Fuzzy–Rough Analysis of ESG Ratings and Financial and Growth Ratios on the Stock Returns of Blue-Chip Stocks in Taiwan

Abstract

This study uses fuzzy–rough analysis to investigate the influence of Environmental, Social, and Governance (ESG) ratings, along with critical financial and growth ratios, on the stock returns of blue-chip companies in Taiwan. The growing importance of ESG factors in investment decisions underscores the need to understand their impact on stock performance. By integrating the fuzzy–rough set theory, which accommodates uncertainty and imprecision in data, we analyze the complex relationships between ESG ratings, traditional financial metrics (such as ROE, return on equity), and stock returns. Our findings provide insights into how ESG considerations, alongside financial indicators, drive the returns of Taiwan’s blue-chip stocks. Three public-listed companies were evaluated using this approach, and the results are consistent with the actual stock performance. This research contributes to the field by offering a robust methodological approach to assess the nuanced effects of ESG factors on financial performance, thus aiding investors and management teams in making informed decisions.

1. Introduction

Environmental, social, and governance (ESG) considerations have increasingly influenced investment decisions globally in recent years [1]. As investors seek to align their portfolios with sustainability goals and ethical principles, evaluating ESG performance has become a key determinant of investment attractiveness [2]. Concurrently, the significance of traditional financial metrics and profit growth ratios in assessing stock performance remains steadfast [3].

This study analyzes the blue-chip stocks in Taiwan to explore the relationship among ESG ratings, financial metrics, profit growth ratios, and stock returns. Blue-chip stocks, renowned for their stability, reliability, and market leadership, represent a vital equity market segment [4]. By examining how ESG factors and financial indicators correlate with stock returns in this select group of companies, this research aims to shed light on the multifaceted dynamics shaping investor perceptions and market valuations.

Taiwan offers a compelling setting for this analysis as a hub of technological innovation and economic dynamism in the Asia–Pacific region. The Taiwanese stock market, characterized by diverse blue-chip companies spanning various sectors, presents a rich landscape for investigating the interrelationship between ESG practices, financial performance, and stock returns.

This paper employs a quantitative approach, leveraging comprehensive empirical data on ESG ratings, financial metrics, profit growth ratios, and historical stock returns of blue-chip companies in Taiwan. Through the use of rough set theory (RST) [5], we seek to elucidate the intricate relationships among these variables, discern patterns, and uncover deep insights into the drivers of stock performance in the Taiwanese market.

The ESG factor and financial ratios provide a structured framework for discerning patterns and dependencies within the data. By employing the RST, which allows for the analysis of imprecise, incomplete, or uncertain information, we can systematically explore how variations in ESG performance influence stock returns. Within this context, RST facilitates the identification of essential attributes or factors that contribute significantly to the classification of stocks based on their ESG ratings and financial ratios. Detecting discernible decision rules from the rough set analysis can provide deeper insights into the nuanced connections between sustainable practices and financial performance metrics. This approach enables us to distill actionable insights for investors and corporate stakeholders, guiding strategic decision-making processes towards more sustainable and value-enhancing practices.

A comprehensive understanding of these dynamics is essential for fostering sustainable investment practices, driving corporate responsibility, and fostering long-term value creation in the Taiwanese equity market. Section 2 reviews related studies. Section 3 reveals the adopted RST model. Section 4 provides a case study using Taiwan’s blue-chip stocks. Section 5 discusses the case’s results, and Section 6 concludes this study.

2. Literature Review

2.1. ESG and Stock Returns

ESG factors have gained considerable attention in investment circles due to their potential to influence corporate performance, risk management, and long-term value creation. This section explores the relationship between ESG considerations and stock returns, synthesizing existing research and highlighting key findings in this evolving field.

Numerous studies have investigated the impact of ESG factors on stock returns, consistently finding evidence of a positive correlation between strong ESG performance and superior financial performance. For instance, Chen et al. (2023) [6] discovered that ESG performance is positively interrelated with financial performance. Also, the influence of ESG ratings on corporate performance is significant for large-scale companies and insignificant for small-scale companies.

Moreover, research by Friede et al. (2015) [7] found that companies with robust ESG practices exhibit lower volatility, higher profitability, and reduced cost of capital, leading to improved stock returns in the long term. These findings underscore the materiality of ESG factors in driving shareholder value and financial performance, highlighting the importance of incorporating ESG considerations into investment decision-making processes.

