## 1wauea2022004

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### EXECUTIVE SUMMARY — Macroeconomic context and banking sector overview
- Growth and projections:
  - Growth averaged 6.4 percent between 2012 and 2019.
  - Growth fell to two percent during the public health crisis in 2020.
  - Projected GDP growth of 5.7 percent for 2021; IMF projections assume a return to the pre-COVID growth path in 2022.
  - Key risks: deteriorating security situation, risk of a COVID-19 resurgence, exhaustion of fiscal space, rising commodity prices and supply shocks that could affect inflation and foreign reserves.
- Banking sector size and composition:
  - Total banking assets: 51.3 percent of regional GDP in 2020 compared to 27.7 percent of GDP in 2008.
  - Outstanding loans to the private sector increased by an average of 12 percent per year during 2010-2019, representing 23 percent of GDP in 2020.
  - Government securities rose to 31 percent of assets in 2020 (from 7.1 percent in 2004).
- Asset quality and capital:
  - Regional average non-performing loans: 11.2 percent in November 2021 compared to 20 percent in 2006.
  - Capital ratio increased from 10.5 percent in 2018 to 12.4 percent in June 2021.
  - 18 banks, representing 10.2 percent of banking assets, did not meet solvency standards at end-June 2021.

### MACROFINANCIAL SCENARIOS AND AT‑RISK METHODOLOGY
- Scenario design:
  - Baseline: V-shaped recovery with a strong and rapid resurgence of growth.
  - Adverse: U-shaped “recovery-at-risk” with persistent weakening of growth before convergence with the baseline at the end of the test period.
  - Cumulative difference between GDP levels in the adverse and baseline scenarios: on the order of 15 percentage points, or 2.2 historical standard deviations on average.
  - In the peak year of stress, the difference would reach 2.3 standard deviations from historical mean.
  - Scenario characterization: “severe but plausible.”
- GaR and IaR models (small-sample adaptations):
  - Growth at Risk (GaR) and Inflation at Risk (IaR) anchor shock magnitudes on tails of empirical distributions conditional on macrofinancial drivers; customized for small and noisy samples.
  - Dual-estimation approach: Theil‑Sen estimator for conditional mean; Firth logit for balance of risks (asymmetry); asymmetric Gaussian distribution fitted from moments (Azzalini 2013).
  - Use of synthetic variables estimated by projection methods (PLS) to aggregate macroeconomic and financial information.
- Explanatory groups (as constructed for GaR and IaR):
  - GaR groups include: Financial conditions; Private demand; Public demand; External demand; Agriculture and climate; Money market rate; Inflation; Private sector GFCF; Public sector GFCF; Terms of trade; Annual production of cotton/coffee/cacao/rice; Maximum annual temperature variation; Climate-related disasters.
  - IaR groups include: Financial conditions; Inflation in trade partners; Commodity prices; WAEMU agricultural production; Money market rate; U.S. inflation; Variation in crude oil price per barrel; Variation in nominal effective exchange rate; Inflation in euro zone; Food products price index on international markets; Inflation in China; Inflation in Nigeria; Annual variation in coffee/rice/cacao production.
- Rationale:
  - At-risk models project conditional future distributions rather than using fixed standard-deviation calibrations.
  - PLS reduces dimensionality, improves degrees of freedom, and captures common factors (e.g., consolidates climate and agricultural indicators).

### STRESS‑TEST FRAMEWORK, CLUSTERING, AND CALIBRATION
- Four-step stress-testing approach:
  1. Construction of base and adverse macroeconomic scenarios.
  2. Clustering of banks into homogeneous groups using statistical methods.
  3. Estimation of sensitivities of probabilities of default (PDs) and return on assets (ROA) to economic conditions.
  4. Projection of deterioration of bank portfolios and profitability under baseline and adverse scenarios.
- Clustering:
  - Banks grouped into four homogeneous clusters using Ward hierarchical clustering on features: total assets; bank capital as a percentage of total assets; ratio of non-performing loans to total loans; profitability.
  - Cluster labels: “large banks,” “weak banks,” “new banks,” and “medium‑sized banks.”
  - Sample coverage: 99 banks (more than 95 percent of sector assets); public banks account for about 10 percent of total assets and are not a separate cluster.
- Quantile regressions and PD estimation:
  - PDs captured via first difference in the ratio of non‑performing loans; conditional PDs estimated by bank type and risk level using quantile regressions at percentiles 50, 75, and 90.
  - Explanatory variables: macroeconomic scenario variables plus bank‑specific controls (market share, profitability).
  - Total estimated coefficients count = 2*10*3*4 = 240 (dependent variable choice ROA/NPL, number of regressors 10, right‑tail quantiles 3, clusters 4).
- Stress-test assumptions:
  - Rate of losses on non‑performing loans constant at 75 percent.
  - Size of bank balance sheets constant over the stressed period (no deleveraging).
  - Projections iterated recursively over a four‑year stress horizon (2021–24), using median projected values as conditioning vector for next stage.

### STRESS TEST RESULTS — SYSTEM‑WIDE RECAPITALIZATION NEEDS
- Aggregate recapitalization orders of magnitude:
  - Recapitalization costs due to shocks to economic growth and inflation are limited as a percentage of regional GDP—to between one and two percent, depending on the type of risk, the scenario, and the degree of risk.
  - Solvency stress tests: capital needed to recapitalize banking system to meet minimum capital requirement after a shock is in the order of 0.5 and 1.2 percent of regional GDP.
  - Interest rate (inflation) shocks: capital needed is in the order of 0.6 to 1.5 percent of regional GDP.
  - Concentration shocks: capital needed to restore regulatory level after cumulative impairment of 1, 5, and 10 largest exposures represents 1, 2, and 3 percent of regional GDP at end‑2020, respectively.
  - Comparative recapitalization ranges:
    - Credit risk: between 0.5 and 1.5 percentage points of WAEMU GDP.
    - Interest rate risk: between 0.6 and 1.5 percent of regional GDP.
    - Concentration risk: around 2 percentage points of WAEMU GDP.
    - Liquidity shock (from other FSAP note): between 0.3 and 2.1 percentage points of WAEMU GDP.
    - Contagion risk: up to 0.8 percentage point of regional GDP.
- Country heterogeneity:
  - Similar country-level recapitalization needs between 0.5 and 1 percent of regional GDP, except Guinea‑Bissau and Togo with costs closer to 3 percent of national GDP.
  - For concentration risk: by country, recapitalization needs range from 1.5 percent of national GDP for Côte d’Ivoire to about 7 percent for Senegal and Togo.
  - Group consolidation: at group level (consolidating exposures and capital buffers), recapitalization needs fall by around 1 percentage points of regional GDP due to intra‑group diversification.

### BANK‑LEVEL VULNERABILITIES AND KEY RISK DRIVERS
- Bank fragility counts:
  - Approximately 30 small banks (out of a sample of 100) are vulnerable to deteriorating macrofinancial conditions.
  - About 20 banks already do not meet the regulatory capital requirement (pre‑stress).
  - Under adverse scenarios and high idiosyncratic risk, a large majority of banks fall below regulatory thresholds (extreme‑tail outcome noted as unlikely).
- Asset quality and profitability impacts:
  - Average ROA in the banking system varies between 1.2 and -0.7 percent, based on the scenario and the level of risk.
  - An increase in NPLs of about 10-15 percentage points under the most unfavorable conditions would reduce the average capital ratio by about six percentage points under the adverse scenario and the highest risk level.
  - Fan‑chart heterogeneity: under the adverse scenario, RWA can vary by 1 percentage point at the median quantile (from 11 to 12 percent of RWA) and by 8 percentage points at the 90th quantile (from 4 to 12 percent of RWA).
- Concentration and large exposures:
  - Median concentration of the largest exposure represents about 50 percent of capital; for nearly two‑thirds of banks, the three largest exposures exceed their entire capital.
  - Current regulatory largest‑exposure limit = 55 percent of capital; planned reduction to 25 percent by 2024.
  - More than one‑third of banks exceed the 55 percent limit; two‑thirds are below 25 percent.
  - Reverse stress tests (loss rates 75 percent and 100 percent): more than 75 percent of banks have insufficient capital buffers to address their largest exposure; one‑third of banks cannot cover their largest exposure with entire capital.

