Tail-Dependent Connectedness Across Carbon, Water, Clean-Energy, Green-Bond, and ESG Markets

1. Introduction

The transition to a low-carbon economy, embedded in the 2030 Agenda for Sustainable Development [1], has created a financial architecture in which environmental regulation, infrastructure, technology, debt financing, and responsible equity investment interact. Carbon allowances attach a market price to emissions through systems such as the EU Emissions Trading System [2]. Water-related firms represent environmental infrastructure and resource scarcity. Clean-energy indices capture expectations about renewable technologies and transition-sensitive companies. Green bonds channel fixed-income capital toward eligible environmental projects within the expanding sustainable-debt market [3], while ESG equity indices integrate sustainability criteria into broad market portfolios. These instruments differ in cash-flow structure, duration, policy exposure, and investor clientele, yet they are linked through the same transition process.

Understanding their connectedness matters for three reasons. First, diversification benefits depend not only on unconditional correlations but also on the direction of shock transmission. An asset that is a receiver in normal conditions may become a transmitter in an extreme state. Second, transition policy may propagate through more than one channel: a carbon-price innovation can alter expected production costs, clean-technology valuations, financing conditions, and broader sustainable-equity sentiment. Third, tail dependence is directly relevant to risk management. Average relationships can conceal stronger propagation when returns are unusually low or high.

Previous studies show that connectedness across carbon, renewable-energy, green-bond, and equity markets varies over time and across market states [9,10,11,12,13,15,16,17]. This evidence motivates a joint examination of sustainable assets whose regulatory, infrastructure, technology, financing, and equity channels may interact differently across the return distribution.

1.1. Research Problem and Motivation

The empirical problem is not simply whether sustainable assets are correlated. It is whether innovations originating in one segment account for forecast uncertainty in another segment, whether that direction changes across the conditional return distribution, and whether the same pattern appears when market stress is defined externally. These distinctions matter because correlation is symmetric, whereas portfolio contagion and policy transmission are directional. A joint decline in two assets does not identify which market carries new information, and an average correlation can remain moderate even when a small number of directional links become economically important.

The five selected markets represent different layers of the transition-finance chain. EUA prices are a regulatory scarcity signal. Water equities combine infrastructure, utility, industrial-technology, and scarcity exposures. Clean-energy equities price innovation, subsidies, input costs, and growth expectations. Green bonds convert environmental objectives into debt-financed projects and introduce duration risk. ESG equities capture a broad investable universe screened or weighted by sustainability criteria. Studying these assets jointly allows the analysis to ask whether the transition-finance ecosystem behaves as one integrated market or as a collection of partially segmented channels.

A second motivation is that “stress” is multidimensional. A lower conditional quantile identifies an extreme location in an asset-specific return distribution; a high VIX identifies elevated option-implied uncertainty in U.S. equities; and a high Treasury yield identifies a restrictive global discount-rate environment. Treating these states as synonyms can produce misleading conclusions. The design therefore estimates quantile-specific networks and subsequently conditions the rolling estimates on VIX and yield states, without inserting either state variable into the sustainable-asset network.

1.2. Research Gap

The literature leaves four related issues unresolved. Sustainable-finance networks rarely include water equities alongside carbon allowances, clean-energy equities, green bonds, and ESG equities. Static quantile estimates also reveal little about whether tail differences persist over time.

Moreover, conditional return tails, option-implied uncertainty, and interest-rate conditions describe different market states and should not be treated as interchangeable. Because rolling connectedness estimates overlap and remain serially dependent, inference must also preserve their chronological dependence.

1.3. Research Objectives and Questions

The general objective is to identify how the level, direction, and temporal intensity of return connectedness across core sustainable-finance markets vary across conditional return states. Six specific objectives follow: (i) estimate full-sample total, directional, and net connectedness at five quantiles; (ii) identify persistent transmitters and receivers; (iii) measure rolling lower- and upper-tail deviations from the median; (iv) compare connectedness across VIX and U.S. Treasury-yield regimes; (v) evaluate whether conclusions are robust to forecast horizon, parameter stability, and serially dependent inference; and (vi) test whether directional connectedness improves out-of-sample tail-risk control relative to conventional allocation benchmarks.

The empirical analysis addresses five research questions. RQ1: Does total connectedness differ economically across the lower tail, center, and upper tail of the sustainable-asset return distribution? RQ2: Which markets act as persistent net transmitters or net receivers, and do these roles change across quantiles? RQ3: Are rolling lower-tail and upper-tail connectedness significantly different from rolling median connectedness after accounting for serial dependence? RQ4: Do high-VIX and high-yield states reproduce the same network pattern as conditional return tails, or do they describe distinct dimensions of market state? RQ5: Does a strictly out-of-sample, state-contingent allocation rule that penalizes dominant shock transmitters reduce volatility, expected shortfall, and drawdown after transaction costs?

1.4. Contributions and Scope

The first contribution is substantive: the paper places a global water-equity portfolio inside a carbon–clean-energy–green-bond–ESG network. The second is conceptual: it distinguishes distributional tails from observable volatility and discount-rate regimes. The third is inferential: it evaluates rolling contrasts with a stationary bootstrap rather than relying on visual inspection or independent-window standard errors. The fourth is communicative: static FEVD matrices, complete directed networks, rolling paths, external-regime summaries, and horizon checks are reported together so that aggregate intensity, pairwise channels, persistence, and robustness can be evaluated consistently. The fifth contribution is practical: the paper converts directional connectedness into a prespecified portfolio rule and evaluates it under a no-look-ahead, transaction-cost-adjusted backtest.

The paper does not claim structural causality or measure environmental outcomes directly. It studies predictive return connectedness among market proxies. The word “transmission” therefore refers to generalized forecast-error variance attribution within the estimated QVAR, not to a policy treatment effect. This boundary is maintained throughout the interpretation and is particularly important when VIX and Treasury-yield regimes are discussed.

These objectives are implemented in a five-node system comprising European Union Allowance prices, the Invesco S&P Global Water ETF, the S&P Global Clean Energy Index, the iShares USD Green Bond ETF, and the S&P 500 ESG Index. Full-sample estimates are obtained at five quantiles, followed by rolling lower-tail, median, and upper-tail analysis. VIX and the U.S. 10-year Treasury yield classify external states after estimation and therefore do not alter the composition of the sustainable-asset network.

The principal result is nuanced. Full-sample total connectedness changes little across quantiles, but the rolling upper tail exceeds the median by a small and statistically supported margin. The lower-tail contrast is not significant. CGW remains the strongest net transmitter across all quantiles, while BGRN remains a receiver. High VIX is associated with lower average TCI in the present specification. Accordingly, sustainable markets display tail dependence, but the evidence does not support a universal claim that every adverse or high-volatility state increases integration.

