7313
[rgb] .906, .902, .90230.4900 [rgb] .906, .902, .9020.0000 Annual Return
0.2412 7.1720 0.0000 Indicator [rgb] .906, .902, .902Annual Volatility [rgb]
.906, .902, .9020.3406 [rgb] .906, .902, .90214.2200 [rgb] .906, .902,
.9020.0000 Annual Return 0.0900 6.0590 0.0000 15 Categories [rgb] .906, .902,
.902Annual Volatility [rgb] .906, .902, .9020.2053 [rgb] .906, .902,
.9029.0240 [rgb] .906, .902, .9020.0000 Annual Return 0.0009 1.0280 0.4243 3
Pillars [rgb] .906, .902, .902Annual Volatility [rgb] .906, .902, .9020.0599
[rgb] .906, .902, .90210.3200 [rgb] .906, .902, .9020.0000 Annual Return
0.0000 0.9954 0.3948 Single Overall [rgb] .906, .902, .902Annual Volatility
[rgb] .906, .902, .9020.0227 [rgb] .906, .902, .90211.2000 [rgb] .906, .902,
.9020.0009 Annual Return 0.0010 1.4240 0.2334

Looking at the raw data level, we use the group of raw data from the combined
top five categories with subset that can best predict the volatility to
predict the volatility. The adjusted R-squared has reached 0.7313. Comparing
with using the raw data from only one category, the highest adjusted R-squared
achieved is 0.4520 (raw data from health and safety category). For predicting
returns, the adjusted R-squared using the grouped raw data is 0.2412. In
comparison, the highest adjusted R-squared achieved with raw data from a
single category is 0.1515 (raw data from community category).

From this results, we found that predictive power of using grouped raw data
are improved significantly. This significant improvement underscores the value
of combining data from multiple categories, as opposed to relying on a
singular category.

Besides, the improvement in predictive power due to the inclusion of raw data
from various categories suggests that the variables across different
categories contribute additional, distinct information. This means that these
variables are not merely duplicates with different names measuring similar
aspects. Instead, they offer unique insights and capture different dimensions
of the data, indicating that the variables across various categories have
their own individual characteristics and impacts.

When comparing the predicted performance between raw data and different levels
of aggregated data, a clear trend emerges with regard to data aggregation
levels and predictive power. Using raw ESG data yields the best results, as
indicated by the highest adjusted R-squared values. This suggests a strong
explanatory power of raw data on stock’s volatility and return. However, as
the ESG data becomes more aggregated, the predictive ability starts to get
weak. When the analysis shifts to using indicators scores, which represent a
first level of aggregation, the adjusted R-squared value drop around by half.
There’s a noticeable drop of adjusted R-squared in prediction for return.

This trend intensifies with category data, which is an even more condensed
form of ESG information, leading to further diminished forecasting strength.
While the adjusted R-squared value for predicting volatility is 0.2053, the
adjusted R-squared value for predicting is almost zero. What is more, the
p-value of f-statistics is not significant, meaning that all the category
scores have no predictive capability for return.

The pattern reaches its peak when using pillar scores and overall ESG scores,
the most aggregated forms of data. Here, the predictive ability is the
weakest.

This trend suggests that: the more specific and detailed the ESG data, the
more effective it is in predicting the outcome, highlighting the importance of
granularity in ESG analysis. As ESG data becomes more aggregated, its power to
predict financial market trends significantly decreases.

####  3.3.2 Validate Model

In the previous analysis, we develop regression models and compare the
performance for each level of ESG data. Next, we aim to validate whether the
model is appropriate for the data. Therefore, we plan to examine the residuals
of models.

The residual is the difference between the observed value and the fitted
value, known as observed error. For linear regression model, the error terms
are assumed to be independent normal random variables, with mean 0 and
constant variance $\sigma^{2}$. If the model is appropriate for the data, the
observed residuals should reflect the properties. Therefore, we are going to
check for assumptions such as homoscedasticity (constant variance) and
normality. This step is crucial in confirming the reliability of our models
and ensuring that our interpretations and conclusions drawn from the ESG data
are well-founded and robust.