Furthermore, studies have shown that companies with strong ESG performance are more resilient to environmental, social, and governance risks, thereby mitigating downside risks and preserving shareholder value during market volatility and uncertainty periods. For example, Eccles et al. (2014) [8] demonstrated that companies with higher ESG scores experienced smaller drawdowns and faster recoveries during market downturns, indicating the importance of ESG factors in enhancing portfolio resilience and risk management.

Additionally, research has examined the impact of specific ESG dimensions on stock returns, with varying results across environmental, social, and governance categories. For instance, studies by Khan et al. (2020) [9] and Gosselin et al. (2018) [10] found evidence of a positive relationship between environmental performance and stock returns, particularly in industries with high environmental risk exposure. Similarly, research by Cheng et al. (2019) [11] highlighted the importance of social factors such as employee relations and community engagement in driving shareholder value and stock returns.

In conclusion, evidence suggests that ESG considerations significantly influence stock returns and financial performance. By incorporating ESG factors into their investment strategies, investors can potentially enhance investment returns and mitigate downside risks. Therefore, the present study includes ESG to explore the plausible effects on stock returns.

2.2. Financial Ratios and Stock Returns

Key financial ratios, such as return on asset (ROA) [12] and growth profitability ratios, are pivotal indicators utilized by investors to assess a company’s potential for future expansion and profitability, thereby aiding in the estimation of stock returns. This section provides an overview of existing research on the significance of growth profitability ratios in predicting stock performance and their implications for investment analysis.

Various profitability growth rates are fundamental metrics that capture a company’s ability; examples are pre-tax net profit growth and sustainable net profit growth ratios, to increase profits over time. Empirical studies have consistently shown a positive association between high-profit growth rates and subsequent stock price appreciation.

Similarly, the revenue growth rate serves as a crucial indicator of a company’s top-line growth and market demand for its products or services. Research by Li and Li (2019) [13] demonstrated a positive correlation between revenue growth rates and stock returns, particularly in sectors characterized by rapid technological innovation and disruptive business models. This highlights the importance of revenue growth as a driver of shareholder value and stock performance.

Return on equity (ROE) is another crucial financial ratio that measures a company’s profitability relative to shareholders’ equity. High ROE reflects efficient capital utilization and strong growth potential, leading to superior stock returns over time. Studies by Durand and May (2021) [14] and Ahmad and Mansoor (2018) [15] corroborated the positive relationship between ROE and stock performance, emphasizing ROE as a critical determinant of investment attractiveness and value creation.

Regarding growth financial ratios, Delen et al. (2013) [16] played a pivotal role in estimating stock returns by providing valuable insights into a company’s growth potential, profitability, and valuation. Investors and analysts can leverage these metrics to identify promising investment opportunities and make informed decisions to optimize portfolio returns. However, it is imperative to consider growth financial ratios in conjunction with other factors such as ESG, industry dynamics, competitive positioning, and macroeconomic trends to achieve comprehensive investment analysis and risk management (Asiri and Hameed (2014)) [17]. Further research could explore advanced methodologies and novel approaches to enhance the predictive power of growth financial ratios in estimating stock returns and optimizing investment strategies in dynamic financial markets.

2.3. RST-Based Financial Modeling

RST has emerged as a powerful tool for analyzing complex datasets and uncovering patterns within them, making it increasingly relevant in the domain of stock prediction [18], particularly when considering the ESG factor alongside financial ratios. This review synthesizes existing research on the application of RST in analyzing stock prediction while integrating ESG and financial metrics.

Several studies have investigated the integration of RST with ESG factors and financial ratios to enhance stock prediction models. For instance, Shen [19] demonstrated the effectiveness of rough-set-based approximations in identifying relevant ESG attributes and financial indicators for predicting stock returns. The findings highlighted the importance of incorporating ESG considerations and financial metrics in stock prediction models to achieve more accurate forecasts.

Moreover, Chen et al. (2018) [20] explored the application of RST in constructing hybrid stock prediction models that leverage both traditional financial ratios and ESG data. Their research emphasized the complementary nature of ESG factors and financial indicators in predicting stock performance, with rough-set-based feature selection facilitating the identification of significant variables for model development.

