Lesson 4.4: Carbon Metrics and Climate Value-at-Risk

01

Overview

Where This Lesson Fits

This is the fourth of six lessons in Module 4: Green Finance Risk Management. Building on the scenario analysis tools from Lesson 4.3, this lesson teaches how to measure carbon exposure using financed emissions, WACI, and Climate Value-at-Risk.

Pedagogical arc: “Now measure the risk. Put numbers on the exposure.” Scenarios tell you WHAT might happen; carbon metrics tell you HOW MUCH you are exposed.

Learning Outcomes

Calculate financed emissions using PCAF attribution methodology
Compute Weighted Average Carbon Intensity (WACI) for multi-sector portfolios
Assess data quality using PCAF tier framework and gap-filling strategies
Derive Climate Value-at-Risk (CVaR) decomposed into physical and transition components
Apply carbon metrics to ASEAN banking portfolios with real-world data challenges

Prerequisites

Lesson 4.3 (Scenario Analysis and Climate Modeling) required. Lessons 4.1 (Climate Risk Taxonomy) and 4.2 (TCFD/TNFD Frameworks) recommended.

02

Slide Deck

Lecture Slides (33 Slides)

Download Slide Deck (PDF)

03

Foundation Level

GHG Protocol — Scope 1, 2, and 3

Three Emission Scopes

Scope 1 — Direct emissions: Emissions from owned or controlled sources (company facilities, vehicle fleet, on-site combustion)
Scope 2 — Indirect energy emissions: Emissions from purchased electricity, heating, and cooling
Scope 3 — Value chain emissions: All other indirect emissions across 15 categories, including Category 15: Investments — this is “financed emissions” for banks and investors

Why Scope 3 Dominates for Financial Institutions

For banks, Scope 3 Category 15 typically accounts for ~85% of total emissions. A bank’s own office electricity (Scope 2) is negligible compared to the emissions of the companies it lends to. This is why measuring financed emissions is the central challenge of carbon accounting in finance.

ASEAN ExampleVietnamese steel manufacturer: Scope 1 (blast furnace) ~60% of total, Scope 2 (coal-fired grid electricity) ~25%, Scope 3 (ore mining, transport) ~15%. For the bank lending to this company, all three scopes become part of its financed emissions.

Financed Emissions Formula

PCAF Attribution Formula

$$FE_i = \frac{Outstanding_i}{EVIC_i} \times Emissions_i$$

Components

$Outstanding_i$ = bank’s outstanding loan amount to borrower $i$
$EVIC_i$ = Enterprise Value Including Cash (total equity + total debt) of borrower $i$
$Emissions_i$ = borrower’s absolute GHG emissions (tCO₂e)

The fraction $Outstanding / EVIC$ is the attribution factor — it allocates the borrower’s emissions proportional to the bank’s financial exposure relative to the firm’s total financing.

Worked Example

Vietnamese steel company: $Outstanding = \$50M$, $EVIC = \$500M$, $Emissions = 200{,}000$ tCO₂e.

$$FE = \frac{50}{500} \times 200{,}000 = 0.10 \times 200{,}000 = 20{,}000 \text{ tCO}_2\text{e}$$

The bank is attributed 10% of the steel company’s emissions, proportional to its 10% share of financing.

Key InsightThe attribution factor ensures that if five banks each lend 20% of a firm’s capital, total attributed emissions equal 100% of the firm’s actual emissions — no double counting, no undercounting.

Weighted Average Carbon Intensity (WACI)

WACI Formula

$$WACI = \sum_i w_i \times \frac{Emissions_i}{Revenue_i}$$

Components

$w_i$ = portfolio weight of holding $i$ (fraction of total portfolio value)
$Emissions_i$ = absolute GHG emissions (Scope 1+2) of company $i$
$Revenue_i$ = total revenue of company $i$

WACI normalizes emissions by revenue, making it comparable across sectors and portfolio sizes. It is the TCFD-recommended metric for portfolio carbon intensity reporting.

