Empirical Asset Pricing Models for Green, Grey, and Red EU Securities: A Fama–French and Carhart Model Approach

Abstract

This study examines the explainability, validity, and applicability of multi-factor models in explaining the returns of Green (eco-friendly), Grey (neutral), and Red (environmentally harmful) EU securities. We apply the Fama–French three-factor and five-factor models, along with the Carhart four-factor model, to analyze changes in risk exposures and adjusted abnormal returns (alphas) before and after the 2009 global financial crisis (GFC). Green and Grey securities exhibit positive SMB loadings, while Grey’s HML shifts from negative to positive over time. Both Green and Red securities show positive SMB and HML factors but negative alphas in the second period, indicating systematic underperformance. Additionally, for Red assets, momentum (MOM), profitability (RMW), and investment (CMA) factors are positive and significant in the first period but become insignificant or negative later. These findings highlight structural shifts in factor exposures and contribute to the ongoing debate on the most suitable classical asset pricing framework for environmentally classified assets, offering insights into the effectiveness of traditional factor models in different classes of environmental assets in finance. Lastly, the three-factor model better captures the common variation in Green and Grey asset returns. Specifically, the 4-factor model and the HML Devil factor prove to be more effective in explaining returns for Red securities.

1. Introduction

The global landscape is witnessing a significant surge in environmental consciousness, with reusing, recycling, and other eco-friendly acts emerging as key drivers of change. Companies with environmental awareness have captivated the attention of researchers, organizations, firms, institutions, and lawmakers. The firm’s aim is profit maximization, but firms competitive environments drive them to facilitate actions and behaviours that bring about environmental improvements for the betterment of society and nature. Consequently, Green stocks possess an inherent allure for investors of all kinds, creating a perception of potentially safe returns by aligning with environmental companies. This research seeks to find answers to the following research questions: (a) Which securities are characterized as Green, Grey, and Red/Brown? (b) How do expected returns vary across these assets? (c) What are the risk exposures that define the asset category returns of Green, Grey, and Red investments? By exploring these questions, this study aims to contribute to a comprehensive understanding of the nature and implications of sustainable investments, thereby informing investment strategies and decision-making in the financial markets.

In the context of financial markets, the terminology associated with ‘Green’ financial instruments, such as eco-investment, Green investment, Green banking, Green stocks, Green bonds, Green mutual funds, Green savings accounts, and Green certificates of deposit, can indeed seem multifaceted and potentially perplexing. However, it is important to clarify that these designations collectively signify a concerted effort towards environmentally responsible investments and sustainable practices. If it is not Green, is it Red or Grey? Unlike their counterparts that might fall into ‘Red’ or ‘Grey’ or unspecified categories, which often involve industries and practices with harmful ecological footprints, ‘Green’ instruments exclude such ventures from their purview.

Extensive academic and financial research has leveraged the Fama–French framework to analyze cross-sectional stock returns by integrating market risk premiums, size effects, and value factors (Fama & French, 1993). Building upon this foundation, Fama and French (2015) expanded their model by introducing two additional variables—profitability and investment—leading to the development of a more comprehensive five-factor asset pricing model. Despite this advancement, their model has struggled to fully account for anomalies in stock returns linked to firm size, the book-to-market ratio, liquidity, price–earnings ratio, cash flow–price ratio, return on equity, volatility, and return reversals (Zhang & Lence, 2022).

Subsequent studies further explored the model’s effectiveness across different regions. Fama and French (2017) found that, in North America, Europe, and the Asia–Pacific region, stock returns exhibited a positive correlation with the book-to-market (B/M) ratio and profitability but a negative association with investment. However, in Japan, while the B/M ratio remained a significant determinant of returns, the relationships with profitability and investment were considerably weaker. Recognizing the need for additional refinement, Fama and French (2018) extended their framework to a six-factor model by incorporating momentum as an explanatory variable. Their study also underscored several methodological challenges in refining factor-based pricing models, including (1) the choice between cash profitability and operating profitability in constructing profitability factors, (2) the selection of long–short spread factors versus excess returns, and (3) whether factors should be based on distinct stock sizes or encompass a broader range of assets.

The applicability of these multi-factor models has been extensively examined in various markets and asset classes. Empirical evidence suggests that while the Fama–French framework performs well in developed equity markets, its predictive power varies across emerging markets and alternative asset classes such as bonds, commodities, and currencies (Cakici, 2015; Guo et al., 2017; Chiah et al., 2019; Erdinc, 2018). These studies highlight both the strengths and limitations of multi-factor models, emphasizing the need for further refinements to enhance their robustness in different financial environments.

The following section presents how previous research categorized stocks at the industry level and how the classification is ambiguous. Even though the institutions have different types of sector classifications, the greatest problem is figuring out if the company’s business activity is (‘really’) beneficial for the environment. Previous research (Badia et al., 2019; Brammer et al., 2009; Climent & Soriano, 2011; Gbenga & Steffen, 2015) focused on the performance of portfolios or funds, which include Green and Red stocks, or just Green, or just a subsector of the Red category. This research contributes to bridging the gap in the prior literature and seeks to find the common relationship and, at the same time, the differences between Green, Grey, and Red security returns by studying the macro-factor exposure. By looking at the overall exposure of environmentally friendly, moderately environmentally friendly, and less environmentally friendly securities to these factors and analyzing how they react to the economy’s ups and downs, participants can gain a deeper understanding of the dynamic interactions between environmental sustainability and financial performance.

In this study, the stock sample is generated from the European market securities. The analysis explores the factors over time and also separates them into two time periods, (i) the ex-crisis and (ii) post-crisis level (with a breakpoint in the year 2009). For this reason, this analysis has two parts. The first part is about how the stocks are grouped. The classification stems from a specific table, which is collected from previous research and reports of financial institutions. Furthermore, the other part is about assessing the risk exposure and how the specific class of securities performs in the market with the asset pricing models, which describe the securities’ return based on equilibrium theories and the models from the previous literature.

The paper is organized as follows: The following sections discuss how previous researchers classified the Green, Grey, and Red/Brown categories, as well as the asset pricing models, which are used for these three categories. Section 3 describes the data collection process and filtering among the Green, Red (or Brown), and Grey stocks. The next part of this research illustrates the methodology and the notion behind the Fama–French models (3FF and 5FF) and the Carhart Model (4-factor model). Section 5 examines the main research questions with the use of empirical models. Section 5 describes the main findings of this research and includes a discussion of improvements and applications of these models.

2. Identifying the Asset Class: Green, Grey, and Red

This section aims to review prior research that provided classifications for Green, Red (or Brown), and Grey securities. By examining previous research contributions, participants and investors can gain a comprehensive understanding of the categorizations and definitions associated with these distinct types of securities. The primary measure is the business activities that the company engages in as an entity that offers a classification in a specific group as a Green, Red (or Brown), or Grey asset.

According to the report by the Kepler Cheuvreux (2015) institution, the FTSE (Financial Times Stock Exchange) was the pioneering institution to introduce the Low-Carbon Economy Industry Classification Scheme (LCEIC). This scheme categorizes industries into seven high-level sectors and twenty-nine subsectors, as outlined in

Table A1. FTSE environmental sectors and subsectors.

E1.0 Renewable and Alternative Energy	E2.0 Energy Efficiency	E3.0 Water Infrastructure and Technologies	E4. 0 Pollution Control	E 5.0 Waste Management and Technologies	E6.0 Environmental Support Services	E 7.0 Food, Agriculture and Forestry
E1.1 Wind Power Generation Equipment	E2.1 Power Network Efficiency	E3.1 Water Infrastructure	E4.1 Pollution Control Solutions	E5.1 Waste Technology Equipment	E6.1 Carbon and Other Environmental Assets Trading	E7.1 Sustainable and Efficient Agriculture
E1.2 Solar Energy Generation Equipment	E2.2 Industrial Energy Efficiency	E3.2 Water Treatment Equipment	E4.2 Environmental Testing and Gas Sensing	E5.2 Recycling and Value Added Waste Processing	E6.2 Environmental Consultancies	E7.2 Logistics and Food Safety and Packaging
E1.3 Other Renewables Equipment	E2.3 Buildings Energy Efficiency	E3.3 Water Utilities		E5.3 Hazardous Waste Management	E6.3 Diversified Environmental	E7.3 Sustainable Forestry and Plantations
E1.4 Renewable Energy Developers and IPPs	E2.4 Transport Energy Efficiency	E3.4 Diversified Water Infrastructure and Technology		E5.4 General Waste Management
E1.5 Biofuels	E2.5 Consumer Energy Efficiency			E5.5 Diversified Waste and Technology
E1.6 Diversified Renewable and Alternative Energy	E2.6 Diversified Energy Efficiency

Note: This table shows a classification within the Green sector. Source: FTSE and Kepler Cheuvreux (2015).

, provided in the Appendix A. Another institution is MSCI, which employs a different classification type, comprising five themes and thirty-seven technologies. Themes that can be identified as ‘contentious’ or ‘Grey’ (e.g., biofuels and general waste management) are included in both the FTSE and MSCI classifications. In order to distinguish the ‘Green’ from the others, these classifications have their benchmarks and are best tailored to industry-level research. In this potentially controversial environment, clarity and transparency are essential. Investors and researchers need to decide which research to follow—whether a consistent classification or a dubious one that varies over time or across databases. It is crucial for them to understand the industry of the companies and exercise caution with category fits in contentious areas. FTSE classification is based on the ‘industrial test of utility’, which evaluates how the investor is economically involved in the solution, including both mitigation and adaptation operations. Therefore, Green stocks are concentrated mainly in areas such as alternative energy, pollution control, carbon reduction, and recycling (

Table 1. Contentious, Grey, Red, and Green sectors.

Contentious	Grey	Red	Green
Gas-fired power, bioenergy, hydropower, nuclear power		Fossil fuels	Solar and wind
Energy efficiency without credentials/standards, or from the perspective of fossil fuels, or at risk of the “rebound effect”			Energy efficiency
	Agri-food
	Real estate
	Forestry
Waste management			Recycling and composting
	Transport		Electric and alternative mobility
	ICT

Source: Kepler Cheuvreux, CBI, FTSE, MSCI, and Kottas (2024).