### RISK‑SPECIFIC FINDINGS — CREDIT, INTEREST RATE, CONCENTRATION
- Credit risk:
  - Credit risk remains the most important risk, amplified by concentration and rising exposure to sovereign risks since 2008.
  - Solvency test recapitalization needs: in the order of 0.5 and 1.2 percent of regional GDP.
- Interest rate risk (inflation impacts):
  - Inflation path: base scenario inflation constant at the BCEAO target level of 2 percent; adverse scenario inflation rises to the 95th percentile—or inflation at 7 percent—then gradually returns to the BCEAO target.
  - Bank profitability is more at risk from inflation than from GDP growth; average ROA can reach -1.5 percent under most unfavorable conditions.
  - Incorporating impairment of credit portfolios, capital ratios of the WAEMU system could decrease by 2 to 8 percentage points according to chosen scenario and level of risk.
  - Recapitalization needs from inflationary shocks: in the order of 0.6 to 1.5 percent of regional GDP.
- Concentration risk:
  - Recapitalization needs from concentration shocks: 1, 2, and 3 percent of regional GDP after cumulative impairment of 1, 5, and 10 largest exposures, respectively.
  - Two‑thirds of banks have three largest exposures exceeding capital; a substantial share of banks need to reduce exposures or increase capital by about 5 percentage points of RWA (or a combination) to comply with tighter limits.
  - Dominant systemic risks overall: concentration and liquidity risks dominate; contagion risk has the lowest impact.

### POLICY RECOMMENDATIONS AND SUPERVISORY MEASURES
- Capital and buffers:
  - Impose additional capital requirements within the Basel Pillar II framework to cover interest rate and concentration risks.
    - Authority: WAEMU Banking Commission (CBU)
    - Priority: ST
  - Impose supplementary capital buffers for fragile banks; supplementary capital should be imposed beyond a minimum concentration threshold and be a non‑linear function of degree of exposure and portfolio diversification.
  - Require supplementary capital to cover interest rate risk under Basel Pillar II, commensurate with interest rate and maturity mismatches; measure mismatches regularly.
- Remedial actions for undercapitalized banks:
  - Address banks that do not meet regulatory solvency requirements via recapitalization or liquidation/resolution.
    - Authority: CBU
    - Priority: MT
- Supervisory tools, methodology adoption, and monitoring:
  - Supplement the BCEAO stress test methodology with the macrofinancial risk models developed in this technical note: design macrofinancial scenarios via risk‑based model; determine bank clusters to conduct analysis by risk clusters; estimate PDs and shocks’ impact on bank profitability at different risk levels via quantile regressions.
    - Authority: BCEAO
    - Priority: ST
  - Supplement the BCEAO’s bank monitoring system with statistical early warning methods to identify banks most at risk.
    - Authority: BCEAO
    - Priority: MT
  - Publish a guidance note for banks on the preparation of stress tests.
    - Authority: BCEAO/CBU
    - Priority: ST
  - Share scenarios and methodology with banks for internal stress tests; supervisors should use FSAP statistical methods to strengthen bank monitoring.
  - IMF technical assistance may be required to support BCEAO in the rollout of these methods.
- Concentration limits and enforcement:
  - Strict application of concentration limits recommended; consider non‑linear supplementary capital buffers tied to exposures and diversification.

### METHODOLOGICAL CAVEATS, ASSUMPTIONS, AND IMPLEMENTATION NOTES
- Small‑sample techniques and synthetic variables:
  - Use of Theil‑Sen estimator for conditional mean; Firth penalized logit for balance of risks; asymmetric Gaussian distribution parametrized from three moments.
  - Synthetic variables estimated by Partial Least Squares (PLS); FSAP used only the first principal component of the PLS for each group of variables.
- Key modelling assumptions:
  - No feedback loops from financial system to real economy (no banking–GDP feedback).
  - Assumption of constant balance sheets (no deleveraging) during stress period—conservative bias.
  - Loss rate on NPLs fixed at 75 percent (Basel Committee practice in absence of granular LGD data).
  - WAEMU sovereigns assumed solvent and fixed exchange rates hold (FCFA/EUR peg); extreme‑tail shocks such as de‑pegging or sovereign default not modeled as “severe but plausible” in this exercise.
- Data and horizon:
  - Macro data: 2000–2020; banking data: 2010–2020; reference date Q4 2020.
  - Stress‑testing horizon: four years (2021–24).

*Source: EXECUTIVE SUMMARY and Annexes (WAEMU FSAP technical note contained in the provided content unit).*

### EXECUTIVE SUMMARY __________________________________________________________________________ 5

### EXECUTIVE SUMMARY

### Introduction
- Growth averaged 6.4 percent between 2012 and 2019.
- Growth fell to two percent during the public health crisis in 2020.
- Projected GDP growth of 5.7 percent for 2021; IMF projections assume a return to the pre-COVID growth path in 2022.
- Key risks: deteriorating security situation, risk of a COVID-19 resurgence, exhaustion of fiscal space, rising commodity prices and supply shocks that could affect inflation and foreign reserves.

- Banking sector size and composition:
  - Total banking assets: 51.3 percent of regional GDP in 2020 compared to 27.7 percent of GDP in 2008.
  - Outstanding loans to the private sector increased by an average of 12 percent per year during 2010-2019, representing 23 percent of GDP in 2020.
  - Government securities rose to 31 percent of assets in 2020 (from 7.1 percent in 2004).

- Asset quality and capital:
  - Regional average non-performing loans: 11.2 percent in November 2021 compared to 20 percent in 2006.
  - Capital ratio increased from 10.5 percent in 2018 to 12.4 percent in June 2021.
  - 18 banks, representing 10.2 percent of banking assets, did not meet solvency standards at end-June 2021.

### Macrofinancial scenarios and at-risk methodology
- Scenario design:
  - Baseline: V-shaped recovery with a strong and rapid resurgence of growth.
  - Adverse: U-shaped “recovery-at-risk” with persistent weakening of growth before convergence with the baseline at the end of the test period.
  - Cumulative difference between GDP levels in the adverse and baseline scenarios: on the order of 15 percentage points, or 2.2 historical standard deviations on average.
  - In the peak year of stress, the difference would reach 2.3 standard deviations from historical mean.
  - These scenarios are characterized as “severe but plausible.”

- New GaR and IaR models:
  - Growth at Risk (GaR) and Inflation at Risk (IaR) models anchor shock magnitudes on the tails of empirical distributions conditional on macrofinancial drivers.
  - Customized for small and noisy samples typical of developing countries; leverage statistical inference literature on small samples.
  - Feature “recovery at risk” scenario designs to simulate different recovery paths and dynamics.