Worked Example: 3-Company Portfolio

Company	Weight	Intensity (tCO₂e/$M)	Contribution
Power utility	40%	800	320.00
Manufacturer	35%	200	70.00
Tech firm	25%	15	3.75

Portfolio WACI = 320.00 + 70.00 + 3.75 = 393.75 tCO₂e/$M revenue

ASEAN BenchmarksTypical ASEAN bank portfolio WACI: ~394 tCO₂e/$M. Global average: ~280 tCO₂e/$M. Paris-aligned target: ~180 tCO₂e/$M. The gap reflects ASEAN’s coal-heavy energy mix and high-emission industrial base.

PCAF Data Quality Tiers

PCAF defines five data quality tiers, ranging from verified company data to broad sector averages:

Tier	Data Source	Uncertainty
Tier 1	Verified borrower-reported emissions	±10%
Tier 2	Unverified borrower-reported emissions	±20%
Tier 3	Estimated using physical activity data	±30%
Tier 4	Estimated using economic activity data	±40%
Tier 5	Sector average estimates	±50%

ASEAN Reality

~5% of ASEAN borrowers at Tier 1–2 (verified or self-reported)
~15% at Tier 3 (physical activity estimates)
~35% at Tier 4 (economic activity estimates)
~45% at Tier 5 (sector averages only)

Improvement pathway: mandatory corporate reporting → third-party verification → Tier 1 coverage across the portfolio.

ASEAN ContextWith ~80% of borrowers at Tier 4–5, ASEAN carbon metrics carry significant estimation uncertainty. This does not mean they are useless — even Tier 5 data reveals concentration risk and relative sector exposure.

Portfolio Alignment Tools

Three Complementary Tools

PACTA (Paris Agreement Capital Transition Assessment): Measures sector-level alignment with Paris decarbonization pathways. Assesses whether lending/investment portfolios are on track for Paris goals by comparing portfolio technology mix to sector benchmarks.
TPI (Transition Pathway Initiative): Dual assessment of management quality scoring and carbon performance benchmarking for listed companies. Rates companies on governance preparedness and emission trajectory.
SBTi (Science Based Targets initiative): Validates that corporate emission reduction targets are consistent with climate science. The Net Zero Standard requires near-term targets (5–10 years) and long-term net-zero commitment.

Key Insight

No single alignment tool is sufficient. Use PACTA for sector pathway alignment, TPI for individual company quality assessment, and SBTi for target validation.

ASEAN AvailabilityPACTA covers major ASEAN sectors (power, automotive, oil & gas). TPI assesses ~40 ASEAN-listed firms. SBTi has ~50 ASEAN corporate commitments. Coverage is improving but remains well below European levels.

04

Intermediate Level

PCAF Methodology per Asset Class

PCAF defines different attribution formulas for each asset class:

Asset Class	Attribution Formula	Key Variable
Corporate loans	Outstanding / EVIC × Emissions	Enterprise value incl. cash
Project finance	Outstanding / Total Project Cost × Project Emissions	100% of project emissions
Mortgages	Outstanding / Property Value × Building Emissions	Energy consumption data
Sovereign debt	PPP-adjusted GDP share × National Emissions	Government bond exposure

Critical Implementation Detail

Each asset class has different attribution logic and data sources. Using the wrong formula can cause 3× estimation error. For example, applying the corporate loan formula to project finance would understate emissions because project finance should attribute 100% of project emissions proportional to the financing share of total project cost.

ASEAN ContextMany ASEAN banks have large mortgage portfolios (30–40% of assets) but limited building energy data. Sovereign debt attribution requires national emissions inventories, which vary in quality across ASEAN member states.

Calculating WACI for an ASEAN Portfolio

Step-by-Step: 10-Borrower Portfolio

Collect emissions data: 4 out of 10 borrowers have verified data; 6 require estimates
Gap-fill: Use PCAF Tier 4–5 sector proxies from the PCAF emissions database for the 6 missing borrowers
Normalize FX effects: Convert all revenues and emissions to a common currency (USD) to avoid exchange rate distortion
Handle double counting: Identify shared borrowers and consortium loans; apply pro-rata attribution to avoid inflating portfolio totals
Calculate weighted sum: WACI = 394 ±28% (confidence interval reflects the mixed data quality across tiers)

Three Challenges

Gap-filling bias: Sector averages may overstate or understate emissions for individual borrowers
FX normalization: Revenue in local currency distorts intensity ratios when converted to USD
Double counting: Consortium loans and interbank exposures can inflate aggregate portfolio emissions

Result InterpretationWACI of 394 tCO₂e/$M significantly exceeds the Paris-aligned target of 180 tCO₂e/$M, indicating a substantial alignment gap. However, the ±28% confidence interval means the true value could range from ~284 to ~504.