).

Cojoianu et al. (2020) adapted different types of classifications by studying the environmental policies and also the new regional environmental knowledge, which affects the Green (environmental), Red (fossil fuel), and Grey (unrelated to natural resources) technologies. Furthermore, his papers refer to the industries that aim to minimize or facilitate the responsible use of environmental degradation as ‘Green’. Within the Grey category, certain industries have been excluded from consideration due to damage to the environment, the exploitation of environmental policies for company gains, and a reliance on natural resources. The final category is the “Brown”; these industries are expected to be significantly influenced by further environmental policies due to their dependency on natural resources and environmental externalities. Additionally, this category is concentrated on non-renewable resources (

Table 2. Industry classification matching.

SASB Industry Classification	Crunchbase Classification	Paper Terminology
Renewable Resources and Alternative Energy and Infrastructure (Utilities and Waste Management).	Battery, Biofuel, Biomass Energy, Clean Energy, CleanTech, Electric Vehicle, Electrical Distribution, Energy Efficiency, Energy Management, Energy Storage, Environmental Consulting, Environmental Engineering, Fuel Cell, Green Building, Green Consumer Goods, GreenTech, Paper Manufacturing, Pollution Control, Power Grid, Renewable Energy, Smart Building, Smart Home, Solar, Sustainability, Timber, Waste Management, Water, Water Purification, Water Transportation, Wind Energy, Wood Processing, and Recycling	Green
Non-Renewable Resources	Fossil Fuels, Fuel, Mineral, Mining Technology, Natural Resources, Oil and Gas, Precious Metals, and Mining	Brown
Healthcare, Financials, Technology and Communications, Transportation, Services, Consumption, and Infrastructure (Infrastructure and Real Estate).	Software, Biotech, Healthcare, Telecommunications, Real Estate, and Other Sectors, Excluding the Ones Above.	Grey

Source: Cojoianu et al. (2020).

).

Previous work by Bolton and Kacperczyk (2021) and Bolton et al. (2022) classified the securities into two categories: Brown and Green. The classification based on carbon emissions is a different approach from this research to measure the Green and Brown companies. The “Brown” securities represent higher-emitting firms, while the “Green” securities represent lower-emitting firms. In the classification of securities into Green and Brown categories, In et al. (2019) and Cheema-Fox et al. (2021) proposed an alternative approach based on emissions scaled by firm size, known as emission intensity. This method allows for a more nuanced assessment of a company’s carbon footprint by considering emissions relative to its operational scale, providing a valuable perspective for investors and policymakers aiming to make informed decisions in the context of climate change and finance. Bauer et al. (2022) applied a combination of the previous two. The methodology was employed to assess the degree of “greenness” by quantifying the level or intensity of CO₂ emissions reported by the emitting entities. By utilizing this approach, they aimed to evaluate the environmental impact of various entities and identify the extent of their carbon footprint. The utilization of CO₂ emissions as a metric enables us to gauge the environmental performance of different entities and discern their commitment to sustainable practices. Lastly, Pástor et al. (2021, 2022) employed the classification based on Environmental, Social, and Governance (ESG) ratings using the “E” component. By leveraging this approach, they were able to determine the environmental sustainability of individual companies and subsequently shortlist them into distinct two categories, namely Green and Brown. This method allowed them to effectively categorize securities based on their environmental practices, aiding investors and stakeholders in making more environmentally conscious investment decisions. The drawbacks of these methods manifest in the variability and consistency of both scores and carbon emissions across different databases.

This research adopts Table 1 to classify the stock universe based on environmental activity. The adoption of an industry-level classification system is performed to provide a clear and consistent framework for analysis. This approach mitigates the inconsistencies and variability found in classifications that rely solely on environmental policies, carbon emissions, or ESG ratings. By focusing on industry-specific classifications, our research offers a more stable and comparable basis for understanding different sectors’ environmental impacts and financial performance. The categorization is aimed at organizing the stocks into meaningful groups, which will enable us to analyze and compare their environmental performance within specific segments. By using reliable institutional reports and adhering to established standards, this analysis ensures the accuracy and consistency of the classification, which is crucial for drawing meaningful conclusions and implications from the research findings.

3. Factor Models

The factor models apply firm-specific and other characteristics that were documented as explaining differences in returns among stocks. The general form to study specific-asset class returns with the factor models can be estimated in their linear form for a fixed time t as Equation (1):

r = B f + e

(1)

where r is the n × 1 column vector of the n asset returns in the investment universe (in this case Green, Red, or Grey), B is the n × k matrix that contains the factor exposures or loadings for the k factors for each asset, f is the k × 1 column vector of factors, and e is the error term or asset-specific component of the returns r.

In theory, the single factor model refers to the CAPM and suggests that the variation in the expected returns on the risky security is explained by the market’s excess return (to a certain degree). The beta coefficient measures the asset’s sensitivity to market movements, the change in the asset’s return in relation to the changes in the overall market portfolio’s return. On the other hand, the alpha coefficient (or Jensen alpha), named after economist Michael Jensen (1967), is a measure of the alpha returns of an asset. In other words, the alpha quantifies the generated returns beyond what is expected given the asset’s level of market risk. This concept, introduced by William Sharpe (1964) and later expanded upon by John Lintner (1965), helps us understand how the expected returns on assets are influenced by their exposure to systematic market risk. Empirical studies (e.g., Choudhry, 2002, 2004) show that the CAPM is not adequate (the performance is poor) to explain the variation in the returns. The most recent literature presents models with higher explanatory power than the CAPM (Black et al., 1972), such as the multi-factor models from Fama and French (1993) and Carhart (1997). While in 1993, Fama and French took the first step on the asset pricing multi-factor models with the 3-factor model, which already included the market excess factor (market return minus the risk-free rate) from the CAPM and added the book-to-market factor (HML, i.e., the difference in high book-to-market value and low book-to-market value stocks on the returns) and the size factor (SMB, i.e., the difference in small-size and big-size stocks on the returns)1. The three-factor model proposed is then (2):

E(r_i,t) − r_f = β_i,M ∗ (E(R_M) − r_f) + β_i,SMB ∗ E(SMB) + β_i,HML ∗ E(HML),

(2)

where $r_f$ is the risk-free interest rate; E(MKT) = E(R_M) − $r_f$, E(SMB) and E(HML) are the expected premiums, and the factor sensitivities from the time-series regression are measured by the coefficients β_i,M, β_i,SMB, and β_i,HML.

As previously noted, the application of multi-factor models, as demonstrated by Fama and French (1993, 1998, 2008) and Carhart (1997), has yielded noteworthy outcomes in explaining securities’ returns. These findings have generated substantial interest among researchers and investors alike (Fama & French, 1993, 1995, 1996, 1998, 2008, 2012; Bali et al., 2012). Carhart (1997) extended the model by adding one more factor to the FF model, the cross-sectional momentum factor MOM (in some research papers, this factor is called the up-minus-down factor (UMD)), which is the difference in the rise (winners) and fall (losers) in value stocks. The proposed Carhart model is then (3):

E(r_i,t) − r_f = β_i,M ∗ (E(R_M) − r_f) + β_i,SMB ∗ E(SMB) + β_i,HML ∗ E(HML) + β_i,MOM ∗ E(MOM),

(3)

Later, another famous paper about the multi-factor models was introduced by Fama and French (2015) and called the 5-factor model. The extended model builds upon the previous 3-factor model by introducing two additional factors, widely recognized as ‘quality’ factors in the literature. Their inclusion enriches the analysis and expands the existing framework, providing a more comprehensive understanding of the underlying securities’ dynamics. These factors are the profitability factor (the difference between high and low operating profitability stocks) and the investment factor (the difference between high and low total asset growth stocks). The proposed five-factor model is then (4):

E(r_i,t) − r_f = β_i,M ∗ (E(R_M) − r_f) +β_i,SMB ∗ E(SMB) + β_i,HML ∗ E(HML) + β_i,RWA ∗ E(RWA) + β_i,CMA ∗ E(CMA),

(4)

Even though the 5-factor model ignores the momentum of the Carhart model, both the 5-factor Fama–French model and the 4-factor Carhart model are extensions of the 3-factor model, which considerably improve the explanatory power of the 3-factor model.

The expansion of equity factor models continues to gain traction in both academic and financial settings. To enhance explanatory power, new factors are frequently introduced to address the random noise affecting asset returns. Several extensions have emerged from the foundational Fama–French three- and five-factor models. Notably, the Fear (VIX) model by Durand et al. (2011) and additional factors such as the quality factor (Asness & Frazzini, 2013; Asness et al., 2019), Value II and betting-against-beta factors (Frazzini & Pedersen, 2014), the momentum-enhanced five-factor model (Dirkx & Peter, 2020), and commodity and currency factors (Connor & Korajczyk, 2022) have contributed to refining asset pricing models. Future research should explore these extended models further, particularly in their ability to capture dynamic market conditions (Feng et al., 2020). The adaptability of factor models is crucial for timely adjustments to market fluctuations.

4. Data Collection

The data sample consists of stocks from twenty-eight (28) European Union countries separated into three categories (Green, Red, and Grey), based on the criteria in Table 1. The dataset contains 2007 Grey, 150 Green, and 367 Red stocks. The data in this study are collected or aggregated at a monthly frequency. The sample data are collected from 1 January 2000 to 31 December 2019. The aim is to study the sensitivity of the risk factors over time, and also with a separation in 2009. The European Union crisis began in the second half of 2009, leading to a shift in systemic risk across EU economies, thereby substantially shaping the influence of various factors2 (Begg, 2012; Bouvet & King, 2013). The financial crisis event had a profound and enduring impact on particular European countries (Greece, Portugal, Spain, Cyprus, Italy, and Ireland), exacerbating the challenges faced during the period spanning from 2010 to 2012. The “classical” risk factors come from the library of Kenneth R. French3, the HML^DEVIL from the Asness and Frazzini database, and the closing stock prices from the Thomson Reuters Eikon4. The variables include the “market excess return”, “risk free rate”, “momentum”, “size”, “value”, “profitability”, and “investment” portfolios (Appendix A 

Table A2. Classical factors: variable names, definition, and description.

