Measuring and Hedging Carbon Risk with Tradeable Factors: Evidence from ETF Carbon Betas

Measuring and Hedging Carbon Risk with Tradeable Factors: Evidence from ETF Carbon Betas | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Measuring and Hedging Carbon Risk with Tradeable Factors: Evidence from ETF Carbon Betas Thiago Gil, Wesley Mendes da Silva This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8041599/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This paper develops a market-based, implementable framework to measure and hedge carbon risk. We construct a tradeable carbon factor from carbon-allowance ETFs and integrate it into an extended Fama–French model to estimate dynamic carbon betas across a large cross-section of exchange-traded funds (ETFs). Using an ETF sample classified into high- and low-carbon universes, we document economically meaningful cross-sectional differences in exposure to the carbon factor: high-carbon ETFs load more strongly on the factor than low-carbon ETFs. To standardize sector/thematic controls, ETFs are labeled with an LLM-assisted, taxonomy-constrained classifier, ensuring consistent category assignment at scale. We then design portfolios intended to target specific decarbonization scenarios via a simple linear interpolation scheme between the two universes. In implementation, realized carbon betas systematically miss their targets because both sleeves retain positive carbon loadings, producing persistent tracking error. Over the sample period, low-carbon allocations delivered superior risk-adjusted performance, implying a negative carbon premium in-sample, but this outperformance did not translate into effective hedging because target exposures were not achieved. Our findings (i) validate carbon risk as a priced covariation component, and (ii) show that naïve green tilts are insufficient to neutralize carbon exposure. The framework standardizes measurement with observable prices and surfaces practical constraints that matter for portfolio construction and risk management. Finance Finance Carbon Climate Finance Factor Models ETF 1. Introduction Investors increasingly recognize that climate transition risk can affect asset prices through policy, technology, and demand channels. Yet the operational question facing practitioners is not merely whether carbon risk is priced, but how to measure it consistently and hedge it in real portfolios. Much of the existing work evaluates carbon exposure with firm-level emissions, sustainability policies, or decarbonized index constructs that are informative but not directly tradeable. As a result, asset managers lack a standardized, market-based tool for diagnosing carbon risk and a clear playbook for implementing hedges at scale. This paper addresses both gaps. We build a tradeable carbon factor from liquid carbon-allowance ETFs that proxy the major compliance markets. We then embed this factor in an extended Fama–French setting to estimate carbon betas for a broad ETF universe, using HAC-robust inference and rolling windows to capture time variation. Focusing on ETFs—rather than single names—reduces idiosyncratic noise, maps cleanly to investable sleeves (high- vs. low-carbon strategies), and mirrors how institutions implement tactical allocations. Our empirical design targets three questions. First, do financial assets exhibit systematic exposure to a market-priced carbon factor? Second, can investors engineer target carbon exposures in long-only portfolios by tilting across high- and low-carbon universes? Third, what are the risk–return trade-offs and implementation frictions of such hedges? We find that high-carbon ETFs have, on average, larger and more frequently significant carbon betas than low-carbon ETFs, confirming that carbon risk is an identifiable covariation component. However, when we construct portfolios to reach specified decarbonization levels through linear interpolation between the two universes, realized carbon betas fail to meet targets and, at times, exceed the exposure of the brown benchmark. The mechanism is straightforward: both sleeves retain positive loadings on the carbon factor, so reweighting alone cannot drive portfolio beta to low or neutral levels. Over our sample, low-carbon tilts also outperform on a risk-adjusted basis, implying a negative in-sample carbon premium—but this performance benefit does not equate to effective hedging because exposure targets are missed. These results deliver three contributions. Measurement: we provide a standardized, market-priced carbon metric—carbon beta—estimated within a familiar multi-factor framework. Validation: we document economically non-trivial cross-sectional dispersion in carbon betas, especially across clearly interpretable ETF cohorts. Implementation: we demonstrate that simple green tilts are insufficient to achieve low or zero carbon exposure and that direct hedging (short overlays in carbon ETFs/futures or assets with negative carbon betas) is required to attain precise targets. The evidence reframes carbon-aware portfolio construction as an exercise in factor engineering under constraints, not merely re-labeling sector tilts. The remainder of the paper presents the literature review; methodology (factor construction, estimation, portfolio design, and LLM-assisted, taxonomy-constrained ETF sector/thematic labeling); reports cross-sectional and portfolio-level results with robustness checks; and discusses implications for asset allocation, risk management, and policy. 2. Literature Review The carbon beta concept builds on the theoretical foundations established by Markowitz ( 1952 ), who introduced modern portfolio theory, and later developed by Sharpe ( 1964 ) and Lintner ( 1965 ) into the Capital Asset Pricing Model (CAPM) framework, while introducing environmental considerations into the risk-return relationship. It can be traced to the work of Görgen et al. ( 2019 ), who proposed measuring the carbon financial risk of equities through their sensitivity to a brown-minus-green (BMG) risk factor. This approach parallels the traditional asset pricing models of Fama and French ( 1992 ), later extended by Carhart ( 1997 ) to include momentum factors and by Fama and French (2015) to incorporate profitability and investment factors, extending multi-factor models to incorporate climate-related systematic risk factors. Researchers have long recognised that climate-related risks can influence asset prices, yet early work focused primarily on measuring firms’ physical carbon footprints and linking emissions to firm value. Aggarwal and Dow ( 2011 ) document that greenhouse-gas mitigation efforts are associated with higher firm valuations, while Cheng et al. ( 2014 ) show that better environmental disclosure improves access to finance. Policy-oriented studies explore how carbon regulation can affect competitiveness and investment decisions (Antimiani et al., 2016 ; Blyth et al., 2007 ). These strands of literature view carbon risk largely as a firm-specific characteristic rather than a systematic factor. Other work has examined ways to hedge climate risk using financial instruments. Andersson, Bolton and Samama ( 2016 ) propose a decarbonised index that reduces carbon exposure while maintaining market-like risk–return characteristics, and Balcilar et al. ( 2016 ) study risk spillovers between energy and carbon markets. Reports by the Carbon Tracker Initiative ( 2013 ) warn of stranded assets in fossil-fuel-heavy industries, highlighting the need for investors to manage transition risk. These studies underscore that carbon risk can be priced and potentially hedged but stop short of constructing a tradeable risk factor. Arkoun et al. ( 2020 ) proposed a time-varying estimation model to assess the dynamics of carbon risk, arguing that carbon beta should not be considered constant over time as originally suggested, as companies' exposure to climate risks evolves with regulatory changes, technological developments, and market conditions. Chenet et al. ( 2021 ) demonstrated how climate risks can be incorporated into asset pricing models through perturbation methods, deriving rules for optimal risk-adjusted social cost of carbon that account for uncertainties in climate and economic factors. The seminal empirical work by Bolton and Kacperczyk ( 2021 ) provided definitive evidence for the existence of a carbon premium in financial markets. Using a comprehensive dataset of U.S. and global firms, they demonstrated that stocks with higher total CO2 emissions earn higher returns after controlling for size, book-to-market, momentum, and other factors. Their global analysis across 77 countries confirmed that carbon-intensive firms command a risk premium, with the premium varying based on countries' climate policy stringency and economic development levels. The empirical literature on carbon exposure has produced mixed findings regarding the pricing of climate risks in financial markets. Engle et al. ( 2020 ) found evidence that carbon-intensive firms exhibit higher systematic risk exposure, supporting the theoretical predictions of carbon beta models. Their research demonstrated that investors require a positive, although small, climate risk premium for holding ‘brown’ assets. However, Battiston et al. (2021) presented a meta-analysis showing that while there is no consensus on the existence of a carbon premium in stock prices, the literature increasingly supports the view that carbon risk is a priced factor in financial markets. Carbon exposure can also be perceived from a risk management angle. Research by Roncalli et al. ( 2021 ) demonstrated that incorporating carbon risk factors into portfolio optimization can reduce both systematic and idiosyncratic risks, particularly during periods of climate-related policy uncertainty. Physical climate risks, including extreme weather events and chronic environmental changes, create direct impacts on asset valuations and corporate cash flows (Hsiang et al., 2017 ). Monasterolo and Battiston ( 2020 ) analyzed how climate stress tests and scenario analysis can quantify the transmission of climate risks through financial systems. Their Climate Extended Risk Model (CERM) demonstrated how climate-related factors can be integrated into traditional credit risk models to estimate incremental losses on loan portfolios. This approach has become increasingly important for banking institutions seeking to comply with regulatory requirements for climate risk disclosure. The NGFS (Network for Greening the Financial System) scenarios have provided standardized frameworks for assessing climate risks across different transition pathways (NGFS, 2021 ). These scenarios enable financial institutions to evaluate portfolio exposure to climate risks under various policy and technological development paths, supporting the practical application of carbon beta measures in risk management. The integration of carbon beta measures with broader ESG (Environmental, Social, Governance) investing frameworks has become a significant area of research. Pedersen et al. ( 2021 ) developed theoretical models showing how ESG preferences affect asset prices through multiple channels, including investor preferences, corporate cash flows, and risk exposure. Their equilibrium framework demonstrates that ESG-conscious investors' actions can generate positive social impact while potentially affecting investment returns. Research specific to carbon footprint optimization in portfolios has shown promising results. Andersson et al. ( 2016 ) demonstrated that carbon-efficient portfolio construction can achieve similar risk-return profiles to traditional portfolios while significantly reducing carbon intensity. The intersection of carbon beta measures with green finance instruments has created new opportunities for climate risk management and sustainable investment. Green bonds, specifically earmarked for climate and environmental projects, have demonstrated complex pricing relationships with conventional bonds, often exhibiting lower yields (greenium effect) at issuance (Zerbib, 2019 ). Practical applications of carbon beta in portfolio management have evolved significantly, with institutional investors increasingly incorporating climate risk factors into investment processes. Research on minimum variance portfolio construction shows that incorporating carbon risk can reduce unrewarded financial risks while maintaining competitive risk-return profiles (Roncalli et al., 2021 ). Despite significant progress in carbon research, several important gaps remain. The standardization of carbon risk measurement methodologies continues to present challenges, with different approaches producing varying results depending on data sources, calculation methods, and temporal frameworks. Moreover, most existing hedging approaches are theoretical; for instance, carbon transition risk is often proxied by firm-level emissions or corporate policies, and decarbonised indices or Brown-minus-Green factors are not directly tradeable To address these limitations, our paper moves beyond firm-level proxies and untradable constructs to propose a market-based, implementable framework for measuring and hedging carbon risk. We construct a tradeable carbon risk factor from carbon-allowance ETFs, integrate it into an extended Fama–French model to estimate dynamic carbon betas for a broad ETF universe, and design portfolios that target specific decarbonisation scenarios through linear interpolation. This methodology not only standardises the carbon-risk metric—because it relies on observable market prices rather than heterogeneous emissions data—but also allows us to test the real-world feasibility of carbon hedging. The resulting portfolios reveal substantial tracking-error challenges, highlighting the complexities of implementing carbon-risk management in practice and underscoring the need for market-based tools to complement traditional, emissions-based research. 3. Methodology This study employs an empirical approach to investigate carbon risk exposure in financial markets and evaluate the effectiveness of carbon hedging strategies. Our methodology addresses three fundamental research questions: (1) Do financial assets exhibit systematic exposure to carbon risk factors? (2) Can investors effectively hedge carbon risk through portfolio construction? and (3) What are the risk-return implications of carbon hedging strategies? Our research design follows a multi-stage approach. First, we construct a tradeable carbon risk factor from carbon allowance ETFs to serve as our primary measure of carbon risk exposure in financial markets. Second, we extend the Fama-French multifactor model to include our carbon risk factor, enabling us to isolate carbon-specific risk exposures from traditional systematic risk factors. Third, we develop a linear interpolation portfolio construction framework that creates portfolios with varying degrees of carbon risk exposure corresponding to different decarbonization scenarios. Finally, we evaluate portfolio performance using comprehensive risk-adjusted metrics and assess implementation challenges through tracking error analysis. Our analysis employs a comprehensive dataset of exchange-traded funds (ETFs) spanning from October 2021 to July 2024. We collect daily price data, assets under management (AUM), and sector classifications from the EODHD financial database. We focus on ETFs rather than individual stocks for several methodological and practical reasons. First, ETFs provide diversified exposure to specific sectors or investment themes, reducing idiosyncratic noise that could obscure systematic carbon risk relationships. Second, ETF classification systems allow for clear delineation between high-carbon and low-carbon investment strategies based on underlying holdings. Third, ETFs are increasingly used by institutional investors for tactical allocation adjustments, making our results directly applicable to contemporary investment practice. Finally, the ETF structure facilitates the construction of implementable carbon hedging strategies that can be readily adopted by practitioners. We categorize ETFs into high-carbon and low-carbon exposure groups based on their underlying sector focus and investment objectives. To standardize sector and theme labels across a large ETF universe, we used a constrained large-language-model classification workflow built on Perplexity PRO. Each ETF (symbol + fund name) was submitted in batched prompts to the chat-completions API with a closed taxonomy covering broad sectors (e.g., Technology, Energy, Financial Services), granular industry slices (e.g., Semiconductors, Oil & Gas Midstream, Clean Energy, Carbon Credits & Decarbonization), factor/style buckets (e.g., Momentum, Low Volatility), geographic cohorts, and fixed-income segments (e.g., TIPS, High Yield Bonds, Green Bonds). The system message instructed the model to return exactly one category from this list and nothing else. To handle occasional off-list or ambiguous outputs, we implemented a nearest-match mapper that projects raw model answers onto the closest valid category in the taxonomy (string-token overlap), plus a keyword fallback heuristic keyed to fund names (e.g., “Treasury,” “Dividend,” “REIT,” “Emerging,” “Technology”) when the API rate-limited or failed; as a last resort, unresolved cases defaulted to the closest high-level bucket (conservatively Technology). A cache ensured identical inputs received identical labels across runs, preserving internal consistency. Post-processing included frequency diagnostics (category histograms) and spot checks of high-count and edge categories. Two caveats accompany the approach: (i) many ETFs have multi-sector exposures or thematic blends, while our procedure assigns a single primary label for tractability; and (ii) ETF mandates can evolve over time. Accordingly, the labels are used for descriptive stratification and control variables in the empirical sections, not as definitive GICS mappings. This LLM-assisted, taxonomy-constrained procedure delivers scalable, reproducible sector tags while minimizing subjective, manual curation. High-carbon sectors include Energy, Oil & Gas Upstream, Oil & Gas Midstream, Oil Services, Materials, Utilities, Transportation & Logistics, and Industrials. Low-carbon sectors comprise Clean Energy, Low Carbon/Climate Action, Solar Energy, Wind Energy, Hydrogen & Fuel Cells, Green Bonds, Sustainable Infrastructure, Autonomous/Electric Vehicles, and Lithium & Battery Tech. Our sample