Factor Structure of Green, Grey, and Red EU Securities

Abstract

This study examined the factor structure of Green, Grey, and Red EU securities using extended asset pricing models built on the Fama–French and Carhart frameworks. The findings show improved return predictability and consistently negative risk-adjusted alpha across categories post-Global Financial Crisis (GFC), suggesting systematic overestimation of expected returns. All environmental asset types are positively linked to the MKTRF, SMB, HML, and HML^Devil factors, indicating exposure to core risk premia. Green securities exhibit elevated currency risk and persistent negative momentum, while Red assets transition from positive to negative momentum. Green and Red securities show stronger gold associations post-GFC, signaling a hedging role. Grey assets shift away from safe-haven behavior, becoming more sensitive to volatility. FEAR factor exposure and QML results suggest evolving sensitivity and declining quality, particularly in Grey assets. These findings underscore the need for enriched asset pricing models to capture dynamic risk characteristics in environmental assets within the EU financial markets.

1. Introduction

In recent decades, financial market dynamics have evolved significantly, with investor preferences shifting towards sustainable investing practices. This transformation has been driven by an increasing awareness of environmental issues, along with the growing social push for environmental responsibility in business operations. Particularly in the European Union (EU), this shift is evident in the rise of “Green assets”, which are financial products linked to environmentally responsible practices. The global market for Green bonds, for example, grew from USD 257.7 billion in 2019 to over USD 5 trillion by 2024, reflecting the growing demand for sustainable investment opportunities (Climate Bonds Initiative 2020, 2024). Similarly, the market for Green stocks—shares of companies actively engaged in environmentally sustainable practices—has expanded significantly. According to the Global Sustainable Investment Alliance (2022) Review, sustainable investment assets in Europe comprised approximately 40% of global totals in 2022, underscoring the importance of sustainable finance in contemporary markets. As investor demand for environmentally sustainable portfolios continues to rise, understanding the risk and return characteristics of these categorized stocks is essential for both investors and policymakers.

The primary objective of this research is to examine the risk–return dynamics of Green, Grey, and Red stocks within the EU financial markets. Grey stocks refer to neutral assets that are neither environmentally friendly nor explicitly harmful, while Red stocks represent eco-enemy assets, typically linked to industries or activities with negative environmental impacts (see

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

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

Source: Kepler Cheuvreux, CBI, FTSE, MSCI, and Kottas (2024, 2025).

). By investigating how various factors influence the returns of these types of assets, this study seeks to offer valuable insights into how these stocks behave in terms of risk and reward. In doing so, it provides essential information for investors aiming to optimize their portfolios by balancing sustainability goals with financial performance. Furthermore, this research is significant to policymakers, as it can inform regulatory measures supporting sustainable investing and help reduce systemic financial risks.

Traditional asset pricing models often fail to fully capture the complexities of an asset’s factor structure, which is why incorporating extended factor models is essential. According to Chiah et al. (2019), analysis shows that while the five-factor model improves upon previous models, it still leaves significant pricing errors, prompting questions about its completeness. The extended models aim to enhance asset pricing predictions by integrating additional factors that account for anomalies and market dynamics overlooked by classical models. Feng et al. (2020) highlight the need to tame the “factor zoo”, referring to the proliferation of numerous factors proposed to explain asset returns. Their study systematically evaluates these factors and identifies those that significantly improve the explanatory power of asset pricing models, thus offering more reliable risk–return assessments. Similarly, Hou et al. (2015) extend the traditional Fama–French three-factor model by adding factors such as momentum and other anomalies, demonstrating that these extensions provide a more comprehensive framework for understanding asset returns. Zhang and Lence (2022) review various asset pricing models, including the Fama–French five-factor framework, highlighting the challenges in consistently capturing cross-sectional return patterns and calling for more flexible and adaptive models. Both studies emphasize that expanding asset pricing models with new factors can deepen our understanding of financial market behavior and enhance investment strategies.

Another part of this study extends the work of Kottas (2025), who focused primarily on the Fama–French and Carhart models, by incorporating a broader set of systematic factors. While the three- and four-factor frameworks provide a solid foundation for capturing size, value, market, and momentum premia, they leave out other important sources of variation in environmental asset returns. To address this, we add additional renowned factors such as BAB (low volatility), FEAR (volatility risk), commodity, currency, and quality (QMJ), all of which are widely used in extended asset pricing models.

The findings of this study make a notable contribution to the growing body of research on environmental finance and asset pricing. By extending traditional models to include factors that account for environmental considerations, this research not only enhances the understanding of risk and return dynamics in the context of Green, Grey, and Red stocks but also informs investment strategies and policy decisions. As sustainable investing continues to gain traction, the insights gained from this study will be valuable for portfolio managers seeking to optimize their investments to align financial returns with environmental values. Additionally, the findings may serve as a guide for policymakers working to develop regulations that promote sustainable investing and mitigate the financial risks associated with environmental issues.

The paper is structured as follows: The subsequent sections review previous classifications of Green, Grey, and Red/Brown assets alongside the asset pricing models applied to these categories. The next section outlines the data collection process and discusses the methodology, focusing on the extension of the Fama–French (3FF and 5FF) and Carhart (4-factor) models. The last section uses empirical models to address the primary research questions and discusses the key findings and applications.

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

This study classifies European securities into Green and Red (Brown) asset categories, drawing upon prior literature and the classification framework established by Kepler Cheuvreux (2015). The classification is conducted at the sectoral level, considering firms’ core business activities. Building the work of Cojoianu et al. (2020), sector classifications are refined by incorporating firms’ carbon emissions and economic activities and categorizing them into Green, Grey, and Red groups.

A methodological approach akin to Bolton and Kacperczyk (2021) and Bolton et al. (2022) differentiates Green and Brown assets based on firms’ carbon emissions. However, our study adopts a distinct classification methodology: Brown assets represent companies with high carbon emissions, while Green assets denote lower-emitting firms. Alternative classification frameworks, such as those proposed by In et al. (2019) and Cheema-Fox et al. (2021), employ emission intensity normalized by firm size to provide a more granular assessment. Bauer et al. (2023) integrate multiple approaches to quantify a firm’s “greenness” through CO₂ emissions measurement. Similarly, Pástor et al. (2021, 2022) utilize environmental ratings to evaluate corporate sustainability. However, these methodologies are subject to limitations arising from inconsistencies in emissions data and variability in rating scores across different databases.

Following Kottas (2024, 2025) and Kepler Cheuvreux (2015) reports, this study adopts a sectoral classification framework based on Table 1, which derives categorization criteria from institutional reports and widely recognized classification standards. This approach facilitates a systematic comparison of environmental performance across industry segments. By leveraging established data sources and standardized methodologies, the study ensures classification consistency and reliability, thereby enhancing the robustness of the empirical analysis.

1.2. Factor Models

In financial asset pricing, the primary goal is to explain both the cross-sectional and time-series variations in asset returns. Factor models offer a parsimonious framework for identifying and capturing the sources of systematic risk. A general form for studying asset returns using factor models is represented as

r = B f + e

(1)

where r is the N × 1 vector of asset returns for N assets (in this case, Green, Grey, or Red securities), B is the N × K matrix of factor loadings (K systematic factors), f is the K × 1 vector of factors, and e is the error term representing the idiosyncratic component of the returns.

Factor models are widely used in finance for portfolio analysis, risk decomposition, performance evaluation, and market efficiency testing. The asset pricing models allow researchers to explain asset returns through exposures to systematic risk factors, such as single-factor (e.g., CAPM) or classical multi-factor models, e.g., the Fama–French three-factor (Fama and French 1993) and five-factor (Fama and French 2015) models, as well as the Carhart (1997) four-factor model. Recent literature has extended these models to improve explanatory power, incorporating additional factors (Asness et al. 2019; Asness and Frazzini 2013; Frazzini and Pedersen 2014; Durand et al. 2011; Connor and Korajczyk 2022).

Our study focuses on extending the Fama–French three/five-factor models and four-factor model by adding several additional factors, including momentum, the Fear (VIX) factor, quality, BAB factor, commodity factors, and currency factors, to better capture asset return variations (Asness et al. 2019; Asness and Frazzini 2013; Frazzini and Pedersen 2014; Durand et al. 2011; Connor and Korajczyk 2022; Feng et al. 2020; Whaley 2009).

The Fama–French five-factor model (Fama and French 2015) builds upon their three-factor model by adding two key factors: profitability (RWA) and investment (CMA). However, in this study, we extend the model further by incorporating the momentum factor (MOM), a factor from Carhart (1997), often referred to as the Up minus Down (UMD) factor, reflecting the difference in returns between winning and losing stocks (Carhart 1997). While the standard five-factor model excludes momentum, Dirkx and Peter (2020) suggest that adding MOM to the five-factor framework enhances its explanatory power. This results in a six-factor model, which includes market excess return, size, value, profitability, investment, and momentum. The model is formulated as

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\mathsf{\beta }}_{i,\mathit{SMB}}\ast \mathrm{E}\left(\mathit{SMB}\right)+{\mathsf{\beta }}_{i,\mathit{HML}}\ast \mathrm{E}\left(\mathit{HML}\right)+{\mathsf{\beta }}_{i,\mathit{RWA}}\ast \mathrm{E}\left(\mathit{RWA}\right)+{\mathsf{\beta }}_{i,\mathit{CMA}}\ast \mathrm{E}\left(\mathit{CMA}\right)+{\mathsf{\beta }}_{i,\mathit{MOM}}\ast \mathrm{E}\left(\mathit{MOM}\right),$$

(2)

Empirical findings suggest that the inclusion of MOM improves model fit, especially in periods of market turbulence, where momentum strategies tend to perform strongly (Asness and Frazzini 2013; Dirkx and Peter 2020). This addition aligns with prior literature advocating for momentum as a persistent risk factor, capturing the cross-sectional return differences between past winners and losers.

