## Annex Table 4.1.1); the banking sector

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### Sample coverage, objective, and composition
- Assets of which account for 73 percent of global banking system assets.
- Objective: include as many banks as necessary to cover at least 80 percent of their respective banking system’s total assets.
- Sample composition: The combined sample contains 347 banks.

### Data and caveats
- Data sources: Fitch, Bloomberg, S&P Global, banks’ financial reports; consolidated annual data covering 1995–2019 for 347 banks.
- Public data limitations:
  - Lower granularity, coverage, and quality compared to supervisory data used in FSAP stress tests.
  - Results should be interpreted with caution when compared with exercises based on supervisory data.
- Key assumptions and features:
  - Static balance sheet assumption for gross loan stocks; only composition of performing and nonperforming assets varies.
  - Financial assets other than loans not actively traded, but market values may vary via trading income/OCI models.
  - Risk weights: held constant for standardized exposures; for IRB exposures a smooth function of changes in PDs.

### Scenarios (2020–2022)
- Scenario set:
  - 2020 WEO baseline (reflects COVID-19: severe recession in 2020 followed by rapid recovery in 2021).
  - October adverse WEO scenario (more severe recession than baseline; assumes second COVID-19 outbreak in early 2021).
  - Severe adverse scenario (protracted pandemic resulting in a two-year recession; assumes no growth in 2022).
  - January 2020 WEO baseline included as reference (pre-COVID-19).
- Key numeric scenario feature:
  - In the June baseline scenario, weighted-average real GDP drops by 8 percent year on year in 2020 for the country sample considered under the GST.
- Macro-financial variables included (seven): real GDP, unemployment rate, short-term interest rates, term spreads, stock price growth, corporate bond spreads, VIX.
- Variable projection approach:
  - For baseline, IMF desk-projected variables from WEO used for all except stock price growth, corporate bond spreads, and VIX; those three are projected via empirical bridge equations.

### Stress testing methodology (two-part)
- Part 1 — Econometric models (cross-bank-country panel regressions) for P&L and OCI components:
  - Modeled components: net loan losses (NLL), net interest margins (NIM), net trading income (NTI), net fee and commission income (NFCI), and a residual income/expense component (RESR).
  - Loan loss model further decomposed into PD and LGD.
  - NTI modeled using bank-specific five-year average and standard deviation with a scalar reflecting scenario-implied stress.
  - Tax and dividend rules: set to zero if projected net income before taxes is negative; otherwise use 2019 effective tax rates and dividend payout ratios. No deferred tax asset accumulation considered.
- Part 2 — Balance sheet projection module:
  - Maps P&L, RWAs, and OCI projections into balance sheets and CET1 impact.
  - Includes dividend distribution and effective tax rate assumptions.
- Estimation approach and model design features:
  - Bank-fixed effects panel structures and a Bayesian Model Averaging (BMA) methodology specific to panel models to account for model uncertainty.
  - Sign constraints imposed on long-run multipliers of macro-financial predictor variables.
  - For internationally active banks (GSIBs), exposure-weighted right-hand side variables used to capture cross-border dependencies without increasing coefficient count.
  - No lags of dependent variables included to maximize predictive content from macro-financial variables.
  - NII defined relative to total interest earning assets net of NPL stocks, so rising NPL ratio reduces absolute NII even with constant NIM.

### Econometric model components (definitions preserved)
- NIM = NII(t) / (av(TEA(t)+PR(t)-NPL(t), TEA(t-1)+PR(t-1)-NPL(t-1)))
  - TEA = Total Earning Assets net of loan loss provisions stocks (PR).
  - NII = Net Interest Income. NPL = Nonperforming Loans.
- NLR = NL(t) / (TEA(t-1)+PR(t-1)-NPL(t-1)) where NL = Net Loan Loss flow.
- NTIR(t) = av(NTIR) - a(t) stdev(NTIR); NTIR(t) = NTI(t) / TA(t).
- NFCIR(t) = NFCI(t) / av(TEA(t)+PR(t), TEA(t-1)+PR(t-1)).
- RESR = RES / av(TEA(t)+PR(t), TEA(t-1)+PR(t-1)); RES = NI after tax + tax + NL – NII – NTI – NFCI.
- DOCIR = (OCI(t)-OCI(t-1)) / av(AFS(t), AFS(t-1)) where AFS = Available for Sale securities.