selection follows a multi-stage filtering process to ensure data quality and sufficient liquidity: Minimum of 300 daily observations with valid pricing data AUM exceeding $ 50 million for low-carbon ETFs and $ 100 million for high-carbon ETFs Successful data collection status in our database Positive trading volume and non-zero closing prices throughout the sample period This filtering process yields a final sample of 190 ETFs: 120 high-carbon and 70 low-carbon ETFs, providing sufficient cross-sectional variation for robust statistical inference. We construct a carbon risk factor using three prominent carbon credit and carbon futures ETFs: KRBN.US (KraneShares Global Carbon Strategy ETF), KCCA.US (KraneShares California Carbon Allowance Strategy ETF), and KEUA.US (KraneShares European Carbon Allowance Strategy ETF). These ETFs provide direct exposure to major carbon pricing mechanisms including the EU Emissions Trading System and California Cap-and-Trade Program, capturing the primary channels through which carbon policy risk affects financial markets. To create a robust carbon risk factor, we implement a winsorization procedure (at the 1st and 99th percentiles) to control for extreme outliers that may distort the factor's properties. We then calculate a value-weighted carbon index using AUM as weights and apply rolling standardization using a 20-period window: We extend the traditional Fama-French five-factor model to include our carbon risk factor. For each ETF j, we estimate the following regression: $$\:{R}_{j,t}-\:R{F}_{t}=\:{\alpha\:}_{j}+\:{\beta\:}_{C,j}\times\:\:CARBO{N}_{t}+\:{\beta\:}_{MKT,j}\times\:\:\left(MK{T}_{t}-\:R{F}_{t}\right)+\:{\beta\:}_{SMB,j}\times\:\:SM{B}_{t}+\:{\beta\:}_{HML,j}\times\:\:HM{L}_{t}+\:{\beta\:}_{RMW,j}\times\:\:RM{W}_{t}+\:{\beta\:}_{CMA,j}\times\:\:CM{A}_{t}+\:{\epsilon\:}_{j,t}$$ 1 Where: \(\:{R}_{j,t}\) - \(\:R{F}_{t}\) is the excess return of ETF j over the risk-free rate \(\:CARBO{N}_{t}\) is our constructed carbon risk factor \(\:MK{T}_{t}-\:R{F}_{t}\) is the market excess return \(\:SM{B}_{t}\) , \(\:HM{L}_{t}\) \(\:RM{W}_{t}\) , \(\:CM{A}_{t}\:\) are the Fama-French size, value, profitability, and investment factors \(\:{\beta\:}_{C,j}\) is the carbon beta, measuring ETF j 's sensitivity to carbon risk We employ Ordinary Least Squares (OLS) with Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors to account for potential serial correlation and heteroskedasticity in residuals. The HAC estimator uses a maximum lag length of 5, following Newey and West (1987). For ETFs with sufficient observations (≥ 52 weekly or ≥ 90 daily), we implement a rolling window estimation approach with window size \(\:W=\text{m}\text{i}\text{n}(52,t-1)\) where \(\:t\) is the total number of observations. This approach captures time-varying risk exposures while maintaining statistical power. Given the large number of simultaneous hypothesis tests (190 ETFs), we apply the Benjamini-Hochberg (1995) false discovery rate correction to control for multiple testing bias: $$\:{p}_{i}^{adj}=\text{min}\left(j\ge\:i,\:{p}_{j}*\:\left(\frac{m}{j}\right)\right)\:\:$$ 2 where \(\:{p}_{i}^{adj}\:\) is the adjusted p-value for ETF j, and m is the total number of tests. We test the null hypothesis that carbon betas are equal across high and low carbon ETF groups using Welch's unequal variance t-test. Additionally, we employ the Mann-Whitney U test as a non-parametric alternative to assess distributional differences in carbon betas. Based on the estimated carbon betas, we construct portfolios with varying degrees of carbon risk exposure corresponding to different decarbonization scenarios. We create carbon-hedged portfolios by solving the following optimization problem: $$\:\underset{w}{\text{min}}CVa{R}_{\alpha\:\left({R}_{p}\right)}$$ 3 Subject to: $$\:{\sum\:}_{i=1}^{N}{w}_{i}=\:1\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(budget\:constraint\right){w}_{i}\ge\:\:0\:\:\forall\:i\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(long-only\:constraint\right){\left|\left|w\:-\:{w}^{0}\right|\right|}_{2}\le\:\:\delta\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(tracking\:error\:constraint\right){\beta\:}_{C\left(w\right)}\le\:\:{\beta\:}_{C}^{target}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(carbon\:beta\:constraint\right)$$ 4 Where: \(\:CVa{R}_{\alpha\:\left({R}_{p}\right)}\) is the conditional value-at-risk at confidence level α \(\:w\) is the base portfolio weight vector \(\:\delta\:\) is the maximum allowed tracking error \(\:{\beta\:}_{C\left(w\right)}\) is the portfolio carbon beta \(\:{\beta\:}_{C}^{target}\) is the target carbon beta level Following DeMiguel et al. (2009), we incorporate parameter uncertainty by replacing point estimates \(\:{\beta\:}_{C,i}\:\) with confidence intervals: $$\:{\beta\:}_{C,i}\in\:\:\left[{\widehat{\beta\:}}_{C,i}-\:\tau\:\:\times\:\:SE\left({\widehat{\beta\:}}_{C,i}\right),\:{\widehat{\beta\:}}_{C,i}+\:\tau\:\:\times\:\:SE\left({\widehat{\beta\:}}_{C,i}\right)\right]$$ 5 Where τ is the robustness parameter and \(\:SE\left({\widehat{\beta\:}}_{C,i}\right)\) is the standard error of the carbon beta estimate. We solve the worst-case optimization problem over this uncertainty set. Within this framework, the optimization problem is reformulated as a two-stage, worst‐case exercise. Rather than maximizing expected return (net of risk) at the single vector of point estimates, the decision‐maker assumes that each true carbon beta may lie anywhere within its prescribed confidence band. The inner problem identifies, for any given portfolio, the particular combination of true betas that minimizes performance. From the betas, we then construct portfolios with different carbon reduction targets: • 20% reduction: = 0.8 × • 20% reduction: \(\:{\beta\:}_{C}^{target}\) = 0.8 × \(\:{\beta\:}_{H}\) • 50% reduction: = 0.5 × • 50% reduction: \(\:{\beta\:}_{C}^{target}\) = 0.5 × \(\:{\beta\:}_{H}\) • 80% reduction: = 0.2 × • 80% reduction: \(\:{\beta\:}_{C}^{target}\) = 0.2 × \(\:{\beta\:}_{H}\) • 100% reduction: = 0 • 100% reduction: \(\:{\beta\:}_{C}^{target}\) = 0 where \(\:{\beta\:}_{H}\) is the carbon beta of the base brown (high-carbon) basket portfolio. Our portfolio construction methodology relies on a linear interpolation approach between high-carbon and low-carbon ETF universes to achieve target carbon exposures. The fundamental assumption underlying this approach is that portfolio carbon betas can be expressed as a weighted average of constituent universe betas: $$\:{\beta\:}_{C}^{target}={w}_{H}\times\:\:{\stackrel{-}{\beta\:}}_{H}+\:{w}_{L}\times\:\:{\stackrel{-}{\beta\:}}_{L}$$ 6 Where: \(\:{w}_{H}\) and \(\:{w}_{L}\) are the weights allocated to high and low carbon universes \(\:{\stackrel{-}{\beta\:}}_{H}\) and \(\:{\stackrel{-}{\beta\:}}_{L}\) are the mean carbon betas of high and low carbon ETF universes The target carbon beta represents our desired level of carbon risk exposure for each portfolio, corresponding to specific carbon reduction strategies. Using linear interpolation between high-carbon ETFs’ betas and low-carbon ETFs’ betas, we calculate the precise weights needed to hit specific carbon exposure levels. For instance, reducing the carbon exposure by 50% would imply finding a 50% lower beta by adding low-carbon investments in the portfolio. Realized Beta is what we actually measure when we regress each constructed portfolio's returns against the carbon factor. This is the portfolio's true carbon sensitivity based on its observed performance, not our theoretical calculation. The difference between the target carbon beta we intended to achieve through portfolio construction and the realized carbon beta is what we call tracking error. In the context of carbon risk management, this deviation is particularly critical because it reveals whether portfolio construction methodologies can successfully implement intended carbon reduction strategies. When portfolios systematically exhibit higher carbon exposure than targeted it indicates a fundamental breakdown in the factor targeting mechanism, suggesting that simple linear interpolation approaches are insufficient for managing complex, time-varying risk factors like carbon exposure. The portfolio performance is evaluated using multiple risk-adjusted metrics: Sharpe Ratio: $$\:S{R}_{p}=\frac{\left({\mu\:}_{p}-\:RF\right)}{{\sigma\:}_{p}}$$ 7 Where \(\:{\sigma\:}_{p}\) is the standard deviation of returns. Sortino Ratio: $$\:Sortin{o}_{p}=\frac{\left({\mu\:}_{p}-\:RF\right)}{{\sigma\:}_{p}^{-}}$$ 8 Where \(\:{\sigma\:}_{p}^{-}\:\) is the downside standard deviation calculated using only negative returns. Calmar Ratio: $$\:Calma{r}_{p}=\frac{{\mu\:}_{p}}{\left|MD{D}_{p}\right|}$$ 9 Where \(\:MD{D}_{p}\) is the maximum drawdown. For risk management considerations, we build the Value-at-Risk (VaR) framework. Using historical simulation, the α-level VaR is: $$\:Va{R}_{\alpha\:}=\:-{F}_{R}^{\left(-1\right)\left(\alpha\:\right)}$$ 10 Where \(\:{F}_{R}^{\left(-1\right)}\) is the inverse cumulative distribution function of portfolio returns. The Conditional Value-at-Risk (CVaR) is defined as: $$\:CVaR\_\alpha\:\:=\:E\left[{R}_{p}\right|\:{R}_{p}\le\:\:-VaR\_\alpha\:]$$ 11 We conduct several robustness checks to ensure our findings are not driven by outliers or sample composition effects: Outlier Exclusion: Re-estimate all tests excluding ETFs with carbon betas in the top and bottom 5% of the distribution Significance Filter: Restrict analysis to ETFs with statistically significant carbon betas (p < 0.05) Model Fit Filter: Include only ETFs with above-median R-squared values to ensure adequate factor model specification We test alternative carbon factor constructions including equal-weighted carbon factors, principal component approaches using carbon ETF returns, and alternative winsorization thresholds to ensure our results are not sensitive to specific methodological choices. Our linear interpolation approach assumes that portfolio carbon betas aggregate linearly from constituent ETF betas. This assumption may be violated when: (1) individual ETF-carbon factor relationships exhibit time-varying heteroskedasticity, (2) cross-correlations between ETFs and the carbon factor change over time, or (3) the carbon factor itself displays regime-switching behavior. These limitations motivate our comprehensive tracking error analysis and suggest avenues for future methodological improvements using optimization-based approaches. This methodology differs from the one proposed by Görgen et al. ( 2019 ). They derive a carbon risk score from company-level CO₂-equivalent emissions and ten qualitative environmental-agenda indicators. Firms are sorted into high- and low-carbon portfolios based on this score, and a Brown-minus-Green (BMG) factor is built as a long–short stock portfolio. In contrast, this study constructs a tradeable carbon factor from carbon-allowance ETFs. This factor proxies carbon price risk rather than firm-level carbon intensity and is a value-weighted index based on ETF assets under management. 4. Results Table 1 reports cross-sectional summaries of the estimated carbon betas ( \(\:{\beta\:}_{C}\) ). The mean \(\:{\beta\:}_{C}\) for the high-carbon group is 0.0015, compared with 0.0008 for the low-carbon group. A Welch two-sample t-test yields t = 2.018, p = 0.045, indicating statistical significance at the 5% level. A non-parametric Mann–Whitney U test, however, fails to reject equality of distributions (p = 0.417), highlighting substantial overlap between groups. Table 1. Cross-Sectional Carbon Betas – High vs. Low Carbon ETF Groups Low N ETFs is the number of funds with valid regressions; Mean/Median \(\:{\beta\:}_{C}\) ₎ are the cross-sectional average and median loadings on the carbon factor (the OLS coefficient on CARBON in weekly regressions); Std. Dev., Min, Max \(\:{\beta\:}_{C}\) ₎ describe the dispersion and range of those loadings; Sig. Count and Sig. % report how many (and what share) of ETFs have \(\:{\beta\:}_{C}\) statistically different from zero at the 5% level (two-sided, HAC errors); Sig. Count (BH) and Sig. % (BH) apply the same threshold after Benjamini–Hochberg FDR correction; Mean R² is the average regression fit; Positive \(\:{\beta\:}_{C}\) % is the share of ETFs with \(\:{\beta\:}_{C}\) 0; the Difference column is High minus Low (percentages shown in percentage points). Panel A: Summary Statistics Metric High Carbon Low Carbon Difference N ETFs 120 70 50 Mean \(\:{\beta\:}_{C}\) 0.001531 0.000894 0.000636 Median \(\:{\beta\:}_{C}\) 0.000987 0.001027 –0.000039 Std. Dev. \(\:{\beta\:}_{C}\) 0.002389 0.001906 0.000483 Min \(\:{\beta\:}_{C}\) –0.002267 –0.006509 0.004241 Max \(\:{\beta\:}_{C}\) 0.010388 0.008145 0.002243 Sig. Count 50 6 — Sig. % 41.67% 8.57% 33.10 p.p. Sig. Count (BH) 23 1 — Sig. % (BH) 19.17% 1.43% 17.74 p.p. Mean R² 0.56 0.55 0.01 Positive \(\:{\beta\:}_{C}\) % 67.50% 80.00% –12.50 p.p. Panel B: Group-Mean Equality Tests Test Statistic p-value Sig. (5%) Welch t-test 2.018 0.045168 Yes Mann–Whitney U 4497 0.417432 No Economic magnitude is modest but non-negligible. Converting to annualized terms, the carbon beta differential translates to 331 basis points annually, representing material exposure that significantly exceeds typical transaction costs and risk management thresholds. This finding indicates that carbon risk represents a systematic factor with economically meaningful implications for portfolio returns. Model fit is comparable across cohorts. Average R² is 0.565 for high-carbon ETFs and 0.559 for low-carbon ETFs, suggesting that adding the carbon factor does not differentially improve explanatory power across groups, but does capture a systematic covariation component. Out of 120 high-carbon ETFs, 50 (41.7%) exhibit \(\:{\beta\:}_{C}\) estimates significant at the 5% level; only 6 of 70 (8.6%) low-carbon ETFs meet this criterion. After controlling for false discovery using Benjamini–Hochberg, the shares fall to 19.2% (23/120) and 1.4% (1/70), respectively. Thus, while many raw p-values are below 0.05, a nontrivial subset still survives standard multiple-testing corrections in the high-carbon group, whereas almost none do in the low-carbon set. Directionally, 67.5% of high-carbon ETFs have positive \(\:{\beta\:}_{C}\) , and so do 80.0% of low-carbon ETFs—their loadings are simply smaller. Only 20% of the latter have negative exposure. Sectoral breakdowns (Table 2) present more insights. Within the high-carbon universe: Oil & Gas Upstream (N = 15) displays the largest average exposure ( \(\:{\beta\:}_{C}\) = 0.0052, p < 0.001), with 86.7% of constituents significant. Oil & Gas Midstream (N = 11) and Energy (N = 25) also load significantly ( \(\:{\beta\:}_{C}\:\) ≈ 0.0023–0.0028). Materials and Utilities have near-zero average \(\:{\beta\:}_{C}\:\) and low significance rates. Transportation/Logistics and Industrials show slightly negative but statistically insignificant mean betas. Interestingly, traditional high-carbon sectors such as Materials and Utilities show minimal carbon sensitivity, while Transportation & Logistics and Industrials exhibit slightly negative mean betas. This heterogeneity suggests that carbon risk exposure varies significantly even within sectors commonly classified as carbon-intensive. In the low-carbon group, mean betas are positive across most categories: Clean Energy (N = 14): \(\:{\beta\:}_{C}\) = 0.0018, p = 0.0002, with 21% individual significance. Sustainable Infrastructure and Low Carbon / Climate Action also show small but positive and often significant exposures. Niche segments (Wind, Hydrogen, Lithium/Batteries) have small samples and low power; their mean betas are positive but insignificant. The low-carbon universe displays more modest but varied carbon exposures. Sustainable Infrastructure and Low Carbon/Climate Action showing positive betas contradicts the common assumption that sustainable investments provide carbon risk hedging. Table 2. Sector-Level Mean Carbon Betas N ETFs is the number of funds with valid regressions; Mean \(\:{\beta\:}_{C}\) is the cross-sectional average loading on the carbon factor (the OLS coefficient on CARBON in weekly regressions; Sig. % reports how many (what share) of ETFs have \(\:{\beta\:}_{C}\) statistically different from zero at the 5% level (two-sided, HAC errors); Mean R² is the average regression fit. Panel A: High-Carbon Sectors Sector N Mean \(\:{\beta\:}_{C}\) p-val Sig% Mean R² Oil & Gas Upstream 15 0.005208 0.0000 86.7 0.410 Oil-Services 5 0.003565 0.0232 60.0 0.537 Energy 25 0.002804 0.0000 68.0 0.566 Oil & Gas Midstream 11 0.002271 0.0000 81.8 0.604 Materials 22 0.000122 0.6188 13.6 0.623 Utilities 17 0.000064 0.7379 5.9 0.416 Transportation & Logistics 10 –0.000395 0.2724 0.0 0.626 Industrials 15 –0.000476 0.1461 26.7 0.740 Panel B: Low-Carbon Sectors Sector N Mean \(\:{\beta\:}_{C}\) p-val Sig% Mean R² Hydrogen & Fuel Cells 2 0.002250 0.4485 0.0 0.478 Wind Energy 1 0.001955 Na na 0.443 Clean Energy 14 0.001772 0.0002 21.4 0.441 Solar Energy 3 0.001437 0.2283 0.0 0.392 Sustainable Infrastructure 7 0.001282 0.0121 28.6 0.549 Lithium & Battery Tech 7 0.000556 0.2980 0.0 0.448 Low Carbon / Climate Action 19 0.000465 0.0320 5.3 0.765 Green Bonds 4 0.000332 0.0382 0.0 0.338 Autonomous / Electric Vehicles 13 0.000309 0.7662 0.0 0.577 We perform four robustness exercises (Table 3 ): To gauge how fragile the High–Low carbon beta gap is to reasonable perturbations of the sample, we ran four complementary exercises: Baseline specification: Using the full set of estimated betas, the mean difference in carbon exposure is 0.0006 per week (High minus Low), with p = 0.045. Statistically significant at 5%, but close to the cutoff. Trimming extreme betas (± 5% tails). Outliers can inflate both means and test statistics. After dropping the top and bottom 5% of \(\:{\beta\:}_{C}\) within each group, the gap falls to 0.0004 and the p-value drifts to 0.052. Two things are happening: the effect size is mechanically smaller because we removed some very large positive High-carbon betas; and the standard error increases slightly because we are working with fewer observations. Keeping only individually significant betas (p < 0.05). Among ETFs where carbon exposure is estimated precisely, how different are the groups? The mean gap rises to 0.0015 with p = 0.002. However, this result is not an independent test; it conditions on statistical significance ex post, which biases the sample toward large absolute betas (and especially large positive ones in the High-carbon