💰 quantitative finance

Temperature Anomalies and Climate Physical Risk in Portfolio Construction

This paper investigates the negative impact of extreme temperature events on global equity sectors and introduces novel, time-varying metrics for climate risk exposure and volatility to enhance multi-objective portfolio optimization, demonstrating through backtesting that integrating these measures builds resilience to physical climate shocks without compromising diversification.

Original authors: Michele Azzone, Carlo Bechi, Gabriele Sbaiz

Published 2026-04-14

📖 5 min read🧠 Deep dive

CC0 1.0

Original authors: Michele Azzone, Carlo Bechi, Gabriele Sbaiz

Original paper dedicated to the public domain under CC0 1.0 (http://creativecommons.org/publicdomain/zero/1.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are the captain of a massive ship (your investment portfolio) sailing through the ocean of the global economy. For decades, you've navigated using a standard map that only shows you two things: how fast you can go (returns) and how rough the waves are (financial risk).

But recently, a new, invisible storm has been brewing: Climate Change.

This paper is like a new navigation manual for captains who want to steer their ships safely through these climate storms without slowing down too much. Here is the story of what the authors discovered, explained simply.

1. The Problem: The "Old Map" is Broken

Traditionally, investors looked at risk as if it were a calm, predictable lake. They assumed that if a storm hit one place, it wouldn't necessarily hit another.

However, the authors found that climate risk is not a calm lake; it's a chaotic, changing weather system.

The Evidence: They looked at temperature data from 1940 to 2025. It's like watching a thermometer that used to stay steady but is now shooting up. They proved that extreme heat events are becoming much more frequent and intense.
The Impact: When they checked the "financial weather report," they found that extreme heat acts like a heavy anchor. When temperatures get too high, stock prices for many companies (especially those with factories, farms, or stores) tend to drop. It's like a heatwave melting the ice cream in your truck; it hurts your business.

2. The New Tools: Two Special "Climate Thermometers"

The authors realized that old risk maps were too static. They were like a map that said, "France is risky," but didn't tell you when or how much.

So, they invented two new, dynamic tools to measure climate risk:

Tool #1: Climate Risk Exposure (The "Threat Level")
- Analogy: Imagine you are walking through a forest. This tool measures how likely it is that a tree will fall on you today.
- It calculates the probability of extreme heat happening in different parts of the world (continents) and weighs it by how much of your money is invested in companies that rely on physical things (like factories or land). If you own a lot of real estate in a place that is getting hotter, your "Threat Level" goes up.
Tool #2: Climate Exposure Volatility (The "Storm Surprise")
- Analogy: This measures how unpredictable the weather is.
- If you have investments in five different countries, and they all get hit by heatwaves at the exact same time, your portfolio gets shaken violently. This tool measures that "shaking." It asks: "If a heatwave hits Asia, will Europe also get hit?" If the answer is "Yes, they are linked," your portfolio is more volatile (shakier).

3. The Solution: A New Compass (Multi-Objective Optimization)

Usually, investors try to find the "perfect" balance between speed (returns) and safety (low risk). The authors added a third goal: Climate Safety.

They used a super-smart computer algorithm (called MOPSO, which acts like a swarm of intelligent birds searching for the best path) to find the best routes.

The Old Way: "Give me the fastest route, even if it's risky."
The New Way: "Give me a route that is fast, safe from normal waves, AND avoids the climate storms."

The result? They found a "Pareto Frontier." Think of this as a Goldilocks Zone. It's a set of portfolios where you can't get more safety without giving up some speed, and you can't get more speed without taking on more risk. But crucially, this zone now includes climate safety.

4. The Test Drive: Did it Work?

The authors ran a "test drive" (backtesting) from 2020 to 2025. They simulated investing with these new rules and compared it to traditional investing.

The Surprise: They found that you don't have to sacrifice your speed to be safe.
Portfolios that ignored climate risk and just chased the highest returns ended up crashing hard (like a car speeding into a wall).
Portfolios that balanced all three goals (Speed, Financial Safety, Climate Safety) performed better than the traditional ones. They had fewer "crashes" (drawdowns) and still made great money.

The Big Takeaway

Think of your investment portfolio like a house.

Traditional Investing builds a house that looks great and is cheap to build, but it's built on a floodplain with no drainage.
Climate-Aware Investing builds a house that is slightly more complex to design, but it has a raised foundation and a storm cellar.

The paper proves that building that "raised foundation" (accounting for temperature anomalies and asset vulnerability) doesn't make your house worse. In fact, when the flood comes (which it does, increasingly often), your house stands tall while the others wash away.

In short: You can build a portfolio that is resilient to the changing climate without losing your money. In fact, doing so might just save you from the biggest storms.

1. Problem Statement

The paper addresses the growing need for asset managers to incorporate physical climate risk (acute hazards and chronic shifts) into portfolio construction. While existing literature focuses heavily on transition risks or uses static country-level indices (e.g., ND-GAIN), there is a significant gap in dynamic, firm-specific quantitative metrics that capture:

The time-varying probability of extreme climate events.
The spatial correlation of these events across different geographic regions.
The specific vulnerability of firms based on their asset intensity and revenue geography.
The trade-offs between financial returns, market variance, and physical climate risk in a multi-objective optimization framework.