The remainder of the paper is organized as follows. Section 2 synthesizes the literature and positions the research expectations. Section 3 presents data collection, alignment, the QVAR–GFEVD framework, rolling design, inference, and reproducibility controls. Section 4 integrates results and discussion, including static and dynamic connectedness, complete network topology, external regimes, robustness, and economic interpretation. Section 5 concludes and separates limitations, practical implications, and future research directions. Section 3 also defines the out-of-sample allocation and evaluation protocol, and Section 4 reports its economic performance and uncertainty.

2. Literature Review

2.1. Connectedness in Sustainable Financial Markets

Connectedness measures translate multivariate forecast-error variance shares into interpretable network statistics. The generalized framework avoids ordering dependence and distinguishes shocks received from shocks transmitted to other variables [5,6,7]. It has therefore become a standard approach for studying financial contagion, systemic risk, and cross-market spillovers.

Within sustainable finance, empirical work shows that green assets are neither isolated nor uniformly integrated. Pham [10] finds that connectedness between green bonds and green equities varies across frequencies and quantiles. Tiwari et al. [11] document event-dependent spillovers among green bonds, renewable-energy equities, and carbon markets during COVID-19. Hanif et al. [12] show nonlinear dependence between clean-energy equity and EUA prices, with important variation across horizons. Chatziantoniou et al. [9] report that green bonds, green equity, sustainable investment, and clean energy exhibit quantile- and frequency-dependent transmission.

More recent evidence broadens the system to traditional energy and multiple green instruments. Wu et al. [13] find stronger spillovers under extreme market conditions and changing transmitter–receiver roles around geopolitical shocks. Broadstock et al. [14] show that ESG performance can matter during market-wide crisis conditions. Mzoughi et al. [15] identify asymmetry between downside and upside risks in green-finance and energy markets, while Dogan et al. [16] emphasize time-varying connectedness between renewable-energy sources and green finance. Using a Bayesian time-varying framework, Bunnag [21] documents changing roles among geopolitical risk and conventional financial markets. Collectively, the literature implies that a single conditional-mean network is insufficient.

Water-related equities extend this literature beyond the more frequently studied carbon, energy, bond, and broad-equity links. Water treatment, distribution, efficiency, and scarcity adaptation require long-lived capital and substantial energy inputs, while listed water firms also share industrial, utility, technology, and market-wide valuation exposures. These characteristics make water equities a plausible transmission channel within sustainable finance.

2.2. Transmission Channels Across Sustainable Assets

Several channels can link the five nodes. A policy-cost channel connects EUA prices to production costs, investment incentives, and the relative value of low-carbon technologies. A financing channel connects Treasury-sensitive green bonds to the cost of capital for eligible environmental projects. A growth and sentiment channel links clean-energy, water, and ESG equities through shared exposure to long-duration cash flows and broad sustainable-investment flows. A resource-infrastructure channel links water services to electricity use, industrial demand, climate adaptation, and municipal or corporate capital expenditure.

These channels need not operate with equal strength or in the same direction. Carbon allowances can remain segmented when regulatory supply and compliance demand dominate global risk sentiment. Green bonds can absorb equity shocks while responding separately to interest-rate movements. Water equities can transmit information because their diversified constituents overlap with global industrial, utility, and technology factors. Consequently, persistent transmitter–receiver roles may coexist with relatively stable system-wide TCI.

The directional interpretation also requires care. A positive NET statistic means that shocks attributed to a market explain more forecast-error variance elsewhere than the market receives from others. It does not imply that the asset is undesirable, intrinsically risky, or causally dominant. A transmitter can still provide diversification when its own innovations are weakly related to some nodes, while a receiver can remain volatile because of idiosyncratic shocks captured by its own variance share. Table 1 synthesizes the closest empirical precedents and identifies the specific opening addressed by the present design.

2.3. Quantile States, External Stress, and Discount Rates

Quantile methods are suitable when conditional relationships are asymmetric or nonlinear [4,8]. At the lower tail, common liquidation, funding pressure, and risk aversion can increase cross-market transmission. At the upper tail, coordinated optimism about policy support, technological progress, or sustainable-fund inflows can also create common repricing. The expected empirical shape is therefore not necessarily monotonic: either tail may exceed the median, and the two tails may differ from each other.

VIX and Treasury yields provide conceptually distinct conditioning information. VIX is forward looking and equity centered; it can signal uncertainty, demand for protection, and broad risk aversion. The 10-year yield affects discount rates, bond duration, capital expenditure, and the present value of growth opportunities. High VIX may synchronize equity-oriented nodes but segment them from carbon and green bonds. High yields may directly pressure BGRN and long-duration clean-energy valuations while leaving short-run EUA compliance demand comparatively insulated.

Because these mechanisms can offset one another, the regime analysis is intentionally descriptive. Mean TCI differences identify conditional association, not causal impact. The modest number of high-stress rolling endpoints also limits claims about rare joint states. This interpretation prevents the paper from converting a convenient percentile split into a structural crisis model.

2.4. Research Expectations and Falsifiable Interpretation

Expectation E1 is that at least one tail exhibits higher connectedness than the median. The expectation would be weakened if both tail-minus-median differences are economically negligible and dependence-aware intervals include zero. Expectation E2 is that equity-oriented sustainable assets are more active transmitters than green bonds, whose fixed-income structure should make it a receiver. The expectation would be contradicted by persistent positive NET values for BGRN or by unstable signs across quantiles.

Expectation E3 is that external stress and rate states modify connectedness, but not necessarily in the same direction as quantile states. Evidence that high-VIX and high-yield means perfectly mirror both tails would support a unified stress interpretation; divergent results would support the multidimensional-state argument. Expectation E4 is that major conclusions remain stable across short FEVD horizons because daily return dynamics decay rapidly. Horizon sensitivity would instead imply that interpretation depends on the arbitrary choice of H.

2.5. Conceptual Positioning

The conceptual framework therefore has two layers. The endogenous layer contains five sustainable-market returns and produces quantile-specific directional variance shares. The contextual layer contains VIX and the U.S. 10-year yield and classifies each rolling endpoint after estimation. Keeping the layers separate avoids allowing a large conventional-market variable to mechanically dominate the sustainable network, while still testing whether observed financial conditions coincide with changes in network integration.

2.6. Literature Synthesis and Empirical Positioning

The literature suggests that system-wide intensity, directional roles, and observed stress regimes describe different aspects of connectedness. TCI measures aggregate integration, NET identifies whether a market predominantly transmits or receives shocks, and rolling tail contrasts show whether quantile differences persist through time. VIX and Treasury-yield classifications provide contextual evidence rather than alternative definitions of a return quantile.