cohort). So this check shows the signal is strong where it exists, but it cannot be used to claim the overall population difference is that large. High fit-quality subsample (R² above the median = 0.587). To mitigate noise from poorly explained return series, we keep only regressions with relatively high explanatory power. The mean difference is 0.0005 and p = 0.080. In other words, when we insist on clean regressions, we still see a positive spread, but losing almost half the sample erodes statistical power enough that we cannot reject equality at 5%. This suggests some of the baseline significance comes from names with moderate fit quality—which is not necessarily problematic, but worth noting. Table 3 Robustness Checks on the High–Low Carbon Beta Spread High_N and Low_N are the numbers of ETFs remaining in each group after the indicated filter. Difference is the mean carbon beta spread ((High Carbon) − Low Carbon)) in weekly units. p-value comes from a two-sided Welch t-test on group means. “Exclude 5% tails” trims the top and bottom 5% of ithin each group. “ETFs with significant retains only funds whose individual is significant at 5% (HAC/Newey–West errors). “High fit only” keeps regressions with R² above the pooled median (0.587). Specification High_N Low_N Difference p-value Baseline (full sample) 120 70 0.000636 0.045168 Exclude 5% tails (both groups) 108 62 0.000429 0.051648 ETFs with significant \(\:{\beta\:}_{C}\) 50 6 0.001508 0.002033 High fit only (R² >median = 0.587) 70 25 0.000563 0.079748 Across all perturbations, the High–Low spread in carbon betas remains positive; what varies is the precision with which we can reject the null of no difference. Modest alterations in the retained sample—e.g., trimming outliers, restricting to high-fit regressions, or conditioning on individually significant betas—move the p-value across conventional thresholds (0.045 → 0.052 → 0.002 → 0.080). Thus, while the qualitative pattern is stable, the statistical strength of the claim is sample-sensitive. This underscores the need for (i) longer time series, (ii) alternative constructions of the carbon factor, and/or (iii) panel estimators with appropriate fixed effects and clustered errors to consolidate inference. Using the estimated carbon betas, we constructed five portfolios with varying carbon risk exposures corresponding to different decarbonization scenarios. The baseline brown portfolio achieves a mean carbon beta of 0.001531, serving as our reference point for carbon risk exposure. Target portfolios are designed to achieve 20%, 50%, 80%, and 100% carbon reduction relative to this baseline. In theory, shifting weight toward the low-carbon sleeve should lower portfolio exposure to the carbon factor. Table 4 shows, in practice, that every decarbonized portfolio (20%, 50%, 80% reduction and “neutral”) ended up with a higher realized beta (≈ 0.0016–0.0017) than the brown benchmark (0.00152). The optimizer was forced to 100% low-carbon weight to chase deeper cuts, but because low-carbon ETFs still have positive carbon loadings, the target could not be met. Table 4 Portfolio Targets, Realized Carbon Betas, and Weights This table reports the ex-ante Target (the desired carbon-factor loading), the ex post Realized from regressing weekly excess returns on the CARBON factor, and the resulting Tracking Error (Realized minus Target). It also lists the portfolio weights w in the High-Carbon and Low-Carbon ETF buckets (summing to 1). Because both sleeves exhibit positive carbon betas, reallocating toward Low-Carbon cannot drive to zero, so tighter targets translate into larger positive tracking errors. Portfolio Target \(\:{\beta\:}_{C}\) Realized \(\:{\beta\:}_{C}\) Tracking Error High-Carbon w Low-Carbon w Brown (Base) 0.001531 0.001518 –0.00001 1.000 0.000 20% Reduction 0.001225 0.001595 0.000370 0.519 0.481 50% Reduction 0.000765 0.001677 0.000912 0.000 1.000 80% Reduction 0.000306 0.001677 0.001371 0.000 1.000 Carbon Neutral 0.000000 0.001677 0.001677 0.000 1.000 The Brown (Base) portfolio generates an 8.92% annual return with the highest intended carbon exposure, while carbon-reduced portfolios achieve substantially higher returns (15.82% for 50% reduction and beyond). This finding, as per Table 5 , suggests that during our sample period, low-carbon investments outperformed their high-carbon counterparts. All risk-adjusted performance metrics favor carbon-reduced portfolios. The 50% Reduction portfolio achieves the highest Sharpe ratio (0.484), Sortino ratio (0.743), and Calmar ratio (0.507), substantially outperforming the Brown portfolio across all metrics. This superior performance occurs despite slightly higher volatility (21.14% vs. 20.00%), indicating that the return enhancement more than compensates for increased risk. Table 5 Portfolio Performance Metrics Annual Return is the geometrically annualized return over the sample; Annual Volatility is the standard deviation of weekly returns scaled by √52. Sharpe Ratio is excess return over volatility, while Sortino Ratio replaces total volatility with downside-only volatility. Calmar Ratio is annual return divided by the absolute Max Drawdown, which is the largest peak-to-trough loss observed. Metric Brown (Base) 20% Reduction 50% Reduction 80% Reduction Carbon Neutral Annual Return 8.92% 12.19% 15.82% 15.82% 15.82% Annual Volatility 20.00% 19.37% 21.14% 21.14% 21.14% Sharpe Ratio 0.204 0.363 0.484 0.484 0.484 Sortino Ratio 0.247 0.471 0.743 0.743 0.743 Calmar Ratio 0.198 0.357 0.507 0.507 0.507 Max Drawdown –21.02% –20.44% –21.26% –21.26% –21.26% The Value-at-Risk analysis reveals modest differences across portfolios. The 5% VaR ranges from − 1.47% (Brown) to -1.81% (carbon-reduced portfolios), while 1% VaR varies from − 3.72% to -3.50%. Conditional Value-at-Risk shows more pronounced differences, with carbon-reduced portfolios exhibiting lower tail risk at the 1% level (-4.10% vs. -5.45% for Brown). The return distributions exhibit significant improvements in higher moments for carbon-reduced portfolios. Skewness increases from − 0.002 (Brown) to 0.804 (carbon-reduced), indicating more favorable return distributions. Kurtosis decreases from 14.287 to 9.112, suggesting reduced extreme event frequency in carbon-reduced portfolios. Table 6 Portfolio Risk & Tail Metrics Volatility and Downside Vol. are total and downside (negative-return) standard deviations, respectively. VaR (x%) is the historical value-at-risk at the x% left tail of the weekly return distribution, and CVaR (x%) (expected shortfall) is the average loss conditional on breaching that VaR threshold. Skewness and Kurtosis summarize distributional asymmetry and tail thickness (kurtosis shown as excess unless noted). All figures are computed on weekly data and expressed in weekly percentage terms. Metric Brown (Base) 20% Reduction 50% Reduction 80% Reduction Carbon Neutral Volatility 20.00% 19.37% 21.14% 21.14% 21.14% Downside Vol. 16.50% 14.95% 13.76% 13.76% 13.76% VaR (5%) –1.47% –1.65% –1.81% –1.81% –1.81% CVaR (5%) –2.93% –2.77% –2.79% –2.79% –2.79% VaR (1%) –3.72% –3.30% –3.50% –3.50% –3.50% CVaR (1%) –5.45% –4.69% –4.10% –4.10% –4.10% Skewness –0.002 0.468 0.804 0.804 0.804 Kurtosis 14.287 13.652 9.112 9.112 9.112 A significant implementation issue emerges in our portfolio construction: realized carbon betas deviate substantially from targets for carbon-reduced portfolios. While the Brown portfolio achieves its target (realized β = 0.001518 vs. target β = 0.001531), carbon-reduced portfolios exhibit higher realized betas than intended. This tracking error (ranging from 0.0004 to 0.0017) suggests limitations in our linear interpolation approach and highlights the challenges of implementing carbon risk management strategies in practice. Our results provide mixed evidence on the existence of a carbon risk premium. While the cross-sectional analysis confirms that high-carbon ETFs exhibit higher carbon betas (supporting the factor validity), the portfolio analysis reveals that low-carbon investments generated superior returns during our sample period. This apparent contradiction suggests that: Carbon risk is a valid systematic factor - evidenced by significant cross-sectional variation in carbon betas The carbon risk premium was negative during 2021–2025 - possibly due to strong ESG investment flows, regulatory support for clean energy, or superior fundamental performance of sustainable businesses Implementation challenges exist - evidenced by significant tracking errors in carbon beta targeting If the hedge objective is a materially lower or zero carbon beta, tilting into green ETFs is insufficient. One needs either (i) assets with negative carbon betas or (ii) direct short positions in the carbon factor (e.g., carbon-credit ETFs/futures) to neutralize the exposure. 5. Discussion Görgen et al. ( 2019 ) find that the BMG factor’s average return is negative (brown stocks underperform green stocks); they interpret this as evidence of a green premium and conclude that carbon transition risk does not command a positive risk premium. Our results similarly show that low-carbon ETFs outperform high-carbon ETFs, implying a negative carbon premium during 2021–2024, but the mechanism differs: the outperformance can be attributed to ESG inflows and clean-energy rallies rather than the structural transition risk quantified in the BMG factor. Crucially, what many investors implement in practice is a naive green tilt—a long-only reweighting toward cleaner or greener assets—rather than an explicit hedge of the carbon factor. This distinction matters because a green tilt changes portfolio composition but does not directly offset exposure to the priced carbon factor. Our findings reveal that investors cannot effectively hedge carbon risk using green tilts or the closely related linear-interpolation portfolio construction methodologies. The tracking-error analysis demonstrates a systematic and substantial failure to achieve intended carbon-risk-reduction targets. While the Brown baseline portfolio successfully achieves its target carbon exposure (realized β = 0.001518 vs. target β = 0.001531), all carbon-reduced portfolios exhibit significantly higher realized carbon exposures than intended. The 50% reduction portfolio, designed to achieve a target beta of 0.000765, actually realizes a beta of 0.001677—representing a 119% tracking error that results in higher carbon exposure than the baseline brown portfolio it was meant to improve upon. This is a hallmark of naive tilts: because both sleeves (high- and low-carbon universes) retain positive loadings on the carbon factor, any long-only convex combination places a floor on achievable exposure that is bounded away from zero and can even drift above the brown benchmark when betas are time-varying. This implementation failure becomes even more pronounced for aggressive targets. The Carbon Neutral portfolio, intended to achieve zero carbon exposure, realizes the same beta of 0.001677. These systematic tracking errors translate to substantial economic impacts, ranging from 192 basis points annually for the 20% reduction portfolio to 872 basis points for the Carbon Neutral strategy. In other words, including greener assets relabels exposure without neutralizing it: they import factor timing risk (through regime-dependent carbon betas) while leaving the sign of exposure unchanged. The magnitude and consistency of these tracking errors indicate that simple linear interpolation and long-only green building blocks are fundamentally inadequate for managing complex, time-varying risk factors like carbon exposure. Superficially, the results suggest that carbon-reduction strategies provide superior risk-adjusted returns, with the 50% reduction achieving an annual return of 15.82% and a Sharpe ratio of 0.484, substantially outperforming the Brown baseline portfolio’s 8.92% return and 0.204 Sharpe ratio. However, this apparent outperformance appears to be a period-specific return pattern. The superior performance of supposedly carbon-reduced portfolios reflects the outperformance of clean-energy and ESG-focused ETFs during our sample period (2021–2024)—a phase marked by regulatory support, strong ESG flows, and favorable sector dynamics—rather than successful carbon-risk management. This regime created a negative carbon risk premium where intended lower carbon exposure coincided with higher realized returns. Regardless of the performance, effective carbon hedging requires direct, tradeable offsets to the carbon factor (e.g., explicit short overlays in carbon futures/ETFs or allocating to assets with negative carbon betas) and optimization that controls factor-exposure precision, rather than relying on long-only reweighting. Consequently, investors should exercise caution in extrapolating these performance patterns across periods or regimes and should not conflate a naïve green tilt with a bona fide carbon hedge. 6. Conclusion This paper proposes and tests a market-based framework for carbon risk measurement and hedging. By constructing a tradeable carbon factor from carbon-allowance ETFs and embedding it in an extended Fama–French model, we estimate carbon betas for a broad set of ETFs and show that high-carbon strategies exhibit materially higher exposure to the factor than low-carbon strategies. That cross-sectional evidence supports the interpretation of carbon risk as a priced covariation component. However, implementation results caution against equating green tilts with effective hedging. Portfolios engineered via linear interpolation between high- and low-carbon sleeves systematically miss their target carbon exposures because both sleeves retain positive loadings. The resulting tracking error is economically meaningful and persists across targets, underscoring that long-only reweighting is not enough to achieve low or neutral carbon betas. While low-carbon allocations outperformed during the sample window, this outperformance reflects period-specific dynamics rather than successful risk neutralization. For practitioners, two implications follow. First, diagnostics should rely on market-priced measures (carbon betas) estimated with robust procedures, not only on emissions-based scores. Second, hedging requires instruments that can directly offset carbon factor exposure—negative-beta assets or explicit short overlays in carbon futures/ETFs—combined with optimization under estimation risk to control tracking error. For researchers, our results motivate deeper work on (i) alternative factor constructions and regime-sensitive specifications; (ii) panel estimators and longer samples to consolidate inference; and (iii) optimization approaches that jointly target return, risk, and factor exposure precision. 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J Banking Finance 98:39–60 APPENDIX List of ETF tickers per sector label === HIGH CARBON LABELS === Energy (25): COAL.US, DBE.US, EINC.US, EIPX.US, ERNZ.US, FENY.US, FILL.US, FXN.US, ISRHF.US, IXC.US, IYE.US, NNPEF.US, NVIR.US, PBD.US, PSCE.US, PXI.US, RSPG.US, SMWFF.US, SPXE.US, SSGUF.US, TEMP.US, USAI.US, VDE.US, WEEI.US, XLE.US Oil & Gas Upstream (15): DBO.US, DRLL.US, FTXN.US, GUNR.US, GUSH.US IEO.US, OIH.US, OILK.US, OILT.US, PXE.US, UCO.US, UNG.US, USL.US, USO.US, XOP.US Oil & Gas Midstream (11): AMLP.US, AMZA.US, ATMP.US, ENFR.US, MLPA.US, MLPB.US, MLPD.US, MLPR.US, MLPX.US, TPYP.US, UMI.US Oil-Services (5): CRAK.US, IEZ.US, PXJ.US, USOY.US, XES.US Materials (22): BCIL.US, DMAT.US, FMAT.US, FTIF.US, FTRI.US, FXZ.US, IGE.US, IYM.US, MXI.US, NANR.US, NRES.US, PSCM.US, PYZ.US, REMX.US, RSPM.US, RTM.US, SSGWF.US, TINT.US, UYM.US, VAW.US, XLB.US, XME.US Utilities (17): CHIU.US, CZAR.US, FUTY.US, FXU.US, IDU.US, ISSZF.US, JXI.US, PSCU.US, PUI.US, RSPU.US, SPWUF.US, ULTY.US, UPW.US, USUTF.US, UTES.US, UTSL.US, XLU.US Transportation & Logistics (10): AIRL.US, BOAT.US, FTXR.US, IYT.US, JETS.US, JETU.US, SEA.US, SHPP.US, SUPL.US, XTN.US Industrials (15):, FXR.US, IDOWF.US, IMSXF.US, ITB.US IYJ.US, PRN.US, PSCI.US, RGI.US, RSPN.US, SSGXF.US, UXI.US, VIS.US, XLI.US === LOW CARBON LABELS === Clean Energy (14): ACES.US, CATF.US, CNRG.US, CTEX.US, FRNW.US ICLN.US, IMSIF.US, KGRN.US, PBW.US, QCLN.US, RNRG.US, RNWZ.US, SULR.US, VCLN.US Low Carbon / Climate Action (19): CCSO.US, CRBN.US, EEMX.US, EFAX.US, EMCR.US, EMCS.US, ETHO.US, FCPI.US, INFL.US, KLMT.US, LCTD.US, LCTU.US, NZAC.US, PABD.US, PABU.US, SPYX.US, USCA.US, USCL.US, USNZ.US Solar Energy (3): RAYS.US, SOLR.US, TAN.US Wind Energy (1): FAN.US Hydrogen & Fuel Cells (2): EVHY.US, HYDR.US Green Bonds (4): BGRN.US, CCSB.US, DFSB.US, GRNB.US Sustainable Infrastructure (7): EFRA.US, GBLD.US, HSUN.US, INFR.US, NBET.US, RNEW.US, UPGR.US Autonomous, Electric Vehicles (13): CARZ.US, DRIV.US, EVAV.US, FDRV.US HAIL.US, IDRV.US, ISELF.US, KARS.US, MOTO.US, TESL.US, TSLT.US, VCAR.US, XKST.US Lithium & Battery Tech (7): BATT.US, IBAT.US, ILIT.US, LIMI.US, LIT.US, LITP.US, WBAT.US Footnotes Here, carbon reduction is assumed as merely the substitution of high-carbon ETFs by low-carbon ETFs. This is not related to actual and measured CO 2 reduction. Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-8041599","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":540604946,"identity":"2d54cafd-a4ca-4f16-af12-893ce5295672","order_by":0,"name":"Thiago Gil","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA+UlEQVRIie2QsQrCMBBALzi4KF1Tqp/gJBTEih/i0i51cncQuVKIk7vO/oM4tgR0KbjWzeIPWHBQHDSpKC5tV8G84e4I97jcASgUvwglKJOIxAvSV+0FRUbtS8FwiUBlXaK8cibyeqYAFCp9w/fSyxiaqK2Q9zbWtDXjYsrEGuROaYS+0YigjTRBPopcakaOULbuCHM/5qChM3CQhkJhnJqBUIioCxT//lE6UtknpQrTU6loHnIilbhsSuywLmS7iCPPmauvYzHFLtiluhieDtfsYrvkeGOWZu6HyfE8sXIVSaUGD+jH9teTndP6hlxl1IKSNoVCofhbnncTZ/nDd93eAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0001-7192-7610","institution":"FGV EAESP","correspondingAuthor":true,"prefix":"","firstName":"Thiago","middleName":"","lastName":"Gil","suffix":""},{"id":540604947,"identity":"65229a76-1840-423c-b41e-c0e60373e035","order_by":1,"name":"Wesley Mendes da Silva","email":"","orcid":"","institution":"FGV EAESP","correspondingAuthor":false,"prefix":"","firstName":"Wesley","middleName":"Mendes da","lastName":"Silva","suffix":""}],"badges":[],"createdAt":"2025-11-05 20:17:12","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-8041599/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8041599/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":95526264,"identity":"721b7ab3-f3a7-4767-bedd-4f460ef05689","added_by":"auto","created_at":"2025-11-10 10:06:39","extension":"docx","order_by":0,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":80257,"visible":true,"origin":"","legend":"","description":"","filename":"CarbonBetaTemplatewithauthors.docx","url":"https://assets-eu.researchsquare.com/files/rs-8041599/v1/6db874fda086be978862a633.docx"},{"id":95388942,"identity":"a34c8023-4f1a-4e0f-a9ac-3fc8d9eb3c63","added_by":"auto","created_at":"2025-11-07 13:35:56","extension":"json","order_by":1,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":342,"visible":true,"origin":"","legend":"","description":"","filename":"rs8041599.json","url":"https://assets-eu.researchsquare.com/files/rs-8041599/v1/e9cdb5db7ce8ae0a0c9a51c0.json"},{"id":95388945,"identity":"65309c3b-6b32-475a-a607-519db402e2b9","added_by":"auto","created_at":"2025-11-07 13:35:56","extension":"xml","order_by":2,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":142117,"visible":true,"origin":"","legend":"","description":"","filename":"rs80415990enriched.xml","url":"https://assets-eu.researchsquare.com/files/rs-8041599/v1/6c5e8f066d3e6eb53f8053f4.xml"},{"id":95388946,"identity":"b16aa7c0-3ecc-46a5-8b9a-8779650d9cca","added_by":"auto","created_at":"2025-11-07 13:35:56","extension":"xml","order_by":3,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":138913,"visible":true,"origin":"","legend":"","description":"","filename":"rs80415990structuring.xml","url":"https://assets-eu.researchsquare.com/files/rs-8041599/v1/cca6f5e685dd06e73e669472.xml"},{"id":95388944,"identity":"c453a742-2217-45c2-886a-47a405e96ba5","added_by":"auto","created_at":"2025-11-07 13:35:56","extension":"html","order_by":4,"title":"","display":"","copyAsset":false,"role":"acdc-reference","size":152472,"visible":true,"origin":"","legend":"","description":"","filename":"earlyproof.html","url":"https://assets-eu.researchsquare.com/files/rs-8041599/v1/967e7a65693bc42fc9eab153.html"},{"id":95530883,"identity":"81a78025-fbfb-418e-b6d5-db3481152601","added_by":"auto","created_at":"2025-11-10 10:22:18","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":838826,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8041599/v1/56e27df1-12a7-4323-8572-375be51c58a0.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003eMeasuring and Hedging Carbon Risk with Tradeable Factors: Evidence from ETF Carbon Betas\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eInvestors increasingly recognize that climate transition risk can affect asset prices through policy, technology, and demand channels. Yet the operational question facing practitioners is not merely whether carbon risk is priced, but how to measure it consistently and hedge it in real portfolios. Much of the existing work evaluates carbon exposure with firm-level emissions, sustainability policies, or decarbonized index constructs that are informative but not directly tradeable. As a result, asset managers lack a standardized, market-based tool for diagnosing carbon risk and a clear playbook for implementing hedges at scale.\u003c/p\u003e\u003cp\u003eThis paper addresses both gaps. We build a tradeable carbon factor from liquid carbon-allowance ETFs that proxy the major compliance markets. We then embed this factor in an extended Fama\u0026ndash;French setting to estimate carbon betas for a broad ETF universe, using HAC-robust inference and rolling windows to capture time variation. Focusing on ETFs\u0026mdash;rather than single names\u0026mdash;reduces idiosyncratic noise, maps cleanly to investable sleeves (high- vs. low-carbon strategies), and mirrors how institutions implement tactical allocations.\u003c/p\u003e\u003cp\u003eOur empirical design targets three questions. First, do financial assets exhibit systematic exposure to a market-priced carbon factor? Second, can investors engineer target carbon exposures in long-only portfolios by tilting across high- and low-carbon universes? Third, what are the risk\u0026ndash;return trade-offs and implementation frictions of such hedges?\u003c/p\u003e\u003cp\u003eWe find that high-carbon ETFs have, on average, larger and more frequently significant carbon betas than low-carbon ETFs, confirming that carbon risk is an identifiable covariation component. However, when we construct portfolios to reach specified decarbonization levels through linear interpolation between the two universes, realized carbon betas fail to meet targets and, at times, exceed the exposure of the brown benchmark. The mechanism is straightforward: both sleeves retain positive loadings on the carbon factor, so reweighting alone cannot drive portfolio beta to low or neutral levels. Over our sample, low-carbon tilts also outperform on a risk-adjusted basis, implying a negative in-sample carbon premium\u0026mdash;but this performance benefit does not equate to effective hedging because exposure targets are missed.\u003c/p\u003e\u003cp\u003eThese results deliver three contributions. Measurement: we provide a standardized, market-priced carbon metric\u0026mdash;carbon beta\u0026mdash;estimated within a familiar multi-factor framework. Validation: we document economically non-trivial cross-sectional dispersion in carbon betas, especially across clearly interpretable ETF cohorts. Implementation: we demonstrate that simple green tilts are insufficient to achieve low or zero carbon exposure and that direct hedging (short overlays in carbon ETFs/futures or assets with negative carbon betas) is required to attain precise targets. The evidence reframes carbon-aware portfolio construction as an exercise in factor engineering under constraints, not merely re-labeling sector tilts.\u003c/p\u003e\u003cp\u003eThe remainder of the paper presents the literature review; methodology (factor construction, estimation, portfolio design, and LLM-assisted, taxonomy-constrained ETF sector/thematic labeling); reports cross-sectional and portfolio-level results with robustness checks; and discusses implications for asset allocation, risk management, and policy.\u003c/p\u003e"},{"header":"2. Literature Review","content":"\u003cp\u003eThe carbon beta concept builds on the theoretical foundations established by Markowitz (\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e1952\u003c/span\u003e), who introduced modern portfolio theory, and later developed by Sharpe (\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1964\u003c/span\u003e) and Lintner (\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e1965\u003c/span\u003e) into the Capital Asset Pricing Model (CAPM) framework, while introducing environmental considerations into the risk-return relationship. It can be traced to the work of G\u0026ouml;rgen et al. (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), who proposed measuring the carbon financial risk of equities through their sensitivity to a brown-minus-green (BMG) risk factor. This approach parallels the traditional asset pricing models of Fama and French (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e1992\u003c/span\u003e), later extended by Carhart (\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e1997\u003c/span\u003e) to include momentum factors and by Fama and French (2015) to incorporate profitability and investment factors, extending multi-factor models to incorporate climate-related systematic risk factors.\u003c/p\u003e\u003cp\u003eResearchers have long recognised that climate-related risks can influence asset prices, yet early work focused primarily on measuring firms\u0026rsquo; physical carbon footprints and linking emissions to firm value. Aggarwal and Dow (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2011\u003c/span\u003e) document that greenhouse-gas mitigation efforts are associated with higher firm valuations, while Cheng et al. (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2014\u003c/span\u003e) show that better environmental disclosure improves access to finance. Policy-oriented studies explore how carbon regulation can affect competitiveness and investment decisions (Antimiani et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Blyth et al., \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). These strands of literature view carbon risk largely as a firm-specific characteristic rather than a systematic factor.\u003c/p\u003e\u003cp\u003eOther work has examined ways to hedge climate risk using financial instruments. Andersson, Bolton and Samama (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) propose a decarbonised index that reduces carbon exposure while maintaining market-like risk\u0026ndash;return characteristics, and Balcilar et al. (\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) study risk spillovers between energy and carbon markets. Reports by the Carbon Tracker Initiative (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) warn of stranded assets in fossil-fuel-heavy industries, highlighting the need for investors to manage transition risk. These studies underscore that carbon risk can be priced and potentially hedged but stop short of constructing a tradeable risk factor.\u003c/p\u003e\u003cp\u003eArkoun et al. (\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) proposed a time-varying estimation model to assess the dynamics of carbon risk, arguing that carbon beta should not be considered constant over time as originally suggested, as companies' exposure to climate risks evolves with regulatory changes, technological developments, and market conditions. Chenet et al. (\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) demonstrated how climate risks can be incorporated into asset pricing models through perturbation methods, deriving rules for optimal risk-adjusted social cost of carbon that account for uncertainties in climate and economic factors.\u003c/p\u003e\u003cp\u003eThe seminal empirical work by Bolton and Kacperczyk (\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) provided definitive evidence for the existence of a carbon premium in financial markets. Using a comprehensive dataset of U.S. and global firms, they demonstrated that stocks with higher total CO2 emissions earn higher returns after controlling for size, book-to-market, momentum, and other factors. Their global analysis across 77 countries confirmed that carbon-intensive firms command a risk premium, with the premium varying based on countries' climate policy stringency and economic development levels.\u003c/p\u003e\u003cp\u003eThe empirical literature on carbon exposure has produced mixed findings regarding the pricing of climate risks in financial markets. Engle et al. (\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) found evidence that carbon-intensive firms exhibit higher systematic risk exposure, supporting the theoretical predictions of carbon beta models. Their research demonstrated that investors require a positive, although small, climate risk premium for holding \u0026lsquo;brown\u0026rsquo; assets. However, Battiston et al. (2021) presented a meta-analysis showing that while there is no consensus on the existence of a carbon premium in stock prices, the literature increasingly supports the view that carbon risk is a priced factor in financial markets.\u003c/p\u003e\u003cp\u003eCarbon exposure can also be perceived from a risk management angle. Research by Roncalli et al. (\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) demonstrated that incorporating carbon risk factors into portfolio optimization can reduce both systematic and idiosyncratic risks, particularly during periods of climate-related policy uncertainty. Physical climate risks, including extreme weather events and chronic environmental changes, create direct impacts on asset valuations and corporate cash flows (Hsiang et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2017\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eMonasterolo and Battiston (\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) analyzed how climate stress tests and scenario analysis can quantify the transmission of climate risks through financial systems. Their Climate Extended Risk Model (CERM) demonstrated how climate-related factors can be integrated into traditional credit risk models to estimate incremental losses on loan portfolios. This approach has become increasingly important for banking institutions seeking to comply with regulatory requirements for climate risk disclosure.\u003c/p\u003e\u003cp\u003eThe NGFS (Network for Greening the Financial System) scenarios have provided standardized frameworks for assessing climate risks across different transition pathways (NGFS, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). These scenarios enable financial institutions to evaluate portfolio exposure to climate risks under various policy and technological development paths, supporting the practical application of carbon beta measures in risk management.\u003c/p\u003e\u003cp\u003eThe integration of carbon beta measures with broader ESG (Environmental, Social, Governance) investing frameworks has become a significant area of research. Pedersen et al. (\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2021\u003c/span\u003e) developed theoretical models showing how ESG preferences affect asset prices through multiple channels, including investor preferences, corporate cash flows, and risk exposure. Their equilibrium framework demonstrates that ESG-conscious investors' actions can generate positive social impact while potentially affecting investment returns.\u003c/p\u003e\u003cp\u003eResearch specific to carbon footprint optimization in portfolios has shown promising results. Andersson et al. (\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) demonstrated that carbon-efficient portfolio construction can achieve similar risk-return profiles to traditional portfolios while significantly reducing carbon intensity.\u003c/p\u003e\u003cp\u003eThe intersection of carbon beta measures with green finance instruments has created new opportunities for climate risk management and sustainable investment. Green bonds, specifically earmarked for climate and environmental projects, have demonstrated complex pricing relationships with conventional bonds, often exhibiting lower yields (greenium effect) at issuance (Zerbib, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e\u003cp\u003ePractical applications of carbon beta in portfolio management have evolved significantly, with institutional investors increasingly incorporating climate risk factors into investment processes. Research on minimum variance portfolio construction shows that incorporating carbon risk can reduce unrewarded financial risks while maintaining competitive risk-return profiles (Roncalli et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e\u003cp\u003eDespite significant progress in carbon research, several important gaps remain. The standardization of carbon risk measurement methodologies continues to present challenges, with different approaches producing varying results depending on data sources, calculation methods, and temporal frameworks. Moreover, most existing hedging approaches are theoretical; for instance, carbon transition risk is often proxied by firm-level emissions or corporate policies, and decarbonised indices or Brown-minus-Green factors are not directly tradeable\u003c/p\u003e\u003cp\u003eTo address these limitations, our paper moves beyond firm-level proxies and untradable constructs to propose a market-based, implementable framework for measuring and hedging carbon risk. We construct a tradeable carbon risk factor from carbon-allowance ETFs, integrate it into an extended Fama\u0026ndash;French model to estimate dynamic carbon betas for a broad ETF universe, and design portfolios that target specific decarbonisation scenarios through linear interpolation. This methodology not only standardises the carbon-risk metric\u0026mdash;because it relies on observable market prices rather than heterogeneous emissions data\u0026mdash;but also allows us to test the real-world feasibility of carbon hedging. The resulting portfolios reveal substantial tracking-error challenges, highlighting the complexities of implementing carbon-risk management in practice and underscoring the need for market-based tools to complement traditional, emissions-based research.\u003c/p\u003e"},{"header":"3. Methodology","content":"\u003cp\u003eThis study employs an empirical approach to investigate carbon risk exposure in financial markets and evaluate the effectiveness of carbon hedging strategies. Our methodology addresses three fundamental research questions: (1) Do financial assets exhibit systematic exposure to carbon risk factors? (2) Can investors effectively hedge carbon risk through portfolio construction? and (3) What are the risk-return implications of carbon hedging strategies?\u003c/p\u003e\u003cp\u003eOur research design follows a multi-stage approach. First, we construct a tradeable carbon risk factor from carbon allowance ETFs to serve as our primary measure of carbon risk exposure in financial markets. Second, we extend the Fama-French multifactor model to include our carbon risk factor, enabling us to isolate carbon-specific risk exposures from traditional systematic risk factors. Third, we develop a linear interpolation portfolio construction framework that creates portfolios with varying degrees of carbon risk exposure corresponding to different decarbonization scenarios. Finally, we evaluate portfolio performance using comprehensive risk-adjusted metrics and assess implementation challenges through tracking error analysis.\u003c/p\u003e\u003cp\u003eOur analysis employs a comprehensive dataset of exchange-traded funds (ETFs) spanning from October 2021 to July 2024. We collect daily price data, assets under management (AUM), and sector classifications from the EODHD financial database.\u003c/p\u003e\u003cp\u003eWe focus on ETFs rather than individual stocks for several methodological and practical reasons. First, ETFs provide diversified exposure to specific sectors or investment themes, reducing idiosyncratic noise that could obscure systematic carbon risk relationships. Second, ETF classification systems allow for clear delineation between high-carbon and low-carbon investment strategies based on underlying holdings. Third, ETFs are increasingly used by institutional investors for tactical allocation adjustments, making our results directly applicable to contemporary investment practice. Finally, the ETF structure facilitates the construction of implementable carbon hedging strategies that can be readily adopted by practitioners.