## 1. Baseline: Selected Bank Balance Sheet Items for Country X, as at End-2009

## Source details

**Canonical URL:** [1. Baseline: Selected Bank Balance Sheet Items for Country X, as at End-2009](https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10282.pdf)

## Other formats

- [Markdown version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10282.pdf.md)
- [Structured JSON version](/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10282.pdf.json)

---

### I. INTRODUCTION
- Global financial crisis increased focus on stress testing: methodologies, assumptions, data quality, and transparency.
- Well-designed stress tests add value to risk management and contingency planning for authorities and individual institutions.
- Top-down stress testing use has expanded to lower-income countries, but such environments commonly feature:
  - Supervisory capacity is often low.
  - Human resources are limited.
  - Regulatory frameworks remain largely inadequate.
  - Implementation and enforcement track records tend to be weak.
  - Data required for stress testing are usually of poor quality (insufficient, incomplete, or inaccurate).
- Stand-alone stress tests in underdeveloped systems can be misleading and potentially harmful if flawed findings prompt inappropriate decisions.
- Paper focus:
  - Problems associated with stress tests applied to underdeveloped banking systems.
  - Proposal of a more useful alternative focused on credit risk and solvency (modified Čihák (2007) credit risk stress test).
  - Stress testing must be closely coordinated with on-site supervision and complemented by other supervisory tools and information.

### II. THE DATA
- Data are hypothetical numerical examples for “Country X,” comprising 5 individual banks.
- Key baseline assumptions:
  - Required capital adequacy ratio (CAR) = 12 percent; banks below this would be required to recapitalize.
  - Risk-weighted assets (RWA) assumed to remain the same post-shock (conservative).
  - Profits assumed zero for the shock period; full impact reflected in capital.
  - Where loan-classification data are available, loans are assumed fully provisioned prior to the shock; otherwise loans may be under-provisioned.
  - Provisions are topped up post-shock to ensure loans are again fully provisioned.

### III. WEAKNESSES IN THE “AD HOC SHOCK” METHOD
- Ideal approach: econometric links between macro shocks and NPLs; absent that, testers use subjective ad hoc shocks.
- Common ad hoc choices:
  1. Shocks to aggregate NPLs vs. to loans by classification:
     - If granular classification data unavailable, shocks applied to aggregate NPLs.
     - Two provisioning estimation methods:
       a. Assume provisions of 100 percent of additional NPLs.
       b. Assume provisions using the average of performing and non-performing provisioning rates.
  2. Shocks to the banking system vs. to individual banks:
     - If individual bank data incomplete, perform system-wide aggregated “back of the envelope” stress tests.
- Key conceptual weaknesses:
  - Short-term shocks should be constrained by amounts in each classification; shock magnitudes exceeding those maxima imply implicit assumptions about under-reporting or longer horizons.
  - Uniform shocks mask heterogeneity of bank loan books; qualitative information should supplement lack of granularity.