Variable Name	Variable Definition	Variable Description
SMB (Small Minus Big)	1/3 (SMB(B/M) + SMB(OP) + SMB(INV)) SMB(B/M) = 1/3 (Small Value + Small Neutral + Small Growth) − 1/3 (Big Value + Big Neutral + Big Growth) SMB(OP) = 1/3 (Small Robust + Small Neutral + Small Weak) − 1/3 (Big Robust + Big Neutral + Big Weak) SMB(INV) = 1/3 (Small Conservative + Small Neutral + Small Aggressive) − 1/3 (Big Conservative + Big Neutral + Big Aggressive)	The average return on the nine small-stock portfolios minus the average return on the nine big-stock portfolios
HML (High Minus Low)	1/2 (Small Value + Big Value) − 1/2 (Small Growth + Big Growth)	The average return on the two value portfolios minus the average return on the two growth portfolios. Basically, the two high B/M portfolios for a region minus the average of the returns for the two low B/M portfolios. For the HML Devil use the book equity and the current market value of equity are calculated at the end of each month that rebalancing frequently the weights for the portfolios.
RMW (Robust Minus Weak)	1/2 (Small Robust + Big Robust) − 1/2 (Small Weak + Big Weak)	The average return on the two robust operating profitability portfolios minus the average return on the two weak operating profitability portfolios
CMA (Conservative Minus Aggressive)	1/2 (Small Conservative + Big Conservative) − 1/2 (Small Aggressive + Big Aggressive)	The average return on the two conservative investment portfolios minus the average return on the two aggressive investment portfolios
Rm–Rf (excess market)		The return on a region’s value-weight market portfolio minus the one-month Euro short-term interest rate (from ECB)
MOM (Monthly momentum)	1/2 (Small High + Big High) − 1/2 (Small Low + Big Low)	The equal-weight average of the returns for the two winner portfolios for a region minus the average of the returns for the two loser portfolios
Data are from 2000 to 2019, taken daily, monthly, and annually. Countries: Austria, Belgium, Switzerland, Germany, Denmark, Spain, Finland, France, Great Britain, Greece, Ireland, Italy, Netherlands, Norway, Portugal, and Sweden. Source: Library Kenneth, Fama–French, and Asness and Frazzini database (for HML Devil).

).

The stock selection process entails considering companies that were listed on the public stock exchange prior to 2015. However, it is essential to acknowledge certain limitations stemming from missing values and varying sizes within each stock universe. The securities without variation (or nulls) are dropped from the sample. These securities are not traded very often, so prices are stale and uninformative. An implicit assumption in the analysis is that stocks are traded across European markets, and the analysis ignores the country in which they are issued. European markets have free access, and stocks can be purchased through ADRs, EDRs, or GDRs between countries, with little or no constraints. It is also worth mentioning that for the investigation, the data is filtered by removing the stocks with more than 80% missing values and cleaned of errors (e.g., stocks with zero prices/missing values between prices, not surviving, huge irrational returns, et cetera).

Lastly, for the analysis, we used winsorization on the data to mitigate the influence of extreme values within the sample, thereby minimizing the potential impacts of outliers that may be spurious in nature. The winsorization was set at 95%, which means every security (i) return belongs within a specific internal (average_i $\pm$ 1.96*s.d._(i)), and the observations above and below the boundaries share 2.5% of the sample and are the outliers. One plausible explanation could be attributed to the occurrence of a massive volume of one-sided position trading in isolated illiquid securities within the market. This phenomenon can lead to substantial fluctuations in the returns of these securities.

5. Methodology

The Fama–French model (including the Carhart model) is employed as a hybrid factor model that integrates estimation techniques derived from both macroeconomic and fundamental factor models. The original Fama and French (1993) model is typically estimated using a time-series regression approach. In this framework, the excess return of each asset is regressed on the returns of factor-mimicking portfolios: the market excess return (MKT), Small Minus Big (SMB, size), and High Minus Low (HML, value). This method is extended in the Fama and French (2015) five-factor model, which adds profitability (RMW) and investment (CMA) factors. Similarly, Carhart (1997) extends the three-factor model by adding a momentum factor (MOM).

While Fama and French (1993, 2015) primarily use time-series regressions to estimate factor loadings for the portfolios of stocks, and occasionally cross-sectional regressions to examine average returns, this study employs a panel data framework using random effects to capture variation across environmentally classified securities and over time. Unlike the traditional two-stage Fama and MacBeth (1973) procedure, which estimates time-series betas in the first stage and risk premia through cross-sectional regressions in the second, the panel approach allows for the simultaneous estimation of exposures and alphas while accounting for unobserved heterogeneity (Racicot & Rentz, 2017; Makwasha et al., 2019). This is particularly useful for analyzing structural differences across Green, Grey, and Red asset classes.

The statistical model is estimated as a panel data model with random effects5, which takes into consideration the individual class of the Green, Grey, and Red securities heterogeneity. Random effects are more appropriate when you are interested in estimating the average relationship between the independent variables and the dependent variable while allowing for variation6 in stock return.

In asset pricing research within the EU stock market, employing random-effects panel data models offers distinct advantages. These models efficiently manage unobserved heterogeneity when this heterogeneity is uncorrelated with the independent variables, allowing for the inclusion of time-invariant variables typically excluded in fixed-effects models (Baltagi, 2005; Greene, 2012). Additionally, random-effects models provide more efficient estimators under certain assumptions, making them particularly useful in financial data analysis (Hsiao, 2014). They also facilitate broader inferences to the population rather than being restricted to the sample, which is crucial given the diversity among EU countries (Wooldridge, 2010). Moreover, random-effects models facilitate broader generalizations across the entire population of EU stocks rather than being limited to specific samples, thus enhancing the robustness and applicability of the results (Arellano, 2003). Empirical studies, such as those by Bekaert and Harvey (1995), Fama and French (1998), and Harvey (1991), underscore the utility of random-effects models in examining international market integration, stock returns, and covariance risk, respectively. Thus, the robust capabilities of random-effects models make them a compelling choice and well suited for examining how different environmental classifications impact stock returns in the EU market, providing valuable insights for investors and policymakers. The model is appropriate as it focuses on capturing potential associations within the same group of data observations.

The dataset is unbalanced because companies list on the stock exchange at different times (e.g., missing values) and different sizes for every category. These sector-level returns are evaluated using random-effects panel regression models, with specifications outlined in Equations (2) to (4) and presented in the general form of Equations (5) to (7):

$$r_{i,t}^j-r_{f,t}=a_i^j+b_{1,i}^j{MKTRF}_t+b_{2,i}^j{SMB}_t+b_{3,i}^j{HML}_t+e_{i,t}^j,3\text{-}\mathrm{factor}\mathrm{Fama}–\mathrm{French}\mathrm{model}$$

(5)

$$r_{i,t}^j-r_{f,t}=a_i+b_{1,i}^j{MKTRF}_t+b_{2,i}^j{SMB}_t+b_{3,i}^j{HML}_t+b_{4,i}^j{MOM}_t{+e}_{i,t}^j,4\text{-}\mathrm{factor}\mathrm{model}/\mathrm{Carhart}\mathrm{model}$$

(6)

$$r_{i,t}^j-r_{f,t}=a_i+b_{1,i}^j{MKTRF}_t+b_{2,i}^j{SMB}_t+b_{3,i}^j{HML}_t+b_{4,i}^j{RMW}_t+b_{5,i}^j{CMA}_t+e_{i,t}^j,5\text{-}\mathrm{factor}\mathrm{Fama}–\mathrm{French}\mathrm{model}$$

(7)

with i = 1,…, n, the n is 150 for Green stocks, 2007 for Grey stocks, and 367 for Red stocks. The n depends on the size of the stock category, and j is an index that groups the stock (0—Green, 1—Grey, 2—Red). The t represents the time period.

$r_{i,t}^j$ is the return of asset i at time t (within the period of 2000–2019); $r_{f,t}$ is the risk-free rate at time t; the ${MKTRF}_t$ is the return on a European region’s (Stoxx Europe 600 Index)7 value-weighted market portfolio at time t; the ${SMB}_t$ is Smal-Minus-Big-size companies; the ${HML}_t$ is High Minus Low based on the value of the companies; the ${RMW}_t$ is robust minus weak based on the operating profitability of the companies at time t; the ${CMA}_t$ is conservative minus aggressive and based on the investment of the companies at time t; the ${MOM}_t$ is the monthly momentum (see Appendix A,

Table A3. Terminology and portfolio construction.

Portfolio Construction to Determine Fama–French Factors
Small	Book to market (B/M)	Small High (SH) Small Neutral (SN) Small Low (SL)
	Profitability (OP)	Small Robust (SR) Small Neutral (SN) Small Weak (SW)
	Investment (INV)	Small Conservatice (SC) Small Neutral (SN) Small Agresive (SA)
Big	Book to market (B/M)	Big High (BH) Big Neutral (BN) Big Low (BL)
	Profitability (OP)	Big Robust (BR) Big Neutral (BN) Big Weak (BW)
	Investment (INV)	Big Conservatice (BC) Big Neutral (BN) Big Agresive (BA)

Source: Library Kenneth, Fama–French, and Erdinç (2018). “Comparison of CAPM, Three-Factor Fama-French Model, and Five-Factor Fama-French Model for the Turkish Stock Market”.

). The a_i is the stock’s alpha performance, and b_k is the coefficient from the specific k-factor (with k = 1,…, 5), as the $r_{i,t}^j$ − $r_{f,t}$ denotes the excess return of portfolio i in the time t with the specific asset class j.

