An Explainable Framework for ESG Portfolio Rebalancing with Transformer Models and Carbon Credit Signals

Abstract

This study proposes an explainable framework for ESG portfolio rebalancing by integrating carbon credit signals, technical indicators, and Transformer-inspired forecasting into a unified decision process. The investable universe consists of six ESG-themed ETFs, namely ESGU, SUSA, ICLN, TAN, KRBN, and KGRN. Carbon-related sustainability information is represented by four S&P carbon indices, including GCC, CCA, EUA, and UCITS. Within the proposed framework, Transformer, Informer, and Temporal Fusion Transformer are used to predict next-day returns, and the forecast outputs are translated into portfolio decisions through threshold filtering, Softmax-based allocation, and inertia smoothing under fixed transaction costs. The empirical results show that the proposed framework remains competitive against Equal Weight, Risk Parity, and Momentum benchmarks, although its advantage is conditional rather than uniformly dominant across all metrics. Informer delivers the strongest Sharpe ratio among the model-based strategies, while Transformer exhibits a more stable risk profile. The ablation results indicate that the smoothing mechanism has the clearest effect on turnover and allocation stability, whereas the incremental value of carbon-related inputs is most visible in Informer. The uncertainty assessment further shows that many benchmark differences are not consistently significant under repeated resampling, but the performance weakening caused by removing carbon inputs in Informer remains identifiable. The subperiod analysis shows that benchmark rules are more competitive in 2024H1, whereas model-based strategies gain relative strength in 2024H2. The explainability analysis indicates that carbon-feature contributions are concentrated more strongly in Intermediate and Carbon-Sensitive asset groups and remain weaker in Broad ESG assets; feature-level and SHAP beeswarm evidence further shows that the three architectures rely on GCC, CCA, EUA, and UCITS in different ways. These findings suggest that carbon-related sustainability signals can provide economically meaningful allocation information in selected settings when they are combined with suitable model architecture and disciplined rebalancing control, thereby supporting a competitive and explainable ESG portfolio rebalancing framework.

1. Introduction

Environmental, Social, and Governance (ESG) factors have become central to business strategy, investment decision-making, and policy design. This shift reflects the view that long-term financial performance is closely tied to sustainability outcomes such as climate resilience, social responsibility, and governance quality. ESG is now treated as an important part of value creation, risk mitigation, and operational resilience, increasing the need for structured disclosure and integration into financial planning [1]. Recent studies further describe ESG as a structural element of global finance and corporate governance [2], and this transition has been reinforced by international standard-setting efforts such as ISSB and CSRD [3].

At the same time, ESG investing has grown into a mainstream force in global financial markets [4]. Yet this expansion also brings challenges. Differences in ESG rating methodologies create inconsistent evaluations and increase the risk of greenwashing [5]. ESG scoring systems may also favor large firms with stronger disclosure capacity, while much of the academic and regulatory development remains concentrated in Western markets [6]. In addition, ESG investment decisions often reflect both financial and non-financial motives, which broadens their appeal but may also increase subjectivity and mismatched expectations [7].

As ESG investing expands, an important issue is how sustainability considerations can be translated into dynamic investment strategies. Portfolio rebalancing is especially relevant in this context because it allows investors to adjust asset weights in response to market conditions or allocation rules, supporting risk control and structural alpha generation [8]. Prior studies show that rebalancing itself can be a major source of portfolio performance. Malladi and Stanoyevitch (2025) [9] show that the rebalancing effect explains a substantial part of equal-weighted portfolio outperformance even under realistic transaction costs. Khan et al. (2024) [10] find that equal-weighted portfolios with algorithmic rebalancing remain resilient during financial stress, while Bányai et al. (2024) [11] show that rebalancing frequency and method can materially affect the Sharpe ratio across asset classes.

Beyond return and risk effects, recent studies have begun to embed sustainability objectives directly into rebalancing design. Șerban (2025) [12] proposes a multi-objective framework incorporating investor behavior and interval uncertainty, showing that ESG-aligned portfolios can be rebalanced dynamically. Rammerstorfer and Weinmayer (2025) [13] apply multi-directional efficiency analysis to integrate ESG metrics into asset allocation, improving financial and sustainability efficiency while maintaining low turnover.

In recent years, Transformer models have been increasingly adopted in financial research, showing strong performance in risk forecasting, portfolio optimization, and fraud detection. Mishra et al. (2024) [14] proposed a hybrid Transformer-LSTM model for market volatility and downside risk forecasting, outperforming ARIMA, GARCH, and standalone LSTM models under turbulent market conditions. In high-frequency cryptocurrency trading, Peng et al. (2024) [15] developed an attention-based CNN-LSTM framework that reduced transaction volume by more than 90% while maintaining stable performance across currencies and time intervals. Wei et al. (2024) [16] designed a multimodal Transformer that integrates time series, company reports, and news articles, achieving an AUC of 0.91 in financial risk classification. Sun et al. (2024) [17] further combined Transformers with deep reinforcement learning and risk budgeting, showing consistent portfolio gains over traditional DRL models in U.S. equities and ETFs.

On the financial security front, An et al. (2024) [18] introduced Finsformer, a Transformer enhanced with cluster-attention to detect irregularities in transactional data. Using real-world and synthetic datasets, the model achieved over 95% in precision and recall, validating its efficacy in fraud detection scenarios. Uddin et al. (2025) [19] benchmarked a range of ML models for both classification and regression tasks in financial prediction. Transformer models delivered the best performance across the board, with an AUC of 0.97 and an R² of 0.97, and led to portfolios with a Sharpe ratio of 1.72 and a drawdown of just −5.9%, indicating strong robustness under market uncertainty. Finally, Feng (2025) [20] contributed a BiLSTM-Transformer hybrid designed for credit card fraud detection. By combining bidirectional temporal encoding with attention mechanisms, the model significantly improved recall and F1 scores over conventional methods, especially when handling imbalanced financial datasets.

Although Transformer-based models excel in financial forecasting, their application in dynamic ESG portfolio rebalancing is underexplored. Prior research often neglects the integration of sustainability objectives into adaptive deep learning frameworks for active management. To address this, we develop an explainable rebalancing framework centered on six ESG ETFs (ESGU, SUSA, ICLN, TAN, KRBN, and KGRN). This system combines price movements, technical indicators, and carbon signals through a Transformer-based forecasting and threshold-triggered allocation process. The primary contribution is a structured and explainable ESG portfolio rebalancing framework that integrates return prediction, carbon-related signals, and weight smoothing within a unified pipeline. Rather than proposing a generally superior allocation method or a new forecasting architecture, this study examines whether carbon-related features can improve portfolio behavior under a competitive, model-dependent, and empirically testable rebalancing design.

The remainder of this paper is organized as follows. Section 2 reviews the related literature. Section 3 presents the methodology and model design. Section 4 reports the experimental setup and empirical results. Section 5 concludes the paper and discusses limitations and future directions.

2. Literature Review

As ESG investing becomes increasingly mainstream, a growing body of research has explored its integration into portfolio management frameworks. This section reviews the development of ESG-related investment strategies, the evolution of portfolio rebalancing methodologies, and the rise of deep learning applications in financial time series modeling. Special attention is given to recent attempts at combining data-driven models with sustainability considerations to support dynamic asset allocation.

Lee, Fan, and Wong (2021) [21] examined the performance of ESG-integrated portfolios in the Australian market under realistic investment conditions. Their study showed that ESG integration can remain economically meaningful in practical portfolio settings, while also highlighting that the performance effect depends on implementation design and market environment. This evidence is relevant to the present study because it supports the view that ESG-related information can influence portfolio outcomes in real-world allocation contexts rather than only in stylized screening exercises. Bertelli and Torricelli (2024) [22] examined the performance of ESG-screened portfolios in the European market using the EURO STOXX index as a benchmark. By applying both positive and negative screenings with varying exclusion thresholds, they found that ESG portfolios only outperformed in the long run when low exclusion thresholds were applied, such as the 80% ESG score portfolio, yielding a mean monthly return of 0.027%. However, during financial crises like the 2008 recession, ESG strategies did not demonstrate safe-haven characteristics, with only marginal gains during the COVID-19 period. Similarly, Useche et al. (2024) [23] evaluated stock data from Chile, Colombia, and Peru, introducing a novel utility function combining mean-variance theory with ESG constraints, and proposed the concept of “psychic dividend.” Their results showed that high-ESG portfolios outperformed in terms of return, Treynor ratio, alpha, VaR, tracking error, and information coefficient, revealing the benefits of ESG investing in emerging markets.

In addition, Long and Liu (2024) [24] constructed a unified capacity-constrained optimization model to analyze how renewable energy endowment and policy incentives influence green microgrid investment strategies. Using solar and wind data from Guangzhou, they demonstrated that while carbon taxes promote green investment, excessively high rates could discourage renewable-only configurations. They also identified a “subsidy trap” in feed-in tariff (FIT) policies where increased support fails in low-resource contexts. Further, Shan (2025) [25] assessed the impact of ESG on higher return moments using Refinitiv ESG, CRSP, and Compustat data (4236 firms, 27,761 observations), finding that a one-standard-deviation increase in ESG score led to a 0.65% drop in average return, a 0.0197 increase in skewness, and a 0.394 reduction in kurtosis-all statistically significant. Marín-Rodríguez et al. (2025) [26] applied scientometric and bibliometric methods to Sustainable ETF literature, showing how Green ETFs evolved from ESG-aligned tools to complex structures incorporating AI, diversified screening, and crisis-resilient design, while noting regulatory inconsistencies and investor education as key barriers.

Portfolio rebalancing is a fundamental mechanism in modern portfolio theory, designed to maintain an optimal balance between risk and return by adjusting asset allocations over time. As market volatility increases and investment instruments diversify, rebalancing strategies have evolved from traditional periodic approaches to more dynamic and data-driven methods. In recent years, the convergence of financial technology and sustainable investing has led to the growing adoption of machine learning (ML) and ESG metrics in portfolio management. A growing body of research shows that data-driven algorithms and sustainability-oriented asset screening enhance risk-adjusted returns while simultaneously improving portfolio robustness and diversification. Biasin et al. (2024) [27] constructed European ESG real estate indexes using Refinitiv ESG data and assessed their performance through Mean-Variance (MV) and Risk Parity (RP) frameworks. Their results indicate that environmentally screened real estate assets (Env50) outperformed traditional portfolios during 2018–2022 under the RP allocation. Env50 achieved an annualized return of 3.42 percent and a Sharpe ratio of 0.264, compared with 2.41 percent and 0.181 for conventional portfolios. These findings imply that ESG-focused real estate investments diversify risk effectively and provide more resilient returns during periods of market volatility.

In the cryptocurrency domain, Bağcı and Kaya Soylu (2024) [28] developed a machine learning framework to classify the optimal rebalancing frequency (ORF) in pairs trading. Using minute-level data from 50 cryptocurrencies on Binance, they simulated 29,400 asset pairs and categorized them by correlation. A pair trading algorithm (PTA) was applied across various rebalancing intervals, and six classifiers were tested. Random Forest (RF) achieved the highest accuracy, with 83.77% for negatively correlated pairs in the short term and 88.47% in the long term. Moreover, PTA outperformed passive strategies in 91.8% of positively correlated pairs, demonstrating that ML-based ORF classification significantly improves rebalancing decisions.

Uysal et al. (2024) [29] introduced an end-to-end neural network framework for portfolio optimization, embedding a risk budgeting model as an implicit layer. Backtesting on seven ETFs (e.g., VTI, AGG, GLD) showed that the model-based approach achieved a Sharpe ratio of 1.16 during 2017–2021, outperforming nominal risk parity (0.83). Incorporating asset selection via stochastic gates further boosted the Sharpe ratio to 1.24. Simulation studies confirmed that the model-based method significantly outperforms model-free alternatives in risk-adjusted returns, demonstrating robustness and practical value in portfolio construction.