- Explanatory variable construction:
  - Use of synthetic variables estimated by projection methods (PLS) to aggregate macroeconomic and financial information into parsimonious signals.
  - GaR explanatory groups: Financial conditions, Private demand, Public demand, External demand, Agriculture and climate, Money market rate, Inflation, Private sector GFCF, Public sector GFCF, Terms of trade, Annual production of cotton/coffee/cacao/rice, Maximum annual temperature variation, Climate-related disasters.
  - IaR explanatory groups: Financial conditions, Inflation in trade partners, Commodity prices, WAEMU agricultural production, Money market rate, U.S. inflation, Variation in crude oil price per barrel, Variation in nominal effective exchange rate, Inflation in euro zone, Food products price index on international markets, Inflation in China, Inflation in Nigeria, Annual variation in coffee/rice/cacao production.

- Rationale for approach:
  - At-risk models project conditional future distributions rather than using fixed standard-deviation calibrations.
  - Projection-to-latent-structure (PLS) reduces dimensionality, improves degrees of freedom, and captures common factors (e.g., consolidates climate and agricultural indicators).

### Stress testing framework and calibration
- Four-step approach:
  1. Construction of base and adverse macroeconomic scenarios.
  2. Clustering of banks into homogeneous groups using statistical methods.
  3. Estimation of sensitivities of probabilities of default (PDs) and return on assets (ROA) to economic conditions.
  4. Projection of deterioration of bank portfolios and profitability under baseline and adverse scenarios.

- Risks analyzed in this technical note:
  - Credit risk (including concentration amplification).
  - Interest rate risk (via impacts on securities portfolio valuations and intermediation margins).
  - Concentration risk tested via reverse stress tests to determine breaking points of cumulative large exposures relative to capital.
- Contagion and liquidity stress tests are addressed separately in other technical notes.

### Stress test results and vulnerabilities
- System-wide recapitalization needs:
  - Recapitalization costs due to shocks to economic growth and inflation are limited as a percentage of regional GDP—to between one and two percent, depending on the type of risk (credit, interest rate, or concentration), the scenario, and the degree of risk.
  - Moderate system-wide recapitalization cost is explained by the relatively small size of the banking sector as a percentage of regional GDP and the soundness of large banks.
  - However, recapitalization costs could be higher in certain countries, especially for concentration risk.

- Bank-level vulnerabilities:
  - Approximately 30 small banks (out of a sample of 100) are vulnerable to deteriorating macrofinancial conditions.
  - About 20 banks already do not meet the regulatory capital requirement.
  - For two-thirds of banks, exposure to large risks exceeded the Basel standard of 25 percent of capital in 2020.

- Major risk drivers and amplifiers:
  - Credit risk remains the most important risk, amplified by concentration and rising exposure to sovereign risks since 2008.
  - Interest rate risk increased due to longer securities maturities and increased recourse to short-term BCEAO financing, exposing banks to margin compression if policy rates rise.
  - Climate change may contribute to credit risk, but exposures are not monitored by supervisors and rarely by banks.
  - Surplus capital to address concentration, contagion, and interest rate risks is limited.

### Measures and policy recommendations
- Summary of key recommendations (Table of Recommendations):
  - Impose additional capital requirements within the Basel Pillar II framework to cover interest rate and concentration risks.
    - Authority: WAEMU Banking Commission (CBU)
    - Priority: ST
  - Address banks that do not meet regulatory solvency requirements via recapitalization or liquidation/resolution.
    - Authority: CBU
    - Priority: MT
  - Supplement the BCEAO stress test methodology with the macrofinancial risk models developed in this technical note, including: designing macrofinancial scenarios via a risk-based model; determining bank clusters to conduct analysis by risk clusters; and estimating PDs and shocks’ impact on bank profitability at different risk levels via quantile regressions.
    - Authority: BCEAO
    - Priority: ST
  - Supplement the BCEAO’s bank monitoring system with statistical early warning methods to identify banks most at risk.
    - Authority: BCEAO
    - Priority: MT
  - Publish a guidance note for banks on the preparation of stress tests.
    - Authority: BCEAO/CBU
    - Priority: ST

- Additional supervisory guidance:
  - Impose additional capital buffers for fragile banks and strictly apply concentration limits.
  - Use statistical methods (clustering, at-risk models, quantile regressions) to strengthen bank monitoring and identify the most vulnerable institutions.
  - IMF technical assistance may be required to support BCEAO in the rollout of these methods.

### Conclusion
- The WAEMU FSAP stress tests, using a new macrofinancial at-risk methodology and bank clustering, find moderate system-wide recapitalization needs but identify material vulnerabilities among smaller banks and certain member countries.
- Targeted supervisory actions—capital buffers, strict concentration limits, enhanced bank monitoring using the presented statistical methods, and remedial action for undercapitalized banks—are recommended to mitigate identified risks.

*Source: EXECUTIVE SUMMARY (WAEMU FSAP technical note).*

### Annex II and Wold, Sjöström, and Eriksson 2001).

### 1wauea2022004 - Annex II and Wold, Sjöström, and Eriksson 2001)

### Synthetic variables and at‑risk methodology
- Synthetic variables filter idiosyncratic noise and retain the common trend; information gain is especially important given noisy original variables.
- FSAP at‑risk models use a dual estimation adapted to small samples (like WAEMU):
  - First model: regress future growth to a one-year horizon on all synthetic variables, adding a constant term and an autoregressive term; estimation uses the Theil‑Sen estimator (Theil 1950; Sen 1968) resilient to outliers and suitable for small samples.
  - Second model: dichotomous/logit model for small samples (Firth 1993) where the separation threshold is the Theil‑Sen projected mean; estimates the relative probability (odd‑ratio) that future growth will be lower or higher than the Theil‑Sen estimate (binary 0/1).
- The two‑regression approach estimates two moments of the conditional distribution: the conditional mean (expectation) and the balance of risks (asymmetry).
- Based on moments, an asymmetric Gaussian distribution is fitted using a closed‑form algebraic method (Azzalini 2013); outcome similar to canonical growth‑at‑risk models (Adrian, Boyarchenko, and Giannone 2019) but more suitable for WAEMU small‑sample context.

### Scenario design, sequencing, and calibration
- FSAP considered two post‑COVID recovery scenarios inspired by historical episodes: base and adverse.
- Dual approach to scenario design:
  - Conditional densities of growth and inflation from at‑risk models, anchored to Risk Assessment Matrix (RAM) qualitative assessments.
  - Specified stressed GDP path over a four‑year horizon based on quantile transposition of past crises to reflect regional responsiveness.
- Base scenario: “V‑shaped” recovery with a sharp upswing in 2022, patterned after the Ivoirian crisis of 2011 (regional GDP rebounded starting in 2012).
- Adverse scenario: slow “U‑shaped” recovery modeled on the 1992 regional crisis, with growth beginning to recover in 2023 and converging to the base by end of stress period; combines RAM risk factors including fiscal adjustment, regional health recovery, security deterioration, an external shock, and a climate shock.
- Climate shock introduced via a synthetic variable aggregating natural disasters, air temperature, and agricultural products (e.g., cacao, coffee, rice); direct granular sector targeting not feasible due to lack of granular data and limited direct exposures.
- Single‑country shock: included a shock to Côte d’Ivoire (highest contribution to regional GDP) to reflect potential security or socio‑political impacts.
- Scenario magnitude derived from at‑risk models by mapping historical crisis percentiles into conditional distributions as of end‑2020 (example: 1992–95 crisis converted in quantile terms based on conditional projection as of 1991Q4).
- Example of mapping: the same shock at the fifth percentile can represent different absolute declines across years (e.g., one percent in 1995 versus two percent in 2020) because the underlying distribution evolves.