Asness et al. (2019) and Asness and Frazzini (2013) introduced an extension to the Fama–French framework by incorporating a quality factor, which is designed to capture the performance of stocks with different levels of operational quality. This factor aims to distinguish high-quality firms from low-quality ones by evaluating profitability, growth, and risk characteristics. The extended model is formulated as

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\mathsf{\beta }}_{i,\mathit{SMB}}\ast \mathrm{E}(\mathit{SMB})+{\mathsf{\beta }}_{i,\mathit{HML}}\ast \mathrm{E}(\mathit{HML})+{\mathsf{\beta }}_{i,\mathit{QMJ}}\ast \mathrm{E}(\mathit{QMJ})+{\mathsf{\beta }}_{i,\mathit{BAB}}\ast \mathrm{E}(\mathit{BAB}),$$

(3a)

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\mathsf{\beta }}_{i,\mathit{SMB}}\ast \mathrm{E}\left(\mathit{SMB}\right)+{\mathsf{\beta }}_{i,\mathit{HML}}\ast \mathrm{E}\left(\mathit{HML}\right)+{\mathsf{\beta }}_{i,\mathit{RWA}}\ast \mathrm{E}\left(\mathit{RWA}\right)+{\mathsf{\beta }}_{i,\mathit{CMA}}\ast \mathrm{E}\left(\mathit{CMA}\right)+{\mathsf{\beta }}_{i,\mathit{QMJ}}\ast \mathrm{E}\left(\mathit{QMJ}\right)+{\mathsf{\beta }}_{i,\mathit{BAB}}\ast \mathrm{E}\left(\mathit{BAB}\right),$$

(3b)

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\mathsf{\beta }}_{i,\mathit{SMB}}\ast \mathrm{E}\left(\mathit{SMB}\right)+{\mathsf{\beta }}_{i,\mathit{HML}}\ast \mathrm{E}\left(\mathit{HML}\right)+{\mathsf{\beta }}_{i,\mathit{MOM}}\ast \mathrm{E}\left(\mathit{MOM}\right)+{\mathsf{\beta }}_{i,\mathit{QMJ}}\ast \mathrm{E}\left(\mathit{QMJ}\right)+{\mathsf{\beta }}_{i,\mathit{BAB}}\ast \mathrm{E}\left(\mathit{BAB}\right),$$

(3c)

Furthermore, the Fear (VIX) factor, introduced by Durand et al. (2011), is designed to capture market fear and volatility and can be incorporated as an additional risk factor:

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\beta }_{i,\mathit{SMB}}\ast \mathrm{E}\left(\mathit{SMB}\right)+{\beta }_{i,\mathit{HML}}\ast \mathrm{E}\left(\mathit{HML}\right)+{\beta }_{i,\mathit{FEAR}}\ast \mathrm{E}\left(\mathit{FEAR}\right),$$

(4a)

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\beta }_{i,\mathit{SMB}}\ast \mathrm{E}\left(\mathit{SMB}\right)+{\beta }_{i,\mathit{HML}}\ast \mathrm{E}\left(\mathit{HML}\right)+{\beta }_{i,\mathit{RWA}}\ast \mathrm{E}\left(\mathit{RWA}\right)+{\beta }_{i,\mathit{CMA}}\ast \mathrm{E}\left(\mathit{CMA}\right)+{\beta }_{i,\mathit{FEAR}}\ast \mathrm{E}\left(\mathit{FEAR}\right),$$

(4b)

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\beta }_{i,\mathit{SMB}}\ast \mathrm{E}\left(\mathit{SMB}\right)+{\beta }_{i,\mathit{HML}}\ast \mathrm{E}\left(\mathit{HML}\right)+{\beta }_{i,\mathit{MOM}}\ast \mathrm{E}\left(\mathit{MOM}\right)+{\beta }_{i,\mathit{FEAR}}\ast \mathrm{E}\left(\mathit{FEAR}\right),$$

(4c)

Likewise, the commodity and currency factors, as discussed by Connor and Korajczyk (2022), are also added to further enhance explanatory power for assets sensitive to these market variables:

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\mathsf{\beta }}_{i,\mathit{SMB}}\ast \mathrm{E}\left(\mathit{SMB}\right)+{\mathsf{\beta }}_{i,\mathit{HML}}\ast \mathrm{E}\left(\mathit{HML}\right)+{\mathsf{\beta }}_{i,\mathit{CURR}}\ast \mathrm{E}\left(\mathit{CURR}\right)+{\mathsf{\beta }}_{i,\mathit{Gold}}\ast \mathrm{E}\left(\mathit{Gold}\right),$$

(5a)

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\beta }_{i,\mathit{SMB}}\ast \mathrm{E}\left(\mathit{SMB}\right)+{\beta }_{i,\mathit{HML}}\ast \mathrm{E}\left(\mathit{HML}\right)+{\beta }_{i,\mathit{RWA}}\ast \mathrm{E}\left(\mathit{RWA}\right)+{\beta }_{i,\mathit{CMA}}\ast \mathrm{E}\left(\mathit{CMA}\right)+{\beta }_{i,\mathit{CURR}}\ast \mathrm{E}\left(\mathit{CURR}\right)+{\beta }_{i,\mathit{Gold}}\ast \mathrm{E}\left(\mathit{Gold}\right),$$

(5b)

$$\mathrm{E}\left(r_i{,}_t\right) - r_f= {\mathsf{\beta }}_{i,M} \ast \left(\mathrm{E}\right(R_M) - r_f)+{\beta }_{i,\mathit{SMB}}\ast \mathrm{E}\left(\mathit{SMB}\right)+{\beta }_{i,\mathit{HML}}\ast \mathrm{E}\left(\mathit{HML}\right)+{\beta }_{i,\mathit{MOM}}\ast \mathrm{E}\left(\mathit{MOM}\right)+{\beta }_{i,\mathit{CURR}}\ast \mathrm{E}\left(\mathit{CURR}\right)+{\beta }_{i,\mathit{Gold}}\ast \mathrm{E}\left(\mathit{Gold}\right),$$

(5c)

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

The introduction of additional factors such as momentum, FEAR (VIX), commodities, and currency aims to capture more comprehensive systematic risk exposures, improving the model’s ability to explain variations in asset returns. These factors allow for a more nuanced understanding of market dynamics, particularly in turbulent market conditions. In addition, Asness et al. (2019), Asness and Frazzini (2013) and Frazzini and Pedersen (2014) further enhance the Fama–French models by incorporating the Value II (known as HML devil) factor and the betting against beta factor, respectively. These factors help account for the variations in returns associated with stocks exhibiting extreme characteristics, such as those with low or high betas.

Our study applied these extended models, including momentum, quality, the Fear (VIX) factor, commodities, and currency factors, to analyze the returns of Green, Grey, and Red EU securities. These extensions offer deeper insights into the risk factors driving returns for sustainable assets, highlighting the role of additional sources of systematic risk that are often overlooked in traditional models (Asness and Frazzini 2013; Connor and Korajczyk 2022).

By incorporating these extensions, our analysis provides a more accurate representation of the asset pricing mechanisms underlying the Green, Grey, and Red stocks in the EU market, with a particular focus on how these factors influence environmentally classified securities. These models allow us to explore the factor structures that drive returns and offer valuable insights into the asset pricing literature.

1.3. Data Collection

This study examined stocks from 28 EU countries, categorized into Green, Red, and Grey groups, with 2007 Grey, 150 Green, and 367 Red stocks, covering the period from 1 January 2000 to 31 December 2019, at a monthly frequency. The focus is on the sensitivity of risk factors before and after the 2009 Global Financial Crisis (GFC). The Classical Risk factors (MKT, SMB, HML, and MOM) are collected from Kenneth R. French’s library, and additional factors (BAB, HML DEVIL, QML) from the Asness and Frazzini database, along with stock prices, EU volatility, commodity prices, and currency data from Thomson Reuters Eikon. The stock sample includes publicly listed companies prior to 2015, excluding those with missing data, infrequent trading, or no price variation. Stocks with over 80% missing data are removed and data are cleaned by addressing errors, zero prices, and extreme returns through winsorization at the 95% level to mitigate outlier effects.

1.4. Methodology

This study employs an extended multi-factor asset pricing model to analyze the return structure of Green, Grey, and Red stocks in the European market. While traditional models like the Fama–French three-factor (FF3), Fama–French five-factor (FF5), and Carhart four-factor (C4F) models have been widely used to explain asset returns (Fama and French 1992, 1993, 1995, 1996, 1998, 2012, 2015; Carhart 1997), our approach directly extends prior research (Kottas 2025) by incorporating additional risk factors. Recent literature highlights the significance of alternative factors such as momentum, betting against beta (BAB), Quality Minus Junk (QMJ), currency, commodity, and Fear (VIX) factors in capturing systematic risk (Asness et al. 2019; Asness and Frazzini 2013; Frazzini and Pedersen 2014; Connor and Korajczyk 2022; Durand et al. 2011; Bartram et al. 2021).

The estimation process follows a two-stage panel regression approach with random effects1, which accounts for heterogeneity across stock categories while allowing broader generalizations to the EU stock market, making the findings more applicable to investors and policymakers (Baltagi 2005; Greene 2012; Hsiao 2014; Kottas 2025). This method efficiently estimates the factor effects on stock returns while accommodating the panel structure of our data. Given that securities are grouped by sector and exhibit repeated observations, random effects estimation ensures robust parameter estimation while preserving time-invariant relationships (Cameron and Trivedi 2009). The models presented below represent a subset of the extended specifications estimated from Equations (2)–(5):

$$r_{i,t}^j- r_{f,t}= a_i+ b_{1,i}^j{MKTRF}_t+b_{2,i}^j{SMB}_t+ b_{3,i}^j{HML}_t+b_{4,i}^j{BAB}_t+ b_{5,i}^j{QMJ}_t+e_{i,t}^j,$$

(6)

$$r_{i,t}^j- r_{f,t}= a_i+ b_{1,i}^j{MKTRF}_t+b_{2,i}^j{SMB}_t+ b_{3,i}^j{HML}_t+b_{4,i}^j{MOM}_t+ b_{5,i}^j{CUR}_t+b_{6,i}^j{Gold}_t{+ e}_{i,t}^j,$$

(7)

$$r_{i,t}^j- r_{f,t}= a_i+ b_{1,i}^j{MKTRF}_t+b_{2,i}^j{SMB}_t+ b_{3,i}^j{HML}_t+b_{4,i}^j{RMW}_t+b_{5,i}^j{CMA}_t+b_{6,i}^j{MOM}_t+e_{i,t}^j, 6\text{-}factormodel$$

(8)

where $r_{i,t}^j$ is the return of asset i at time t (within the period, 2000–2019) and j the type of asset, Green, Red, or Grey; $r_{f,t}$ is the risk-free rate at time t; MKTRF (market excess return), SMB (size factor), HML^Devil (updated value factor), MOM (momentum factor), RMW (profitability factor), CMA (investment factor), BAB (betting against beta), QMJ (quality minus junk), Currency and Commodities, and VIX (investor sentiment) are the independent risk factors. The a_i is the risk-adjusted alpha performance, and b_k is the coefficient from the specific k-factor and measures the exposure of assets i to the k-factor, while $e_{i,t}^j$ represents the error term.

Including currency and commodity factors captures the impact of exchange rate fluctuations and commodity price changes on stock returns. Institutional investors utilize these factors to hedge risks in globally diversified portfolios (Pojarliev and Levich 2008). While commodities historically provided a hedge against inflation and diversification benefits, their performance during the 2008–2009 Global Financial Crisis raised concerns about their stability as an asset class (Blitz and De Groot 2014; Bartram and Bodnar 2009).