Bayat et al. (2024) [30] proposed a scenario-based stochastic risk budgeting model that accounts for uncertainty in asset return means and covariance matrices. The model optimizes portfolios based on expected risk across scenarios. To address practical constraints on asset count, a cardinality-constrained bi-level formulation was introduced and solved via a hybrid cross-entropy (HCE) algorithm. Empirical results on datasets like FTSE100 showed that the proposed model outperformed nominal and worst-case models in robustness and Sharpe ratio. The HCE algorithm efficiently found optimal solutions in small instances and performed well on large-scale problems. Finally, Trabelsi Karoui et al. (2024) [31] evaluated the performance of seven leading US AI and robotics companies (e.g., Nvidia, Symbotic, C3.ai) from 2021 to 2023, comparing them to the Nasdaq index and AI/robotics ETFs. Using various investment strategies (e.g., daily rebalancing, buy-and-hold), the study found that AI stock portfolios generally outperformed traditional IT benchmarks in terms of return and risk-adjusted metrics like Sharpe and Treynor ratios. Daily rebalancing yielded the highest cumulative return (2.321), highlighting AI stocks’ speculative potential and volatility. The findings suggest AI stocks are valuable for portfolio diversification but require careful risk management. These studies illustrate the growing relevance of machine learning and sustainability-oriented strategies across diverse asset classes and market conditions. Whether used for rebalancing frequency prediction, risk budgeting, technical classification, or ESG screening, these approaches enhance portfolio resilience and performance, offering valuable insights for future intelligent investing.

Deep learning has also shown promise in financial modeling, especially for capturing complex patterns in asset behavior. Yet, its integration with portfolio rebalancing remains underexplored. Most studies focus on prediction tasks, while few address how deep learning can guide dynamic rebalancing decisions. Challenges such as interpretability, stability, and practical implementation further highlight the need for deeper investigation in this area. Recent advances in deep learning and reinforcement learning have increasingly focused on intelligent portfolio rebalancing. Yang et al. (2022) [32] introduced a Q-learning agent enhanced with LSTM to forecast three-day prices and correct lag in EMA and MACD indicators. The agent dynamically adjusts asset weights under varying market conditions, with gradual rebalancing (30% per day) significantly improving returns and reducing drawdowns. Building on this, Kim and Lee (2023) [33] proposed PredACGAN, a GAN-based model that generates probabilistic return distributions and filters high-risk assets using entropy. Trained on 30 years of S&P 500 and NASDAQ 100 data, the model achieved 9.123% annual return and a Sharpe ratio of 1.054, outperforming risk-agnostic baselines.

To integrate financial theory, Jang and Seong (2023) [34] combined Modern Portfolio Theory with DDPG reinforcement learning. Using 3D CNNs and Tucker decomposition, the model processes technical indicators and asset correlations, dynamically rebalancing Dow Jones stocks every 10 days. It outperformed baselines in Sharpe ratio (2.0067), drawdown (8.29%), and final portfolio value. Dai et al. (2024) [35] introduced a two-stage multiresolution grid (MRG) model that optimizes the Bellman equation under computational constraints. Using Monte Carlo simulation and Lagrange multipliers, MRG prioritizes high-probability regions and outperforms traditional strategies in the Sharpe ratio and cost efficiency. Kan et al. (2024) [36] proposed an interpretable fuzzy deep neural network (IFDNN) combining POPFNN and LSTM to forecast 15-day prices and enhance MACD (f-MACD). A2C and DDPG manage rebalancing, with DDPG achieving 184% return and 0.745 Sharpe ratio, demonstrating strong interpretability and performance.

In 2025, Sattar et al. [37] introduced an RMS-driven DRL framework incorporating sentiment and earnings data into state representations. Using Max Drawdown as a reward component, A2C_RMS achieved the best performance (10% annual return, 0.66 Sharpe), with news sentiment identified as the most impactful feature. Gollart and Okhrin (2025) [38] developed a model-free DDPG-based RL framework for dynamic portfolio optimization. Operating in continuous state-action spaces, the model approximates optimal strategies without market assumptions and demonstrates robustness across seeds and market models. Li and Xu (2025) [39] proposed a hybrid GAN-Transformer model integrating FinBERT sentiment, technical and economic indicators. A VAE denoises inputs for a GRU-GAN generator and Transformer discriminator. Apple test RMSE reached 3.33, with 30.27% predicted ROI, validated by Sharpe, Treynor, and Jensen’s alpha.

In 2025, Wang and Liu [40] proposed the Adaptive Risk-Sensitive Transformer-based Deep Reinforcement Learning (ART-DRL) framework for portfolio optimization in petroleum futures markets. By integrating Transformer-based temporal encoding and dynamic agent switching, the model adapts to volatile conditions and outperforms static DRL strategies. Among the three tested methods, ART-DRL achieved the best risk-adjusted performance, with a Sharpe ratio of 4.340, Sortino ratio of 57.77, and Calmar ratio of 19.17, while maintaining strong drawdown control. Though its annualized return (1.353) was slightly below DQN (1.476), ART-DRL demonstrated superior consistency and robustness across regimes, validating its practical value in commodity trading.

In summary, prior studies have demonstrated the potential of integrating deep learning with rebalancing strategies, covering technical indicators, generative models, and risk control. However, dynamic rebalancing for ESG-focused portfolios remains underexplored, especially in multi-asset settings that incorporate carbon pricing and sustainability signals. This study addresses the gap by proposing a Transformer-based framework centered on ESG ETFs, using diverse features and a threshold-triggered mechanism to examine how sustainability factors influence allocation and timing.

3. Research Method

This study proposes a two-stage explainable framework for ESG-driven portfolio rebalancing using deep learning techniques. The first stage consists of a Transformer-based forecasting module that predicts the next-day return of multiple ESG-themed ETFs using historical technical indicators and carbon-related sustainability signals. Rather than relying on ETF prices alone, this study incorporates publicly available carbon credit indices as structured ESG proxies to reduce information leakage and improve model generalizability. The forecasting module is designed to accommodate multiple Transformer variants, including Transformer, Informer, and Temporal Fusion Transformer (TFT), allowing consistent model comparison within the same framework.

The second stage consists of a dynamic rebalancing module that converts forecast outputs into portfolio weights. Reallocation is triggered when expected returns deviate beyond a predefined threshold and is implemented through signal filtering, weight mapping, and smoothing under allocation constraints. To support this framework, this study combines price-based variables, technical indicators, and standardized ESG signals derived from global carbon credit indices. Algorithmic details and evaluation metrics are presented together with the model design to show how the framework links prediction, allocation, and portfolio evaluation in a unified decision process.

3.1. Data Indicators and Sustainability Features

To support ESG-oriented portfolio forecasting and rebalancing, this study constructs a multivariate time series input based on market data, technical signals, and quantifiable sustainability proxies. The selected indicators are designed to capture both financial momentum and environmental trends in a format suitable for deep learning-based modeling. Specifically, the feature set includes: (1) daily return and price series from a selected set of ESG-themed ETFs, (2) conventional technical indicators that reflect short- and long-term market behavior, and (3) carbon credit indices that serve as structured ESG signals with daily frequency and global coverage. The following subsections detail the construction and motivation of each component in the feature space.

3.1.1. ESG-Themed ETFs

Environmental, Social, and Governance (ESG)-themed Exchange-Traded Funds (ETFs) have become essential instruments for investors seeking to align their portfolios with sustainability objectives while maintaining exposure to diversified financial markets. ESG ETFs typically track indices composed of companies selected based on sustainability-related criteria, such as environmental performance, carbon efficiency, clean energy focus, or corporate governance practices. These funds serve as accessible vehicles for integrating ESG considerations into investment strategies without requiring direct stock-level selection or custom screening.

This study focuses on six ESG-themed ETFs that collectively span multiple sustainability dimensions, including broad ESG screening, clean energy development, and carbon pricing exposure. The selection reflects a balance between thematic diversity, regional representation, and data availability. All ETFs are publicly traded and provide daily price and return data, making them suitable for machine learning-based forecasting and portfolio simulation:

✓

ESGU (iShares ESG Aware MSCI USA ETF) [41]: A broad-market ESG ETF that tracks U.S. large- and mid-cap companies screened based on MSCI ESG criteria. ESGU excludes companies involved in controversial weapons, tobacco, and thermal coal, and applies sector-neutral ESG integration.

✓

SUSA (iShares MSCI USA ESG Select ETF) [42]: This fund applies to a more stringent ESG screen, selecting top ESG performers within each sector. Compared to ESGU, SUSA emphasizes higher ESG scores and excludes firms with weaker sustainability practices, offering more concentrated ESG exposure.

✓

ICLN (iShares Global Clean Energy ETF) [43]: Tracks global companies involved in the production of clean energy from solar, wind, and other renewable sources. ICLN serves as a proxy for the environmental transition theme, with exposure to both utility and technology sectors.

✓

KRBN (KraneShares Global Carbon ETF) [44]: Provides exposure to the global carbon credit markets by investing in futures contracts tied to cap-and-trade systems, such as the EU ETS and California’s CCA. KRBN serves as both an investment in carbon pricing and a hedge against climate policy risk.

✓

TAN (Invesco Solar ETF) [45]: Focused exclusively on the solar energy sector, TAN invests in companies across the solar value chain, including panel manufacturers, equipment suppliers, and energy developers. It represents a high-beta segment of the renewable energy space.

✓

KGRN (KraneShares MSCI China Clean Technology ETF) [46]: Targets Chinese companies that derive the majority of their revenue from clean technology activities, such as electric vehicles, energy efficiency, and sustainable agriculture. KGRN offers geographic diversification and emerging market ESG exposure.

These six ETFs reflect a comprehensive spectrum of ESG investment themes and serve as the target assets in our forecasting and rebalancing framework.

3.1.2. Technical Indicators

To enhance the predictive capability of the deep learning model, this study incorporates technical indicators that capture underlying market structure and short-term dynamics. These indicators are widely used in financial forecasting and are particularly useful for representing patterns such as trend persistence, price reversals, and overbought or oversold conditions. This study includes two main types of technical indicators: moving average-based and momentum-based.

A.

Moving Average-Based Indicators

Moving averages are designed to smooth out price fluctuations over a specified window and are often used to detect trend direction or support/resistance levels. This study applies both the Simple Moving Average (SMA) and the Exponential Moving Average (EMA). The Simple Moving Average (SMA) over a window of length n is defined as:

$${\mathrm{S}\mathrm{M}\mathrm{A}}_t^{\left(n\right)}={\displaystyle \frac{1}{n}}{\displaystyle \sum _{i=0}^{n-1}}{P}_{t-i}$$

(1)

where $P_t$ denotes the closing price at time t, and n is the look-back period. SMA gives equal weight to each price in the window.

The Exponential Moving Average (EMA) applies a decaying weight to past prices, allowing more emphasis on recent data:

$${\mathrm{E}\mathrm{M}\mathrm{A}}_t^{\left(n\right)}=\alpha \cdot P_t+\left(1-\alpha \right)\cdot {\mathrm{E}\mathrm{M}\mathrm{A}}_{t-1}^{\left(n\right)} , \alpha ={\displaystyle \frac{2}{n+1}}$$

(2)

Here, $\alpha$ is the smoothing constant, and ${\mathrm{E}\mathrm{M}\mathrm{A}}_{t-1}^{\left(n\right)}$ is the previous day’s EMA value. EMA reacts more sensitively to recent price changes and is often preferred in volatile markets.

B.

Momentum-Based Indicators

Momentum-based indicators assess the strength and direction of price movement, offering early signals of trend continuation or potential reversals. This study includes the Relative Strength Index (RSI) and the Moving Average Convergence Divergence (MACD).

The Relative Strength Index (RSI) is computed as:

$${\mathrm{R}\mathrm{S}\mathrm{I}}_t=100-\left({\displaystyle \frac{100}{1+{RS}_t}}\right), {RS}_t={\displaystyle \frac{{\mathrm{E}\mathrm{M}\mathrm{A}}_n^{\left(+\right)}\left(t\right)}{{\mathrm{E}\mathrm{M}\mathrm{A}}_n^{\left(-\right)}\left(t\right)}}$$

(3)

In this formulation, ${RS}_t$ is the ratio of exponentially smoothed average gains to average losses over a period n, with ${\mathrm{E}\mathrm{M}\mathrm{A}}_n^{\left(+\right)}\left(t\right)$ and ${\mathrm{E}\mathrm{M}\mathrm{A}}_n^{\left(-\right)}\left(t\right)$ representing the average positive and negative price changes, respectively. RSI values above 70 or below 30 are often interpreted as overbought or oversold signals.