\u003c/p\u003e\u003cp\u003eWe categorize ETFs into high-carbon and low-carbon exposure groups based on their underlying sector focus and investment objectives. To standardize sector and theme labels across a large ETF universe, we used a constrained large-language-model classification workflow built on Perplexity PRO. Each ETF (symbol\u0026thinsp;+\u0026thinsp;fund name) was submitted in batched prompts to the chat-completions API with a closed taxonomy covering broad sectors (e.g., Technology, Energy, Financial Services), granular industry slices (e.g., Semiconductors, Oil \u0026amp; Gas Midstream, Clean Energy, Carbon Credits \u0026amp; Decarbonization), factor/style buckets (e.g., Momentum, Low Volatility), geographic cohorts, and fixed-income segments (e.g., TIPS, High Yield Bonds, Green Bonds). The system message instructed the model to return exactly one category from this list and nothing else.\u003c/p\u003e\u003cp\u003eTo handle occasional off-list or ambiguous outputs, we implemented a nearest-match mapper that projects raw model answers onto the closest valid category in the taxonomy (string-token overlap), plus a keyword fallback heuristic keyed to fund names (e.g., \u0026ldquo;Treasury,\u0026rdquo; \u0026ldquo;Dividend,\u0026rdquo; \u0026ldquo;REIT,\u0026rdquo; \u0026ldquo;Emerging,\u0026rdquo; \u0026ldquo;Technology\u0026rdquo;) when the API rate-limited or failed; as a last resort, unresolved cases defaulted to the closest high-level bucket (conservatively Technology). A cache ensured identical inputs received identical labels across runs, preserving internal consistency. Post-processing included frequency diagnostics (category histograms) and spot checks of high-count and edge categories. Two caveats accompany the approach: (i) many ETFs have multi-sector exposures or thematic blends, while our procedure assigns a single primary label for tractability; and (ii) ETF mandates can evolve over time. Accordingly, the labels are used for descriptive stratification and control variables in the empirical sections, not as definitive GICS mappings. This LLM-assisted, taxonomy-constrained procedure delivers scalable, reproducible sector tags while minimizing subjective, manual curation.\u003c/p\u003e\u003cp\u003eHigh-carbon sectors include Energy, Oil \u0026amp; Gas Upstream, Oil \u0026amp; Gas Midstream, Oil Services, Materials, Utilities, Transportation \u0026amp; Logistics, and Industrials. Low-carbon sectors comprise Clean Energy, Low Carbon/Climate Action, Solar Energy, Wind Energy, Hydrogen \u0026amp; Fuel Cells, Green Bonds, Sustainable Infrastructure, Autonomous/Electric Vehicles, and Lithium \u0026amp; Battery Tech.\u003c/p\u003e\u003cp\u003eOur sample selection follows a multi-stage filtering process to ensure data quality and sufficient liquidity:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eMinimum of 300 daily observations with valid pricing data\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eAUM exceeding \u003cspan\u003e$\u003c/span\u003e50\u0026nbsp;million for low-carbon ETFs and \u003cspan\u003e$\u003c/span\u003e100\u0026nbsp;million for high-carbon ETFs\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eSuccessful data collection status in our database\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003ePositive trading volume and non-zero closing prices throughout the sample period\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThis filtering process yields a final sample of 190 ETFs: 120 high-carbon and 70 low-carbon ETFs, providing sufficient cross-sectional variation for robust statistical inference.\u003c/p\u003e\u003cp\u003eWe construct a carbon risk factor using three prominent carbon credit and carbon futures ETFs: KRBN.US (KraneShares Global Carbon Strategy ETF), KCCA.US (KraneShares California Carbon Allowance Strategy ETF), and KEUA.US (KraneShares European Carbon Allowance Strategy ETF). These ETFs provide direct exposure to major carbon pricing mechanisms including the EU Emissions Trading System and California Cap-and-Trade Program, capturing the primary channels through which carbon policy risk affects financial markets.\u003c/p\u003e\u003cp\u003eTo create a robust carbon risk factor, we implement a winsorization procedure (at the 1st and 99th percentiles) to control for extreme outliers that may distort the factor's properties. We then calculate a value-weighted carbon index using AUM as weights and apply rolling standardization using a 20-period window:\u003c/p\u003e\u003cp\u003eWe extend the traditional Fama-French five-factor model to include our carbon risk factor. For each ETF j, we estimate the following regression:\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:{R}_{j,t}-\\:R{F}_{t}=\\:{\\alpha\\:}_{j}+\\:{\\beta\\:}_{C,j}\\times\\:\\:CARBO{N}_{t}+\\:{\\beta\\:}_{MKT,j}\\times\\:\\:\\left(MK{T}_{t}-\\:R{F}_{t}\\right)+\\:{\\beta\\:}_{SMB,j}\\times\\:\\:SM{B}_{t}+\\:{\\beta\\:}_{HML,j}\\times\\:\\:HM{L}_{t}+\\:{\\beta\\:}_{RMW,j}\\times\\:\\:RM{W}_{t}+\\:{\\beta\\:}_{CMA,j}\\times\\:\\:CM{A}_{t}+\\:{\\epsilon\\:}_{j,t}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{R}_{j,t}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e-\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:R{F}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the excess return of ETF \u003cem\u003ej\u003c/em\u003e over the risk-free rate\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:CARBO{N}_{t}\\)\u003c/span\u003e\u003c/span\u003e is our constructed carbon risk factor\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:MK{T}_{t}-\\:R{F}_{t}\\)\u003c/span\u003e\u003c/span\u003e is the market excess return\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:SM{B}_{t}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:HM{L}_{t}\\)\u003c/span\u003e\u003c/span\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:RM{W}_{t}\\)\u003c/span\u003e\u003c/span\u003e, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:CM{A}_{t}\\:\\)\u003c/span\u003e\u003c/span\u003eare the Fama-French size, value, profitability, and investment factors\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C,j}\\)\u003c/span\u003e\u003c/span\u003e is the carbon beta, measuring ETF \u003cem\u003ej\u003c/em\u003e's sensitivity to carbon risk\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eWe employ Ordinary Least Squares (OLS) with Newey-West heteroskedasticity and autocorrelation consistent (HAC) standard errors to account for potential serial correlation and heteroskedasticity in residuals. The HAC estimator uses a maximum lag length of 5, following Newey and West (1987).\u003c/p\u003e\u003cp\u003eFor ETFs with sufficient observations (\u0026ge;\u0026thinsp;52 weekly or \u0026ge;\u0026thinsp;90 daily), we implement a rolling window estimation approach with window size \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:W=\\text{m}\\text{i}\\text{n}(52,t-1)\\)\u003c/span\u003e\u003c/span\u003e where \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:t\\)\u003c/span\u003e\u003c/span\u003e is the total number of observations. This approach captures time-varying risk exposures while maintaining statistical power.\u003c/p\u003e\u003cp\u003eGiven the large number of simultaneous hypothesis tests (190 ETFs), we apply the Benjamini-Hochberg (1995) false discovery rate correction to control for multiple testing bias:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{p}_{i}^{adj}=\\text{min}\\left(j\\ge\\:i,\\:{p}_{j}*\\:\\left(\\frac{m}{j}\\right)\\right)\\:\\:$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{p}_{i}^{adj}\\:\\)\u003c/span\u003e\u003c/span\u003eis the adjusted p-value for ETF j, and m is the total number of tests.\u003c/p\u003e\u003cp\u003eWe test the null hypothesis that carbon betas are equal across high and low carbon ETF groups using Welch's unequal variance t-test. Additionally, we employ the Mann-Whitney U test as a non-parametric alternative to assess distributional differences in carbon betas.\u003c/p\u003e\u003cp\u003eBased on the estimated carbon betas, we construct portfolios with varying degrees of carbon risk exposure corresponding to different decarbonization scenarios. We create carbon-hedged portfolios by solving the following optimization problem:\u003cdiv id=\"Equ3\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ3\" name=\"EquationSource\"\u003e\n$$\\:\\underset{w}{\\text{min}}CVa{R}_{\\alpha\\:\\left({R}_{p}\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e3\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eSubject to:\u003cdiv id=\"Equ4\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ4\" name=\"EquationSource\"\u003e\n$$\\:{\\sum\\:}_{i=1}^{N}{w}_{i}=\\:1\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(budget\\:constraint\\right){w}_{i}\\ge\\:\\:0\\:\\:\\forall\\:i\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(long-only\\:constraint\\right){\\left|\\left|w\\:-\\:{w}^{0}\\right|\\right|}_{2}\\le\\:\\:\\delta\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(tracking\\:error\\:constraint\\right){\\beta\\:}_{C\\left(w\\right)}\\le\\:\\:{\\beta\\:}_{C}^{target}\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\:\\left(carbon\\:beta\\:constraint\\right)$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e4\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:CVa{R}_{\\alpha\\:\\left({R}_{p}\\right)}\\)\u003c/span\u003e\u003c/span\u003e is the conditional value-at-risk at confidence level \u003cem\u003eα\u003c/em\u003e\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:w\\)\u003c/span\u003e\u003c/span\u003e is the base portfolio weight vector\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\delta\\:\\)\u003c/span\u003e\u003c/span\u003e is the maximum allowed tracking error\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C\\left(w\\right)}\\)\u003c/span\u003e\u003c/span\u003e is the portfolio carbon beta\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}^{target}\\)\u003c/span\u003e\u003c/span\u003e is the target carbon beta level\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eFollowing DeMiguel et al. (2009), we incorporate parameter uncertainty by replacing point estimates \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C,i}\\:\\)\u003c/span\u003e\u003c/span\u003ewith confidence intervals:\u003cdiv id=\"Equ5\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ5\" name=\"EquationSource\"\u003e\n$$\\:{\\beta\\:}_{C,i}\\in\\:\\:\\left[{\\widehat{\\beta\\:}}_{C,i}-\\:\\tau\\:\\:\\times\\:\\:SE\\left({\\widehat{\\beta\\:}}_{C,i}\\right),\\:{\\widehat{\\beta\\:}}_{C,i}+\\:\\tau\\:\\:\\times\\:\\:SE\\left({\\widehat{\\beta\\:}}_{C,i}\\right)\\right]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e5\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere τ is the robustness parameter and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:SE\\left({\\widehat{\\beta\\:}}_{C,i}\\right)\\)\u003c/span\u003e\u003c/span\u003e is the standard error of the carbon beta estimate. We solve the worst-case optimization problem over this uncertainty set.\u003c/p\u003e\u003cp\u003eWithin this framework, the optimization problem is reformulated as a two-stage, worst‐case exercise. Rather than maximizing expected return (net of risk) at the single vector of point estimates, the decision‐maker assumes that each true carbon beta may lie anywhere within its prescribed confidence band. The inner problem identifies, for any given portfolio, the particular combination of true betas that minimizes performance.\u003c/p\u003e\u003cp\u003eFrom the betas, we then construct portfolios with different carbon reduction\u003ca class=\"FNLink\" href=\"#Fn1\" id=\"#FNLinkFn1\"\u003e\u003c/a\u003e targets:\u003c/p\u003e\n\u003ch3\u003e• 20% reduction: = 0.8 × \u003c/h3\u003e\n\u003cdiv class=\"Heading\"\u003e\u0026bull; 20% reduction: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}^{target}\\)\u003c/span\u003e\u003c/span\u003e = 0.8 \u0026times; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{H}\\)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\n\u003ch3\u003e• 50% reduction: = 0.5 × \u003c/h3\u003e\n\u003cdiv class=\"Heading\"\u003e\u0026bull; 50% reduction: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}^{target}\\)\u003c/span\u003e\u003c/span\u003e= 0.5 \u0026times; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{H}\\)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\n\u003ch3\u003e• 80% reduction: = 0.2 × \u003c/h3\u003e\n\u003cdiv class=\"Heading\"\u003e\u0026bull; 80% reduction: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}^{target}\\)\u003c/span\u003e\u003c/span\u003e= 0.2 \u0026times; \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{H}\\)\u003c/span\u003e\u003c/span\u003e\u003c/div\u003e\n\u003ch3\u003e• 100% reduction: = 0\u003c/h3\u003e\n\u003cdiv class=\"Heading\"\u003e\u0026bull; 100% reduction: \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}^{target}\\)\u003c/span\u003e\u003c/span\u003e= 0\u003c/div\u003e\u003cp\u003ewhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{H}\\)\u003c/span\u003e\u003c/span\u003e is the carbon beta of the base brown (high-carbon) basket portfolio.\u003c/p\u003e\u003cp\u003eOur portfolio construction methodology relies on a linear interpolation approach between high-carbon and low-carbon ETF universes to achieve target carbon exposures. The fundamental assumption underlying this approach is that portfolio carbon betas can be expressed as a weighted average of constituent universe betas:\u003cdiv id=\"Equ6\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ6\" name=\"EquationSource\"\u003e\n$$\\:{\\beta\\:}_{C}^{target}={w}_{H}\\times\\:\\:{\\stackrel{-}{\\beta\\:}}_{H}+\\:{w}_{L}\\times\\:\\:{\\stackrel{-}{\\beta\\:}}_{L}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e6\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{H}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{w}_{L}\\)\u003c/span\u003e\u003c/span\u003e are the weights allocated to high and low carbon universes\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{\\beta\\:}}_{H}\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\stackrel{-}{\\beta\\:}}_{L}\\)\u003c/span\u003e\u003c/span\u003e are the mean carbon betas of high and low carbon ETF universes\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThe target carbon beta represents our desired level of carbon risk exposure for each portfolio, corresponding to specific carbon reduction strategies. Using linear interpolation between high-carbon ETFs\u0026rsquo; betas and low-carbon ETFs\u0026rsquo; betas, we calculate the precise weights needed to hit specific carbon exposure levels. For instance, reducing the carbon exposure by 50% would imply finding a 50% lower beta by adding low-carbon investments in the portfolio.\u003c/p\u003e\u003cp\u003eRealized Beta is what we actually measure when we regress each constructed portfolio's returns against the carbon factor. This is the portfolio's true carbon sensitivity based on its observed performance, not our theoretical calculation. The difference between the target carbon beta we intended to achieve through portfolio construction and the realized carbon beta is what we call tracking error.\u003c/p\u003e\u003cp\u003eIn the context of carbon risk management, this deviation is particularly critical because it reveals whether portfolio construction methodologies can successfully implement intended carbon reduction strategies. When portfolios systematically exhibit higher carbon exposure than targeted it indicates a fundamental breakdown in the factor targeting mechanism, suggesting that simple linear interpolation approaches are insufficient for managing complex, time-varying risk factors like carbon exposure.\u003c/p\u003e\u003cp\u003eThe portfolio performance is evaluated using multiple risk-adjusted metrics:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eSharpe Ratio:\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv id=\"Equ7\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ7\" name=\"EquationSource\"\u003e\n$$\\:S{R}_{p}=\\frac{\\left({\\mu\\:}_{p}-\\:RF\\right)}{{\\sigma\\:}_{p}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{p}\\)\u003c/span\u003e\u003c/span\u003e is the standard deviation of returns.\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eSortino Ratio:\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv id=\"Equ8\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ8\" name=\"EquationSource\"\u003e\n$$\\:Sortin{o}_{p}=\\frac{\\left({\\mu\\:}_{p}-\\:RF\\right)}{{\\sigma\\:}_{p}^{-}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e8\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\sigma\\:}_{p}^{-}\\:\\)\u003c/span\u003e\u003c/span\u003eis the downside standard deviation calculated using only negative returns.\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eCalmar Ratio:\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003cdiv id=\"Equ9\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ9\" name=\"EquationSource\"\u003e\n$$\\:Calma{r}_{p}=\\frac{{\\mu\\:}_{p}}{\\left|MD{D}_{p}\\right|}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e9\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:MD{D}_{p}\\)\u003c/span\u003e\u003c/span\u003e is the maximum drawdown.\u003c/p\u003e\u003cp\u003eFor risk management considerations, we build the Value-at-Risk (VaR) framework. Using historical simulation, the α-level VaR is:\u003cdiv id=\"Equ10\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ10\" name=\"EquationSource\"\u003e\n$$\\:Va{R}_{\\alpha\\:}=\\:-{F}_{R}^{\\left(-1\\right)\\left(\\alpha\\:\\right)}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e10\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{F}_{R}^{\\left(-1\\right)}\\)\u003c/span\u003e\u003c/span\u003e is the inverse cumulative distribution function of portfolio returns.\u003c/p\u003e\u003cp\u003eThe Conditional Value-at-Risk (CVaR) is defined as:\u003cdiv id=\"Equ11\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ11\" name=\"EquationSource\"\u003e\n$$\\:CVaR\\_\\alpha\\:\\:=\\:E\\left[{R}_{p}\\right|\\:{R}_{p}\\le\\:\\:-VaR\\_\\alpha\\:]$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e11\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWe conduct several robustness checks to ensure our findings are not driven by outliers or sample composition effects:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eOutlier Exclusion: Re-estimate all tests excluding ETFs with carbon betas in the top and bottom 5% of the distribution\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eSignificance Filter: Restrict analysis to ETFs with statistically significant carbon betas (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05)\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eModel Fit Filter: Include only ETFs with above-median R-squared values to ensure adequate factor model specification\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eWe test alternative carbon factor constructions including equal-weighted carbon factors, principal component approaches using carbon ETF returns, and alternative winsorization thresholds to ensure our results are not sensitive to specific methodological choices.