Lastly, the Fear (VIX) factor reflects investor sentiment and expected market volatility, serving as a proxy for risk aversion in financial markets (Durand et al. 2011). Given its influence on stock returns, its inclusion provides insights into the relationship between investor behavior and asset pricing.

1.5. Empirical Results and Findings

Table 2. Cross-sectional averages of time-series moments for monthly simple returns from the three categories before and after winsorization.

Asset Class		Green Securities Returns		Grey Securities Returns		Red Securities Returns
Period	Summary Stats	Winsorization		Winsorization		Winsorization
		Before	After	Before	After	Before	After
2000–2009	Mean	1.16	0.89	0.7	0.4	1.18	0.99
	Variance	328.18	201.4	310.81	171.83	222.99	133.37
	Skewness	4.27	1.19	5.87	0.89	5.03	0.83
	Kurtosis	65.83	7.30	135.59	6.2	96.12	7.41
	Min	−95.8	−51.06	−95.66	−59.44	−96.94	−60.92
	Max	437.38	140.12	698.02	199.11	414.37	125.57
	T; n	120; 120	120; 120	120; 1652	120; 1652	120; 286	120; 286
2010–2019	Mean	0.68	0.15	0.85	0.59	0.35	0.05
	Variance	395.95	186.7	224.25	133.83	298.15	186.11
	Skewness	9.5	1.26	8.24	1.67	6.01	1.75
	Kurtosis	203.93	8.95	223.26	19.01	107.18	18.77
	Min	−94.64	−57.59	−98.91	−74.13	−95.71	−73.97
	Max	621.19	140.12	687.66	275.62	526.91	233.94
	T; n	120; 150	120; 150	120; 2007	120; 2007	120; 367	120; 367
2000–2019	Mean	0.86	0.42	0.8	0.51	0.65	0.39
	Variance	371.04	192.24	258.77	148.99	271.11	167.23
	Skewness	7.92	1.23	7.08	1.29	5.77	1.51
	Kurtosis	165.5	8.29	178.88	12.56	106.14	16.51
	Min	−95.8	−57.59	−98.91	−74.13	−96.94	−73.97
	Max	621.19	140.12	698.02	275.62	526.91	233.94
	T; n	240; 150	240; 150	240; 2007	240; 2007	240; 367	240; 367

The table shows the first four moments of Green, Red, and Grey returns (in percentage, %) and the minimum and maximum return within the two subperiods, and the whole period (the observations time is between 1/2000 and 12/2019, with separation in 12/2009). The table includes the results from before and after winsorization at 95% and the number of cross-sectional (n) securities, and the total months include every security (T).

reports summary statistics for the Green, Grey, and Red (or Brown) stock returns and compares them before and after the winsorization method. At the end of the specific period, we mention the dimension of the sample.

I.

Summary statistics of Green, Grey, and Red securities returns

Table 2 reports summary statistics on Green, Red, and Grey asset returns with Green having 120 assets in the first half of the period and 150 assets in the second half of the period and for the whole period. The Red stocks comprise 286 assets in the first period and 367 assets in the second half of the period, and the whole sample. For Green assets, the mean return for the period 2000–2009 was 1.16% per month, decreasing to 0.89% after winsorization. For the period 2010–2019, the mean return decreased from 0.68% to 0.15% after winsorization. Over the entire 2000–2019 period, the mean return decreased from 0.86% to 0.42% after winsorization. Winsorization also led to reductions in variance, skewness, and kurtosis, indicating a more stable return distribution, a reduction in volatility and tail risk. For the opposite type of securities (Red), the mean return before winsorization was observed to be 0.7% for the period 2000–2009, decreasing to 0.4% (after winsorization). For the period 2010–2019, the mean return decreased from 0.85% to 0.59% after winsorization. Over the entire 2000–2019 period, the mean return decreased from 0.8% to 0.51% after winsorization. Lastly, for the neutral type of securities (Grey), the mean return for the period 2000–2009 was 1.18%, decreasing to 0.99% after winsorization. For the period 2010–2019, the mean return decreased from 0.35% to 0.05% after winsorization. Over the entire 2000–2019 period, the mean return decreased from 0.65% to 0.39% after winsorization. Winsorization significantly impacted variance, skewness, and kurtosis, resulting in a more robust data representation. Comparing the effects of winsorization across the three categories, we observe that Grey Securities experienced the most significant reduction in mean returns after winsorization, indicating a substantial impact on their performance. In contrast, Red Securities showed more moderate changes, while Green Securities experienced a relatively moderate decrease in mean returns.

The analysis of monthly simple returns for Green, Grey, and Red Securities reveals that winsorization effectively mitigates the influence of outliers and stabilizes the distribution of simple returns. The reduction in moments (Mean, Variance, Skewness, and Kurtosis) indicates a more reliable representation of the underlying data. The comparison across categories highlights varying degrees of impact, with Grey Securities being most affected and Red Securities and Green Securities showing more resilience. These findings provide valuable insights for investors and researchers seeking to better understand the behavior of different categories of securities and the effect of the extreme values in the distribution.

In our research, we analyze data on a monthly frequency, and we test the optimal level of winsorization at 0.01, 0.05, and 0.10, and the most suitable level was 0.05 to draw conclusions. The reason we employ the standardization technique known as winsorization is to mitigate the impact of extreme price fluctuations.

II.

Factor structure of Green, Grey, and Red securities

The extended models are utilized to characterize the factor structure of the Green, Grey, and Red stock universe. The analysis is based on empirical results derived from random effects regression using simple returns for the full period of 2000–2019, as well as sub-periods (2000–2009 and 2010–2019). These extension models enhance the explanatory power of traditional asset pricing frameworks and allow for a more nuanced understanding of the risk–return dynamics within the three categories of stocks.

Table 3. Empirical results for Green returns—extension (period 2000–2019 and the sub-periods).

Period	Model	Alpha	MktRf	SMB	HML/ HML II *	BAB	QML	FEAR	R-sq Within	R-sq Between	R-sq Overall
2000–2009	[1]	0.27	0.95	0.57	0.15	0.01			17.54%	1.39%	17.36%
	[2]	0.29	0.94	0.56	0.14	0.02	−0.03		17.54%	1.36%	17.36%
	[3]	0.27	0.94	0.57	0.15	0.01		−0.01	17.55%	1.41%	17.36%
	[4] *	0.26	0.94	0.55	0.11	0.04			17.53%	1.56%	17.36%
	[5] *	0.25	0.94	0.55	0.11	0.04		−0.001	17.53%	1.57%	17.36%
2010–2019	[1]	−0.56	1.03	0.83	0.35	0.03			14.52%	1.34%	14.33%
	[2]	−0.48	1.00	0.79	0.26	0.06	−0.16		14.53%	1.38%	14.34%
	[3]	−0.55	1.00	0.86	0.36	0.05		−0.01	14.53%	1.36%	14.34%
	[4] *	−0.54	1.04	0.79	0.37	0.09			14.46%	1.56%	14.27%
	[5] *	−0.51	0.99	0.83	0.39	0.11		−0.02	14.48%	1.62%	14.29%
2000–2019	[1]	−0.30	0.99	0.69	0.30	−0.01			15.50%	2.67%	15.39%
	[2]	−0.28	0.98	0.68	0.28	−0.00	−0.03		15.50%	2.65%	15.39%
	[3]	−0.29	0.97	0.70	0.30	0.001		−0.01	15.50%	2.72%	15.40%
	[4] *	−0.32	0.99	0.66	0.23	0.05			15.42%	2.50%	15.31%
	[5] *	−0.32	0.97	0.67	0.24	0.06		−0.01	15.42%	2.57%	15.32%

The table shows the alpha and beta value of the MktRf, SMB, HML, BAB, QML, and FEAR factors from the random effect regression (after winsorization). The global factors are collected from the Kenneth R. French, Datastream, and Asness data library. Additionally, the results report both dependent variables, which are simple returns. We denote models 1, 2, and 3; as an extension, we use the 3-factor Fama–French model by applying additional factors from Asness and Durand. Models 4 and 5 are the same, but substitute HML with HML II (or Devil) and denoted with *. The table reports the results using extension models with different factors. 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 that we mentioned in our table (below and over 5%).

,

Table 4. Empirical results for Green returns—extension II (period 2000–2019 and the sub-periods).

Period	Model	Alpha	MktRf	SMB	HML/ HML II *	MOM	UK/ EUR	GOLD	R-sq Within	R-sq Between	R-sq Overall
2000–2009	[1]	0.2	0.93	0.61	0.13		0.18		17.64%	0.94%	17.46%
	[2]	0.27	0.95	0.57	0.15			0.002	17.54%	1.4%	17.36%
	[3]	0.2	0.93	0.61	0.13		0.18	0.01	17.64%	0.94%	17.46%
	[4]	0.2	0.93	0.61	0.13	−0.01	0.18		17.64%	0.93%	17.46%
	[5]	0.27	0.95	0.57	0.15	0.01		0.001	17.55%	1.39%	17.36%
	[6]	0.19	0.93	0.61	0.13	−0.01	0.19	0.01	17.64%	0.93%	17.46%
	[7] *	0.18	0.92	0.63	0.12		0.21		17.65%	0.93%	17.48%
	[8] *	0.3	0.94	0.58	0.1			−0.003	17.52%	1.58%	17.34%
	[9] *	0.17	0.92	0.62	0.12		0.22	0.01	17.66%	0.93%	17.48%
2010–2019	[1]	−0.54	1.03	0.84	0.33		0.15		14.57%	2.07%	14.38%
	[2]	−0.57	1.04	0.85	0.38			0.07	14.56%	1.66%	14.37%
	[3]	−0.57	1.04	0.85	0.36		0.15	0.07	14.61%	2.45%	14.43%
	[4]	−0.42	1.02	0.85	0.27	−0.13	0.19		14.62%	2.37%	14.43%
	[5]	−0.49	1.03	0.85	0.34	−0.09		0.06	14.58%	1.75%	14.4%
	[6]	−0.46	1.03	0.85	0.3	−0.12	0.18	0.06	14.66%	2.75%	14.47%
	[7] *	−0.47	1.03	0.82	0.35		0.19		14.53%	2.6%	14.35%
	[8] *	−0.5	1.04	0.82	0.35			0.01	14.45%	1.54%	14.26%
	[9] *	−0.48	1.04	0.82	0.34		0.19	0.02	14.45%	1.54%	14.26%
2000–2019	[1]	−0.32	0.98	0.71	0.28		0.17		15.57%	3.17%	15.47%
	[2]	−0.34	0.99	0.68	0.31			0.04	15.51%	2.86%	15.41%
	[3]	−0.35	0.98	0.70	0.29		0.17	0.04	15.59%	3.37%	15.48%
	[4]	−0.29	0.97	0.71	0.26	−0.03	0.18		15.58%	3.18%	15.47%
	[5]	−0.32	0.99	0.69	0.31	−0.09		0.04	15.51%	2.86%	15.41%
	[6]	−0.32	0.97	0.71	0.28	−0.03	0.18	0.04	15.59%	3.39%	15.49%
	[7] *	−0.30	0.97	0.71	0.23		0.21		15.53%	3.15%	15.42%
	[8] *	−0.30	0.99	0.69	0.22			0.01	15.41%	2.31%	15.30%
	[9] *	−0.31	0.98	0.71	0.23		0.21	0.02	15.53%	3.21%	15.42%

The table shows the alpha and beta value of the MktRf, SMB, HML, MOM, UK/EUR, and Gold factors from the random effect regression (after winsorization). The global factors are collected from the Kenneth R. French, Datastream, and Asness data library. Additionally, the results report both dependent variables, which are simple returns. We denote models 1, 2, and 3; as an extension, we use the 3-factor Fama–French and 4-factor Carhart models by applying additional factors of commodities and currencies. Models 7, 8, and 9 are the same, but substitute HML with HML II (or Devil) and denoted with *. The table reports the results using the extension models with different factors. 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 that we mentioned in our table (below and over 5%).