The MACD indicator is the difference between two EMAs of different lengths:

$${\mathrm{M}\mathrm{A}\mathrm{C}\mathrm{D}}_t={\mathrm{E}\mathrm{M}\mathrm{A}}_{12}\left(P_t\right)-{\mathrm{E}\mathrm{M}\mathrm{A}}_{26}\left(P_t\right)$$

(4)

where $P_t$ is the closing price. A signal line is calculated as:

$${\mathrm{S}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{a}\mathrm{l}}_t={\mathrm{E}\mathrm{M}\mathrm{A}}_9\left({\mathrm{M}\mathrm{A}\mathrm{C}\mathrm{D}}_t\right)$$

(5)

The crossover between the MACD and its signal line is frequently used to identify bullish or bearish momentum shifts. All technical indicators are computed using daily closing prices and are standardized before being input into the forecasting model. These indicators provide complementary trend and momentum information for the forecasting model and are used together with the ESG signals introduced in the next section.

3.1.3. Carbon Credit Indicators

To represent dynamic and quantifiable ESG information beyond conventional firm-level ratings, this study incorporates four carbon credit indices published by S&P Global. These indices are derived from the pricing of emissions allowances traded on ICE Futures and reflect various regional and global carbon markets. Each index provides high-frequency sustainability signals tied to institutional expectations around decarbonization, environmental regulation, and compliance trading [47].

A.

S&P Global Carbon Credit Index

The S&P Global Carbon Credit Index (GCC) [48] serves as a diversified benchmark of the most liquid carbon credit futures across multiple markets, including EUA (European Union Allowances), UKA (United Kingdom Allowances), CCA (California Carbon Allowances), RGGI (Regional Greenhouse Gas Initiative), and WCA (Western Climate Initiative). Only December-dated contracts from the current or following year are eligible. The index value at time t is computed as the sum of contract prices weighted by adjusted notional units:

$${\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}}_t^{\mathrm{G}\mathrm{C}\mathrm{C}}={\displaystyle \sum _{i=1}^n}{P}_{i,t}\cdot Q_{i,t}$$

(6)

In this formulation, $P_{i,t}$ denotes the futures price of contract i on day t, while $Q_{i,t}$ represents its contract quantity, determined based on the six-month average trading volume and adjusted semiannually. To ensure diversification, a single region’s weight is capped at 65%, and each constituent contract must contribute at least 10% of the index weight. This global index captures aggregate carbon pricing sentiment and serves as a macro-level sustainability proxy.

B.

S&P Global Carbon Credit UCITS Index

The UCITS version [49] of the carbon credit index follows the same contract composition as the GCC Index but adjusts its structure to comply with the European UCITS (Undertakings for Collective Investment in Transferable Securities) 35/20 diversification rule. This requirement imposes concentration limits for institutional investors. As a result, the UCITS index incorporates an additional cash allocation component $C_t$, yielding the modified formula:

$${\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}}_t^{\mathrm{U}\mathrm{C}\mathrm{I}\mathrm{T}\mathrm{S}}=\left({\displaystyle \sum _{i=1}^n}{P}_{i,t}\cdot Q_{i,t}\right)+C_t$$

(7)

Here, $C_t$ represents the allocated cash buffer that ensures regulatory compliance with UCITS thresholds, particularly that no single holding exceeds 35% and no combination of holdings above 20% exceeds 45%. The remaining terms match the definitions in the GCC Index. This variant provides a benchmark for ESG exposure under constrained portfolio allocation rules.

C.

S&P Carbon Credit CCA Index

The CCA Index [50] focuses exclusively on California Carbon Allowances (CCA), which are traded under California’s cap-and-trade system and regulated by the California Air Resources Board. This index reflects North American subnational policy actions and is used to isolate U.S.-based carbon market pricing. The value at time t is computed as:

$${\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}}_t^{\mathrm{C}\mathrm{C}\mathrm{A}}=P_{\mathrm{C}\mathrm{C}\mathrm{A}, t}\cdot Q_{\mathrm{C}\mathrm{C}\mathrm{A}, t}$$

(8)

In this context, $P_{\mathrm{C}\mathrm{C}\mathrm{A},t}$ refers to the CCA futures price, while $Q_{\mathrm{C}\mathrm{C}\mathrm{A},t}$ is the corresponding quantity weight. The rebalancing and weighting methodologies are consistent with those applied in the GCC index. This index offers localized ESG signals associated with state-level climate policy and regulatory risk pricing.

D.

S&P Carbon Credit EUA Index

The EUA Index [51] is designed to track futures prices of European Union Allowances under the EU Emissions Trading System (EU ETS), the world’s most established and liquid carbon market. The value of the EUA Index at time t is given by:

$${\mathrm{I}\mathrm{n}\mathrm{d}\mathrm{e}\mathrm{x}}_t^{\mathrm{E}\mathrm{U}\mathrm{A}}=P_{\mathrm{E}\mathrm{U}\mathrm{A}, t}\cdot Q_{\mathrm{E}\mathrm{U}\mathrm{A}, t}$$

(9)

Here, $P_{\mathrm{E}\mathrm{U}\mathrm{A},t}$ is the EUA futures price and $Q_{\mathrm{E}\mathrm{U}\mathrm{A},t}$ denotes the rebalancing-adjusted unit quantity. Like the CCA Index, the EUA Index uses ICE pricing data and is recalibrated periodically. Due to the maturity and scale of the EU ETS, this index provides globally relevant signals for policy-driven decarbonization momentum.

All four carbon credit indices are aligned with the ESG-themed ETF data and incorporated as daily explanatory features in the forecasting model. Prior to model input, each index is normalized using the z-score method:

$$z_t^{\left(j\right)}={\displaystyle \frac{P_t^{\left(j\right)}-{\mu }_t^{\left(j\right)}}{{\sigma }_t^{\left(j\right)}}}$$

(10)

where $P_t^{\left(j\right)}$ denotes the price of carbon index j on day t, and ${\mu }_t^{\left(j\right)}$, ${\sigma }_t^{\left(j\right)}$ are the rolling mean and standard deviation over a specified look-back window. This transformation ensures stationarity and comparability across indicators of differing scales. By embedding standardized daily movements in carbon pricing, the model can capture the real-time sustainability signals associated with global and regional carbon markets. These signals inform the rebalancing strategy by enabling the dynamic adjustment of portfolio weights in response to shifts in exogenous ESG conditions.

3.2. Algorithm Design

As shown in Figure 1, the proposed framework is organized as a sequential pipeline linking data preparation, forecasting, portfolio construction, performance evaluation, and explainability analysis. The forecasting module compares three Transformer-inspired architectures, namely the Ordinary Transformer [52], Informer [53], and Temporal Fusion Transformer [54], under a common input format and aligned target setting. This design allows the full workflow to be presented more clearly while preserving methodological consistency across model comparisons.

3.2.1. Forecasting Algorithm: Transformer-Based Daily Return Prediction

This subsection presents the forecasting procedure used to generate one-step-ahead return predictions for the ESG-themed ETFs. The task is formulated as a multivariate regression problem based on normalized financial and carbon-related inputs over a fixed-length historical window. The resulting forecasts are then used as the input signals for the subsequent portfolio rebalancing stage.

In Algorithm 1, the joint input matrix ${\mathbf{Z}}_t$ combines normalized ETF features and carbon-credit indicators over a rolling historical window of length $T$. The forecasting task is formulated as a one-step-ahead prediction problem under a chronological train-validation-test split, with rolling normalization computed using past observations only. Although Transformer, Informer, and TFT encode temporal dependencies in different ways, all three architectures are trained under the same mean squared error objective with validation-based model selection. The resulting one-step-ahead return forecasts are then passed to the subsequent ESG-aware rebalancing stage.

Algorithm 1: Transformer-Based Daily Return Forecasting Algorithm

Input: $X_t$: Daily return and OHLCV of six ESG ETFs $C_t$: Carbon credit indices $\left[{GCC}_t,{UCITS}_t, {EUA}_t, {CCA}_t\right]$ $T$: Encoder input length $h=1$: Forecast horizon $\eta$: Learning rate $\mathcal{A}$:$\left\{{\mathrm{a}}_1,{\mathrm{a}}_2,\dots ,{\mathrm{a}}_6\right\}$: ETF asset set $M\in$ {Transformer, Informer, TFT}: Selected forecasting model $E$: Maximum number of training epochs $B$: Mini-batch size Output: ${\widehat{\mathbf{y}}}_{t+1}=[{\widehat{y}}_{t+1}^{\left(1\right)},{\widehat{y}}_{t+1}^{\left(2\right)},\dots ,{\widehat{y}}_{t+1}^{\left(6\right)}]$: One-step-ahead predicted returns for six ETFs

1 Chronological Data Split 1.1 Split the full sample into training, validation, and testing periods in chronological order. 1.2 For each forecast origin $t$, use only information available up to time $t$. 2. Feature Normalization and Sequence Construction 2.1 For each feature $j$, compute rolling z-score normalization: $$Z_t^{\left(j\right)}={\displaystyle \frac{x_t^{\left(j\right)}-{\mu }_t^{\left(j\right)}}{{\sigma }_t^{\left(j\right)}}}$$ where ${\mu }_t^{\left(j\right)}$ and ${\sigma }_t^{\left(j\right)}$ are estimated using past observations only. 2.2 Construct the joint input matrix: $${\mathbf{Z}}_t=[X_t\mid C_t]\in {\mathbb{R}}^{T\times d}$$ where $d$ is the total number of input features. 2.3 For each day $t$, generate rolling input-output pairs: $$\left({\mathbf{Z}}_{t-T+1:t}\right|{\mathbf{y}}_{t+1})$$ where ${\mathbf{y}}_{t+1}$ is the next-day return vector for all ETFs. 3. Model Initialization 3.1 Select model architecture $M\in \left\{\mathrm{Transformer}, \mathrm{Informer}, \mathrm{TFT}\right\}$. 3.2 Initialize model parameters $\theta$. 3.3 Set optimizer, learning rate $\eta$, and loss function as mean squared error. 4. Model Training for epoch $=1$ to $E$ do 4.1 Shuffle training samples by mini-batch of size $B$ for each mini-batch $\left(Z^{\left(b\right)}\right|y^{\left(b\right)})$ do 4.2 Encode input sequence using the selected architecture: – For Transformer: Apply full self-attention over sequence – For Informer: Use sparse attention and top-$k$ selection – For TFT: Apply GRN, variable selection, and temporal fusion 4.3 Obtain encoded representation: $$H_t=M\left(Z_{t-T+1:t}\right)$$ 4.4 Decode and project into prediction layer: $${\widehat{\mathbf{y}}}_{t+1}=W_o\cdot Decoder\left(H_t\right)+b_o$$ 4.5 Compute batch loss: $${\mathcal{L}}_{batch}={\displaystyle \frac{1}{N_b}}{\displaystyle \sum _{n=1}^{N_b}}{\left(y_{t+1}^{\left(n\right)}\right|{\widehat{y}}_{t+1}^{\left(n\right)})}^2$$ 4.6 Update parameters: $$\theta \leftarrow \theta -\eta {\nabla }_{\theta }{\mathcal{L}}_{batch}$$ end for 4.7 Evaluate validation loss and apply early stopping if performance does not improve. end for 5. Forecast Generation 5.1 Use the best validation model to generate one-step-ahead return forecasts on the test set. 5.2 For each test day $t$, output: $${\widehat{\mathbf{y}}}_{t+1}=[{\widehat{y}}_{t+1}^{\left(1\right)},{\widehat{y}}_{t+1}^{\left(2\right)},\dots ,{\widehat{y}}_{t+1}^{\left(6\right)}]$$ 6. Return Forecast Output 6.1 Store the forecast vector for each day. 6.2 Pass ${\widehat{\mathbf{y}}}_{t+1}$ to the subsequent ESG-aware rebalancing stage.