\u003c/p\u003e\u003cp\u003eOur linear interpolation approach assumes that portfolio carbon betas aggregate linearly from constituent ETF betas. This assumption may be violated when: (1) individual ETF-carbon factor relationships exhibit time-varying heteroskedasticity, (2) cross-correlations between ETFs and the carbon factor change over time, or (3) the carbon factor itself displays regime-switching behavior. These limitations motivate our comprehensive tracking error analysis and suggest avenues for future methodological improvements using optimization-based approaches.\u003c/p\u003e\u003cp\u003eThis methodology differs from the one proposed by G\u0026ouml;rgen et al. (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). They derive a carbon risk score from company-level CO₂-equivalent emissions and ten qualitative environmental-agenda indicators. Firms are sorted into high- and low-carbon portfolios based on this score, and a Brown-minus-Green (BMG) factor is built as a long\u0026ndash;short stock portfolio. In contrast, this study constructs a tradeable carbon factor from carbon-allowance ETFs. This factor proxies carbon price risk rather than firm-level carbon intensity and is a value-weighted index based on ETF assets under management.\u003c/p\u003e"},{"header":"4. Results","content":"\u003cp\u003eTable\u0026nbsp;1 reports cross-sectional summaries of the estimated carbon betas (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e). The mean \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e for the high-carbon group is 0.0015, compared with 0.0008 for the low-carbon group. A Welch two-sample t-test yields t\u0026thinsp;=\u0026thinsp;2.018, p\u0026thinsp;=\u0026thinsp;0.045, indicating statistical significance at the 5% level. A non-parametric Mann\u0026ndash;Whitney U test, however, fails to reject equality of distributions (p\u0026thinsp;=\u0026thinsp;0.417), highlighting substantial overlap between groups.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;1. Cross-Sectional Carbon Betas \u0026ndash; High vs. Low Carbon ETF Groups\u003c/p\u003e\u003cp\u003e\u003cem\u003eLow N ETFs is the number of funds with valid regressions; Mean/Median\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e₎ are the cross-sectional average and median loadings on the carbon factor (the OLS coefficient on CARBON in weekly regressions); Std. Dev., Min, Max\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e₎ describe the dispersion and range of those loadings; Sig. Count and Sig. % report how many (and what share) of ETFs have\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003estatistically different from zero at the 5% level (two-sided, HAC errors); Sig. Count (BH) and Sig. % (BH) apply the same threshold after Benjamini\u0026ndash;Hochberg FDR correction; Mean R\u0026sup2; is the average regression fit; Positive\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003cem\u003e% is the share of ETFs with\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003e0; the Difference column is High minus Low (percentages shown in percentage points).\u003c/em\u003e\u003c/p\u003e\u003cp\u003ePanel A: Summary Statistics\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMetric\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHigh Carbon\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLow Carbon\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eDifference\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eN ETFs\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e120\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e50\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMean \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.001531\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.000894\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.000636\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMedian \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.000987\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.001027\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026ndash;0.000039\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eStd. Dev. \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.002389\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.001906\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.000483\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMin \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u0026ndash;0.002267\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u0026ndash;0.006509\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.004241\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMax \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.010388\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.008145\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.002243\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSig. Count\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSig. %\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e41.67%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e8.57%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e33.10 p.p.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSig. Count (BH)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e23\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026mdash;\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSig. % (BH)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e19.17%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e1.43%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e17.74 p.p.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMean R\u0026sup2;\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.56\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.55\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.01\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePositive \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e67.50%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e80.00%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u0026ndash;12.50 p.p.\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ePanel B: Group-Mean Equality Tests\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e\u003ccolgroup cols=\"4\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTest\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eStatistic\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003ep-value\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eSig. (5%)\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWelch t-test\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e2.018\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.045168\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eYes\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMann\u0026ndash;Whitney U\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e4497\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.417432\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eNo\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eEconomic magnitude is modest but non-negligible. Converting to annualized terms, the carbon beta differential translates to 331 basis points annually, representing material exposure that significantly exceeds typical transaction costs and risk management thresholds. This finding indicates that carbon risk represents a systematic factor with economically meaningful implications for portfolio returns.\u003c/p\u003e\u003cp\u003eModel fit is comparable across cohorts. Average R\u0026sup2; is 0.565 for high-carbon ETFs and 0.559 for low-carbon ETFs, suggesting that adding the carbon factor does not differentially improve explanatory power across groups, but does capture a systematic covariation component.\u003c/p\u003e\u003cp\u003eOut of 120 high-carbon ETFs, 50 (41.7%) exhibit \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e estimates significant at the 5% level; only 6 of 70 (8.6%) low-carbon ETFs meet this criterion. After controlling for false discovery using Benjamini\u0026ndash;Hochberg, the shares fall to 19.2% (23/120) and 1.4% (1/70), respectively. Thus, while many raw p-values are below 0.05, a nontrivial subset still survives standard multiple-testing corrections in the high-carbon group, whereas almost none do in the low-carbon set.\u003c/p\u003e\u003cp\u003eDirectionally, 67.5% of high-carbon ETFs have positive \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e, and so do 80.0% of low-carbon ETFs\u0026mdash;their loadings are simply smaller. Only 20% of the latter have negative exposure.\u003c/p\u003e\u003cp\u003eSectoral breakdowns (Table\u0026nbsp;2) present more insights. Within the high-carbon universe:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eOil \u0026amp; Gas Upstream (N\u0026thinsp;=\u0026thinsp;15) displays the largest average exposure (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e = 0.0052, p\u0026thinsp;\u0026lt;\u0026thinsp;0.001), with 86.7% of constituents significant.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eOil \u0026amp; Gas Midstream (N\u0026thinsp;=\u0026thinsp;11) and Energy (N\u0026thinsp;=\u0026thinsp;25) also load significantly (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\:\\)\u003c/span\u003e\u003c/span\u003e\u0026asymp; 0.0023\u0026ndash;0.0028).\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eMaterials and Utilities have near-zero average \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\:\\)\u003c/span\u003e\u003c/span\u003eand low significance rates.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eTransportation/Logistics and Industrials show slightly negative but statistically insignificant mean betas.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eInterestingly, traditional high-carbon sectors such as Materials and Utilities show minimal carbon sensitivity, while Transportation \u0026amp; Logistics and Industrials exhibit slightly negative mean betas. This heterogeneity suggests that carbon risk exposure varies significantly even within sectors commonly classified as carbon-intensive.\u003c/p\u003e\u003cp\u003eIn the low-carbon group, mean betas are positive across most categories:\u003c/p\u003e\u003cp\u003e\u003cul\u003e\u003cli\u003e\u003cp\u003eClean Energy (N\u0026thinsp;=\u0026thinsp;14): \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e = 0.0018, p = 0.0002, with 21% individual significance.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eSustainable Infrastructure and Low Carbon / Climate Action also show small but positive and often significant exposures.\u003c/p\u003e\u003c/li\u003e\u003cli\u003e\u003cp\u003eNiche segments (Wind, Hydrogen, Lithium/Batteries) have small samples and low power; their mean betas are positive but insignificant.\u003c/p\u003e\u003c/li\u003e\u003c/ul\u003e\u003c/p\u003e\u003cp\u003eThe low-carbon universe displays more modest but varied carbon exposures. Sustainable Infrastructure and Low Carbon/Climate Action showing positive betas contradicts the common assumption that sustainable investments provide carbon risk hedging.\u003c/p\u003e\u003cp\u003eTable\u0026nbsp;2. Sector-Level Mean Carbon Betas\u003c/p\u003e\u003cp\u003e\u003cem\u003eN ETFs is the number of funds with valid regressions; Mean\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003eis the cross-sectional average loading on the carbon factor (the OLS coefficient on CARBON in weekly regressions; Sig. % reports how many (what share) of ETFs have\u003c/em\u003e \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e \u003cem\u003estatistically different from zero at the 5% level (two-sided, HAC errors); Mean R\u0026sup2; is the average regression fit.\u003c/em\u003e\u003c/p\u003e\u003cp\u003ePanel A: High-Carbon Sectors\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSector\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMean \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ep-val\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eSig%\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMean R\u0026sup2;\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOil \u0026amp; Gas Upstream\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.005208\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e86.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.410\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOil-Services\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e5\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.003565\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0232\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e60.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.537\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eEnergy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.002804\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e68.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.566\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eOil \u0026amp; Gas Midstream\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e11\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.002271\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.0000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e81.8\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.604\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMaterials\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e22\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.000122\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.6188\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e13.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.623\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eUtilities\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e17\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.000064\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.7379\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e5.9\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.416\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eTransportation \u0026amp; Logistics\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e10\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u0026ndash;0.000395\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.2724\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.626\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eIndustrials\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e15\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u0026ndash;0.000476\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.1461\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e26.7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.740\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003ePanel B: Low-Carbon Sectors\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabd\" border=\"1\"\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSector\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eN\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eMean \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003ep-val\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eSig%\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eMean R\u0026sup2;\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHydrogen \u0026amp; Fuel Cells\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e2\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.002250\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.4485\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.478\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eWind Energy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e1\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001955\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003eNa\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003ena\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.443\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eClean Energy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e14\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001772\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0002\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e21.4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.441\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSolar Energy\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001437\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2283\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.392\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSustainable Infrastructure\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001282\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0121\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e28.6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.549\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLithium \u0026amp; Battery Tech\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e7\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.000556\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.2980\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.448\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eLow Carbon / Climate Action\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e19\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.000465\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0320\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e5.3\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.765\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eGreen Bonds\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e4\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.000332\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.0382\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.338\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAutonomous / Electric Vehicles\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e13\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.000309\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.7662\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.0\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.577\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eWe perform four robustness exercises (Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e3\u003c/span\u003e):\u003c/p\u003e\u003cp\u003eTo gauge how fragile the High\u0026ndash;Low carbon beta gap is to reasonable perturbations of the sample, we ran four complementary exercises:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eBaseline specification: Using the full set of estimated betas, the mean difference in carbon exposure is 0.0006 per week (High minus Low), with p\u0026thinsp;=\u0026thinsp;0.045. Statistically significant at 5%, but close to the cutoff.