The Fama and French model is constructed with the help of SMB, HML, RMW, and CMA factors (and some of these factors are also used in the Carhart model). To build these factors, we sort stocks into two market caps (small and big) and three individual layers as book-to-market equity (B/M), operating profitability (OP), and investment (INV) portfolios (see Appendix A Table A2 and Table A3). To create the MOM factor for the Carhart model, the data sort stocks by size and lagged momentum. The lagged momentum return is a stock’s cumulative return from day t–250 to day t–20. Big stocks are those in the top 90% of the June market cap in the Europe stock region, and small stocks are those stocks appearing in the bottom 10%. The B/M, OP, INV, and momentum breakpoints for a region are the 30th and 70th percentiles of the respective ratios and the lagged momentum returns for the region’s big stocks.

In addition to the standard High-Minus-Low (HML) factor introduced by Fama and French (1993), this study incorporates the HML Devil factor, following the construction and rationale outlined in Asness and Frazzini (2013). The HML Devil factor is a refined value factor that adjusts for the limitations of the traditional HML by accounting for more extreme value–growth spreads and using additional filters to improve robustness. It is constructed by going long on high book-to-market stocks and short on low book-to-market stocks, similar to HML, but with modifications such as excluding the most speculative growth stocks to reduce noise and better isolate the value premium. The inclusion of the HML Devil factor is motivated by its demonstrated ability to enhance explanatory power in cross-sectional return models, particularly in contexts where traditional value measures may underperform or misrepresent risk exposure. Given the structural differences across Green, Grey, and Red assets, especially in valuation metrics, the HML Devil factor provides a more nuanced measure of value exposure that may capture risk–return relationships more effectively than the standard HML factor alone.

6. Empirical Results and Findings

Based on the collected factors, the next subsection presents a descriptive statistical analysis.

Table 3. First four moments of time-series classical factors.

Period	4th Moments	MKTRF	SMB	HML	RMW	CMA	MOM	HMLDevil
2000–2009	Mean	0.2157	0.2808	1.0369	0.2431	0.6456	0.583	1.001
	Variance	31.8938	5.8499	7.8006	3.1746	5.4433	28.8496	0.14
	Skewness	−0.7150	−0.2492	0.2890	−0.2521	0.3066	−1.2397	0.2475
	Kurtosis	1.8174	1.3917	2.9661	1.2966	2.0848	4.8051	8.3661
2009–2019	Mean	0.5723	0.1730	−0.2422	0.3903	−0.05	0.9543	−0.40
	Variance	22.1077	2.5565	5.1270	2.3882	1.2670	7.8426	0.04
	Skewness	−0.2237	0.1131	0.4236	−0.2796	0.1413	0.0602	0.1499
	Kurtosis	0.3276	0.0580	−0.0704	−0.3309	0.0256	1.3830	−0.4825
2000–2019	Mean	0.394	0.2269	0.3974	0.3167	0.2978	0.7686	0.30
	Variance	26.9197	4.1886	6.8475	2.7752	3.4626	18.3039	0.09
	Skewness	−0.5562	−0.1453	0.4528	−0.2813	0.6534	−1.12778	0.6163
	Kurtosis	1.4715	1.7404	1.9745	0.7472	3.7802	7.0922	10.0138

The table shows the first four moments of the six factors within each of the two subperiods and the whole period. MKTRF, SMB, HML, CMA, and RMW are the Fama–French market, size, value, profitability, and investment factors; MOM is the Carhart momentum factor. The results are expressed as percentages (%).

reports summary statistics of the factors and

Table 4. Correlation of the six factors on the period of 2000–2009.

Variables	Mkt-RF	SMB	HML	RMW	CMA	MOM
Mkt-RF	1
SMB	−0.07	1
HML	0.03	−0.07	1
RMW	−0.38	0.11	−0.36	1
CMA	−0.40	−0.15	0.62	−0.06	1
MOM	−0.50	0.25	−0.20	0.49	0.21	1

This table shows the correlation of the six factors within the period of 2000–2009. MKTRF, SMB, HML, CMA, and RMW are the Fama–French market, size, value, profitability, and investment factors; MOM is the Carhart momentum factor.

,

Table 5. Correlation of the six factors for the period of 2010–2019.

Variables	Mkt-RF	SMB	HML	RMW	CMA	MOM
Mkt-RF	1
SMB	−0.12	1
HML	0.47	−0.04	1
RMW	−0.41	−0.05	−0.82	1
CMA	0.03	−0.10	0.57	−0.47	1
MOM	−0.34	0.05	−0.44	0.42	−0.05	1

This table shows the correlation of the six factors within the period of 2010–2019. MKTRF, SMB, HML, CMA, and RMW are the Fama–French market, size, value, profitability, and investment factors; MOM is the Carhart momentum factor.

and

Table 6. Correlation of the six factors for the period of 2000–2019.

Variables	Mkt-RF	SMB	HML	RMW	CMA	MOM
Mkt-RF	1
SMB	−0.09	1
HML	0.19	−0.05	1
RMW	−0.39	0.05	−0.54	1
CMA	−0.27	−0.13	0.61	−0.18	1
MOM	−0.44	0.19	−0.27	0.46	0.14	1

This table shows the correlation of the six factors within the period of 2000–2019. MKTRF, SMB, HML, CMA, and RMW are the Fama–French market, size, value, profitability, and investment factors; MOM is the Carhart momentum factor.

report the matrix correlation. In the last subsection, the results of the asset pricing models of the Green, Grey, and Red assets are included with the factors.

I.

Summary statistics and correlation matrix

Table 3 presents the first four moments—mean, variance, skewness, and kurtosis—of the time-series returns for classical asset pricing factors, including the market excess return (MKTRF), size (SMB), value (HML), profitability (RMW), investment (CMA), momentum (MOM), and the HML Devil factor, across three time periods: 2000–2009, 2009–2019, and the full sample from 2000 to 2019. These statistics provide insights into the distributional properties of these factors and their evolving behaviour across different market conditions.

The mean values indicate notable shifts in factor performance over time. The market risk premium (MKTRF) increased significantly from 0.2157 in 2000–2009 to 0.5723 in 2009–2019, suggesting a stronger equity market performance in the post-financial crisis period. This reflects the recovery and sustained growth following the 2008 crisis. The SMB factor remained positive in both periods but declined in magnitude, indicating a weakening small-cap premium. In contrast, the HML factor, which was positive in the earlier period, turned negative after 2009, suggesting that value stocks underperformed growth stocks in the latter decade. The profitability factor (RMW) showed an increase in mean returns post-2009, reinforcing the role of profitability in asset pricing, while the investment factor (CMA) displayed a slightly negative mean, particularly in 2009–2019, aligning with prior findings that firms with aggressive investment strategies tend to underperform. The momentum factor exhibited strong mean returns across both subperiods, with an increase from 0.583 in 2000–2009 to 0.9543 in 2009–2019, supporting the persistent profitability of momentum-based strategies.

Variance estimates reveal changes in factor risk dynamics over time. The market factor (MKTRF) exhibited higher variance in 2000–2009 at 31.89, which declined to 22.10 in 2009–2019, reflecting lower overall market volatility in the post-crisis era. The momentum factor had the highest variance in 2000–2009 at 28.85, which later decreased to 7.84, suggesting reduced momentum-driven fluctuations and lower extreme return events. The size and value factors showed relatively stable variance levels, while the profitability and investment factors displayed a lower risk compared to other factors. The HML Devil factor exhibited consistently low variance, indicating its relative stability.

Skewness values provided insights into the asymmetry of return distributions. The market factor (MKTRF) exhibited negative skewness in both periods, with values of −0.7150 in 2000–2009 and −0.2237 in 2009–2019, indicating a higher probability of extreme negative returns. The RMW factor also showed negative skewness across both subperiods, suggesting a downside risk in profitability-based strategies. The HML and SMB factors exhibited positive skewness, particularly in 2009–2019, indicating a higher likelihood of extreme positive returns for value and small-cap stocks in that period. The momentum factor displayed highly negative skewness in 2000–2009 at −1.2397, highlighting its vulnerability to sharp reversals, but this effect diminished in 2009–2019. The HML Devil factor showed positive skewness throughout, suggesting a higher frequency of large positive returns.

Kurtosis values indicate the presence of extreme return events. The momentum factor exhibited high kurtosis in 2000–2009 at 4.8051, confirming the presence of fat tails and frequent extreme return observations. However, its kurtosis significantly declined post-2009, suggesting a more normal return distribution in the latter period. The HML Devil factor had the highest kurtosis, particularly in 2000–2009 (8.3661) and over the full period (10.0138), indicating a strong tail risk and the occurrence of extreme events in value-based strategies. Other factors displayed moderate kurtosis levels, with some declining post-2009, suggesting a stabilization in return distributions.

These results highlight significant changes in factor behaviour over time. The reduction in market and momentum factor volatility, the declining value premium, and the persistence of momentum-based returns suggest evolving market dynamics that impact the explanatory power of factor-based asset pricing models. The findings emphasize the need for the continued exploration of factor model performance under different economic and financial conditions. Future research could investigate the underlying drivers of the diminishing value effect and whether the stability of momentum returns persists in different market environments.

II.

Correlation matrix

Table 4, Table 5 and Table 6 present the correlation matrices for the six asset pricing factors—market excess return (Mkt-RF), size (SMB), value (HML), profitability (RMW), investment (CMA), and momentum (MOM)—over three periods: 2000–2009, 2010–2019, and the full sample from 2000 to 2019. These correlation coefficients provide insights into the relationships between factors and how they evolved over time, influencing asset pricing models and investment strategies.

In the period from 2000 to 2009, the market excess return (Mkt-RF) exhibited weak negative correlations with the profitability (RMW) and investment (CMA) factors at −0.38 and −0.40, respectively, suggesting that firms with high profitability and conservative investment tended to perform better when the market return declined. The strongest negative correlation was observed between Mkt-RF and MOM at −0.50, indicating that momentum strategies were inversely related to market movements, potentially reflecting momentum crashes during downturns. The relationship between SMB and other factors was relatively weak, with the highest correlation being 0.25 with MOM, suggesting that momentum effects were more pronounced among small-cap stocks. The value factor (HML) had a moderate positive correlation with CMA (0.62), reinforcing the notion that high book-to-market firms often follow conservative investment policies.