3.2.2. ESG-Aware Rebalancing Strategy

This study develops an ESG-aware rebalancing strategy that updates portfolio weights on a daily basis using model-generated return forecasts. The mechanism consists of two steps, namely signal filtering and weight adjustment, which together translate forecast information into implementable allocations.

• Step 1: Signal Filtering by Return Deviation

Given the predicted return ${\widehat{y}}_{t+1}^{\left(n\right)}$, for asset $a_n$ and the average forecast across all N assets ${\overline{y}}_{t+1}$, a deviation threshold $\tau$ is applied to suppress weak signals. If an asset’s forecast deviates insufficiently from the average, it is replaced with the mean value:

$${\widehat{y}}_{t+1}^{\left(n\right)} :=\{\begin{array}{c}{\overline{y}}_{t+1}, \mathrm{i}\mathrm{f} \left|{\widehat{y}}_{t+1}^{\left(n\right)}-{\overline{y}}_{t+1}\right|<\tau \\ {\widehat{y}}_{t+1}^{\left(n\right)}, \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}$$

(11)

This filtering mechanism effectively reduces noise sensitivity by de-emphasizing assets with marginal return predictions. The allocation process therefore focuses on assets with more pronounced and confident model signals, potentially improving signal-to-noise ratio in downstream portfolio decisions.

• Step 2: Return-Based Weight Assignment and Inertia Smoothing

Next, the filtered return predictions are transformed into allocation weights via the Softmax function. This approach emphasizes relative differences in return forecasts, with the parameter $\alpha$ controlling the degree of allocation sharpness:

$$w_{t+1}^{\left(n\right)}={\displaystyle \frac{\mathrm{e}\mathrm{x}\mathrm{p}\left(\alpha \cdot {\widehat{y}}_{t+1}^{\left(n\right)}\right)}{{\sum }_{j=1}^N\mathrm{e}\mathrm{x}\mathrm{p}\left(\alpha \cdot {\widehat{y}}_{t+1}^{\left(j\right)}\right)}}$$

(12)

while effective in amplifying signal-based preferences, pure Softmax-based weights can lead to unstable allocations and high turnover. To mitigate this, an inertia-based smoothing step is applied using the previous day’s allocation ${\tilde{w}}_t^{\left(n\right)}$. The updated final weight is given by:

$${\tilde{w}}_{t+1}^{\left(n\right)}=\left(1-\delta \right)\cdot w_{t+1}^{\left(n\right)}+\delta \cdot {\tilde{w}}_t^{\left(n\right)}$$

(13)

Here, $\delta \in \left[\mathrm{0,1}\right]$ denotes the smoothing coefficient, which balances reactivity against stability. Higher values of $\delta$ result in slower adjustments, preserving past allocations and reducing trading frequency.

These two steps define the core decision mechanism of the proposed rebalancing framework. In all subsequent experiments, τ denotes the return deviation threshold in Step 1, α denotes the Softmax sharpness parameter in the score-to-weight mapping, and δ denotes the inertia-based smoothing coefficient in portfolio updating. The sensitivity analysis examines how α and δ affect portfolio performance under the baseline and no-carbon settings while preserving the same notation and economic interpretation.

3.3. Evaluation Metrics

To comprehensively evaluate the performance of both the prediction model and the rebalancing strategy, this study adopts two categories of metrics: forecasting accuracy and portfolio-level performance. The first category assesses the model’s ability to predict next-day returns, while the second quantifies the financial and risk-adjusted performance of the resulting portfolio under different rebalancing settings.

3.3.1. Root Mean Squared Error (RMSE)

The Root Mean Squared Error (RMSE) quantifies the average squared deviation between the model’s predicted return and the actual observed return. It is mathematically defined as:

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{{\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T}{\left({\widehat{y}}_t-y_t\right)}^2}$$

(14)

where ${\widehat{y}}_t$ denotes the predicted return at time t, $y_t$ is the actual return, and $T$ is the total number of time points in the evaluation period. RMSE penalizes large prediction errors more heavily than small ones due to the squaring operation, making it particularly suitable when outlier performance deviations are important to identify. In this study, RMSE is used to measure how closely the model forecasts align with true asset-level daily returns, and lower values indicate higher precision.

3.3.2. Mean Absolute Error (MAE)

The Mean Absolute Error (MAE) serves as a complementary metric to RMSE, measuring the average magnitude of the prediction error without considering its direction or squaring its value. It is calculated by:

$$\mathrm{M}\mathrm{A}\mathrm{E}={\displaystyle \frac{1}{T}}{\displaystyle \sum _{t=1}^T}\left|{\widehat{y}}_t-y_t\right|$$

(15)

Compared to RMSE, MAE is more robust to outliers and offers an intuitive measure of typical prediction deviation. While RMSE emphasizes larger errors, MAE gives equal weight to all errors. In portfolio prediction contexts, MAE helps determine whether the model is consistently off-target across most time steps, which is valuable for interpreting day-to-day forecast reliability.

3.3.3. Coefficient of Determination (R²)

The $R^2$ score, or coefficient of determination, reflects the proportion of variance in actual returns that can be explained by the model’s predictions. It is defined as:

$$R^2=1-{\displaystyle \frac{{\displaystyle {\sum }_{t=1}^T}{\left({\widehat{y}}_t-y_t\right)}^2}{{\displaystyle {\sum }_{t=1}^T}{\left({\widehat{y}}_t-\overline{y}\right)}^2}}$$

(16)

where $\overline{y}$ is the average of all actual returns over the evaluation window. An R² value of 1 indicates perfect prediction, while values closer to 0 suggest weak explanatory power. In this study, R² is used to assess whether the model captures structural trends or is simply fitting noise. It adds interpretability to error-based metrics by quantifying how well the prediction traces the actual return curve.

3.3.4. Sharpe Ratio

The Sharpe Ratio evaluates the return of an investment relative to its risk, providing a normalized measure of performance adjusted for volatility. It is calculated as:

$$\mathrm{Sharpe} \mathrm{Ratio} ={\displaystyle \frac{{\overline{R}}_p-R_f}{{\sigma }_p}}$$

(17)

In this expression, ${\overline{R}}_p$ is the average return of the portfolio over the test period, $R_f$ is the risk-free rate (set to zero in daily return evaluation), and ${\sigma }_p$ is the standard deviation of portfolio returns. The Sharpe Ratio is particularly useful in comparing portfolios with different risk levels, as it captures how efficiently returns are generated relative to the inherent volatility. A higher ratio indicates better performance per unit of risk taken.

3.3.5. Maximum Drawdown (MDD)

Maximum Drawdown (MDD) measures the largest observed loss from a portfolio’s peak value to a subsequent trough before a new peak is achieved. It is expressed as:

$$\mathrm{MDD} =\underset{t\in \left[1,T\right]}{\mathrm{m}\mathrm{a}\mathrm{x}}\left({\displaystyle \frac{P_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}{-P}_t}{P_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}}}\right)$$

(18)

where $P_t$ is the portfolio value at time t, and $P_{\mathrm{p}\mathrm{e}\mathrm{a}\mathrm{k}}$ is the historical maximum up to that point. MDD is critical for assessing downside risk and capital preservation, especially during high volatility or crisis periods. In this study, it serves to benchmark rebalancing strategies under adverse market conditions.

3.3.6. Hit Ratio

The Hit Ratio is a directional accuracy metric that assesses whether the model correctly predicts the direction of price movement, regardless of the exact return magnitude. Although this study employs a regression-based forecasting model to predict continuous return values, the Hit Ratio remains applicable by comparing the sign of the predicted return with the sign of the actual return. The metric is computed as:

$$\mathrm{Hit} \mathrm{Ratio} ={\displaystyle \frac{1}{T}} {\displaystyle {\sum }_{t=1}^T}\mathbf{1}\left(\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left({\widehat{y}}_t\right)=\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\left(y_t\right)\right)$$

(19)

Here, the indicator function $\mathbf{1}\left(\cdot \right)$ equals 1 when the predicted and actual returns have the same sign, and 0 otherwise. The Hit Ratio is especially relevant for tactical allocation strategies where the correct identification of trend direction is more important than precise return value prediction.

4. Experimental Results and Discussion

This section outlines the experimental framework used to evaluate the forecasting and rebalancing strategy proposed in this study. The goal is to assess the prediction accuracy of different Transformer-based models and examine the effectiveness of the rebalancing mechanism under realistic market conditions. Section 4.1 describes the data sources, feature design, model setup, rebalancing parameters, and evaluation procedure. Section 4.2 presents the experimental results and performance comparisons between the proposed methods and several baseline strategies.

4.1. Experimental Setup

The experimental framework of this study is designed to evaluate the effectiveness of the proposed forecasting and rebalancing mechanisms using real-world financial data. All experiments are conducted using daily observations covering the period from January 2022 to December 2024. The primary prediction targets are six ESG-themed ETFs, selected for their relevance to sustainability-oriented investment themes and accessibility through public data platforms. These ETFs span U.S.-based ESG-compliant equity indices, global clean energy sectors, China’s green technology markets, and direct exposure to global carbon pricing through carbon allowance markets. Each ETF’s adjusted closing price is collected via Yahoo Finance and aligned into a synchronized daily sequence. These prices are transformed into daily log returns, which serve as the regression targets for the forecasting models.

The technical indicators are drawn from two primary categories-moving average-based and momentum-based metrics- specifically including SMA, EMA, RSI, and MACD. These indicators are computed using the ETF price series and are treated as dynamic, model-aware signals for trend characterization and price momentum. Meanwhile, carbon-related market signals are represented by four daily indices retrieved from the S&P Global Carbon Credit Index family. These include benchmarks that reflect pricing developments in both compliance markets (e.g., EUA, CCA) and broader global carbon allowance portfolios. To ensure consistency in scale and interpretation, all carbon indices are standardized using z-score normalization, preserving temporal fluctuation patterns while aligning value distributions across assets.

The forecasting task is performed using three Transformer-inspired deep learning architectures: the Ordinary Transformer, Informer, and TFT. Each model is trained independently using the same data inputs and evaluation splits, with the objective of predicting next-day returns for all six ETFs. The use of these three architectures is intended to compare how differences in attention sparsity, temporal filtering, and gating mechanisms influence sequence prediction in financial domains. The target of each model is a one-step-ahead prediction for each asset, formulated as a univariate regression per ETF per day. All models are trained using Mean Squared Error as the loss function, with early stopping criteria based on validation loss. The training-validation-testing split follows a chronological split strategy, using the earliest portion of data for training and the latest for testing to simulate realistic deployment. To avoid information leakage, all rolling normalization statistics were computed using only information available up to each forecast origin, and the validation and test periods were evaluated strictly out-of-sample under the chronological split.

On top of the forecasting output, this study applies the two-step rebalancing strategy defined in Section 3.2.2. In Step 1, predicted next-day returns are filtered by a return deviation threshold $\tau$. When the deviation of an asset-specific forecast from the cross-asset average is smaller than $\tau$, that forecast is replaced by the average forecast in order to suppress weak relative signals. In Step 2, the filtered forecasts are converted into portfolio weights through a Softmax mapping, where $\alpha$ controls the sharpness of the score-to-weight transformation. The resulting weights are then updated through inertia smoothing, where $\delta$ determines the extent to which the previous day’s portfolio weights are retained. In the main experiment, the return deviation threshold is fixed at $\tau$ = 0.005 to suppress minor cross-asset noise while preserving economically meaningful forecast dispersion. The parameters $\alpha$ and $\delta$ are examined in the sensitivity analysis to evaluate the trade-off among responsiveness, stability, and turnover under the baseline and no-carbon settings.

These parameters are fixed during the primary experiment and later varied in robustness analysis to evaluate stability and sensitivity. Model performance is evaluated through a set of six metrics. RMSE, MAE, and the coefficient of determination $R^2$ are used to measure prediction accuracy. Sharpe Ratio, MDD, and Hit Ratio are used to assess the portfolio-level implications of the predictions under the rebalancing strategy. All evaluation metrics are computed based on the daily predictions and resulting portfolio performance, using rolling windows where appropriate to capture short- and mid-term dynamics. The experimental protocol emphasizes both pointwise error analysis and trend consistency in directional forecasting.