We used some diagnostic plots of residuals to provide information.

  * •

plot of residuals against predicted values

  * •

normal probability plot of residuals

Firstly, we plot the residuals against the predicted value. This graphical
representation allows us to visually inspect the distribution and pattern of
residuals, which are the differences between observed and predicted values.
Ideally, in a well-fitting model, these residuals should display no
discernible pattern; they should be randomly scattered around the horizontal
axis (zero line), indicating a uniform variance (homoscedasticity). If the
residuals display a systematic pattern, such as a curve, or a trend, it
suggests issues like non-linearity, heteroscedasticity, or model
misspecification. See the figure 2.

Figure 2: Plot of residuals against the predicted values

The plots on the left-hand side is for the volatility, while the plots on the
right-hand side is for the return. Each row represents an example using a
different level of data. From top to bottom, the used data are as follows: raw
data, category scores, pillar scores, and overall scores.

The plots for volatility shows a downward trend. This is because the actual
volatility value are always positive. However, in contrast, our model predicts
negative values for volatility.

The residuals for the return have no clear pattern, being uniformly
distributed. We may conclude that it is homoscedasticity.

In the residual plots for both volatility and return, the absence of a bowl-
shaped pattern suggests that the relationship between the response variables
and the data is likely linear. Thus, a linear model is a suitable choice for
this data.

Secondly, we plot Q-Q plot of residuals.

One of the key assumptions in linear regression is that the residuals are
normally distributed. This assumption is crucial for the validity of various
statistical tests, including hypothesis tests on the regression coefficients
and the construction of confidence intervals. Especially in our case, we have
small sample size. Non-normal residuals can significantly affect the validity
of statistical inferences. See the figure 3.

Figure 3: Q-Q plots of residuals

The Q-Q plot does not align with the line suggest that the residuals does not
follow a normal distribution. Particularly for volatility, the deviation in
the Q-Q plot is more obvious. Specifically, it was observed that a majority of
the data points closely aligned with the theoretical line. However, a notable
deviation was detected on the far right-hand side of the plot. This deviation
signifies the presence of extreme large values in the residuals.

In summary, after careful examination of the residual plots, it became evident
that the residuals do not follow a normal distribution. This observation is
crucial, as the assumption of normally distributed residuals is fundamental to
many statistical models, especially in linear regression analysis. The
deviation from normality in the residuals can impact the reliability and
validity of the model’s inferences. To address this issue, transforming the
data becomes a necessary step.

####  3.3.3 Data Transformation

We are going to fix the violation of non-normality of residuals. The Box-Cox
transformation is an effective statistical technique for addressing non-
normality in data. Specifically, it takes the following form:

$y(\lambda)=\begin{cases}\frac{y^{\lambda}-1}{\lambda}&\text{if }\lambda\neq
0\\\ \log(y)&\text{if }\lambda=0\end{cases}$ (1)

The parameter $\lambda$ in the Box-Cox transformation is a variable that needs
to be determined. The box-cox transformation will prepare a range of values
for $\lambda$ and then identify the optimal exponent for correcting skewness
and non-normality in the data.

The box-cox results indicate the best value for $\lambda$ is -0.0202. We round
it to 0, which means taking the log transformation. The decision to apply a
logarithmic transformation to our data aligns perfectly with the findings from
our residual analysis. Firstly, we observed that some predicted values were
negative, which is inconsistent with the actual nature of volatility that
cannot be negative. Log transformation is particularly useful in this scenario
as it inherently accommodates and adjusts for negative values in the
predictions. Secondly, the analysis of the Q-Q plot revealed that while most
residuals closely follow the theoretical line, there are notable outliers on
the right-hand side. These outliers indicate the presence of unusually large
residuals. By taking a logarithmic transformation, we can effectively mitigate
these large deviations. Log transformation inherently compresses large values
more than smaller ones, thereby smoothing out the jumps in the data and
bringing the residuals closer to what is expected under normal distribution.
This approach not only addresses the issue of negative predictions but also
helps in managing the skewness and reducing the impact of outliers, leading to
a more stable and reliable model.

