[Paper Review] The Market Measure of Carbon Risk and its Impact on the Minimum Variance Portfolio

Théo Roncalli, Théo Le Guenedal+3 more|arXiv (Cornell University)|Jan 26, 2021

Climate Change Policy and Economics7 references5 citations

TL;DR

This paper proposes a market-based measure of carbon risk using time-varying carbon betas derived from a brown-minus-green (BMG) risk factor via Kalman filtering. It demonstrates that incorporating carbon beta constraints into minimum variance portfolios significantly alters portfolio construction, with relative carbon risk (negative beta) favoring green stocks and absolute carbon risk (zero beta) acting as a hedging strategy, while combining both approaches improves risk control beyond carbon intensity alone.

ABSTRACT

Like ESG investing, climate change is an important concern for asset managers and owners, and a new challenge for portfolio construction. Until now, investors have mainly measured carbon risk using fundamental approaches, such as with carbon intensity metrics. Nevertheless, it has not been proven that asset prices are directly impacted by these fundamental-based measures. In this paper, we focus on another approach, which consists in measuring the sensitivity of stock prices with respect to a carbon risk factor. In our opinion, carbon betas are market-based measures that are complementary to carbon intensities or fundamental-based measures when managing investment portfolios, because carbon betas may be viewed as an extension or forward-looking measure of the current carbon footprint. In particular, we show how this new metric can be used to build minimum variance strategies and how they impact their portfolio construction.

Motivation & Objective

• To develop a market-based measure of carbon risk that complements fundamental metrics like carbon intensity.
• To examine how carbon beta—defined as stock sensitivity to a BMG risk factor—affects minimum variance portfolio construction.
• To compare the impact of managing relative carbon risk (negative beta) versus absolute carbon risk (zero beta) in portfolio optimization.
• To assess the effectiveness of combining market-based carbon beta constraints with fundamental carbon intensity constraints in reducing portfolio carbon risk.
• To evaluate whether carbon beta constraints have a stronger impact on portfolio risk than carbon intensity constraints.

Proposed method

• Estimate time-varying carbon betas using a two-step approach: first, construct a BMG risk factor from firm-level carbon data; second, apply Kalman filtering to capture dynamic exposures.
• Formulate a two-factor minimum variance optimization model that includes equity risk and carbon risk, with constraints on carbon beta and weighted average carbon intensity (WACI).
• Implement portfolio optimization under two distinct carbon risk management objectives: (1) relative risk (negative beta) and (2) absolute risk (zero beta).
• Use the BMG risk factor as a proxy for systematic carbon risk, enabling the decomposition of carbon risk into systematic (beta) and idiosyncratic (specific) components.
• Compare portfolio allocations under different constraints using weight overlap (WO) metrics to assess changes in holdings when adding carbon beta constraints.
• Constrain the optimization using both WACI and BMG beta thresholds to evaluate the joint impact of fundamental and market-based carbon risk measures.

Experimental results

Research questions

• RQ1 How does a market-based carbon beta measure differ from fundamental carbon intensity in capturing equity price sensitivity to climate risk?
• RQ2 What is the impact of imposing a carbon beta constraint on minimum variance portfolio construction, and how does it compare to intensity-based constraints?
• RQ3 How do relative carbon risk (negative beta) and absolute carbon risk (zero beta) strategies differ in their portfolio allocation and risk exposure?
• RQ4 To what extent does managing carbon beta reduce portfolio carbon risk compared to managing carbon intensity alone?
• RQ5 Can combining market-based carbon beta constraints with fundamental WACI constraints lead to more robust carbon risk mitigation in minimum variance portfolios?

Key findings

• Carbon beta, estimated via Kalman filtering on a BMG risk factor, provides a dynamic, market-based measure of carbon risk that differs significantly from static carbon intensity metrics.
• Managing relative carbon risk by targeting negative carbon beta leads to a 75% average weight overlap with the WACI-optimized portfolio, indicating substantial rebalancing when adding beta constraints.
• The WACI constraint effectively reduces idiosyncratic carbon risk, while the beta constraint targets systematic carbon risk, showing that both are necessary for comprehensive risk control.
• When β_BMG+ is set to -20%, the portfolio’s carbon beta is constrained to -20%, but the WACI constraint remains binding only at lower thresholds (e.g., WACI+ ≤ 100), indicating limited overlap in risk reduction.
• Carbon beta constraints have a stronger impact on portfolio construction than carbon intensity constraints, but the reverse is not true—intensity constraints have minimal effect on beta exposure.
• Combining WACI and β_BMG constraints results in a more diversified and resilient portfolio, with 75% weight overlap on average, suggesting that dual constraints enhance risk mitigation without excessive turnover.