### Scenario magnitudes and inflation path
- Adverse scenario cumulative GDP shock: 15 percentage points over four years relative to base.
- That cumulative shock equals 2.2 annualized standard deviations of WAEMU GDP over the last 30 years.
- FSAP practice aligns with “severe but plausible” adverse scenarios calibrated around cumulative shocks often between 2 and 2.5 historical standard deviations.
- Inflation dynamics:
  - Base scenario: inflation constant at the BCEAO target level of 2 percent.
  - Adverse scenario: inflation rises to the 95th percentile of the shocked conditional distribution—or inflation at 7 percent—then gradually returns to the BCEAO target at the end of the period.

### Ancillary variables and density estimation
- Ancillary variables (factors affecting bank credit portfolios and profitability) are anchored to main growth and inflation scenarios using regressive models.
- For each percentage level of growth and inflation, the model projects corresponding levels in the distribution of each ancillary variable.
- Distributions for ancillary variables obtained by direct adjustment of historical data; optimal distribution family selected using Bayesian information criteria.
- FSAP designed base and adverse scenarios covering seven variables over a four‑year stressed period using reduced‑form methods with macroeconomic data alone.

### Aggregation through statistical clustering
- Banks grouped into four homogeneous clusters to identify typical bank profiles and to estimate asset profitability and portfolio deterioration separately for each cluster.
- Clustering avoids assuming homogeneous marginal effects across banks (unlike panel fixed effects) and yields distinct marginal effects per cluster.
- Ward metric used in hierarchical aggregation to determine optimal number of clusters based on features: total assets, bank capital as a percentage of total assets, ratio of non‑performing loans to total loans, and profitability.
- Four clusters chosen as compromise between model parsimony, homogeneity, and separation; clusters visualized in two‑dimensional subspace.
- Cluster labels based on average characteristics: “large banks,” “weak banks,” “new banks” (small credit portfolio size and significant share of capital), and “medium‑sized banks.”
- Sample covers both private and public banks; public banks account for about 10 percent of total assets and are not a separate cluster.

### Credit risk estimation (PDs) and quantile regressions
- Due to lack of granular long‑run data, PDs captured via first difference in the ratio of non‑performing loans (the stock first difference represents an aggregate flow at the bank level); this flow is modeled based on economic conditions per IMF recommendation when granular data are lacking (IMF 2015).
- Conditional PDs estimated by bank type and risk level using quantile regressions at percentiles set at 50, 75, and 90.
- Explanatory variables include scenario macroeconomic variables (GDP growth, financial conditions, agricultural production, climate conditions) plus bank‑specific controls (market share, profitability).
- Marginal effect of macro environment on non‑performing loans depends on synthetic variable, bank type, and risk level.
- Quantile regressions capture heterogeneity across clusters: whole‑sample regressions can show flat marginal effects (misleading), while cluster‑specific regressions reveal significant and sometimes opposite slopes across bank types (e.g., medium‑sized and large banks show intuitive positive marginal GDP effect on NPLs; new and weak banks show null or opposite effects).
- Nonlinearities and interactions captured across many regressors: total estimated coefficients count = 2*10*3*4 = 240 reflecting dependent variable choice (ROA/NPL), number of regressors (10), right‑tail quantiles (3), and clusters (4).

### Solvency, profitability, and three risk sources
- Solvency tests also evaluate scenario impact on return on assets (ROA) using same regressors and approach; elasticity varies sharply by bank type with large banks showing largest absolute coefficients across most quantiles.
- Three sources of risk modeled:
  - Macroeconomic/contextual risk from base and adverse scenarios estimated via at‑risk models.
  - Financial risk introduced via bank‑specific variables (capital ratios, loans as share of total assets, etc.); under‑capitalized banks face greater additional portfolio degradation risk.
  - Idiosyncratic risk (PD) estimated by quantile regressions at different risk levels, capturing non‑linear crisis impacts where PD marginal effects increase with risk level.
- Combining the three sources yields a more complete view of financial stability risks than panel OLS with fixed effects.

### Loss projection, capital ratios, and stress test assumptions
- Bank losses projected recursively over the stress horizon by replacing explanatory variables with scenario levels and iterating the first difference of non‑performing loans and ROA over the stressed horizon.
- Two key stress test assumptions:
  - Rate of losses on non‑performing loans constant at 75 percent (consistent with Basel Committee practice in absence of granular loss‑given‑default data).
  - Size of bank balance sheets constant over the stressed period (no deleveraging), consistent with IMF practice and modeling constraints.
- Projected earnings are used to offset provisions for non‑performing loans, reflecting impacts on flows and stocks.
- Once losses are known, capital ratios computed under different recovery rates; positive cash flow used to cover part of provisioning costs.
- Projection methodology detailed in Annex VI.

*Source: 1wauea2022004 - Annex II and Wold, Sjöström, and Eriksson 2001).*

### 28.      The stress test projections show a significant effect of deteriorating economic

### 1wauea2022004 - 28.      The stress test projections show a significant effect of deteriorating economic

### Credit risk and solvency stress-test findings
- Average return on assets (ROA) in the banking system varies between 1.2 and -0.7 percent, based on the scenario retained and the level of risk (Figure 4.4).
- An increase in non-performing loans (NPLs) of about 10-15 percentage points under the most unfavorable conditions would reduce the average capital ratio in the banking system by about six percentage points under the adverse scenario and the highest risk level (Figure 4.3).
- Fan charts (Figures 4.3 and 4.4) show substantial heterogeneity across quantiles for impacts on capital ratio and profitability:
  - Under the adverse scenario, RWA can vary by 1 percentage point at the median quantile (from 11 to 12 percent of RWA) and by 8 percentage points at the 90th quantile (from 4 to 12 percent of RWA).
- Identification of bank-level fragility:
  - 20 fragile banks identified; these are below regulatory capital thresholds under base scenario at median-level risk and are already under-capitalized prior to stress testing.
  - Around 30 vulnerable banks fall below regulatory thresholds only under unfavorable conditions (adverse scenario and idiosyncratic risk at 75 percent).
  - Under extreme idiosyncratic risk, a large majority of banks fall below regulatory thresholds (noted as unlikely due to magnitude of risk).
  - Sound banks resilient under most unfavorable conditions are generally large, well-capitalized with limited credit portfolios relative to balance sheets.
- Recapitalization needs from solvency stress tests:
  - Capital needed to recapitalize banking system to meet minimum capital requirement after a shock is in the order of 0.5 and 1.2 percent of regional GDP (Figure 4.6).
  - Similar across countries: between 0.5 and 1 percent of regional GDP, except Guinea-Bissau and Togo with costs closer to 3 percent of national GDP.

### Interest rate risk
- Modeling approach:
  - Interest rate risk captured via sensitivity of bank ROA to inflation and interest rates using inflation-at-risk scenarios (base at 2 percent; adverse rising to 7 percent before decreasing).
  - Indirect assessment via impact on returns on assets due to lack of granular data on securities portfolios and bank loans; allows granular estimation of (i) duration risk on securities and (ii) mismatch in interest rate structure between bank assets and liabilities.
  - Methods follow credit-risk framework with variable of interest = inflation and scenarios from inflation-at-risk model; results from quantile regressions presented in Figures 5.1 and 5.2.
- Impact on profitability and capital:
  - Bank profitability is more at risk from inflation than from GDP growth, with an average level that can reach -1.5 percent under the most unfavorable conditions (Figure 5.3).
  - Incorporating impairment of credit portfolios, capital ratios of the WAEMU system could decrease by 2 to 8 percentage points according to chosen scenario and level of risk (Figure 5.4).
- Recapitalization needs from interest rate shocks:
  - Capital needed to meet minimum capital requirements following an inflationary shock is in the order of 0.6 to 1.5 percent of regional GDP (Figure 5.6).
  - This range is slightly more significant than for credit risk due to stronger impact on profitability.