### IV. BASELINE: SELECTED BANK BALANCE SHEET ITEMS (END-2009) — key baseline figures (values in millions of domestic currency units unless stated)
- Capital (1): All Banks 530.0; Bank 1 30.0; Bank 2 160.0; Bank 3 220.0; Bank 4 80.0; Bank 5 40.0.
- RWA (2): All Banks 3,520.0; Bank 1 170.0; Bank 2 1,100.0; Bank 3 1,400.0; Bank 4 550.0; Bank 5 300.0.
- CAR (in percent) (3) = (1)/(2)*100: All Banks 15.1; Bank 1 17.6; Bank 2 14.5; Bank 3 15.7; Bank 4 14.5; Bank 5 13.3.
- Total loans (4) = (5)+(8): All Banks 1,448.0; Bank 1 71.0; Bank 2 385.0; Bank 3 615.0; Bank 4 287.0; Bank 5 90.0.
- Performing loans (5) = (6)+(7): All Banks 1,375.0; Bank 1 65.0; Bank 2 365.0; Bank 3 590.0; Bank 4 275.0; Bank 5 80.0.
- Normal and pass loans (6): All Banks 1,250.0; Bank 1 55.0; Bank 2 330.0; Bank 3 530.0; Bank 4 260.0; Bank 5 75.0.
- Special mention loans (7): All Banks 125.0; Bank 1 10.0; Bank 2 35.0; Bank 3 60.0; Bank 4 15.0; Bank 5 5.0.
- NPLs (8) = (9)+(10)+(11): All Banks 73.0; Bank 1 6.0; Bank 2 20.0; Bank 3 25.0; Bank 4 12.0; Bank 5 10.0.
  - Substandard (9): All Banks 26.0; Bank 1 3.0; Bank 2 10.0; Bank 3 5.0; Bank 4 5.0; Bank 5 3.0.
  - Doubtful (10): All Banks 20.0; Bank 1 2.0; Bank 2 5.0; Bank 3 10.0; Bank 4 2.0; Bank 5 1.0.
  - Loss (11): All Banks 27.0; Bank 1 1.0; Bank 2 5.0; Bank 3 10.0; Bank 4 5.0; Bank 5 6.0.
- NPL ratio (in percent) (12) = (8)/(4)*100: All Banks 5.0; Bank 1 8.5; Bank 2 5.2; Bank 3 4.1; Bank 4 4.2; Bank 5 11.1.
- Total provisions currently held (13): All Banks 58.5; Bank 1 3.5; Bank 2 13.9; Bank 3 23.1; Bank 4 10.1; Bank 5 8.0.
- Total provisions that should be held (14) = (15)+(17): All Banks 58.5; Bank 1 3.5; Bank 2 13.9; Bank 3 23.1; Bank 4 10.1; Bank 5 8.0.
  - General provision (15) = (16): All Banks 12.5; Bank 1 0.6; Bank 2 3.3; Bank 3 5.3; Bank 4 2.6; Bank 5 0.8.
  - Rate against normal and pass loans 0.01 (16): All Banks 12.5; Bank 1 0.6; Bank 2 3.3; Bank 3 5.3; Bank 4 2.6; Bank 5 0.8.
  - Specific provision (17) = (18)+(19)+(20)+(21): All Banks 46.0; Bank 1 2.9; Bank 2 10.6; Bank 3 17.8; Bank 4 7.5; Bank 5 7.3.
    - (18) = (7)*Rate against special mention loans 0.03: All Banks 3.8; Bank 1 0.3; Bank 2 1.1; Bank 3 1.8; Bank 4 0.5; Bank 5 0.2.
    - (19) = (9)*Rate against substandard loans 0.20: All Banks 5.2; Bank 1 0.6; Bank 2 2.0; Bank 3 1.0; Bank 4 1.0; Bank 5 0.6.
    - (20) = (10)*Rate against doubtful loans 0.50: All Banks 10.0; Bank 1 1.0; Bank 2 2.5; Bank 3 5.0; Bank 4 1.0; Bank 5 0.5.
    - (21) = (11)*Rate against loss loans 1.00: All Banks 27.0; Bank 1 1.0; Bank 2 5.0; Bank 3 10.0; Bank 4 5.0; Bank 5 6.0.
- Under/over-provisioning (22) = (13)-(14): All Banks 0.0; all banks 0.0.

### V. MAXIMUM MIGRATION EXAMPLE — worst-case where all loans migrate one category down (selected post-shock figures)
- Post-shock (all loans migrate one classification down):
  - NPLs (26): All Banks 198.0.
  - Total provisions that should be held (30): All Banks 122.5.
  - Under/over-provisioning (38) = (13)-(30): All Banks -64.1.
  - New capital (39) = (1)+(38): All Banks 466.0.
  - New CAR (in percent) (40) = (39)/(2)*100: All Banks 13.2.
  - Impact on CAR (in percent) (41) = (40)-(3): All Banks -1.8.
  - Bank-level impact on CAR (row 41): Bank 1 -2.8; Bank 2 -1.6; Bank 3 -2.0; Bank 4 -1.9; Bank 5 -1.3.
- Conclusion: under this extreme migration none of the banks would be required to recapitalize in the example; system CAR falls by 1.8 percentage points from 15.1 to 13.2.

### VI. SCENARIO 1a: Shock to aggregate NPLs (400 percent) with 100 percent provisioning assumption vs. shock to loans by classification (graduated provisions) — key numeric outcomes (All Banks)
- Shock to Aggregate NPLs (100 percent provisioning assumption):
  - Total provisions that should be held (9) = (6)*Rate 1.00 = 73.0.
  - Under/over-provisioning (10) = (8)-(9) = -14.6.
  - New capital (15) = (1)+(14) = 281.9.
  - New CAR (in percent) (16) = (15)/(2)*100 = 8.0.
  - Impact on CAR (in percent) (17) = (15)-(3) = -7.0.
- Shock to NPLs by Classification (graduated provisions):
  - Total provisions that should be held (30) = 223.8.
  - Under/over-provisioning (38) = (13)-(30) = -165.3.
  - New capital (39) = (1)+(38) = 364.7.
  - New CAR (in percent) (40) = (39)/(2)*100 = 10.4.
  - Impact on CAR (in percent) (41) = (40)-(3) = -4.7.
- Interpretation:
  - Aggregate-100% method yields system-wide CAR falling by 7.0 percentage points to 8.0 percent.
  - Detailed classification method yields CAR falling by 4.7 percentage points to 10.4 percent.
  - Aggregate-100% method overstates impact (around one-third larger decline in CAR).

