Analysing the volatility of financed emissions

In this post we analyse the variability profile of reported financed emissions of financial institutions such as banks. The discussion will concern primarily loan portfolios but similar considerations apply to other capital instruments. Our context are the so-called Scope 3 - Category 15 emissions under the terminology of the GHG Protocol, namely the emissions of the companies being financed by the loan portfolio.

Problem Statement

Reporting of financed emissions entails attributing (assigning) CO2 equivalent emissions to the lending or investment operations of a financial entity. The estimation and attribution of emissions for the wide range of instruments and types of financed companies is a topic of considerable complexity. We will use as a blueprint the widely adopted PCAF methodology, which, as we will see below, will be represented by one simple aggregation formula. Broadly speaking financed emissions attribution philosophies are based on the proportional share of financial products in the capital structure of the financed company. We will not dwell here on possible variations of implementation of this broader concept.

Reporting financed emissions is not a one-of exercise but a regular event. The outcomes will reflect the dynamic and uncertain nature of any economic activity. For the reports to serve their signaling role to internal and external stakeholders, any variability in period-on-period reports must be understood and explained - to the degree possible. The problem statement can be expressed as follows:

Given two sequential financed emissions reports (e.g., on two successive years), how do we explain the reported changes? How do we decompose, both qualitatively and quantitatively, the observed difference in total emissions into smaller intermediate changes that have defined, understood and homogeneous drivers?

The question is relevant both for internal management purposes and for external stakeholders reviewing such reports. This type of period-on-period analysis is the first step in assessing the climate risk inherent in a bank’s operations. The analysis we present is a component of a broader Sustainable Portfolio Management toolkit.

The first step is to catalog and understand the qualitative nature of any relevant change factors that are in operation and which potentially affect reported outcomes. Subsequently, we will see how to quantify them.

Qualitative factors behind period-on-period changes

As time evolves various developments will act in concert to modify the emissions profile of the portfolio. Let us enumerate the important qualitative dimensions by grouping them in four major categories:

• Portfolio Dynamics, the changing composition of the financial institutions portfolio, which can be the result of own decisions, scheduled actions, and unpredictable events.
• Economic Activity Developments resulting in actual changes in emitting activities
• Capital Structure Dynamics of the financed company
• Methodological Changes, measurement revisions etc.

Let us unpack these categories further one by one.

Portfolio Dynamics

The reported financed emissions of a portfolio are sensitive to divestment of assets, to new investments and other portfolio changes. E.g., a bank may show a material decline in portfolio emissions simply by selling off financial assets that have been attributed high-carbon estimates.

In more detail we can identify the following drivers as components of a changing investment portfolio:

• Old investments exiting the portfolio (either divested or matured naturally)
• New investments entering the portfolio (acquisitions, originations etc.)
• Existing investments changing in outstanding amounts. These changes can be either:
  • Scheduled changes (e.g. amortization)
  • Unscheduled changes (e.g., unexpected repayments or further draw-downs)

NB: Monitoring and explaining such portfolio changes is already part of general financial portfolio management, the task of explaining financed emissions simply call attention to isolating their impact in terms of emissions metrics.

Economic Activity Developments

The changing economic activities of the investee companies will modify the emissions profile attributed to investments to those companies. Such changes can be further decomposed into:

• Changing volumes of economic activity (measured in monetary and/or physical units): In other words, more or less goods and services produced, which correspondingly is attributed a different emissions quantum. This volatility may reflect strategy changes of the investee company, competition in the markets they operate, changing consumer preferences etc.
• Changes in the technologies used by the investee company to produce goods or services (e.g. decarbonisation), which will be reflected in the emission factors that are attached to each item in the portfolio.

Obviously this set of drivers is of critical interest from a sustainability perspective as it isolates the underlying economic behavior from other overlay effects.

Capital Structure Dynamics

Yet another driver of reported emissions change will be any capital structure changes of the investee company. This is a bit more esoteric, but it makes sense (and is unavoidable) in the context of the methodology. Namely, attribution methodologies like PCAF use an attribution factor that sizes the centrality of the role of the bank in financing the corporate entity. If that centrality increases or is reduced, then a larger or smaller fraction of the entity’s emissions is attributable to the bank. Depending on the precise inputs used for calculating that capital structure financing share, significant period-on-period changes in a company’s capital structure and/or market capitalization can shift reported emissions. Notably this can be the case even if the bank’s actual portfolio position and the company’s economic activities are entirely unchanged.