2. Methodology

The authors propose a three-stage framework:

A. Modeling Temperature Anomalies and Probabilities

Data Source: Monthly mean temperature data (1940–2025) for six continents (excluding Antarctica) from Our World in Data.
Anomaly Detection: A statistical detection method establishes a baseline (1960–1990). Monthly temperatures are standardized ( $Z_{k,t}$ ). An extreme event is defined as a standardized temperature exceeding a threshold of 2 ( $B_{k,t} = 1$ if $Z_{k,t} > 2$ ).
Probability Estimation: A logistic regression with a quadratic time trend is used to model the time-varying probability ( $p_{k,t}$ ) of an extreme event occurring in continent $k$ at time $t$ . This captures the non-stationary and accelerating nature of climate risk.
Spatial Dependence: The authors analyze the Pearson correlation between binary anomaly time series across continents. They verify these empirical correlations against Fréchet-Hoeffding bounds to ensure mathematical consistency for Bernoulli variables.

B. Impact on Equity Returns

Regression Analysis: The authors extend the Capital Asset Pricing Model (CAPM) by regressing sectoral excess returns against extreme temperature indicators ( $B_{k,t}$ ) for each continent.
Findings: Panel regressions with fixed effects confirm that extreme temperature anomalies exert a statistically significant negative effect on returns for most sectors (e.g., Chemicals, Food & Beverages, Real Estate). The global coefficient $\Gamma$ is negative and highly significant, validating physical risk as a systematic risk factor.

C. Novel Risk Metrics

The paper introduces two dynamic metrics to quantify portfolio exposure:

Climate Risk Exposure (CRE): The expected value of the portfolio's exposure to extreme events. It weights the time-varying probabilities ( $p_{k,t}$ ) by climate-normalized portfolio weights ( $\alpha_k$ ), which account for firm-level asset intensity and revenue geography.
$CRE(w, t) = \sum_{k=1}^{K} \alpha_k(w) \cdot p_{k,t}$
Climate Exposure Volatility (CEV): The variance of the portfolio's climate exposure. It captures the instability of risk and the systemic risk arising from correlations between continents.
$CEV(w, t) = \sum_{k=1}^{K} \alpha_k^2 Var(B_{k,t}) + 2 \sum_{k<j} \alpha_k \alpha_j Cov(B_{k,t}, B_{j,t})$
- This metric penalizes lack of geographic diversification and high correlation between extreme events.

D. Portfolio Optimization

Framework: A Multi-Objective Optimization problem is formulated to minimize three objectives simultaneously:
1. Negative Expected Return ( $-w^T r$ ).
2. Market Variance ( $w^T \Sigma w$ ).
3. Climate Exposure Volatility ($CEV(w)$).
Algorithm: The authors employ Multi-Objective Particle Swarm Optimization (MOPSO) to generate the Pareto frontier. This allows for the identification of non-dominated solutions where improving one objective (e.g., return) does not worsen the others without trade-offs.
Constraints: Long-only positions, full investment in risky assets.

3. Key Contributions

Dynamic Risk Metrics: Unlike static indices, the proposed CRE and CEV metrics are time-varying, incorporating the accelerating probability of extreme events and the specific asset intensity of firms.
Systemic Risk Quantification: The CEV metric explicitly models the systemic component of climate risk via inter-continental correlations, demonstrating that geographic diversification is crucial but limited by global correlation structures.
Empirical Validation of Physical Risk: The paper provides robust statistical evidence that temperature anomalies negatively impact sectoral returns, justifying their inclusion as a risk factor in asset pricing models.
Optimization Framework: It extends the traditional Mean-Variance paradigm to a three-objective framework (Return, Market Risk, Climate Risk), proving that climate resilience can be optimized without analytical intractability.

4. Results

Backtesting Performance (Jan 2020 – Apr 2025)

The authors conducted a rolling-window backtest comparing various strategies on the Pareto frontier against benchmarks (Market-Cap Weighted, Equally Weighted).

Risk Mitigation: Portfolios minimizing Climate Exposure Volatility (Min CEV) successfully reduced realized climate risk (lowest r-CEV and r-CRE) but exhibited higher market volatility and drawdowns compared to variance-minimizing portfolios.
Balanced Strategies: Strategies that balanced all three objectives (e.g., equal weights to Return, Variance, and CEV) achieved superior risk-adjusted returns.
- The (1/3, 1/3, 1/3) strategy achieved the highest CAGR (33.54%) with a Sharpe Ratio of 1.153.
- The (1/4, 1/2, 1/4) strategy (prioritizing variance minimization) offered the best compromise, yielding a high Sharpe Ratio (1.312) and a low Maximum Drawdown (20.78%).
Diversification Benefit: Incorporating CEV into the optimization increased the average number of active positions (from ~14 in standard Mean-Variance to ~22-55), indicating that the climate constraint forces the optimizer to avoid over-concentration in climate-vulnerable assets, thereby enhancing diversification.
No Performance Penalty: Contrary to the belief that ESG/climate constraints hurt returns, the study found that climate-aware strategies on the Pareto frontier often outperformed traditional benchmarks in terms of CAGR and drawdown control.

5. Significance

Practical Application: The paper offers a concrete, data-driven methodology for asset managers to construct climate-resilient portfolios that are not just "green" but financially robust against physical shocks.
Paradigm Shift: It challenges the assumption that climate risk is static or purely a transition issue, demonstrating that physical risk is a dynamic, non-stationary factor that must be modeled with time-varying probabilities.
Diversification Insight: The study highlights that while geographic diversification reduces idiosyncratic climate risk, the systemic correlation of climate events remains a critical constraint that must be managed through active portfolio optimization rather than passive aggregation.
Policy & Industry Impact: The results suggest that integrating physical climate risk metrics can serve as an effective diversification mechanism, potentially improving portfolio stability during extreme climate events without sacrificing long-term returns.