Measuring climate risk exposure with a flexible and readable metric: carbon beta

The reform of the Solvency II Directive, set to be enforced no later than January 30, 2027, introduces new sustainability-related risk requirements. These include (i) the creation of transition plans with quantifiable goals and processes to monitor and address financial risks from sustainability factors in the short, medium, and long term and (ii) an assessment of a company’s climate change-related risk exposure. In the absence of regulatory technical standards for assessing climate risk exposure materiality, insurers are exploring new models and tools.

One such approach is carbon beta, a flexible and interpretable tool based on market data, which can be used to assess the exposure of asset portfolios to the risks associated with climate transition. Empirical results for indices like the CAC 40, the STOXX Europe 600 and diverse equity portfolios have demonstrated the inter and intra-sector variability of the carbon beta, highlighting its relevance in managing transition risks for insurance companies.

1. A growing need to measure exposure to climate risk

Global warming, primarily caused by anthropogenic greenhouse gas (GHG) emissions, introduces new risks to society. Considering the broad economic implications of these risks, it is imperative for insurance and reinsurance companies to fully integrate them into their strategic planning. These companies have a critical role to play in:

• Directing capital towards sustainable investments;
• Anticipating and managing risks associated with sustainability issues, which are expected to grow in scale;
• Addressing new and evolving risks faced by their customers and adapting their insurance policies.

Physical and transition risks

It is well known that insurers and reinsurers face physical risks from direct losses due to extreme events like storms, floods, fires and heatwaves, as well as chronic climatic changes like rising temperatures and sea levels. Yet, the insurance industry is also significantly exposed to transition risks stemming from the economic and financial impacts associated with a transition toward a low-GHG-emission economy[1]. These transition risks include:

• Regulatory changes related to products or services deemed to have high GHG emissions, such as bans or taxes on certain emissions;
• Shifts in consumer behaviors toward more sustainable products and services;
• Technological advancements that substitute existing high-emission products and services with greener alternatives.

Solvency II requirements on climate risk integration in ORSA

Acknowledging the growing importance of climate risks, the European Insurance and Occupational Pensions Authority (EIOPA)[2] has issued specific recommendations to ensure climate risk is addressed in insurers’ Own Risk and Solvency Assessment (ORSA). These recommendations have been incorporated into the Solvency II revision, which will come into force no later than January 30, 2027. These recommendations suggest that insurance and reinsurance companies:

• Incorporate both short-term and long-term climate risks into their ORSA;
• Identify material exposures to climate risks using qualitative analyses;
• Supplement qualitative analyses with quantitative assessments when significant exposures are found. These should include at least two scenarios: one where global temperature rises exceed 2°C, and another where temperatures remain below this threshold (and preferably below 1.5°C).

Performing quantitative analyses poses substantial operational challenges, particularly due to the granularity at which shocks are applied (typically at a sectoral level) and the extended projection horizons required, which often go beyond standard business plans. Additionally, the methodology for qualitative analyses remains underdeveloped. While it is understood that climate risks must be integrated into risk mapping, questions arise about the most appropriate metrics to assess transition risk exposure.

2. Carbon beta: a market-based measure of exposure

The CARIMA (Carbon Risk Management) project and the research by Görgen et al. (2020) introduced the concept of carbon beta as a market-based metric for measuring an asset’s exposure to carbon risk, particularly its exposure to transition risk (e.g. an increase of carbon taxation). The advantage of this approach is that it exclusively uses market information, eliminating the need to gather specific data such as GHG emissions or rely on companies’ potential commitments to emission reduction targets.

Carbon beta measures the correlation between the return on a specific asset and the return on a benchmark portfolio known as the BMG (Brown-Minus-Green) portfolio. This correlation is controlled for other performance variables, meaning that it is measured as if all other performance variables were being held equal. The BMG portfolio comprises long positions in “brown” assets (high carbon-intensive) and short positions in “green” assets (low carbon-intensive).

The classification of assets into “brown” and “green” is determined using the BGS (Brown-Green Score). This score is derived from Environmental, Social and Governance (ESG) reporting data for a large number of companies (over 40,000 in the CARIMA project). Companies are ranked by their BGS: those below the 30th percentile are classified as “green,” while those above the 70th percentile are considered “brown.” Companies in the middle range (between the 30th and 70th percentiles) are excluded from the construction of the BMG portfolio.

Ranking of companies based on their BGS – source: Forvis Mazars study

In practice, BMG portfolio yields were available on the CARIMA project website. However, as this project is not funded anymore, the series has been discontinued. Other publications, such as Roncalli et al. (2020) or Huij et al. (2023), construct a portfolio equivalent to the BMG, but requiring fewer ESG variables and relying mainly on carbon intensity (representing the emissions produced per € of sales). Historical data for the yields of these portfolios are also available online.

Cumulative performance of the BMG – source: Huij et al. (2023)

Once the BMG factor is constructed, it is integrated into a linear regression explaining yields by market factors, as in the MEDAF / CAPM[3]:

Alternative specifications, including the market factors popularised by Fama & French[4] are also possible:

This coefficient can be estimated both for the portfolio as a whole and for each financial instrument.

Hereafter is how to interpretate the outcomes of the estimation:

• If the carbon beta is positive and high, the asset’s returns are highly positively correlated with those of the BMG. This suggests that the asset behaves more like “brown assets,” which are considered to be exposed to transition risk.
• If the carbon beta is negative and high, the asset’s returns are highly negatively correlated with those of the BMG. In this case, the asset is expected to behave more like “green assets,” which are likely to benefit from the transition.
• Otherwise, if the asset’s returns are uncorrelated with the BMG, exposure to transition risk is presumed to be low.