Implied Temperature Rise (ITR)

What ITR Measures

ITR maps a portfolio’s carbon emissions trajectory to a temperature outcome: the global warming that would result if the entire economy had the same carbon trajectory as your portfolio.

Temperature Zones

Zone	ITR Range	Interpretation
<1.5°C	Paris-aligned	Portfolio consistent with strongest Paris goal
1.5–2.0°C	Well-below 2°C	Consistent with broader Paris Agreement range
2.0–3.0°C	Significant transition risk	Portfolio faces material repricing under policy tightening
>3.0°C	High physical risk	Portfolio exposed to severe climate damage

Typical ASEAN bank: ITR of ~2.5–3.2°C (mostly in the orange zone).

Limitations

Depends on scenario choice and sector pathway assumptions
Forward-looking credibility of corporate targets is uncertain
Aggregation across heterogeneous sectors introduces methodological noise

ASEAN Data Challenges

Four Structural Challenges

Low coverage: Only ~15% of ASEAN listed firms report verified GHG emissions. Unlisted firms (the vast majority of bank borrowers) report almost none.
Scope 3 near-zero: Almost no Scope 3 data is available for emerging market firms. This is critical because Scope 3 often exceeds Scope 1+2 combined.
Sector-proxy limits: Global sector average emissions may not reflect ASEAN-specific technology mixes (e.g., coal-dominated grids vs European gas/renewables).
Tier 4–5 reliance: ~80% of ASEAN portfolio emissions are estimated at the lowest quality tiers, introducing systematic uncertainty.

Pathways Forward

Mandatory reporting timelines: Vietnam, Thailand, and the Philippines are implementing phased disclosure requirements
Capacity building: Training borrowers to collect and report emissions data
Technology platforms: Satellite data, IoT sensors, and AI-assisted estimation for agriculture and land use
Regional collaboration: ASEAN Taxonomy and shared emissions databases across member states

Vietnam — Financed Emissions Decomposition

Bank Profile: $30B Total Loans

Sector	Loan Share	Amount ($B)	FE (tCO₂e)	FE Share
Agriculture	18%	5.4	810,000	38%
Coal	3%	0.9	360,000	17%
Manufacturing	15%	4.5	320,000	15%
Power	8%	2.4	280,000	13%
Real estate	20%	6.0	200,000	9%
Other	36%	10.8	163,000	8%

Key Insight

Coal is only 3% of loans but 17% of financed emissions (extremely high carbon intensity per dollar lent). Agriculture is 18% of loans and 38% of financed emissions (high exposure combined with moderate intensity). These disproportionate contributions drive the CVaR results explored in the PhD section.

05

PhD Extension

Climate Value-at-Risk (CVaR) Framework

Climate Value-at-Risk

$$CVaR = V_{t_0} - \mathbb{E}[V_{t_T} \mid \text{Scenario}]$$

Where $V_{t_0}$ is the current portfolio value and $\mathbb{E}[V_{t_T} \mid \text{Scenario}]$ is the expected future value under a specific climate scenario at time horizon $T$.

Three Key Differences from Standard VaR

Scenario-conditional: CVaR is computed under a specific climate scenario (e.g., NGFS Net Zero 2050), not from historical return distributions
Multi-decade horizon: Time horizons of 10–30+ years, versus 1–10 days for market VaR
Decomposable: CVaR splits into Physical CVaR + Transition CVaR, each with distinct drivers

CVaR Pipeline

Measure FE: Calculate financed emissions per borrower using PCAF formulas
Map to scenario: Select NGFS scenario and map to sector-level shocks
Estimate climate-adjusted PD: Apply scenario-driven PD shifts per borrower
Estimate LGD: Adjust LGD for physical damage and collateral impairment
Aggregate: Sum expected losses across all borrowers to get portfolio CVaR

Research QuestionHow sensitive is CVaR to the choice of climate scenario and time horizon? Does the ranking of portfolio sectors by CVaR contribution change between Net Zero 2050 and Hot House World?

