# Unraveling the Paradox: Green Premium vs. Climate Risk Premium in Sustainable Investing

Ramakrishna Ramadugu

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Ramakrishna Ramadugu. Unraveling the Paradox: Green Premium vs. Climate Risk Premium in Sustainable Investing. ABS International Journal of Management, Asian business school; ABSIC 2024 - 12th International Conference, Nov 2024, Noida, India. pp.71-89. hal-04931523

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# Unraveling the Paradox: Green Premium vs. Climate Risk Premium in Sustainable Investing

Ramakrishna Ramadugu

ramadugu@gmail.com

Abstract—This research paper delves into the paradoxical dynamics of sustainable investing, exploring the contrasting narratives between the aggregate-level performance of Green portfolios and firm-level empirical analyses. At the aggregate level, Green portfolios, comprising companies with lower carbon emissions or higher ESG scores, consistently outperform their Brown counterparts, indicative of a "green premium" driven by increasing concerns over climate change and sustainability. However, firm-level empirical data presents a contradictory picture, suggesting a "climate risk premium" where Brown firms, associated with higher carbon footprints or lower ESG scores, yield higher expected stock returns. Through rigorous analyses combining cross-sectional evidence, portfolio performance assessments, and firm-level investigations, this paper unveils that under varying assumptions and model specifications, firm-level results align with aggregate portfolio analysis. It reveals that Brown firms with higher carbon footprints are more exposed to climate change-related risks and tend to underperform Green firms during periods of heightened climate concern. These insights contribute to a nuanced understanding of the interplay between sustainability and financial returns, offering valuable implications for investment decisions and sustainable practices in an evolving global landscape.

## I. INTRODUCTION

In the face of mounting challenges such as geopolitical conflicts, pandemics, and climate change, the call for sustainable investment and environmentally responsible production has never been more urgent. These pressing global concerns have underscored the critical need to prioritize sustainability as a central pillar of my collective future. In addressing these challenges, the United Nations, as outlined in (1), has published Sustainable Development Goals (SDG), which comprises 17 interlinked objectives

that emphasize the intricate connections between environmental, social, and economic aspects of sustainable development. Furthermore, the call for sustainable practices extends into the financial market, where sustainable investing has gained significant traction. Investors are increasingly recognizing the importance of integrating environmental, social, and governance (ESG) criteria into their decision-making processes, as discussed in the report by (2). In this context, the introduction of the Green minus Brown factor (GMB) in the current asset pricing literature, alongside established aggregate risk factors like small minus big (SMB), high minus low (HML), and robust minus weak (RMW), has emerged as a relevant factor explaining risks associated with climate change. Empirical evidence often shows that Green portfolios, in both stock and bond markets, outperform their Brown counterparts. However, classic asset pricing theories propose a contrasting view. These theories suggest that Brown assets, bearing greater risks associated with climate change, should offer higher returns as compensation for this increased risk. This presents a notable contradiction between empirical findings and theoretical predictions.

Investors frequently turn to ESG (Environmental, Social, and Governance) scores when evaluating companies to gauge their environmental, social, and governance practices, especially the E scores for the environment. These scores play an important role in categorizing companies into "Green" and "Brown", signifying their commitment to sustainable practices or their lack thereof. However, a notable challenge arises from the fact that multiple
ESG rating agencies, such as MSCI ESG Ratings, Sustainalytics, and Bloomberg, among others, operate concurrently. Each of these agencies employs distinct valuation metrics and methodologies, leading to divergent ESG ratings for the same companies. In fact, recent research, as highlighted by (3), has revealed that this variation in ESG assessments can introduce uncertainty into the market. Such uncertainty has the potential to increase market premiums, diminish demand for the related stocks that exhibit higher ESG uncertainty, and create a complex landscape for investors to navigate. To circumvent the challenges associated with rating uncertainty, this paper adopts a pragmatic approach by relying on a single yet robust indicator to gauge companies' environmental performance: the Green House Gas (GHG) emissions. GHG emissions are recognized as a primary driver of global warming, and they are mandated for disclosure by various stakeholders, including the Securities and Exchange Commission (SEC), investors, and the public media. By focusing on this widely accepted and easily measurable metric, this study seeks to provide an unambiguous assessment of firms' sustainability practice and their stock returns.

Our analysis investigates whether firms characterized as "Brown" due to their higher carbon emissions experience higher stock returns compared to "Green" firms, as posited by classic theoretical studies suggesting that higher risk exposure is associated with higher returns. This analysis focuses exclusively on the U.S. stock market. The dataset utilized in this study encompasses all publicly traded stocks in the U.S. stock market from 2002 to 2021. The initial step of this research involves an exploratory analysis of the relationship between firms' carbon emissions and their stock returns cross-sectionally. For the entire dataset, I categorize all the observations into percentiles based on total CO2 emissions, subsequently computing the average stock return within each percentile. The findings reveal that stocks situated in the lower percentiles consistently exhibit higher average stock returns, with a decline in returns observed as percentiles progress toward the 100th percentile. Remarkably, this pattern persists when I consider

different scopes of carbon emissions. It's worth noting that while one might attribute this trend to other firm characteristics such as size, as carbon emissions tend to be positively correlated with firm size, my analysis does not reveal a similar pattern between firm size and stock returns, as well as other factors such as leverage, profitability, and growth. Furthermore, I apply a similar methodology to examine the relationship between firms' stock returns and carbon intensity, defined as a firm's carbon emissions scaled by its revenue. This metric is a crucial proxy for a firm's carbon footprint in the current corporate finance literature. However, in contrast to my findings on carbon emissions, I do not identify a clear and consistent relationship between firms' stock returns and carbon intensity.

Is it, however, conclusive to assert that firms with lower carbon emissions consistently yield higher stock returns? Not necessarily, as there is significant heterogeneity in carbon emissions across different industries. For instance, the Power and Renewable Electricity sector<fnref n="1" /> leads with an average emission of 38.15 million tons annually, a stark contrast to the Mortgage Real Estate Investment Trusts (REITs) 0.03 million tons. This disparity makes a direct comparison between firms belonging to different industries, which is akin to contrasting apples with bananas. To address this, I conduct a more nuanced analysis. Stocks within each sector are divided into quintiles based on their carbon emissions. Within each industry, I then create value-weighted portfolios: 'Green' for stocks with the lowest emissions, 'Brown' for the highest, and 'Neutral'<fnref n="2" /> for the middle range<fnref n="3" />. Over the entire dataset spanning from 2002 to 2021, the Green portfolios have delivered impressive cumulative returns, exceeding 600%, while their Brown counterparts achieved approximately 270% in cumulative returns; the re-

<footnote n="1">¹The industry classification in this paper follows the Global Industry Classification Standards (GICS).</footnote>

<footnote n="2">²Here the carbon neutral portfolios do not mean that the underlying companies have zero carbon emission, but these companies are ranked in the middle tertiles in the industry with respect to carbon emission.</footnote>

<footnote n="3">³The second and fourth quintiles are excluded from my analysis for a more distinguish comparison between firms in different range of carbon emissions.</footnote>
result coincides with (4) who use ESG scores to construct Green and Brown portfolios. However, when I replicate this approach using firms’ carbon intensity, the results diverge. The outperformance of green portfolios is not as clear as before, and it is only observed after 2010.

The green portfolio outperforms the brown by an average of 1.45% each month throughout the sample period. The GMB (green-minus-brown) portfolio, created by taking long positions in green stocks and short positions in brown stocks, demonstrates an economically and statistically significant alpha of above 1% on a monthly basis. Notably, this alpha cannot be explained by various factor models currently prevalent in asset pricing literature. This finding presents strong empirical evidence against traditional asset pricing theory, which suggests that green stocks, presumed to have lower climate change risk exposure, actually achieve higher returns than their brown counterparts. It also implies that using carbon emissions as an indicator to quantify a firm’s green practices is effective and comparable to ESG scores. However, similar results are not observed when considering firms’ carbon intensity.

In the aggregated portfolio analysis, I confirm the efficacy of carbon emissions quantifying firms’ sustainable practice, and my findings align with (4), who find that Green portfolio, which encompasses firms with higher ESG scores (lower carbon emissions in my case), tend to outperform their Brown counterparts. also corroborates these results cite-friede2015esg, who also indicate that Green firms often exhibit better financial performance. However, when I delve into firm-level analyses, as conducted by (5), a stark contradiction emerges. Their research suggests that firms with higher carbon emissions tend to yield higher stock returns, directly conflicting with my portfolio performance findings. To address this discrepancy, I shift my focus to firm-level data and employ a regression model to explore the relationship between firms’ total carbon emissions and stock returns. Recognizing the presence of unobserved time-variant factors and time-invariant industry-specific factors, I incorporate Industry + Time fixed effects in my panel regression model. my

results reveal a positive correlation between firms’ stock returns and total carbon emissions, indicating that firms with higher carbon emissions tend to have higher stock returns on average, yet this relationship lacks statistical significance.

The choice to incorporate Industry + Time two-way fixed effects is rooted in the assumption that unobserved time-variant factors associated with periods and time-invariant factors linked to industries exist. This assumption hinges on the belief that firms within the same industry during the same period exhibit similar stock return behaviors. A more stringent assumption is that even in the same industry, firms’ stock returns still behave differently due to some distinctive characteristics associated with each specific firm. Under this new assumption, I apply Entity + Time two-way fixed effects. The results of this analysis reveal a significant and negative relationship between firms’ carbon emissions and stock returns, both statistically and economically. Specifically, a 1% increase in firms’ total carbon emissions corresponds to a 0.66% decrease in stock returns, on average. These findings provide robust support for the notion that higher carbon emissions are associated with lower stock returns alongside my portfolio analysis, emphasizing the importance of accounting for idiosyncratic firm-level characteristics in my study. In my robustness analysis, I systematically vary the fixed effects and cluster standard errors at different levels. Notably, whenever I incorporate entity-fixed effects into the model, my findings consistently align with those of my benchmark model. This robustness underscores the reliability and stability of my results across various specifications, affirming the significance of entity-fixed effects in my analysis. In the face of escalating global challenges such as geopolitical conflicts, pandemics, and climate change, the need for sustainable investment and environmentally responsible production has become increasingly urgent (6). These critical concerns underscore the necessity of sustainability as a key pillar of my collective future. In response, the United Nations has outlined 17 Sustainable Development Goals (SDGs) that address environmental, social, and economic facets of sustainable development, highlighting the
interconnectedness of these areasing these goals,
the financial market has witnessed a significant rise
in sustainable investing, with a focus on environ-
mental, social, and governance (ESG) criteria that
influence investors' decisions, as evidenced by the
growing emphasis on integrating ESG into port-
folio management (7). To delve deeper, the study
constructs porthin industries, classifying firms by
emission levels to contrast Green and Brown portfo-
lios. This intra-industry approach provides insights
into the financial returns associated with carbon
emissions while accounting for industry-specific
factors. my findings reveal that the Green portfo-
lios consistently outperform the Brown portfolios
over the study period, echoing recent studies that
suggest environmental factors are becoming more
critical in shaping financial outcomes (8). Nonethe-
less, firm-level analyses suggest a more complex
relationship between emissions and stock returns,
especially when considering firm-specific character-
istics. Through robust testing, I confirm that high
carbon correlates with lower returns, strengthening
the case for sustainability-focused investing as a
financially viable strategy.