### VII. SCENARIO 1b: Shock to aggregate NPLs (400 percent) using average provisioning rates vs. loans by classification — key numeric outcomes (All Banks)
- Average provisioning rates used: 0.02 for performing loans (arithmetic average of 0.01 and 0.03) and 0.567 for NPLs (arithmetic average of 0.2, 0.5 and 1.0).
- Shock to Aggregate NPLs (average provisioning rates):
  - Total provisions that should be held (15) = (16)+(17) = 228.5.
  - Under/over-provisioning (18) = (8)-(15) = -170.0.
  - New capital (19) = (1)+(18) = 360.0.
  - New CAR (in percent) (20) = (19)/(2)*100 = 10.2.
  - Impact on CAR (in percent) (21) = (20)-(3) = -4.8.
- Shock to NPLs by Classification:
  - Impact on CAR (in percent) (41) = -4.7.
- Interpretation:
  - Average provisioning method yields impact nearly identical to detailed classifications: CAR falls by 4.8 percentage points (aggregate-average) vs. 4.7 percentage points (classification).

### VIII. SCENARIO 2: Shock to the banking system vs. to individual banks — heterogeneity and masking by aggregates
- Example for a 400 percent increase in NPLs across loan classifications (post-shock New CARs in percent):
  - All Banks 10.4; Bank 1 11.7; Bank 2 11.2; Bank 3 11.2; Bank 4 9.6; Bank 5 4.0.
- Impact on CAR (in percent):
  - All Banks -4.7; Bank 1 -5.9; Bank 2 -3.4; Bank 3 -4.5; Bank 4 -5.0; Bank 5 -9.3.
- Notable outcomes:
  - Bank 5 CAR declined by 9.3 percentage points to 4.0 percent.
  - Bank 2 capitalization fell by 3.4 percentage points to 11.2 percent, which is below required minimum of 12 percent.
- Interpretation:
  - System aggregates (All Banks) can mask significant distress at individual banks.

### IX. SCENARIO 3: Shocks of increasingly larger magnitudes to NPLs and performing-loan migration — exact New CAR results (in percent)
- New CARs under NPL increases:
  - NPLs increase by 100 percent: All Banks 13.9; Bank 1 16.2; Bank 2 13.7; Bank 3 14.7; Bank 4 13.3; Bank 5 10.9.
  - NPLs increase by 200 percent: All Banks 12.7; Bank 1 14.6; Bank 2 12.9; Bank 3 13.5; Bank 4 12.0; Bank 5 8.5.
  - NPLs increase by 400 percent: All Banks 11.5; Bank 1 13.1; Bank 2 12.0; Bank 3 12.4; Bank 4 10.7; Bank 5 6.0.
- New CARs where performing loans migrate to NPLs:
  - 10 percent of performing loans become NPLs: All Banks 12.8; Bank 1 16.0; Bank 2 12.9; Bank 3 13.0; Bank 4 11.5; Bank 5 11.3.
  - 20 percent of performing loans become NPLs: All Banks 10.4; Bank 1 14.2; Bank 2 11.3; Bank 3 10.2; Bank 4 8.5; Bank 5 9.4.
  - 40 percent of performing loans become NPLs: All Banks 5.7; Bank 1 10.8; Bank 2 8.0; Bank 3 4.6; Bank 4 2.5; Bank 5 5.5.
- Impact on CAR relative to pre-shock CARs (15.1; 17.6; 14.5; 15.7; 14.5; 13.3 respectively):
  - NPLs increase by 100 percent: All Banks -1.2; Bank 1 -1.5; Bank 2 -0.8; Bank 3 -1.1; Bank 4 -1.3; Bank 5 -2.5.
  - NPLs increase by 200 percent: All Banks -2.4; Bank 1 -3.0; Bank 2 -1.7; Bank 3 -2.2; Bank 4 -2.6; Bank 5 -4.9.
  - NPLs increase by 400 percent: All Banks -3.6; Bank 1 -4.6; Bank 2 -2.6; Bank 3 -3.3; Bank 4 -3.9; Bank 5 -7.3.
  - 10 percent migration: All Banks -2.3; Bank 1 -1.7; Bank 2 -1.6; Bank 3 -2.7; Bank 4 -3.0; Bank 5 -2.0.
  - 20 percent migration: All Banks -4.6; Bank 1 -3.4; Bank 2 -3.3; Bank 3 -5.5; Bank 4 -6.0; Bank 5 -3.9.
  - 40 percent migration: All Banks -9.3; Bank 1 -6.9; Bank 2 -6.5; Bank 3 -11.1; Bank 4 -12.1; Bank 5 -7.8.
- Observation: larger increases in NPLs (or larger migration of performing loans to NPLs) mechanically produce larger decreases in CARs; extreme shocks can push CARs well below required minimum.