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eTrimming extreme betas (\u0026plusmn;\u0026thinsp;5% tails). Outliers can inflate both means and test statistics. After dropping the top and bottom 5% of \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e within each group, the gap falls to 0.0004 and the p-value drifts to 0.052. Two things are happening: the effect size is mechanically smaller because we removed some very large positive High-carbon betas; and the standard error increases slightly because we are working with fewer observations.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eKeeping only individually significant betas (p\u0026thinsp;\u0026lt;\u0026thinsp;0.05). Among ETFs where carbon exposure is estimated precisely, how different are the groups? The mean gap rises to 0.0015 with p\u0026thinsp;=\u0026thinsp;0.002. However, this result is not an independent test; it conditions on statistical significance ex post, which biases the sample toward large absolute betas (and especially large positive ones in the High-carbon cohort). So this check shows the signal is strong where it exists, but it cannot be used to claim the overall population difference is that large.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eHigh fit-quality subsample (R\u0026sup2; above the median\u0026thinsp;=\u0026thinsp;0.587). To mitigate noise from poorly explained return series, we keep only regressions with relatively high explanatory power. The mean difference is 0.0005 and p\u0026thinsp;=\u0026thinsp;0.080. In other words, when we insist on clean regressions, we still see a positive spread, but losing almost half the sample erodes statistical power enough that we cannot reject equality at 5%. This suggests some of the baseline significance comes from names with moderate fit quality\u0026mdash;which is not necessarily problematic, but worth noting.\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003eRobustness Checks on the High\u0026ndash;Low Carbon Beta Spread \u003cem\u003eHigh_N and Low_N are the numbers of ETFs remaining in each group after the indicated filter. Difference is the mean carbon beta spread ((High Carbon) \u0026minus; Low Carbon)) in weekly units. p-value comes from a two-sided Welch t-test on group means. \u0026ldquo;Exclude 5% tails\u0026rdquo; trims the top and bottom 5% of ithin each group. \u0026ldquo;ETFs with significant retains only funds whose individual is significant at 5% (HAC/Newey\u0026ndash;West errors). \u0026ldquo;High fit only\u0026rdquo; keeps regressions with R\u0026sup2; above the pooled median (0.587).\u003c/em\u003e\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"5\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSpecification\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eHigh_N\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eLow_N\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eDifference\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003ep-value\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBaseline (full sample)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e120\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.000636\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.045168\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eExclude 5% tails (both groups)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e108\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e62\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.000429\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.051648\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eETFs with significant \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e50\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e6\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.001508\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.002033\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eHigh fit only (R\u0026sup2; \u0026gt;median\u0026thinsp;=\u0026thinsp;0.587)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e70\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e25\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.000563\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.079748\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eAcross all perturbations, the High\u0026ndash;Low spread in carbon betas remains positive; what varies is the precision with which we can reject the null of no difference. Modest alterations in the retained sample\u0026mdash;e.g., trimming outliers, restricting to high-fit regressions, or conditioning on individually significant betas\u0026mdash;move the p-value across conventional thresholds (0.045 \u0026rarr; 0.052 \u0026rarr; 0.002 \u0026rarr; 0.080). Thus, while the qualitative pattern is stable, the statistical strength of the claim is sample-sensitive. This underscores the need for (i) longer time series, (ii) alternative constructions of the carbon factor, and/or (iii) panel estimators with appropriate fixed effects and clustered errors to consolidate inference.\u003c/p\u003e\u003cp\u003eUsing the estimated carbon betas, we constructed five portfolios with varying carbon risk exposures corresponding to different decarbonization scenarios. The baseline brown portfolio achieves a mean carbon beta of 0.001531, serving as our reference point for carbon risk exposure. Target portfolios are designed to achieve 20%, 50%, 80%, and 100% carbon reduction relative to this baseline.\u003c/p\u003e\u003cp\u003eIn theory, shifting weight toward the low-carbon sleeve should lower portfolio exposure to the carbon factor. Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows, in practice, that every decarbonized portfolio (20%, 50%, 80% reduction and \u0026ldquo;neutral\u0026rdquo;) ended up with a higher realized beta (\u0026asymp;\u0026thinsp;0.0016\u0026ndash;0.0017) than the brown benchmark (0.00152). The optimizer was forced to 100% low-carbon weight to chase deeper cuts, but because low-carbon ETFs still have positive carbon loadings, the target could not be met.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePortfolio Targets, Realized Carbon Betas, and Weights \u003cem\u003eThis table reports the ex-ante Target (the desired carbon-factor loading), the ex post Realized from regressing weekly excess returns on the CARBON factor, and the resulting Tracking Error (Realized minus Target). It also lists the portfolio weights\u003c/em\u003e w \u003cem\u003ein the High-Carbon and Low-Carbon ETF buckets (summing to 1). Because both sleeves exhibit positive carbon betas, reallocating toward Low-Carbon cannot drive to zero, so tighter targets translate into larger positive tracking errors.\u003c/em\u003e\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003ePortfolio\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eTarget \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003eRealized \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\beta\\:}_{C}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003eTracking Error\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003eHigh-Carbon w\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eLow-Carbon w\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eBrown (Base)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.001531\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001518\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026ndash;0.00001\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e1.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e20% Reduction\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.001225\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001595\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.000370\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.519\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.481\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e50% Reduction\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.000765\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001677\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.000912\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e80% Reduction\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.000306\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001677\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.001371\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCarbon Neutral\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e0.000000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.001677\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.001677\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.000\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e1.000\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe Brown (Base) portfolio generates an 8.92% annual return with the highest intended carbon exposure, while carbon-reduced portfolios achieve substantially higher returns (15.82% for 50% reduction and beyond). This finding, as per Table \u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e5\u003c/span\u003e, suggests that during our sample period, low-carbon investments outperformed their high-carbon counterparts.\u003c/p\u003e\u003cp\u003eAll risk-adjusted performance metrics favor carbon-reduced portfolios. The 50% Reduction portfolio achieves the highest Sharpe ratio (0.484), Sortino ratio (0.743), and Calmar ratio (0.507), substantially outperforming the Brown portfolio across all metrics. This superior performance occurs despite slightly higher volatility (21.14% vs. 20.00%), indicating that the return enhancement more than compensates for increased risk.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePortfolio Performance Metrics \u003cem\u003eAnnual Return is the geometrically annualized return over the sample; Annual Volatility is the standard deviation of weekly returns scaled by \u0026radic;52. Sharpe Ratio is excess return over volatility, while Sortino Ratio replaces total volatility with downside-only volatility. Calmar Ratio is annual return divided by the absolute Max Drawdown, which is the largest peak-to-trough loss observed.\u003c/em\u003e\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMetric\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBrown (Base)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e20% Reduction\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e50% Reduction\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e80% Reduction\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eCarbon Neutral\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAnnual Return\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e8.92%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e12.19%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e15.82%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e15.82%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e15.82%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eAnnual Volatility\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e20.00%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e19.37%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e21.14%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e21.14%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e21.14%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSharpe Ratio\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.204\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.363\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.484\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.484\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.484\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSortino Ratio\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.247\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.471\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.743\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.743\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.743\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCalmar Ratio\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e0.198\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e0.357\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e0.507\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e0.507\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e0.507\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMax Drawdown\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c2\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e\u003ccolgroup cols=\"1\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026ndash;21.02%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c3\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabf\" border=\"1\"\u003e\u003ccolgroup cols=\"1\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026ndash;20.44%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c4\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabg\" border=\"1\"\u003e\u003ccolgroup cols=\"1\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026ndash;21.26%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c5\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabh\" border=\"1\"\u003e\u003ccolgroup cols=\"1\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026ndash;21.26%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"left\" colname=\"c6\"\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabi\" border=\"1\"\u003e\u003ccolgroup cols=\"1\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003e\u0026ndash;21.26%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eThe Value-at-Risk analysis reveals modest differences across portfolios. The 5% VaR ranges from \u0026minus;\u0026thinsp;1.47% (Brown) to -1.81% (carbon-reduced portfolios), while 1% VaR varies from \u0026minus;\u0026thinsp;3.72% to -3.50%. Conditional Value-at-Risk shows more pronounced differences, with carbon-reduced portfolios exhibiting lower tail risk at the 1% level (-4.10% vs. -5.45% for Brown).\u003c/p\u003e\u003cp\u003eThe return distributions exhibit significant improvements in higher moments for carbon-reduced portfolios. Skewness increases from \u0026minus;\u0026thinsp;0.002 (Brown) to 0.804 (carbon-reduced), indicating more favorable return distributions. Kurtosis decreases from 14.287 to 9.112, suggesting reduced extreme event frequency in carbon-reduced portfolios.\u003c/p\u003e\u003cp\u003e\u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e\u003ccaption language=\"En\"\u003e\u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e\u003cdiv class=\"CaptionContent\"\u003e\u003cp\u003ePortfolio Risk \u0026amp; Tail Metrics \u003cem\u003eVolatility and Downside Vol. are total and downside (negative-return) standard deviations, respectively. VaR (x%) is the historical value-at-risk at the x% left tail of the weekly return distribution, and CVaR (x%) (expected shortfall) is the average loss conditional on breaching that VaR threshold. Skewness and Kurtosis summarize distributional asymmetry and tail thickness (kurtosis shown as excess unless noted). All figures are computed on weekly data and expressed in weekly percentage terms.\u003c/em\u003e\u003c/p\u003e\u003c/div\u003e\u003c/caption\u003e\u003ccolgroup cols=\"6\"\u003e\u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e\u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e\u003cthead\u003e\u003ctr\u003e\u003cth align=\"left\" colname=\"c1\"\u003e\u003cp\u003eMetric\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c2\"\u003e\u003cp\u003eBrown (Base)\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c3\"\u003e\u003cp\u003e20% Reduction\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c4\"\u003e\u003cp\u003e50% Reduction\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c5\"\u003e\u003cp\u003e80% Reduction\u003c/p\u003e\u003c/th\u003e\u003cth align=\"left\" colname=\"c6\"\u003e\u003cp\u003eCarbon Neutral\u003c/p\u003e\u003c/th\u003e\u003c/tr\u003e\u003c/thead\u003e\u003ctbody\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVolatility\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e20.00%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e19.37%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e21.14%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e21.14%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e21.14%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eDownside Vol.