,

Table 5. Empirical results for Grey returns—extension (period 2000–2019 and the sub-periods).

Period	Model	Alpha	MktRf	SMB	HML/ HML II *	BAB	QML	FEAR	R-sq Within	R-sq Between	R-sq Overall
2000–2009	[1]	0.08	0.91	0.72	−0.18	−0.12			17.45%	11.54%	17.34%
	[2]	0.31	0.78	0.58	−0.32	0.01	−0.37		17.56%	12.53%	17.46%
	[3]	0.07	0.93	0.73	−0.18	−0.14		0.01	17.46%	11.48%	17.36%
	[4] *	0.002	0.90	0.74	−0.06	−0.15			17.34%	12.42%	17.24%
	[5] *	−0.002	0.92	0.75	−0.06	−0.17		0.01	17.35%	12.41%	17.25%
2010–2019	[1]	−0.11	0.86	0.72	0.16	0.10			13.18%	0.56%	13.04%
	[2]	−0.08	0.85	0.71	0.13	0.11	−0.06		13.18%	0.56%	13.04%
	[3]	−0.10	0.84	0.75	0.16	0.11		−0.01	13.19%	0.54%	13.05%
	[4] *	−0.12	0.88	0.71	0.11	0.11			13.13%	0.58%	12.99%
	[5] *	−0.11	0.85	0.73	0.13	0.13		−0.01	13.14%	0.57%	13.01%
2000–2019	[1]	−0.08	0.90	0.73	−0.03	−0.08			14.95%	1.08%	14.87%
	[2]	0.12	0.81	0.62	−0.16	0.02	−0.32		15.04%	0.97%	14.96%
	[3]	−0.08	0.91	0.72	−0.03	−0.08		0.002	14.95%	1.08%	14.87%
	[4] *	−0.08	0.90	0.73	−0.01	−0.08			14.95%	1.13%	14.87%
	[5] *	−0.08	0.90	0.73	−0.01	−0.09		0.002	14.95%	1.12%	14.87%

The table shows the alpha and beta value of the MktRf, SMB, HML, BAB, QML, and FEAR factors from the random effect regression (after winsorization). The global factors are collected from the Kenneth R. French, Datastream, and Asness data library. Additionally, the results report both dependent variables, which are simple returns. We denote models 1, 2, and 3; as an extension, we use the 3-factor Fama–French model by applying additional factors from Asness and Durand. Models 4 and 5 are the same, but substitute HML with HML II (or Devil) and denoted with *. The table reports the results using extension models with different factors. 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 that we mentioned in our table (below and over 5%).

,

Table 6. Empirical results for Grey returns—extension II (period 2000–2019 and the sub-periods).

Period	Model	Alpha	MktRf	SMB	HML/ HML II *	MOM	UK/ EUR	GOLD	R-sq Within	R-sq Between	R-sq Overall
2000–2009	[1]	−0.04	0.90	0.64	−0.23		0.13		17.37%	12.02%	17.27%
	[2]	0.03	0.91	0.63	−0.22			−0.03	17.33%	12.33%	17.23%
	[3]	−0.007	0.90	0.65	−0.23		0.12	−0.03	17.37%	12.11%	17.27%
	[4]	0.06	0.84	0.69	−0.27	−0.12	0.16		17.53%	11.01%	17.42%
	[5]	0.11	0.87	0.66	−0.25	−0.10		−0.02	17.45%	11.68%	17.34%
	[6]	0.06	0.84	0.69	−0.27	0.12	0.16	−0.01	17.53%	11.06%	17.42%
	[7] *	−0.21	0.89	0.63	−0.02		0.10		17.17%	12.88%	17.07%
	[8] *	−0.15	0.90	0.62	−0.02			−0.01	17.14%	12.98%	17.04%
	[9] *	−0.20	0.89	0.64	−0.02		0.10	−0.01	17.17%	12.90%	17.07%
2010–2019	[1]	−0.04	0.86	0.76	0.14		0.14		13.22%	0.62%	13.08%
	[2]	−0.05	0.86	0.76	0.16			0.01	13.15%	0.56%	13.01%
	[3]	−0.04	0.86	0.76	0.14		0.14	0.003	13.22%	0.62%	13.08%
	[4]	0.05	0.85	0.76	0.09	−0.10	0.17		13.26%	0.57%	13.12%
	[5]	0.05	0.86	0.76	0.13	−0.07		0.002	13.17%	0.53%	13.04%
	[6]	0.05	0.85	0.76	0.09	−0.10	0.17	−0.0003	13.26%	0.57%	13.12%
	[7] *	−0.04	0.87	0.75	0.09		0.16		13.18%	0.66%	13.05%
	[8] *	−0.04	0.87	0.75	0.10			−0.02	13.10%	0.55%	12.96%
	[9] *	−0.03	0.87	0.75	0.10		0.16	−0.02	13.18%	0.63%	13.05%
2000–2019	[1]	−0.14	0.90	0.69	−0.06		0.14		14.98%	1.24%	14.90%
	[2]	−0.12	0.90	0.68	−0.05			−0.02	14.92%	1.08%	14.84%
	[3]	−0.13	0.89	0.69	−0.06		0.14	−0.02	14.98%	1.19%	14.90%
	[4]	−0.04	0.86	0.71	−0.10	−0.11	0.16		15.08%	1.21%	14.99%
	[5]	−0.03	0.87	0.70	−0.08	−0.09		−0.02	14.99%	1.05%	14.91%
	[6]	−0.03	0.86	0.72	−0.10	−0.11	0.16	−0.01	15.08%	1.17%	15.00%
	[7] *	−0.14	0.89	0.69	0.01		0.13		14.97%	1.33%	14.89%
	[8] *	−0.13	0.89	0.68	0.01			−0.01	14.91%	1.18%	14.83%
	[9] *	−0.14	0.89	0.69	0.01		0.13	−0.01	14.97%	1.31%	14.89%

The table shows the alpha and beta value of the MktRf, SMB, HML, MOM, UKEUR, and Gold factors from the random effect regression (after winsorization). The global factors are collected from the Kenneth R. French, Datastream, and Asness data library. Additionally, the results report both dependent variables, which are simple returns. We denote models 1, 2, and 3; as an extension, we use the 3-factor Fama–French and 4-factor Carhart models by applying additional factors of commodities and currencies. Models 7, 8, and 9 are the same, but substitute the HML with HML II (or Devil) and denoted with *. The table reports the results using extension models with different factors. 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 that we mentioned in our table (below and over 5%).

,

Table 7. Empirical results for Red returns—extension (period 2000–2019 and the sub-periods).

Period	Model	Alpha	MktRf	SMB	HML/ HML II *	BAB	QML	FEAR	R-sq Within	R-sq Between	R-sq Overall
2000–2009	[1]	0.18	0.80	0.51	0.11	0.22			19.68%	20.72%	19.54%
	[2]	0.19	0.80	0.50	0.11	0.22	−0.004		19.68%	20.70%	19.54%
	[3]	0.19	0.77	0.49	0.13	0.25		−0.02	19.75%	20.21%	19.60%
	[4] *	0.07	0.78	0.49	0.20	0.27			19.93%	20.11%	19.77%
	[5] *	0.08	0.74	0.47	0.20	0.30		−0.02	19.99%	19.63%	19.83%
2010–2019	[1]	−0.61	0.93	0.55	0.37	0.09			11.73%	1.34%	11.64%
	[2]	−0.58	0.92	0.54	0.34	0.10	−0.05		11.73%	1.32%	11.64%
	[3]	−0.61	0.93	0.55	0.37	0.09		−0.0006	11.73%	1.34%	11.64%
	[4] *	−0.42	0.86	0.47	0.73	0.19			12.26%	1.39%	12.17%
	[5] *	−0.40	0.83	0.50	0.75	0.21		−0.01	12.27%	1.38%	12.18%
2000–2019	[1]	−0.41	0.86	0.53	0.31	0.17			13.8%	11.43%	13.77%
	[2]	−0.46	0.89	0.56	0.35	0.15	0.09		13.81%	11.64%	13.78%
	[3]	−0.40	0.83	0.54	0.32	0.19		−0.01	13.82%	11.40%	13.79%
	[4] *	−0.44	0.84	0.49	0.40	0.26			14.07%	12.82%	14.04%
	[5] *	−0.43	0.80	0.50	0.41	0.28		−0.01	14.10%	12.68%	14.08%

The table shows the alpha and beta value of the MktRf, SMB, HML, BAB, QML, and FEAR factors from the random effect regression (after winsorization). The global factors are collected from the Kenneth R. French, Datastream, and Asness data library. Additionally, the results report both dependent variables, which are simple returns. We denote models 1, 2, and 3; as an extension, we use the 3-factor Fama–French model by applying additional factors from Asness and Durand. Models 4 and 5 are the same, but substitute the HML with HML II (or Devil) and denoted with *. The table reports the results using extension models with different factors. 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 that we mentioned in our table (below and over 5%).

and

Table 8. Empirical results for Red returns—extension II (period 2000–2019 and the sub-periods).