Methodology Factors

Finally, it would be expected that over time the data quality of reported emissions would improve. E.g., proxied (estimated) data might be replaced over time by verified emissions. This may prompt recalculations and materially different statements. There might be changes in scope or other methodological changes.

With a given taxonomy of change drivers, we are seeking to develop a type of waterfall diagram where the two period results are connected quantitatively, as per the hypothetical illustration below.

The starting period emissions are stated as 4000 million tonnes CO2e/year. The end period have increased to 7375 million tonnes CO2e/year. Management and external stakeholders are very keen to understand why this happened. By laying out the changes produced by all factors this is made explicit. But how do we compute those factors $F_{i}$? This is the topic of the next section.

Quantitative Formulation

Our starting point is the total financed emissions $E^{T}_{t}$ attributed to a portfolio of financial products, at some reporting time $t$. It is a scalar number expressing tonnes CO2e/year, where the observation period in question concerns the immediately previous period $(t-1,t)$.

We will work at the company level. There might be multiple financial products extended by the bank to the same company. We assume these have been consolidated into one overall item. The procedure can be refined at the product level.

The waterfall diagram can be expressed as the following equation:

$$ E^{T}_{t+1} = \sum_{a=1}^{f} F_a + E^{i}_{t} $$

where $F_a$ are the different contributions to the changing total. The total number is the simple sum of individually financed emissions $E^{i}_{t}$ attributed to each financed company $i$.

$$ E^{T}_{t} = \sum_{i=1}^{N(t)} E^{i}_{t} $$

where $N(t)$ is the number of financial products in the portfolio during that period.

Isolating portfolio composition changes

The first step is to separate from the variability calculus changes that are either automatic (deterministic) or due to decisions of the financial institution itself (hence presumably known). For example, the maturity profile (amortization) of the existing portfolio produces deterministic variation of financed emissions even if all other elements remain constant. The impact of new investments can similarly already be projected at the time of origination and hence need not come as a surprise.

To separate out these effects, the portfolio index running over investments can be decomposed into items that have left the portfolio (e.g., repaid as scheduled) at the end of the period (so will not be contributing to future emissions), items that are new and will only contribute in the next period and ongoing items. For simplicity, we assume all contracts have maturity that is a multiple of $\Delta t$ and new contracts are only created at the endpoints $t$, not in-between.

The total count of items $N(t)$ is ever-increasing. New portfolio additions are augmenting the list at the end. $N(t)$ can be decomposed on a running basis into three segments:

$$ (1, \ldots, O(t), \ldots, M(t), \ldots N(t)), $$

where

• $O(t)$ is the cumulative count of matured investments up to time $t-1$, hence their emissions no longer included in the portfolio
• $M(t)$ are additional items that matured during $(t-1, t)$, so their emissions are included
• $N(t)$ is the count of ongoing items.

New investments are entering the portfolio at this time, but their emissions will only be included at $t+1$. After the lapse of the period $(t, t+1)$, there will be a new total emissions profile at time $t+1$. Using the above index machinery this can be composed as follows:

$$ \begin{align} E^{T}_{t+1} & = \sum_{i=1}^{N(t+1)} E^{i}_{t+1} \\ & = \sum_{i=O(t+1)+1}^{N(t)} E^{i}_{t+1} + \sum_{i=N(t)+1}^{N(t+1)} E^{i}_{t+1} \\ & = \sum_{i=O(t+1)+1}^{N(t)} (E^{i}_{t+1} - E^{i}_{t}) + \sum_{i=O(t+1)+1}^{N(t)} E^{i}_{t} + \mbox{NE}_{t+1} \\ \end{align} $$

where $\mbox{NE}_{t+1}$ are emissions reported at time $t+1$ from new investments at time $t$.

On the other hand,

$$ \begin{align} E^{T}_{t} & = \sum_{i=1}^{N(t)} E^{i}_{t} \\ & = \sum_{i=O(t)+1}^{M(t)} E^{i}_{t} + \sum_{i=M(t)+1}^{N(t)} E^{i}_{t} \\ & = \mbox{DE}_{t} + \sum_{i=O(t+1)+1}^{N(t)} E^{i}_{t} \\ \end{align} $$

where $\mbox{DE}_{t}$ are emissions from matured investments at time $t$.