### X. KEY WEAKNESSES OF AD HOC/EXTREME SHOCKS (summary)
- Assuming 100 percent provisioning for all additional NPLs:
  - Significantly overstates additional provisions required; understates resulting capitalization.
  - Ignores typical progressive migration through classifications with graduating provisioning.
- Aggregated uniform shocks:
  - Mask wide variation in balance sheet soundness across banks.
  - Risk supervisors base contingency planning on potentially meaningless aggregate outputs.
- Extremity of shocks:
  - Extremely large ad hoc shocks will algebraically break any bank/system; without empirical support these results are of limited policy use.
  - Poor raw data quality precludes ability to justify large shocks.

### XI. PROPOSED COMPROMISE: THE “BREAKING POINT” METHOD (REVERSE STRESS TESTING)
- Concept and advantages:
  - Reverse stress test that estimates amounts of classified loans which would reduce a bank’s CAR to a chosen breaking point (example breaking point: 12 percent).
  - Advantages: (i) less dependent on quality of reported data; (ii) does not require ex ante assumptions on size of NPL shocks.
  - Must be complemented by on-site supervisory examinations; not intended as a standalone tool.
- Scenario A: Aggregate breaking point (Table 9) — exact aggregate figures:
  - Pre-shock CAR All Banks 15.1 percent (row 3).
  - Pre-shock NPL ratio 5.0 percent (row 7).
  - Breaking point NPL ratio for banking system (row 13): 17.5 percent.
  - Total NPLs at breaking point (row 14): 253.4.
  - Increase in NPLs (row 16): 180.4.
  - Rate of increase in NPLs (in percent) (row 17): 247.1.
  - Total provisions that should be held post-shock (row 18): 167.5.
  - Under/over-provisioning post-shock (row 21): -109.0.
  - New capital amount required (row 22): 421.0.
  - New CAR after full provisioning (in percent) (row 23): 12.0.
  - Interpretation: system breaking-point NPL ratio ~17.5 percent (from current 5.0 percent); NPLs must increase by 247.1 percent to reach aggregate breaking point; aggregate breaking point masks bank-level heterogeneity.
- Scenario B: Breaking point by loans classification (Table 10) — selected exact figures
  - Breaking-point NPL ratios (row 23): All Banks 18.5; Bank 1 40.5; Bank 2 20.7; Bank 3 17.4; Bank 4 12.7; Bank 5 17.5.
  - Total NPLs at breaking point (row 24): All Banks 267.7; Bank 1 28.8; Bank 2 79.7; Bank 3 107.0; Bank 4 36.4; Bank 5 15.8.
  - Increase in NPLs (row 31): All Banks 194.7; Bank 1 22.8; Bank 2 59.7; Bank 3 82.0; Bank 4 24.4; Bank 5 5.8.
  - Rate of increase in NPLs (in percent) (row 32): All Banks 266.7; Bank 1 379.3; Bank 2 298.5; Bank 3 328.0; Bank 4 203.7; Bank 5 57.5.
  - Total provisions that should be held (row 33): All Banks 165.2; Bank 1 13.0; Bank 2 41.5; Bank 3 74.6; Bank 4 24.0; Bank 5 12.0.
  - Under/over-provisioning (row 41): All Banks -106.7; Bank 1 -9.6; Bank 2 -27.6; Bank 3 -51.5; Bank 4 -14.0; Bank 5 -4.0.
  - New capital amount required after full provisioning (row 42): All Banks 423.3; Bank 1 20.4; Bank 2 132.4; Bank 3 168.5; Bank 4 66.0; Bank 5 36.0.
  - New CAR after full provisioning (in percent) (row 43): All Banks 12.0; Bank 1 12.0; Bank 2 12.0; Bank 3 12.0; Bank 4 12.0; Bank 5 12.0.
- Interpretation:
  - Breaking-point NPL ratios vary widely across banks, reflecting balance-sheet composition and credit exposure relative to capital (e.g., Bank 1 breaking point 40.5 percent vs. Bank 4 breaking point 12.7 percent).