Period	Model	Alpha	MktRf	SMB	HML/ HML II *	MOM	UK/ EUR	GOLD	R-sq Within	R-sq Between	R-sq Overall
2000–2009	[1]	0.31	0.80	0.68	0.17		−0.02		19.15%	23.39%	19.02%
	[2]	0.27	0.80	0.68	0.17			0.03	19.16%	23.53%	19.03%
	[3]	0.27	0.80	0.68	0.17		−0.01	0.03	19.16%	23.48%	19.03%
	[4]	0.25	0.84	0.65	0.21	0.09	−0.05		19.25%	22.87%	19.12%
	[5]	0.22	0.83	0.66	0.20	0.08		0.02	19.24%	23.13%	19.11%
	[6]	0.35	0.84	0.65	0.21	0.08	−0.04	0.01	19.25%	22.94%	19.12%
	[7] *	0.30	0.78	0.70	0.14		0.02		19.16%	23.85%	19.03%
	[8] *	0.28	0.79	0.69	0.14			0.03	19.17%	23.86%	19.03%
	[9] *	0.26	0.79	0.70	0.14		0.02	0.03	19.17%	23.91%	19.04%
2010–2019	[1]	−0.54	0.92	0.58	0.37		0.03		11.72%	1.24%	11.63%
	[2]	−0.59	0.94	0.59	0.42			0.11	11.83%	1.30%	11.74%
	[3]	−0.59	0.94	0.59	0.42		0.03	0.11	11.83%	1.28%	11.74%
	[4]	−0.42	0.91	0.59	0.30	−0.14	0.07		11.78%	0.87%	11.68%
	[5]	−0.49	0.93	0.60	0.37	−0.11		0.10	11.87%	1.01%	11.78%
	[6]	−0.48	0.93	0.60	0.36	−0.12	0.06	0.10	11.88%	0.93%	11.79%
	[7] *	−0.31	0.86	0.54	0.70		0.07		12.20%	1.18%	12.10%
	[8] *	−0.34	0.88	0.54	0.69			0.04	12.20%	1.18%	12.10%
	[9] *	−0.33	0.87	0.54	0.69		0.07	0.04	12.21%	1.20%	12.12%
2000–2019	[1]	−0.29	0.86	0.64	0.33		0.001		13.67%	11.03%	13.63%
	[2]	−0.35	0.87	0.62	0.36			0.08	13.74%	12.10%	13.71%
	[3]	−0.36	0.87	0.63	0.36		0.001	0.08	13.74%	12.11%	13.71%
	[4]	−0.33	0.87	0.63	0.35	0.04	−0.001		13.68%	11.17%	13.64%
	[5]	−0.38	0.88	0.62	0.37	0.03		0.08	13.75%	12.20%	13.71%
	[6]	−0.38	0.88	0.62	0.37	0.03	−0.003	0.08	13.75%	12.19%	13.71%
	[7] *	−0.27	0.84	0.65	0.35		0.05		13.77%	12.36%	13.73%
	[8] *	−0.30	0.86	0.64	0.35			0.05	13.79%	12.53%	13.75%
	[9] *	−0.31	0.85	0.64	0.35		0.05	0.05	13.80%	12.67%	13.76%

The table shows the alpha and beta value of the MktRf, SMB, HML, MOM, UKEUR, and Gold factors from the random effect regression (after winsorization). The global factors are collected from the Kenneth R. French, Datastream, and Asness data library. Additionally, the results report both dependent variables, which are simple returns. We denote models 1, 2, and 3; as an extension, we use 3-factor Fama–French and 4-factor Carhart models by applying additional factors of commodities and currencies. Models 7, 8, and 9 are the same, but substitute the HML with HML II (or Devil) and denoted with *. The table reports the results using the extension models with different factors. 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 that we mentioned in our table (below and over 5%).

exhibit the findings from the extensions of two asset pricing models: the 3-factor and 4-factor models. Each pair of tables corresponds to a specific asset class return (Green, Grey, and Red, respectively), employing explanatory factors sourced from the Kenneth R. French library, Datastream, and Asness database. The empirical results are produced from the estimation of Equations (2)–(5) and their extensions by employing additional European factors for the construction of our models. Likewise,

Table A8. Empirical results of the extension models for Green returns.

Green R. Factors	2000–2009 Ex-Ante EU Crisis				2009–2019 Post-Ante EU Crisis				2000–2019 Full Period
alpha	0.18	0.18	0.28	0.45	−0.49	−0.44	−0.47	−0.14	−0.31	−0.31	−0.26	−0.10
MktRf	0.97	0.98	0.91	0.76	1.00	1.02	0.96	0.84	0.98	1.00	0.95	0.80
SMB	0.59	0.60	0.54	0.48	0.85	0.84	0.81	0.75	0.71	0.71	0.68	0.62
HML	0.13	0.12	0.05		0.36	0.31	0.32		0.27	0.25	0.23
MOM		−0.01		0.15		−0.09		−0.02		−0.03		0.07
RMW	0.12	0.12	0.27	0.55	−0.07	−0.04	−0.05	0.03	0.01	0.03	0.1	0.3
CMA	0.11	0.12	0.18	−0.02	−0.11	−0.05	−0.1	−0.05	0.08	0.1	0.13	0.14
BAB			0.05	0.11			0.09	0.01			0.03	0.02
HML DEVIL				0.12				0.2				0.13
QMJ			−0.25	−0.76			−0.17	−0.4			−0.15	−0.55
FEAR	−0.01		−0.01	0.01	−0.01		−0.01	−0.02	−0.01		−0.01	−0.01
US/EUR				−0.79				0.32				0.21
JAP/EUR				0.12				−0.07				0.03
UK/EUR				0.44				0.12				0.17
KR/EUR				0.7				−0.11				−0.05
CHN/EUR				−0.05				0.09				0.04
Lumber				0.02				−0.01				0.002
Brent				−0.001				−0.03				−0.01
Aluminium				−0.06				0.02				−0.01
Gold				0.02				0.05				0.05
R2-within	17.6%	17.6%	17.6%	18.1%	14.5%	14.5%	14.5%	14.7%	15.5%	15.5%	15.5%	15.7%
R2-between	1.81%	1.83%	1.91%	0.75%	1.41%	1.44%	1.46%	3.57%	2.77%	2.74%	2.78%	3.79%
R2-overall	17.4%	17.4%	17.4%	17.9%	14.3%	14.4%	14.4%	14.6%	15.4%	15.4%	15.4%	15.6%

The table shows the alpha and beta value of MktRf, SMB, HML, MOM, RMW, CMA, MOM, HML(Devil), FEAR, BAB, QML, four commodities, and five currencies factors from the random effect regression (after winsorization). The global factors were collected from the Kenneth R. French data library, DataStream, and the Asness & Frazzini library. The results include the period 2000–2019 and the sub-periods ex- and post-EU crisis. The table reports the results from the extensions models, and the last 3 rows 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 at 5%.

,

Table A9. Empirical results of the extension models for Grey returns.

Grey R. Factors	2000–2009 Ex-Ante EU Crisis				2009–2019 Post-Ante EU Crisis				2000–2019 Full Period
alpha	0.23	0.25	0.29	0.30	−0.06	−0.01	−0.05	0.16	0.04	0.07	0.11	0.22
MktRf	0.89	0.86	0.88	0.78	0.86	0.87	0.81	0.75	0.88	0.87	0.85	0.75
SMB	0.65	0.68	0.69	0.76	0.78	0.78	0.72	0.65	0.68	0.70	0.67	0.69
HML	−0.38	−0.42	−0.42		0.17	0.12	0.13		−0.22	−0.26	−0.27
MOM		−0.07		−0.04		−0.08		−0.10		−0.08		−0.08
RMW	−0.53	−0.46	−0.38	−0.37	0.06	0.08	0.18	0.24	−0.41	−0.36	−0.28	−0.14
CMA	0.08	0.15	0.17	−0.18	0.08	0.14	0.08	0.14	0.06	0.13	0.13	−0.04
BAB			−0.05	−0.14			0.14	0.09			−0.00	−0.08
HML DEVIL				−0.13				−0.07				−0.17
QMJ			−0.14	−0.04			−0.19	−0.39			−0.17	−0.21
FEAR	0.01		0.01	0.001	−0.01		−0.01	−0.01	−0.00		−0.00	−0.01
US/EUR				0.25				0.22				0.32
JAP/EUR				−0.12				−0.02				−0.08
UK/EUR				−0.01				0.17				0.08
KR/EUR				0.001				−0.17				−0.11
CHN/EUR				0.04				0.09				0.04
Lumber				0.03				0.01				0.02
Brent				−0.02				−0.01				−0.01
Aluminium				−0.02				−0.02				−0.01
Gold				−0.02				0.02				0.01
R2-within	17.7%	17.7%	17.7%	17.8%	13.2%	13.2%	13.2%	13.4%	15.1%	15.1%	15.1%	15.3%
R2-between	13.1%	12.5%	12.6%	12.2%	0.55%	0.53%	0.53%	0.68%	0.93%	0.91%	0.9%	1.09%
R2-overall	17.6%	17.6%	17.6%	17.7%	13%	13.1%	13.1%	13.2%	15%	15%	15%	15.2%

The table shows the alpha and beta value of MktRf, SMB, HML, MOM, RMW, CMA, MOM, HML(Devil), FEAR, BAB, QML, four commodities, and five currencies factors from the random effect regression (after winsorization). The global factors were collected from the Kenneth R. French data library, DataStream, and the Asness & Frazzini library. The results include the period 2000–2019 and the sub-periods ex- and post-EU crisis. The table reports the results from the extensions models, and the last 3 rows 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 at 5%.

and

Table A10. Empirical results of the extension models for Red returns.