All training and inference procedures are conducted in a high-performance computing environment to ensure scalability and reproducibility. The experimental system runs on a workstation with Windows 11 Pro, powered by an Intel^® Core™ i9-12900K processor (Intel, Santa Clara, CA, USA) and 32 GB of RAM. GPU acceleration is enabled through an NVIDIA GeForce RTX 4080 (NVIDIA, Santa Clara, CA, USA) graphics card, which supports efficient attention matrix computation, parallelized backpropagation, and time-series batching during model training. This configuration provides sufficient capacity to handle multivariate time series inputs and high-resolution output across long evaluation periods.

4.2. Experimental Results

In this experiment, all models are trained using a fixed chronological data split: the training set includes data from January 2022 to June 2023, the validation set spans July 2023 to December 2023, and the testing set covers January 2024 to December 2024. Input sequences are constructed using a rolling window of 30 trading days, with the model predicting the return on the next day. The batch size is set to 32, and early stopping is employed based on validation loss with a patience of 20 epochs. Three Transformer-based architectures are implemented under the same preprocessing pipeline. The ordinary Transformer adopts a full self-attention mechanism and positional encoding without specialized temporal modules. The Informer model incorporates a sparse self-attention structure that reduces computational cost in long sequences by focusing on dominant patterns. It also uses a distilling decoder for improved efficiency. The TFT introduces interpretable elements, including variable selection networks, gating mechanisms, and temporal fusion layers, which allow the model to dynamically weight both input variables and time steps. All models are optimized using the Adam optimizer with a learning rate of 0.01, and weight decay set to 1 × 10⁻⁵.

This section presents the empirical results of the proposed ESG portfolio rebalancing framework. Section 4.2.1 examines forecasting diagnostics across models and assets. Section 4.2.2 analyzes sensitivity to the Softmax sharpness and smoothing parameters. Section 4.2.3 compares the proposed strategies with stronger benchmark allocation rules, while Section 4.2.4 reports the ablation results of the main rebalancing components. Section 4.2.5 evaluates statistical uncertainty through bootstrap confidence intervals, and Section 4.2.6 examines subperiod robustness across 2024H1 and 2024H2. Section 4.2.7 then investigates explainability from grouped, feature-level, and local SHAP perspectives, followed by a comprehensive empirical evaluation in Section 4.2.8.

4.2.1. Forecast Error Diagnostics Across Models

This subsection assesses the reasonableness and stability of one-day-ahead forecasts by comparing three deep models (Transformer, Informer, TFT) against classical baselines (LSTM, GRU, SVR) across six ETFs (ESGU, ICLN, KGRN, KRBN, SUSA, TAN). Figure 2 and Figure 3 report the cross-ticker dispersion of MAE and RMSE, while Figure 4 summarizes R². For a concise cross-model comparison, we also average each metric over all tickers and report the results in

Table 1. Forecast metrics summary by model (mean).

Model/Metrics	MAE	RMSE	R2
Informer	0.0045	0.0059	0.84390
TFT	0.0074	0.0088	0.60210
GRU	0.0080	0.0108	0.46110
LSTM	0.0089	0.0110	−0.27010
Transformer	0.0124	0.0158	−0.03810
SVR	0.0101	0.0134	0.20100

.

The evidence indicates that Informer achieves the strongest aggregate forecasting performance across the six ETFs, with the lowest average MAE and RMSE and consistently competitive R², suggesting better alignment with the underlying price dynamics. TFT follows as the next most stable deep model in the aggregate summary, although its advantage is less pronounced and its forecasts remain closer to the benchmark in later portfolio analysis. Transformer shows competitive behavior on selected tickers, especially in more volatile names, but its error metrics are less consistent across the full universe and therefore do not match Informer’s overall average performance. Among the remaining baselines, GRU generally occupies a middle position without a clear leading pattern, while SVR and LSTM exhibit weaker and less stable results on several assets, including larger errors or negative R² values on specific tickers.

In this experiment, Informer delivers the clearest and most consistent forecasting advantage in both error minimization and explanatory power (R²). TFT remains the second most stable deep model in the aggregate evaluation, whereas Transformer is better characterized as selectively competitive rather than uniformly strong across all tickers. This distinction is important for the later portfolio analysis: lower average forecasting error does not automatically guarantee the best allocation path, because portfolio outcomes also depend on cross-asset score dispersion, rebalancing sensitivity, and turnover interaction. For this reason, the subsequent portfolio backtests and explainability analysis focus on the three deep sequence models, which provide the most relevant comparison for understanding how predictive structure is translated into portfolio decisions.

Before proceeding to portfolio-level evaluations, it is essential to examine whether the models produce return forecasts that resonate with actual market movements. Figure 5, Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10 plot the next-day log returns for each of the six ETFs, superimposed with their corresponding price series for context. The black curve marks the observed log return, whereas Transformer, Informer, and TFT are shown in blue, orange dashed, and purple dotted lines, respectively. These figures are used to assess whether the model outputs broadly track market turning behavior and whether the resulting forecast signals are sufficiently informative to support the subsequent rebalancing analysis.

In the case of ESGU, the market environment is relatively tranquil, with a steady uptrend and moderate return volatility. All three models track the general shape of the return curve, though discrepancies emerge in their vertical positioning. Informer remains consistently above the zero line, indicating a positive bias, while Transformer and TFT fluctuate closer to a zero-mean band, capturing several subtle spikes. Here, the key difference lies in the level shift rather than direction. Even if turning points are correctly identified, persistent deviation from the baseline inflates error metrics, particularly MAE.

As for ICLN, which experiences a strong mid-year rally followed by a fourth-quarter decline, the performance gap between models becomes more pronounced. Transformer aligns well with the actual series, mirroring both the upward surges and corrective dips. TFT tends to be more cautious, undershooting rebounds during drawdowns and reacting less decisively to market swings. Informer, while smoother, exhibits a gentle downward tilt for long stretches, deviating from the true curve in a systematic fashion. This explains why Transformer outperforms on ICLN in terms of both RMSE and MAE.

The return sequence for KGRN is dominated by oscillatory waves, with recurring rise-and-fade cycles. Transformer effectively mirrors both the timing and the amplitude of these cycles, offering a balanced representation. In contrast, Informer and TFT appear more constrained, failing to fully register the extremes. As volatility intensifies mid-year, Transformer retains its phase alignment without being drawn away from a neutral baseline. This characteristic is crucial in our two-step allocation method, as score stability directly impacts portfolio weight calibration.

A different dynamic plays out in KRBN, a carbon-credit ETF that often exhibits sudden price shocks and reversals. All models dampen the magnitude of these extreme movements, likely due to risk-aware architectures. However, Transformer still manages to capture the correct directional shifts, whereas Informer periodically drifts upward and TFT becomes noisier near inflection points. In this jump-revert regime, directional accuracy proves more valuable than perfect magnitude estimation, and Transformer strikes that balance more effectively.

With SUSA, we enter low-volatility territory. The predicted return curves are tightly packed and nearly indistinguishable at a glance. Transformer, Informer, and TFT converge around the zero line, with minor variation in smoothness: Informer is the smoothest and carries a slight upward bias, Transformer is centered and slightly more dynamic, while TFT exhibits small, rapid fluctuations. In such cases, exploitable alpha is minimal, and model differentiation becomes a matter of noise control and stability rather than signal quality.

TAN introduces the opposite scenario, being the most volatile ETF in this group. The price curve shows frequent reversals, particularly sharp toward the year’s end. Transformer maintains close tracking with the truth while staying near the baseline, showing restraint without sacrificing directional accuracy. TFT overshoots both upswings and downswings, producing conspicuous spikes, especially in the final quarter. Informer remains moderate but can drift negatively. Here, volatility magnifies the contrasts among models, providing clear visual evidence of their behavioral traits.

This set of overlays illustrates three central observations. First, all models maintain reasonable phase alignment with the truth, satisfying the primary requirement for our Softmax-based rebalancing. Second, systematic traits-Informer’s level drift and TFT’s reactivity-manifest more visibly in volatile contexts and explain their relatively higher residual errors. Third, the clarity of visual separation among models is directly related to volatility: high-volatility ETFs like TAN and KRBN accentuate the differences, while low-volatility ones like SUSA compress them. These graphical checks complement our earlier numerical results and help explain why Transformer may exhibit a comparatively smoother portfolio path in subsequent experiments, even when its aggregate forecast errors are not the lowest.

4.2.2. Sensitivity to Softmax Sharpness and Rebalancing Smoothing: Baseline vs. No-Carbon

This section investigates how variations in the Softmax sharpness parameter $\alpha$ and the inertia smoothing coefficient $\delta$ affect portfolio-level performance under the baseline and no-carbon settings. Performance is evaluated through changes in Sharpe ratio, maximum drawdown, hit ratio, and turnover. Here, $\alpha$ controls how aggressively filtered return scores are translated into cross-asset allocation differences, whereas $\delta$ controls how strongly previous portfolio weights are retained during rebalancing. Figure 11 summarizes these sensitivity patterns across the three deep sequence models and helps identify whether performance changes are mainly associated with allocation concentration, smoothing intensity, or the presence of carbon-related inputs.

As shown in Figure 11a, $\mathsf{\Delta }$Sharpe steadily increases with $\alpha$ for both Informer and Transformer. This pattern indicates that the performance contribution of carbon-informed forecasts becomes more visible when the score-to-weight mapping is sharper. TFT displays the opposite tendency, suggesting that a more concentrated allocation rule does not help it convert the baseline forecasts into superior portfolio outcomes. The contrast across models shows that the value of carbon information depends on how effectively each architecture converts forecast dispersion into allocation signals.

Turning to directional accuracy, hit ratios remain mostly stable across α variations. As illustrated in Figure 11c, ΔHit values hover around zero for all three models, with only minor dips for Informer and Transformer in select α regions. This supports the conclusion that carbon signals do not significantly affect the ability to predict market direction. When analyzing $\delta$ (with $\alpha$ fixed at 1.2), the trends shift. In Figure 11d, all models perform best under low $\delta$, where allocations are based mostly on current scores. This highlights the importance of responsiveness in capturing short-term opportunities. As $\delta$ increases, Transformer and Informer gradually lose this edge, while TFT shows moderate improvement, benefiting from persistence in smoother market conditions. A different dynamic appears in Figure 11e, which charts drawdown sensitivity. Informer and Transformer benefit from increased $\delta$, as smoother allocations help limit large losses. Conversely, TFT’s Δ MDD worsens with rising $\delta$, possibly due to lagged reactions that magnify losses during downturns. These results reflect each model’s trade-off between adaptability and stability. Figure 11f revisits the hit ratio across $\delta$ levels and confirms earlier findings—directional accuracy remains largely unchanged. ΔHit values stay near zero, with no consistent advantage from smoothing, reinforcing that model structure, not δ, dictates forecast accuracy. Figure 11g tracks changes in turnover. Higher $\delta$ consistently lowers ΔTurnover, particularly for Transformer, suggesting reduced trading activity and improved cost-efficiency. Informer sees the steepest increase in turnover at low $\delta$, where quick responsiveness comes at a price. These cost implications are essential when evaluating post-transaction net returns.

The $\alpha -\delta$ sensitivity analysis reveals the nuanced interplay between responsiveness, stability, and model structure. Carbon signals can improve portfolio outcomes when they are aligned with each model’s learning dynamics and with an appropriately calibrated allocation rule.

4.2.3. Benchmark Comparison with Stronger Allocation Baselines

This experiment evaluates portfolio-level allocation performance rather than forecasting accuracy for individual assets. Using three deep learning models, namely Transformer, Informer, and TFT, this study constructs dynamic portfolio weights across six ESG-themed ETFs, including ESGU, SUSA, ICLN, TAN, KRBN, and KGRN. In addition to the model-based strategies, three benchmark allocation methods are considered, namely Equal Weight, Risk Parity, and Momentum, in order to provide a stronger comparative basis for portfolio evaluation. Figure 12a,b further illustrate the corresponding equity and drawdown trajectories over the aligned test period.

Table 2. Performance comparison of benchmark and deep learning-based portfolio rebalancing strategies over the aligned test period. Sharpe ratio, maximum drawdown, hit ratio, profit factor, and average turnover are reported after transaction costs.

