Fuzzy clustering approach to portfolio management considering ESG criteria: empirical evidence from the investment strategies of the EURO STOXX Index

This article is a summary of the scientific work published by Andrii Kaminskyi, Maryna Nehrey

The original source can be accessed via DOI 10.33111/nfmte.2023.040

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As ESG (Environmental, Social, and Governance) investing moves from niche to mainstream, the financial world is undergoing a major shift. Forecasts estimate that ESG assets will exceed $50 trillion by 2025, accounting for roughly one-third of all global assets under management. Institutional investors, asset managers, and financial platforms are increasingly under pressure to incorporate ESG factors not just as a reputational add-on, but as a core component of investment strategy. However, this creates a fundamental challenge: how to reconcile ESG priorities with the traditional goals of maximizing returns and minimizing risk.

Most current approaches to ESG integration fall into two camps—negative screening, which excludes companies with poor ESG performance (such as fossil fuel or tobacco firms), and positive screening, which favors companies with high ESG scores. While straightforward, these methods typically rely on classical portfolio optimization tools like Modern Portfolio Theory (MPT), which are not designed to handle the added complexity of ESG scoring. The result is often an uncomfortable trade-off: a portfolio optimized for return and risk, but diluted in ESG consistency due to over-diversification across assets with varying sustainability profiles.

To overcome this, a new data-driven methodology is gaining attention: fuzzy clustering. Unlike rigid screening methods, fuzzy clustering groups investment assets based on multiple overlapping criteria, including ESG score, expected return, and risk profile. This allows investors to build portfolios that reflect a more refined and adaptive understanding of market behavior, aligning more closely with both performance and sustainability goals. In essence, fuzzy clustering enables a middle path—maintaining ESG integrity without sacrificing the portfolio's financial foundation.

This article explores how fuzzy clustering is redefining ESG investment strategy by offering a smarter, more consistent way to manage assets. It highlights how this approach can unlock new opportunities for institutional investors seeking to align their portfolios with environmental and social values—without compromising on profitability.

A Smarter Framework for ESG Portfolio Construction: Fuzzy Clustering Meets Value-Added Indexing

As ESG investing becomes a cornerstone of modern portfolio management, investors are increasingly looking for methods that go beyond basic exclusion or screening. The challenge is no longer just integrating Environmental, Social, and Governance (ESG) factors—it’s how to integrate them meaningfully while still optimizing for performance. This is where a new methodology based on fuzzy clustering and dynamic portfolio optimization offers a breakthrough.

At the core of this approach is a fusion of ESG scoring, traditional risk-return metrics, and advanced data-driven modeling. It begins with an index-based investment strategy, which provides a liquid and efficient foundation. Investors select a benchmark index—an approach particularly attractive to retail investors due to ease of rebalancing and transparency.

The next step is ESG integration using quantitative ESG scores provided by reputable agencies like S&P Global and Refinitiv. While methodologies vary across providers, the research leverages S&P Global ESG Scores due to their transparent construction through the Corporate Sustainability Assessment (CSA), which evaluates more than 10,000 companies globally.

Importantly, ESG scoring systems are hierarchical. Investors can work with the overall ESG score, or drill down to the E (Environmental), S (Social), and G (Governance) subcomponents—and even further into specific measurable attributes.

The differences between ESG scoring systems are highlighted in the comparison below, showing how each provider defines subcomponents.

Once ESG and financial metrics are defined, the fuzzy clustering process begins. Companies are grouped into clusters based on their ESG score, expected return, and risk (standard deviation). Fuzzy clustering allows companies to belong to multiple clusters to varying degrees, enabling more nuanced portfolio construction. This is especially valuable because investors can choose a cluster that reflects their specific priorities—whether ESG strength, high return, or low risk.

From each cluster, a core group of companies that best meet the investor’s priorities is selected. This forms the base portfolio. Then, using a step-by-step optimization process, additional stocks from the fuzzy part of the cluster are incrementally added, each time recalculating the portfolio using the Markowitz framework to minimize risk.

To evaluate the performance of each portfolio configuration, the methodology introduces a custom metric: the Value Added Weekly Index (VAWI). Inspired by the Value Added Monthly Index (VAMI), VAWI measures the portfolio’s cumulative value-added over time. For every iteration (each new stock added from the fuzzy segment), a VAWI is generated. The investor then follows the portfolio with the highest VAWI at any given time, effectively combining a passive cluster-based structure with active rebalancing logic.

This creates a dynamic investment strategy where the portfolio is continuously optimized within the investor’s chosen ESG framework. It captures both market movements and sustainability signals, enabling higher performance consistency without compromising on ESG alignment.