Related Literature

Our study contributes to a vast empirical liter-
ature on sustainable investing, encompassing both
aggregated portfolio and firm-level analyses. In a
broader context, research in this field has gained sig-
nificant momentum due to growing concerns about
climate change and sustainability. For instance, (9)
conducted a study using survey data to investigate
climate perception and found that climate risks,
particularly those related to regulations, have started
to materialize. Their research indicates that many
investors, particularly those with a long-term per-
spective, larger portfolios, and a focus on ESG
(Environmental, Social, and Governance) factors,
prioritize risk management and engagement over
divestment strategies. This underscores the evolving
priorities and strategy of investors in response to
climate-related challenges.

Similarly, (10) conducted groundbreaking re-
search to assess whether market-wide physical or
transition climate risks are priced into U.S. stocks.

They found that only the climate-policy factor is
priced, especially after 2012. Interestingly, their
study revealed that investors seem to be less con-
cerned about natural disasters, global warming, and
decisions made at international climate summits.
This research highlights the complexity of inte-
grating climate risk into financial markets and the
selective focus of investors on specific aspects of
climate-related factors.

In the midst of this dynamic landscape, my
study adds to the body of knowledge by examining
the relationship between firms’ carbon emissions,
climate change concerns, and stock returns. How-
ever, the current literature diverges when it comes
to the performance of Green and Brown assets.
(11) have utilized carbon ratios to select stocks,
revealing that lower carbon ratios are associated
with higher stock returns and increased profitabil-
ity. (12) constructed “Efficient-Minus-Inefficient”
portfolios based on carbon intensity, demonstrating
their ability to generate positive alpha since 2009.
Meanwhile, (13) introduced a low carbon index
and found that when climate change mitigation is
pending, the low carbon index performs the same
as the benchmark; when carbon emission is priced,
the index outperforms the benchmark. Addition-
ally, (14) investigated the impact of toxic emis-
sions intensity within industries, showcasing that
the portfolio premium could not be explained by
traditional factors, sentiment, political connections,
or corporate governance, emphasizing the unique
role of toxic emissions in stock returns. These
studies all suggest that Green assets characterized
by lower carbon emissions generate climate risk
premiums and outperform Brown assets, especially
when there are emission-related policy shocks.

Another branch of study declares that investors
are already demanding compensation for carbon
emission risk. Hence, Brown assets are associated
with higher expected returns. Notably, studies like
(5) and (15) have found that firms with high
CO2 emissions tend to yield higher stock returns,
showcasing the influence of carbon intensity on
investment choices for institutional investors, par-
ticularly in salient industries. (16) delved into the
world of green bonds, which are used for envi-
ronmentally sensitive purposes, and identified that green bonds are issued at a premium compared to otherwise similar ordinary bonds, highlighting investor demand for environmentally responsible investments. Meanwhile, (17) introduced the concept of exclusion premia, encompassing sin stocks, to elucidate the relationship between ESG factors and financial performance. They found that exclusion effects amounted to 2.79% annually, with taste effects varying from -1.12% to 0.14%. Moreover, (18) analyzed the impact of a firm's environmental profile on its cost of equity and debt capital, discovering that investors demanded significantly higher expected returns on stocks excluded by environmental screens compared to firms without such concerns. These excluded firms also exhibited lower institutional ownership and fewer banks participating in their loan syndicates. Additionally, (19) estimated the market-based premium associated with carbon risk at the firm level across 77 countries, uncovering a widespread carbon premium characterized by higher stock returns for companies with higher levels of carbon emissions. Lastly, (20) found that Brown firms tended to yield higher average returns, while decreases in the greenness of firms were associated with lower announcement returns. However, when they constructed a carbon risk factor-mimicking portfolio, they did not find evidence of a carbon risk premium, emphasizing the complexity of the relationship between carbon risk and investment returns.

In response to the significant divergence between two contradictory branches of existing literature, this study adopts a comprehensive approach encompassing aggregated portfolio analysis and firm-level investigations. By bridging the gap and synthesizing findings from both methods, I aim to provide a more holistic and nuanced understanding of the relationship between stocks' greenness, measured by their carbon emissions, and their corresponding stock returns.

## II. METHODOLOGY

The current literature presents seemingly contradictory findings regarding the relationship between a firm's environmental practices and its stock performance.

Conventional theoretical studies typically associate higher risk exposure with increased return compensation. (5) use firm-level data and find a positive correlation between a firm's carbon emissions and its stock returns, indicating that brown assets outperform green ones. They argue that investors demand higher returns as compensation for climate-related risks, which aligns with the theoretical perspectives. In contrast, (21) develop a new theoretical model suggesting that environmentally friendly assets typically yield higher returns, particularly in the face of unexpected climate change concerns. This model is further supported by empirical evidence from (4), who find that in the U.S. stock market, portfolios with higher Environmental, Social, and Governance (ESG) scores (Green portfolios) outperform those with lower ESG scores (Brown portfolios). A similar trend is observed with German green bonds outperforming their brown counterparts. This paper aims to reconcile these seemingly contradictory findings from existing literature. The methodologies used in this empirical study are introduced in this section.

### A. Quantify Firms' Environmental Practices

Two primary methods are employed in the existing research to quantify firms' environmental practices. The first one involves utilizing ESG scores provided by third-party rating agencies, such as Bloomberg, Thomson Reuters, MSCI ESG Ratings, and Sustainalytics. However, the diversity of rating agencies and their differing methodologies often lead to variations in the final ESG scores for the same company. This inconsistency can introduce what is known as ESG uncertainty. (3) demonstrate that this ESG uncertainty can result in increased CAPM alpha and effective beta, as well as investment outflows from stocks exhibiting high ESG uncertainty. Additionally, ESG scores are susceptible to influences that may not directly relate to a firm's environmental performance. For instance, larger corporations often have greater resources for managing their public image and ESG reporting, potentially resulting in inflated scores (known as 'greenwash') that may not accurately reflect their
environmental practices, especially in comparison to smaller companies.

The second method for quantifying firms’ environmental practices involves direct measurements of specific environmental metrics, such as carbon emissions, water usage, and waste production. This method offers a more objective and quantifiable approach, independent of the subjective assessments of third-party ESG ratings. In this paper, following the precedent set by (5) and (22), I focus on carbon emissions as a key metric for assessing firms’ environmental practices. Carbon emissions are a significant contributor to climate change. Their reporting has become increasingly mandated by regulatory bodies in recent years, providing a more consistent and standardized data set for analysis. Additionally, this paper considers carbon intensity - a metric that relates a firm’s carbon emissions to its revenue. Carbon intensity measures the efficiency with which a firm generates revenue relative to the Greenhouse Gases (GHG) it emits, as highlighted by (23).

## B. Aggregate Portfolio Analysis

Comparing CO2 emissions directly across companies from different industries can be misleading due to their unique operational requirements and regulatory environments inherent to different industries. For instance, the high emissions in the energy sector, particularly from fossil fuels, cannot be directly compared with the lower emissions of the technology or service sectors. Therefore, in this paper, I take a more accurate assessment by comparing emissions within the same industry, allowing for fair benchmarking against industry-specific standards and regulations. This approach highlights companies leading in sustainability and green practices relative to their peers, and it could provide a realistic view of each company’s efforts to reduce emissions. It can be expressed in the following equation:

$$Greenness_{i,t} = \mathbb{E}[Greenness_{i,t} | CO2\ Emissions_{i,t}, Industry_{i}] \quad (1)$$

In Equation 1, I measure company i’s sustainable practices at time t within industry, based on its carbon emission. Essentially, this method accounts for the heterogeneity between industries, offering a more nuanced understanding of environmental impacts and sustainability efforts. Utilizing this method, I categorize stocks into quintiles on a monthly basis and create value-weighted portfolios for each quintile. Stocks in the lowest quintile construct a "Green" portfolio characterized by low carbon emissions. Conversely, portfolios formulated by stocks from the top and middle quintiles are defined as "Brown" and "Natural," respectively. I also build a "Green-Brown" portfolio by longing the lowest deciles and shorting the top deciles aligning with (4).

## C. Individual Stock Analysis

For the analysis of individual stocks, I directly examine the relationship between a firm’s carbon emissions and its stock returns. I utilize the two-way fixed effects (TWFE) panel regression in my benchmark regression to investigate this relationship. The specific regression model, denoted as 2, assesses the impact of carbon emissions on stock returns:

$$RET_{i,t} = \alpha + \beta^{co2} * \log(co2 \ emission_{i,t}) + \beta^{contr} * Controls_{i,t} + \epsilon_{i,t} \quad (2)$$

Here, the subscript i refers to a specific company, and t indicates a specific month. RET$_{i,t}$ represents the return of stock i in month t. The term α is the cross-sectional intercept, while β$^{co2}$ is the coefficient on firms’ carbon emissions. The logarithmic normalized carbon emissions are expressed as log(co2 emission$_{i,t}$). The vector β$^{contr}$ comprises coefficients for a series of control variables. Lastly, ϵ$_{i,t}$ denotes the idiosyncratic error term. The parameter of interest is β$^{co2}$, which presents the relationship between carbon emissions and firms’ stock returns. A significant positive β$^{co2}$ demonstrates empirical evidence that higher carbon emissions is associated with higher stock returns, which aligns with the classic asset pricing framework that
higher risk exposure is associated with higher return compensation.

### D. Preference Shift Quantified by UMC

To understand the discrepancy between recent empirical studies and classic asset pricing theory, I propose an explanation based on the studies of (24) and (21). Classic asset pricing theory states that higher risk should correspond with higher returns. However, this principle could be overthrown by the preference shift in the financial market. Two primary factors contribute to this change: firstly, the desire to hedge against climate change-related risks, and secondly, the increasing trend of sustainable investing mandates, especially among institutional investors. This shift in preference leads to an increased demand for green assets and divestment from brown ones. Given the high price elasticity in asset demand, as discussed by (25) and (26), even a modest rise in demand can significantly elevate asset prices, thereby resulting in higher realized returns. I use the unexpected media climate change concern index to quantify this preference shift in the financial market as proposed by (22).

To empirically test this hypothesis, I employ a multivariate linear regression model that controls for other factors influencing stock returns. I specifically regress the returns of "Green-Brown," "Green," "Brown," and "Neutral" portfolios against the (UMC_t) as stated in Equation 4:

$$RET_{p,t} = \alpha_p + \beta_p^{UMC} \cdot UMC_t + \beta_p^{contr} \cdot Controls_t + \epsilon_{p,t} \quad (4)$$

In this model, RET_{p,t} represent the return of portfolio p, at time t. The intercept is denoted as α_p, while β_p^{UMC} is the coefficient for UMC index, β_p^{contr} presents a vector of coefficients corresponding to a series of control factors, and ϵ is the idiosyncratic error term. The UMC_t index quantifies unexpected media climate change concerns derived from news about climate change in widely circulated U.S. newspapers. An increase in this index suggests heightened concerns about climate change, which is expected to trigger a shift in investor preferences towards green assets.