After applying the log transformation on the independent variable, we examine
the residuals again. The plots of residuals are displayed in figure 4. These
residual plots revealed a marked improvement. The distribution of residuals
now more closely approximates a normal distribution compared to the pre-
transformation state.

Figure 4: Plots of residuals after log transformation

####  3.3.4 Conclusive Comparison

From the previous analysis, we found that the logarithmic transformation of
volatility aligns more appropriately with the linear model’s assumptions.
Consequently, we plan to revise our approach in the subsequent analysis. We
will replace the original volatility with log volatility and then re-conduct
the prior experiments. The results are displayed in the table 3.

Table 3: Compare Difference in predictive capabilities of ESG raw scores
versus aggregated scores (log volatility)

Independent Variable Response Variable adj.r.squared f.statistics p.value Raw
Data [rgb] .906, .902, .902Log Annual Volatility [rgb] .906, .902, .9020.6504
[rgb] .906, .902, .90223.2300 [rgb] .906, .902, .9020.0000 Annual Return
0.2412 7.1720 0.0000 Indicator [rgb] .906, .902, .902Log Annual Volatility
[rgb] .906, .902, .9020.3166 [rgb] .906, .902, .90212.8600 [rgb] .906, .902,
.9020.0000 Annual Return 0.0900 6.0590 0.0000 15 Categories [rgb] .906, .902,
.902Log Annual Volatility [rgb] .906, .902, .9020.1086 [rgb] .906, .902,
.9024.7870 [rgb] .906, .902, .9020.0000 Annual Return 0.0162 4.8412 0.0083 3
Pillars [rgb] .906, .902, .902Log Annual Volatility [rgb] .906, .902,
.9020.0278 [rgb] .906, .902, .9025.1860 [rgb] .906, .902, .9020.0016 Annual
Return 0.0030 2.3070 0.1295 Single Overall [rgb] .906, .902, .902Log Annual
Volatility [rgb] .906, .902, .9020.0014 [rgb] .906, .902, .9021.6220 [rgb]
.906, .902, .9020.2035 Annual Return 0.0010 1.4240 0.2334

After adopting log volatility as the independent variable in our model, a
decreasing shift was observed in the adjusted R-squared values across all
levels of data. Despite this reduction in the adjusted R-squared, the
fundamental trend observed previously remained intact. The model using raw
data continued to exhibit the highest predictive power. As the data became
more aggregated, there was a consistent decline in this predictive power.

In our previous analysis, we use entire dataset for modeling. To ensure the
model can be generalized to new, unseen data, we performed the 10-fold cross
validation. This process involves dividing the data into multiple subsets or
’folds’, using some for training the model and others for testing it. The
results are displayed in the table 4 and table 5.

Table 4: MSE for volatility on in sample and out sample data | In-sample MSE | Out-of-sample MSE
---|---|---
|  [rgb] .906, .902, .902Mean | SD |  [rgb] .906, .902, .902Mean | SD
Raw Data |  [rgb] .906, .902, .9020.3877 | 0.0276 |  [rgb] .906, .902, .9021.0478 | 0.8054
Indicator |  [rgb] .906, .902, .9020.9702 | 0.0458 |  [rgb] .906, .902, .9021.1626 | 0.3841
Category |  [rgb] .906, .902, .9021.2090 | 0.0259 |  [rgb] .906, .902, .9021.2863 | 0.2443
Pillar |  [rgb] .906, .902, .9021.4269 | 0.0193 |  [rgb] .906, .902, .9021.4477 | 0.1743
Overall |  [rgb] .906, .902, .9021.4730 | 0.0216 |  [rgb] .906, .902, .9021.4813 | 0.1938
Mean of Dependent Variable |  [rgb] .906, .902, .9021.4786 | 0.0230 |  [rgb] .906, .902, .9021.4567 | 0.2129
Table 5: MSE for return on in sample and out sample data | In-sample MSE | Out-of-sample MSE
---|---|---
|  [rgb] .906, .902, .902Mean | SD |  [rgb] .906, .902, .902Mean | SD
Raw Data |  [rgb] .906, .902, .9020.1458 | 0.0071 |  [rgb] .906, .902, .9020.2266 | 0.0573
Indicator |  [rgb] .906, .902, .9020.1484 | 0.0082 |  [rgb] .906, .902, .9020.2232 | 0.0763
Category |  [rgb] .906, .902, .9020.2032 | 0.0082 |  [rgb] .906, .902, .9020.2220 | 0.0776
Pillar |  [rgb] .906, .902, .9020.2146 | 0.0052 |  [rgb] .906, .902, .9020.2179 | 0.0470
Overall |  [rgb] .906, .902, .9020.2154 | 0.0051 |  [rgb] .906, .902, .9020.2174 | 0.0462
Mean of Dependent Variable |  [rgb] .906, .902, .9020.2162 | 0.0054 |  [rgb] .906, .902, .9020.2138 | 0.0479