### Concentration risk
- Asset concentration metrics:
  - Median concentration of the largest exposure represents about 50 percent of capital; for nearly two-thirds of banks, the three largest exposures exceed their entire capital (Figures 6.1 and 6.2).
- Regulatory compliance on exposure diversification:
  - Current regulatory largest-exposure limit = 55 percent of capital; planned reduction to 25 percent by 2024.
  - More than one-third of banks exceed the 55 percent limit; two-thirds are below 25 percent.
  - To comply, banks should reduce exposures or substantially increase capital—in the order of 5 percentage points of risk-weighted assets—or a combination.
- Reverse stress-test analysis:
  - Two loss rates considered: 75 percent and 100 percent; two coverage metrics: entire capital and only capital buffers.
  - More than 75 percent of banks have insufficient capital buffers to address their largest exposure (Figure 6.4).
  - One-third of banks cannot cover their largest exposure with entire capital; starting with fourth cumulative exposure, more than half of banks exhaust all capital; under complete loss rate most banks exhaust capital by second cumulative exposure.
- Recapitalization needs from concentration shocks:
  - Capital needed to restore regulatory level (8.25 percent of RWA) after cumulative impairment of 1, 5, and 10 largest exposures represents 1, 2, and 3 percent of regional GDP at end-2020, respectively (Figures 6.5 and 6.6).
  - By country, recapitalization needs range from 1.5 percent of national GDP for Côte d’Ivoire to about 7 percent for Senegal and Togo.
  - At group level (consolidating exposures and capital buffers), recapitalization needs fall by around 1 percentage points of regional GDP due to intra-group diversification.

### Measures and policy recommendations
- Capital requirements and buffers:
  - Impose supplementary capital buffers for fragile banks to strengthen resilience to macrofinancial risks; supplementary capital should be imposed beyond a minimum concentration threshold and be a non-linear function of degree of exposure and portfolio diversification.
  - Require supplementary capital to cover interest rate risk under Basel Pillar II, commensurate with interest rate and maturity mismatches; measure mismatches regularly.
- Supervisory tools and methodology adoption:
  - New small-sample econometrics and biostatistics approaches customized to WAEMU data; macroeconomic scenarios via conditional distributions and recovery-at-risk paths; clustering methods to classify banks and allocate supervisory resources; projection methods by type of bank and level of risk.
  - Share scenarios and methodology with banks for internal stress tests; supervisors should use FSAP statistical methods to strengthen bank monitoring.
- Concentration limits and enforcement:
  - Strict application of concentration limits recommended; consider non-linear supplementary capital buffers tied to exposures and diversification.

### Comparative impacts and dominant risks (summary)
- Recapitalization cost ranges reported:
  - Credit risk: between 0.5 and 1.5 percentage points of WAEMU GDP.
  - Interest rate risk: between 0.6 and 1.5 percent of regional GDP (noted as in the order of 0.6 to 1.5 percent).
  - Concentration risk: around 2 percentage points of WAEMU GDP (solvency tests suggest concentration shock would require recapitalization of around two percentage points of regional GDP).
  - Liquidity shock (from other FSAP note): between 0.3 and 2.1 percentage points of WAEMU GDP.
  - Contagion risk: up to 0.8 percentage point of regional GDP.
- Dominant systemic risks: concentration and liquidity risks dominate; contagion risk has the lowest impact.
- Bank-level vulnerability summary:
  - Around 20 banks already below regulatory thresholds pre-stress test.
  - Around 30 additional small banks are vulnerable to macroeconomic deterioration.

### Methodological caveats and assumptions
- Common caveats shared with traditional IMF stress tests:
  - No feedback loops from financial system to real economy (possible amplification of GDP contraction by bank deterioration).
  - Limited data granularity: lack of bank portfolio decompositions required indirect modeling of interest rate risk via profitability.
  - Assumption of constant balance sheets (no deleveraging) during stress period—introduces conservative bias.
  - Assumption that WAEMU sovereigns remain solvent and fixed exchange rates hold (FCFA/EUR peg); extreme-tail shocks (de-pegging or sovereign default) not modeled in standard stress test and not considered as “severe but plausible” for WAEMU in this exercise.

_Excerpted from the IMF WAEMU FSAP technical note contained in the provided content unit._

### References

### References; Annex I. “At-risk” Models on Small, Noisy Samples; Annex II. Estimating Synthetic Variables by Partial Least Squares

### References (selected works cited)
- Adrian, T., N. Boyarchenko, and D. Giannone. 2019. “Vulnerable Growth.” American Economic Review 109 (4): 1263-89.
- Adrian, M. T., M. J. Morsink, and M. B. Schumacher. 2020. “Stress Testing at the IMF.” Departmental Paper 2020/001, International Monetary Fund, Washington, DC.
- Anderson, D., B. Hunt, M. Kortelainen, M. Kumhof, D. Laxton, D. Muir, S. Mursula, and S. Snudden. 2015. “Getting to Know GIMF: The Simulation Properties of the Global Integrated Monetary and Fiscal Model.” IMF Working Paper 13/55, International Monetary Fund, Washington, DC.
- Azzalini, A. 2013. The Skew-Normal and Related Families. Cambridge, U.K.: Cambridge University Press.
- Delaigle, A., and P. Hall. 2012. “Methodology and Theory for Partial Least Squares applied to Functional Data.” The Annals of Statistics 40 (1) 322–52.
- Firth, D. 1993. “Bias Reduction of Maximum Likelihood Estimates.” Biometrika 80 (1): 27–38.
- Hastie et al., 2017. [Missing reference; see page 42]
- IMF (International Monetary Fund). 2022a. “United Kingdom: Select Issues in Systemic Risk Oversight and Macroprudential Policy.” Financial Sector Assessment Program, International Monetary Fund, Washington, DC.
- IMF (International Monetary Fund). 2022b. “Vulnerabilities in NBFIs, Market-based Finance, and Systemic Liquidity.” Financial Sector Assessment Program, International Monetary Fund, Washington, DC.
- IMF (International Monetary Fund). 2022c. “West African Economic and Monetary Union: Financial Sector Assessment Program–Financial System Stability Assessment.” Financial Sector Assessment Program, International Monetary Fund, Washington, DC.
- IMF (International Monetary Fund). 2015. “Stress Testing Guidance Note,” IMF Guidance Note.
- Kapetanios, G., and S. Price. 2018. “A U.K. Financial Conditions Index Using Targeted Data Reduction: Forecasting and Structural Identification.” Econometrics and Statistics 7 (July): 1-17.
- Koenker, R., and K. F. Hallock. 2001. “Quantile Regression.” Journal of Economic Perspectives 15 (4): 143–56.
- McKean, J. W. 2004. “Robust Analysis of Linear Models.” Statistical Science 19 (4): 562–70.
- Ong, M. L. L. 2014. A Guide to IMF Stress Testing: Methods and Models. Washington, DC: International Monetary Fund.
- Peng, H., S. Wang, and X. Wang. 2008. “Consistency and Asymptotic Distribution of the Theil–Sen Estimator.” Journal of Statistical Planning and Inference 138 (6): 1836–50.
- Prasad, M. A., S. Elekdag, M. P. Jeasakul, R. Lafarguette, M. A. Alter, A. X. Feng, and C. Wang. 2019. “Growth at Risk: Concept and Application in IMF Country Surveillance.” IMF Working Paper 19/36, International Monetary Fund, Washington, DC.
- Sen, P. 1968. “Estimates of the Regression Coefficient Based on Kendall’s Tau.” Journal of the American Statistical Association 63 (324): 1379-1389.
- Theil, H.1950. “A Rank-Invariant Method of Linear and Polynomial Regression Analysis.” In Henri Theil’s Contributions to Economics and Econometrics: Econometric Theory and Methodology, edited by B. Raj and J. Koerts, 345–81. Dordrecht, Netherlands: Springer.
- Tibshirani, R., and T. Hastie. 2016. The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Second Edition. New York, NY: Springer.
- Wold, S., M. Sjöström, and L. Eriksson. 2001. “PLS-regression: A Basic Tool of Chemometrics.” Chemometrics and Intelligent Laboratory Systems 58 (2): 109–30.