Accordingly, the empirical design combines static and rolling QVAR–GFEVD estimates, dependence-aware inference, and external regime comparisons. This structure allows moderate average integration to coexist with persistent market roles or selective tail amplification without interpreting predictive variance shares as structural causality.

3. Methodology and Data Collection

3.1. Data Sources and Variable Definition

Daily closing observations were collected from Investing.com [25]. The raw series have different trading calendars and starting dates. EUA, CGW, CLEAN, VIX, and the U.S. 10-year yield begin on 14 November 2018; BGRN begins on 28 November 2018; and SPESG begins on 16 March 2020. After retaining the intersection of valid dates across all five network variables and both external state variables, the common level sample runs from 16 March 2020 to 31 December 2025 and contains 1,441 observations. First differences of logarithms produce 1,440 returns. Table 2 summarizes the market proxy, transition-finance role, and model treatment of each series.

3.1.1. Data Collection Protocol and Audit Trail

For each symbol, the historical daily table was downloaded separately and retained with its date and closing-value fields. The audit sequence consisted of identifying the source instrument, standardizing date strings, coercing price fields to numeric values, removing exact duplicate dates, sorting chronologically, and checking for missing or nonpositive observations. The raw files were not forward filled. This matters because forward filling a market that was closed would create artificial zero returns and could distort cross-market variance shares.

The master calendar was formed by the intersection of dates with valid observations for all five network nodes and both external state variables. Returns were computed only after this common-date intersection, so each return compares adjacent observations on the synchronized trading calendar. This design sacrifices some market-specific observations but gives each QVAR row the same information date. It is transparent and reproducible, although it cannot completely remove nonsynchronous-closing effects across regions.

Instrument labels are treated as economic proxies rather than literal measures of physical outcomes. CGW is a listed-equity portfolio, not a water-price series; CLEAN is an equity index, not renewable generation; BGRN is a tradable green-bond fund, not the universe of issued climate debt; and SPESG is an ESG-screened equity benchmark, not a direct ESG-performance measure. The paper therefore interprets results as financial-market connectedness across transition-related investment segments.

The start date places the common sample at the onset of the COVID-19 disruption and allows the study to cover the subsequent recovery, the global inflation and monetary-tightening cycle, energy-security shocks, and changing carbon-policy expectations. The sample is therefore suitable for examining both calm and stressed sustainable-finance conditions, although it does not cover the pre-2020 behavior of SPESG.

3.2. Data Alignment, Return Construction, and Preliminary Evidence

For each network variable, the continuously compounded percentage return is calculated as rᵢ,t = 100 ln(Pᵢ,t/Pᵢ,t−1). Returns are formed only after the synchronized calendar is established. VIX and the U.S. 10-year Treasury yield remain in levels because they classify external states rather than enter the QVAR system.

3.2.1. Measurement Choices and Timing Controls

The factor of 100 expresses log returns in percentage points without altering the connectedness ordering. No volatility transformation is applied because the analysis concerns return transmission. Keeping VIX and the Treasury yield outside the return vector also prevents their index and yield units from being interpreted as comparable asset returns.

Pre-estimation diagnostics are reported in Table A5. Augmented Dickey–Fuller (ADF) tests [20] with BIC-selected augmentation lags reject a unit root for all five return series at the 1% level. ARCH-LM(20) tests reject homoskedasticity for every market (p < 0.001), documenting pronounced conditional heteroskedasticity. These findings support a distribution-sensitive quantile specification; the ARCH evidence is treated as a feature of the data rather than as a validity condition for QVAR–GFEVD.

Potential nonsynchronous trading is managed in three ways. First, only common observation dates are retained. Second, the model uses one lag, allowing yesterday’s information to enter today’s equations. Third, conclusions are framed as predictive variance attribution rather than contemporaneous structural causality. A future extension could shift regional closes, use intraday overlap, or repeat the analysis at weekly frequency, but those alternatives answer a different timing question and reduce the number of observations available for rolling tails.

rᵢ,ₜ = 100 × [ln(Pᵢ,ₜ) − ln(Pᵢ,ₜ₋₁)]

(1)

Table 3 and Table 4 summarize the return distributions and contemporaneous correlations. EUA is the most volatile series, with a standard deviation of 2.634%, followed by CLEAN at 1.789%. BGRN has the lowest volatility, consistent with its fixed-income structure. The extreme observations of all equity- and carbon-related series are substantially larger than their interquartile movements, motivating quantile analysis. The highest pairwise return correlation is between CGW and SPESG (0.795), reflecting their equity-market component. CLEAN is moderately correlated with both CGW (0.580) and SPESG (0.520). EUA has relatively low correlations with the remaining assets, while EUA and BGRN are slightly negatively correlated (-0.035). These correlations suggest diversification potential but cannot identify direction or indirect transmission. Figure 1 complements these statistics by showing the normalized level paths over the common sample.

3.3. Quantile Connectedness Research Design

3.3.1. Quantile Vector Autoregression

Let yₜ be the 5 × 1 vector of sustainable-market returns. At conditional quantile τ, the first-order quantile vector autoregression is written as:

yₜ = c(τ) + A₁(τ)yₜ₋₁ + εₜ(τ), τ ∈ {0.05, 0.25, 0.50, 0.75, 0.95}

(2)

Each equation is estimated by unpenalized quantile regression with an intercept. For equation i, the coefficient vector minimizes the sum of the check loss ρτ(u) = u[τ − I(u < 0)] [4]. A single lag keeps the parameterization parsimonious for rolling estimation and aligns with common QVAR connectedness applications [8]. The maximum spectral radius is recorded for every fit. No full-sample or rolling model requires stability rescaling in the reported baseline results.

3.3.1.1. Lag Choice, Estimation, and Stability

The baseline QVAR(1) balances economic memory against rolling-sample dimensionality. With five equations, five lagged returns, and an intercept per equation, each 500-observation window remains well identified even at the 0.05 and 0.95 quantiles. Adding many lags would increase parameter uncertainty in the tails and could cause unstable companion matrices. The one-lag design is also consistent with the short persistence commonly observed in daily returns and with prior quantile-connectedness applications [8,9].

After estimation, the spectral radius of A₁(τ) is calculated. A value below unity is required for a decaying moving-average representation. The reported full-sample radii lie between 0.064 and 0.195, and no rolling fit requires stabilization. Residual covariance is estimated from the vector of fitted equation residuals at each quantile. Because quantile residuals need not be Gaussian, the FEVD is used as a descriptive predictive decomposition rather than a likelihood-based structural identification.