Substituting we get:

$$ \begin{align} E^{T}_{t+1} & = \sum_{i=O(t+1)+1}^{N(t)} (E^{i}_{t+1} - E^{i}_{t}) - \mbox{DE}_{t} + \mbox{NE}_{t+1} + E^{T}_{t} \\ \end{align} $$

This equation identifies the first three change factors for our waterfall diagram:

$$ \begin{align} F_1 & = - \mbox{DE}_{t} \\ F_2 & = + \mbox{NE}_{t+1} \\ F_3 & = + \Delta E^{T}_{t} \\ \end{align} $$

where

$$ \begin{align} \Delta E^{T}_{t} & = \sum_{i=O(t+1)+1}^{N(t)} (E^{i}_{t+1} - E^{i}_{t}) \end{align} $$

The Variability Formula

We have isolated the changes in the emissions profile that are not due to new and maturing investments. Now we are ready to explore factors of variability that are beyond the control of the portfolio manager and have to do with changing economic activities, capital structures and/or methodologies. For this task we will use the general attribution equation of PCAF type methodologies which reads as follows:

$$ E^{T}_{t} = \sum_{i}^{N} \frac{O^{i}_{t}}{V^{i}_{t}} G^{i}_{t} $$

The above equation expresses financed emissions using just three variables for each investment (financed company) in the portfolio.

This simplification is abstracting away the complexities of actual financial portfolios, the large variety of contracts, multiple contracts per client, complex cash flows, optionality, different types of economic activities measured differently

In detail, we have:

• $O^{i}_{t}$ the outstanding aggregated financed amount at time $t$
• $V^{i}_{t}$ the total economic value of the company at that time
• $G^{i}_{t}$ the absolute GHG emissions of the company during the period

While reported emissions per company may follow any of a number of methodologies, the typical methodology is linear in nature, computing emissions as the product of some economic activity and a corresponding effective emissions factor. Introducing the corresponding variables $A^{i}_{t}$ for activity and $f^{i}_{t}$ for the applicable effective emission factor (might be an average) we get:

$$ E^{T}_{t} = \sum_{i}^{N} \frac{O^{i}_{t}}{V^{i}_{t}} A^{i}_{t} f^{i}_{t} $$

At a subsequent period the total emissions will be given by the same aggregation, with an increment of the index to $t+1$, hence the delta we are interested to explain is:

$$ \begin{align} \Delta E^{T}_{t} & = \sum_{i}^{N} (\frac{O^{i}_{t+1}}{V^{i}_{t+1}} A^{i}_{t+1} f^{i}_{t+1} - \frac{O^{i}_{t}}{V^{i}_{t}} A^{i}_{t} f^{i}_{t}) \\ \end{align} $$

It is sufficient for our purposes to focus on first-order differences only. This means that all differences in the above formula are expanded:

$$ \begin{align} O^{i}_{t+1} - O^{i}_{t} & = \Delta O^{i}_{t} \\ V^{i}_{t+1} - V^{i}_{t} & = \Delta V^{i}_{t} \\ A^{i}_{t+1} - A^{i}_{t} & = \Delta A^{i}_{t} \\ f^{i}_{t+1} - f^{i}_{t} & = \Delta f^{i}_{t} \\ \end{align} $$

This linearisation of differences gives:

$$ \begin{align} \Delta E^{T}_{t} & = \sum_{i}^{N} (\frac{\Delta O^{i}_{t}}{V^{i}_{t}} A^{i}_{t} f^{i}_{t} - \frac{O^{i}_{t}}{(V^{i}_{t})^2} \Delta V^{i}_{t} A^{i}_{t} f^{i}_{t} + \frac{O^{i}_{t}}{V^{i}_{t}} \Delta A^{i}_{t} f^{i}_{t} +\frac{O^{i}_{t}}{V^{i}_{t}} A^{i}_{t} \Delta f^{i}_{t}) + F_c \\ & = \sum_{i}^{N} (\frac{\Delta O^{i}_{t}}{O^{i}_{t}} - \frac{\Delta V^{i}_{t}}{V^{i}_{t}} + \frac{\Delta A^{i}_{t}}{A^{i}_{t}} +\frac{\Delta f^{i}_{t}}{f^{i}_{t}}) E^{i}_{t} + F_c \\ & = F_O + F_V + F_A + F_f + F_c \end{align} $$

where $F_c$ is a closure term that expresses the non-linear (interaction) terms. The other factors capture respectively:

• $F_O$, the change due to changing notionals (scheduled or unscheduled)
• $F_V$, the change in value due to enterprise value changes
• $F_A$, economic activity volume changes
• $F_f$, emissions type changes (including possibly methodological)

This concludes our journey decomposing period-on-period emissions into contributing drivers. It is a-priory obviously not possible to determine which of the $F_a$ terms are dominant.