During the period from 2010 to 2019, several shifts in factor correlations emerged. The correlation between Mkt-RF and HML turned significantly positive at 0.47, in contrast to the weak relationship observed in the earlier period, indicating that value stocks were more aligned with market performance in this decade. The correlation between HML and RMW became strongly negative at −0.82, suggesting that firms classified as value stocks exhibited lower profitability, a pattern that aligns with the declining effectiveness of the value factor in explaining returns. The previously strong positive relationship between HML and CMA persisted at 0.57, maintaining the association between value stocks and conservative investment policies. The correlation between Mkt-RF and MOM remained negative but declined in magnitude to −0.34, indicating a weaker inverse relationship between momentum and market performance compared to the 2000–2009 period.

Examining the full period from 2000 to 2019, the correlation trends reinforce the findings from the two subperiods. Mkt-RF maintained a negative correlation with profitability (−0.39) and investment (−0.27), consistent with the idea that firms with higher profitability and lower investment tended to be more defensive during market downturns. The value factor exhibited a moderate negative correlation with profitability (−0.54), indicating a persistent inverse relationship between value stocks and firm profitability. The positive correlation between HML and CMA (0.61) remained stable, suggesting that value-oriented firms continued to adopt more conservative investment strategies. The momentum factor exhibited a strong negative correlation with HML (−0.27) and Mkt-RF (−0.44), highlighting its tendency to perform poorly during periods of market weakness and value stock outperformance.

Overall, the correlation matrices revealed key structural changes in factor relationships over time. The increasing positive correlation between HML and Mkt-RF after 2010 suggests that value stocks became more sensitive to overall market movements, while the deepening negative correlation between HML and RMW highlights the growing divergence between value- and profitability-based investment strategies. The persistent inverse relationship between momentum and market excess returns suggests that momentum strategies remained effective as contrarian approaches to market risk. These findings emphasize the dynamic nature of factor interactions and their implications for multi-factor asset pricing models. Future research could explore whether these trends persist in subsequent market cycles and how factor correlations evolve under different economic conditions.

III.

Asset pricing models for Green, Grey, and Red securities

In this subsection, the study combines the asset pricing models from Fama–French, Carhart, and extension models to characterize the factor structure of the Green, Grey, and Red stock universe. This study analyzes the empirical results obtained from random-effect regression using simple returns for the period of 2000–2019, along with subperiods (2000–2009 and 2010–2019).

Table 7. Empirical results for Green simple returns (for the period of 2000–2019 and the subperiods).

Period	Model	Alpha	MktRf	SMB	HML/ HML II *	MOM	RMW	CMA	R-sq Within	R-sq Between	R-sq Overall
2000–2009	[1]	0.27	0.95	0.58	0.15				17.54%	1.39%	17.36%
	[2]	0.27	0.95	0.58	0.15	0.01			17.55%	1.39%	17.36%
	[3]	0.18	0.98	0.59	0.13		0.11	0.11	17.57%	1.78%	17.39%
	[4] *	0.27	0.94	0.58	0.10				17.52%	1.59%	17.34%
	[5] *	0.18	0.97	0.57	0.19	0.09			17.56%	1.54%	17.38%
	[6] *	0.14	0.98	0.61	0.1		0.14	0.16	17.57%	2.07%	17.4%
2010–2019	[1]	−0.54	1.03	0.84	0.35				14.51%	1.33%	14.33%
	[2]	−0.46	1.02	0.84	0.31	−0.10			14.54%	1.41%	14.36%
	[3]	−0.52	1.02	0.83	0.36		−0.06	−0.12	14.52%	1.4%	14.33%
	[4] *	−0.49	1.04	0.82	0.35				14.44%	1.49%	14.26%
	[5] *	−0.49	1.04	0.83	0.29	−0.08			14.46%	1.5%	14.27%
	[6] *	−0.42	1.03	0.8	0.24		−0.27	−0.01	14.46%	1.5%	14.27%
2000–2019	[1]	−0.31	0.98	0.69	–0.30				15.49%	2.68%	15.39%
	[2]	−0.30	0.98	0.69	0.29	−0.01			15.50%	2.67%	15.39%
	[3]	−0.33	1.00	0.70	0.27		0.01	0.08	15.50%	2.72%	15.39%
	[4] *	−0.29	0.99	0.69	0.22				15.41%	2.28%	15.30%
	[5] *	−0.34	1.00	0.68	0.28	0.06			15.42%	2.57%	15.32%
	[6] *	−0.31	1.01	0.72	0.15		−0.07	0.22	15.47%	2.59%	15.36%

* The same model but using the HML II (or Devil). This table shows the alpha and beta values of the MktRf, SMB, HML, MOM, RMW, and CMA factors from the random-effect regression (after winsorization). The global factors are collected from the Kenneth R. French data library. Additionally, the results report both dependent variables, which are the returns. Models 1, 2, and 3 are denoted as the 3-Factor Fama and French model, the 4-factor Carhart model, and the 5-factor Fama and French model, respectively. Models 4, 5, and 6 are the same models but substitute the HML with the HML II (or Devil). The table reports the results from Equations (2) to (4). The last 3 columns are the R-squared for within, between, and overall. Numbers in bold are significantly greater than zero with 95% confidence. The results are expressed as percentages (%) and rounded to the 2nd decimal. The use of robust standard errors does not change the significance level mentioned in the table (below and over 5%).

,

Table 8. Empirical results for Grey simple returns (for the period of 2000–2019 and the subperiods).

Period	Model	Alpha	MktRf	SMB	HML/ HML II *	MOM	RMW	CMA	R-sq Within	R-sq Between	R-sq Overall
2000–2009	[1]	−0.01	0.91	0.62	−0.21				17.32%	12.24%	17.22%
	[2]	0.09	0.87	0.65	−0.22	−0.11			17.44%	11.59%	17.34%
	[3]	0.23	0.88	0.65	−0.37		−0.52	0.08	17.67%	13.03%	17.57%
	[4] *	−0.17	0.90	0.62	−0.02				17.14%	12.95%	17.04%
	[5] *	0.07	0.85	0.66	−0.18	−0.17			17.31%	12.67%	17.21%
	[6] *	0.13	0.82	0.60	−0.08		−0.45	−0.18	17.41%	13.61%	17.32%
2010–2019	[1]	−0.05	0.86	0.76	0.16				13.15%	0.56%	13.01%
	[2]	0.02	0.85	0.76	0.13	−0.07			13.17%	0.53%	13.04%
	[3]	−0.06	0.87	0.77	0.17		−0.06	0.08	13.16%	0.55%	13.02%
	[4] *	−0.06	0.88	0.75	0.09				13.09%	0.58%	12.96%
	[5] *	0.01	0.88	0.76	0.01	−0.10			13.13%	0.53%	12.99%
	[6] *	−0.06	0.89	0.76	0.002		−0.09	0.18	13.13%	0.56%	13.00%
2000–2019	[1]	−0.13	0.90	0.68	−0.04				14.92%	1.13%	14.83%
	[2]	−0.04	0.88	0.69	−0.07	−0.09			14.99%	1.09%	14.91%
	[3]	0.04	0.88	0.68	−0.22		−0.41	0.06	15.09%	0.93%	15.00%
	[4] *	−0.14	0.90	0.68	0.01				14.91%	1.21%	14.83%
	[5] *	−0.02	0.87	0.70	−0.10	−0.13			15.00%	0.99%	14.92%
	[6] *	0.01	0.86	0.66	−0.06		−0.31	−0.09	15.02%	1.09%	14.94%

* The same model but using the HML II (or Devil). This table shows the alpha and beta values of the MktRf, SMB, HML, MOM, RMW, and CMA factors from the random-effect regression (after winsorization). The global factors are collected from the Kenneth R. French data library. Additionally, the results report both dependent variables, which are the returns. Models 1, 2, and 3 denote the 3-factor Fama and French model, the 4-factor Carhart model, and the 5-factor Fama and French model, respectively. Models 4, 5, and 6 are the same models but substitute the HML with the HML II (or Devil). The table reports the results from Equations (2) to (4). The last 3 columns are the R-squared for within, between, and overall. Numbers in bold are significantly greater than zero with 95% confidence. The results are expressed as percentages (%) and rounded to the 2nd decimal. The use of robust standard errors does not change the significance level mentioned in the table (below and over 5%).

and

Table 9. Empirical results for Red simple returns (for the period of 2000–2019 and the subperiods).

Period	Model	Alpha	MktRf	SMB	HML/ HML II *	MOM	RMW	CMA	R-sq Within	R-sq Between	R-sq Overall
2000–2009	[1]	0.30	0.80	0.69	0.17				19.15%	23.46%	19.02%
	[2]	0.24	0.83	0.66	0.20	0.08			19.24%	23.05%	19.11%
	[3]	0.12	0.84	0.69	0.21		0.33	0.08	19.33%	24.23%	19.19%
	[4] *	0.31	0.79	0.70	0.14				19.16%	23.81%	19.03%
	[5] *	−0.02	0.86	0.65	0.38	0.25			19.62%	22.54%	19.48%
	[6] *	0.04	0.85	0.72	0.19		0.39	0.16	19.43%	24.27%	19.28%
2010–2019	[1]	−0.54	0.92	0.58	0.37				11.72%	1.27%	11.62%
	[2]	−0.44	0.91	0.59	0.32	−0.12			11.76%	0.95%	11.67%
	[3]	−0.58	0.93	0.6	0.41		0.12	0.08	11.72%	1.35%	11.64%
	[4] *	−0.31	0.87	0.54	0.70				12.18%	1.24%	12.09%
	[5] *	−0.33	0.87	0.54	0.74	0.05			12.19%	1.36%	12.09%
	[6] *	−0.34	0.87	0.55	0.74		0.11	0.01	12.19%	1.33%	12.10%
2000–2019	[1]	−0.29	0.86	0.64	0.33				13.67%	11.03%	13.63%
	[2]	−0.33	0.87	0.63	0.35	0.04			13.68%	11.19%	13.64%
	[3]	−0.41	0.89	0.66	0.36		0.22	0.13	13.72%	12.14%	13.69%
	[4] *	−0.26	0.85	0.64	0.35				13.76%	12.21%	13.72%
	[5] *	−0.45	0.88	0.61	0.54	0.22			13.97%	13.52%	13.94%
	[6] *	−0.40	0.89	0.68	0.34		0.19	0.25	13.84%	13.05%	13.81%