For instance, a carbon beta of 62% means that the asset’s returns increase by 62 basis points when BMG returns rise by 100 basis points. This corresponds to an improvement in “brown” asset yields or a degradation in “green” asset yields. The graph below illustrates the carbon beta for several companies in our database:

Carbon beta for a few companies from STOXX Europe 600

Carbon beta provides a qualitative assessment of an asset portfolio’s exposure to transition risk. This metric is simple to implement for monitoring purposes and it only depends on market data. It can also be integrated as a constraint into portfolio optimisation problems, enabling a more granular targeting of the most exposed investments.

Nevertheless, there are limitations to the use of the carbon beta: an asset with a low carbon beta could still be exposed to contagion risk if significant carbon taxation impacts the financial markets. Additionally, it is important to consider the time horizon factored into market expectations. This measure should therefore be supplemented with other metrics, such as “net zero metrics”, which assess the alignment between a company’s actual emissions and its reduction plans. The conclusions of analyses using the carbon beta can also be nuanced by comparing them to those drawn from non-financial reporting (e.g.  “Taxonomy” regulation, SFDR[5], etc.).

3. Practical application of carbon beta and lessons learned

We summarise here a study presented at the 2023 French Actuarial Congress. This study aimed at challenging empirical findings on the carbon beta measure. For this purpose, we calculate the carbon beta, first for the CAC40, then for an equity mutual fund from a bank-insurer (insurance and banking service providers within the same group).

These analyses confirmed empirical findings from the literature, such as:

• The inclusion of the BMG factor in the linear regression significantly improves the quality of the factor model, as evidenced by the reduction in Root Mean Square Error.
• The inter-sectoral variability of the carbon beta is noticeable: with sectors such as “materials”, “energy”, and “utilities” standing out as the most “brown”, while sectors like “information technology” and “financials” are classified as “green”. This is consistent with their lower direct emissions volumes.

Distribution of carbon beta by sector within a test portfolio – source: Forvis Mazars study

• The intra-sectoral variability of the carbon beta is significant: some sectors, particularly the energy sector, include both companies with the highest and lowest carbon betas. This finding is significant. Studies such as the ACPR’s[6] climate stress tests rely on sectoral classifications to apply shocks from transition scenarios. However, their approach may be too broad, potentially penalising assets that could be considered ‘green’ simply because they belong to a sector classified as ‘brown.’ This observation aligns with EIOPA’s conclusions in its December 2023 consultation[7], which noted that sector-based classification often fails to capture the specific transition risk characteristics of individual companies.
• Additionally, only a relatively small portion of assets—between 20% and 30%, depending on the case—have a carbon beta significantly different from zero.

This last finding evidences a significant limitation in the use of the carbon beta as a climate risk measure. Consequently, we conducted additional analyses, this time focusing on the STOXX Europe 600 index, a European index that replicates nearly 90% of the underlying market. We gathered the returns of all companies included in the index, ensuring a broad and diversified portfolio for our study.

The analysis confirmed the results regarding both the inter and intra-sectoral variability of the carbon beta, as well as the relevance of including the BMG factor in the model.

We then focused on identifying the cases for which the coefficient (i.e. the carbon beta) was significant. For carbon betas with an economically significant value, the majority (over 75%) of coefficients were indeed statistically significant.

This supports the value of carbon beta as a measure of exposure: it is statistically informative for high absolute values, i.e. for the “brownest” and “greenest” assets.

Carbon beta is set to play a significant role in tools designed to better measure climate risk. This indicator compensates for the lack of reliable ESG data by requiring market data production. Its flexibility and interpretability make it an ideal tool for managing an insurance company’s transition risks, as it can be used to communicate the overall exposure of an asset portfolio and target the most relevant asset lines. It also illustrates the limitations of the sectoral approach usually employed in climate stress-testing exercises. While it does have its limitations, such as the measurement of intra-sector contagion and the time horizon considered by the market, our initial analyses show that it is an indicator that seems robust and relevant within a risk management environment, provided it is supplemented by other analyses.

[1] There is a third category of risk, known as “liability risk”, representing the risk of a legal entity having to pay damages in the event of being held responsible for the consequences of global warming; [2] The EIOPA is a European Union financial regulatory institution, whose mission is defined as “protect[ing] the public interest by contributing to the short-, medium- and long-term stability, effectiveness and sustainability of the financial system for the Union’s economy, citizens and businesses.” This mission is pursued by “promoting a sound regulatory framework and consistent supervisory practices in order to protect the rights of policyholders, pension scheme members and beneficiaries and contribute to public confidence in the EU’s insurance and occupational pensions sectors”; [3] We denote rMkt(t) the returns at time t of the portfolio representing the entire market; [4] We recall that these factors are also constructed via the returns of the following long-short portfolios: Small Minus Big, representing the difference between small and large caps, High Minus Low, representing the difference between high and low book-to-market, Winner Minus Loser, representing the difference in “inertia” (cumulative return over the past year); [5] Sustainable Finance Disclosure Regulation; [6] Autorité de Contrôle Prudentiel et de Résolution: French insurance supervisor; [7] https://www.eiopa.europa.eu/consultations/consultation-prudential-treatment-sustainability-risks_en