β̂ᵢ(τ) = arg minβ Σₜ ρτ(yᵢ,ₜ − xₜ′β)

(3)

3.3.2. Generalized Forecast-Error Variance Decomposition

For a stable QVAR, the moving-average representation is yₜ = μ(τ) + Σₕ₌₀∞ Ψₕ(τ)εₜ₋ₕ(τ), where Ψ₀ is the identity matrix and Ψₕ = A₁ʰ. Let Σ(τ) denote the quantile-specific residual covariance matrix. Following Pesaran and Shin [5] and Diebold and Yilmaz [6,7], the H-step generalized forecast-error variance share attributable to shock j in the forecast error variance of variable i is:

θᵍᵢⱼ(H,τ) = σⱼⱼ⁻¹ Σₕ₌₀ᴴ⁻¹(eᵢ′ΨₕΣeⱼ)² / Σₕ₌₀ᴴ⁻¹(eᵢ′ΨₕΣΨₕ′eᵢ)

(4)

Generalized shares do not necessarily sum to one across shock sources. They are normalized by row:

3.3.2.1. Normalization, Direction, and Network Construction

Row normalization is essential because generalized shocks are not orthogonal. Each normalized row sums to one, so an off-diagonal element can be interpreted as the percentage share of variable i’s H-step forecast uncertainty attributed to innovations in variable j. The diagonal is the own share. FROMᵢ sums row i outside the diagonal; TOᵢ sums column i outside the diagonal; NETᵢ equals TOᵢ minus FROMᵢ. Summing NET across all nodes yields zero up to rounding, providing an internal accounting check.

In the network diagrams, columns are shock sources and rows are receivers; an arrow therefore points from j to i when θ̃ᵍᵢⱼ is positive. Figure 5 displays all 20 directed off-diagonal links among the five nodes. Edge width and opacity scale continuously with the FEVD share, while node locations and colors remain fixed across quantiles so that visual differences reflect the estimates rather than layout changes.

θ̃ᵍᵢⱼ(H,τ) = θᵍᵢⱼ(H,τ) / Σⱼ₌₁ᴺ θᵍᵢⱼ(H,τ)

(5)

The directional connectedness FROM others, TO others, net directional connectedness, and total connectedness index are:

FROMᵢ = Σⱼ≠ᵢ θ̃ᵍᵢⱼ; TOᵢ = Σⱼ≠ᵢ θ̃ᵍⱼᵢ; NETᵢ = TOᵢ − FROMᵢ

(6)

TCI(H,τ) = (1/N) Σᵢ₌₁ᴺ Σⱼ≠ᵢ θ̃ᵍᵢⱼ(H,τ) × 100

(7)

A positive NET value identifies a net transmitter; a negative value identifies a net receiver. The baseline forecast horizon is H = 10 trading days. H = 5 and H = 20 are used for sensitivity analysis.

3.3.3. Rolling Estimation, External Regimes, and Dependence-Aware Inference

Dynamic connectedness is estimated using a 500-observation rolling window advanced by five observations. The rolling analysis focuses on τ = 0.05, 0.50, and 0.95, producing 189 window endpoints. Three contrasts are calculated at every endpoint: lower tail minus median, upper tail minus median, and the average of both tails minus median.

3.3.3.1. Rolling-Window Design

A 500-observation window contains approximately two years of synchronized trading days and is long enough to estimate extreme quantiles with a usable effective number of tail observations. Advancing the window by five observations reduces computational redundancy while preserving weekly-scale temporal resolution. The first endpoint occurs only after the full window is available; hence the dynamic sample is shorter than the static sample. Every endpoint is dated by the last observation in its estimation window.

The rolling contrasts are calculated within the same window and date. This paired construction removes the common temporal level of connectedness before inference: Δᴸₜ = TCIₜ(0.05) − TCIₜ(0.50), Δᵁₜ = TCIₜ(0.95) − TCIₜ(0.50), and Δᴬₜ = [TCIₜ(0.05)+TCIₜ(0.95)]/2 − TCIₜ(0.50). The reported mean is the time average of each contrast, measured in percentage points.

3.3.3.2. Stationary Bootstrap and Regime Classification

The stationary bootstrap samples blocks whose lengths follow a geometric distribution with mean ten endpoints [19]. For each replication, blocks are concatenated until the original contrast-series length is reached, and the resampled mean is recorded. Percentile limits from 2,000 replications form the 95% interval. The procedure respects ordering within resampled blocks and is more appropriate than resampling isolated endpoints from overlapping windows.

VIX and US10Y states are assigned using information available at each rolling endpoint. Values above the full-sample 75th percentiles—24.0825 for VIX and 4.21% for the U.S. 10-year yield—define the high states. The thresholds are fixed before the regime comparison and are not optimized for significance. Group means are reported with their endpoint counts and interpreted as descriptive conditional summaries; no strong inference is drawn from the sparse joint high-VIX/high-yield cell.

3.3.3.3. Prespecified Cluster Decomposition

To identify the source of a VIX-state difference in TCI, the off-diagonal generalized-FEVD shares are partitioned before inspecting the regime results. The equity-oriented set is E = {CGW, CLEAN, SPESG}, and the complementary policy/fixed-income set is D = {EUA, BGRN}. This asset-class partition is used only for accounting; it does not impose zero restrictions or alter QVAR estimation. With normalized variance shares expressed in percentage units and N = 5, the three additive components are:

Cᴱₜ(τ) = N⁻¹∑ᵢ∈ᴱ∑ⱼ∈ᴱ,ⱼ≠ᵢ θ̃ᵢⱼ,ₜ(τ); Cᴰₜ(τ) = N⁻¹∑ᵢ∈ᴰ∑ⱼ∈ᴰ,ⱼ≠ᵢ θ̃ᵢⱼ,ₜ(τ); Cᴱᴰₜ(τ) = N⁻¹[∑ᵢ∈ᴱ∑ⱼ∈ᴰ θ̃ᵢⱼ,ₜ(τ) + ∑ᵢ∈ᴰ∑ⱼ∈ᴱ θ̃ᵢⱼ,ₜ(τ)].

By construction, TCIₜ(τ) = Cᴱₜ(τ) + Cᴰₜ(τ) + Cᴱᴰₜ(τ). The same partition is averaged separately over high- and lower-VIX endpoints. Consequently, Table 8 is an exact decomposition of the reported TCI rather than a post-estimation clustering exercise. Because rolling windows overlap, the component differences remain descriptive associations.