### Annex I — “At-risk” models on small, noisy samples: key methods, assumptions, and simulation
- Context and challenge:
  - Standard GaR (growth at risk) approaches (Adrian, Boyarchenko, and Giannone 2019; Prasad et al., 2019) require at least 60 to 80 observations, or 15 to 20 years of quarterly data.
  - WAEMU long-term macroeconomic data are annual and cover only 20 years, i.e., three to four times fewer observations than required for usual risk models.
- Methodological response:
  - Adopt methods from robust econometrics and biostatistics suitable for small samples (McKean 2004 cited).
  - Use two distinct models to capture two conditional moments of the dependent-variable distribution:
    - Theil-Sen model (Theil 1950; Sen 1968): a robust regression estimator delivering the conditional mean.
      - Tolerance to outliers: 29 percent (Peng, Wang, and Wang 2008).
      - Specification mirrors OLS: y_{t+h} = α + β^{TS} X_t + ε^{TS}_t, with conditional mean y_{t0} = α̂ + β̂^{TS} X_{t0}.
      - Jackknife Theil-Sen estimator: systematically remove one observation at a time (e.g., for 20 observations, create 20 subsamples of 19 observations), estimate OLS on each subsample and average coefficients (median also used to reduce extreme coefficient impact).
      - Clarification: Theil-Sen is a conditional average estimator (not a quantile regression).
    - Firth Logit model (Firth 1993): a logistic regression with penalized likelihood to reduce bias in small/noisy samples or low separation.
      - Estimates probability of a binary event, e.g., ℙ[y_{t+h} > ȳ | X_t] = α + β^{FIRTH} X_t + ε^{FIRTH}_t, where ȳ is a threshold (often the Theil-Sen projection).
      - Penalized-likelihood modification eliminates estimation bias typical of classical logistic MLE in small samples.
      - Used to estimate balance of risks around the Theil-Sen average projection (e.g., probability that growth is higher than the Theil-Sen mean).
- Combining moments into a distribution:
  - Theil-Sen provides conditional expectation E[y_{t+h} | X_{t0}] = α̂ + β̂^{TS} X_{t0}.
  - Firth provides asymmetry via cumulative density at the conditional mean: F(y_{t+h} | X_t) = α̂ + β̂^{FIRTH} X_{t0}.
  - Conditional variance is assumed unconditional and equal to the residual variance of the Theil-Sen estimation (constant heteroskedasticity assumed).
  - Thus three conditional moments obtained: expectation (Theil-Sen), variance (residual variance from Theil-Sen), skewness/asymmetry (from Firth).
  - Parametrize an asymmetrical Gaussian distribution from these three moments:
    - Rationale: asymmetric Gaussian encompasses standard normal and asymmetric cases, provides closed-form mappings between moments, cumulative density, and parameters (Azzalini 2013).
    - Avoids requiring four moments (e.g., for asymmetric Student) or nonparametric kernels which are unsuitable for very small samples.
- Shock simulation (reduced-form, without identification):
  - Synthetic variables (from PLS; Annex II) are shocked (often by one or two standard deviations) to obtain a shocked conditioning vector X_{tT} = X_t + (0,..., ΔX_j, ..., 0).
  - Project shocked conditional mean: E[y_{t+h} | X_{tT}] = α̂ + β̂^{TS} X_{tT}.
  - Re-estimate Firth model on shocked conditioning and adjust asymmetric-Gaussian distribution accordingly.
- Practical notes and outputs:
  - Approach stabilizes projections and provides entire conditional-distribution impacts (central tendency, tails, balance of risks, values at risk).
  - Python codes used in the exercise are available at https://romainlafarguette.github.io/software/ (URL provided in source).

### Annex II — Estimating synthetic variables by Partial Least Squares (PLS): method and role
- Purpose:
  - Synthetic variables used in growth-at-risk and inflation-at-risk models are obtained via data reduction on themed variable sets (see source Tables 2 and 3).
  - PLS is a supervised data-reduction method that maximizes covariance between Y and X latent projections, unlike PCA which is unsupervised.
- Key properties and algorithmic structure:
  - PLS models the covariance between Y and X by projecting both onto a lower-dimensional latent subspace that maximizes covariance between projections.
  - PLS helpful when X contains numerous multicollinear, noisy, or incomplete variables; PLS precision increases as multicollinearity increases.
  - Matrix decompositions (following Wold, Sjöström, and Eriksson 2001):
    - X = T P'_X + E_X
    - Y = U P'_Y + E_Y
    - Where:
      - P'_X and P'_Y are the scores of X and Y (latent structure).
      - T and U are loadings on X and Y (projections on latent structure).
      - E_X and E_Y are error terms (assumed i.i.d.).
      - X-scores T form linear combinations of original X; coefficients are the T = X W weights.
  - Components:
    - PLS components are recursive orthogonal projections; first component explains most covariance between Y and X, second is orthogonal to first and explains remaining covariance, etc.
  - Predictive property:
    - X-scores T are good predictors of Y when projected on Y’s latent structure; Y = T P'_Y + F, hence X-scores can predict Y.
- Conceptual summary:
  - PLS performs dimensionality reduction of X into a vectorial subspace where X-scores are highly correlated with Y, extracting a reduced X signal that preserves maximal covariance with Y.
  - Compared with OLS projection of Y on X, PLS uses an intermediate latent structure to overcome multicollinearity and improve predictive performance.

*Source: 1wauea2022004 - References; Annex I and Annex II, “WEST AFRICAN ECONOMIC AND MONETARY UNION,” INTERNATIONAL MONETARY FUND*

### 7.      In the WAEMU FSAP, the team used only the first principal component of the PLS

### 1wauea2022004 - 7.      In the WAEMU FSAP, the team used only the first principal component of the PLS

### Partial Least Squares (PLS) versus Principal Component Analysis (PCA)
- Method choice and rationale:
  - The FSAP used only the first principal component of the PLS estimated on each group of variables.
  - Using one principal component per group:
    - Provides a simple interpretation: the best representation of a group of variables.
    - Avoids the difficulty of interpreting two principal components that are different linear combinations with different explanatory power.
    - Limits the number of regressors in second-stage regressions, preserving the advantage of data reduction methods.
  - PLS supervision:
    - The FSAP uses future real GDP growth (the Y matrix) for the GaR model and future inflation for the IaR model as supervision variables.
    - Supervision variables optimize predictive power by maximizing covariance with the dependent variable.
    - Because the dependent variable is one-year ahead, this approach does not create endogeneity problems with contemporaneous X variables.
  - Comparison to PCA:
    - PCA is unsupervised and depends only on the projection of the X matrix variance.
    - PLS offers supervision that improves interpretability and increases predictive power; this motivates the WAEMU FSAP choice of PLS.