Similar to my aggregate portfolio analysis, it is equally interesting to investigate the impact of UMC at the individual stock level, particularly how the interaction between a firm's carbon emissions and UMC influences the firm's stock returns. To assess this, I employ a firm fixed-effect panel regression model as follows:

$$RET_{i,t} = \alpha + \beta^{co2} \cdot \log(co2\ emission_{i,t}) + \beta^{umc} \cdot UMC_t \quad (5)$$

$$\begin{aligned} UMC \\ &+ \beta^* \cdot (\log(co2\ emission_{i,t}) \cdot UMC_t) \\ &+ \beta^{contr} \cdot Controls_{i,t} + \epsilon_{i,t} \end{aligned} \quad (6)$$

Different from Equation 2, I include UMC_t and the interaction between log(co2 emission_{i,t}) and UMC_t in Equation 5. The key coefficient, β^*, is of particular interest as it determines whether UMC amplifies or diminishes the link between a firm's carbon emissions and its stock return. The relationship is detailed in Equation 7. If β^{co2} and β^{umc} are both positive, high unexpected climate change concerns could lead to even higher returns for brown stocks to compensate for increased risk exposure. Conversely, if β^{co2} and β^{umc} both have negative signs, the green stocks will realize even higher returns. If β^{co2} and β^{umc} have opposite signs, the impact of unexpected climate change concerns on the relationship between carbon emissions and stock returns could be mitigated.

$$\frac{\partial RET_{i,t}}{\partial \log(co2\ emission_{i,t})} = \beta^{co2} + \beta^{umc} \cdot UMC_t \quad (7)$$

## III. DATA

This study exclusively examines publicly traded companies in the U.S. stock market from 2002 to 2021. my dataset merges carbon emission data from Trucost, financial accounting information from Compustat, and stock return figures from CRSP (The Center for Research in Security Prices), with the CUSIP-PERMNO linkage table serving as the connector. Trucost's dataset offers insights into the environmental impacts of various business activities
and evaluates risks associated with a wide array
of environmental issues. These include carbon and
other pollutants, water dependency, natural resource
efficiency, and waste management. The data from
Trucost includes both raw and calculated values at
both the company and sector levels. Following the
approach of (15), I opt for the calculated carbon
emission data, considering its comprehensiveness
and relevance to stock returns. The merged dataset
comprises 5,250 companies, totaling 526,393 ob-
servations. As illustrated in Figure 1, the graph
displays the annual count of both companies and
observations. Notably, the carbon emission data col-
lection began in 2002 with limited coverage. How-
ever, since 2016, there has been a substantial surge
in the number of companies included in the dataset,
for the coverage for small- and mid-cap companies
start from 2016. This remarkable expansion aligns
with the assignment of various international agree-
ments during this period, such as the *Addis Ababa
Action Agenda* (AAAA), the *Sendai Framework for
Disaster Risk Reduction 2015-2030* (SFDRR), and
*The Paris Agreement on Climate Change*. These
agreements, as discussed by (27), (28), and (29),
have played an important role in addressing global
climate challenges, emphasizing the importance of
sustainable development and initiatives targeting
climate change.

A. *Variable definition and summary statistics*

I provide explanations for key variables outlined
in Table I. The stock return data incorporates stocks'
capital gains and dividends, which are observed
monthly. The companies' total carbon emission data
is the sum of all three scopes of emissions collected
by Trucost following the Greenhouse Gas Protocol:
Scope 1 entails direct greenhouse gas emissions,
Scope 2 covers indirect emissions from purchased
energy consumption, and Scope 3 encompasses a
wider range of upstream and downstream indirect
emissions. Meanwhile, carbon intensity is calcu-
lated as the ratio of carbon emissions to revenue
(tons/million(USD)), indicating how effectively a
company utilizes its CO2 emissions to generate rev-
enue. Control variables in this analysis encapsulate
fundamental financial conditions, which have been

substantiated as pertinent factors influencing stock
returns through extensive literature such as (30),
(31), and (32). The size is a firm's market capital-
ization in logarithmic form, serving as a measure
of its economic scale; leverage, which quantifies
a firm's financial structure risk by assessing the
ratio of total liability to market capitalization; B/M
(Book-to-Market Ratio) indicating the difference
between firms' book value and market valuation;
RoE (Return on Equity) capturing firms' profitabil-
ity through the return generated on shareholders'
equity; Invest/AT (Investment to Total Assets) re-
flecting firms' innovation efforts by scaling invest-
ment with total assets; PPE (Property, Plant, and
Equipment) measuring their fixed assets; SaleGR
(Sales Growth) gauging revenue growth; EPS (Earn-
ings Per Share) as another indicator of profitability;
Staff_num, the number of employees presented in
logarithmic form; and Firm_age, representing the
firm's age since its foundation. These variables
collectively provide insights into various financial,
operational, and growth aspects that are pertinent to
my analysis of the interplay between environmental
factors and stock returns.

Table ?? provides a summary of the statistical
characteristics for the majority of variables used
in this study. To mitigate the potential impact of

<figure><img src="image_3.png" /><figcaption>Fig. 1. Number of Firms and Observations</figcaption></figure>
<table><caption>TABLE I
VARIABLE DEFINITION</caption><thead><tr><td>Variables</td><td>Definition</td></tr></thead><tbody><tr><td>RET</td><td>Monthly stock return</td></tr><tr><td>Co2_tot</td><td>Total carbon emissions (log)</td></tr><tr><td>Co2_int</td><td>Carbon intensity</td></tr><tr><td>Size</td><td>Total market capitalization (log)</td></tr><tr><td>Leverage</td><td>Total liability over market capitalization</td></tr><tr><td>B/M</td><td>Book to market ratio</td></tr><tr><td>RoE</td><td>Return on equity</td></tr><tr><td>Inves/AT</td><td>Investment over total assets</td></tr><tr><td>PPE</td><td>Property, plant, and equipment (log)</td></tr><tr><td>SaleGR</td><td>Growth in revenue</td></tr><tr><td>EPS</td><td>Earning per share</td></tr><tr><td>Staff_num</td><td>Number of employees (log)</td></tr><tr><td>Firm_age</td><td>Firm age since foundation</td></tr></tbody></table>

This table presents the definition of variables used in my analysis.

outliers, I have applied winsorization to some of the variables at 1% thresholds. This process involves capping extreme values to ensure that the dataset maintains a reasonable balance between standard deviation and mean values. Within the entire dataset, the monthly stock returns in the dataset ranged from -92% to 1625%, with an average of 1% and a standard deviation of 15%. Following winsorization at the 1% level, the mean and median remained unchanged, but the standard deviation decreased to 10%, at the cost of the exclusion of 10,526 observations. Additionally, I scale certain variables using natural logarithms. For instance, firms' total CO2 emissions had an average of 5 million tons and a maximum of 400 million tons. After logarithmic transformation, the mean and standard deviation are reduced to 12.75 and 2.66, respectively. Detailed summary statistics for these variables, both before and after manipulation, are available in Table ??.

In Table III, I report the pairwise Pearson correlations among all the independent variables. Notably, two carbon footprint indicators, namely total carbon emissions and emission intensity, exhibit a positive correlation. However, the correlation coefficient of 0.63 suggests some divergence between these two indicators. Firms' size demonstrates a strong positive correlation with their total CO2 emissions, with a coefficient of 0.66. This implies that larger firms tend to have higher total CO2 emissions.

Conversely, the correlation between firm size and CO2 intensity is only 0.09, indicating a lack of a strong relationship between firm size and its carbon intensity. This highlights that larger firms may have varying levels of carbon intensity, with some large firms exhibiting low carbon intensity. The highest correlations are observed between PPE (Property, Plant and Equipment) and CO2 emissions, PPE and firm size, Staff_num (number of employees) and total CO2 emissions, and Staff_num and firm size. In each of these cases, the correlation exceeds 0.6 in absolute value, signifying that firms with more PPE and a greater number of employees tend to be larger firms with higher CO2 emissions. Nevertheless, these correlations do not indicate a strong association with CO2 intensity, emphasizing that the relationship between firm characteristics and carbon intensity is not as pronounced.

## B. Carbon Emissions & Intensity

In the current corporate finance literature there are two important indicators quantifying firms' carbon footprints. Alongside firms' total carbon emissions, carbon intensity emerges as a critical metric for evaluating their environmental sustainability. Carbon intensity precisely measures the rate of emissions of a specific pollutant concerning the scale of firms' production activities. In my study, I employ carbon intensity, calculated as firms' total carbon emissions normalized by their revenue, as a
<table><caption>TABLE II
SUMMARY STATISTICS</caption><thead><tr><th rowspan="2"></th><th colspan="5">Before Data Manipulation</th><th colspan="5">After Data Manipulation</th></tr><tr><th>Count</th><th>Mean</th><th>STD</th><th>Min</th><th>Median</th><th>Max</th><th>Count</th><th>Mean</th><th>STD</th><th>Min</th><th>Median</th><th>Max</th></tr></thead><tbody><tr><td>RET</td><td>526,393</td><td>0.01</td><td>0.15</td><td>-0.92</td><td>0.01</td><td>16.25</td><td>515,865</td><td>0.01</td><td>0.10</td><td>-0.33</td><td>0.01</td><td>0.42</td></tr><tr><td>Co2_tot</td><td>526,393</td><td>5.43M</td><td>21.71M</td><td>0.27</td><td>401.87K</td><td>414.45M</td><td>526,393</td><td>12.75</td><td>2.66</td><td>0.24</td><td>12.90</td><td>19.84</td></tr><tr><td>Intensity_tot</td><td>526,393</td><td>485.55</td><td>1315.78</td><td>20.43</td><td>148.24</td><td>89.99K</td><td>526,393</td><td>5.18</td><td>1.26</td><td>3.06</td><td>5.01</td><td>11.41</td></tr><tr><td>Marketcap</td><td>522,812</td><td>320.59K</td><td>13.80M</td><td>0.01</td><td>3666.73</td><td>998.73M</td><td>522,812</td><td>8.21</td><td>1.81</td><td>0.01</td><td>8.21</td><td>20.72</td></tr><tr><td>Leverage</td><td>522,175</td><td>0.61</td><td>0.27</td><td>0.00</td><td>0.61</td><td>6.92</td><td>522,175</td><td>0.61</td><td>0.27</td><td>0.00</td><td>0.61</td><td>6.92</td></tr><tr><td>B/M</td><td>521,618</td><td>5.21</td><td>937.08</td><td>-4127.45</td><td>0.44</td><td>274.70K</td><td>511,184</td><td>0.53</td><td>0.43</td><td>-0.54</td><td>0.44</td><td>3.01</td></tr><tr><td>RoE</td><td>521,900</td><td>-1.38</td><td>215.97</td><td>-31837</td><td>0.10</td><td>388.70</td><td>511,472</td><td>0.06</td><td>0.40</td><td>-3.20</td><td>0.10</td><td>2.77</td></tr><tr><td>Inves/AT</td><td>520,278</td><td>0.04</td><td>0.05</td><td>-0.19</td><td>0.03</td><td>0.87</td><td>520,278</td><td>0.04</td><td>0.05</td><td>-0.19</td><td>0.03</td><td>0.87</td></tr><tr><td>PPE</td><td>459,439</td><td>10.59K</td><td>35.44K</td><td>0.00</td><td>1.42K</td><td>635.15K</td><td>459,439</td><td>7.07</td><td>2.42</td><td>0.00</td><td>7.26</td><td>13.36</td></tr><tr><td>SaleGR</td><td>467,731</td><td>1.75</td><td>96.71</td><td>-1.00</td><td>0.06</td><td>9945.00</td><td>458,396</td><td>0.10</td><td>0.29</td><td>-0.64</td><td>0.06</td><td>2.60</td></tr><tr><td>EPS</td><td>522,856</td><td>5.75</td><td>151.89</td><td>-998.26</td><td>1.44</td><td>8548.00</td><td>512,453</td><td>1.75</td><td>3.02</td><td>-9.78</td><td>1.44</td><td>18.27</td></tr><tr><td>Staff_num</td><td>515,253</td><td>26.59</td><td>72.31</td><td>0.00</td><td>6.10</td><td>2300.00</td><td>515,253</td><td>2.11</td><td>1.49</td><td>0.00</td><td>1.96</td><td>7.74</td></tr><tr><td>Firm_age</td><td>513,763</td><td>70.56</td><td>52.56</td><td>2.00</td><td>54.00</td><td>657.00</td><td>513,763</td><td>3.99</td><td>0.79</td><td>1.10</td><td>4.01</td><td>6.49</td></tr></tbody></table>

