The role of damage functions in assessing physical climate risks

Because physical risks are both uncertain and interlinked, one hazard can trigger cascading consequences. To better assess their exposure, investors are increasingly relying on physical risk damage functions within climate scenario modeling frameworks, to estimate potential losses and manage climate risks more effectively across both short and longer-term investment horizons. These models help them to consider not only for the potential impacts if such risks materialize, but also for how financial markets might respond to changes in the perceived likelihood of these events.

Understanding physical risk damage functions

In a simple context, physical risk damage functions quantify the relationship between climate variables, such as temperature, and resulting economic or physical damages. Different assumptions can be made about how damages evolve with rising temperatures -for example, a linear relationship implies a steady, proportional increase in damages, while an exponential one suggests that damages accelerate rapidly as temperatures rise, reflecting growing vulnerability or compounding effects.

Damage functions in the climate scenario analysis context

The most widely used forms incorporated in climate scenario analysis are quadratic and logistic models, each reflecting different assumptions about the escalation and adaptation to climate change. Quadratic models assume a gradual, accelerating relationship - e.g. damages increasing with the square of temperature rise, while logistic models reflect threshold effects, where impacts remain limited until a tipping point is reached, after which damages rise sharply.

The NGFS’ approach: Quadratic damage functions

The publicly available and most widely utilized Network for Greening the Financial System (NGFS) climate scenarios primarily employ quadratic damage functions, whereby economic damage increases with the square of the temperature rise. For instance, a 4°C increase results in four times the damage of a 2°C increase, indicating accelerating losses in a relative manner to warming temperatures. In their most recent Phase V update, the NGFS integrated additional climate stressors and lagged economic effects in comparison to the preceding Phase IV iteration by increasing projected physical damages by two to fourfold by mid-century. This adjustment delivers an overall increase in the damage assessment, seeking to address widespread criticism of the model’s underestimation of physical risks, but it fundamentally retains the quadratic function form and does not account for tipping-point dynamics.

The challenge with quadratic damage functions

The quadratic function’s main limitation is that it assumes a smooth and continuous increase in damages, without accounting for any sudden shifts or tipping points in climate impacts. This prevents it from capturing abrupt disruptions, such as those arising from tipping points, which are considered increasingly probable beyond 2°C of global warming¹. Additionally, it may misrepresent the magnitude of impacts if accelerants like tipping points are triggered. While it can adequately assess the impacts within the 1.5°C –2 °C warming range, quadratic damage functions risks significantly underestimating damages beyond this threshold.

The limiting threshold of quadratic damage functions under increasing climate change

The World Meteorological Organization (WMO) has confirmed that 2024 was the warmest year on record, reaching 1.55 °C above pre-industrial levels (1850–1900). ²This finding suggests that investors are approaching the upper bound of reliability for quadratic damage functions. Climate scenarios that simulate high levels of transition and decarbonization activity, limiting further additional warming to about 0.5°C by 2100, remain within the effective range of quadratic models for assessment. However, the reliability of quadratic functions fades in scenarios where warming is expected to exceed 2 °C due to less ambitious decarbonization efforts, and in turn, sees the emergence of non-linear impacts.

The Logistic Damage Function: An alternative to quadratic

The logistic (S‑curve) damage function, originally used for modeling population dynamics, captures three distinct phases of climate change and physical impacts: slow initial rise in damages, rapid escalation past a threshold, and eventual saturation. This model is well-suited to assess climate risk because it reflects thresholds where physical impacts remain modest until a threshold, followed by a sharp acceleration that mimics the impact of climate tipping points, such as the AMOC collapse. It also acknowledges saturation, recognizing that beyond certain levels, further temperature increases yield diminishing additional damages, either due to system collapse or economic breakdown. Logistic models also tend to lean towards higher GDP losses compared to quadratic functions, especially in higher-warming scenarios, reflecting tail risks and abrupt economic disruption.

Why is the logistic function more suitable for climate risk modeling?

Logistic damage functions offer a more realistic approach to modeling physical risk by incorporating climate change’s key characteristics. This includes threshold-triggered escalations, saturation effects that limit additional damages beyond collapse, and higher tail-risk estimates, far exceeding those observed by quadratic models.

As a comprehensive climate risk modeling framework relies heavily on the inclusion of a broad range of plausible climate scenarios, it is important that the chosen damage function is suitable for both lower warming scenarios (up to 2°C) and higher ones (over 2°C). This consideration effectively excludes quadratic functions and supports the use of a logistic damage function as the only appropriate option.

Logistic damage function limitations in an investment context

While the logistic damage function will more realistically simulate the overall physical impacts of climate change, its relatively simplistic application does limit its ability to account for crucial differences between the effects of chronic and acute physical risks. The steady, gradual progression of chronic risks can be reasonably captured by a single linear-type damage function. In contrast, the complex nature of acute physical risks, driven by compounding effects from both the increasing frequency and magnitude of extreme weather events, and further amplified by tipping points, warrants a more sophisticated non-linear damage function, such as the logistic, to adequately represent their impacts.

How do these limitations affect institutional investors? Can they be overcome?

From an investor’s perspective, these differences can have a material impact on the risk exposure of asset classes across a portfolio, as both geographical and sectoral characteristics influence perceived vulnerability and actual return outcomes. Thus, separating acute and chronic physical risk exposure using distinct models that reflect their specific characteristics, rather than modeling them jointly through a single logistic damage function, is a pragmatic approach that can provide more decision-useful insights to guide investment strategies and strategic asset allocation.

Is this approach available to investors?