### Risk Assessment Matrix (selected risks and expected impacts)
- RAM 1: A lethal and highly contagious local outbreak of COVID-19
  - Relative Probability/Horizon: High
  - Expected Impact if Realized: High; Short to medium term
  - Key implications:
    - Low vaccination rates raise probability of reimposing containment measures → weaker growth, worsened fiscal situation, elevated debt sustainability concerns.
    - New large-scale lockdowns → contraction in private sector demand; constrained public sector response due to limited fiscal space.
    - Slowdown → deterioration in banks’ asset quality; exacerbated by weaknesses in the WAEMU’s health system.
- RAM 2: Systematic deterioration of the security situation in the region
  - Relative Probability/Horizon: Medium
  - Expected Impact if Realized: High; Short to medium term
  - Key implications:
    - Intensified security incidents with cross-border spillovers → slower economic activity, impaired public finances and policy implementation.
    - Slowdown → deterioration in banks’ asset quality.
- RAM 3: De-anchoring of inflation expectations in the U.S. and/or advanced European countries leading to a rise in interest rates and risk premia
  - Relative Probability/Horizon: Medium
  - Expected Impact if Realized: High; Short to medium term
  - Key implications:
    - Unanchoring could prompt early U.S. monetary tightening → tighter global financial conditions, higher risk premia for frontier markets.
    - Consequences: reduced capital inflows and official foreign reserves; possible loss of global market access; interest rate spikes; accelerated fiscal correction; credit contraction; banks’ asset quality deterioration; squeezed margins.
- RAM 4: Rising and volatile food and energy prices
  - Relative Probability/Horizon: High
  - Expected Impact if Realized: Medium; Short to medium term
  - Key implications:
    - Post-pandemic demand and supply disruptions → raw material price rises and volatility, especially oil; fiscal implications as WAEMU is a net oil importer.
    - Effects: higher inflation, drop in foreign reserves, higher interest rates, lower private sector demand, deterioration in banks’ asset quality, squeezed profitability.
- RAM 5: Rise in frequency and intensity of natural disasters related to climate change
  - Relative Probability/Horizon: Medium
  - Expected Impact if Realized: High; Short to medium term
  - Key implications:
    - Negative effects on agricultural production and exports; increased subsidy needs; reduced standard of living.
    - Reduced yields → dampened growth via lower net exports; impaired bank asset quality for agricultural exposures; government guarantees transfer losses to public sector; subsidy use diverts resources.

### Grouping Banks by Statistical Clustering
- Objectives of clustering:
  - Create homogeneous groups to estimate predictive models with more information and less idiosyncratic heterogeneity.
  - Provide representative synthetic bank (centroid) for clustered-based hot deck imputation of missing values.
  - Serve as first stage for scoring models to prioritize supervisory inspections.
- Clustering method:
  - Optimum number of clusters determined by hierarchical classification using Ward distance (Tibshirani and Hastie, 2016).
  - Ward distance defined as the square of the Euclidean distance on the variables’ vector subspace.
  - The algorithm aggregates pairs of clusters to minimize intra-cluster variance; results shown in a dendrogram suggesting four or five groups appropriate (corresponding to a Ward metric of around 12.5).
  - Choosing three rather than four groups drastically increases intra-cluster variance; choosing four instead of five (or five instead of six) entails limited intra-variance increase — gain in parsimony.
- Diagnostics and choice:
  - Diagnostics computed: breakdown of inertia, silhouette, Calinski-Harabasz and Davies-Bouldin scores.
  - Four clusters chosen: confirmed by good silhouette ratio and correct scores; inertia criterion did not distinguish an optimal clustering; five clusters would be acceptable but four chosen for parsimony.
- Cluster characteristics (summary):
  - Cluster 3 (green): "the weak banks" — strongest rate of non-performing loans, nearly null profitability, small balance sheet, very limited capital (under-capitalized with very degraded portfolios).
  - Cluster 2 (red): large banks — largest asset size, best profitability, limited non-performing loan rates.
  - Cluster 4 (brown): very small, newly created banks — very few assets, few non-performing loans, very high capital-to-assets ratio, very negative profitability (balance sheets mostly capital, few loans).
  - Cluster 1 (blue): medium-sized banks — largest number of banks, average characteristics and most homogeneity.

### Stress-testing via Quantile Regressions
- Approach and motivation:
  - Conditional probabilities of default (PDs) and profitability estimated by bank type and risk level using quantile regressions on clusters.
  - Quantile regressions estimate conditional quantiles (not conditional mean like OLS) — robust for noisy data and capture idiosyncratic (tail) risk.
  - Advantage: captures risk that PDs and profitability may reside in tails rather than at conditional average; avoids omission of idiosyncratic risk common in OLS-based stress tests.
- Model specifics:
  - For each cluster, two estimations: return on assets (ROA) and flow of non-performing loans (ΔNNP N_i).
  - Regressions projected for t+1 to eliminate simultaneity bias.
  - Regression forms (for bank i in cluster C, at quantile q):
    - Q̂ROA_{i,t+1,q} = α_{L,C,q} + β_{R,C,q} Mmac_t + γ_{R,C,q} Bmacro_{i,t} + ε_{i,t,q}, ∀ i ∈ C
    - Q̂ΔNNP N_{i,t+1,q} = α_{N,C,q} + β_{N,C,q} Mmac_t + γ_{N,C,q} Bmacro_{i,t} + ε_{i,t,q}, ∀ i ∈ C
  - Definitions:
    - Mmac_t: macroeconomic clusters vector reflecting base/adverse scenarios (GDP, inflation, domestic financial conditions, climate change, agricultural production, etc.).
    - Bmacro_{i,t}: individual banking variables (past profitability, non-performing loans level, capital ratio, bank’s market share, etc.).
    - q: quantile level reflecting different levels of risk.
    - C: cluster related to bank i.
- Coefficients and estimation:
  - Coefficient vectors α_{C,q}, β_{C,q}, γ_{C,q} are cluster- and quantile-dependent and estimated via standard quantile regressions on each cluster.
  - Cluster estimation allows cluster-dependent coefficients using simpler quantile regressions rather than panel quantile regressions.
  - Quantile approach addresses slope heterogeneity and limited granular data; no direct fixed-effect OLS equivalent in quantile regressions.
- Sources of risk captured in projections:
  - Macroeconomic risk via coefficients on Mmac_t (base/adverse scenarios).
  - Financial risk via coefficients on Bmacro_{i,t} (bank-specific balance sheet impacts).
  - Idiosyncratic risk via different quantile coefficients (PDs at risk and profitability at risk reflecting tail outcomes).
- Noted outputs:
  - Figures referenced (4.1, 4.2) present coefficients for GDP growth at quantiles, medians, and ten percentiles for each cluster (other explanatory variables fixed at late 2020 level).