The table presents summary statistics for the main variables across the entire sample period, with definitions provided in Table I. Data manipulation methods have been applied to scale certain variables and exclude outliers.

means to assess their emission efficiency. Figure 3 illustrates the historical trajectory of firms’ carbon footprints, as represented by both of total carbon emissions and carbon intensity. Across the entire sampling period, I observe a consistent downward trend in both metrics for measuring firms’ carbon footprint. Notably, a substantial decline is evident in the year 2016 for both total CO2 emissions and intensity. This reduction can primarily be attributed to the expanded data coverage of the TRUCOST database in that year, encompassing a broader spectrum of small and medium-sized companies. The overarching decline in both CO2 emissions and intensity, except for the significant drop in 2016, underscores the collective endeavor towards greener practices by companies. Furthermore, it reflects the tangible impact of effective green policies on shaping firms’ environmental behavior and fostering environmentally conscious practices.

### C. Total Carbon Emissions in Different Industries

Table IV provides a ranking of industries according to their average total carbon emissions over the period from 2002 to 2021. Notably, the industries with the most substantial average carbon emissions are Power and Renewable Electricity Productions, which exhibit an annual average of approximately 38.15 million tons. Electric Utilities and Oil, Gas,

and Automobiles sectors secure the second and third positions, emitting around 37.46 million and 30.04 million tons of CO2 on average during the entire sampling period, respectively. These sectors are renowned for their notable environmental im-

<figure><img src="image_4.png" /><figcaption>Fig. 3. Carbon Emissions & Intensity</figcaption></figure>

Fig. 4. *

This graphic illustrates the historical trajectory of firms’ total carbon emissions and intensity on average. Firms’ total carbon emissions are measured in thousand tons, while intensity is quantified by tons of CO2 emitted per million US dollars of revenue. Both trajectories represent the mean value in each specific year.
<table><caption>TABLE III
CONTROL VARIABLES' PEARSON CORRELATION</caption><thead><tr><th>Firm_age</th><th>CO2</th><th>Intensity</th><th>Size</th><th>Leverage</th><th>B/M</th><th>RoE</th><th>Inv/AT</th><th>PPE</th><th>SaleGR</th><th>EPS</th><th>Staff_num</th></tr></thead><tbody><tr><td>CO2</td><td>1.0***</td><td>0.63***</td><td>0.66***</td><td>0.09***</td><td>0.02***</td><td>0.22***</td><td>0.24***</td><td>0.85***</td><td>-0.1***</td><td>0.3***</td><td>0.72***</td></tr><tr><td>0.38***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Intensity</td><td></td><td>1.0***</td><td>0.08***</td><td>-0.13***</td><td>-0.00</td><td>0.01***</td><td>0.37***</td><td>0.44***</td><td>-0.04***</td><td>-0.00</td><td>0.13***</td></tr><tr><td>0.10***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Size</td><td></td><td></td><td>1.0***</td><td>0.02***</td><td>-0.21***</td><td>0.23***</td><td>0.05***</td><td>0.68***</td><td>0.01***</td><td>0.39***</td><td>0.69***</td></tr><tr><td>0.30***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Leverage</td><td></td><td></td><td></td><td>1.0***</td><td>-0.06***</td><td>0.06***</td><td>-0.08***</td><td>0.18***</td><td>-0.09***</td><td>0.03***</td><td>0.15***</td></tr><tr><td>0.20***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>B/M</td><td></td><td></td><td></td><td></td><td>1.0***</td><td>-0.09***</td><td>-0.04***</td><td>0.11***</td><td>-0.12***</td><td>-0.06***</td><td>-0.05***</td></tr><tr><td>0.04***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>RoE</td><td></td><td></td><td></td><td></td><td></td><td>1.0***</td><td>0.03***</td><td>0.18***</td><td>0.03***</td><td>0.39***</td><td>0.19***</td></tr><tr><td>0.17***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Inv/AT</td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.0***</td><td>0.33***</td><td>0.07***</td><td>0.01***</td><td>0.05***</td></tr><tr><td>-0.04***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>PPE</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.0***</td><td>-0.13***</td><td>0.27***</td><td>0.71***</td></tr><tr><td>0.39***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>SaleGR</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.0***</td><td>0.05***</td><td>-0.11***</td></tr><tr><td>-0.16***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>EPS</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.0***</td><td>0.29***</td></tr><tr><td>0.25***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Staff_num</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>1.0***</td></tr><tr><td>0.40***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Firm_age</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>1.0***</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr></tbody></table>

This table reports the pairwise Pearson correlations among all the control variables and firms' carbon footprint variables. * means significance at 10%, ** at 5%, *** at 1%.

pacts due to the higher levels of carbon emissions they generate. On the contrary, industries with the least average carbon emissions encompass Industrial REITs, Health Care Technology, and Mortgage Real Estate Investment Trusts (REITs) sectors, showcasing relatively smaller environmental footprints based on their total carbon emissions. Taking into account the entire sampling period and a comprehensive range of industries, the average greenhouse gas emissions stand at 5.43 million tons. Strikingly, the most environmentally impactful sector, exemplified by Independent Power and Renewable Electricity Productions, demonstrates total CO2 emissions that are nearly 8 times higher than the average. In contrast, the most environmentally friendly industries, like Health Care Technology and Mortgage Real Estate Investment Trusts (REITs) sectors, emit only approximately 1/100th of the average emissions. This highlights a substantial diver-

sity across industries concerning their total carbon emissions, underlining the significant heterogeneity in their environmental impacts.

## IV. RESULT

The primary goal of this paper is to explore the relationship between firms' carbon emissions and their stock returns. my approach is structured in several steps. Initially, in Section IV-A, I conduct a preliminary analysis to examine the unconditional relationship between firms' carbon emissions and stock returns. Next, in Section IV-B, I delve into portfolio analysis. The third step, detailed in Section IV-C, involves presenting firm-level evidence. Finally, in Section IV-D, I attempt to resolve the contradictions observed in the empirical analysis vis-à-vis traditional asset pricing theory.

<footnote>* p<.1, ** p<.05, *** p<.01</footnote>
<table><caption>TABLE IV
INDUSTRIES RANKED BY AVERAGE TOTAL CO2 EMISSION</caption><thead><tr><th>Rank</th><th>GICS Industry Name</th><th>Total CO2 Emission</th><th>Rank</th><th>GICS Industry Name</th><th>Total CO2 Emission</th></tr></thead><tbody><tr><td>1</td><td>Power and Renewable Electricity Producers</td><td>38.15</td><td>38</td><td>Electronic Equipment, Instruments and Components</td><td>1.23</td></tr><tr><td>2</td><td>Electric Utilities</td><td>37.46</td><td>39</td><td>Semiconductors and Semiconductor Equipment</td><td>1.11</td></tr><tr><td>3</td><td>Automobiles</td><td>30.04</td><td>40</td><td>Specialty Retail</td><td>1.09</td></tr><tr><td>4</td><td>Oil, Gas and Consumable Fuels</td><td>28.28</td><td>41</td><td>Textiles, Apparel and Luxury Goods</td><td>1.08</td></tr><tr><td>5</td><td>Multi-Utilities</td><td>21.05</td><td>42</td><td>Construction and Engineering</td><td>1.07</td></tr><tr><td>6</td><td>Passenger Airlines</td><td>16.34</td><td>43</td><td>Marine Transportation</td><td>1.05</td></tr><tr><td>7</td><td>Construction Materials</td><td>16.25</td><td>44</td><td>Communications Equipment</td><td>1.01</td></tr><tr><td>8</td><td>Industrial Conglomerates</td><td>14.31</td><td>45</td><td>Health Care Equipment and Supplies</td><td>0.93</td></tr><tr><td>9</td><td>Metals and Mining</td><td>13.48</td><td>46</td><td>Trading Companies and Distributors</td><td>0.86</td></tr><tr><td>10</td><td>Food Products</td><td>12.75</td><td>47</td><td>Leisure Products</td><td>0.86</td></tr><tr><td>11</td><td>Financial Services</td><td>10.05</td><td>48</td><td>Specialized REITs</td><td>0.82</td></tr><tr><td>12</td><td>Chemicals</td><td>9.66</td><td>49</td><td>IT Services</td><td>0.78</td></tr><tr><td>13</td><td>Personal Care Products</td><td>9.11</td><td>50</td><td>Interactive Media and Services</td><td>0.71</td></tr><tr><td>14</td><td>Consumer Staples Distribution and Retail</td><td>7.62</td><td>51</td><td>Distributors</td><td>0.70</td></tr><tr><td>15</td><td>Household Products</td><td>7.48</td><td>52</td><td>Life Sciences Tools and Services</td><td>0.63</td></tr><tr><td>16</td><td>Tobacco</td><td>7.22</td><td>53</td><td>Entertainment</td><td>0.61</td></tr><tr><td>17</td><td>Aerospace and Defense</td><td>6.28</td><td>54</td><td>Media</td><td>0.56</td></tr><tr><td>18</td><td>Air Freight and Logistics</td><td>6.26</td><td>55</td><td>Capital Markets</td><td>0.45</td></tr><tr><td>19</td><td>Containers and Packaging</td><td>6.25</td><td>56</td><td>Insurance</td><td>0.40</td></tr><tr><td>20</td><td>Beverages</td><td>5.90</td><td>57</td><td>Transportation Infrastructure</td><td>0.36</td></tr><tr><td>21</td><td>Paper and Forest Products</td><td>3.88</td><td>58</td><td>Water Utilities</td><td>0.31</td></tr><tr><td>22</td><td>Technology Hardware, Storage and Peripherals</td><td>3.80</td><td>59</td><td>Diversified Consumer Services</td><td>0.29</td></tr><tr><td>23</td><td>Automobile Components</td><td>3.72</td><td>60</td><td>Banks</td><td>0.26</td></tr><tr><td>24</td><td>Building Products</td><td>2.90</td><td>61</td><td>Professional Services</td><td>0.23</td></tr><tr><td>25</td><td>Ground Transportation</td><td>2.64</td><td>62</td><td>Software</td><td>0.21</td></tr><tr><td>26</td><td>Household Durables</td><td>2.59</td><td>63</td><td>Consumer Finance</td><td>0.21</td></tr><tr><td>27</td><td>Machinery</td><td>2.37</td><td>64</td><td>Hotel and Resort REITs</td><td>0.20</td></tr><tr><td>28</td><td>Diversified Telecommunication Services</td><td>2.15</td><td>65</td><td>Real Estate Management and Development</td><td>0.18</td></tr><tr><td>29</td><td>Energy Equipment and Services</td><td>2.07</td><td>66</td><td>Health Care REITs</td><td>0.17</td></tr><tr><td>30</td><td>Broadline Retail</td><td>2.07</td><td>67</td><td>Office REITs</td><td>0.13</td></tr><tr><td>31</td><td>Wireless Telecommunication Services</td><td>2.05</td><td>68</td><td>Biotechnology</td><td>0.11</td></tr><tr><td>32</td><td>Health Care Providers and Services</td><td>2.00</td><td>69</td><td>Retail REITs</td><td>0.11</td></tr><tr><td>33</td><td>Pharmaceuticals</td><td>1.91</td><td>70</td><td>Diversified REITs</td><td>0.11</td></tr><tr><td>34</td><td>Gas Utilities</td><td>1.87</td><td>71</td><td>Residential REITs</td><td>0.09</td></tr><tr><td>35</td><td>Electrical Equipment</td><td>1.40</td><td>72</td><td>Industrial REITs</td><td>0.06</td></tr><tr><td>36</td><td>Commercial Services and Supplies</td><td>1.38</td><td>73</td><td>Health Care Technology</td><td>0.06</td></tr><tr><td>37</td><td>Hotels, Restaurants and Leisure</td><td>1.31</td><td>74</td><td>Mortgage Real Estate Investment Trusts (REITs)</td><td>0.03</td></tr></tbody></table>

This table presents the ranking of different industries based on their average total CO2 emissions. The measurements for total CO2 emissions are provided in a million tons. And the industry is categorized according to the GICS (Global Industry Classification Standard) industry classification.