As sustainable investing moves into the mainstream, the challenge for asset managers is no longer whether to integrate ESG factors—but how to do so while maintaining performance and managing risk. To test a practical solution, our research team applied a fuzzy clustering–based ESG investment strategy to the EURO STOXX 50, a leading index composed of 50 blue-chip stocks across 11 Eurozone countries. Its high liquidity and strong institutional coverage make it a compelling benchmark for building ESG-integrated portfolios that can be actively managed without incurring excessive transaction costs.

The study was conducted over two distinct time frames. The period from 2016 to 2018 was used to build clusters and define portfolio structures, while the 2019 to 2022 window was used to track the dynamic performance of these portfolios in real market conditions. Notably, the second period includes the COVID-19 pandemic, allowing the model to be tested under heightened volatility. Weekly returns were calculated to capture detailed performance movements across portfolios.

Of the 50 companies in the index, 47 were included in the study after data cleansing (three were excluded due to incomplete records). Using the FANNY algorithm in R—a fuzzy clustering method based on exponentially declining membership values—we segmented these companies into three clusters. Importantly, each company could partially belong to more than one cluster, reflecting the real-world ambiguity of ESG and financial performance overlap. For the clustering rules, we required that each cluster include at least five companies to ensure diversification and set a fuzzy membership threshold of 0.3.

The results of the clustering are summarized in the table below, which details the average expected return (ER), risk (as standard deviation, STD), and ESG score for each cluster:

Cluster 1 emerged as the most ESG-friendly, with an average ESG score of 80.35, the highest expected return (0.11%), and the highest volatility (3.47%). This cluster appeals to investors prioritizing sustainability and growth potential. Cluster 2 had moderate ESG scores (68.36), the lowest return (0.05%), and a relatively low risk level. Cluster 3, in contrast, delivered relatively high returns (0.09%) and the lowest risk (3.01%), but with the lowest ESG score (33.08). These differences illustrate the inherent trade-offs in ESG investing and underscore the value of segmenting portfolios according to investor priorities.

To dive deeper into the structure of each cluster, we analyzed the core companies and overlapping members—a feature made possible through fuzzy clustering’s ability to capture partial memberships. This segmentation enables investors to fine-tune strategies by choosing from pure-core investments or blending them with intersecting firms for diversification.

Cluster 1’s core group, for instance, included high-profile firms such as AXAF, DTEGn, and PHG. These companies not only offered strong ESG credentials (average score of 81.94) but also outperformed in returns (0.13%)—albeit with higher volatility. Meanwhile, Cluster 3’s core featured names like LVMH and FLTRX, providing decent returns with lower ESG ratings but also lower risk. The intersections between clusters further reveal companies like ASML or ENI, which embody blended characteristics, offering investors more flexibility in how strictly they want to adhere to ESG or risk-return preferences.

Ultimately, these results affirm that fuzzy clustering can serve as a powerful decision-support tool in ESG investing. Instead of forcing a one-size-fits-all portfolio, investors can select the cluster—or blend of clusters—that best reflects their risk appetite, return expectations, and sustainability goals. This framework ensures that ESG is not just a filter but a core structural component of portfolio strategy, dynamically adapted through active monitoring and rebalancing.

As ESG standards evolve and data becomes richer, tools like fuzzy clustering offer a way forward: data-driven, investor-personalized, and financially sound. For any institution serious about integrating ESG without compromising returns, this methodology presents a compelling, scalable approach.

Visualizing the Clusters: ESG-Driven Risk-Return Trade-offs

To gain a clearer picture of how companies within each cluster relate to ESG, risk, and return, the methodology mapped the fuzzy and core components of Clusters 1 and 2 onto a 2D risk-return plane. In the visualizations below, expected return is plotted on the vertical axis, risk on the horizontal, and ESG score is represented by the diameter of each data point. This multi-dimensional mapping provides a powerful tool for investors to assess trade-offs at a glance.

The visual clustering analysis confirms key differences between groups. Cluster 1’s core companies are relatively concentrated in terms of risk-return profiles, with generally larger ESG scores. Cluster 2, by contrast, presents tighter risk levels but with more variability in expected return. The intersection of the two clusters—the “fuzzy” region—contains companies that partially belong to both, allowing for a blended strategy.

To demonstrate how the clustering results can be transformed into actionable investment strategies, the study constructed minimum-risk portfolios around the core groups of Clusters 1 and 2. In each case, companies from the fuzzy overlap region were added incrementally, and portfolio metrics were recalculated using the Markowitz risk minimization model.