Strategy	Average Turnover	Sharpe Ratio	Max Drawdown	Hit Ratio	Profit Factor
Equal Weight	0	5.49 × 10−1	−1.33 × 10−1	5.16 × 10−1	1.09
RiskParity 20D	3.21 × 10−2	3.06 × 10−1	−1.28 × 10−1	5.04 × 10−1	1.05
Momentum 20D	3.29 × 10−1	−2.22 × 10−1	−2.42 × 10−1	4.76 × 10−1	9.64 × 10−1
Transformer	1.50 × 10−3	2.27 × 10−1	−1.25 × 10−1	4.98 × 10−1	1.04
Informer	4.88 × 10−3	2.88 × 10−1	−1.20 × 10−1	4.98 × 10−1	1.05
TFT	0	1.97 × 10−1	−1.26 × 10−1	4.98 × 10−1	1.03

shows that the benchmark strategies display heterogeneous behavior across performance dimensions. Equal Weight achieves the highest Sharpe ratio among all reported strategies, whereas Momentum exhibits the weakest overall performance, with the lowest Sharpe ratio and the deepest drawdown. Risk Parity remains more stable than Momentum, but its overall risk-adjusted performance is still limited. Against these stronger baselines, the three deep learning-based strategies remain competitive. Informer delivers the strongest Sharpe ratio among the model-based approaches, while Transformer and TFT produce comparable drawdown levels with relatively low average turnover. These results suggest that the proposed framework does not rely on comparison with a weak baseline only, but retains reasonable portfolio performance when evaluated against standard benchmark allocation rules.

From the trajectory perspective, Figure 12a indicates that the model-based strategies generally move within a similar range, although their cumulative paths differ from those of the benchmark rules during several subperiods. Figure 12b shows that the deep learning-based strategies avoid the pronounced drawdown deterioration observed under the Momentum benchmark, while remaining broadly comparable to Equal Weight and Risk Parity in downside behavior. This pattern suggests that the proposed rebalancing mechanism provides a competitive alternative to conventional allocation rules, although its advantage is better interpreted as moderate and context-dependent rather than uniformly dominant across all metrics.

Starting from Figure 12a, the equity curves reveal clear differences between standard benchmark rules and model-based rebalancing strategies over the aligned test period. Equal Weight remains one of the strongest performers in cumulative return terms, while Momentum shows a visibly weaker trajectory and loses competitiveness in the latter half of the sample. Risk Parity follows a more stable path, although its cumulative growth remains moderate. Against these benchmark rules, the Transformer-, Informer-, and TFT-based strategies remain within a comparable performance range. Their equity paths do not indicate uniformly dominant outperformance, but they do show that the proposed framework can maintain competitive portfolio growth without relying on comparison against a weak baseline alone. Figure 12b further compares the drawdown behavior of these strategies. The most pronounced deterioration is observed under the Momentum benchmark, which experiences substantially deeper and more persistent drawdowns than the other strategies. In contrast, the three deep learning-based strategies remain closer to Equal Weight and Risk Parity in downside behavior, suggesting that the proposed rebalancing mechanism avoids the most severe drawdown episodes while maintaining broadly comparable risk characteristics. Among the model-based strategies, the differences are moderate rather than extreme, which implies that their relative advantages are better interpreted in terms of stability and allocation behavior instead of sharply different directional success rates. This visual and metric-based comparison should therefore be interpreted primarily as evidence of competitiveness, especially because the later bootstrap analysis shows that many benchmark-based differences are not statistically significant at the 95% level.

4.2.4. Ablation Analysis of the Proposed Framework

To further examine whether the proposed framework derives its performance from a meaningful combination of components rather than from a single design choice, this study conducts an ablation analysis on the main rebalancing mechanism. The analysis considers five settings for each forecasting architecture, namely the Full Model, No Carbon, No Threshold, α = 0, and δ = 0. The Full Model uses the selected hyperparameter setting for each forecasting model, whereas the remaining variants remove or deactivate one component at a time while keeping the other elements unchanged. This design makes it possible to evaluate the separate roles of carbon-related inputs, threshold filtering, score concentration, and smoothing-based portfolio updating.

As shown in

Table 3. Ablation analysis of the proposed framework under different component settings. Sharpe ratio, maximum drawdown, hit ratio, profit factor, and average turnover are reported after transaction costs.

Model	Setting	Avg Turnover	Sharpe Ratio	MDD	Hit Ratio	Profit Factor
Informer	α = 0	0	4.07 × 10−1	−1.13 × 10−1	4.98 × 10−1	1.07
Informer	δ = 0	2.20 × 10−2	7.51 × 10−1	−9.34 × 10−2	5.02 × 10−1	1.13
Informer	Full Model	4.88 × 10−3	4.97 × 10−1	−1.08 × 10−1	5.02 × 10−1	1.08
Informer	No Carbon	3.83 × 10−3	4.72 × 10−1	−1.10 × 10−1	4.98 × 10−1	1.08
Informer	No Threshold	4.88 × 10−3	4.98 × 10−1	−1.08 × 10−1	5.02 × 10−1	1.08
TFT	α = 0	0	4.07 × 10−1	−1.13 × 10−1	4.98 × 10−1	1.07
TFT	δ = 0	0	4.07 × 10−1	−1.13 × 10−1	4.98 × 10−1	1.07
TFT	Full Model	0	4.07 × 10−1	−1.13 × 10−1	4.98 × 10−1	1.07
TFT	No Carbon	0	4.07 × 10−1	−1.13 × 10−1	4.98 × 10−1	1.07
TFT	No Threshold	0	4.07 × 10−1	−1.13 × 10−1	4.98 × 10−1	1.07
Transformer	α = 0	0	4.07 × 10−1	−1.13 × 10−1	4.98 × 10−1	1.07
Transformer	δ = 0	4.72 × 10−3	4.93 × 10−1	−1.09 × 10−1	5.02 × 10−1	1.08
Transformer	Full Model	1.50 × 10−3	4.37 × 10−1	−1.13 × 10−1	5.02 × 10−1	1.07
Transformer	No Carbon	1.23 × 10−3	4.34 × 10−1	−1.13 × 10−1	5.02 × 10−1	1.07
Transformer	No Threshold	1.47 × 10−3	4.38 × 10−1	−1.13 × 10−1	5.02 × 10−1	1.07

Note: The Full Model uses the selected hyperparameters for each forecasting architecture. “No Carbon” removes carbon-related inputs, “No Threshold” disables threshold filtering, and α = 0 and δ = 0 denote ablation settings with the corresponding parameter fixed at zero. Sharpe ratio, maximum drawdown (MDD), hit ratio, profit factor, and average turnover are reported after transaction costs.

, the three model families respond differently to the removal of individual components. For Transformer, the Full Model records a Sharpe ratio of about 0.44, while the No Carbon and No Threshold settings remain close to this level. When α = 0, the Sharpe ratio declines to about 0.41, whereas setting δ = 0 increases it to approximately 0.49. Informer exhibits the strongest sensitivity to the ablation design. Its Full Model produces a Sharpe ratio near 0.50, the No Carbon setting declines moderately to around 0.47, and δ = 0 leads to the largest increase, reaching roughly 0.75. By contrast, TFT remains relatively stable across all settings, with Sharpe ratios clustered around 0.41. TFT exhibits minimal sensitivity across the tested ablation settings, indicating that its allocation output remains relatively invariant under the current parameterization. These results suggest that the contribution of each module is model-dependent rather than uniform across architectures.

From the risk perspective, the maximum drawdown values remain relatively close across most ablation settings, indicating that the removal of individual components does not radically alter downside behavior over the test window. This pattern is important because it implies that the observed performance differences are driven more by return efficiency and trading dynamics than by extreme changes in drawdown alone. In practical portfolio terms, the framework appears to modify the quality of allocation decisions and rebalancing behavior more strongly than it changes the broad scale of downside risk.

Figure 13a provides a visual summary of the Sharpe-ratio differences reported in Table 3. The figure shows that the Full Model, No Carbon, and No Threshold settings remain relatively close for Transformer and Informer, whereas the α = 0 setting lowers performance and the δ = 0 setting increases performance most strongly, especially for Informer. For TFT, the variation is much smaller, which suggests that its portfolio behavior is less sensitive to the removal of any single component. This also implies that the performance of the proposed framework is not driven by carbon features alone, because removing carbon inputs does not fully collapse the strategy performance. Instead, the model output is shaped by the interaction between predictive structure and allocation mapping. Figure 13b offers a clearer interpretation of the smoothing mechanism. When α = 0, average turnover is reduced to nearly zero across the models, which is consistent with the loss of differentiated score-to-weight mapping. In contrast, setting δ = 0 increases turnover sharply, most visibly for Informer, where the value rises to about 0.022, compared with approximately 0.0049 under the Full Model. Transformer also shows a turnover increase from around 0.0015 to about 0.0047 when smoothing is removed. These changes indicate that the smoothing component plays a direct role in controlling trading intensity and portfolio stability. Even when higher Sharpe ratios are observed under δ = 0, the associated turnover expansion suggests a less conservative and potentially less implementable allocation process from a practical portfolio management perspective.

The ablation results support two conclusions. First, the proposed framework does not depend on a single isolated component, since different ablation settings alter performance in different ways across models. Second, the smoothing mechanism has the clearest financial interpretation, because it directly governs turnover and thereby influences the trade-off between responsiveness and implementation stability. Carbon inputs and threshold filtering still provide useful refinements, but their effects appear more moderate and architecture-dependent. This evidence strengthens the argument that the framework operates as a coordinated decision system rather than as a simple stacking of unrelated modules.

4.2.5. Statistical Confidence and Uncertainty Assessment

To complement the preceding performance comparisons, this study further evaluates the uncertainty associated with selected benchmark and ablation comparisons by constructing bootstrap-based confidence intervals. The purpose of this analysis is to determine whether the observed differences in Sharpe ratio and maximum drawdown remain stable after accounting for sampling variability. Because portfolio return paths exhibit temporal dependence, moving-block bootstrap resampling is adopted so that local time-series structure can be preserved when estimating confidence intervals.

As shown in

Table 4. Bootstrap confidence intervals for selected performance differences.

Comparison	Metric	Estimate	CI Lower	CI Upper	Sig. at 95%
Informer: Full vs. No Carbon	Δ MDD	2.34 × 10−3	5.99 × 10−5	3.74 × 10−3	TRUE
Informer: Full vs. No Carbon	Δ Sharpe Ratio	2.55 × 10−3	1.40 × 10−2	4.12 × 10−2	TRUE
Informer vs. Equal Weight	Δ MDD	6.00 × 10−3	−1.41 × 10−1	1.57 × 10−1	FALSE
Informer vs. Equal Weight	Δ Sharpe Ratio	−9.27 × 10−2	−2.55	2.65	FALSE
Informer vs. Risk Parity 20D	Δ MDD	7.49 × 10−3	−1.52 × 10−1	1.34 × 10−1	FALSE
Informer vs. Risk Parity 20D	Δ Sharpe Ratio	2.15 × 10−1	−2.31	3.07	FALSE
TFT: Full vs. No Carbon	Δ MDD	0	0	0	FALSE
TFT: Full vs. No Carbon	Δ Sharpe Ratio	0	0	0	FALSE
TFT vs. Equal Weight	Δ MDD	8.22 × 10−5	−1.50 × 10−1	1.53 × 10−1	FALSE
TFT vs. Equal Weight	Δ Sharpe Ratio	−1.83 × 10−1	−2.63	2.58	FALSE
Transformer: Full vs. No Carbon	Δ MDD	1.10 × 10−4	−3.06 × 10−4	6.95 × 10−4	FALSE
Transformer: Full vs. No Carbon	Δ Sharpe Ratio	3.16 × 10−3	−1.84 × 10−3	9.07 × 10−3	FALSE
Transformer vs. Equal Weight	Δ MDD	9.98 × 10−4	−1.48 × 10−1	1.55 × 10−1	FALSE
Transformer vs. Equal Weight	Δ Sharpe Ratio	−1.53 × 10−1	−2.60	2.61	FALSE

Note: Point estimates and 95% confidence intervals are reported for selected benchmark and ablation comparisons. Confidence intervals are obtained from moving-block bootstrap resampling with 2000 replications and block size = 10.