Red R. Factors	2000–2009 Ex-Ante EU Crisis				2009–2019 Post-Ante EU Crisis				2000–2019 Full Period
alpha	0.12	0.11	0.22	−0.20	−0.59	−0.48	−0.56	−0.27	−0.41	−0.42	−0.43	−0.44
MktRf	0.84	0.85	0.71	0.80	0.94	0.93	0.89	0.65	0.88	0.89	0.84	0.71
SMB	0.69	0.67	0.43	0.43	0.59	0.62	0.52	0.37	0.67	0.66	0.55	0.42
HML	0.21	0.24	0.14		0.41	0.33	0.36		0.37	0.37	0.34
MOM		0.05		0.16		−0.14		0.04		0.01		0.13
RMW	0.33	0.29	0.23	0.16	0.12	0.15	0.27	0.12	0.23	0.22	0.16	0.08
CMA	0.09	0.04	−0.05	−0.17	0.08	0.18	0.10	−0.02	0.13	0.12	0.05	0.03
BAB			0.29	0.21			0.13	0.12			0.18	0.12
HML DEVIL				0.44				0.59				0.47
QMJ			−0.18	0.04			−0.23	−0.19			−0.05	−0.08
FEAR	−0.00		−0.02	−0.01	0.00		0.00	−0.01	−0.00		−0.01	−0.01
US/EUR				−0.05				0.38				0.32
JAP/EUR				−0.04				−0.03				−0.01
UK/EUR				0.06				0.03				−0.01
KR/EUR				0.03				−0.16				−0.16
CHN/EUR				0.05				0.02				0.06
Lumber				−0.00				0.02				0.01
Brent				0.5				0.10				0.09
Aluminium				−0.02				0.02				0.01
Gold				−0.01				0.03				0.03
R2-within	19.3%	19.4%	19.8%	20.4%	11.7%	11.8%	11.8%	12.7%	13.7%	13.7%	13.8%	14.6%
R2-between	24.2%	22.9%	19.9%	20.4%	1.39%	1.11%	1.45%	1.74%	12.1%	12.1%	11.8%	13.5%
R2-overall	19.2%	19.2%	19.7%	20.3%	11.6%	11.7%	11.7%	12.6%	13.7%	13.7%	13.8%	14.6%

The table shows the alpha and beta value of MktRf, SMB, HML, MOM, RMW, CMA, MOM, HML(Devil), FEAR, BAB, QML, four commodities, and five currencies factors from the random effect regression (after winsorization). The global factors were collected from the Kenneth R. French data library, DataStream, and the Asness & Frazzini library. The results report dependent variables as simple returns. The table reports the results from the extensions models, and the last 3 rows 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 that we mentioned in our table (below and over 5%).

present the results from the extension asset pricing models from the Fama–French 5-factor model. The empirical results are produced by estimating the extended equations of the classical 3-, 4-, and 5-factor models.

In analyzing the behavior of various stock categories within portfolios, our study reveals noteworthy patterns regarding Green, Red and Grey stocks, particularly during distinct time periods. Notably, the alpha for the Green, Red (except the first half of the period), and Grey (except the first half of the period) asset classes is mostly negative, suggesting potential underperformance. The adjusted alpha decreases for the Red and Grey assets by switching from positive to negative alphas. The value of the beta MktRf for the Red, Green, and Grey asset classes are consistently around 0.9, indicating a positive strong correlation with market movements. Coefficients for other factors (HML, MOM, RMW, CMA, FEAR, BAB, and QML) exhibit variations across sub-periods, with some factors being statistically significant in certain periods. Comparing the previous table’s 5FF model and the 5-factor model substituting HML(devil), we can conclude that HML(Devil) does not add significant information for the Green and Grey stocks. However, for the Red securities, HML(Devil) shows a considerable improvement on the model comparing the results from Table 7 and Table 8.

Every asset class has similar significant factors with dissimilar relative exposure, and the level of exposure changes significantly from model to model. The most common observations indicate that stocks classified as Red and Grey (during the post-crisis period and whole period) tend to exhibit high beta portfolios. Grey assets during the first half of the period typically demonstrate exposure to low beta portfolios, while those classified as Red (in the first half of the period) and Grey (in the second half of the period) are adversely affected by high volatility, which means that they are impacted by the high level uncertainty in the market. Notably, within the Grey category, three factors—HML, FEAR, and BAB—exhibit switching behavior from the pre-crisis to the post-crisis period. This shift may be attributed to changing market dynamics and investor sentiments during these distinct periods. This phenomenon underscores the dynamic nature of market influences on Grey stocks, necessitating further examination to elucidate the underlying mechanisms driving these shifts. Moreover, the coefficient for the momentum (MOM) factor is negative for Grey stocks and, in the second half, for Green and Red stocks. Conversely, in the first half of the period, it is positive for Red stocks. The coefficient representing the change in the exchange rate of the UK currency (with the euro as the base currency) is positive for Green and Grey stocks. Conversely, the negative coefficient for the Quality Minus Junk (QMJ) factor in Grey stocks highlights exposure to lower quality or ‘junk’ stocks, suggesting a higher risk profile compared to stocks with stronger financial fundamentals. Also, the favorable influence of the UK pound exchange rate underscores the significance of currency factors, aligning with the findings of Pojarliev and Levich (2008) that establish a connection between stock returns and currencies. One notable dissimilarity observed in our analysis is the positive impact of changes in gold on the Red and Green asset class (in the second half of the period), contrasting with the negative impact on the Grey asset class. This finding aligns with the assumption made by Bams et al. (2017) regarding the strong relationship between stocks and commodities, particularly gold and oil price. Red stocks are typically linked to industries heavily reliant on non-renewable energy sources and commodities, such as oil. This assumption suggests that Red stocks tend to exhibit a positive exposure to fluctuations in commodity prices, especially oil and gold (Baur and Lucey 2010). This expectation stems from the observation that industries like energy, mining, and materials are directly influenced by changes in commodity prices. When commodity prices, including oil, rise, companies operating within these sectors often experience increased revenues and profitability. This, in turn, leads to higher stock prices. Thus, the sensitivity of Red stocks to commodity price fluctuations may result in a positive relationship between Red stocks and gold prices. Investor sentiment and market perception play a significant role in influencing asset prices. This assumption acknowledges the impact of positive sentiment surrounding the energy sector. Factors such as rising global energy demand, geopolitical events, and supply constraints can foster optimistic outlooks for the energy sector, prompting increased investments in Red stocks. This heightened investor interest can subsequently drive up the prices of Red stocks in response to surges in commodity prices, particularly in the case of oil and gold (see Appendix A Table A9).

In conclusion, the premise of Red stocks displaying a positive exposure to changes in gold and oil prices aligns with the assumption of a robust stock–commodity relationship, particularly for sectors closely intertwined with non-renewable energies. Nevertheless, it is imperative to acknowledge the intricacies of these relationships and their susceptibility to variations over time and under diverse circumstances. Another application is when investors want to adopt portfolio diversification strategies encompassing assets from various sectors, including those associated with non-renewable energies. This assumption recognizes that such diversification strategies may inadvertently lead to positive exposure to commodity price changes. By diversifying across sectors, investors may indirectly embrace the broader market dynamics influenced by commodity movements. Investors and researchers should consider these multifaceted factors when analyzing and interpreting asset pricing models in the broader dynamics of financial markets.

Over the two sub-periods and the whole inquiry period, we 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 altered the economic environment between the first the second sub-period.

This research analysis offers 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 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 coefficients for 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 continuous monitoring of their performance in order to optimize portfolio outcomes.

The three-factor Fama–French model extensions best explain return behavior for Red, Green, and Grey assets. The extended model shows superior performance, with higher R-squared values, typically ranging from 13% to 20% overall. The R-squared for Green and Grey assets is lower in cross-sectional data compared to time-series data, due to greater heterogeneity in cross-sectional data. The optimal model balances the R-squared between and within time and cross-sectional variations in asset returns.

During crisis periods, Red asset returns show lower R-squared values compared to non-crisis periods, indicating higher variability. This is due to increased idiosyncratic risk, market dislocations, investor flight to safety, and liquidity constraints. The lower R-squared highlights the complexity of asset pricing during crises and highlights the need for a deeper understanding of asset group behavior in such conditions.

Taken together, the evidence points to three central insights: (i) persistent underperformance of these asset categories on a risk-adjusted basis, (ii) shifting factor exposures that vary across time and market conditions, and (iii) limitations in model predictability during crises. For investors, these findings highlight the importance of tailoring portfolio strategies not only to long-term structural exposures but also to dynamic shifts in factor sensitivities across sub-periods.

2. Robustness Testing and Factor Stability

Robustness testing in asset pricing models is crucial for evaluating the stability and reliability of results across different factor specifications and data samples. The robustness tests are based on the monthly returns of Green, Grey, and Red asset groups by adjusting model specifications, including or excluding variables based on relevant literature, and employing various estimation techniques, such as standard panel data regression and robust panel data regression with random effects.

As presented in Table 3, Table 4, Table 5, Table 6, Table 7 and Table 8 and further detailed in Appendix A Table A8, Table A9 and Table A10, the performance of our extended factor models remains consistent compared to over 15 alternative asset pricing models. As mentioned, these models integrate various extensions of the Fama–French and Carhart frameworks from the recent literature. Furthermore, robustness is assessed by estimating the models over different time periods, specifically before and after the financial crisis. This approach helps determine whether the relationships captured by the model remain consistent over time, providing additional confidence in the model’s robustness.

The results reveal that core factors remain largely stable before and after a crisis, although some exhibit variations in statistical significance or direction. These variations underscore the dynamic nature of asset pricing relationships, particularly in response to major economic events. Through systematic robustness testing using monthly returns data, we strengthen confidence in the stability of our model and identify areas where factor performance may be affected by different market conditions, such as a crisis period.

A key observation is the strong correlations among certain factors (see Appendix A 

Table A5. Correlation for all factors in the period 2000–2009.

Variables	Mkt-RF	SMB	HML	RMW	CMA	MOM	BAB	HML DEVIL	QMJ	VSTOXX	US/EURO	JAP/EURO	UK/EURO	KR/EURO	CHN/EURO	Lumber	Brent	Aluminium	Gold
Mkt-RF	1.00
SMB	−0.07	1.00
HML	0.03	−0.07	1.00
RMW	−0.39	0.11	−0.35	1.00
CMA	−0.40	−0.16	0.62	−0.07	1.00
MOM	−0.50	0.24	−0.20	0.50	0.20	1.00
BAB	−0.12	0.43	0.19	0.28	0.25	0.46	1.00
HML DEVIL	0.19	−0.16	0.71	−0.52	0.35	−0.66	−0.18	1.00
QMJ	−0.73	0.03	−0.25	0.71	0.28	0.74	0.45	−0.55	1.00
VSTOXX	−0.59	0.10	0.06	0.32	0.32	0.36	0.38	−0.18	0.53	1.00
US/EURO	0.47	0.05	0.08	−0.08	0.01	0.00	0.50	−0.05	−0.03	0.01	1.00
JAP/EURO	0.39	0.06	0.05	0.01	−0.18	−0.03	0.32	−0.01	−0.07	−0.25	0.59	1.00
UK/EURO	0.26	−0.15	0.12	−0.23	0.15	−0.04	0.07	0.01	−0.01	−0.16	0.60	0.32	1.00
KR/EURO	0.53	0.01	0.09	−0.11	0.00	−0.04	0.47	−0.01	−0.07	−0.03	0.97	0.59	0.59	1.00
CHN/EURO	−0.08	−0.05	−0.07	0.13	0.21	0.24	0.35	−0.12	0.34	0.15	0.39	0.31	0.28	0.40	1.00
Lumber	0.21	0.05	−0.07	0.17	−0.04	−0.12	0.03	0.05	−0.07	−0.28	0.09	0.11	−0.03	0.10	−0.06	1.00
Brent	0.21	0.29	−0.11	0.12	−0.30	0.03	0.21	−0.08	−0.05	−0.15	0.12	0.10	−0.10	0.11	−0.01	0.21	1.00
Aluminium	0.41	0.12	0.05	−0.22	−0.24	−0.16	0.05	0.10	−0.34	−0.21	0.23	0.28	0.06	0.24	−0.14	0.14	0.27	1.00
Gold	−0.20	0.15	−0.15	0.08	−0.03	0.26	0.07	−0.18	0.16	0.14	−0.15	−0.22	−0.20	−0.13	0.01	−0.01	0.13	−0.03	1.00

,

Table A6. Correlation for all factors in the period 2010–2019.