## A. Average Monthly Return on Firms' Carbon Footprint

Our first practice delves into the unconditional relationship between firms' carbon footprint and their stock returns. Over the entire sample period, I adopt a cross-sectional approach, sorting carbon emissions into 100 percentiles. Within each percentile, I compute the average monthly stock returns to gain an overarching understanding of the link between firms' carbon emissions and their stock performance. Figure 5 visually presents these findings. Panel A focuses on the average stock returns concerning firms' total carbon emissions, while panels B, C, and D examine emissions within

different emission scopes. Across all four panels, a distinguished downward trend emerges, indicating that firms with higher carbon emissions tend to exhibit lower stock returns on average. Additionally, I observe peaks in average stock returns occurring when firms' carbon emissions fall around the 1st percentile for all scopes. Another set of peaks in average returns is notable for different emissions categories, such as total carbon emissions around the 58th percentile, scope one emissions near the 65th percentile, scope two emissions at approximately the 79th percentile, and scope three emissions around the 55th percentile. These clusters of companies may share common characteristics,
possibly belonging to the same industry, with sim-
ilarities in terms of size, profitability, and growth.
It's important to note that in this analysis, I specif-
ically sort firms based on their carbon emissions
only, without considering other stock return-related
factors. Nevertheless, these initial findings provide
valuable insights into the preliminary relationship
between firms' carbon emissions and their realized
stock returns.

<figure><img src="image_5.png" /><figcaption>Fig. 6. *</figcaption></figure>

This presents the average monthly stock returns in relation to different percentiles of carbon emissions. Panel A depicts the average stock return in relation to firms’ total carbon emissions, while Panel B illustrates the average stock return concerning firms’ scope 1 carbon emissions. Panel C showcases the average stock return with respect to firms’ scope two carbon emissions, and Panel D presents the average stock return in connection with firms’ scope three carbon emissions.

Following the same analytical approach, I explore
whether a similar pattern emerges with another cru-
cial indicator in corporate finance literature pertain-
ing to firms’ carbon footprint. Figure 7 illustrates
the average monthly stock returns across different
percentiles of firms’ carbon intensity. In contrast
to the previous analysis of carbon emissions, I do
not discern a clear and consistent trend in firms’
average monthly stock returns across all four panels,
with each representing different scopes of firms’
carbon intensity. The absence of a discernible trend

suggests that the relationship between firms’ carbon
intensity and their stock returns may not exhibit the
same patterns as strongly as observed with carbon
emissions.

<figure><img src="image_6.png" /><figcaption>Fig. 8. *</figcaption></figure>

This presents the average monthly stock returns in relation to different percentiles of carbon intensity. Panel A depicts the average stock return in relation to firms’ total carbon intensity, while Panel B illustrates the average stock return concerning firms’ scope one carbon intensity. Panel C showcases the average stock return with respect to firms’ scope two carbon intensity, and Panel D presents the average stock return in connection with firms’ scope three carbon intensity.

Similar patterns are not observed when plotting
other key firm characteristics alongside stock re-
turns. Some may raise concerns that the cross-
sectional relationship between firms’ stock returns
and carbon emissions could be influenced by con-
founding factors such as firm size, leverage, prof-
itability, and growth, as illustrated in Table III the
strong correlation between firms’ carbon emissions
and some characteristic variables. Notably, there is
a high and statistically significant positive corre-
lation between firms’ carbon emissions and size.
To address these concerns, I present the average
monthly stock returns in relation to various firms’
characteristics in Figure 9. In panel (A), I observe
a positive association between firm size and stock
returns within the first 20 percentiles; however,
beyond this range, the relationship becomes less
apparent. It is important to remember that firm size
has a high correlation with carbon emissions. The
most similar pattern emerges from the plot between
leverage and stock return, however the correlation
between leverage and carbon emission only is 0.09.
While other patterns emerge in stock returns con-
cerning variables like RoE and revenue growth, it's
essential to note that these variables exhibit weak
correlations with firms' carbon emissions.

<figure><img src="image_7.png" /><figcaption>Fig. 10. *</figcaption></figure>

This presents the average monthly stock returns in relation to different percentiles of various firms’ characteristic indicators. Panel A depicts the average stock return in relation to firms’ market capitalization, while Panel B illustrates the average stock return concerning firms’ leverage. Panel C showcases the average stock return with respect to firms’ profitability ROE, and Panel D presents the average stock return in connection with firms’ growth in revenue.

B. Realized Cumulative Return for Green and Brown Portfolios

The green portfolio outperforms its brown coun-
terpart over the entire sample period, with firm total
carbon emissions determining their categorization.
Following the methodology presented in Equation
1, I sort stocks into quintiles monthly based on
their industry-specific carbon emissions. Generally,
firms with higher emissions, categorized as brown,

are those exceeding the 80th percentile in carbon
emissions due to their significant environmental im-
pact. Conversely, firms below the 20th percentile are
assigned to the green portfolio. Those between the
40th and 60th percentiles are placed in the neutral
portfolio. Firms falling between the 20th and 40th
percentiles, as well as those between the 60th and
80th, are excluded for a clearer comparison. The
green portfolio demonstrates superior cumulative
realized returns, as depicted in Figures 11 for the
period from 2002 to 2021. Each portfolio is value-
weighted based on the market capitalization of the
included firms to ensure fairness and accuracy<fnref n="4" />.
Notably, portfolio reallocation is an annual process
due to the yearly update of firms’ carbon emission
data, allowing me to disregard transaction fees in
this analysis. At the end of the sample period, the
brown portfolio realized less than 300% cumulative
returns, while the green portfolio realized cumula-
tive returns more than 600% twice higher than its
brown counterpart.

The green portfolio, categorized based on firms'
carbon intensity, shows only slight outperformance
compared to its brown counterpart, and this out-
perform is observed only after 2011. Following the
same methodology, I group stocks into green and
brown groups based on their carbon intensity. The
cumulative returns of these portfolios are presented
in Figure 13. Throughout the entire sample period,
the green portfolio achieves a cumulative return of
approximately 400%, and its brown counterpart re-
alizes a cumulative return of around 300%. Notably,
the green portfolio's outperformance is only evident
post-2011; prior to this, both portfolios exhibited
similar cumulative return trajectories.

Considering carbon emissions, the green-minus-
brown (GMB) portfolio, which is constructed by
a long position in the green portfolio and a short
position in the brown, yielded a monthly return
of 1.45%, statistically significant at the 1% level.
Compared with (4), who used the E score from

<footnote n="4">⁴In the portfolio analysis, I use the data without manipula-
tion. Since the outliers are often observed in small-cap stocks
and the portfolio is constructed by value-weighted, the influence
of these outliers will be minimized. And then the un-manipulated
data help avoid the criticism of data manipulation.</footnote>
<figure><img src="image_8.png" /><figcaption>Fig. 12. *</figcaption></figure>

This graphic depicts the cumulative return of green and brown portfolios, categorized based on firms’ carbon emissions. The shaded regions represent recession periods as suggested by the National Bureau of Economic Research (NBER).

<figure><img src="image_9.png" /><figcaption>Fig. 14. *</figcaption></figure>

This graphic depicts the cumulative return of green and brown portfolios, categorized based on firms’ carbon intensity. The shaded regions represent recession periods as suggested by the NBER.

MSCI ESG scores to construct a GMB portfolio averaging a 0.65% monthly return, this result indicates that the carbon emission indicator is as good as ESG scores in quantifying a company’s green practices<fnref n="5" />. The results are detailed in Table V, where the first column highlights the GMB premium based on firms’ overall carbon emissions. Conversely, the 4th column of Table V presents the GMB premium based on firms’ CO2 intensity. Here, the Green portfolio shows a smaller outperformance of only 0.39% against the Brown portfolio with a standard error of 23.4 bp. This performance is less pronounced than that observed with carbon emissions.

In columns 2, 3, and 4 of Table V, the GMB portfolio’s return is regressed on the Fama-French 3 and 5 factors models, as well as FF5 + MOM (momentum factor) + LIQ (liquidity factor), following the discussions in (33), (34), (35), and (36).

The results provide consistent evidence that the strong performance of the GMB portfolio cannot be fully attributed to the return factors commonly recognized in asset pricing literature, as indicated by the economically and statistically significant intercepts. This significant alpha implies, on the one hand, the effectiveness of carbon emissions in quantifying firms’ sustainable practices and on the other hand, it challenges the traditional asset pricing theory that less risky green assets outperform brown ones. When constructing the GMB portfolio based on firms’ carbon intensity, as shown in columns 6-8 of Table V, I observe mixed evidence. The difference between using total carbon emissions versus carbon intensity to shape the portfolio is significant. The empirical data highlights total carbon emissions as a more robust indicator for assessing firms’ greenness, contrary to the intuitive appeal of carbon intensity. This finding underscores that, as per the current data, carbon intensity does not hold a superior position as an indicator of greenness.