### Panel econometric models and model selection
- Model structure: y_t = a_i + b_ig X_i,t,g + ε_it with bank fixed effects; X includes contemporaneous and lagged macro-financial predictors.
- Predictor set: real GDP growth, unemployment rates (and year-on-year changes), stock price growth, short-term interest rates, term spreads, corporate bond spreads, VIX; plus first lags — 16 variables total.
- Model space combinatorics:
  - K = 16, L = 5 leads to I = 6,884 initial models.
  - Restrictions (no unemployment levels and changes together; each equation must contain at least one macro variable) reduced models to 4,722.
- Model averaging:
  - Individual models combined via predictive performance-weighted averages using Bayesian Information Criteria (BIC).
  - Sign constraints on long-run multipliers ensure economically consistent long-run effects; models failing constraints removed from candidate pool.
- Asset correlation: set to 10 percent in PD/LGD decomposition.

### Decomposing net loan loss rates into PD and LGD
- Decomposition rationale: infer dynamics of performing and nonperforming loan stocks to compute NII and other balance sheet items.
- Steps:
  1. Compute bank-specific LGD risk index k using through-the-cycle (TTC) LGD proxy equal to historical long-term average coverage ratio (accounting provision stocks over NPL stocks). TTC PD proxy derived by dividing long-term average net loss rates (NLR) by TTC LGD proxy. Asset correlation set to 10 percent. LGD index k assumed constant over scenario horizon.
     - Note: Online Annex Figure 4.1.1 reports TTC PD and LGD proxies for 261 entities (locational data).
  2. Imply point-in-time (PiT) PD using k and PiT NLR projections: PiT PD formula given as P P D_i^h_PiT = Φ( Φ^{-1}(N L R_i^h_PiT) + k_i ).
  3. Imply PiT LGDs: LGD_i^h_PiT = NLR_i^h_PiT / PPD_i^h_PiT.

### Satellite analysis: corporate vs household loan loss provisions
- Purpose: decompose aggregate loan loss provision dynamics into corporate and household borrower risk contributions.
- Data universe (quarterly consolidated bank financials):
  - Sample period: 2005:Q1 – 2020:Q1.
  - 910 banks; 15 advanced economies and 9 emerging economies.
  - Data sources: SNL, EBA, Bloomberg; LGD data from EBA.
  - Advanced Economy (15): AUT, BEL, CAN, DEU, DNK, ESP, FIN, GBR, ITA, KOR, NLD, NOR, SGP, SWE, USA.
  - Emerging Economy (9): CHN, IDN, IND, MEX, MYS, POL, RUS, THA, TUR.
- Empirical approach:
  - Local projection method (Jordà 2005) with the specification in equation (1) to project loan loss provisions per average loans.
  - Key variables: bank fixed effects, time fixed effects, corporate exposure share, household exposure share, changes in expected losses for corporate and consumer loans.
  - Changes in riskiness measured using country-average PDs for nonfinancial private firms from Moody’s KMV and LGDs from EBA; where EBA data not available, average LGD used.
  - Normalization: PDs for retail loans proxied as ρ ⋅ Z_c,t-1 where Z is harmonized unemployment rate from OECD; ρ estimated by regressing EBA retail loan PDs on unemployment rate.
- Estimation details:
  - Equations estimated by OLS.
  - Observations weighted by country GDP divided by the number of observations for that country to give each country weight equal to economy size.
- Decomposition outcome:
  - Provision changes decomposed into corporate-related component and household-related component via coefficients β_h and γ_h.
  - Share formula for corporate contribution to provisioning provided; Online Annex Figure 4.1.2 illustrates country-level distribution of the share of increase in LLP coming from corporate risk for main GST sample.