* The same model but using the HML II (or Devil). This table shows the alpha and beta values of the MktRf, SMB, HML, MOM, RMW, and CMA factors from the random-effect regression (after winsorization). The global factors are collected from the Kenneth R. French data library. Additionally, the results report both dependent variables, which are the returns. The models 1, 2, and 3 denote the 3-factor Fama and French model, the 4-factor Carhart model, and the 5-factor Fama and French model, respectively. Models 4, 5, and 6 are the same models but substitute the HML with the HML II (or Devil). The table reports the results from Equations (2) to (4). The last 3 columns are the R-squared for within, between, and overall. Numbers in bold are significantly greater than zero with 95% confidence. The results are expressed as percentages (%) and rounded to the 4th decimal. The use of robust standard errors does not change the significance level mentioned in the table (below and over 5%).

present the results from three prominent asset pricing models (3-factor model, 4-factor model, and 5-factor model) and the corresponding table for each of the three-asset class returns (Green, Grey, and Red) and using the explanatory factors provided by the Kenneth R. French library and the Asness library. Furthermore, the first three models, exclusively using the factors from the Kenneth R. French library, and the last three models (4, 5, and 6) are the same models but substitute the HML with the HML II (or Devil).

Table 7 presents the results for the Green asset class. The coefficients show interesting dynamics over different time periods and models. For the period of 2000–2009, all three models (1, 2, and 3) consistently display non-significant alphas. On the other hand, for the period of 2010–2019, and the whole period, the alphas are negative for the returns, indicating that assets in the Green category underperformed in the market on a risk-adjusted basis. Generally, the coefficients for MktRf, SMB, HML, and HML II are positive, suggesting that Green stocks have a positive exposure to those factors, and RMW (statistically significant in a few models) has a negative impact, suggesting the opposite effect. The coefficients for MktRf (market factor), SMB (size factor), and HML (value factor) remain relatively stable when comparing the 2000–2009 and 2010–2019 periods. This consistency suggests that market movements and the value and size of the firms continue to be influential factors for the returns of the Green asset. In practical terms, this implies that investors with portfolios sensitive to market performance, value, and firm size may have experienced consistent effects on their Green asset holdings throughout these two decades. The positive and statistically significant HML coefficients for Green assets indicate that these securities exhibit a stronger exposure to the value factor. This finding suggests that higher returns associated with Green assets are due to an increased loading on a systematic risk factor and therefore represent compensation for bearing additional value-related risk, rather than abnormal returns exceeding risk-adjusted expectations. In other words, these higher returns should not be interpreted as “favourable” in the sense of excess performance; rather, they reflect the standard risk–return trade-off in asset pricing. Furthermore, the positive HML loading may also imply that Green firms are disproportionately characterized by higher book-to-market ratios, making them naturally more sensitive to the value premium. This structural exposure suggests that Green companies, on average, may possess financial attributes more commonly associated with value stocks, thereby aligning their return behaviour with that of the broader value segment of the market. During the 2010–2019 period, the MOM and RMW factors exhibit, in particular models, a negative impact on Green asset returns. In contrast to HML, the RMW and MOM factors show a negative impact on Green asset returns in the 2010–2019 period based on the construction of the factor model. This observation implies that the stocks of firms with robust profitability profiles or momentum may not have performed as well within the Green asset context during this decade. Investors focusing on factors related to firm profitability or momentum should take note of this influence when crafting their investment strategies. This finding bears practical significance for investors seeking to enhance their risk-adjusted returns, gain a deeper understanding of underlying market dynamics, and combine a strategy using the proxies’ portfolios. It is not clear whether incorporating HML Devil into asset pricing models can provide more accurate risk assessments, facilitating informed investment decisions. The empirical results reveal nuanced insights that can guide investors in their decision-making processes. Understanding the positive or negative exposures to factors such as HML and RMW, alongside the choice between HML and HML Devil, empowers investors to tailor their portfolio strategies to different market conditions and financial goals. The stability of MktRf, HML (both), and SMB coefficients highlights their enduring significance for Green asset returns. Conversely, the fluctuations in RMW, MOM, and CMA coefficients across time periods and models underscore the importance of adapting to evolving market dynamics. This variability of the factors suggests that different factor models attempt to capture the common variation in the asset returns in distinct ways. Climent and Soriano (2011), for the period of 1987–2009, found similar results for the Green asset returns regarding the coefficients of the market and growth factors in the US market. The opposite empirical results for the US Green class and a subsector of the Red asset class were found in Gbenga and Steffen (2015) for the period of 1991–2014, in which the adjusted alpha is negative for black and Green portfolios, and the MOM is a significant factor for the Green portfolio returns.

In Table 8, the coefficients for the Grey asset class also demonstrate diverse patterns over different time periods and models. The period of 2000–2009 exhibits mostly positive alphas, indicating that assets in the Grey asset class outperformed the market on a risk-adjusted basis. The coefficients for MktRf and SMB are positive and significant, suggesting that these factors had a positive impact on the Grey asset class’s returns. On the contrary, the coefficients for MOM and RMW are negative and significant, suggesting that these factors had a negative impact on the Grey asset class’s returns. However, HML coefficients show slight variations across periods, specifically in the second half, changing from negative to positive. Furthermore, the CMA coefficients demonstrate variations across models, particularly noticeable when transitioning from the HML to the HML devil factor.

The calculated alpha values for the Grey asset class have noteworthy behavior. The alpha is mostly positive for the models in the first half, and in the second half, they are mostly statistically insignificant. The adjusted alpha coefficient becomes insignificant, implying that the systematic risk factors included in the model sufficiently capture the variation in the returns of the Grey asset. In other words, the added factors explain more of the variation in asset returns, rendering the adjusted alpha term statistically insignificant. This divergence highlights the importance of return measurement methods in assessing the performance of the Grey asset class. Across the observed periods, the coefficients for the market factor (MktRf), size factor (SMB), momentum factor (MOM), and robust-minus-weak factor (RMW) demonstrated a remarkable level of consistency. This stability suggests that these factors have an enduring influence on the Grey asset class’s returns, reinforcing their relevance in asset pricing models. However, it is essential to note the variations observed in the HML factor, particularly during the second half of the study period. These variations indicate that the HML may have responded to changing market conditions or specific economic events. This underscores the dynamic nature of factors and their potential impacts on asset returns. An intriguing observation arises from the post-crisis period analysis, where a significant decrease is evident in the coefficients’ magnitude. The observed decline in the magnitude of coefficient estimates for assets can be primarily attributed to an increase in idiosyncratic risk following the global financial crisis. In the aftermath of the crisis, market dynamics underwent significant shifts, leading to a greater emphasis on asset-specific factors over systemic market influences. This rise in idiosyncratic risk diminished the correlation between individual asset returns and overall market movements, thereby reducing the sensitivity of assets as measured by their beta coefficients. Additionally, changes in investor behaviour, market liquidity, and regulatory adjustments post-crisis further contributed to this decline. As a result, assets displayed lower beta values, reflecting a market environment where individual risks became more pronounced, relative to broad market risks. This emphasizes the importance of considering historical context and events when interpreting asset pricing results. Consistently, the analysis reaffirms the superiority of HML models compared to the HML II (or Devil) model in explaining the returns of the Grey asset class. The practical implication here is that employing the HML factor enables better risk-adjusted performance and a more comprehensive capture of the underlying market dynamics specific to the Grey asset class.

For investors and financial institutions, these findings hold crucial practical implications. Firstly, recognizing the influence of return measurement methods on alpha calculations can help investors make more informed decisions when assessing the performance of the Grey asset class within their portfolios. The choice between the HML and CMA models can significantly impact perceived asset performance, leading to different allocation strategies. Secondly, the stability of factors such as MktRf, SMB, MOM, and RMW underscores their enduring relevance for constructing asset portfolios. Financial institutions can utilize this stability to design more robust investment strategies and tailor their product offerings to align with the risk–return preferences in their portfolios. Lastly, the observed variations in factor coefficients, especially during unique periods like the post-crisis era, highlight the importance of dynamic asset management. Investors and financial institutions should remain agile and adapt to changing market conditions, incorporating updated factor insights into their investment strategies to mitigate risks and seize opportunities effectively.

Table 9 illustrates a range of coefficient patterns associated with Red asset returns across various timeframes and models. Specifically, throughout the 2000–2009 period, the models (1, 2, and 4) exhibit mostly positive alphas. This suggests that assets within the Red asset class consistently overperformed the market when considering risk-adjusted performance.

In the observed analysis, the coefficients for market factor (MktRf), size factor (SMB), and value factor (HML) are positive and statistically significant, indicating that these factors have historically exerted a positive influence on the returns of the Red asset class. For the first half period and whole period, the momentum factor (MOM), profitability factor (CMA), and robust-minus-weak factor (RMW) were predominantly positive and statistically significant. Conversely, the momentum factor (MOM) exhibited a negative impact on Red asset returns in the second half. However, it is crucial to note that the value factor (HML II or Devil) displayed an improving role across different models. These variations may reflect subtle differences in the measurement or modelling of this factor but generally confirm its positive influence on Red asset returns.