Consider the MSE analysis for volatility 4. The cross-validation results
demonstrate a pattern where the out-of-sample mean squared error (MSE)
decreases as the data become more aggregated, from raw data to overall scores.
This trend is consistent with our observations regarding adjusted R-squared.
This again suggests that with each level of aggregation—from raw data to
indicators, categories, and then to pillars and overall scores—the predictive
power for volatility diminishes.

Compare the in-sample MSE with out-sample MSE regarding to volatility. Take
the raw data level as an example, the in-sample MSE is 0.3877 while the out-
sample MSE is 1.0478. This substantial discrepancy indicates concerns about
overfitting, suggesting that while the model may fit the training data well,
it is less adept at generalizing to unseen data.

Consider the MSE analysis for return 5. The MSE for out-sample data is
fluctuated around 0.22. Unlike the results for predicting volatility, the MSE
for predicting returns does not consistently increase with the level of data
aggregation. This is not consistent with the trend observed in the adjusted
R-squared for return. More importantly, the MSE when using ESG data as a
predictor was even higher than when simply using the mean of the return as a
baseline predictor. This outcome implies that, in the context of predicting
returns, ESG data may not be as effective as anticipated. ESG data provide
limited additional useful information.

##  4 Conclusion

After conducting a thorough comparison of predictive performance for
volatility and return using various levels of ESG data—ranging from raw data
to progressively aggregated forms such as indicator level data, category data,
pillar data, and the most aggregated, overall data—we observed a clear
pattern. It emerged that the predictive power was at its peak when using raw
data, and it gradually weakens through successive stages of aggregation, with
the overall scores exhibiting the weakest predictive capability. This finding
underscores the significant advantage of using detailed, granular ESG
information over aggregated forms. While aggregated data, like indicators,
categories, pillars, and overall scores, provide a more condensed view of ESG
factors, they also tend to obscure the nuanced impacts that specific ESG
elements can have on financial metrics. In contrast, raw ESG data retains this
granularity, enabling a more accurate and insightful analysis. This result
highlights the effectiveness of raw ESG data in capturing the complex dynamics
between ESG factors and financial performance, making it the superior choice
in further study.

Comparing the predictive power for stock return and volatility, ESG scores
demonstrate a more robust capability in explaining stock volatility than stock
returns. This finding indicates that ESG data can be considered as a tool for
assessing volatility, and risk-adjusted return. This also suggests that ESG
data can be effectively used in developing more resilient investment
strategies.

Comparing between in-sample and out-of-sample mean squared error revealed a
concern regarding overfitting. While the MSE shows favorable results in in-
sample data, its performance diminishes when applied to out-of-sample data.
This discrepancy serves as a cautionary note in the analysis of ESG data’s
relationship with stock performance. Even in instances where the adjusted
R-squared value is high, indicating a good fit of the model to the in-sample
data, there remains a risk of overfitting. Such a scenario could lead to
overly optimistic interpretations of the model’s predictive power. Therefore,
when studying the relationship between ESG data and stock performance, it’s
crucial to maintain a critical perspective, especially in drawing conclusions,
to ensure that the insights are robust and applicable beyond the initial data
set.

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