Additionally, studies such as one by Wang et al. [21] have investigated the interpretability of rough-set-based stock prediction models to incorporate ESG and financial data. By employing RST to generate decision rules from the data, researchers can provide insights into the relationships between ESG factors, financial metrics, and stock returns, thereby enhancing the transparency of predictive models.

Furthermore, the integration of RST with machine learning algorithms has garnered attention in the realm of stock prediction. For instance, Hu et al. [22] proposed a hybrid rough-set-based support vector regression model for predicting stock returns using ESG and financial data. Their research demonstrated the efficacy of combining RST with machine learning techniques to improve prediction accuracy while incorporating ESG considerations.

Overall, the literature underscores the significance of leveraging RST in analyzing stock prediction models that consider both ESG factors and financial ratios [23]. By enabling feature selection, model interpretability, and the integration of diverse datasets, RST offers a robust framework [24] for developing predictive models that capture the complex interactions between sustainability performance, financial metrics, and stock returns.

3. RST-Based Bipolar Model

Classical RST cannot handle the dominance relationship in decision-making problems; therefore, we adopt the dominance-based rough set approach (DRSA) [24] as a foundation to form a decision model in this study. Unlike the conventional RST [25], the DRSA begins by defining a 4-tuple information system, where $IS=〈U,A,V,f〉$, in which $U$ is a finite set of n objects, i.e., $U=\left\{O_i;i=1,\dots ,n\right\}$. A is the attribute set comprising $A^C=\left\{a^1,\dots ,a^m\right\}$ (condition attributes) and $A^D=\left\{a^D\right\}$ (decision attribute). In addition, $A=A^C\cup A^D$ and $A^C\cap A^D=⌀$. V is the value domain of A, and f is a total function such that $f\left(x,a_k\right)\in V$ for each $x\in U$ and $a_k\in A$. If $f_i\left(x\right)\ge f_i\left(y\right)$, then $x{\underset{¯}{\succ }}_{a_i}y$, termed as the monotonic relationship. Among a finite set of classes (Cls), an object $O_i\in U$ can be categorized in only one class, where $Cl=\left\{C{l}_t:C{l}_1,C{l}_2,\dots ,C{l}_h\right\}$. Thus, an outranking relation ${\underset{¯}{\succ }}_{a_k}$ can be defined for any $a^k\in A^C$ and $o_i,o_j\in U$. If $O_i{\underset{¯}{\succ }}_{a^k}{O}_j$ for any $O_i,O_j\in U$, it indicates that “$O_i$ is at least as good as $O_j$ regarding $a^k$. The predefined preference order thus forms two types of unions: one is the upward union ($C{l}_t^{\ge }={\cup }_{s\underset{¯}{\succ }t}C{l}_s$), and the other is the downward one of classes ($C{l}_t^{\le }={\cup }_{s\underset{¯}{\prec }t}C{l}_s$). For brevity, the following discussion uses the upward unions as examples. As a result, if $O_i$ dominates $O_j$ on a partial set of $A^C$ ($p\subseteq A^C$), it can be expressed as $O_i{D}_p{O}_j$. $D_P$ denotes the dominance relation. Therefore, if a set of objects is dominating $O_i$ regarding p, it is called the p-dominating set ($D_p^{\Delta }\left(O_i\right)=\left\{O_i,O_j\in U:O_i{D}_p{O}_j\right\}$). Likewise, if a set of objects is dominated regarding p, it is called the p-dominated set ($D_P^{\nabla }\left(O_i\right)=\left\{O_j,O_i\in U:O_j{D}_p{O}_i\right\}$). Thus, the p-lower ($\underset{¯}{P}\left(C{l}_t^{\underset{¯}{>}}\right)$) and p-upper ($\overline{P}\left(C{l}_t^{\ge }\right)$) approximations can be denoted as Equations (1) and (2). The boundary region is defined in Equation (3).

$$\underset{¯}{P}\left(C{l}_t^{\underset{¯}{>}}\right)=\{O\in U:D_P^{\Delta }\left(O_i\right)\subseteq C{l}_t^{\underset{¯}{>}}\}$$

(1)

$$\overline{P}\left(C{l}_t^{\ge }\right)=\left\{O\in U:D_p^{\nabla }\left(O_i\right)\cap C_t^{\ge }\ne ⌀\right\}$$

(2)

$$P^{Bou}=\overline{P}\left(C{l}_t^{\ge }\right)-\underset{¯}{P}\left(C{l}_t^{\underset{¯}{>}}\right)$$

(3)

In other words, $\underset{¯}{P}\left(C{l}_t^{\underset{¯}{>}}\right)\subseteq C{l}_t^{\ge }\subseteq \overline{P}\left(C{l}_t^{\ge }\right)$ for all $p\in A^C$. The three types of rough regions support the generation of decision rules. The details of this can be found in Błaszczyński et al. (2012) [26].