, most benchmark-based comparisons do not produce statistically decisive differences at the 95% level. For example, the Sharpe-ratio differences between Informer and Equal Weight, between Informer and Risk Parity, and between Transformer and Equal Weight are all associated with confidence intervals that cross zero. A similar pattern is observed for the corresponding maximum drawdown differences. These results indicate that, although the model-based strategies remain competitive relative to standard allocation rules, the magnitude and direction of their apparent advantage are not uniformly stable across repeated resampling.

At the same time, the uncertainty assessment does not suggest that all effects are negligible. In the comparison between the Informer Full Model and the No Carbon setting, both performance indicators show statistically significant differences. The estimated change in maximum drawdown is approximately $2.34\times {10}^{-3}$, with a positive 95% confidence interval ranging from about $5.99\times {10}^{-5}$ to $3.74\times {10}^{-3}$. The corresponding change in Sharpe ratio is about $2.55\times {10}^{-2}$, with a 95% confidence interval from roughly $1.40\times {10}^{-2}$ to $4.12\times {10}^{-2}$. This suggests that, at least within the Informer framework, the removal of carbon-related inputs leads to a measurable weakening of portfolio performance, even though the absolute size of the effect remains moderate.

By contrast, TFT shows virtually no difference between the Full Model and the No Carbon setting, with point estimates equal to zero for both Sharpe ratio and maximum drawdown. Transformer exhibits only small positive point estimates in the same comparison, but the corresponding confidence intervals still overlap zero. This pattern indicates that the usefulness of carbon-related inputs is not identical across architectures. Instead, their marginal contribution appears to be more pronounced in Informer, while the same information provides weaker incremental benefit in Transformer and almost no measurable effect in TFT under the present evaluation setting.

From an empirical perspective, Table 4 supports a more nuanced interpretation of the portfolio results. Several benchmark differences are visible at the level of point estimates, yet many of these differences are not sufficiently stable to warrant strong claims of general superiority. In contrast, the carbon-input ablation within Informer remains statistically identifiable. Taken together, the confidence-interval evidence suggests that the proposed framework should be interpreted in terms of competitive performance, architecture-dependent behavior, and mechanism-level variation rather than as a universally dominant allocation rule across all metrics.

4.2.6. Subperiod Robustness Analysis

To further examine whether the portfolio results remain stable across different market phases, this study divides the 2024 test period into two subperiods, namely 2024H1 and 2024H2, and compares benchmark and model-based strategies within each segment. This design makes it possible to distinguish whether the observed portfolio behavior is persistent across time or driven mainly by one particular market regime. Because the allocation rules and model outputs may react differently under changing return dispersion and sector rotation, subperiod analysis provides an additional robustness check beyond full-period averages.

As shown in

Table 5. Subperiod robustness of benchmark and deep learning-based portfolio strategies during the 2024 test period. Sharpe ratio, maximum drawdown, hit ratio, profit factor, and average turnover are reported after transaction costs for 2024H1 and 2024H2.

Subperiod	Strategy	Avg Turnover	Sharpe Ratio	MDD	Hit Ratio	Profit Factor
2024H1	Equal Weight	0	1.03	−9.90 × 10−2	5.40 × 10−1	1.18
2024H1	Momentum	3.28 × 10−1	4.52 × 10−1	−1.55 × 10−1	4.84 × 10−1	1.08
2024H1	Risk Parity	2.86 × 10−2	6.82 × 10−1	−9.35 × 10−2	5.24 × 10−1	1.11
2024H1	Informer	4.38 × 10−3	3.22 × 10−1	−9.71 × 10−2	5.16 × 10−1	1.05
2024H1	TFT	0	2.39 × 10−1	−9.89 × 10−2	5.05 × 10−1	1.04
2024H1	Transformer	1.54 × 10−3	2.67 × 10−1	−9.91 × 10−2	5.16 × 10−1	1.04
2024H2	Equal Weight	0	5.20 × 10−1	−1.02 × 10−1	4.92 × 10−1	1.09
2024H2	Momentum	3.31 × 10−1	−4.09 × 10−1	−1.59 × 10−1	4.77 × 10−1	9.34 × 10−1
2024H2	Risk Parity	3.55 × 10−2	3.22 × 10−1	−7.69 × 10−2	4.92 × 10−1	1.05
2024H2	Informer	5.25 × 10−3	6.15 × 10−1	−9.90 × 10−2	4.92 × 10−1	1.11
2024H2	TFT	0	5.20 × 10−1	−1.02 × 10−1	4.92 × 10−1	1.09
2024H2	Transformer	1.47 × 10−3	5.51 × 10−1	−1.01 × 10−1	4.92 × 10−1	1.09

, the benchmark and model-based strategies display clear subperiod heterogeneity. In 2024H1, Equal Weight records the strongest Sharpe ratio at approximately 1.03, followed by Risk Parity at about 0.68, while Momentum remains positive at roughly 0.45. By contrast, the three model-based strategies produce lower Sharpe ratios in the first half of the year, with Informer around 0.32, Transformer around 0.27, and TFT around 0.24. These results suggest that during the earlier subperiod, simpler benchmark rules remain highly competitive, especially under conditions in which broad market exposure appears to be rewarded more consistently than model-driven reallocations. The ranking changes noticeably in 2024H2. Equal Weight remains positive, with a Sharpe ratio near 0.52, but Informer rises to about 0.62 and becomes the strongest performer in this subperiod. Transformer also improves materially to around 0.55, while TFT increases to approximately 0.52. In contrast, Momentum deteriorates sharply and turns negative, with a Sharpe ratio near −0.41. Risk Parity remains positive but moderate, at about 0.32. This shift indicates that the relative advantage of the model-based strategies becomes more visible in the later subperiod, particularly when the benchmark based on recent price continuation becomes less reliable.

From the downside-risk perspective, maximum drawdown differences are smaller than Sharpe-ratio differences, but the relative pattern is still informative. As shown in Table 5 and Figure 14b, Momentum exhibits the deepest drawdowns in both subperiods, approximately −0.155 in 2024H1 and −0.159 in 2024H2, which is clearly worse than the remaining strategies. Equal Weight, Transformer, Informer, and TFT remain clustered near the −0.10 range across both subperiods, while Risk Parity produces the shallowest drawdown in 2024H2 at about −0.077. These results suggest that the main cross-period distinction is driven less by radical changes in downside exposure and more by changes in return efficiency and allocation effectiveness.

Figure 14a visualizes the shift in risk-adjusted performance across the two subperiods. The figure shows that benchmark rules dominate more clearly in 2024H1, especially Equal Weight and Risk Parity, whereas the model-based strategies gain relative strength in 2024H2. Informer presents the clearest improvement, but Transformer and TFT also move upward relative to the benchmark set. Figure 14b shows that drawdown profiles remain comparatively stable for most strategies except Momentum, whose downside deterioration is consistently more severe than that of the other approaches. Taken together, these two panels indicate that the proposed framework does not deliver a uniform advantage in every subperiod, but its relative competitiveness becomes stronger in the latter half of the year.

The turnover statistics in Table 5 also help explain part of this behavior. Momentum maintains by far the highest turnover in both subperiods, exceeding 0.32, whereas the model-based strategies remain much lower, with Informer around 0.004 to 0.005, Transformer near 0.0015, and TFT effectively close to zero. This implies that the model-based strategies achieve their improved second-half competitiveness without requiring turnover levels comparable to the most active benchmark rule. From a portfolio management perspective, this pattern is meaningful because it suggests that later-period performance improvement is not simply purchased through excessive trading intensity.

The subperiod analysis leads to two main conclusions. First, the relative ordering of strategies is period-dependent rather than fixed, which means that full-sample averages should not be interpreted as universally representative of all market conditions. Second, the model-based strategies appear more resilient in 2024H2, while benchmark rules, especially Equal Weight and Risk Parity, remain more competitive in 2024H1. Therefore, the robustness evidence supports a balanced interpretation in which the proposed framework functions as a competitive and adaptive allocation mechanism, with strengths that become more visible under selected subperiod conditions rather than under every regime uniformly.

4.2.7. Explainability Analysis

To further clarify how carbon-related information influences portfolio construction, this study conducts a multi-level explainability analysis based on grouped contribution summaries, feature-level decomposition, and detailed SHAP beeswarm inspection. Rather than relying on a single interpretability plot, the analysis is organized from aggregated patterns to local attribution behavior. This design makes it possible to explain not only whether carbon-related inputs matter, but also how their contribution varies across asset groups, individual carbon indicators, and model architectures.

As shown in

Table 6. Group-level summary of carbon-feature contributions across models and asset groups. Mean, median, and total contribution statistics, together with within-model contribution shares, are reported to compare explainability patterns across Broad ESG, Intermediate, and Carbon-Sensitive asset groups.

Model	Asset Group	Mean Absolute Contribution	Median Absolute Contribution	Total Contribution	Total Contribution Share
Informer	Broad ESG	1.01 × 10−3	6.30 × 10−4	8.07 × 10−3	2.44 × 10−1
Informer	Carbon-Sensitive	1.66 × 10−3	1.24 × 10−3	1.33 × 10−2	4.03 × 10−1
Informer	Intermediate	1.46 × 10−3	1.34 × 10−3	1.17 × 10−2	3.53 × 10−1
TFT	Broad ESG	2.59 × 10−4	2.75 × 10−4	2.07 × 10−3	6.54 × 10−2
TFT	Carbon-Sensitive	1.99 × 10−3	1.96 × 10−3	1.59 × 10−2	5.03 × 10−1
TFT	Intermediate	1.71 × 10−3	1.28 × 10−3	1.37 × 10−2	4.31 × 10−1
Transformer	Broad ESG	4.41 × 10−4	4.82 × 10−4	3.53 × 10−3	1.52 × 10−1
Transformer	Carbon-Sensitive	8.49 × 10−4	6.00 × 10−4	6.79 × 10−3	2.93 × 10−1
Transformer	Intermediate	1.60 × 10−3	9.42 × 10−4	1.28 × 10−2	5.54 × 10−1

Note: Contribution share denotes the proportion of total carbon-feature contribution accounted for by each asset group within the same model.

, the contribution of carbon-related features differs systematically across both models and asset groups. For Informer, the Carbon-Sensitive group records the highest mean absolute contribution at approximately $1.66\times {10}^{-3}$, followed by the Intermediate group at about $1.46\times {10}^{-3}$, while Broad ESG remains lower at roughly $1.01\times {10}^{-3}$. A similar pattern appears in TFT, where Carbon-Sensitive reaches about $1.99\times {10}^{-3}$, Intermediate about $1.71\times {10}^{-3}$, and Broad ESG only around $2.59\times {10}^{-4}$. Transformer differs slightly in structure: its Intermediate group exhibits the largest mean absolute contribution, approximately $1.60\times {10}^{-3}$, while Carbon-Sensitive is lower at about $8.49\times {10}^{-4}$, and Broad ESG remains the smallest at roughly $4.41\times {10}^{-4}$. The within-model contribution shares reinforce the same conclusion. Informer assigns about 40.3% of the grouped carbon-feature contribution to Carbon-Sensitive assets, TFT assigns about 50.3%, and Transformer allocates its largest share, around 55.4%, to the Intermediate group. These results indicate that carbon information is not uniformly distributed across the investment universe, but becomes more influential in asset groups with stronger thematic or market sensitivity.

Figure 15 provides a visual summary of the grouped contribution structure reported in Table 6. Figure 15a shows that Broad ESG consistently receives the weakest carbon-feature contribution, whereas Intermediate and Carbon-Sensitive groups account for most of the explainable variation. Figure 15b makes this contrast more visible by showing the concentration of stronger values in the Intermediate and Carbon-Sensitive regions, while Broad ESG remains relatively subdued across the three architectures. Figure 15c confirms the same ranking pattern from an alternative grouped comparison view. From a financial perspective, this result is plausible because carbon-related information should be more relevant when the target assets are more directly connected to environmental themes, energy transition exposure, or carbon-sensitive market fluctuations. Broad ESG funds, by construction, are usually more diversified and therefore less likely to translate carbon-related signals into large short-horizon forecasting effects.