For Cluster 1, the base portfolio begins with 17 companies. As additional companies from the fuzzy region are added one at a time, the portfolio’s risk slightly declines, but so does the average ESG score. This reflects the trade-off between expanding diversification and maintaining ESG purity.

For example, the initial 17-stock portfolio offers a return of 0.136% and an ESG score of 83.53. By the time it grows to 23 stocks, the risk decreases from 2.093% to 1.983%, but the ESG score drops to 80.41—still strong, but clearly lower. This type of analysis allows investors to quantify exactly how much ESG exposure they’re sacrificing in exchange for better diversification or marginally lower volatility.

A similar structure was applied to Cluster 2, where the core of 13 companies is gradually expanded. As new members are added, both risk and ESG score slightly fluctuate, providing investors with an expanded range of portfolio options that remain anchored in ESG alignment but tuned for volatility management.

The cluster selection process becomes the first decision point in this ESG-aligned investment strategy. Once the investor selects a cluster that reflects their values—whether they prioritize ESG scores, risk control, or return potential—the model builds a base portfolio around the cluster’s core.

The next step involves selecting a portfolio construction method. While the study uses Markowitz optimization to demonstrate minimum-risk design, alternative models could easily be applied—such as Sharpe ratio maximization or equal-weighted diversification. The flexibility of this approach means investors can tailor it not only to their ESG views but also to their preferred financial framework.

This cluster-based ESG investing method ultimately bridges the gap between data science and portfolio strategy. It delivers practical tools for building high-performing portfolios without abandoning sustainability objectives—turning ESG from a static label into a dynamic decision variable.

From Strategy to Execution: Tracking ESG Portfolio Value Over Time

The final component of this methodology introduces real-time portfolio adjustment based on performance metrics derived from a family of VAWI curves. These curves reflect the cumulative investment value over time for each portfolio constructed from a cluster’s core and fuzzy components.

After selecting an ESG-aligned cluster (e.g., Cluster 1 or 2), and constructing portfolios by sequentially adding stocks from the fuzzy zone, the investor calculates VAWI values for each of these portfolios. These VAWIs reflect cumulative weekly returns, as shown in the dynamic visualization below.

The fourth step of the strategy is the key innovation—identifying which VAWI curve is currently at the top (i.e., which portfolio has delivered the greatest cumulative return at time T). This “upper circumferential line” is a visual and computational guide for dynamic portfolio switching. When another portfolio’s VAWI overtakes the current leader, a switch is made to that new optimal configuration.

This technique was applied to portfolios from Cluster 1, resulting in 14 switches between 2019 and 2022. The upper envelope of the VAWI family is shown below:

A similar analysis for Cluster 2 portfolios shows 16 switches over the same time frame, emphasizing that the strategy is active, data-driven, and responsive to changing market performance. ‍

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This four-step strategy offers a practical framework for navigating ESG investing with measurable, performance-based logic:

1. Select a cluster matching ESG, risk, and return priorities.
2. Build core and fuzzy portfolios using clustering and Markowitz optimization.
3. Track performance over time using VAWIs.
4. Switch dynamically to the best-performing portfolio via the upper circumferential line.
   

By combining sustainable finance, advanced clustering, and continuous performance tracking, this methodology empowers investors to pursue both impact and return—flexibly, measurably, and intelligently.

Conclusion

Fuzzy clustering enables flexible and dynamic ESG portfolio construction by balancing the three key investor priorities: risk, return, and ESG score. Portfolios are built around a stable core of companies that meet chosen criteria, while the surrounding fuzzy elements allow for adaptive rebalancing in response to market changes.

The method improves on classical Markowitz approaches by incorporating ESG performance directly into the portfolio structure without sacrificing transparency or manageability. Value Added Weekly Indexes (VAWIs) provide a clear benchmark for portfolio performance, guiding when to switch between portfolio variants based on which one delivers the highest investment value at a given time.

Rebalancing decisions are data-driven and infrequent—just 14 times for Cluster 1 and 16 for Cluster 2 over a three-year period—helping to keep transaction costs low. The approach supports automation, making it ideal for implementation via robo-advisors and scalable through ETF structures, where the cluster core provides long-term positioning and fuzzy elements allow for tactical adjustments.

Limitations include the absence of a universal rule for selecting the optimal number of clusters, the risk of reduced diversification with small clusters, and the hierarchical complexity of ESG scoring systems. Despite these, the methodology offers a robust framework for ESG-aligned investment strategies that are transparent, data-based, and well-suited for both institutional and retail investors.

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