3.3.4. Reproducibility and Software

Data cleaning, return construction, descriptive statistics, QVAR estimation, recursive moving-average coefficients, GFEVD normalization, directional measures, rolling estimation, stationary bootstrap, regime summaries, and figures were implemented in Python. Core routines use pandas and NumPy for data handling and linear algebra, scikit-learn for linear-programming quantile regression, SciPy for optimization and supporting calculations, and Matplotlib for visualization. A fixed seed of 2026 is used for resampling. Intermediate outputs include synchronized levels, returns, static FEVD matrices, rolling TCI paths, directional statistics, bootstrap draws, and horizon-sensitivity tables. The portfolio extension additionally uses Ledoit–Wolf covariance shrinkage and linear programming for historical CVaR minimization.

Reproducibility checks verify row sums of the normalized FEVD, the zero-sum identity of NET measures, equality of observation counts across nodes, uniqueness and monotonicity of dates, and spectral radii below unity. Numeric tables are generated from stored result files rather than manually transcribed values. These controls reduce the risk that figure labels, table values, and narrative interpretation refer to different model runs.

3.3.5. Model Validation and Interpretation

Generalized FEVD is invariant to variable ordering, which is useful when no defensible contemporaneous causal order exists among global sustainable markets [5,6,7]. Because generalized shocks are correlated, the shares require row normalization and represent predictive variance attribution rather than structural causal effects. Network arrows therefore identify estimated transmission direction, not responses to policy interventions.

Three families of validation checks are applied. Data checks verify dates, duplicate removal, common observations, and return construction. Model checks verify coefficient dimensions, spectral stability, finite residual covariance, and decaying moving-average coefficients. Connectedness checks verify normalized row sums, nonnegative variance shares, the equality between system off-diagonal sums and TCI, and the zero-sum NET identity. A run failing any check is not used in tables or figures.

The interpretation follows prespecified rules. Tail amplification requires a positive mean tail-minus-median contrast whose 95% stationary-bootstrap interval excludes zero. A persistent transmitter or receiver must retain the same NET sign across all five static quantiles, while horizon robustness requires the qualitative ranking and TCI to remain effectively unchanged at H = 5, 10, and 20. Formal rolling inference is limited to three contrasts—lower minus median, upper minus median, and their average minus median—to avoid searching over many quantile pairs.

Economic significance is evaluated in percentage-point units relative to the median TCI. Statistical support does not imply a large change in integration, and a stable NET sign does not imply that every directional magnitude is economically large. External-regime differences are consequently described by their sign, magnitude, and sample size rather than interpreted as causal effects.

3.4. Out-of-Sample Portfolio and Decision-Value Evaluation

A portfolio extension evaluates whether the estimated network provides incremental decision value rather than only descriptive evidence. The initial estimation window contains 500 returns. Portfolios are re-estimated every five observations using information available through decision date t and are held over t+1 through t+5. This produces 940 genuinely out-of-sample daily returns. The expanding 75th percentile of VIX is calculated using only information available at t; the allocation uses the lower-tail network (tau = 0.05) when VIX is high and the median network (tau = 0.50) otherwise. No future return or full-sample regime threshold enters the weight calculation.

Four long-only, fully invested strategies are compared. Equal weighting provides the 1/N benchmark [26]. The minimum-variance portfolio uses a Ledoit-Wolf shrinkage covariance matrix [28]. The minimum-CVaR portfolio minimizes historical 5% expected shortfall using the linear programming representation of Rockafellar and Uryasev [27]. The state-contingent connectedness-adjusted minimum-variance portfolio (State-QVAR CAMV) adds a penalty for exposure to nodes with large directional TO connectedness.

$${\mathbf{w}}_t^{\mathrm{CAMV}}=\underset{\begin{array}{c}\mathbf{w}\ge 0\\ 1^{\mathrm{\text{'}}}\mathbf{w}=1\end{array}}{\mathrm{argmin}}\left\{{\mathbf{w}}^{\mathrm{\text{'}}}{\mathsf{\Sigma }}_t\mathbf{w}+\lambda {\bar{\sigma }}_t^2{\mathbf{w}}^{\mathrm{\text{'}}}{\mathbf{s}}_t\right\}.$$

(8)

Here, Σ_t is the Ledoit–Wolf covariance estimate from the current 500-observation window; ${\bar{\sigma }}_t^2=N^{-1}\mathrm{tr}\left({\mathsf{\Sigma }}_t\right)$ is the mean diagonal variance; and s_i,t = TO_i,t/max_j(TO_j,t) is the normalized transmitter score from the selected QVAR state. The tuning coefficient λ = 0.05 is held fixed throughout the evaluation rather than reoptimized across windows. The variance scaling keeps the penalty comparable across windows. Because the objective contains no expected-return term, the rule is interpreted as a risk-control allocation rather than a return forecast.

$${\mathrm{Turnover}}_t={\displaystyle \frac{1}{2}}{\displaystyle \sum _{i=1}^N}\left|w_{i,t}-w_{i,t-1}\right|, r_{p,t}^{\mathrm{net}}=r_{p,t}^{\mathrm{gross}}-0.001\hspace{0.17em}{\mathrm{Turnover}}_t.$$

(9)

Here, $r_{p,t}^{\mathrm{gross}}$ and $r_{p,t}^{\mathrm{net}}$ denote the gross and transaction-cost-adjusted portfolio returns, respectively. The term 0.001 Turnover_t charges 10 basis points per unit of one-way turnover at each rebalance. Evaluation reports annualized return and volatility, zero-rate Sharpe and Sortino ratios, 5% VaR and CVaR, maximum drawdown, turnover, and cumulative return. Paired stationary-bootstrap intervals resample candidate and benchmark returns with the same random blocks (2,000 repetitions; expected block length 10), preserving temporal and cross-strategy dependence. Inference focuses on volatility and CVaR differences relative to equal weighting.

4. Results and Discussion

4.1. Full-Sample Quantile Connectedness

Table 5 reports full-sample TCI and net directional connectedness. TCI varies within a narrow range, from 33.902% at τ = 0.25 to 34.161% at τ = 0.95. The median estimate is 33.973%. Thus, the full-sample network is moderately connected, but tail connectedness is not dramatically larger than central connectedness. The modest U-shaped pattern in Figure 2a should be interpreted in magnitude as well as direction: the upper-tail-minus-median gap is only 0.188 percentage points in the full sample.

Directional roles are more economically distinctive. CGW is the strongest net transmitter at every quantile, with NET values from 10.345 to 10.908 percentage points. SPESG is also a net transmitter, ranging from 3.858 to 5.271. BGRN is the strongest net receiver at τ = 0.05 and 0.95, while CLEAN is an important receiver in central quantiles. EUA remains a receiver throughout. These persistent signs indicate structural segmentation in who originates and absorbs shocks even when aggregate TCI changes little.