### XII. POLICY AND SUPERVISORY IMPLICATIONS
- Limitations of simple ad hoc extreme stress tests:
  - Often flawed; may produce results of limited supervisory utility without empirical justification.
  - Reliance on extreme assumptions (e.g., 100 percent provisioning) can produce misleadingly severe outcomes.
- Role and use of the breaking-point method:
  - Reverse testing provides a potentially more informative tool where NPL reporting is unreliable.
  - Useful for off-site supervisors to prioritize banks for on-site inspection.
  - Must be complemented by on-site examinations and other supervisory information.
- Comprehensive testing considerations:
  - Stress tests should include other risks (e.g., liquidity risk) in addition to solvency (credit and market risk).
  - Where data are unavailable or unreliable, sometimes refraining from stress testing is preferable to producing misleading results.

_Italic: Source: _wp10282 - 1. Baseline: Selected Bank Balance Sheet Items for Country X, as at End-2009 (excerpt)._

### 1. Baseline: Selected Bank Balance Sheet Items for Country X, as at End-2009 .....................6

### 1. Baseline: Selected Bank Balance Sheet Items for Country X, as at End-2009

### I. INTRODUCTION
- The global financial crisis has placed the topic of stress testing firmly in the spotlight.
- Key issues under scrutiny: methodologies and assumptions applied in stress tests; availability and quality of data used in those tests; debate about transparency and desirability of making stress test results public.
- Well-designed stress tests can add significant value to risk management and contingency planning for both authorities and individual financial institutions in more advanced financial systems.
- Robust stress tests are useful for financial surveillance by international financial institutions, including the International Monetary Fund (IMF).
- Top-down stress testing use has expanded to lower-income countries with underdeveloped financial systems, but:
  - Supervisory capacity is often low.
  - Human resources are limited.
  - Regulatory frameworks remain largely inadequate.
  - Implementation and enforcement track records tend to be weak.
  - Data required for stress testing are usually of poor quality (insufficient, incomplete, or inaccurate).
- Stand-alone stress tests in such environments can be misleading and potentially harmful if flawed findings cause undue consternation or inappropriate decisions.
- Paper focus:
  - Problems associated with stress tests applied to underdeveloped banking systems.
  - Proposes a more useful alternative focused on credit risk and solvency.
  - Demonstrates how a modified version of Čihák’s (2007) credit risk stress test could complement supervisory actions, including on-site examinations.
  - Suggests stress testing must be closely coordinated with on-site supervision and complemented by other supervisory tools and information.

### II. THE DATA
- Data used are hypothetical numerical examples illustrating the issues.
- Baseline data components:
  - An assumed set of capitalization and credit data for the banking system of “Country X,” which comprises 5 individual banks.
  - Assumed local definitions of loan classifications and corresponding provisioning requirements.
  - Required capital adequacy ratio (CAR) for banks in Country X is assumed to be 12 percent, below which banks would be required to recapitalize.
- Key assumptions for CAR calculation:
  - Risk-weighted assets (RWA) are assumed to remain the same post-shock, which would translate to a more conservative result.
  - Profits are assumed to be zero for the period of the shock, so the full impact is reflected in capital.
  - Where loans by classification are available, they are assumed to have been fully provisioned for prior to the shock; where less granular information is available, loans may be under-provisioned for.
  - In all cases, provisions are topped up post-shock to ensure that loans are again fully provisioned for.

### III. WEAKNESSES IN THE “AD HOC SHOCK” METHOD
- Ideal approach: use reliable macroeconomic and financial data and econometric models to quantify historical relationships between macro shocks and non-performing loans (NPLs), then apply macro-scenarios to estimate effects on NPLs, provisions, and capitalization.
- In absence of such data, stress testers make subjective assumptions about shock sizes and may use shortcuts in top-down stress tests.
- Common ad hoc scenarios and methodological choices:
  1. Shocks to aggregate NPLs vs. to loans by classification:
     - When granular loan-classification data are unavailable, shocks are applied directly to aggregate NPLs of the banking system.
     - Two provisioning estimation methods depending on data availability:
       a. Assume provisions of 100 percent of NPLs when calculating impact on capital adequacy, in the absence of more granular information on provisioning requirements.
       b. Assume provisions using the average of performing and non-performing provisioning rates, where information on provisioning requirements is available.
  2. Shocks to the banking system vs. to individual banks:
     - When individual bank data are not provided or incomplete, “back of the envelope” stress tests are performed on the system as a whole using aggregated data.

### IV. STRUCTURE OF THE PAPER (AS PRESENTED)
- Section II: Data description (hypothetical for Country X).
- Section III: Discussion of problems in simple stress test models commonly used in basic financial systems with questionable data quality.
- Section IV: Proposal of an alternative method for stress testing that is less dependent on data quality and highly subjective assumptions, designed to complement on-site supervision.
- Section V: Concluding thoughts.