The results for the Red asset class in the period from 2010 to 2019 take a divergent turn. During this period, the models indicate negative alphas for the Red asset class. This shift in alpha sign may raise questions for potential investors who seek clarity on what to expect going forward. The change in alpha sign for Red stocks hinges on several factors. It is essential to recognize that historical performance patterns do not guarantee future outcomes. Instead, alpha’s direction may depend on evolving market conditions, economic variables, and the unique characteristics of the Red asset class. Investors should consider these elements when forming expectations for alpha. For investors, this implies that relying solely on historical alpha trends may not provide a clear-cut forecast. Instead, they should maintain a forward-looking perspective and continuously assess the evolving landscape. Alpha’s sign may depend on factors such as market sentiment, economic cycles, or shifts in investor preferences. Therefore, potential investors should exercise caution, conduct thorough due diligence, and remain adaptable in their investment decisions. It is worth noting that while alpha may change, the coefficients for MktRf, SMB, and HML remain relatively consistent with the previous period in the 2010–2019 era. However, there are variations in the profitability factor (CMA) and the robust-minus-weak factor (RMW) coefficient, which is not statistically significant, and the momentum factor (MOM), which exhibits a negative impact on Red returns during this period. Considering the entire period from 2000 to 2019, the models consistently display negative alphas for the Red asset class. This consistent pattern suggests that investors should approach the Red asset class with caution, particularly if they have a historical perspective. However, it is important to recognize that past performance may not always mirror future results, and investors should consider the broader context.

In conclusion, the change in the sign of alpha for Red stocks underscores the dynamic nature of financial markets. Investors should approach their decisions with caution, considering a broader set of factors and recognizing that historical trends are not infallible interpreters of future outcomes.

Comparing the beta coefficients of different securities across two distinct subperiods revealed significant changes in risk sensitivities and exposures. For Red and Grey securities, notable fluctuations in their beta values were observed, indicating either an increase or a decrease in their sensitivity to market risk. This suggests that the risk profiles of these securities have altered over time. Furthermore, there is a noticeable change in risk exposures, particularly for Green and Red securities. This variation indicates shifts in how these securities respond to broader market movements, reflecting changes in their market behaviour and risk profiles. These findings enhance the understanding of how economic conditions have evolved between the two periods. The observed changes in beta values and risk exposures underscore that shifts in the economic environment have impacted the risk behaviour of different types of securities. This underscores the broader implication that market conditions and investor perceptions have undergone significant transformations over time, influencing the risk dynamics of securities categorized as Red, Grey, and Green.

The coefficient of the SMB is positive; this suggests that the securities have exposure to small-cap stocks, but the degree of exposure depends on the beta value of the SMB, which for Green and Grey stocks increases from subperiod to subperiod. The positive coefficient of the HML in Green and Red assets suggests that the stocks have exposure to high book-to-market (value) stocks, and the Grey assets have exposure to low-value stocks (in the first half). The momentum (MOM) coefficient has a negative sign for Grey assets, which suggests that these types of assets have exposure to a portfolio with aggressive loser momentum. In other words, these assets tend to perform worse when it comes to stocks that have been experiencing strong negative momentum or losing streaks. Negative momentum implies that stocks with a history of poor recent performance will continue to perform poorly in the short term. Investors typically view negative momentum as a sign of weakness or distress in those stocks. It could be due to factors such as poor earnings, unfavourable news, or market sentiment turning against them. For investors and financial institutions, this has practical implications. It suggests that when constructing portfolios that include Grey assets, they should be aware of the potential impact of stocks with aggressive loser momentum. These assets may be more susceptible to underperformance during periods when stocks with negative momentum are struggling. Additionally, investors should assess their risk tolerance and portfolio diversification strategies, especially when considering investments in assets with negative momentum exposure. It may be important to balance such assets with other investments to manage risk effectively. For example, they might choose to allocate smaller proportions of their portfolios to Grey assets during periods when negative momentum stocks dominate the market. Alternatively, they may implement risk mitigation strategies, such as stop-loss orders or hedging techniques, to protect their portfolios in the face of adverse momentum trends.

The CMA estimated coefficients are negative and statistically significant (at 5%), which means that the asset class is exposed to the firms investing aggressively. Corresponding to the findings of the profitability (RMW) factor coefficient, the Red stock is exposed to high operating profitability firms, and contrariwise, the Grey stock indicates exposure to low operating profitability firms. Furthermore, the Green and Red stocks increase their exposure to the market (MktRf) factor substantially, even though this exposure has the most significant impact among the other factors. In contrast, Grey securities decrease their exposure to the global market from the first to the second half period.

In some cases, the assets show similar behaviour (or risk exposure) since the economy represents the systematic risk, where it cannot diversify away. That means that during periods of economic turbulence or significant market events, many assets may respond in a similar way because they are influenced by the same underlying economic or market forces. This phenomenon is often observed when economic conditions lead to increased correlations between the risk factors (as indicated in Table 4, Table 5 and Table 6). Diversification is an investment strategy where investors spread their investments across different asset classes to reduce risk. However, systematic risk cannot be diversified away because it affects all assets within a particular market or the entire economy. Even a well-diversified portfolio may still be exposed to systematic risk, as it is inherent to the broader economic environment. In some cases, it can be challenging to generate alpha consistently because systematic risk dominates, leaving limited room for active managers or investors to outperform the market.

Moreover, the overall R-sq and the relatively consistent coefficients between the subperiods underscore the robustness of our results and ensure that they detects meaningful relationships between the asset class and the factors from the asset pricing models. The principles of the asset pricing models contribute to accurately capturing the distinct characteristics of the asset class returns and the significant results, enhancing the confidence in the reliability of our conclusions.

The empirical results have several implications for investors. The positive alphas observed for the Grey and Red assets (for the first half period) imply that it has provided excess returns beyond what could be explained by traditional risk factors. This finding may attract investors seeking higher returns. On the other hand, the mixed results observed for the Green, Grey, and Red assets (for the second period and the whole period) suggest that they may not always outperform the market on a risk-adjusted basis. Investors interested in these asset classes should exercise caution and conduct further analysis to understand the underlying risk factors driving their performance.

Over the two subperiods and the whole inquiry period, this study observed a sharp change or shift in the risk sensitivities and the significant level of the betas, which strengthened our belief that the financial crisis changed the economic environment from the first to the second subperiod.

The findings from this research analysis offer valuable insights for investors and their understanding of the financial market for these asset classes. The Grey asset class shows potential for underperformance, especially in the post-ante EU crisis period. The Green asset class exhibits a relatively consistent performance with negative alpha values, albeit smaller in magnitude. The Red asset class consistently displays negative alpha values, indicating the potential for unattractive risk-adjusted returns. Investors should consider these results while making investment decisions and building diversified portfolios. The variations in the coefficients for the risk factors highlight the importance of assessing each asset class’s unique risk–return profile and tailoring investments to align with individual investment goals and risk tolerance. Overall, this research analysis emphasizes the importance of rigorous analysis when evaluating asset classes and the need for the continuous monitoring of their performance to optimize portfolio outcomes.

The unadjusted overall R-squared is consistently higher for almost every asset group in the five-factor Fama and French model, except for the second subperiod, in which the performance is slightly better with the 4-factor model in Grey and Red. This improvement in the results is generally due to model expansion and not necessarily better explanatory performance. In most cases, the unadjusted R-squared values for the Green and Grey stocks are low in cross-sectional data compared to time-series data. This discrepancy arises due to the relatively higher heterogeneity present in the cross-sectional data, where each stock represents a distinct entity, and the dataset is predominantly cross-sectional in nature and not time-dominant. The low R² between the values for the Green and Grey assets reflects the high heterogeneity in the cross-sectional panel data—each asset behaves uniquely, and sector-wide patterns are less pronounced. The results suggest that the models perform better at capturing time-series variations (within assets) rather than differences across companies. This means that the R-squared between is lower than the R-squared within and, therefore, the R-squared overall. An optimal model is the trade-off for the R-sq between and after within, and that model explains the variation within time and cross-sectional asset returns.

Table 10. Overall adjusted R-squared decomposition by model and asset class.

Asset Class	Period	Model 1	Model 2	Model 3	Model 4	Model 5	Model 6
Green	2000–2009	15.22%	14.49%	13.77%	15.20%	14.51%	13.78%
	2010–2019	12.57%	12.00%	11.36%	12.50%	11.91%	11.29%
	2000–2019	13.65%	13.06%	12.45%	13.56%	12.98%	12.42%
Grey	2000–2009	17.07%	17.14%	17.32%	16.89%	17.01%	17.07%
	2010–2019	12.88%	12.87%	12.80%	12.83%	12.82%	12.78%
	2000–2019	14.70%	14.74%	14.79%	14.70%	14.75%	14.73%
Red	2000–2009	18.16%	17.96%	17.75%	18.17%	18.33%	17.84%
	2010–2019	10.89%	10.69%	10.42%	11.36%	11.12%	10.88%
	2000–2019	12.92%	12.69%	12.49%	13.01%	12.99%	12.62%

This table shows the overall adjusted R² (pseudo R²)8 from the models 1, 2, 3, 4, 5, and 6 per asset group (Green, Red, and Grey) per period, where the first three models are the 3-factor Fama and French model, the 4-factor Carhart model, and the 5-factor Fama and French model, respectively, and the last models 4, 5, and 6 are the same with the HML Devil.

presents the overall adjusted R² values, which assess the models that most effectively explain the behaviour of the asset returns. Looking at the adjusted R² results, the three-factor Fama and French model (Model 1) often provides a better trade-off between complexity and explanatory power, particularly for the Green and Red asset groups. For instance, the adjusted R² for Model 1 is 13.65% for Green, 12.92% for Red, and 14.70% for Grey, compared to 12.45%, 12.49%, and 14.79%, respectively, in the five-factor model. This suggests that simpler models may offer a better fit relative to their complexity, particularly for Green and Grey assets. This pattern suggests that the marginal explanatory gain from additional factors in Model 3 is insufficient to compensate for their added complexity. The same applies to the Carhart model variants (Models 2–5), where the adjusted R² values remain lower than or equal to those of the simpler models (1–4). In the case of the Red assets, models 2–5 have better performance compared to models 1 and 3.

During periods of crisis, the behaviour of the Red asset returns group is of particular interest due to the heightened market volatility and disruptions in financial markets. In the analysis, the unadjusted R-squared within was notably lower compared to the ex-crisis period. This suggests that a significant proportion of the variability in the dependent variable can be attributed to factors specific to the assets within the group. This phenomenon is likely influenced by several factors that are specific to crisis periods. Firstly, heightened idiosyncratic risk within individual assets (or sectors) may play a significant role, stemming from company-specific factors, operational challenges, or market sentiment. Additionally, market dislocations and disruptions during crises contribute to significant deviations in asset prices from their fundamental values within each asset group, leading to increased variability in asset returns.