<footnote n="5">⁵While the GMB portfolio in this study shows a higher monthly average return, it does not necessarily imply that firms’ carbon emissions are a superior indicator compared to ESG scores for quantifying firms’ sustainable practices. This is because the methodologies for grouping stocks into green and brown portfolios differ between the two studies.</footnote>
<table><caption>TABLE V
GREEN - BROWN PORTFOLIOS REGRESS ON FACTORS</caption><thead><tr><th rowspan="2"></th><th colspan="4">CO2 Emission</th><th colspan="4">Intensity</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th></tr></thead><tbody><tr><td>Intercept</td><td>1.454***<br>(0.319)</td><td>1.169***<br>(0.268)</td><td>1.181***<br>(0.280)</td><td>1.073***<br>(0.298)</td><td>0.395*<br>(0.234)</td><td>0.124<br>(0.209)</td><td>0.080<br>(0.218)</td><td>1.073***<br>(0.298)</td></tr><tr><td>Mkt_RF</td><td></td><td>0.072<br>(0.065)</td><td>0.070<br>(0.069)</td><td>0.120<br>(0.073)</td><td></td><td>0.251***<br>(0.051)</td><td>0.266***<br>(0.054)</td><td>0.120<br>(0.073)</td></tr><tr><td>SMB</td><td></td><td>1.092***<br>(0.113)</td><td>1.078***<br>(0.119)</td><td>1.039***<br>(0.119)</td><td></td><td>0.199**<br>(0.088)</td><td>0.200**<br>(0.092)</td><td>1.039***<br>(0.119)</td></tr><tr><td>HML</td><td></td><td>-0.543***<br>(0.100)</td><td>-0.554***<br>(0.114)</td><td>-0.470***<br>(0.119)</td><td></td><td>-0.575***<br>(0.078)</td><td>-0.625***<br>(0.089)</td><td>-0.470***<br>(0.119)</td></tr><tr><td>RMW</td><td></td><td></td><td>-0.045<br>(0.138)</td><td>-0.112<br>(0.140)</td><td></td><td></td><td>0.030<br>(0.107)</td><td>-0.112<br>(0.140)</td></tr><tr><td>CMA</td><td></td><td></td><td>0.062<br>(0.182)</td><td>0.071<br>(0.181)</td><td></td><td></td><td>0.173<br>(0.142)</td><td>0.071<br>(0.181)</td></tr><tr><td>MOM</td><td></td><td></td><td></td><td>0.178**<br>(0.076)</td><td></td><td></td><td></td><td>0.178**<br>(0.076)</td></tr><tr><td>LIQ</td><td></td><td></td><td></td><td>-2.381<br>(4.143)</td><td></td><td></td><td></td><td>-2.381<br>(4.143)</td></tr><tr><td>Obs</td><td>240</td><td>240</td><td>240</td><td>240</td><td>240</td><td>240</td><td>240</td><td>240</td></tr><tr><td>R-squared</td><td>0.000</td><td>0.327</td><td>0.327</td><td>0.343</td><td>-0.000</td><td>0.243</td><td>0.248</td><td>0.343</td></tr></tbody></table>

This table presents the regression results of the Green minus Brown portfolio on different factor models. In the left panel, the portfolio is formulated based on firms' total carbon emissions, and in the right panel, the portfolio is based on firms' carbon intensity. Columns 1 and 5 only show regression results with intercept, the rest columns show regression results with various factors model.

### C. Firm Level Evidence

In the previous section, I constructed green and brown portfolios based on firms' total carbon emissions. Interestingly, my findings showcase the green portfolio's consistent outperformance over the brown counterpart. This observation deviates from traditional asset pricing theory. In this section, I present firm-level evidence to further illustrate the relationship between firms' carbon emissions and their stock returns.

1) Benchmark Result: Based on Equation 2, the findings are presented in Table VI, showcasing the results of firm-level analysis across two different fixed effects specifications for both the restricted and unrestricted models. In my approach, I use time-fixed effects at the month level. This choice serves to mitigate the impact of temporal variations across time, including the overall economic conditions, shifts in investors' sentiments in the stock market, the evolving concern for climate change, and other unobserved time-dependent factors. Columns 1 and 2 present the outcomes of

the regression analysis for the unrestricted and restricted models, respectively, both with Month + Industry two-way fixed effects. Notably, these techniques align with the methodologies employed by (5). By integrating industry-fixed effect, I effectively control for variations across distinct industries. This approach permits me to find the average correlation between firms' total carbon emissions and stock return cross-sectionally without the influence to which industry a firm belongs.

In column 1's unrestricted model, I observe a positive correlation between firms' total carbon emissions and stock returns. However, the near-zero R-squared value suggests limited explanatory power, possibly due to omitted variables. In column 2, I present the outcomes of the restricted model with a series of control variables, including Size, leverage, B/M, Inves/AT, PP&E, SaleGR, EPS, Stuff_num, Firm_age. I have noticed that the positive relationship between firms' total carbon emissions and stock returns continues, albeit without statistical significance. This contrasts with (5), who

<footnote>* p<.1, ** p<.05, *** p<.01</footnote>
find a significant positive relationship between stock returns and various scopes of carbon emissions by excluding firms from specific industries (GIC 19, 20, 23). In my analysis, I include all firms, regardless of their industry<fnref n="6" />. This result aligns with the classic asset pricing theory that higher risk exposure associates higher return compensation, however, this raises the question: Why does the firm-level analysis again yield results that contradict my portfolio analysis?

Fortunately, I am not the first to address this issue. (15) have warned the carbon premium should be treated cautiously and noted the high collinearity between firms’ carbon emissions and factors such as firm size, production volume, and industry classification. They suggest that this collinearity could significantly bias the estimated relationship between firms’ carbon emissions and stock returns. It is widely recognized that larger firms typically have higher carbon emissions, and firms with greater production or those in certain industries are likely to emit more carbon dioxide. However, industry-level fixed effects alone may not sufficiently account for this collinearity. my solution is to adopt Month + Entity (firm) two-way fixed effects to address this issue. Different from Month + Industry two-way fixed effects, with Month + Entity fixed effects, the analysis considers both time-specific variations and variations unique to individual entities (firms). By including Entity-fixed effects, I am accounting for firm-specific factors that may be constant over time but vary across different firms. This is a more stringent restriction by the assumption that investors not only distinguish industry-specific characteristics but also place a heightened emphasis on each firm’s specific inherent attributes. Columns 3 and 4 in Table VI showcase the results for un-/restricted models with this new specification.

First, it is important to note that the results remain consistent between the unrestricted models presented in columns 3 and 4. Then, the most intriguing revelation arises from the incorporation

of Month + Entity two-way fixed effects, leading to an astonishing sign reversal of the coefficient on carbon emissions. This change takes place under the assumption that investors place greater emphasis on each firm's intrinsic attributes rather than industry-specific characteristics. Specifically, firms with higher carbon emissions, implying increased exposure to climate risks, tend to exhibit lower stock returns on average. Importantly, this observation maintains both economic and statistical significance. And it's important to underscore that this finding aligns with the persistent outperformance of the green portfolio over the brown counterpart. Finally, given that the negative relationship between firm size and stock returns persists, the collinearity problem between carbon emissions and firm size in predicting stock returns, as brought up by (15) is confirmed. This is corroborated by Table III, which indicates a positive correlation between firms' carbon emissions and size, and both factors negatively correlate with stock returns.

2) *Robustness Check:* In the context of the regression model 2, the choice of fixed effects can vary depending on the underlying assumptions. In conventional cross-sectional stock return analyses, it is a common practice to assume significant heterogeneity between industries, with the belief that firms within a particular industry exhibit similar characteristics in terms of their stock returns. This assumption has garnered substantial empirical support in the existing literature. However, it's crucial to recognize that investors base their investment allocation decisions on more than just industry categorizations. While they may initially screen industries, their ultimate investment choices often depend on the specific attributes of individual companies. In such scenarios, even firms within the same industry can exhibit significant variations in their stock performance. Therefore, considering heterogeneity at the firm level may be a more suitable approach than relying solely on industry-level assumptions. In the following analysis, I perform a robustness check with various fixed effects and cluster standard errors at different levels.

The first six models depicted in Figure 15 include the benchmark model along with variations

<footnote n="6">⁶To align with their research design, I have applied winsorization to certain variables in my data set to mitigate the influence of outliers, a common practice in regression analysis. Detailed information about the data can be found in Table above.</footnote>
<table><caption>TABLE VI
FIRM LEVEL ANALYSIS</caption><thead><tr><th></th><th colspan="4">Returns</th></tr><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>CO2_tot</td><td>0.075*<br>(0.040)</td><td>0.034<br>(0.053)</td><td>-0.176**<br>(0.090)</td><td>-0.659***<br>(0.127)</td></tr><tr><td>Size</td><td></td><td>0.250**<br>(0.101)</td><td></td><td>1.535***<br>(0.197)</td></tr><tr><td>Levarage</td><td></td><td>-0.226<br>(0.203)</td><td></td><td>0.173<br>(0.422)</td></tr><tr><td>B/M</td><td></td><td>-1.879***<br>(0.181)</td><td></td><td>-2.729***<br>(0.276)</td></tr><tr><td>RoE</td><td></td><td>0.526***<br>(0.086)</td><td></td><td>0.292***<br>(0.101)</td></tr><tr><td>Inves/AT</td><td></td><td>-4.447***<br>(1.132)</td><td></td><td>-12.650***<br>(1.874)</td></tr><tr><td>PPE</td><td></td><td>-0.008<br>(0.048)</td><td></td><td>-0.426***<br>(0.162)</td></tr><tr><td>SaleGR</td><td></td><td>0.916***<br>(0.224)</td><td></td><td>0.799***<br>(0.237)</td></tr><tr><td>EPS</td><td></td><td>0.057***<br>(0.022)</td><td></td><td>0.018<br>(0.027)</td></tr><tr><td>Staff_num</td><td></td><td>-0.278***<br>(0.066)</td><td></td><td>-0.835***<br>(0.213)</td></tr><tr><td>Firm_age</td><td></td><td>-0.047<br>(0.065)</td><td></td><td>1.789***<br>(0.517)</td></tr><tr><td>Constant</td><td>0.162<br>(0.505)</td><td>0.526<br>(0.643)</td><td>3.353***<br>(1.137)</td><td>-3.421<br>(2.940)</td></tr><tr><td>Firm F.E.</td><td>No</td><td>No</td><td>Yes</td><td>Yes</td></tr><tr><td>Industry F.E.</td><td>Yes</td><td>Yes</td><td>No</td><td>No</td></tr><tr><td>Year-Month F.E.</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Obs</td><td>466999</td><td>295704</td><td>466999</td><td>295704</td></tr><tr><td>R-squared</td><td>0.000</td><td>0.013</td><td>0.000</td><td>0.019</td></tr></tbody></table>

This table presents the regression results depicting the influence of firms' CO2 emissions on stock returns. To account for potential dependencies within the data, the standard errors are clustered at the specified level along with the fixed effects integrated into the model.

involving different fixed effects. In the case of considering only the Entity fixed effect, I observe a coefficient of -0.81 for total carbon emissions, which is statistically significant at the 1% level. Similarly, when I incorporate both Entity and Year two-way fixed effects, the coefficient on carbon emissions remains statistically significant at the 1% level, with a slightly reduced value of -0.77. These specifications maintain consistency with the benchmark model, showing only minor coefficient adjustments. Moving on to models 4, 5, and 6, where I introduce industry fixed effects, Industry + Month, and Industry + Year two-way fixed effects, I observe a different pattern. In these models, the coefficients on carbon emissions all become statis-

tically insignificant and approach zero.

(37) in his seminar paper first introduced Robust standard errors in econometrics to account for heteroscedasticity. In Model 2, where I retain the same fixed effects as the benchmark model, the application of robust standard errors significantly increases statistical significance and narrows down the confidence intervals as depicted by the 7th model in Figure 15. Furthermore, as highlighted by (38), when dealing with panel data the residuals may be correlated across firms or across time. In such cases, standard errors can be biased. To mitigate this, Petersen recommends clustering standard errors at the same level, as is done in my benchmark model. Additionally, (39) advocates for clustering

<footnote>* p<.1, ** p<.05, *** p<.01</footnote>
standard errors at a level one step above the sample data. In line with this recommendation, I cluster the standard errors at the industry and year level for the benchmark model to test its robustness. After applying clustering to standard errors at the Industry + Year level, I observe a slight increase in standard errors compared to the benchmark model. Nonetheless, the results remain statistically significant at the 1% level, as shown by the last model in Figure 15.