*Source: _wp10282 - 1. Baseline: Selected Bank Balance Sheet Items for Country X, as at End-2009*

### 3.      Shocks of ever larger magnitudes to NPLs. Credit shocks of increasingly larger

### 3.      Shocks of ever larger magnitudes to NPLs. Credit shocks of increasingly larger magnitudes are applied to estimate the impact on capitalization

### Stress test scenarios and ad hoc shocks (Table 3)
- Scenario types (ad hoc shocks applied to each scenario):
  - Scenario 1. Shock to aggregate NPLs vs. to loans by classification:
    - Aggregate NPLs increase by 400 percent with provisions assumed at 100 percent vs. each NPL classification increases by 400 percent with performing loans representing the remainder, distributed proportionally and with graduating provisions.
  - Scenario 2. Shock to the banking system vs. to individual banks:
    - Each NPL classification increases by 400 percent with performing loans representing the remainder, distributed proportionally and with graduating provisions.
  - Scenario 3. Shocks of ever larger magnitudes to NPLs:
    - Shock to NPLs:
      - NPLs increase by 100 percent.
      - NPLs increase by 200 percent.
      - NPLs increase by 400percent.
    - Shock to performing loans:
      - 10 percent of performing loans become NPLs.
      - 20 percent of performing loans become NPLs.
      - 40 percent of performing loans become NPLs.

- Loan classification provisioning requirements (Table 3):
  - Performing loans — Normal and pass loans: Provisioning Requirement 1 (In percent of outstanding amount).
  - Special mention loans (past due 30–89 days): 3.
  - NPLs:
    - Substandard loans (past due 90–179 days): 20.
    - Doubtful loans (past due 180–359 days): 50.
    - Loss loans (past due 360 days or more): 100.

### Baseline: Selected Bank Balance Sheet Items for Country X, as at End-2009 (Table 1)
- System-wide and bank-level selected items (values in millions of domestic currency units unless stated otherwise):
  - (1) Capital: All Banks 530.0; Bank 1 30.0; Bank 2 160.0; Bank 3 220.0; Bank 4 80.0; Bank 5 40.0.
  - (2) RWA: All Banks 3,520.0; Bank 1 170.0; Bank 2 1,100.0; Bank 3 1,400.0; Bank 4 550.0; Bank 5 300.0.
  - (3) CAR (in percent) = (1)/(2)*100: All Banks 15.1; Bank 1 17.6; Bank 2 14.5; Bank 3 15.7; Bank 4 14.5; Bank 5 13.3.
  - (4) Total loans = (5)+(8): All Banks 1,448.0; Bank 1 71.0; Bank 2 385.0; Bank 3 615.0; Bank 4 287.0; Bank 5 90.0.
  - (5) Performing loans = (6)+(7): All Banks 1,375.0; Bank 1 65.0; Bank 2 365.0; Bank 3 590.0; Bank 4 275.0; Bank 5 80.0.
  - (6) Normal and pass loans: All Banks 1,250.0; Bank 1 55.0; Bank 2 330.0; Bank 3 530.0; Bank 4 260.0; Bank 5 75.0.
  - (7) Special mention loans: All Banks 125.0; Bank 1 10.0; Bank 2 35.0; Bank 3 60.0; Bank 4 15.0; Bank 5 5.0.
  - (8) NPLs = (9)+(10)+(11): All Banks 73.0; Bank 1 6.0; Bank 2 20.0; Bank 3 25.0; Bank 4 12.0; Bank 5 10.0.
  - (9) Substandard loans: All Banks 26.0; Bank 1 3.0; Bank 2 10.0; Bank 3 5.0; Bank 4 5.0; Bank 5 3.0.
  - (10) Doubtful loans: All Banks 20.0; Bank 1 2.0; Bank 2 5.0; Bank 3 10.0; Bank 4 2.0; Bank 5 1.0.
  - (11) Loss loans: All Banks 27.0; Bank 1 1.0; Bank 2 5.0; Bank 3 10.0; Bank 4 5.0; Bank 5 6.0.
  - (12) NPL ratio (in percent) = (8)/(4)*100: All Banks 5.0; Bank 1 8.5; Bank 2 5.2; Bank 3 4.1; Bank 4 4.2; Bank 5 11.1.
  - (13) Total provisions currently held 1/: All Banks 58.5; Bank 1 3.5; Bank 2 13.9; Bank 3 23.1; Bank 4 10.1; Bank 5 8.0.
  - (14) Total provisions that should be held = (15)+(17): All Banks 58.5; Bank 1 3.5; Bank 2 13.9; Bank 3 23.1; Bank 4 10.1; Bank 5 8.0.
  - (15) General provision = (16): All Banks 12.5; Bank 1 0.6; Bank 2 3.3; Bank 3 5.3; Bank 4 2.6; Bank 5 0.8.
  - (16) = (6)*Rate against normal and pass loans 0.01: All Banks 12.5; Bank 1 0.6; Bank 2 3.3; Bank 3 5.3; Bank 4 2.6; Bank 5 0.8.
  - (17) Specific provision = (18)+(19)+(20)+(21): All Banks 46.0; Bank 1 2.9; Bank 2 10.6; Bank 3 17.8; Bank 4 7.5; Bank 5 7.3.
  - (18) = (7)*Rate against special mention loans 0.03: All Banks 3.8; Bank 1 0.3; Bank 2 1.1; Bank 3 1.8; Bank 4 0.5; Bank 5 0.2.
  - (19) = (9)*Rate against substandard loans 0.20: All Banks 5.2; Bank 1 0.6; Bank 2 2.0; Bank 3 1.0; Bank 4 1.0; Bank 5 0.6.
  - (20) = (10)*Rate against doubtful loans 0.50: All Banks 10.0; Bank 1 1.0; Bank 2 2.5; Bank 3 5.0; Bank 4 1.0; Bank 5 0.5.
  - (21) = (11)*Rate against loss loans 1.00: All Banks 27.0; Bank 1 1.0; Bank 2 5.0; Bank 3 10.0; Bank 4 5.0; Bank 5 6.0.
  - (22) Under/over-provisioning = (13)-(14): All Banks 0.0; all banks 0.0.