Variables	Mkt-RF	SMB	HML	RMW	CMA	MOM	BAB	HML DEVIL	QMJ	VSTOXX	US/EURO	JAP/EURO	UK/EURO	KR/EURO	CHN/EURO	Lumber	Brent	Aluminium	Gold
Mkt-RF	1.00
SMB	−0.12	1.00
HML	0.47	−0.04	1.00
RMW	−0.41	−0.05	−0.83	1.00
CMA	0.03	−0.10	0.57	−0.46	1.00
MOM	−0.33	0.04	−0.44	0.42	−0.05	1.00
BAB	−0.06	0.25	−0.02	−0.02	0.13	0.23	1.00
HML DEVIL	0.49	0.02	0.80	−0.62	0.40	−0.59	−0.15	1.00
QMJ	−0.71	−0.08	−0.80	0.82	−0.23	0.55	0.16	−0.72	1.00
VSTOXX	−0.67	0.32	−0.27	0.20	0.00	0.31	0.25	−0.24	0.41	1.00
US/EURO	0.69	0.10	0.42	−0.35	0.10	−0.25	0.44	0.37	−0.46	−0.30	1.00
JAP/EURO	0.64	−0.04	0.49	−0.42	0.13	−0.31	0.11	0.32	−0.51	−0.44	0.67	1.00
UK/EURO	0.11	−0.01	0.17	−0.12	0.21	0.10	0.20	0.06	0.01	0.00	0.45	0.21	1.00
KR/EURO	0.56	0.07	0.41	−0.35	0.10	−0.20	0.42	0.35	−0.39	−0.19	0.90	0.63	0.52	1.00
CHN/EURO	0.09	0.10	0.21	−0.32	0.26	−0.10	0.34	0.01	−0.14	0.01	0.44	0.38	0.35	0.50	1.00
Lumber	0.30	0.21	0.03	0.09	−0.10	0.00	−0.10	0.16	−0.11	−0.19	0.17	0.10	−0.05	0.05	−0.27	1.00
Brent	0.44	0.02	0.25	−0.24	0.01	−0.25	−0.05	0.43	−0.37	−0.30	0.30	0.25	−0.07	0.22	0.06	0.20	1.00
Aluminium	0.41	−0.04	0.26	−0.23	0.08	−0.16	−0.02	0.35	−0.32	−0.22	0.37	0.22	0.31	0.32	0.00	0.12	0.34	1.00
Gold	0.78	−0.37	0.31	−0.26	−0.05	−0.35	−0.47	0.33	−0.57	−0.77	0.14	0.39	−0.21	0.03	−0.20	0.16	0.26	0.15	1.00

and

Table A7. Correlation for all factors in the period 2000–2019.

Variables	Mkt-RF	SMB	HML	RMW	CMA	MOM	BAB	HML DEVIL	QMJ	VSTOXX	US/EURO	JAP/EURO	UK/EURO	KR/EURO	CHN/EURO	Lumber	Brent	Aluminium	Gold
Mkt-RF	1.00
SMB	−0.09	1.00
HML	0.19	−0.05	1.00
RMW	−0.40	0.05	−0.54	1.00
CMA	−0.27	−0.14	0.61	−0.18	1.00
MOM	−0.44	0.19	−0.27	0.46	0.14	1.00
BAB	−0.10	0.39	0.15	0.19	0.24	0.41	1.00
HML DEVIL	0.26	−0.11	0.74	−0.53	0.39	−0.64	−0.15	1.00
QMJ	−0.72	−0.01	−0.44	0.75	0.14	0.68	0.37	−0.58	1.00
VSTOXX	−0.62	0.19	−0.08	0.27	0.20	0.32	0.32	−0.18	0.47	1.00
US/EURO	0.56	0.07	0.23	−0.20	0.05	−0.08	0.47	0.09	−0.19	−0.13	1.00
JAP/EURO	0.50	0.02	0.25	−0.19	−0.06	−0.12	0.24	0.11	−0.25	−0.35	0.63	1.00
UK/EURO	0.19	−0.10	0.16	−0.18	0.18	0.00	0.11	0.04	0.00	−0.08	0.54	0.27	1.00
KR/EURO	0.54	0.03	0.23	−0.21	0.04	−0.09	0.45	0.11	−0.19	−0.10	0.94	0.60	0.56	1.00
CHN/EURO	−0.02	0.00	0.04	−0.03	0.23	0.15	0.35	−0.07	0.19	0.09	0.40	0.33	0.30	0.44	1.00
Lumber	0.25	0.11	−0.04	0.14	−0.07	−0.08	−0.01	0.07	−0.08	−0.24	0.12	0.10	−0.04	0.08	−0.14	1.00
Brent	0.30	0.21	0.03	−0.02	−0.21	−0.05	0.14	0.07	−0.16	−0.21	0.19	0.16	−0.08	0.15	0.01	0.20	1.00
Aluminium	0.41	0.06	0.15	−0.22	−0.13	−0.16	0.03	0.18	−0.33	−0.21	0.30	0.25	0.18	0.27	−0.08	0.13	0.30	1.00
Gold	−0.22	0.09	−0.21	0.18	−0.06	0.19	0.01	−0.11	0.20	0.20	−0.21	−0.37	−0.12	−0.19	−0.11	−0.01	0.06	0.04	1.00

), which could influence the sign and significance of factors in the multi-factor models. Correlations often exceed 40%, and in some instances, even 60%, particularly following a crisis. This heightened correlation indicates that financial market disruptions have led to increased interdependencies among the factors, possibly due to shifts in investor behavior, market regulations, or economic fundamentals. Such correlations suggest that some factors may overlap in their explanatory power, leading to fluctuations in significance when new factors are added to the model. This reinforces the need for careful attention to factor relationships and model specifications during the analysis.

Our independent variables aim to capture the variation in Green, Grey, and Red stock returns in European markets. In this context, we focus on extended factor models that go beyond classical factors. Descriptive statistics for the sample variables are presented in

Table A1. First four moments of time-series classical factors.

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

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

,

Table A2. First four moments of time-series additional macro-factors.

Period	Moments	HMLDevil	BAB	QMJ	FEAR
2000–2009	Mean	1.001	1.33	0.52	1.4928
	Variance	0.14	0.20	0.08	377.5288
	Skewness	0.2475	−0.1838	−0.3164	1.4734
	Kurtosis	8.3661	0.6383	4.2059	3.2561
2009–2019	Mean	−0.40	0.71	0.63	1.0243
	Variance	0.04	0.04	0.04	387.4558
	Skewness	0.1499	0.1783	0.1739	0.5694
	Kurtosis	−0.4825	−0.0889	0.2477	0.1491
2000–2019	Mean	0.30	1.02	0.58	1.2585
	Variance	0.09	0.12	0.06	382.5471
	Skewness	0.6163	0.0006	−0.2014	1.0055
	Kurtosis	10.0138	1.9711	3.8053	1.6235

The table shows the first four moments of the four additional macro factors within each of the two sub-periods and the whole period. HML^Devil, BAB, QMJ, and FEAR INDEX are the alternative value, betting beta, quality, and volatility factors. The results are expressed as percentages (%).

,

Table A3. First four moments of time-series commodities factors.

Period	Moments	Oil	XAU	LME	LB1
2000–2009	Mean	1.1578	0.9447	0.5198	−0.0156
	Variance	132.6818	18.5857	36.1586	99.4060
	Skewness	−0.2096	0.5134	0.2022	0.3958
	Kurtosis	0.9508	0.7592	0.3493	0.2335
2009–2019	Mean	0.2376	0.4965	−0.0958	0.7359
	Variance	67.5711	21.9274	29.7042	79.5892
	Skewness	0.0071	0.1023	0.2448	0.1462
	Kurtosis	0.8095	0.8291	−0.1237	0.8018
2000–2019	Mean	0.6977	0.7206	0.2120	0.3602
	Variance	100.3382	20.3068	33.0261	89.6388
	Skewness	−0.1114	0.2680	0.2347	0.2772
	Kurtosis	1.2559	0.8136	0.1623	0.4345

The table shows the first four moments of the four factors within each of the two sub-periods and the whole period. Oil, XAU, LME, and LB1 are commodity factors. The results are expressed as percentages (%).

and

Table A4. First four moments of time-series currency factors.

Period	Moments	EURUSD	EURGBP	EURJPY	EURKRW	EURCNY
2000–2009	Mean	0.3492	0.2826	0.2481	0.1478	0.3264
	Variance	9.0223	5.7042	10.9481	8.9145	12.7521
	Skewness	0.0969	1.2768	−0.8892	0.0227	1.0489
	Kurtosis	1.3208	8.6531	4.4673	1.3000	3.8117
2009–2019	Mean	−0.1083	−0.0814	−0.0968	−0.1923	−0.1288
	Variance	6.4482	4.4550	11.4099	5.9280	4.7807
	Skewness	−0.2491	0.4509	−0.2722	−0.3836	−0.0879
	Kurtosis	0.5350	0.8711	0.6048	0.3687	−0.0213
2000–2019	Mean	0.1204	0.1006	0.0756	−0.0223	0.0988
	Variance	7.7876	5.1127	11.2087	7.4502	8.8182
	Skewness	0.0077	0.9594	−0.5686	−0.0828	0.9934
	Kurtosis	1.1561	5.8017	2.3094	1.1596	4.7773

The table shows the first four moments of the six factors within each of the two sub-periods and the whole period. EURUSD, EURGBP, EURJPY, EURKRW, and EURCNY are currency factors. The results are expressed as percentages (%).

, while Table A5, Table A6 and Table A7 provide the correlation matrix for the independent variables. The increased correlations after a crisis highlight the importance of examining dynamic, multi-factor models to account for evolving interrelationships between factors. These risk factors not only are theoretical constructs but also function as practical instruments for explaining stock returns in liquid markets.

3. Implementation of Extended Factor Models

The analysis demonstrates that extended factor models significantly enhance the understanding of return dynamics and risk exposures across Green, Red, and Grey stocks, particularly when segmented across sub-periods defined by key macroeconomic events (e.g., the EU crisis). These models are especially effective when applied to portfolio construction and risk management strategies such as smart beta, risk parity, and portfolio tilting, which seek to optimize exposure to rewarded risk factors.