### Quantification of the impact of government guarantees
- Simplifying assumptions:
  a. Guarantees have full uptake and are kept for whole analysis period.
  b. Guarantees cover only credit to non-financial corporations (NFC).
  c. All banks in a country are equally covered by guarantees.
  d. Guarantees do not impact borrower probability of default.
- Representation in model:
  - Guarantees reduce LGD of corporate loans proportionally to program size relative to credit to NFC and to banks’ corporate lending share.
  - Example: if guarantees = 5 percent of domestic credit to NFC, then LGD for corporate lending decreases by 5 percentage points (5 percent of losses absorbed by government).
- Provision calculation with guarantees:
  - L L P_i,c = (1 − ShCorp_i) * L L P_i,household + ShCorp_i * (L L P_c,corporate − g_c) ** PPD_i,c
    - g_c is ratio of guarantees program size to credit to NFC.
    - ShCorp_i is share of provisioning from corporate risk absent guarantees.
    - L L P_c,corporate_t_c is country-level loss given default on corporate loans from EBA.
  - If L L P_c,corporate_t_c < g_c, then L L P_i,c = (1 − ShCorp_i) * L L P_i,household.
- Inputs: GST loan loss provision model provides total provisioning; satellite analysis provides household vs corporate decomposition, enabling computation of provisioning with guarantees.

### Mitigation policies: taxonomy and impact on banks
- Policy tracking data sources and counts:
  - European Systemic Risk Board: 1,113 policies (Europe).
  - Financial Stability Board: 2,119 policies (Global).
  - IMF (Financial sector regulation and supervision): 353 policies (Global).
  - Keefe, Bruyette and Woods: 118 policies (US, Europe, Japan).
  - Yale School of Management COVID-19 tracker: 3,705 policies (Global).
  - IMF and UBS country aggregate fiscal policy databases (used for guarantees estimates).
- Scope of quantified policies:
  - Excludes very broad policies affecting general macroeconomic conditions (captured via macro scenarios).
  - Excludes policies that indirectly lower provisions via borrower support or recognition deferrals (largely embedded in scenarios or difficult to quantify).
  - Focuses on policies that operate directly on bank capital by:
    - Lowering the denominator of capital ratios (RWA or leverage exposure).
    - Reducing capital deductions.
    - Eliminating or softening capital buffer requirements (countercyclical, conservation, systemic risk buffers).
- Policy classification and modeling principles:
  - Policies reviewed for 29 countries and classified by effect on bank capital; pan-European policies applied to relevant SSM/EBA banks where appropriate.
  - Five financial accounts used to capture policy impacts: CET1, Tier 1, risk-weighted assets, leverage exposure, and change in minimum capital requirement (CET1 buffers).
  - Common modeling patterns:
    e. Capital buffer impacts expressed relative to RWA; estimates reference future RWA.
    f. Dividend cancellation: applied based on forecast dividends in stress test model; typically limited to 2020 with resumption thereafter.
    g. Share buybacks: modeled assuming 2019 buyback levels would have continued in 2020, with effect limited to policy horizon.
    h. Exclusions from leverage exposure (deposits with central bank, domestic government bonds) straightforwardly reduce leverage exposure.
- Illustrative unique policy treatments:
  i. U.S. mortgage risk-weighting suspension: system-wide overdue mortgages rose from about 3.0 percent pre-COVID to about 7.9 percent by end-May; model assumes risk-weight rises from 20 percent to 80 percent on downgrade and applies to each bank’s reported on-balance sheet mortgages outstanding.
  j. U.S. Payroll Protection Program (PPP): program size reported as $659 billion; model assumes stress-tested banks (over 80 percent of US bank assets) account for all PPP loans and that PPP RWA density equals each bank’s overall credit RWA density.
- Aggregation:
  - Bank-specific estimates of policy impacts on balance sheet metrics converted into pro-forma effects on capital ratios.
  - Bank-level pro-forma capital effects aggregated to country, regional, and global estimates.

*Source: IMF staff (online annex).*

### Annex Table 4.1.1); the banking sector

### Annex Table 4.1.1); the banking sector

### Sample coverage
- Assets of which account for 73 percent of global banking system assets.

### Objective
- The objective was to include as many banks as necessary to cover at least 80 percent of their respective banking system’s total assets.