Let us consider a simple example to explain the concepts. We can begin by defining a decision table (

Table 1. Exemplary decision table with evaluations of notebooks.

Notebooks	Style (a1)	Performance (a2)	Price (a3)	Overall Evaluation (aD)
N1	Good	Medium	Bad	Bad
N2	Medium	Medium	Bad	Medium
N3	Medium	Medium	Medium	Medium
N4	Good	Good	Medium	Good
N5	Good	Medium	Good	Good

) to indicate the 4-tuple information system. When evaluating notebooks, there are five alternatives (N1 to N5) and three condition attributes (Style, Performance, and Price). $Cl=\left\{Good,Medium,Bad\right\}$, and $h=3$. Here, N4 dominates N3 (i.e., N4 $\succ$ N3) considering $a^1$ and $a^2$, i.e., $\mathrm{N}4{\underset{¯}{\succ }}_P\mathrm{N}5$ and $P=\left\{a^1,a^2\right\}$.

In addition, for every $p\in A$, the quality of approximation is defined as the ratio of the objects that are p-consistent with the dominance principle for all the objects in $U$, shown in Equation (4) [27,28], where $\left|•\right|$ denotes the cardinality.

$${\varpi }_p\left(Cl\right)={\displaystyle \frac{\left|U-{\displaystyle \underset{t=2,\dots ,m}{\cup }{p}^{Bou}\left(C{l}_t^{\ge }\right)}\right|}{\left|U\right|}}$$

(4)

The dominance principle requires that if an object x dominates y on all the considered attributes p, x should also dominate y on the decision attribute; objects that satisfy this principle are called consistent in the DRSA. The dominance-based rough approximations of the upward and downward union of decision classes can serve to induce decision rules [26]. In this study, the DOMLEM algorithm [29] was adopted to generate decision rules.

The obtained rules support the formation of a rule-based decision-making model. The rule-based model adopts the rules associated with upward and downward unions of classes. The key idea is to evaluate an object more similar to the rules related to the upward union of classes (or positive rules) and dissimilar to the downward union of classes (or negative rules), termed the bipolar approach [30].

In a rule-based bipolar model, the supports of each rule need to be normalized so that the total weights are equal to 100% in both the positive (i.e., ${\displaystyle \sum _{i=1}^k{w}_i^P}=100\%$) and negative groups (i.e., ${\displaystyle \sum _{j=1}^l{w}_j^N}=100\%$). The final performance of each stock is synthesized as Equation (5):

$$S_j={\displaystyle \sum _{i=1}^n{w}_i^P\otimes F_i^P\times \frac{\left|P_{ip}\right|}{\left|R_i\right|}}-{\displaystyle \sum _{j=1}^m{w}_j^N\otimes F_j^N\times \frac{\left|P_{jk}\right|}{\left|R_j\right|}, \mathrm{where} i = 1, 2, \dots , n \mathrm{and} j = 1, 2, \dots , m.}$$

(5)

In Equation (5), $\left|•\right|$ denotes the cardinality; $\left|R_i\right|$ and $\left|R_j\right|$ are the number of antecedents of the i-th positive rule and j-th negative rule. $\left|P_{ip}\right|$ and $\left|P_{jk}\right|$ are the numbers of satisfied antecedents of the i-th positive rule and j-th negative rule. In addition, $F_i^P$ and $F_j^N$ denote the fuzzy confidence level an expert holds toward the evaluation of a rule (Kao et al. (2022)) [31]; a fuzzy triangular membership function is adopted here.

4. A Case Study from Taiwan

The present study adopted the top 50 listed blue-chip stocks in Taiwan (TW50) as a case to analyze the results. First, this study applied the Delphi method to retrieve the critical profitability and growth ratios, categorized as the condition attributes. The obtained consensus indicators are shown in

Table 2. Profitability growth ratios and ESG indicator.