### Analysis — constraints, data quality, and loan migration (section A)
- Data reliability and maximum short-term shock constraints:
  - If reported data are reliable, short-term shocks should be constrained by the amount of loans in each classification.
  - By definition, past due loans typically migrate down classifications over time, so any shock—no matter how severe—should be limited to the outstanding amount in any one loan classification.
  - The maximum amount by which a loan category can increase in the short-term following any shock should be equivalent to the balance in the category above it.
  - If shocks applied to asset quality in each loan classification exceed the maximum possible amount, then the stress test must be assuming actual shocks plus some under-reporting of NPLs, or that the stress test horizon is over the medium- to long-term.
- Heterogeneity of bank loan books:
  - Loan books may be very different across banks and thus affected differently by a shock.
  - Application of uniform shocks across banks may be unrealistic and uninformative.
  - Where granular data are unavailable, stress test design may need to incorporate qualitative information (e.g., anecdotal evidence on loan book composition).

### Maximum possible migration down classifications (Table 4) — illustrative worst-case shock and impact on capitalization
- Pre-shock summary (selected rows reproduced):
  - (1) Capital: All Banks 530.0.
  - (2) RWA: All Banks 3,520.0.
  - (3) CAR (in percent): All Banks 15.1.
  - (4) Total loans: All Banks 1,448.0.
  - (5) Performing loans: All Banks 1,375.0.
  - (6) Normal and pass loans: All Banks 1,250.0.
  - (7) Special mention loans: All Banks 125.0.
  - (8) NPLs: All Banks 73.0.
  - (13) Total provisions currently held: All Banks 58.5.
  - (14) Total provisions that should be held: All Banks 58.5.
- Post-shock (Shock: All loans migrate from one classification down to the next):
  - (26) NPLs 2/ = 198.0 (All Banks).
  - (30) Total provisions that should be held: 122.5 (All Banks).
  - (38) Under/over-provisioning = (13)-(30): -64.1 (All Banks).
  - Assuming full provisioning after shock:
    - (39) New capital = (1)+(38): 466.0 (All Banks).
    - (40) New CAR (in percent) = (39)/(2)*100: 13.2 (All Banks).
    - (41) Impact on CAR (in percent) = (40)-(3): -1.8 (All Banks).
  - Bank-level impact on CAR (impact on CAR in percent, row 41):
    - Bank 1: -2.8.
    - Bank 2: -1.6.
    - Bank 3: -2.0.
    - Bank 4: -1.9.
    - Bank 5: -1.3.
  - Conclusion from this worst-possible migration example:
    - Resulting impact on capitalization from required increase in provisions appears relatively modest (row 41) at between 1.3–2.8 percentage points.
    - None of the banks in the example would be required to recapitalize following the shock (per the example).