Furthermore, flight-to-safety behaviour among investors during crises may lead to increased correlations within certain asset classes or sectors, further contributing to a higher variability in returns within the asset group. Additionally, liquidity constraints may exacerbate variability in asset returns within the group as investors face challenges in executing trades. Practically, the elevated R² within the Red group may stem from an increased systemic risk, correlated shocks, or investor behaviour under stress, such as herding and flight-to-safety tendencies. In contrast, Green and Grey asset returns remain more idiosyncratic and harder to explain through standard factor models during such periods.

In conclusion, while the five-factor model has the highest unadjusted R² overall, the three-factor Fama and French model (Model 1) consistently provides the best adjusted fit, especially for Green and Grey asset classes, and the four-factor model mostly does so for the Red asset. This highlights the importance of balancing model complexity with parsimony, particularly in panel data with cross-sectional heterogeneity. The results underscore that in turbulent periods, asset return behaviour becomes more complex, and a model’s ability to explain variations depends not just on more variables but on capturing the correct dynamics with minimal overfitting. Furthermore, it highlights the importance of analyzing and understanding the behaviour of asset returns within specific asset groups during periods of crisis, as this variability may provide valuable insights into the underlying factors driving market fluctuations and investor behaviour.

7. Discussion and Conclusions

The primary purpose of this research is to examine the factor structure of Green, Grey, and Red stock returns. In essence, this research examines the risk sensitivities of EU Green, Grey, and Red securities. As mentioned, a Red asset return is the return associated with the equity returns of environmentally unfriendly companies. Conversely, a Green asset return is an implicit return associated with environmentally friendly equities. In the analysis, the included “Grey” equities are neither Red nor Green (essentially, all other equities in the database after excluding unspecified activities or unknown industry companies or securities without any variation in the sample).

This study is based on a combination of previous research, which provides a solid background for academics and practitioners to understand Green, Grey, and Red’s classification, and research to assess their risk–return profile. The significance of certain factors in explaining the specific asset group returns can lead to a deeper understanding of the underlying market dynamics. For instance, the positive and significant coefficients of certain factors for the Green asset class may suggest that size, value, and currency have a substantial impact on returns in this type of group. Similarly, exploring the factors that significantly influence the Red and Grey asset classes can offer insights into their unique risk–return profiles. Overall, this analysis underscores the importance of asset pricing models and the need for investors to carefully consider market dynamics when making investment decisions. The findings contribute to a more nuanced understanding of asset pricing for different asset classes and encourage further research to develop more sophisticated models for improved investment outcomes. Investors should remain vigilant and tailor their investment strategies based on the specific risk factors driving each asset class’s returns to achieve their financial goals effectively.

One of the significant findings of this research is the presence of negative alpha within the majority of asset class categories when evaluated within the framework of factor models. This negative alpha is consistently observed in comparison to the market proxy portfolio and the other proxy portfolios that contribute to explaining the risk-adjusted returns. Every asset class diverges in either the exposure to the global factor or the significance level. Despite this fact, the samples have different business activities between the asset classes but have similar risk behaviours, and a reason for this is an adaptation in the economic environment or possible behavioural herding for these asset classes. According to the findings, the Green and Red stocks are exposed to small-cap and generally high-value stocks, implying that these firms behave similarly to small-cap stocks in their return profiles. This indicates a shared sensitivity to size-related risks—such as limited access to capital markets or greater earnings volatility—but it also suggests potential to benefit from the small-cap premium when market conditions are favourable. Grey stocks, however, show weaker or negligible SMB loadings during the first half and whole period, which places them closer to large-cap or more stable firms in terms of risk exposure.

Regarding the HML (High Minus Low) factor, results show a positive and significant loading for Green stocks across most periods and models, indicating that Green stocks tend to behave like value stocks, or at least have a stronger exposure to the value premium. One interpretation is that these firms hold relatively higher book-to-market ratios, thus capturing compensation for bearing value-related risks. Alternatively, this could reflect the structural features of Green firms, such as capital intensity or underappreciated earnings, that result in a value-like return profile. Grey stocks, on the other hand, often show negative or weak HML loadings, especially in the earlier periods, aligning them more closely with growth firms that derive valuations from expected future performance rather than current fundamentals.

The analysis reveals that Red stocks exhibit a notable affinity for low-profitability stocks, as indicated by the RMW (robust minus weak) factor. Conversely, Grey stocks display a predilection for investments associated with higher levels of profitability. This highlights the contrasting investment profiles between the two categories of stocks based on their exposure to the RMW factor. For all the periods, the market factor mostly occurs with the highest risk exposure compared to the other factors for any asset class. These differences give insights into risk and return and help us better understand the vulnerabilities for every asset class. An important consideration in assessing asset risk is how an asset reacted before and after the economic downturn; the Green assets show a stable risk profile compared to the other two asset classes. Looking at the prominent models’ risk exposures indicates at least three stable factors and at least five on the extension models for every class in European monthly stock returns.

A striking and puzzling result is the high similarity in factor exposures between Green and Red stocks. Despite representing seemingly opposite categories in terms of sector focus or strategic orientation, the alpha and beta parameters for these two groups have nearly identical behaviour across models and time periods. This challenges the expectation that asset classes with different sectoral or operational profiles should exhibit divergent pricing behaviours. In particular, the similarity in their exposures to the major proxy factors (market, size, value, profitability, and investment) suggests that shared market or structural characteristics outweigh class-level distinctions in explaining their returns. This similarity in risk exposure is particularly surprising given the theoretical expectations that these asset types should differ in pricing between expected and realized returns, as argued by Pástor et al. (2021, 2022). One would expect sustainability characteristics, investor preferences, or regulatory outlooks to cause meaningful divergence in factor sensitivities, especially in risk premia like value, size, or profitability. This convergence may reflect overlapping economic realities, such as similar levels of profitability, investment behaviour, or capital structure. Alternatively, it may point to a lack of price differentiation between these categories in European equity markets—meaning that, based on standard factor models, investors do not currently demand or reward different risk premiums for the characteristics that distinguish Green from Red assets. This may also imply that investor segmentation or preferences have not yet created strong enough market frictions to generate divergence in risk pricing between these groups. Further research could investigate whether this alignment persists in different regions or under changing regulatory environments.

Ultimately, the findings raise important questions about how systematically priced characteristics manifest in different asset groups and whether more refined or alternative factors are needed to explain cross-sectional differences in returns beyond those captured by the standard Fama–French extensions.

Cochrane (2001) and Bartram et al. (2021) emerged with the case of the “factors zoo” and offered a new technique to differentiate between beneficial, worthless, and redundant factors, which systematically examines and assesses potential factors on the asset price model.

According to Jegadeesh et al. (2019), portfolios are extensively used to evaluate asset pricing models to mitigate an inherent errors-in-variables bias; yet, portfolios may obscure significant risk–return-related aspects of individual equities. Applying the instrumental variables technique allows the use of particular Green, Grey, and Red assets while still producing consistent ex-post-risk premium estimates.

Overall, while the five-factor Fama and French model yields the highest unadjusted R² across most asset classes, the adjusted R² results suggest that simpler models—particularly the three-factor model—often strike a better balance between explanatory power and model complexity. This is especially evident for Green and Red assets. Additionally, the consistently higher within R² values point to stronger time-series explanatory power relative to cross-sectional variation, underscoring the importance of capturing temporal dynamics in asset return modelling.

Every asset class includes a lot of securities from different countries; therefore, the data density for this is hard to explain with a small partition of signals/factors. Also, this study reveals that the factor exposure changes from period to period, which is consistent with mispricing history and important for future research to broaden the analysis with additional market signals. The inducement in the crisis showed that the previous conditions could lead to complacency and the underpricing of risk and that the financial world was arguably lulled into a false sense of confidence by the quiet–good economic conditions in earlier (pre-crisis) years. The methodology maintains the relationships between security returns and risk factors that have been observed in the past. Also, the complexity of the securities market infrastructure changes the risk models’ life cycle, especially after the EU crisis event.

Since all studies face limitations, focusing on the results from the first subperiod may possibly produce a misleading outcome for the later years. The results are based on stocks within the European markets and are affected by EU policies. In the asset pricing models, the application requires a liquid market, which is reflected in the securities’ returns. However, in some rare cases, the sample has access to illiquid securities on which the transformation method is applied to reveal the impact of the factors. Additionally, we can explore other macro-factors or create them for the European securities, such as the liquidity (LIQ) factor (Pástor & Stambaugh, 2003), which gauges the liquidity risk. Another factor is the combination of the ESG (Environmental, Social, Governance) and the sales divided by the producing emission, called the greenness factor. This factor is suitable to consider a new aspect of the Red (or Grey) stocks and how the sales of the Red companies are associated with carbon emissions. One noteworthy issue that merits discussion is whether the Green company is complying with Green activities, as detailed in regulation policies, to be characterized “Green”.

The factor models provide further insights and control into multi- or single-asset class investing; therefore, one key feature of finance theory is to retain several asset classes so that they can generate a diversified portfolio. In other words, the investors can use the signals from the factors’ exposure and expect that when one asset class has poor returns, then another may have good returns (Markowitz, 1952). By employing these ideas of conventional philosophy, investors will develop vehicles to allocate investment within the three classes (Green, Grey, and Red) and create a cross-sectional equity strategy. Firms or investors can apply an easier strategy and apply it to a similar industry-specific class by using this classification and seeking to maintain optimal exposure to a diverse set of factors. Therefore, the investor can identify the types of stocks or cases where other classes overperform. The factors develop new trading strategies for the specific asset group, seeking higher returns and understanding the risk exposure. Those elements drive the financial performance of the group securities, and the next step is the optimization framework. The research reveals the characteristics of every asset class, which the participants can use to identify whether the investment process is suitable to perform for their risk tolerance and also to benefit from using an appropriate mix of investments and strategies between the asset classes.