### Sample composition
- The combined sample contains 347 banks.

*This is an Annex to Chapter 4 of the October 2020 Global Financial Stability Report.*

### Annex include John Caparusso, Marco Gross, Nicola Pierri, and Tomohiro Tsuruga.

### Annex include John Caparusso, Marco Gross, Nicola Pierri, and Tomohiro Tsuruga.

### Data and Caveats
- Data sources: Fitch, Bloomberg, S&P Global, banks’ financial reports; consolidated annual data covering 1995–2019 for 347 banks.
- Public data limitations:
  - Lower granularity, coverage, and quality compared to supervisory data used in FSAP stress tests.
  - Results should be interpreted with caution when compared with exercises based on supervisory data.
- Assumptions and features:
  - Static balance sheet assumption for gross loan stocks; only composition of performing and nonperforming assets varies.
  - Financial assets other than loans not actively traded, but market values may vary via trading income/OCI models.
  - Risk weights: held constant for standardized exposures; for IRB exposures a smooth function of changes in PDs.

### Scenarios (2020–2022)
- Scenario set:
  - 2020 WEO baseline (reflects COVID-19: severe recession in 2020 followed by rapid recovery in 2021).
  - October adverse WEO scenario (more severe recession than baseline; assumes second COVID-19 outbreak in early 2021).
  - Severe adverse scenario (protracted pandemic resulting in a two-year recession; assumes no growth in 2022).
  - January 2020 WEO baseline included as reference (pre-COVID-19).
- Key numeric scenario features:
  - In the June baseline scenario, weighted-average real GDP drops by 8 percent year on year in 2020 for the country sample considered under the GST.
- Macro-financial variables included (seven):
  - real GDP, unemployment rate, short-term interest rates, term spreads, stock price growth, corporate bond spreads, VIX.
- Variable projection approach:
  - For baseline, IMF desk-projected variables from WEO used for all except stock price growth, corporate bond spreads, and VIX; those three are projected via empirical bridge equations.

### Stress Testing Methodology
- Two-part methodology:
  1. Econometric models (cross-bank-country panel regressions) for P&L and OCI components:
     - Modeled components: net loan losses (NLL), net interest margins (NIM), net trading income (NTI), net fee and commission income (NFCI), and a residual income/expense component (RESR).
     - Additional decomposition of loan loss model into PD and LGD (see Section C).
     - NTI modeled using bank-specific five-year average and standard deviation with a scalar reflecting scenario-implied stress.
     - Tax and dividend rules: set to zero if projected net income before taxes is negative; otherwise use 2019 effective tax rates and dividend payout ratios. No deferred tax asset accumulation considered.
  2. Balance sheet projection module:
     - Maps P&L, RWAs, and OCI projections into balance sheets and CET1 impact.
     - Includes dividend distribution and effective tax rate assumptions.
- Estimation approach:
  - Bank-fixed effects panel structures and a Bayesian Model Averaging (BMA) methodology specific to panel models to account for model uncertainty.
  - Sign constraints imposed on long-run multipliers of macro-financial predictor variables.
  - For internationally active banks (GSIBs), exposure-weighted right-hand side variables used to capture cross-border dependencies without increasing coefficient count.
- Model design features:
  - No lags of dependent variables included to maximize predictive content from macro-financial variables.
  - NII defined relative to total interest earning assets net of NPL stocks, so rising NPL ratio reduces absolute NII even with constant NIM.

### Methodology: Econometric Model Components (definitions preserved)
- NIM = NII(t) / (av(TEA(t)+PR(t)-NPL(t), TEA(t-1)+PR(t-1)-NPL(t-1)))
  - TEA = Total Earning Assets net of loan loss provisions stocks (PR).
  - NII = Net Interest Income. NPL = Nonperforming Loans.
- NLR = NL(t) / (TEA(t-1)+PR(t-1)-NPL(t-1)) where NL = Net Loan Loss flow.
- NTIR(t) = av(NTIR) - a(t) stdev(NTIR); NTIR(t) = NTI(t) / TA(t).
- NFCIR(t) = NFCI(t) / av(TEA(t)+PR(t), TEA(t-1)+PR(t-1)).
- RESR = RES / av(TEA(t)+PR(t), TEA(t-1)+PR(t-1)); RES = NI after tax + tax + NL – NII – NTI – NFCI.
- DOCIR = (OCI(t)-OCI(t-1)) / av(AFS(t), AFS(t-1)) where AFS = Available for Sale securities.