Smart beta strategies, as an alternative to traditional market-cap-weighted investing, systematically tilt portfolios toward specific factors such as size (SMB), value (HML), momentum (MOM), profitability (RMW), low volatility (e.g., BAB), or quality (QMJ). In our models, the exposure of Green, Red, and Grey stocks to these factors varies not only in magnitude but also in direction and significance across time. For example, the momentum factor (MOM) positively influenced Red stocks in the pre-crisis period but reversed in the post-crisis period, highlighting the need for dynamic allocation strategies that adapt to changing market regimes. Similarly, the negative coefficient for QMJ in Grey stocks points to an overweight in lower-quality assets, suggesting a higher risk profile that smart beta approaches could help mitigate through systematic rebalancing toward quality.

Portfolio tilting, in this context, refers to the intentional over- or underweighting of assets to gain exposure to specific risk premia. Our empirical findings suggest that tilting toward volatility (captured by factors such as FEAR) would be beneficial for understanding the behavior of Grey and Red stocks, which exhibited strong sensitivity to volatility, especially in the post-crisis period. Conversely, Green stocks maintained more stable exposures, but similarly for post-GFC showed consistent negative alpha values—implying underperformance even after controlling for standard risk factors. These insights underscore how factor tilts, particularly toward momentum and volatility, can be leveraged to pursue return enhancements or manage downside risk depending on market conditions.

An additional layer of sophistication in portfolio design is introduced through risk parity strategies across factor exposures. Rather than equal-weighting by capital, risk parity seeks to equalize the contribution of each factor to total portfolio risk. Given the relatively high and consistent market beta (~0.9) across all asset classes in our sample, a traditional market-weighted portfolio could unintentionally concentrate risk in the market factor. However, our findings show that factors such as HML, BAB, and FEAR vary significantly in their influence across sub-periods and asset classes. For instance, the switching behavior of HML, FEAR, and BAB for Grey assets between pre- and post-crisis periods illustrates the dynamic and asymmetric nature of risk contributions. Risk parity approaches that rebalance according to the evolving volatility of these factors may result in more robust portfolio performance under changing economic environments.

The empirical evidence also highlights that factor exposures are both time-varying and asset-class-specific, further justifying the need for these adaptive allocation strategies. The HML(Devil) variant, for example, did not add explanatory power for Green or Grey stocks but provided significant improvements for Red stocks, suggesting that traditional value measures might miss critical pricing dynamics in energy-related sectors. Lastly, the Red stocks show a positive relationship with gold and oil prices—particularly in the second half of the sample period—reinforcing the importance of integrating commodity factors in asset pricing models for sectors reliant on non-renewable resources (as supported by Bams et al. 2017; Baur and Lucey 2010).

In contrast, currency fluctuations—specifically changes in the UK pound relative to the euro—showed a positive influence on Green and Grey stocks. This is consistent with Pojarliev and Levich (2008), who highlight the critical role of currency risk in global asset pricing. For diversified portfolios, especially those including international or climate-related assets, incorporating currency exposures via portfolio tilts or hedging strategies may enhance risk-adjusted returns.

The findings reinforce the notion that systematic factors dominate asset behavior, while alpha tends to be negative or insignificant post-crisis after adjusting for these factors. For example, risk-adjusted alpha values for Green, Red, and Grey stocks turned negative in the second period despite being insignificant or positive in earlier phases. These changes, coupled with rising volatility exposure, suggest that macroeconomic shifts such as the EU crisis altered the risk landscape, emphasizing the importance of monitoring time-varying sensitivities in portfolio management.

Moreover, the finding that Grey stocks were highly sensitive to volatility and quality factors, yet demonstrated underperformance post-crisis, signals potential limitations in passive investment strategies for these assets. Smart beta and factor-aware strategies may better control for such exposures, particularly when combined with the ongoing monitoring of factor loadings. Likewise, the consistent underperformance of Green stocks despite stable beta and exposure to traditional factors suggests that investors should consider integrating stock-specific alongside global factors.

In conclusion, the implementation of extended factor models provides a valuable foundation for advanced portfolio management strategies. By combining smart beta, risk parity, and factor tilting approaches, investors can better navigate the complex and shifting relationships between macroeconomic forces, investor sentiment, and asset class behavior. Our findings emphasize the need for dynamic and data-driven allocation strategies that can respond to structural market changes—whether driven by crises, commodity cycles, or currency fluctuations. These insights support the development of more resilient portfolios capable of capturing systematic risk premia while managing exposure to undesirable risks.

4. Conclusions and Future Directions

The primary objective of this research is to analyze the factor structure of stock returns, with a particular focus on understanding the risk sensitivities across various asset classes. By extending a prior study (Kottas 2025) with traditional asset pricing models, this paper seeks to offer a more nuanced understanding of the factors driving asset returns. Specifically, it explores a wide range of influences, including exposure to market risk, the relationship between low and high volatility stocks, currency fluctuations, commodity prices (especially gold), company size, value versus growth characteristics, corporate profitability, price momentum, investment behaviors, and overall market uncertainty. Through this comprehensive approach, the study aims to provide deeper insights into how these diverse drivers affect asset prices and their implications for investment strategies. Building on prior research by Kottas (2025), which analyzed the three-, four-, and five-factor asset pricing models, our study confirms that the factor exposures remain relatively stable across time and asset classes. Consistent with our evidence, the market, size (SMB), and value (HML) factors exhibit the strongest influence and persistent explanatory power, while the profitability and investment factors introduced in the five-factor framework also remain comparable to those in prior research. The results present stability for the traditional factors; however, in both studies, the HML factor in Grey assets and the momentum (MOM) factor in both Green and Red assets exhibit notable shifts between periods. These variations suggest that while the Market and SMB factor structures remain robust overall, the securities are sensitive to changes in value and momentum dynamics, underscoring the need to understand economic environment changes and extend models to capture these evolving risk exposures.

Our findings highlight that certain risk factors, such as volatility, value, and quality, play an influential role in explaining asset returns. The addition of factors like volatility, value II, betting against beta (BAB), currency, and commodity exposure leads to a significant improvement in the models’ explanatory power. These expanded models provide a clearer picture of how asset returns are shaped by a wider range of variables beyond the traditional ones used in classical factor models (Fama and French 1993, 2012, 2015). For instance, incorporating the EU VSTOXX (Fear Index) factor enhances the understanding of how market sentiment impacts asset returns, especially during periods of heightened market uncertainty (Cochrane 2001).

Furthermore, exposure to specific commodities, such as gold, reveals a negative relationship with asset returns, reinforcing prior studies that observe similar dynamics between stocks and commodity prices (Bams et al. 2017). The introduction of factors like the Robust Minus Weak (RMW) factor (Fama and French 1993) highlights the varying impact of profitability on asset classes, demonstrating how some stocks may exhibit a strong preference for low-profitability assets, while others are more closely aligned with high-profitability ones.

These expanded models provide valuable insights into the complex risk–return profiles of asset classes, emphasizing the importance of incorporating a broader set of risk factors to improve asset pricing accuracy. By extending classical models with these additional factors, this study offers a more comprehensive framework for understanding how different assets react to market and economic conditions, aiding participants in making more informed decisions.

The inclusion of additional factors such as momentum, BAB, FEAR, currency, commodity, and quality strengthens the interpretive power of the extended models and notably influence, as these are recognized proxy portfolios in asset pricing literature. Their adoption follows established precedent, allowing exposures of Green, Grey, and Red stocks to be meaningfully mapped to long–short strategies that capture relevant dimensions of environmental asset performance. While correlations among factors are naturally high—reflecting overlapping investment styles—the interpretive value lies in understanding how assets load onto these systematic strategies. The models are not designed for predictive purposes but rather for the interpretation of exposures, making the observed collinearity less of a limitation and more a feature of capturing the shared structure of financial markets.

From a practical perspective, the findings illustrate that systematic factors dominate return behavior and that exposures are both time-varying and asset-class-specific. This dynamic has direct implications for investors and asset managers implementing smart beta, risk parity, hedging, or portfolio tilting strategies. For instance, the momentum reversal in Red stocks between pre- and post-crisis periods, or the persistent underperformance of Green stocks despite stable betas, highlights the importance of dynamic allocation and the ongoing monitoring of factor loadings. Factor-aware portfolio design can help mitigate risks associated with volatility-sensitive Grey stocks or weak-quality exposures, while also capturing opportunities from commodity and currency linkages—such as the positive sensitivity of Red stocks to oil and gold or the influence of pound–euro movements on Green and Grey assets.

For policymakers, the extended models clarify how sectoral environmental classifications (Green, Grey, Red) are embedded in broader market risk structures and transition processes. The underperformance of Green stocks post-crisis, even after controlling for traditional risk factors, underscores the challenges of financing the transition toward sustainable investments. Similarly, the heightened volatility sensitivity of Grey and Red stocks demonstrates the systemic risks tied to non-renewable sectors, reinforcing the policy relevance of factor-based risk monitoring frameworks. By highlighting these dynamics, the study provides investors, asset managers, and policymakers with an analytical foundation for both managing portfolio exposures and shaping policies in line with long-term transition risks.

In sum, the implementation of extended factor models enhances not only the methodological rigor of the analysis but also its practical applicability. The empirical evidence suggests that adaptive allocation strategies—combining smart beta, factor tilting, hedging, and risk parity—are better suited to navigate structural shifts brought about by crises, commodity cycles, and currency fluctuations. These insights equip practitioners with tools to build more resilient portfolios, while also offering policymakers guidance on how environmental classifications map onto systematic risk premia. The study therefore contributes both to academic debates on asset pricing and to the practical design of climate-aware investment strategies.

Future research could further refine asset pricing models by incorporating additional macroeconomic factors, such as liquidity (Pástor and Stambaugh 2003), or exploring the integration of Environmental, Social, and Governance (ESG) factors into asset pricing models (Alessi et al. 2021). The growing focus on sustainable investing could lead to more nuanced models that better capture the effects of ESG considerations on asset returns.

Additionally, the relationship between commodities and asset returns, especially in times of market volatility, could be explored more deeply. Research could apply techniques such as principal component analysis (PCA) to reduce dimensionality and address multicollinearity in currencies and commodities factors, potentially leading to more robust predictions. Investigating other EU global factors, such as the Liquidity factor (Pástor and Stambaugh 2003), which influences asset returns, could also contribute to a more holistic understanding of market dynamics.

An important limitation of this study is that the dataset terminates in January 2020, thereby precluding the empirical analysis of more recent shocks and structural changes. This temporal restriction narrows the scope of inference, particularly with respect to the COVID-19 pandemic and the subsequent energy crisis. Addressing these developments remains a promising avenue for future research regarding the factor behavior of these asset classes.