Physical CVaR Calculation

Physical CVaR

$$\text{Physical CVaR} = \sum_i Exposure_i \times PD_i^{climate} \times LGD_i$$

Two Types of Physical Risk

Acute physical risks: Typhoons, floods, droughts, wildfires → sudden PD spikes and collateral damage
Chronic physical risks: Sea-level rise, average temperature increase, changing precipitation → gradual PD deterioration over years

Worked Example: Vietnamese Rice Farming

$Exposure = \$10M$ (outstanding agricultural loan)
$PD_{base} = 3\%$; $PD_{climate} = 10\%$ (climate-adjusted, +7 percentage points from Mekong Delta flooding/salinity intrusion)
$LGD = 65\%$ (high due to low insurance penetration and crop-specific collateral)

$$\text{Physical CVaR} = \$10M \times 0.07 \times 0.65 = \$455{,}000$$

The $\Delta PD = 7\%$ captures only the incremental default risk from climate change, not the baseline credit risk.

Research QuestionHow do acute versus chronic physical risks interact in compound climate events? For example, does a typhoon following a drought create nonlinear PD effects that exceed the sum of individual risk estimates?

Transition CVaR Calculation

Transition CVaR

$$\text{Transition CVaR} = \sum_i Exposure_i \times \Delta PD_i^{carbon\_tax} \times LGD_i$$

Three Transition Channels

Carbon pricing (direct cost): A carbon tax increases production costs for emission-intensive borrowers, compressing margins and raising default probability
Stranded assets (value write-down): Fossil fuel reserves and carbon-intensive infrastructure lose value as decarbonization accelerates
Technology shift (demand substitution): Competitive advantage shifts from fossil to renewable technologies, displacing incumbents

Worked Example: Vietnamese Coal Power

$Exposure = \$20M$ (project finance for coal plant)
$\Delta PD = +15$ percentage points under a $75/tCO₂ carbon tax scenario
$LGD = 55\%$ (moderate recovery from physical plant assets)

$$\text{Transition CVaR} = \$20M \times 0.15 \times 0.55 = \$1{,}650{,}000$$

Research QuestionAt what carbon price level does transition risk become systemic for ASEAN banking sectors? Is there a threshold beyond which correlated defaults in coal, cement, and steel could trigger a credit crisis?

Carbon Beta and Asset Pricing

Carbon Beta Model

$$R_i = \alpha + \beta_{mkt} R_m + \beta_{carbon} \times CI_i + \varepsilon_i$$

Where $R_i$ is the return on asset $i$, $R_m$ is the market return, and $CI_i$ is the carbon intensity of firm $i$.

Bolton & Kacperczyk (2021) Findings

$\beta_{carbon}$ is positive and statistically significant across US and global equities
Magnitude: ~1.2–1.8% annual return premium per standard deviation of carbon intensity
Interpretation: markets are beginning to price carbon risk, demanding higher returns from carbon-intensive firms

ASEAN Evidence

Preliminary analysis of ASEAN equities: $\beta_{carbon} = 0.023$ (t-stat = 3.2), $R^2 = 0.08$. The carbon premium exists in ASEAN but is weaker and noisier than in US/EU markets, consistent with lower data availability and less regulatory pressure.

Research QuestionIs the carbon premium driven by physical risk exposure, transition risk exposure, or investor preferences (divestment)? Can you disentangle the three channels using ASEAN data where physical and transition risk are relatively orthogonal?

Empirical Methods — Event Study and Difference-in-Differences

Event Study Design

Measure abnormal stock returns around carbon policy announcements. Example: Vietnam Green Finance Roadmap (2022). Estimation window: [-250, -30] trading days. Event window: [-5, +10] days. Test whether cumulative abnormal returns (CARs) differ between high-carbon and low-carbon firms.

Difference-in-Differences (DiD) Design

Treatment group: High-carbon firms (above median carbon intensity)
Control group: Low-carbon firms (below median carbon intensity)
Before/After: Pre- and post-policy announcement periods
Key assumption: Parallel trends — both groups would have followed the same path absent the policy

Key Reference

Sautner et al. (2023) construct a firm-level climate change exposure measure from earnings call transcripts, enabling event studies that distinguish between physical risk discussions and transition risk discussions.