The difference between aggregate stability and directional heterogeneity is central. A TCI near 34% means that roughly one third of the average forecast-error variance is attributed to cross-market shocks, while roughly two thirds remains own-market variance. This is economically meaningful integration, not a nearly isolated system, yet it is far from complete comovement. Because the aggregate is an average of 20 off-diagonal shares, it can remain stable when individual channels strengthen and weaken in offsetting directions.

The quantile pattern is also asymmetric in scale. Relative to the median TCI of 33.973%, the lower tail is 0.096 percentage points lower, and the upper tail is 0.188 percentage points higher. These static gaps are too small to support a dramatic full-sample contagion claim. The value of the quantile design is instead to reveal directional roles and to create rolling within-window contrasts that can be evaluated over time.

4.2. Rolling Tail Connectedness

The rolling estimates in Figure 3 fluctuate more than the static estimates, with TCI generally ranging from the high 20s to the high 30s. The three quantile paths frequently move together, confirming that common time variation is important. Nevertheless, the upper-tail path tends to lie above the median during a sufficient number of windows to produce a statistically supported average difference.

Table 6 shows that τ = 0.95 exceeds τ = 0.50 by 0.672 percentage points on average. Its stationary-bootstrap 95% confidence interval, [0.372, 0.961], excludes zero. The average of both tails exceeds the median by 0.534 percentage points, with an interval of [0.239, 0.828]. In contrast, the lower-tail-minus-median mean is 0.395, but its interval [-0.088, 0.860] crosses zero. The evidence therefore supports upper-tail amplification and average-tail amplification, but not a separate lower-tail effect at the 5% level.

This asymmetry is substantive. Sustainable-asset connectedness appears to rise more consistently during unusually strong conditional-return states than during lower-tail states. One possible mechanism is coordinated repricing of transition-sensitive equities when policy support, technology expectations, or broad risk appetite improves. By contrast, negative shocks may differentiate fixed-income, carbon, and equity exposures, weakening a uniform lower-tail response.

Statistical significance does not by itself imply large economic magnitude. The 0.672-point upper-tail premium is about two percent of the median TCI level. It is sufficiently persistent for its interval to exclude zero, but it does not convert the network from segmented to fully integrated. The appropriate conclusion is selective upper-tail amplification, not generalized contagion.

The dynamic path also shows that most large movements are shared across quantiles. TCI rises through parts of 2023–2024 and declines during later windows, while the vertical separation among quantiles remains comparatively modest. Thus, calendar-time variation in common market conditions explains more of the visual movement than the unconditional quantile ranking. Reporting both dimensions prevents the tail result from being detached from its broader temporal context.

4.3. External Stress and Interest-Rate Regimes

Table 7 and Table 8 and Figure 4 compare mean rolling TCI across external regimes. Contrary to a generic contagion narrative, high-VIX endpoints have lower mean TCI at every reported quantile. At τ = 0.05, mean TCI is 34.267 in the lower-VIX state and 31.868 in the high-VIX state. Corresponding means at τ = 0.50 are 33.828 and 31.713, and at τ = 0.95 are 34.427 and 32.786. High volatility therefore does not mechanically synchronize these sustainable assets.

The negative high-VIX difference is robust in sign across the three reported quantiles: −2.398 points at τ = 0.05, −2.115 at τ = 0.50, and −1.641 at τ = 0.95. Table 8 localizes this result. Within-cluster transmission among CGW, CLEAN, and SPESG rises slightly in high-VIX states (+0.215 to +0.602 percentage points), and the EUA–BGRN bilateral contribution also rises (+0.189 to +0.621 points). By contrast, cross-cluster transmission falls by 2.784–3.026 points. The lower TCI is therefore an accounting consequence of weaker links between the equity-oriented cluster and EUA/BGRN, not a general collapse of dependence within sustainable equities.

Yield-state differences are smaller and vary by quantile. These results are descriptive because regimes are defined contemporaneously and the rolling estimates overlap. They nevertheless demonstrate why quantile tails, VIX, and yields should not be collapsed into a single crisis category. An upper conditional-return tail can exhibit amplified within-system transmission even when externally observed volatility is low or moderate.

Only three window endpoints fall jointly into the high-VIX/high-yield group. No strong inference should be drawn from that joint cell. The separate high-VIX and high-yield comparisons are more informative, but they remain associations rather than causal estimates.

The decomposition converts the decoupling interpretation from a narrative conjecture into an exact accounting result. Elevated VIX does not weaken the CGW–CLEAN–SPESG core; it selectively separates that equity-oriented core from the carbon-policy and green-bond nodes. Market-wide uncertainty can therefore coexist with stronger local clustering and lower system-wide connectedness.

4.4. Complete Network Structure

Figure 5 visualizes the complete directed generalized-FEVD network at τ = 0.05, 0.50, and 0.95. All 20 off-diagonal links are retained, while line width and opacity distinguish large from small transmission shares. The dominant equity-related cluster links CGW, CLEAN, and SPESG. CGW’s transmitter status reflects both strong bilateral relationships and its ability to distribute shocks to the broader sustainable-equity segment. BGRN is more peripheral and primarily absorbs shocks, consistent with its lower return volatility and fixed-income exposure. EUA is also relatively segmented, indicating that carbon-policy pricing contains information not fully shared by diversified environmental and ESG portfolios.

The complete network reveals three features. CGW and SPESG form the strongest reciprocal pair: SPESG shocks explain about 30% of CGW forecast uncertainty, while CGW shocks explain about 31.5% of SPESG uncertainty. CGW is also strongly connected to CLEAN in both directions, with the CGW-to-CLEAN share generally larger. EUA links are comparatively weak, whereas BGRN receives several modest cross-market shares while retaining an own share above 80%.

Showing every directed off-diagonal link avoids confusing a display threshold with an estimated zero. The faintest edges remain part of the accounting system even when their economic contribution is small. Because the layout is identical at τ=0.05, 0.50, and 0.95, the visual stability of the core CGW–CLEAN–SPESG cluster is consistent with the narrow static TCI range and persistent NET signs.

The persistence of role signs across quantiles is an important finding. Quantile dependence does not require every market to change from sender to receiver. Instead, the magnitude of transmission and the system-wide TCI can shift while structural roles remain stable. This helps distinguish robust economic architecture from state-specific intensity.

4.5. Comparison with Previous Evidence

The results both confirm and qualify earlier studies. The presence of quantile-specific transmission is consistent with Chatziantoniou et al. [9], Pham [10], and Wu et al. [13]. However, the small full-sample differences show that extreme-state amplification is not universal in magnitude. The statistically supported rolling upper-tail contrast is more specific than a general statement that both tails are more connected.