Figure 16 extends the group-level evidence by decomposing the contribution into four specific carbon indicators, namely GCC, CCA, EUA, and UCITS. The figure shows that the contribution pattern is not driven by a single universal proxy. Instead, the relative importance of carbon indicators changes across models and asset groups. In the Transformer panel, GCC and UCITS appear especially strong for the Intermediate group, while Broad ESG remains comparatively weak across most features. In Informer, the contribution pattern is more distributed: GCC and CCA show strong values in Carbon-Sensitive and Intermediate assets, EUA remains substantial in the same two groups, and UCITS becomes particularly strong for Broad ESG. In TFT, the strongest feature-level responses are concentrated in the Carbon-Sensitive group, especially for GCC, CCA, and UCITS, while EUA stands out most strongly in the Intermediate group. These differences indicate that the models do not exploit carbon-related information in the same way. Instead, each architecture emphasizes a different subset of carbon indicators when translating forecasts into portfolio-level behavior.

The feature-level evidence also helps interpret why portfolio performance can differ even when aggregate forecasting metrics are relatively close. A model may not dominate in raw prediction error, yet still produce a different allocation outcome if it reacts more strongly to selected carbon indicators in specific asset groups. In this sense, the explainability results complement the performance analysis by showing that cross-model differences are linked not only to forecast quality but also to the structure through which carbon information is encoded and weighted.

To preserve local attribution detail, Figure 17 reports the original carbon-only SHAP beeswarm plots across the three forecasting models and six ETFs. Each panel presents the SHAP value distribution of EUA, GCC, CCA, and UCITS for one model–ticker pair. The horizontal axis denotes the sign and magnitude of local contribution, while the color encodes the underlying feature level. In general, Transformer exhibits the most concentrated and directionally coherent clouds, especially for major carbon features in carbon-linked or more volatile assets. Informer retains a similar directional structure but often shows wider dispersion and longer tails, indicating stronger amplification under variable market conditions. TFT, in contrast, presents flatter and more interleaved distributions in several cases, implying a more selective and less uniformly monotonic response pattern.

Cross-ticker contrasts are also clear in Figure 17. KRBN and TAN display stronger positive shifts under Transformer and Informer, especially for key carbon features, which is consistent with the larger grouped contribution observed earlier for Carbon-Sensitive assets. ESGU and SUSA remain much more tightly centered around zero, suggesting weaker short-horizon explanatory power of carbon information for broader and more defensive ESG allocations. ICLN and KGRN lie between these two extremes, with visible but less uniform carbon-feature effects. This local evidence aligns closely with the grouped summaries in Table 6 and Figure 15, and therefore provides a consistent interpretability narrative from aggregate structure to daily feature attribution. This pattern is also economically plausible. KRBN is directly linked to global carbon-credit markets, so movements in carbon-related indices are more likely to contain immediate information about its valuation and expected return dynamics. TAN, while not a carbon-credit fund, is concentrated in the solar and energy-transition segment, whose pricing can be influenced by climate policy expectations, decarbonization incentives, and the relative attractiveness of clean-energy investment under changing carbon-market conditions. By contrast, broader ESG funds such as ESGU and SUSA are more diversified and therefore less likely to translate short-horizon carbon-market variation into large cross-asset return differentials.

The explainability analysis reveals a clear hierarchical pattern. Table 6 and Figure 15 establish that grouped carbon-feature importance is concentrated more heavily in Intermediate and Carbon-Sensitive assets than in Broad ESG assets. Figure 16 then shows that this structure is carried by different combinations of GCC, CCA, EUA, and UCITS across models. Figure 17 finally confirms that these grouped patterns are supported by local SHAP distributions at the ticker level. Therefore, the proposed framework can be interpreted as explainable in a substantive sense: carbon-related information is not merely present in the input space, but contributes in structured, model-dependent, and asset-sensitive ways to portfolio formation.

4.2.8. Deep Models for Carbon-Credit-Aware Rebalancing: A Comprehensive Empirical Evaluation

The empirical evidence indicates that the portfolio outcomes of this study are shaped by the joint interaction of forecasting architecture, allocation mapping, smoothing intensity, and the economic relevance of carbon-related inputs. The three Transformer-inspired models do not generate identical portfolio behavior, even when they are trained on the same ESG-themed ETF universe and processed under the same rebalancing pipeline. This difference is not explained by forecasting error alone. Instead, it reflects how each architecture converts cross-asset forecast dispersion into allocation decisions and how effectively carbon-related signals are translated into investable portfolio adjustments. In this sense, the contribution of the framework lies in transparent integration and empirical validation of the full rebalancing pipeline.

From the forecasting perspective, Informer provides the strongest aggregate prediction quality, while Transformer remains competitive on selected assets and market phases. TFT is more stable than aggressive, and its predictive structure tends to produce allocation outcomes that remain closer to passive or weakly differentiated benchmark behavior when the rebalancing rule is not sufficiently responsive. This distinction becomes important at the portfolio level, where small differences in forecast dispersion can produce noticeably different allocation paths after threshold filtering, Softmax transformation, and inertia smoothing are applied. The results therefore suggest that portfolio performance depends less on a single pointwise prediction metric and more on whether the model generates sufficiently meaningful relative signals across assets.

The benchmark comparison further clarifies the practical role of the proposed framework. Equal Weight remains a strong benchmark throughout the full evaluation period, and Risk Parity also preserves reasonable downside control. This indicates that the ESG ETF universe itself contains substantial passive structure, and any model-based strategy must compete against already viable allocation rules. Under this setting, the deep learning-based approaches do not exhibit universal dominance, yet they remain competitive and avoid the severe deterioration observed under the momentum benchmark. Informer delivers the strongest Sharpe ratio among the model-based strategies, while Transformer and TFT remain close in drawdown behavior with substantially lower turnover than the most active benchmark rule. This pattern suggests that the framework is not artificially advantaged by weak baselines, but operates as a viable alternative allocation mechanism under realistic comparison settings.

The ablation evidence offers a more direct view of how the framework functions internally. Carbon-related inputs, threshold filtering, score concentration, and smoothing do not contribute equally across architectures. In Informer, removing carbon features leads to a visible decline in Sharpe ratio, while suppressing smoothing raises return efficiency but also produces a strong increase in turnover. The Transformer shows a similar but milder pattern. TFT, by contrast, remains much less sensitive to most ablation changes, implying that its portfolio behavior is less dependent on any single component under the present specification. These findings show that the rebalancing framework cannot be reduced to one isolated design choice. The mechanism operates through the interaction between model structure and allocation control, with smoothing playing the clearest operational role in governing trading intensity and implementation stability.

The uncertainty analysis refines this interpretation. Several benchmark differences are visible at the level of point estimates, but many of them are not stable enough to support strong claims of general superiority once sampling variation is taken into account. At the same time, the carbon-input ablation within Informer remains statistically identifiable, indicating that at least part of the framework’s advantage is tied to the informative content of carbon-related signals rather than to noise in the allocation process. This result is important because it supports a measured interpretation of the evidence. The proposed method should be understood as competitive and conditionally effective, rather than uniformly superior in every comparison and under every metric.

The subperiod analysis reinforces the same conclusion from a time-varying perspective. Strategy ranking changes between 2024H1 and 2024H2, indicating that performance is regime-dependent rather than fixed. Benchmark rules, especially Equal Weight and Risk Parity, remain highly competitive in the first half of the year. In the second half, model-based strategies gain relative strength, with Informer showing the clearest improvement and Transformer and TFT also moving upward. Meanwhile, drawdown profiles remain broadly comparable across most strategies except for Momentum, whose downside deterioration is consistently more severe. This suggests that the relative advantage of the proposed framework becomes more visible when market conditions place greater value on adaptive cross-asset differentiation, whereas simpler allocation rules remain effective when broad exposure is already well rewarded.

The explainability analysis provides the economic interpretation that links these portfolio outcomes back to the input space. Carbon-related contributions are not uniformly distributed across assets. Their influence is weakest in Broad ESG funds and becomes stronger in Intermediate and Carbon-Sensitive groups. Informer and TFT place a larger share of grouped contribution on Carbon-Sensitive assets, while Transformer assigns its largest share to the Intermediate group. At the feature level, the four carbon indicators do not contribute in the same way across architectures, indicating that each model extracts different forms of carbon-related information. The local SHAP beeswarm patterns further confirm that carbon-linked and more volatile assets, especially KRBN and TAN, exhibit clearer and more directional carbon-feature effects, whereas broader and more defensive ESG funds such as ESGU and SUSA remain closer to zero. This evidence explains why portfolio-level differences widen when carbon sensitivity and market volatility become more pronounced. This interpretation is economically consistent with the fact that KRBN has direct exposure to carbon-credit pricing, while TAN is more tightly connected to renewable-energy valuation and transition-sensitive capital flows than broad ESG funds.

The empirical results show that the framework is most effective when carbon-related information is preserved, forecast dispersion is translated into sufficiently differentiated portfolio weights, and the rebalancing rule balances responsiveness against turnover through moderate smoothing. Informer appears to make the most effective use of this interaction under the current setting, while Transformer provides a comparatively stable profile with moderate implementation intensity. TFT remains informative from an interpretability perspective, but its portfolio contribution is more selective and less forceful unless allocation differentiation becomes sufficiently strong. These findings support the view that carbon-credit-aware rebalancing should be interpreted as a competitive and explainable framework whose usefulness depends on model architecture, market conditions, and the way sustainability signals are translated into allocation behavior.

5. Conclusions

This study proposes an explainable framework for ESG portfolio rebalancing by combining carbon credit information, technical indicators, and Transformer-inspired forecasts within a unified allocation process. Using a six-ETF ESG universe, the framework translates next-day return forecasts into implementable portfolio decisions through threshold filtering, Softmax-based weighting, and inertia smoothing under transaction costs. The empirical results show that the framework remains competitive when compared with Equal Weight, Risk Parity, and Momentum benchmarks, but its effectiveness is better understood as conditional and architecture-dependent rather than as uniformly dominant across all performance dimensions.

Among the model-based strategies, Informer delivers the strongest Sharpe ratio, whereas Transformer provides a more balanced risk profile with relatively low trading intensity. The ablation analysis shows that the smoothing mechanism has the clearest effect on turnover and allocation stability, while the roles of carbon inputs and threshold filtering are more moderate and vary across architectures. The uncertainty assessment indicates more directly that many benchmark differences are not statistically significant under repeated resampling, even when point estimates appear favorable; in contrast, the performance weakening caused by removing carbon-related inputs in Informer remains identifiable. The subperiod analysis further shows that benchmark rules remain highly competitive in 2024H1, whereas model-based strategies gain relative strength in 2024H2. This implies that the value of the proposed framework is period-dependent and becomes more visible when market conditions place greater weight on adaptive cross-asset differentiation.

The explainability evidence shows that carbon-related contributions are concentrated more strongly in Intermediate and Carbon-Sensitive asset groups, while their role remains weaker in Broad ESG assets. Feature-level decomposition and SHAP beeswarm results further indicate that the three architectures rely on GCC, CCA, EUA, and UCITS in different ways, and that carbon-feature effects are most evident in more carbon-sensitive or volatile assets such as KRBN and TAN. These findings suggest that portfolio behavior is shaped not only by forecast accuracy but also by how carbon information is encoded, amplified, and translated into allocation decisions. In the present setting, the framework operates most effectively when carbon inputs are retained, the score-to-weight mapping remains sufficiently differentiated, and the smoothing mechanism is kept at a moderate level.

Several limitations remain. The investable universe is restricted to six ESG-themed ETFs, the data frequency is daily, and the test horizon is relatively compact. In particular, the present robustness analysis does not extend to alternative ESG asset universes or longer out-of-sample periods. Transaction costs are modeled as a fixed rate and do not fully capture slippage, liquidity variation, or execution constraints. The role of carbon-related signals is not fully separated from broader market factors, and the forecasting models are trained on a per-asset basis rather than through a joint multi-asset learning structure. Future research can extend the framework to broader ESG asset universes, longer evaluation horizons, richer execution settings, and more scalable multi-asset learning architectures in order to strengthen its practical relevance for portfolio management and decision support.