Methodological Considerations

Parallel trends assumption must be tested and reported
Confounding events (market-wide shocks, industry regulation) must be controlled for
Sample selection: ASEAN equity markets have thinner trading and more noise than US/EU

Research QuestionCan we identify causal effects of climate disclosure mandates on bank lending behavior in ASEAN? Does mandatory carbon reporting change loan pricing, collateral requirements, or sector allocation?

06

Quantitative Lab

Lab: ASEAN Carbon Metrics Pipeline

Task:Build a complete carbon metrics pipeline for a synthetic 50-borrower ASEAN portfolio Method:Python (pandas, numpy, matplotlib, statsmodels) Output:Portfolio carbon dashboard with emissions waterfall, CVaR decomposition chart, and regression summary table

Step-by-Step Instructions

Generate synthetic portfolio: Create 50 borrowers with sector, country, loan size, and emissions attributes drawn from ASEAN sector distributions
Calculate financed emissions: Apply PCAF attribution formula per borrower: $FE_i = \frac{Outstanding_i}{EVIC_i} \times Emissions_i$
Compute portfolio WACI and ITR: Aggregate to portfolio-level Weighted Average Carbon Intensity and map to Implied Temperature Rise
Calculate Physical and Transition CVaR: Under Net Zero 2050 and Hot House World scenarios using climate-adjusted PD and LGD
Estimate carbon beta: Run OLS regression of synthetic historical returns on carbon intensity
Produce carbon dashboard: Emissions waterfall + CVaR decomposition + regression summary table

Python Pseudocode

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

np.random.seed(42)

n_borrowers = 50

# Step 2: Calculate financed emissions per borrower

df['attribution'] = df['outstanding'] / df['evic']

df['financed_emissions'] = df['attribution'] * df['emissions_tco2e']

# Step 3: Portfolio WACI

df['weight'] = df['outstanding'] / df['outstanding'].sum()

df['carbon_intensity'] = df['emissions_tco2e'] / df['revenue']

waci = (df['weight'] * df['carbon_intensity']).sum()

# Step 4: Climate Value-at-Risk

df['physical_cvar'] = df['exposure'] * df['delta_pd_physical'] * df['lgd']

df['transition_cvar'] = df['exposure'] * df['delta_pd_transition'] * df['lgd']

total_cvar = df[['physical_cvar', 'transition_cvar']].sum().sum()

Data Sources

PCAF Standard NGFS Scenario Explorer

07

Case Study: Vietnam — Financed Emissions of the Banking Sector

Context

The Vietnamese banking sector has total assets of approximately $700 billion, with ~18% exposure to agriculture and ~3% to coal and fossil fuels. The State Bank of Vietnam began implementing climate risk requirements following its 2022 Green Finance Roadmap. A representative Vietnamese bank with $30 billion in total loans serves as the case.

The Task

Calculate financed emissions for the bank, decompose by sector and scope, compute Physical versus Transition CVaR, and explain the agriculture-coal CVaR inversion.

Key Numbers Agriculture Physical CVaR = $281M (Exposure $5.4B × ΔPD +8% × LGD 65%)
Coal Transition CVaR = $74M (Exposure $0.9B × ΔPD +15% × LGD 55%)
Agriculture Physical CVaR is 3.8× larger than Coal Transition CVaR

Three Drivers of the CVaR Inversion

Exposure size: Agriculture loan book ($5.4B) is 6× larger than coal ($0.9B). Even with lower carbon intensity, the sheer volume of exposure dominates.
Physical vulnerability: Mekong Delta flooding and salinity intrusion directly destroy agricultural output, causing acute PD spikes.
Insurance gap: Agricultural insurance penetration in Vietnam is ~7%, meaning almost all physical losses are absorbed by borrowers (and their banks).

A fourth factor: agriculture is rarely subject to carbon pricing, so its transition risk is low — but its physical risk is extreme.

Discussion Questions

Why does loan exposure size matter more than carbon intensity for determining CVaR?
How would introducing a carbon tax on agricultural emissions change the CVaR comparison between agriculture and coal?
What role does insurance penetration play in determining Physical CVaR, and how would increasing coverage from 7% to 40% change the result?
How should a Vietnamese bank prioritize risk mitigation: reduce agriculture exposure, hedge physical risk through insurance, or diversify away from the Mekong Delta?