<figure><img src="image_10.png" /><figcaption>Fig. 16. *</figcaption></figure>

This graphic presents coefficients and associated confidence intervals for various fixed effects and clustered standard error configurations. The benchmark model includes Entity + Month fixed effects, with standard errors clustered at the same level. In the 'Fixed Effects' group, I explore different fixed effects for each model, while maintaining standard errors clustered at the same level. In the 'Clustered Standard Errors' group, I examine how standard errors are clustered at various levels while keeping the fixed effects consistent with the benchmark model.

## D. Expalin the Contradiction Between Empirical and Theoretical Studies

Building upon the equilibrium model by (21) and (40), along with the demand system asset pricing model by (24), I aim to present empirical evidence supporting the notion that a shift in financial market preferences due to climate change has led to the observed contradiction between empirical findings and classic asset pricing theory, regarding the risk-return puzzle.

1) Quantify the Preference Shift in the Financial Market: The shift in financial market preferences due to unanticipated climate change risks can be measured using the Unexpected Media Climate

Change Concern Index (UMC), developed by (22). To construct this index, they gather news from eight major U.S. newspapers and two prevalent newswires, known for their extensive circulation. For each article, a unique "concern score" is assigned, reflecting the degree of negativity and risk addressed in the content. Considering the diversity in coverage, thematic focus, and levels of concern, they normalize the scores of individual articles adjusting for heterogeneity across newspapers. These normalized scores are then aggregated to form a comprehensive daily Media Climate Change Concern Index (MCCC)<fnref n="7" />, encapsulating the overall media sentiment on climate change. The historical trajectory of the monthly MCCC index is plotted in Figure 17.

<figure><img src="image_11.png" /><figcaption>Fig. 18. *
This figure presents the monthly MCCC (Media Climate Change Concerns) index from 2003 to 2022 together with the major climate-related events.</figcaption></figure>

Ardia et al. construct the UMC by calculating the difference between actual *MCCC*<sub>t</sub> and its expected *MCCC*<sub>t</sub> index by an ARX model as specified in Equation 8. Their model incorporates a variety of control variables, including the FF5 factors, momentum factor, WTI return, gas return,

<footnote n="7">⁷It is noteworthy that several other studies have explored text-based methodologies for constructing similar indices, including (41), (42), and (43).</footnote>
propane return, U.S. economic policy uncertainty index, VIX, TED spread, term factor, default factor, etc. In my study, I use a different set of control variables in the model, which includes the FF5 factors, CFNAI index, investor sentiment index, WTI index, VIX index, and a lagged one-period MCCC index to compute UMC, but the difference between the resultant two UMC indices is found to be negligible. The construction of the UMC index makes it an appropriate proxy for measuring shifts in market preferences. An increase in UMC, indicating heightened concerns about climate change risks, is likely to bolster investor demand for green assets and lead to divestment from brown ones, and vice versa.

$$MCCC_t = \alpha + \beta MCCC_{t-1} + \gamma Controls_t + \epsilon \quad (8)$$

2) Portfolio analysis with UMC: Next, I are going to test my hypothesis empirically by using regression analysis as outlined by the Equation 4, wherein I regress GMB, Green, Brown, and Neutral<fnref n="8" /> portfolios on UMC. As presented in Table VII, the regression findings illuminate the outcomes of diverse portfolios structured based on firms' CO2 emissions in relation to the UMC index, accompanied by a set of control variables.

For the green portfolio, as shown in the second column of Table VII, the coefficient on UMC is 1.786. This suggests that a one-unit increase in the UMC index could lead to a 1.786% increase in returns for the green portfolio. Conversely, for the brown portfolio (third column), the coefficient on UMC is -1.263%, indicating that a one-unit increase in the UMC index could result in a 1.263% decrease in returns. These results strongly support the idea that shifts in financial market preferences due to climate change significantly impact the returns of green and brown assets. An increase in climate change concerns favors green assets and, conversely, reduces the returns of brown assets. For the GMB portfolios, the coefficient on UMC is 3.049,

implying that a one-unit increase in UMC could lead to an average return increase of 3.049% for GMB portfolios. All the results mentioned demonstrate both economic and statistical significance at the 1% level. In contrast, for the neutral portfolio, the coefficient on UMC is relatively minor and does not reach statistical significance.

3) Firm level analysis with UMC: In the firm-level analysis of the previous section, I observe a negative relationship between firms' carbon emissions and stock returns, particularly when employing Month + Entity two-way fixed effects. I propose that this negative relationship may stem from a shift in financial market preferences, motivated by a desire to hedge against climate change risks and a growing commitment to sustainable investing. A likely hypothesis is that during periods of heightened climate concern, firms with higher CO2 emissions (i.e., more environmentally impactful) tend to see lower stock returns. This outcome occurs as investors increasingly avoid brown stocks in favor of green ones, leading to a surge in demand and consequently higher returns for green assets. Following Equation 5, I further explore how the interaction between firms' carbon emissions and the UMC index impacts stock returns.

Table VIII presents the regression results for Model 5. Alongside a list of control variables reflecting firms' fundamental characteristics such as size, leverage, B/M, RoE, Investment, PP&E, SaleGR, EPS, staff number, and firm age (included in Controlsᵢₜ), I also incorporate variables to capture global macroeconomic conditions, including the FF5 factors, investor sentiment, WTI index, CFNAI index, and VIX. Across all specifications, the coefficient on CO₂_totᵢₜ consistently displays a statistically significant negative relationship with stock returns, in line with the results in Table VI. Additionally, the coefficient on UMC_t is consistently positive, suggesting that higher unexpected climate concerns correlate with increased stock returns. Moreover, the coefficient on interactionᵢₜ remains negative across various controls. As Equation 7 indicates, this implies that during periods of heightened unexpected climate concern, the stock returns of brown firms, identified by higher total

<footnote n="8">⁸It is important to clarify that the neutral portfolio does not signify null CO2 emissions. Instead, firms within this portfolio exhibit total carbon emissions ranging between the 34th and 66th percentiles across the entire sample.</footnote>
<table><caption>TABLE VII
GREEN - BROWN ON UMC</caption><thead><tr><th rowspan="2"></th><th colspan="4">Dependent Variable</th></tr><tr><th>Green-Brown</th><th>Green</th><th>Brown</th><th>Neutral</th></tr></thead><tbody><tr><td>Intercept</td><td>1.310<br>(1.179)</td><td>1.665**<br>(0.844)</td><td>0.355<br>(0.857)</td><td>1.040**<br>(0.430)</td></tr><tr><td>UMC</td><td>3.049***<br>(1.029)</td><td>1.786**<br>(0.736)</td><td>-1.263*<br>(0.748)</td><td>-0.029<br>(0.375)</td></tr><tr><td>Mkt_RF</td><td>0.083<br>(0.080)</td><td>0.920***<br>(0.057)</td><td>0.837***<br>(0.058)</td><td>0.965***<br>(0.029)</td></tr><tr><td>SMB</td><td>1.079***<br>(0.133)</td><td>0.724***<br>(0.095)</td><td>-0.355***<br>(0.096)</td><td>0.318***<br>(0.048)</td></tr><tr><td>HML</td><td>-0.557***<br>(0.122)</td><td>-0.216**<br>(0.088)</td><td>0.341***<br>(0.089)</td><td>-0.008<br>(0.045)</td></tr><tr><td>RMW</td><td>-0.164<br>(0.167)</td><td>-0.198*<br>(0.119)</td><td>-0.033<br>(0.121)</td><td>-0.024<br>(0.061)</td></tr><tr><td>CMA</td><td>0.112<br>(0.208)</td><td>0.041<br>(0.149)</td><td>-0.070<br>(0.151)</td><td>-0.145*<br>(0.076)</td></tr><tr><td>SENT</td><td>1.277**<br>(0.611)</td><td>0.971**<br>(0.437)</td><td>-0.306<br>(0.444)</td><td>0.072<br>(0.223)</td></tr><tr><td>WTI</td><td>-0.010<br>(0.012)</td><td>-0.014*<br>(0.009)</td><td>-0.005<br>(0.009)</td><td>-0.006<br>(0.004)</td></tr><tr><td>CFNAI</td><td>-0.046<br>(0.200)</td><td>0.121<br>(0.143)</td><td>0.167<br>(0.145)</td><td>-0.016<br>(0.073)</td></tr><tr><td>VIX</td><td>0.037<br>(0.040)</td><td>0.062**<br>(0.028)</td><td>0.025<br>(0.029)</td><td>0.016<br>(0.014)</td></tr><tr><td>Obs</td><td>227</td><td>227</td><td>227</td><td>227</td></tr><tr><td>R-squared</td><td>0.368</td><td>0.742</td><td>0.590</td><td>0.903</td></tr></tbody></table>

This table represents the regression results of Green-Brown, Green, Brown, and Neutral portfolios on the UMC index and a group of control variables. (22) constructed the MCCC index since January 2003, hence the number of observations is less than 240. The Green Portfolio contains firms with total CO2 emissions up to the 20rd percentile, Neutral Portfolio contains firms with total CO2 emissions ranging from the 40th to 60th percentile, and firms with CO2 emissions higher than the 80th percentile are included in the Brown Portfolio. Green-Brown Portfolio is the monthly difference between Green and Brown portfolios.

CO2 emissions, tend to decrease further, green stocks on the contrary are benefited from the unexpected climate change concerns, with the statistical significance maintained at the 1% level.

## V. CONCLUSION

This paper seeks to unravel a paradox that has emerged in recent years in the realm of sustainable investing. On one hand, the aggregate performance of Green portfolios, composed of companies with lower carbon emissions or higher ESG (Environmental, Social, and Governance) scores, has exhibited a consistent and noteworthy outperformance compared to their Brown counterparts. This phenomenon is commonly referred to as the "green premium" and is attributed to the increasing concerns surrounding climate change and environmen-

tal sustainability. It reflects a growing trend among investors who are increasingly inclined to allocate capital to assets that align with sustainable and environmentally responsible practices.

However, when I shift my focus to the firm-level empirical analysis, a seemingly contradictory picture emerges. Here, the data often presents a different narrative, one where Brown firms, those associated with higher carbon footprints or lower ESG scores, appear to yield higher expected stock returns. This observation challenges the conventional wisdom of sustainable investing and introduces the notion of a "climate risk premium." Investors seem to be demanding higher returns as compensation for investing in companies with perceived sustainability and climate-related risks.