Earlier work establishes that sustainable-market dependence varies across quantiles and frequencies [9,10]. The present evidence adds three qualifications: static tail differences are small, only the rolling upper-tail contrast is statistically supported, and high VIX is associated with lower TCI. Together, these results favor a state-specific interpretation over a general contagion narrative.

Relative to COVID-centered evidence [11,24], the common sample begins during the pandemic but continues through recovery, inflation, monetary tightening, and energy-security disturbances. The rolling design therefore does not label one event as the sole regime. Relative to carbon–energy studies [12,22], the inclusion of water, green bonds, and ESG broadens the economic channels while preserving the distinct EUA node. Relative to fossil-versus-clean comparisons [17,23], the design focuses on the internal architecture of sustainable finance.

The receiver role of green bonds is consistent with evidence that fixed-income green instruments often absorb shocks from equity and energy-transition markets [9,10,11]. Their low daily volatility and duration exposure distinguish them from clean-energy and ESG equities. CGW, by contrast, is a listed-equity portfolio of utility, infrastructure, industrial-technology, and environmental-service firms rather than a physical-water price. Its exposure to capital expenditure, energy and treatment costs, discount rates, business cycles, and broad equity flows is consistent with its 0.795 correlation with SPESG and its strong bilateral links with CLEAN and SPESG. The transmitter role should therefore be interpreted as portfolio-level financial centrality, not as evidence that physical water scarcity causes spillovers.

ETF creation and redemption, index rebalancing, and institutional allocation provide additional plausible transmission channels because CGW is a tradable portfolio rather than a physical-water price. The available data do not contain constituent-level holdings or fund-flow observations, however. These channels are therefore interpretations consistent with the estimated network—not causal mechanisms identified by the model.

The relatively segmented EUA node is also plausible. Allowance prices respond to cap design, auction supply, energy substitution, industrial activity, and regulatory expectations. These drivers overlap with clean-energy valuations but are not identical. The result is consistent with the nonlinear and horizon-dependent carbon-clean-energy relationship reported by Hanif et al. [12].

The high-VIX result qualifies studies that report generalized crisis amplification [11,13]. Table 8 shows that the apparent divergence is attributable to the composition of the network: uncertainty strengthens local clustering but weakens transmission between asset-class groups. The return-based estimand and the coexistence of carbon-policy, fixed-income, and equity nodes therefore explain why individual risk can rise without producing a higher system-wide variance share.

4.6. Economic, Portfolio, and Policy Interpretation

For investors, the moderate TCI indicates that diversification remains available, but the CGW–CLEAN–SPESG cluster should be treated as a partially integrated equity block rather than three independent sustainability exposures. EUA and BGRN provide greater structural separation through carbon-policy and fixed-income channels, although their idiosyncratic risks remain material. Because upper-tail synchronization is statistically clearer than lower-tail amplification, stress tests and rebalancing rules should cover favorable extreme states as well as selloffs. The out-of-sample evidence makes this implication operational: transmitter-penalized allocation can materially reduce volatility, expected shortfall, and drawdown, but it does not guarantee superior returns. The decision value is therefore strongest for risk-budgeting and capital-preservation mandates.

For policymakers, the partial segmentation of carbon allowances suggests that carbon-price signals do not transmit uniformly into all sustainable-finance segments. Stronger informational bridges may require credible long-horizon policy, transparent use of allowance revenues, and financing structures that translate regulatory incentives into investable transition projects. The distinction between distributional tails and observable stress states is also relevant for financial-stability monitoring. A high VIX alone is not a sufficient proxy for integration within sustainable markets.

These implications support Sustainable Development Goals 6, 7, 9, 13, and 17 by clarifying how market-based environmental policy, water infrastructure, clean technology, green financing, and ESG capital allocation interact. The analysis does not measure real environmental outcomes directly; it identifies financial transmission channels through which transition funding and risk may propagate.

4.7. Robustness and Diagnostic Evidence

4.7.1. Forecast-Horizon and Stability Diagnostics

The horizon sensitivity in Table A1 shows virtually unchanged TCI estimates at H = 5, 10, and 20. This occurs because the estimated QVAR dynamics decay rapidly. Spectral radii range from 0.064 to 0.195 across full-sample quantiles, well below unity. Consequently, the central conclusions do not depend on the chosen FEVD horizon. All rolling fits are checked for stability, and the baseline results require no coefficient rescaling.

4.7.2. Inferential Safeguards and Boundary Conditions

Several design choices reduce overstatement. Tail differences are evaluated with stationary-bootstrap intervals rather than independent-observation tests. VIX and Treasury yields are treated as external regime classifiers and not as endogenous network variables. The small joint high-VIX/high-yield cell is explicitly excluded from strong inference. Full-sample point estimates are interpreted in percentage-point magnitude rather than only by rank.

Additional accounting diagnostics support internal consistency. Each normalized FEVD row sums to 100% apart from rounding, and NET measures sum to approximately zero at every quantile. The dominant qualitative roles are unchanged across τ. Horizon results at H=5, 10, and 20 are numerically almost identical, which is consistent with the low spectral radii and rapid decay of daily return dynamics. Table A5 further confirms that all return series reject a unit root at 1% and exhibit strong ARCH effects, supporting the use of return inputs and a distribution-sensitive conditional-quantile framework.

Robustness does not eliminate specification dependence. The results remain conditional on the five selected proxies, QVAR lag length, rolling-window size, percentile definition of external regimes, and generalized identification. The purpose of the checks is therefore to identify whether the reported conclusion is fragile to immediate alternatives, not to claim invariance to every feasible model.

4.8. Out-of-Sample Portfolio Evidence

Table 9 converts the connectedness estimates into a strict out-of-sample test. All three optimized portfolios materially reduce risk relative to equal weighting. State-QVAR CAMV records annualized volatility of 5.907%, compared with 13.215% for equal weighting, while maximum drawdown improves from -21.390% to -13.220%. Its 5% CVaR improves from -1.858% to -0.857% per day. The allocation therefore contains downside exposure substantially more effectively, after charging transaction costs.

The paired bootstrap in Table 10 confirms that these risk reductions are not an artifact of treating daily observations as independent. For State-QVAR CAMV, the annualized-volatility difference relative to equal weighting is -7.308 percentage points, with a 95% interval of [-8.244, -6.381]. The CVaR difference is +1.001 percentage points, with an interval of [0.775, 1.229]; a positive value means a less severe expected shortfall. The connectedness adjustment also improves volatility, CVaR, and drawdown modestly relative to conventional minimum variance, although the incremental gain is small.