Symbol	Full Name	Definition or Short Explanation
ROA	Return on asset	Net profit/Total asset
ROE	Return on equity	Net profit/Equity
Rev_G	Revenue growth	Revenuet − Revenuet−1/Revenuet−1
NAV_G	Net asset value growth rate	(Net asset valuet − net asset valuet−1)/Net asset valuet−1
PreTaxProfit_G	Pre-tax income margin growth rate	(Pre-tax incomet − pre-tax incomet−1)/Pre-tax incomet−1
AfterNProfit_G	Net profit margin growth rate	(Net profitt − net profitt−1)/Net profitt−1
Earning_G	Compound Annual Growth Rate of Net Income	(Net ending valuet/Net ending valuet−1) − 1
SusNetProfit_G	Compound Annual Growth Rate of Continuous Net Income	(Net incomet/Net incomet−1) − 1
TAsset_G	Total asset growth rate	(Total assett − Total assett−1)/Total assett−1
TAssetProfit_G	ROA growth rate	(ROAt − ROAt−1)/ROAt−1
TESG	TESG grade	The ESG grade given by TEJ

. The 50 blue-chip stocks’ figures in three years, 2021, 2022, and 2023, were discretized into 1, 2, and 3 to indicate low (L), mid (M), and high (H), respectively. In addition, the condition data in 2021 were associated with the decision attribute, which is in 2022, to form the training set. Similarly, the condition data in 2022 were associated with the decision attribute in 2023 to form the testing set. The discretization adopts the normal distribution approach, where figures below mean − ${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$SD were categorized into 1 (L), above mean + ${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$SD as 3 (H), and the remaining as 2 (M).

The raw data come from the TEJ database [32], including the TESG ratings, which were assigned by TEJ as 1 (B−), 2 (B), 3 (B+), 4 (A−), 5 (A), and 6 (A+). In addition, the stock price returns were assigned as the decision attribute, which also follows the normal distribution approach to be categorized as 3 (good/positive), 2 (mid/others), and 1 (bad/negative). The 3-fold cross-validation was carried out three times for the training set, and the associated classification accuracy is in

Table 3. Three-fold cross-validation for the training set.

	Classification Accuracy (DRSA)	VC-DRSA (Consistency = 0.9)
1st	66.0%	57%
2nd	64.0%	54%
3rd	69.0%	55%
average	66.33%	55.33%
SD	2.05%	1.25%

.

The average classification by using the DRSA is 66.33%, which is higher than the VC-DRSA (variable consistency DRSA) algorithm. The DRSA model was used to examine the testing set, showing a classification accuracy of 52.00%. These figures lay the foundation to explore the rules required to form a bipolar decision model. The trained model was used to obtain the rules associated with at least positive (≥positive) (or others (≥others)) and at most negative (≤negative) (or others (≤others)), summarized in

Table 4. Positive and negative rules of the bipolar model.

Number of Rules	Rules	Supports	Normalized Weights
Positive P1	NAV_G ≥ 3 & TESG ≥ 6 ⇒ S_Return ≥ 2	3	100%
Negative N1	ROA ≤ 2 & TESG ≤ 2 ⇒ S_Return ≤ 1	5	3.70%
Negative N2	TAsset_G ≤ 2 & TESG ≤ 2 ⇒ S_Return ≤ 1	5	3.70%
Negative N3	TAssetProfit_G ≤ 1 & TESG ≤ 3 ⇒ S_Return ≤ 1	6	4.44%
Negative N4	ROA ≤ 2 & Rev_G ≤ 1 ⇒ S_Return ≤ 2	21	15.56%
Negative N5	ROA ≤ 2 & TESG ≤ 3 ⇒ S_Return ≤ 2	27	20.00%
Negative N6	TAsset_G ≤ 2 & TESG ≤ 3 ⇒ S_Return ≤ 2	26	19.26%
Negative N7	ROE ≤ 1 & TESG ≤ 5 ⇒ S_Return ≤ 2	22	16.30%
Negative N8	ROA ≤ 1 & Rev_G ≤ 2 & AfterNProfit_G ≤ 2 & TESG ≤ 5 ⇒ S_Return ≤ 2	23	17.04%

.