### Recursive Dynamic Projection Model (stress-test mechanics)
- Projection mechanics:
  - Solvency calculated by recursive projections one-by-one for each bank.
  - Evolution of profitability and PDs projected for next period based on regressors evaluated at conditioning vector at date t:
    - Conditioning vector expressed as [Mmac_t | SMScen_mpo, AB___, XMS BCoss sss_i,t] (notation as provided in source).
  - For each cluster, conditional quantiles projected with estimated quantile regression coefficients:
    - ∀ q, Q̂ROA_{i,t+1,q} = α_{L,q}^  + β_{R,q}^ Mmac_t + γ_{R,q}^ Bmacro_{i,t}
    - ∀ q, Q̂ΔNNP N_{i,t+1,q} = α_{N,q}^ + β_{N,q}^ Mmac_t + γ_{N,q}^ Bmacro_{i,t}
- Net losses and loss assumptions:
  - Net losses for each risk level computed by subtracting from projected profitability the provision for non-performing loans, assuming a rate of loss at 75 percent.
  - Profitability can absorb a portion of loan portfolio losses; negative profitability adds to loan portfolio losses.
  - Loss formula presented as:
    - Losses Loss_s: ROÂ − 1{ΔNNP N>0} * 0.75 ΔNNP N
- Capital and regulatory ratio transitions:
  - Capital transition: capital_{t+1} = capital_{t} − 1{NetLosses<0} * NetLosses
  - Regulatory ratio transition shown with provided notation:
    - cBci t+1 L t+1 LR A t0 = cBci t L t −1 (LLL BBBB <0) * LLL BBBB / LR A t0
  - Important FSAP assumption: bank balance sheet size remains constant during stress period (no deleveraging).
    - Rationale: behavioral model for loan volume projections is challenging; maintaining balance sheet size avoids exacerbating crisis via sudden deleveraging; common practice in IMF FSAP stress tests.

_International Monetary Fund — WAEMU FSAP content as provided in the source unit_

### 5.      The projections are then iterated by updating the conditioning vector based on past

### 5.      The projections are then iterated by updating the conditioning vector based on past

### Recursive projections and conditioning vector
- The projections are iterated by updating the conditioning vector based on past scenarios and projections.
- Choice of risk level for determining the conditioning vector is critical; using a high level of risk (95 percent) at each stage would be unrealistic because it would assume banks suffer an extreme idiosyncratic shock at each period.
- To proceed to the next stage, the team retained the median value of the projected variables as the starting point for:
  - 푅푅푅푅퐴퐴
  - Δ푁푁푃푃 푁푁
  - 푐푐퐵퐵푐푐푖푖푡푡퐵퐵 푙푙
    푡푡+1
    퐿퐿푅푅 퐴퐴
    푡푡0
- Projection of conditional quantiles for each period produces the fan charts for:
  - credit risk (Figures 4.3 and 4.5)
  - rate risk (Figures 5.3 and 5.5)

*WEST AFRICAN ECONOMIC AND MONETARY UNION — Annex VI: Matrix of Banking Sector Stress Tests*

### 1. Institutional perimeter
- Institutions included:
  - 99 banks (almost all); several very small banks with insignificant activity or missing data were excluded.
- Market share:
  - More than 95 percent of banking sector assets in the region.
- Data and baseline date:
  - 2000–2020 (macro data), 2010–2020 (banking data).
  - Reference date: Q4 2020.
  - Bank-by-bank data provided by the authorities include historical series over about ten years for:
    - balance sheets, P&L statements, equity, credit breakdowns, and securities holdings.
    - credit risk (e.g., doubtful debts), concentration risk (for deposits and loans), interest rate risk, foreign exchange risk, and liquidity risk.
  - Macroeconomic data (e.g., interest rates, inflation, and climate index) from leading sources (e.g., Bloomberg, Haver, IMF) are used to model macroeconomic linkages.

### 2. Risk propagation channels and methodology
- Methodology:
  - A macroeconomic growth-at-risk model projects the future distribution of real GDP growth as a function of current macrofinancial conditions.
  - Propagation of risks to WAEMU growth is captured by nonlinear density estimators, with shocks transmitted nonlinearly across the GDP distribution.
  - The FSAP team developed a density projection model specifically adapted to low-income countries, with estimation methods that are robust to measurement errors and accurate for small samples.
  - The 99 banks are divided into four groups via statistical learning methods and form clusters that are homogeneous in terms of asset quality, size, capitalization, and asset returns.
  - The conditional distribution of doubtful debts explained by the macroeconomic variables is estimated separately for each group to predict the rise in the probabilities of default (PDs) under each macroeconomic scenario and risk level.
  - Loss recovery assumptions are ad hoc, due to the lack of adequate historical data.
  - The stress test of bank credit portfolios was conducted via a balance sheet method—including estimation of the PDs, calculation of default losses, and equity absorption—and assumed a static balance sheet size and composition during the stressed period.
  - The WAEMU FSAP team used statistical learning methods for processing noisy data and addressing the issue of small sample size.
  - The same methodology has been used to estimate an inflation-at-risk model and its impact on banks’ capital.
- Satellite models:
  - Based on growth-at-risk and inflation-at-risk estimates, and the stress paths over a three-year horizon, the team used a series of satellite models to infer the dynamic of macroeconomic variables of interest (interest rate, inflation, etc.).
- Stress testing horizon:
  - Four years (2021–24).

### 3. Tail shocks, scenarios, and sensitivity analysis
- Scenario analysis:
  - The FSAP constructed a baseline scenario and an adverse scenario.
  - Due to the current COVID-19 crisis, the scenarios entail a recovery-at-risk, modeling the risks of a slow U-shaped recovery and a rapid V-shaped recovery.
  - The baseline scenario is aligned with the IMF’s latest World Economic Outlook and is consistent with WAEMU’s Article IV.
  - The adverse scenarios are structured dynamically as a function of:
    - (i) the macroeconomic shocks of the Article IV report’s Risk Assessment Matrix (RAM);
    - (ii) historical crisis paths in the WAEMU; and
    - (iii) the level of assumed risk (e.g., value at risk of 5 percent).
- Sensitivity analysis:
  - The stress test of concentration risk is conducted by a sensitivity analysis with ad hoc tests of defaults of largest borrowers and withdrawals of largest depositors.

### 4. Risks, buffers, and behavioral adjustments
- Risks/factors assessed:
  - The FSAP models a set of macrofinancial shocks derived from the Article IV report (external demand shock, worsening of the COVID-19 pandemic, climate change, deterioration of international financial conditions, etc.).
  - Propagation of shocks emanating from each country of the monetary zone to the region.
  - The modeling of shocks is nonlinear and dynamic, with the shocks corresponding to points in the distributions of GDP, inflation, and associated macroeconomic variables.
  - The shocks are calibrated based on the unconditional distribution of the explanatory variables.
- Behavioral adjustments:
  - Bank balance sheet compositions and sizes are assumed to be static over the entire stress period.
  - Dividend distributions are only permitted for banks that meet the regulatory capital requirements and have positive profits.

### 5. Regulatory and market-based standards and parameters
- Calibration of risk parameters:
  - The risk parameters are estimated via density models using structural relationships and estimated distributions conditional on the macrofinancial conditions at the reference date.
  - This approach permits time series modeling of relationships, while also accounting for the already exceptionally strong shock of COVID-19.
  - The risk paths are calibrated—in distribution percentiles—on the WAEMU’s crises of 1982, 1994, and 2011, which enables different recoveries (U-shaped and V-shaped) to be captured.
- Regulatory, accounting, and market-based standards:
  - Use of regulatory ratios and minimum capital requirements imposed by the BCEAO as IMF stress test standard.

### 6. Reporting format for results
- Output presentation includes:
  - A decline in banking sector capital during the stress period, under different scenarios.
  - Number of banks and share of banking sector assets of banks whose capital falls below the regulatory minimum.
  - Recapitalization needs in percent of GDP.

*Source: WEST AFRICAN ECONOMIC AND MONETARY UNION — INTERNATIONAL MONETARY FUND (Annex VI: Matrix of Banking Sector Stress Tests).*

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_Source: https://www.imf.org/-/media/files/publications/cr/2022/english/1wauea2022004.pdf_