### Panel Econometric Models and Model Selection
- Model structure: y_t = a_i + b_ig X_i,t,g + ε_it with bank fixed effects; X includes contemporaneous and lagged macro-financial predictors.
- Predictor set: real GDP growth, unemployment rates (and year-on-year changes), stock price growth, short-term interest rates, term spreads, corporate bond spreads, VIX; plus first lags — 16 variables total.
- Model space combinatorics:
  - K = 16, L = 5 leads to I = 6,884 initial models.
  - Restrictions (no unemployment levels and changes together; each equation must contain at least one macro variable) reduced models to 4,722.
- Model averaging:
  - Individual models combined via predictive performance-weighted averages using Bayesian Information Criteria (BIC).
  - Sign constraints on long-run multipliers ensure economically consistent long-run effects; models failing constraints removed from candidate pool.
- Asset correlation: set to 10 percent in PD/LGD decomposition.

### Decomposing Net Loan Loss Rates into PD and LGD
- Decomposition rationale: infer dynamics of performing and nonperforming loan stocks to compute NII and other balance sheet items.
- Steps:
  1. Compute bank-specific LGD risk index k using through-the-cycle (TTC) LGD proxy equal to historical long-term average coverage ratio (accounting provision stocks over NPL stocks). TTC PD proxy derived by dividing long-term average net loss rates (NLR) by TTC LGD proxy. Asset correlation set to 10 percent. LGD index k assumed constant over scenario horizon.
     - Note: Online Annex Figure 4.1.1 reports TTC PD and LGD proxies for 261 entities (locational data).
  2. Imply point-in-time (PiT) PD using k and PiT NLR projections: PiT PD formula given as P P D_i^h_PiT = Φ( Φ^{-1}(N L R_i^h_PiT) + k_i ).
  3. Imply PiT LGDs: LGD_i^h_PiT = NLR_i^h_PiT / PPD_i^h_PiT.

### Satellite Analysis: Corporate vs Consumer Loan Loss Provisions
- Purpose: decompose aggregate loan loss provision dynamics into corporate and household borrower risk contributions.
- Data universe (quarterly consolidated bank financials):
  - Sample period: 2005:Q1 – 2020:Q1.
  - 910 banks; 15 advanced economies and 9 emerging economies.
  - Data sources: SNL, EBA, Bloomberg; LGD data from EBA.
  - Advanced Economy (15): AUT, BEL, CAN, DEU, DNK, ESP, FIN, GBR, ITA, KOR, NLD, NOR, SGP, SWE, USA.
  - Emerging Economy (9): CHN, IDN, IND, MEX, MYS, POL, RUS, THA, TUR.
- Empirical approach:
  - Local projection method (Jordà 2005) with the specification in equation (1) to project loan loss provisions per average loans.
  - Key variables: bank fixed effects, time fixed effects, corporate exposure share, household exposure share, changes in expected losses for corporate and consumer loans.
  - Changes in riskiness measured using country-average PDs for nonfinancial private firms from Moody’s KMV and LGDs from EBA; where EBA data not available, average LGD used.
  - Normalization: PDs for retail loans proxied as ρ ⋅ Z_c,t-1 where Z is harmonized unemployment rate from OECD; ρ estimated by regressing EBA retail loan PDs on unemployment rate.
- Estimation details:
  - Equations estimated by OLS.
  - Observations weighted by country GDP divided by the number of observations for that country to give each country weight equal to economy size.
- Decomposition outcome:
  - Provision changes decomposed into corporate-related component and household-related component via coefficients β_h and γ_h.
  - Share formula for corporate contribution to provisioning provided; Online Annex Figure 4.1.2 illustrates country-level distribution of the share of increase in LLP coming from corporate risk for main GST sample.