In Table 4, we have one positive rule and eight negative rules. The support weights of the negative rules should sum up to 100% for the negative group, and thus, the normalized weight of each rule can be calculated. At the evaluation phase, an expert was invited to gauge the fuzzy confidence level of the stocks on each rule. The expert has over 20 years of experience in the financial sector, and his previous positions include being a CEO, Vice President, and President. The fuzzy confidence level adopts the commonly used triangular membership function, and the evaluations are low (L), mid (M), and high (H). First, we collected the expert’s opinions on L, M, and H, and the fuzzy parameters are (0, 0%, 30%), (25%, 50%, 75%), and (70%, 100%, 100%), respectively.

Three sample stocks’ data in 2022 (as the condition attributes) were adopted in this study: Nan Ya Plastics (N), Quanta (Q), and ASE Holding (A). First, the three companies’ values on the 11 condition attributes were adopted to evaluate the crisp performance of the three companies, shown in

Table 5. Condition attributes of the three sample stocks.

	Companies
Symbols	N	Q	A
ROA	3	3	3
ROE	3	3	3
Rev_G	1	1	1
NAV_G	1	3	1
PreTaxProfit_G	1	3	1
AfterNProfit_G	1	3	1
Earning_G	1	3	1
SusNetProfit_G	1	3	1
Tasset_G	1	1	1
TAssetProfit_G	3	3	1
TESG	3	6	5

and

Table 6. Bipolar evaluation model.

Rules	P1	N1	N2	N3	N4	N5	N6	N7	N8	Final Scores
Weights	100.00%	3.70%	3.70%	4.44%	15.56%	20.00%	19.26%	16.30%	17.04%
N	0.00%	0.00%	50.00%	100.00%	50.00%	50.00%	100.00%	50.00%	75.00%	−64.26%
Q	100.00%	0.00%	50.00%	0.00%	50.00%	0.00%	50.00%	0.00%	25.00%	76.48%
A	0.00%	0.00%	50.00%	0.00%	50.00%	0.00%	50.00%	50.00%	75.00%	−40.19%

.

In Table 6, take the P1 rule as an example. After cross-referencing Table 4 and Table 5, N does not satisfy the two antecedents of P1; therefore, its score on this rule is 0.00%. Likewise, N satisfies three of the four antecedents of N8, and its score on N8 is 75.00%. Next, we collected the fuzzy confidence level of each object (i.e., the three companies) on each rule based on an expert’s opinions, which is shown in

Table 7. Fuzzy confidence level from the expert.

Rules	P1	N1	N2	N3	N4	N5	N6	N7	N8
N	H	H	M	H	M	M	H	M	M
Q	H	H	H	H	H	H	H	H	M
A	H	H	H	H	H	H	H	H	H

. In addition, the actual stock performance ranking is consistent with the crisp evaluation (Table 6) and fuzzy-confidence-based evaluation result (Table 7 and

Table 8. Fuzzy-confidence-based bipolar evaluation.

Rules	P1	N1	N2	N3	N4	N5	N6	N7	N8	Final Scores
Weights	100.00%	3.70%	3.70%	4.44%	15.56%	20.00%	19.26%	16.30%	17.04%
N	0.00%	0.00%	29.17%	80.00%	29.17%	29.17%	80.00%	29.17%	43.75%	−42.62%
Q	80.00%	0.00%	40.00%	0.00%	40.00%	0.00%	40.00%	0.00%	14.58%	62.11%
A	0.00%	0.00%	40.00%	0.00%	40.00%	0.00%	40.00%	40.00%	60.00%	−32.15%

), i.e., $Q\succ A\succ N$.

5. Discussion

Among the nine rules, TESG appears in eight of them (8/9), which has the highest importance. The following two are ROA (4/9) and Rev_G (3/9), shown in

Table 9. The importance of attributes among the rules.

Rules	P1	N1	N2	N3	N4	N5	N6	N7	N8	Ratio
ROA		●			●	●			●	4/9
ROE								●		1/9
Rev_G	●				●				●	3/9
NAV_G										0/9
PreTaxProfit_G										0/9
AfterNProfit_G									●	1/9
Earning_G										0/9
SusNetProfit_G										0/9
TAsset_G			●				●			2/9
TAssetProfit_G				●						1/9
TESG	●	●	●	●		●	●	●	●	8/9

, which indicate the crucial role of TESG. “●” means that an attribute appears in a rule.