08

Key Concepts

Glossary

Attribution factor: The share of a borrower’s emissions allocated to the bank, calculated as $Outstanding / EVIC$
Carbon beta ($\beta_{carbon}$): Cross-sectional asset pricing factor measuring the return premium associated with carbon intensity
Carbon intensity: GHG emissions per unit of revenue (tCO₂e/$M), used in WACI calculation
Carbon premium: Higher expected returns demanded by investors for holding carbon-intensive assets; Bolton & Kacperczyk (2021) estimate ~1.2–1.8% per SD
Climate Value-at-Risk (CVaR): Portfolio value loss under a specific climate scenario over a defined time horizon: $CVaR = V_{t_0} - \mathbb{E}[V_{t_T} \mid \text{Scenario}]$
Difference-in-Differences (DiD): Quasi-experimental method comparing treatment (high-carbon) and control (low-carbon) groups before and after a policy change
Event study: Method measuring abnormal financial returns around a specific event date (e.g., carbon policy announcement)
EVIC: Enterprise Value Including Cash — total equity plus total debt of a borrower; denominator in the PCAF attribution formula
Financed emissions: GHG emissions attributable to a financial institution through its lending and investment activities, calculated via PCAF methodology
GHG Protocol: International standard for measuring and managing greenhouse gas emissions across Scope 1 (direct), Scope 2 (energy), and Scope 3 (value chain)
Implied Temperature Rise (ITR): Estimated global warming that would result if the whole economy had the same carbon trajectory as a given portfolio
Loss Given Default (LGD): Percentage of exposure lost when a borrower defaults; climate-adjusted LGD incorporates physical damage to collateral
PACTA: Paris Agreement Capital Transition Assessment — tool measuring sector-level alignment of portfolios with Paris decarbonization goals
PCAF: Partnership for Carbon Accounting Financials — global standard for measuring and reporting financed emissions
PCAF Data Quality Tiers: Five-level quality scoring from Tier 1 (verified borrower data, ±10%) to Tier 5 (sector average, ±50%)
Physical CVaR: Portfolio loss from acute (typhoons, floods) and chronic (sea-level rise, temperature) physical climate risks
Probability of Default (PD): Likelihood that a borrower will default on obligations; climate-adjusted PD incorporates scenario-driven stress
SBTi: Science Based Targets initiative — validates corporate emission reduction targets against climate science pathways
Scope 1 / 2 / 3: Direct emissions (1), purchased energy emissions (2), value chain emissions including investments (3)
Sector proxy: Using industry average emissions when borrower-specific data is unavailable; associated with PCAF Tier 4–5
TPI: Transition Pathway Initiative — assesses management quality and carbon performance of listed companies against Paris benchmarks
Transition CVaR: Portfolio loss from policy changes (carbon pricing), stranded assets, and technology shifts in the low-carbon transition
WACI: Weighted Average Carbon Intensity — portfolio-weighted sum of revenue-normalized emissions (tCO₂e/$M revenue); TCFD-recommended metric

09

References

Key References

2024 PCAF. The Global GHG Accounting and Reporting Standard for the Financial Industry (3rd edition). Partnership for Carbon Accounting Financials.
2021 Bolton, P. & Kacperczyk, M. “Do Investors Care About Carbon Risk?” Journal of Financial Economics, 142(2), 517–549.
2017 Battiston, S., Mandel, A., Monasterolo, I., et al. “A Climate Stress-Test of the Financial System.” Nature Climate Change, 7(4), 283–288.
2024 2DII. PACTA Methodology Documentation. 2 Degrees Investing Initiative.
2023 Sautner, Z., van Lent, L., Vilkov, G. & Zhang, R. “Firm-Level Climate Change Exposure.” Journal of Finance, 78(3), 1449–1498.

Supplementary References

2023 PCAF. Financed Emissions in Southeast Asia: Implementation Guide.
2022 State Bank of Vietnam. Green Finance Roadmap.
2023 ASEAN Taxonomy Board. ASEAN Taxonomy for Sustainable Finance, Version 2.

10

Downloads

Materials

Download Slide Deck (PDF)

Data Resources

PCAF Standard NGFS Scenario Explorer Bolton & Kacperczyk Replication Data