### Quantification of the Impact of Government Guarantees
- Simplifying assumptions for quantification:
  a. Guarantees have full uptake and are kept for whole analysis period.
  b. Guarantees cover only credit to non-financial corporations (NFC).
  c. All banks in a country are equally covered by guarantees.
  d. Guarantees do not impact borrower probability of default.
- Representation in model:
  - Guarantees reduce LGD of corporate loans proportionally to program size relative to credit to NFC and to banks’ corporate lending share.
  - Example: if guarantees = 5 percent of domestic credit to NFC, then LGD for corporate lending decreases by 5 percentage points (5 percent of losses absorbed by government).
- Provision calculation with guarantees:
  - L L P_i,c = (1 − ShCorp_i) * L L P_i,household + ShCorp_i * (L L P_c,corporate − g_c) ** PPD_i,c
    - g_c is ratio of guarantees program size to credit to NFC.
    - ShCorp_i is share of provisioning from corporate risk absent guarantees.
    - L L P_c,corporate_t_c is country-level loss given default on corporate loans from EBA.
  - If L L P_c,corporate_t_c < g_c, then L L P_i,c = (1 − ShCorp_i) * L L P_i,household.
- Inputs: GST loan loss provision model provides total provisioning; satellite analysis provides household vs corporate decomposition, enabling computation of provisioning with guarantees.

### Mitigation Policies: Taxonomy and Impact on Banks
- Data sources for policy tracking:
  - European Systemic Risk Board: 1,113 policies (Europe).
  - Financial Stability Board: 2,119 policies (Global).
  - IMF (Financial sector regulation and supervision): 353 policies (Global).
  - Keefe, Bruyette and Woods: 118 policies (US, Europe, Japan).
  - Yale School of Management COVID-19 tracker: 3,705 policies (Global).
  - IMF and UBS country aggregate fiscal policy databases (used for guarantees estimates).
- Scope of quantified policies:
  - Excludes very broad policies affecting general macroeconomic conditions (captured via macro scenarios).
  - Excludes policies that indirectly lower provisions via borrower support or recognition deferrals (largely embedded in scenarios or difficult to quantify).
  - Focuses on policies that operate directly on bank capital by:
    - Lowering the denominator of capital ratios (RWA or leverage exposure).
    - Reducing capital deductions.
    - Eliminating or softening capital buffer requirements (countercyclical, conservation, systemic risk buffers).
- Policy classification and modeling principles:
  - Policies reviewed for 29 countries and classified by effect on bank capital; pan-European policies applied to relevant SSM/EBA banks where appropriate.
  - Five financial accounts used to capture policy impacts: CET1, Tier 1, risk-weighted assets, leverage exposure, and change in minimum capital requirement (CET1 buffers).
  - Common modeling patterns:
    e. Capital buffer impacts expressed relative to RWA; estimates reference future RWA.
    f. Dividend cancellation: applied based on forecast dividends in stress test model; typically limited to 2020 with resumption thereafter.
    g. Share buybacks: modeled assuming 2019 buyback levels would have continued in 2020, with effect limited to policy horizon.
    h. Exclusions from leverage exposure (deposits with central bank, domestic government bonds) straightforwardly reduce leverage exposure.
- Illustrative unique policy treatments:
  i. U.S. mortgage risk-weighting suspension: system-wide overdue mortgages rose from about 3.0 percent pre-COVID to about 7.9 percent by end-May; model assumes risk-weight rises from 20 percent to 80 percent on downgrade and applies to each bank’s reported on-balance sheet mortgages outstanding.
  j. U.S. Payroll Protection Program (PPP): program size reported as $659 billion; model assumes stress-tested banks (over 80 percent of US bank assets) account for all PPP loans and that PPP RWA density equals each bank’s overall credit RWA density.
- Aggregation:
  - Bank-specific estimates of policy impacts on balance sheet metrics converted into pro-forma effects on capital ratios.
  - Bank-level pro-forma capital effects aggregated to country, regional, and global estimates.

*Source: IMF staff (online annex).*

### References

### onlineannex41 - References

### Cited works
- Gross, M., and J. Población. 2017. “Implications of Model Uncertainty for Bank Stress Testing.” Journal of Financial Services Research 55:31–58.
- Jordà, Ò. 2005. “Estimation and Inference of Impulse Responses by Local Projections.” American Economic Review 95 (1): 161–82.

*Source: onlineannex41 - References (onlineannex41 - References)*

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_Source: https://www.imf.org/-/media/files/publications/gfsr/2020/october/english/onlineannex41.pdf_