In addition, an RGMM (row geometric mean prioritization method)-based AHP approach was adopted to make a comparative analysis. A senior domain expert provided his opinion regarding the relative importance of each criterion over the others. The RGMM result reveals that TESG is the most important criterion, which shows a consistent ranking outcome with the proposed approach; it also indicates the validity of this study.

Despite the model’s capability to rank the sample stocks, it can also be applied to guide improvement planning. Take the top-ranked Q and its crisp evaluation as an example: its weighted performance scores on the nine rules are shown in

Table 10. Improvement analysis of Q.

Rules	P1	N1	N2	N3	N4	N5	N6	N7	N8
Weights	100.00%	3.70%	3.70%	4.44%	15.56%	20.00%	19.26%	16.30%	17.04%
Q	100.00%	0.00%	50.00%	0.00%	50.00%	0.00%	50.00%	0.00%	25.00%
Gaps	0.00%	0.00%	50.00%	0.00%	50.00%	0.00%.	50.00%	0.00%	75.00%
Weighted gaps	0.00%	0.00%	1.85%	0.00%	7.78%	0.00%	9.63%	0.00%	12.78%

. Among the weighted gaps, its score on N8 is the highest, at 12.78%. We may learn that focusing on this rule (i.e., N8) may bring the highest marginal improvement effect. Referring to Table 5, the four antecedents are ROA ≤ 1, Rev_G ≤ 2, AfterNProfit_G ≤ 2, and TESG ≤ 5. Q satisfies “Rev_G ≤ 2”, which stands for the highest weighted gap (i.e., 12.78%). Thus, if Q may improve Rev_G to “3”, it could make the biggest improvement.

Similarly, the second priority is N6, and the antecedents are “TAsset_G ≤ 2” and “TESG ≤ 3”. Q satisfies “TAsset_G ≤ 2”, which holds the second weighted gap. In other words, if Q wants to plan for stock price improvement, its top two priorities are Rev_G and TAsset_G, respectively. This analysis not only supports a company in guiding its improvement but also reveals a hint for investors to observe, which indicates informed decision making.

6. Concluding Remarks

To conclude, the proposed approach examines the relationship between ESG, profitability, growth ratios, and stock returns. Using RST, researchers can effectively handle imprecise and uncertain information, often prevalent in financial datasets. This methodology allows for identifying significant patterns and relationships without requiring prior assumptions about the data distribution.

The primary advantage of RST lies in its ability to discern and analyze the dependency between financial ratios and stock returns through the reduction of redundant data and the extraction of decision rules. This results in more precise decision-making rules and improved predictive models. Additionally, in this case, RST can highlight the most influential attribute, i.e., TESG, providing investors and analysts with valuable insights for making informed investment decisions. This study concludes that ESG is the most critical factor influencing stock returns. This finding is consistent with previous research (e.g., Chen et al. (2023) [6]), in which ESG performance is positively interrelated with financial performance but only significant for large blue-chip stocks. Also, Friede et al. (2015) [7] show that roughly 90% of their selected studies find a non-negative ESG–CFP (corporate financial performance) relation, which corroborates the importance of ESG performance on stock returns.

Despite its advantages, using RST to evaluate the relationship among ESG, financial ratios, and stock returns has several limitations. First, we have to assume that the ESG grading is consistent and of high quality. Variations in ESG reporting standards across different countries (or regions) can limit the applicability of findings from Taiwan to other markets where ESG data quality and consistency might differ. Additionally, when calculating the importance of each rule, we have to assume that each antecedent in a decision rule is equally weighted. Moreover, while identifying dependencies and patterns, it needs to quantify the strength or direction of relationships, potentially limiting its utility for more nuanced financial forecasting. These limitations necessitate a cautious interpretation of results and often require complementary methods to fully understand the financial phenomena under study. Future research may incorporate other decision-making methods to explore the directional influence among the attributes.

Overall, applying RST into the evaluation of financial ratios and stock returns enhances the analytical capabilities of financial research, offering a powerful tool for uncovering hidden relationships and improving the accuracy of stock return predictions. Future research may investigate how ESG ratings affect stock returns in different industries or sectors, as the impact might vary across various types of businesses. It is also suggested to examine the relationship between ESG ratings and stock returns over a longer period to identify trends and long-term impacts. In addition, the proposed approach can be extended by considering more general models in rough set theory, such as the integration of a rough set and a fuzzy set [33], sequences of relations that are refinements on a universe [34], or rough sets based on tolerances [35].