\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e16.50%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e14.95%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e13.76%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e13.76%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e13.76%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVaR (5%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u0026ndash;1.47%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u0026ndash;1.65%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026ndash;1.81%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026ndash;1.81%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026ndash;1.81%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCVaR (5%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u0026ndash;2.93%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u0026ndash;2.77%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026ndash;2.79%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026ndash;2.79%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026ndash;2.79%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eVaR (1%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u0026ndash;3.72%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u0026ndash;3.30%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026ndash;3.50%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026ndash;3.50%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026ndash;3.50%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eCVaR (1%)\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u0026ndash;5.45%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e\u0026ndash;4.69%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e\u0026ndash;4.10%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e\u0026ndash;4.10%\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e\u0026ndash;4.10%\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eSkewness\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e\u0026ndash;0.002\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e0.468\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e0.804\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e0.804\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e0.804\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003ctr\u003e\u003ctd align=\"left\" colname=\"c1\"\u003e\u003cp\u003eKurtosis\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e\u003cp\u003e14.287\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e\u003cp\u003e13.652\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e\u003cp\u003e9.112\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e\u003cp\u003e9.112\u003c/p\u003e\u003c/td\u003e\u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e\u003cp\u003e9.112\u003c/p\u003e\u003c/td\u003e\u003c/tr\u003e\u003c/tbody\u003e\u003c/colgroup\u003e\u003c/table\u003e\u003c/div\u003e\u003c/p\u003e\u003cp\u003eA significant implementation issue emerges in our portfolio construction: realized carbon betas deviate substantially from targets for carbon-reduced portfolios. While the Brown portfolio achieves its target (realized β\u0026thinsp;=\u0026thinsp;0.001518 vs. target β\u0026thinsp;=\u0026thinsp;0.001531), carbon-reduced portfolios exhibit higher realized betas than intended. This tracking error (ranging from 0.0004 to 0.0017) suggests limitations in our linear interpolation approach and highlights the challenges of implementing carbon risk management strategies in practice.\u003c/p\u003e\u003cp\u003eOur results provide mixed evidence on the existence of a carbon risk premium. While the cross-sectional analysis confirms that high-carbon ETFs exhibit higher carbon betas (supporting the factor validity), the portfolio analysis reveals that low-carbon investments generated superior returns during our sample period. This apparent contradiction suggests that:\u003c/p\u003e\u003cp\u003e\u003col\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eCarbon risk is a valid systematic factor - evidenced by significant cross-sectional variation in carbon betas\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eThe carbon risk premium was negative during 2021\u0026ndash;2025 - possibly due to strong ESG investment flows, regulatory support for clean energy, or superior fundamental performance of sustainable businesses\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003cspan\u003e\u003cli\u003e\u003cp\u003eImplementation challenges exist - evidenced by significant tracking errors in carbon beta targeting\u003c/p\u003e\u003c/li\u003e\u003c/span\u003e\u003c/ol\u003e\u003c/p\u003e\u003cp\u003eIf the hedge objective is a materially lower or zero carbon beta, tilting into green ETFs is insufficient. One needs either (i) assets with negative carbon betas or (ii) direct short positions in the carbon factor (e.g., carbon-credit ETFs/futures) to neutralize the exposure.\u003c/p\u003e"},{"header":"5. Discussion","content":"\u003cp\u003eG\u0026ouml;rgen et al. (\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2019\u003c/span\u003e) find that the BMG factor\u0026rsquo;s average return is negative (brown stocks underperform green stocks); they interpret this as evidence of a green premium and conclude that carbon transition risk does not command a positive risk premium. Our results similarly show that low-carbon ETFs outperform high-carbon ETFs, implying a negative carbon premium during 2021\u0026ndash;2024, but the mechanism differs: the outperformance can be attributed to ESG inflows and clean-energy rallies rather than the structural transition risk quantified in the BMG factor.\u003c/p\u003e\u003cp\u003eCrucially, what many investors implement in practice is a naive green tilt\u0026mdash;a long-only reweighting toward cleaner or greener assets\u0026mdash;rather than an explicit hedge of the carbon factor. This distinction matters because a green tilt changes portfolio composition but does not directly offset exposure to the priced carbon factor.\u003c/p\u003e\u003cp\u003eOur findings reveal that investors cannot effectively hedge carbon risk using green tilts or the closely related linear-interpolation portfolio construction methodologies. The tracking-error analysis demonstrates a systematic and substantial failure to achieve intended carbon-risk-reduction targets. While the Brown baseline portfolio successfully achieves its target carbon exposure (realized β\u0026thinsp;=\u0026thinsp;0.001518 vs. target β\u0026thinsp;=\u0026thinsp;0.001531), all carbon-reduced portfolios exhibit significantly higher realized carbon exposures than intended.\u003c/p\u003e\u003cp\u003eThe 50% reduction portfolio, designed to achieve a target beta of 0.000765, actually realizes a beta of 0.001677\u0026mdash;representing a 119% tracking error that results in higher carbon exposure than the baseline brown portfolio it was meant to improve upon. This is a hallmark of naive tilts: because both sleeves (high- and low-carbon universes) retain positive loadings on the carbon factor, any long-only convex combination places a floor on achievable exposure that is bounded away from zero and can even drift above the brown benchmark when betas are time-varying.\u003c/p\u003e\u003cp\u003eThis implementation failure becomes even more pronounced for aggressive targets. The Carbon Neutral portfolio, intended to achieve zero carbon exposure, realizes the same beta of 0.001677. These systematic tracking errors translate to substantial economic impacts, ranging from 192 basis points annually for the 20% reduction portfolio to 872 basis points for the Carbon Neutral strategy. In other words, including greener assets relabels exposure without neutralizing it: they import factor timing risk (through regime-dependent carbon betas) while leaving the sign of exposure unchanged. The magnitude and consistency of these tracking errors indicate that simple linear interpolation and long-only green building blocks are fundamentally inadequate for managing complex, time-varying risk factors like carbon exposure.\u003c/p\u003e\u003cp\u003eSuperficially, the results suggest that carbon-reduction strategies provide superior risk-adjusted returns, with the 50% reduction achieving an annual return of 15.82% and a Sharpe ratio of 0.484, substantially outperforming the Brown baseline portfolio\u0026rsquo;s 8.92% return and 0.204 Sharpe ratio. However, this apparent outperformance appears to be a period-specific return pattern.\u003c/p\u003e\u003cp\u003eThe superior performance of supposedly carbon-reduced portfolios reflects the outperformance of clean-energy and ESG-focused ETFs during our sample period (2021\u0026ndash;2024)\u0026mdash;a phase marked by regulatory support, strong ESG flows, and favorable sector dynamics\u0026mdash;rather than successful carbon-risk management. This regime created a negative carbon risk premium where intended lower carbon exposure coincided with higher realized returns.\u003c/p\u003e\u003cp\u003eRegardless of the performance, effective carbon hedging requires direct, tradeable offsets to the carbon factor (e.g., explicit short overlays in carbon futures/ETFs or allocating to assets with negative carbon betas) and optimization that controls factor-exposure precision, rather than relying on long-only reweighting. Consequently, investors should exercise caution in extrapolating these performance patterns across periods or regimes and should not conflate a na\u0026iuml;ve green tilt with a bona fide carbon hedge.\u003c/p\u003e"},{"header":"6. Conclusion","content":"\u003cp\u003eThis paper proposes and tests a market-based framework for carbon risk measurement and hedging. By constructing a tradeable carbon factor from carbon-allowance ETFs and embedding it in an extended Fama\u0026ndash;French model, we estimate carbon betas for a broad set of ETFs and show that high-carbon strategies exhibit materially higher exposure to the factor than low-carbon strategies. That cross-sectional evidence supports the interpretation of carbon risk as a priced covariation component.\u003c/p\u003e\u003cp\u003eHowever, implementation results caution against equating green tilts with effective hedging. Portfolios engineered via linear interpolation between high- and low-carbon sleeves systematically miss their target carbon exposures because both sleeves retain positive loadings. The resulting tracking error is economically meaningful and persists across targets, underscoring that long-only reweighting is not enough to achieve low or neutral carbon betas. While low-carbon allocations outperformed during the sample window, this outperformance reflects period-specific dynamics rather than successful risk neutralization.\u003c/p\u003e\u003cp\u003eFor practitioners, two implications follow. First, diagnostics should rely on market-priced measures (carbon betas) estimated with robust procedures, not only on emissions-based scores. Second, hedging requires instruments that can directly offset carbon factor exposure\u0026mdash;negative-beta assets or explicit short overlays in carbon futures/ETFs\u0026mdash;combined with optimization under estimation risk to control tracking error. For researchers, our results motivate deeper work on (i) alternative factor constructions and regime-sensitive specifications; (ii) panel estimators and longer samples to consolidate inference; and (iii) optimization approaches that jointly target return, risk, and factor exposure precision.\u003c/p\u003e\u003cp\u003eIn sum, we standardize measurement with observable prices, validate carbon risk as an economically relevant factor, and demonstrate the practical limits of na\u0026iuml;ve decarbonization tilts. Effective carbon risk management is feasible\u0026mdash;but only with tradeable hedges and portfolio engineering that explicitly controls the exposure to the carbon factor.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eAggarwal R, Dow S (2011) \u003cem\u003eGreenhouse gas emissions mitigation and firm value: A study of large North American and European firms\u003c/em\u003e. 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Science 356(6345):1362\u0026ndash;1369\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLintner J (1965) The valuation of risk assets and the selection of risky investments in stock portfolios and capital budgets. Rev Econ Stat 47(1):13\u0026ndash;37\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMarkowitz HM (1952) Portfolio selection. J Finance 7(1):77\u0026ndash;91\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMonasterolo I, Battiston S (2020) The EIRIN flow-of-funds behavioural model of green fiscal policies and green sovereign bonds. Ecol Econ 144:106728\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eNGFS (2021) NGFS climate scenarios for central banks and supervisors. Network for Greening the Financial System\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003ePedersen LH, Fitzgibbons S, Pomorski L (2021) Responsible investing: The ESG-efficient frontier. J Financ Econ 142(2):572\u0026ndash;597\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eRoncalli T, Le Guenedal T, Lepetit F, Roncalli T, Sekine T (2021) The market measure of carbon risk and its impact on the minimum variance portfolio. SSRN Electron J\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSharpe WF (1964) Capital asset prices: A theory of market equilibrium under conditions of risk. J Finance 19(3):425\u0026ndash;442\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eZerbib OD (2019) The effect of pro-environmental preferences on bond prices: Evidence from green bonds. J Banking Finance 98:39\u0026ndash;60\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAPPENDIX\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eList of ETF tickers per sector label\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e=== HIGH CARBON LABELS ===\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eEnergy (25): COAL.US, DBE.US, EINC.US, EIPX.US, ERNZ.US, FENY.US, FILL.US, FXN.US, ISRHF.US, IXC.US, IYE.US, NNPEF.US, NVIR.US, PBD.US, PSCE.US, PXI.US, RSPG.US, SMWFF.US, SPXE.US, SSGUF.US, TEMP.US, USAI.US, VDE.US, WEEI.US, XLE.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eOil \u0026amp; Gas Upstream (15): DBO.US, DRLL.US, FTXN.US, GUNR.US, GUSH.US IEO.US, OIH.US, OILK.US, OILT.US, PXE.US, UCO.US, UNG.US, USL.US, USO.US, XOP.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eOil \u0026amp; Gas Midstream (11): AMLP.US, AMZA.US, ATMP.US, ENFR.US, MLPA.US, MLPB.US, MLPD.US, MLPR.US, MLPX.US, TPYP.US, UMI.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eOil-Services (5): CRAK.US, IEZ.US, PXJ.US, USOY.US, XES.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eMaterials (22): BCIL.US, DMAT.US, FMAT.US, FTIF.US, FTRI.US, FXZ.US, IGE.US, IYM.US, MXI.US, NANR.US, NRES.US, PSCM.US, PYZ.US, REMX.US, RSPM.US, RTM.US, SSGWF.US, TINT.US, UYM.US, VAW.US, XLB.US, XME.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eUtilities (17): CHIU.US, CZAR.US, FUTY.US, FXU.US, IDU.US, ISSZF.US, JXI.US, PSCU.US, PUI.US, RSPU.US, SPWUF.US, ULTY.US, UPW.US, USUTF.US, UTES.US, UTSL.US, XLU.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eTransportation \u0026amp; Logistics (10): AIRL.US, BOAT.US, FTXR.US, IYT.US, JETS.US, JETU.US, SEA.US, SHPP.US, SUPL.US, XTN.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eIndustrials (15):, FXR.US, IDOWF.US, IMSXF.US, ITB.US IYJ.US, PRN.US, PSCI.US, RGI.US, RSPN.US, SSGXF.US, UXI.US, VIS.US, XLI.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e=== LOW CARBON LABELS ===\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eClean Energy (14): ACES.US, CATF.US, CNRG.US, CTEX.US, FRNW.US ICLN.US, IMSIF.US, KGRN.US, PBW.US, QCLN.US, RNRG.US, RNWZ.US, SULR.US, VCLN.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLow Carbon / Climate Action (19): CCSO.US, CRBN.US, EEMX.US, EFAX.US, EMCR.US, EMCS.US, ETHO.US, FCPI.US, INFL.US, KLMT.US, LCTD.US, LCTU.US, NZAC.US, PABD.US, PABU.US, SPYX.US, USCA.US, USCL.US, USNZ.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSolar Energy (3): RAYS.US, SOLR.US, TAN.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eWind Energy (1): FAN.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eHydrogen \u0026amp; Fuel Cells (2): EVHY.US, HYDR.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eGreen Bonds (4): BGRN.US, CCSB.US, DFSB.US, GRNB.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eSustainable Infrastructure (7): EFRA.US, GBLD.US, HSUN.US, INFR.US, NBET.US, RNEW.US, UPGR.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eAutonomous, Electric Vehicles (13): CARZ.US, DRIV.US, EVAV.US, FDRV.US HAIL.US, IDRV.US, ISELF.US, KARS.US, MOTO.US, TESL.US, TSLT.US, VCAR.US, XKST.US\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eLithium \u0026amp; Battery Tech (7): BATT.US, IBAT.US, ILIT.US, LIMI.US, LIT.US, LITP.US, WBAT.US\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e Here, carbon reduction is assumed as merely the substitution of high-carbon ETFs by low-carbon ETFs. This is not related to actual and measured CO\u003csub\u003e2\u003c/sub\u003e reduction.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Carbon, Climate Finance, Factor Models, ETF","lastPublishedDoi":"10.21203/rs.3.rs-8041599/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-8041599/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis paper develops a market-based, implementable framework to measure and hedge carbon risk. We construct a tradeable carbon factor from carbon-allowance ETFs and integrate it into an extended Fama\u0026ndash;French model to estimate dynamic carbon betas across a large cross-section of exchange-traded funds (ETFs). Using an ETF sample classified into high- and low-carbon universes, we document economically meaningful cross-sectional differences in exposure to the carbon factor: high-carbon ETFs load more strongly on the factor than low-carbon ETFs. To standardize sector/thematic controls, ETFs are labeled with an LLM-assisted, taxonomy-constrained classifier, ensuring consistent category assignment at scale. We then design portfolios intended to target specific decarbonization scenarios via a simple linear interpolation scheme between the two universes. In implementation, realized carbon betas systematically miss their targets because both sleeves retain positive carbon loadings, producing persistent tracking error. Over the sample period, low-carbon allocations delivered superior risk-adjusted performance, implying a negative carbon premium in-sample, but this outperformance did not translate into effective hedging because target exposures were not achieved. Our findings (i) validate carbon risk as a priced covariation component, and (ii) show that na\u0026iuml;ve green tilts are insufficient to neutralize carbon exposure. The framework standardizes measurement with observable prices and surfaces practical constraints that matter for portfolio construction and risk management.\u003c/p\u003e","manuscriptTitle":"Measuring and Hedging Carbon Risk with Tradeable Factors: Evidence from ETF Carbon Betas","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-07 13:35:51","doi":"10.21203/rs.3.rs-8041599/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"20b1fdd7-8b22-4c0f-b657-6d354fd1b27f","owner":[],"postedDate":"November 7th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":57509676,"name":"Finance"},{"id":57509677,"name":"Finance"}],"tags":[],"updatedAt":"2025-11-07T13:35:51+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-07 13:35:51","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8041599","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8041599","identity":"rs-8041599","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}