The existence of this paradox raises crucial ques-

<footnote>* p<.1, ** p<.05, *** p<.01</footnote>
<table><caption>TABLE VIII
CROSS-SECTION STOCK RETURN WITH UMC</caption><thead><tr><th rowspan="2"></th><th colspan="4">Dependent variable: Return</th></tr><tr><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>CO2_tot</td><td>-0.569***<br>(0.112)</td><td>-0.580***<br>(0.109)</td><td>-0.580***<br>(0.109)</td><td>-0.578***<br>(0.111)</td></tr><tr><td>UMC</td><td>1.648***<br>(0.402)</td><td>1.688***<br>(0.401)</td><td>1.460***<br>(0.403)</td><td>1.749***<br>(0.405)</td></tr><tr><td>interaction</td><td>-0.135***<br>(0.029)</td><td>-0.145***<br>(0.028)</td><td>-0.133***<br>(0.029)</td><td>-0.150***<br>(0.029)</td></tr><tr><td>Mkt_RF</td><td>0.999***<br>(0.010)</td><td>0.909***<br>(0.009)</td><td>0.915***<br>(0.008)</td><td>0.949***<br>(0.009)</td></tr><tr><td>SMB</td><td></td><td>0.383***<br>(0.013)</td><td>0.360***<br>(0.013)</td><td>0.321***<br>(0.013)</td></tr><tr><td>HML</td><td></td><td>0.012<br>(0.010)</td><td>0.002<br>(0.010)</td><td>0.046***<br>(0.010)</td></tr><tr><td>RMW</td><td></td><td></td><td>-0.065***<br>(0.014)</td><td>-0.042***<br>(0.015)</td></tr><tr><td>CMA</td><td></td><td></td><td>0.063***<br>(0.016)</td><td>0.048***<br>(0.016)</td></tr><tr><td>SENT</td><td></td><td></td><td></td><td>-0.497***<br>(0.042)</td></tr><tr><td>WTI</td><td></td><td></td><td></td><td>-0.009***<br>(0.001)</td></tr><tr><td>CFNAI</td><td></td><td></td><td></td><td>0.012<br>(0.013)</td></tr><tr><td>VIX</td><td></td><td></td><td></td><td>0.047***<br>(0.003)</td></tr><tr><td>Constant</td><td>1.828<br>(1.915)</td><td>1.100<br>(1.940)</td><td>0.992<br>(1.946)</td><td>-0.911<br>(1.936)</td></tr><tr><td>Controls</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Entity F.E.</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Obs</td><td>295215</td><td>295215</td><td>295215</td><td>295215</td></tr><tr><td>R-squared</td><td>0.203</td><td>0.212</td><td>0.213</td><td>0.215</td></tr></tbody></table>

tions and calls for a deeper examination. Why do Green portfolios, at the aggregate level, consistently outperform their Brown counterparts when firm-level data suggests otherwise? Is the green premium truly a reflection of superior financial performance, or are there underlying factors that need to be considered? Moreover, what explains the climate risk premium observed at the firm level, and how do these findings align with the broader goals of sustainable and responsible investing?

This paper embarks on a comprehensive journey to dissect these questions and shed light on the complex and evolving landscape of sustainable investing. By conducting rigorous analyses that combine cross-sectional evidence, portfolio performance assessments, and firm-level empirical investigations,

I find that, under different assumptions with varying model specifications, firm-level results coincide with aggregate portfolio analysis. Specifically, Brown firms with higher carbon footprints are more exposed to climate change-related risks and tend to underperform Green firms with lower carbon footprints in terms of stock returns, particularly when there are heightened concerns about unexpected climate change. Through these endeavors, I aim to provide valuable insights that can inform investment decisions, drive sustainable practices, and contribute to a more nuanced understanding of the relationship between sustainability and financial returns in the context of my ever-changing global landscape

<footnote>* p<.1, ** p<.05, *** p<.01</footnote>
REFERENCES

[1] S. FUND, "Sustainable development goals," Available at this link: https://www.un.org/sustainabledevelopment/inequality, 2015.

[2] B. Paribas, "The esg global survey 2023 (4th edition)," BNP Paribas Securities Services, Tech. Rep., 2023.

[3] D. Avramov, S. Cheng, A. Lioui, and A. Tarelli, "Sustainable investing with esg rating uncertainty," *Journal of Financial Economics*, vol. 145, no. 2, pp. 642–664, 2022.

[4] L. Pástor, R. F. Stambaugh, and L. A. Taylor, "Dissecting green returns," *Journal of Financial Economics*, vol. 146, no. 2, pp. 403–424, 2022.

[5] P. Bolton and M. Kacperczyk, “Do investors care about carbon risk?” *Journal of Financial Economics*, vol. 142, no. 2, pp. 517–549, 2021.

[6] D. Machin and Y. Liu, “How tick list sustainability distracts from actual sustainable action: the un 2030 agenda for sustainable development,” *Critical discourse studies*, vol. 21, no. 2, pp. 164–181, 2024.

[7] M. Folque, E. Escrig-Olmedo, and T. Corzo Santamaría, “Integration of advanced sri practices into the european asset management industry: A survey of drivers,” *SAGE Open*, vol. 14, no. 1, p. 21582440241237893, 2024.

[8] B. Cheng, Y. Ma, and S. Lu, “Carbon emission risk and corporate employment creation: Evidence from a quasi-natural experiment based on the paris agreement,” *Managerial and Decision Economics*, vol. 45, no. 2, pp. 685–701, 2024.

[9] P. Krueger, Z. Sautner, and L. T. Starks, “The importance of climate risks for institutional investors,” *The Review of Financial Studies*, vol. 33, no. 3, pp. 1067–1111, 2020.

[10] R. Faccini, R. Matin, and G. Skiadopoulos, "Dissecting climate risks: Are they reflected in stock prices?" *Journal of Banking & Finance*, vol. 155, p. 1069-48, 2023.

[11] G. T. Garvey, M. Iyer, and J. Nash, “Carbon footprint and productivity: does the “e” in esg

capture efficiency as well as environment," *Journal of Investment Management*, vol. 16, no. 1, pp. 59-69, 2018.

[12] S. Y. In, K. Y. Park, and A. Monk, “Is “being green” rewarded in the market? an empirical investigation of decarbonization risk and stock returns,” *International Association for Energy Economics (Singapore Issue)*, vol. 46, no. 48, 2017.

[13] M. Andersson, P. Bolton, and F. Samama, “Hedging climate risk,” *Financial Analysts Journal*, vol. 72, no. 3, pp. 13–32, 2016.

[14] P.-h. Hsu, K. Li, and C.-y. Tsou, “The pol- lution premium,” *The Journal of Finance*, vol. 78, no. 3, pp. 1343–1392, 2023.

[15] J. Aswani, A. Raghunandan, and S. Rajgopal, “Are carbon emissions associated with stock returns?” *Review of Finance, forthcoming*, 2023.

[16] M. Baker, D. Bergstresser, G. Serafeim, and J. Wurgler, “Financing the response to cli- mate change: The pricing and ownership of us green bonds,” National Bureau of Economic Research, Tech. Rep., 2018.

[17] O. D. Zerbib, “A sustainable capital asset pricing model (s-capm): Evidence from envi- ronmental integration and sin stock exclusion,” *Review of Finance*, vol. 26, no. 6, pp. 1345– 1388, 2022.

[18] S. Chava, “Environmental externalities and cost of capital,” *Management Science*, vol. 60, no. 9, pp. 2223–2247, 2014.

[19] P. Bolton and M. Kacperczyk, “Global pricing of carbon-transition risk,” National Bureau of Economic Research, Tech. Rep., 2021.

[20] M. Görgen, A. Jacob, M. Nerlinger, R. Rior- dan, M. Rohleder, and M. Wilkens, “Carbon risk,” *Available at SSRN 2930897*, 2020.

[21] L. Pástor, R. F. Stambaugh, and L. A. Taylor, “Sustainable investing in equilibrium,” *Journal of Financial Economics*, vol. 142, no. 2, pp. 550–571, 2021.

[22] D. Ardia, K. Bluteau, K. Boudt, and K. In- ghelbrecht, “Climate change concerns and the performance of green vs. brown stocks,” *Management Science*, 2022.
[23] E. Ilhan, Z. Sautner, and G. Vilkov, “Carbon tail risk,” *The Review of Financial Studies*, vol. 34, no. 3, pp. 1540–1571, 2021.

[24] R. S. Koijen and M. Yogo, “A demand system approach to asset pricing,” *Journal of Political Economy*, vol. 127, no. 4, pp. 1475–1515, 2019.

[25] X. Gabaix and R. S. Koijen, “In search of the origins of financial fluctuations: The inelastic markets hypothesis,” National Bureau of Economic Research, Tech. Rep., 2021.

[26] S. M. Hartzmark and D. H. Solomon, “Predictable price pressure,” National Bureau of Economic Research, Tech. Rep., 2022.

[27] L. Engberg-Pedersen, “Is the influence of neoliberalism on development norms waning? evidence from the addis ababa action agenda and the 2030 agenda for sustainable development,” *Development Policy Review*, vol. 39, no. 4, pp. 682–700, 2021.

[28] I. Kelman, “Climate change and the sendai framework for disaster risk reduction,” *International Journal of Disaster Risk Science*, vol. 6, pp. 117–127, 2015.

[29] R. S. Dimitrov, “The paris agreement on climate change: Behind closed doors,” *Global Environmental Politics*, vol. 16, no. 3, pp. 1–11, 2016.

[30] G. Perez-Quiros and A. Timmermann, “Firm size and cyclical variations in stock returns,” *The Journal of Finance*, vol. 55, no. 3, pp. 1229–1262, 2000.

[31] T. J. George and C.-Y. Hwang, “A resolution of the distress risk and leverage puzzles in the cross section of stock returns,” *Journal of financial economics*, vol. 96, no. 1, pp. 56–79, 2010.

[32] O. A. Lamont, “Investment plans and stock returns,” *The Journal of Finance*, vol. 55, no. 6, pp. 2719–2745, 2000.

[33] E. F. Fama and K. R. French, “A five-factor asset pricing model,” *Journal of Financial Economics*, vol. 116, no. 1, pp. 1–22, 2015.

[34] ——, “Common risk factors in the returns on stocks and bonds,” *Journal of Financial Economics*, vol. 33, no. 1, pp. 3–56, 1993.

[35] N. Jegadeesh and S. Titman, “Returns to buying winners and selling losers: Implications for stock market efficiency,” *The Journal of finance*, vol. 48, no. 1, pp. 65–91, 1993.

[36] L. Pástor and R. F. Stambaugh, “Liquidity risk and expected stock returns,” *Journal of Political economy*, vol. 111, no. 3, pp. 642–685, 2003.

[37] H. White, “A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity,” *Econometrica*, pp. 817–838, 1980.

[38] M. A. Petersen, “Estimating standard errors in finance panel data sets: Comparing approaches,” *The Review of Financial Studies*, vol. 22, no. 1, pp. 435–480, 2008.

[39] J. D. Angrist and J.-S. Pischke, *Mostly harmless econometrics: An empiricist's companion*. Princeton University Press, 2009.

[40] L. H. Pedersen, S. Fitzgibbons, and L. Poerski, “Responsible investing: The efficient frontier,” *Journal of Financial Economics*, vol. 142, no. 2, pp. 572–597, 2021.

[41] R. F. Engle, S. Giglio, B. Kelly, H. Lee, and J. Stroebel, “Hedging climate change news,” *The Review of Financial Studies*, vol. 33, no. 3, pp. 1184–1216, 2020.

[42] F. Kapfhammer, V. H. Larsen, and L. A. Thorsrud, “Climate risk and commodity currencies,” 2020.

[43] R. Faccini, R. Matin, and G. Skiadopoulos, “Are climate change risks priced in the us stock market?” Danmarks Nationalbank Working Papers, Tech. Rep., 2021.