Figure 6. Transaction-cost-adjusted out-of-sample portfolio performance. Panel (a) reports the growth of one unit; Panel (b) compares annualized volatility and the absolute maximum drawdown.

Figure 6. Transaction-cost-adjusted out-of-sample portfolio performance. Panel (a) reports the growth of one unit; Panel (b) compares annualized volatility and the absolute maximum drawdown.

The return evidence imposes an important boundary on the practical claim. Equal weighting earns 1.993% annualized, whereas State-QVAR CAMV earns -1.509%. The paired mean-loss interval includes zero, so the analysis does not establish return dominance. Instead, the implementable value of connectedness lies in a transparent reduction of volatility and tail loss at the cost of foregone upside. This risk-return trade-off is consistent with the portfolio rule being designed for capital preservation rather than return timing.

5. Conclusions, Limitations, Implications, and Future Work

5.1. Conclusions

This study examines tail-dependent return connectedness across five complementary components of sustainable finance: carbon allowances, water investment, clean energy, green bonds, and ESG equity. The synchronized data comprise 1,441 daily levels from 16 March 2020 to 31 December 2025, yielding 1,440 percentage log returns. The empirical design combines QVAR-based generalized variance decomposition, rolling estimation, stationary-bootstrap inference, external VIX and yield regimes, and forecast-horizon sensitivity.

Four conclusions emerge. First, full-sample connectedness is moderate and stable across quantiles, with TCI between 33.90% and 34.16%. Second, rolling upper-tail connectedness exceeds median connectedness by 0.672 percentage points on average, and the bootstrap interval excludes zero; the lower-tail contrast is not significant. Third, directional roles are structurally persistent: CGW is the leading net transmitter, SPESG is a secondary transmitter, and BGRN is the principal receiver. Fourth, the strictly timed portfolio experiment confirms that directional connectedness can support tail-risk containment: State-QVAR CAMV halves annualized volatility relative to equal weighting and reduces drawdown, although the protection carries a return cost.

The findings show that tail dependence is selective rather than universal. Observable stress does not automatically produce stronger integration: high-VIX windows have lower average TCI because cross-cluster links weaken even as connectedness inside the CGW–CLEAN–SPESG cluster rises slightly. For researchers and practitioners, quantile states, volatility regimes, and interest-rate regimes should therefore be modeled as distinct concepts. For sustainable-finance policy, carbon signals, environmental infrastructure, technology equities, and green debt form a connected but still diversified ecosystem whose transmission mechanisms vary by state.

5.2. Theoretical and Methodological Implications

Theoretically, the results favor a layered view of sustainable finance. Transition-linked markets share a meaningful network, but market design, asset class, regulation, and investor clientele preserve segmentation. State dependence operates through changes in intensity around a comparatively stable directional architecture. This explains how a moderate TCI, persistent sender–receiver roles, and selective upper-tail amplification can coexist.

Methodologically, the paper shows why static quantile rankings, rolling contrasts, and external regimes should be reported separately. A static upper-tail premium of 0.188 points is not equivalent to the mean rolling premium of 0.672 points, and neither is equivalent to a high-VIX comparison. The stationary-bootstrap interval further distinguishes a repeatable rolling pattern from a visual difference that may reflect overlapping windows.

5.3. Practical and Policy Implications

Investors should recognize the CGW–CLEAN–SPESG equity cluster when allocating risk and should not infer independence merely from different sustainability labels. EUA and BGRN contribute diversification through distinct policy and fixed-income structures, although neither is immune to idiosyncratic volatility or external conditions. Stress testing should include favorable extreme states as well as selloffs because upper-tail synchronization is statistically clearer in this sample. A practical implementation is to combine conventional covariance control with a modest, state-dependent penalty on dominant transmitters rather than replacing portfolio theory with connectedness rankings alone.

Policy institutions can use directional connectedness as a diagnostic of whether carbon-price information and green-financing conditions propagate across the investment ecosystem. The weak EUA links suggest that regulatory price signals may require complementary disclosure, project development, and financial intermediation to influence broader sustainable portfolios. The centrality of water equities indicates that adaptation infrastructure belongs in transition-finance monitoring alongside mitigation assets.

5.4. Limitations

The first limitation is sample coverage. SPESG restricts the common period to March 2020 onward, so the study cannot estimate a pre-pandemic baseline with the same instruments. Second, the selected ETFs and indices are investable proxies whose composition, rebalancing, domicile, and currency exposure may influence measured linkages. Alternative carbon, water, clean-energy, green-bond, or ESG benchmarks could produce different levels and roles.

Third, common-date synchronization does not completely solve different closing times, regional holidays, or information arriving between market closes. Fourth, QVAR–GFEVD measures predictive association under generalized shocks and does not establish structural causality. Fifth, the rolling window and five-day step involve a bias–variance trade-off and create serial persistence. The stationary bootstrap addresses dependence in mean contrasts but not uncertainty from choosing the model, window length, proxies, or regime thresholds.

Sixth, the analysis concerns financial returns rather than physical emissions reductions, water outcomes, renewable generation, or verified project impact. Financial connectedness can inform transition-risk management, but it cannot by itself establish environmental additionality. Seventh, VIX and US10Y regime comparisons are descriptive and based on sample percentiles; they should not be interpreted as causal experiments or universal crisis thresholds. Eighth, the portfolio exercise is conditional on long-only constraints, a fixed penalty coefficient, a 10-basis-point cost assumption, and one rebalance frequency; it establishes sample-specific risk reduction rather than universal economic dominance.

5.5. Future Work

Future research can extend the network along four dimensions. A market dimension could compare alternative regional carbon schemes, water benchmarks, green-bond currencies, and climate-policy portfolios. A time dimension could incorporate intraday or weekly alignment to evaluate nonsynchronous trading. A methodological dimension could combine quantile connectedness with frequency decomposition [18], quantile-on-quantile designs, regularized high-dimensional QVARs, or Bayesian time-varying parameters.

An impact dimension should link financial nodes to verified emissions, renewable generation, water stress, capital expenditure, and project-level use-of-proceeds measures. A forecasting dimension could test whether dynamic NET or pairwise FEVD measures improve out-of-sample portfolio loss, tail risk, or hedge ratios relative to correlation-based benchmarks. Such extensions would move from documenting transmission toward evaluating whether connectedness provides incremental decision value. A capital-flow dimension should integrate ETF creations and redemptions, institutional holdings, and ESG-fund flows to distinguish transmission arising from firm fundamentals from transmission driven by investor reallocation, liquidity, and market sentiment. Future portfolio research should test alternative penalty calibration, utility functions, short-sale constraints, turnover controls, and nested validation across other sustainable asset universes.