### Scenario 1a: Shock to aggregate NPLs using a 100 percent provisioning rate vs. to loans by classification (Table 5) — key findings
- Approach differences:
  - When only aggregate NPL data are used, stress tester may assume provisions at 100 percent of the additional NPLs (i.e., all are loss loans).
  - Where data on classified loans are available, graduated provisions across NPL classifications are applied.
- Quantitative outcomes for a 400 percent increase in NPLs:
  - Shock to Aggregate NPLs (100 percent provisioning assumption):
    - Total provisions that should be held (9) = (6)*Rate 1.00 = 73.0 (All Banks).
    - Under/over-provisioning (10) = (8)-(9) = -14.6 (All Banks).
    - New capital (15) = (1)+(14) = 281.9 (All Banks).
    - New CAR (in percent) (16) = (15)/(2)*100 = 8.0 (All Banks).
    - Impact on CAR (in percent) (17) = (15)-(3) = -7.0 (All Banks).
  - Shock to NPLs by Classification (graduated provisions):
    - Total provisions that should be held (30) = 223.8 (All Banks).
    - Under/over-provisioning (38) = (13)-(30) = -165.3 (All Banks).
    - New capital (39) = (1)+(38) = 364.7 (All Banks).
    - New CAR (in percent) (40) = (39)/(2)*100 = 10.4 (All Banks).
    - Impact on CAR (in percent) (41) = (40)-(3) = -4.7 (All Banks).
- Interpretation:
  - Using aggregate NPLs with a 100 percent provisioning assumption would result in system-wide CAR falling by 7 percentage points.
  - Using detailed NPL classifications with graduated provisions results in a more moderate decline in CAR of 4.7 percentage points.
  - The estimated impact from the aggregate-100% method is around one-third larger (i.e., the aggregate method yields a larger decline in CAR).

### Scenario 1b: Shock to aggregate NPLs using an average provisioning rate vs. to loans by classification (Table 6) — key findings
- Average provisioning method:
  - Use average rate of 0.02 (arithmetic average of 0.01 and 0.03) for performing loans and average rate of 0.567 (arithmetic average of 0.2, 0.5 and 1.0) for NPLs.
- Quantitative outcomes for a 400 percent increase in NPLs:
  - Shock to Aggregate NPLs (average provisioning rates):
    - Total provisions that should be held (15) = (16)+(17) = 228.5 (All Banks).
    - Under/over-provisioning (18) = (8)-(15) = -170.0 (All Banks).
    - New capital (19) = (1)+(18) = 360.0 (All Banks).
    - New CAR (in percent) (20) = (19)/(2)*100 = 10.2 (All Banks).
    - Impact on CAR (in percent) (21) = (20)-(3) = -4.8 (All Banks).
  - Shock to NPLs by Classification:
    - Impact on CAR (in percent) (41) = -4.7 (All Banks).
- Interpretation:
  - The average provisioning-rate method yields an impact (CAR falling by 4.8 percentage points) almost identical to that from using detailed classifications (4.7 percentage points).
  - Similarity of impact between methods depends on the distribution across NPL classifications.

### Scenario 2: Shock to the banking system vs. to individual banks — key finding (prelude to Table 7)
- Using aggregate system data versus bank-by-bank data:
  - Information derived from shocks to the aggregate system could mask problems among individual banks.
  - Example quantitative result for a 400 percent increase in NPLs across the board:
    - System’s CAR declines by 4.7 percentage points to 10.4 percent (column 1, rows 41 and 40, respectively).

_Italic: Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10282.pdf_

### 1.6 percentage points below the required minimum of 12 percent.

### _wp10282 - 1.6 percentage points below the required minimum of 12 percent.

### Scenario 3: Shocks of increasingly larger magnitudes to NPLs
- Framework:
  - Shocks applied to NPLs range from increases by 100, 200, and 400 percent, and alternative shocks where 10, 20, and 40 percent of performing loans become NPLs (Table 8).
  - It is assumed that loans are fully provisioned for initially. It is assumed that RWA remains the same.
- Key outcome patterns (exact figures from Table 8):
  - New CARs (in percent) under shocks:
    - NPLs increase by 100 percent: All Banks 13.9; Bank 1 16.2; Bank 2 13.7; Bank 3 14.7; Bank 4 13.3; Bank 5 10.9.
    - NPLs increase by 200 percent: All Banks 12.7; Bank 1 14.6; Bank 2 12.9; Bank 3 13.5; Bank 4 12.0; Bank 5 8.5.
    - NPLs increase by 400 percent: All Banks 11.5; Bank 1 13.1; Bank 2 12.0; Bank 3 12.4; Bank 4 10.7; Bank 5 6.0.
    - 10 percent of performing loans become NPLs: All Banks 12.8; Bank 1 16.0; Bank 2 12.9; Bank 3 13.0; Bank 4 11.5; Bank 5 11.3.
    - 20 percent of performing loans become NPLs: All Banks 10.4; Bank 1 14.2; Bank 2 11.3; Bank 3 10.2; Bank 4 8.5; Bank 5 9.4.
    - 40 percent of performing loans become NPLs: All Banks 5.7; Bank 1 10.8; Bank 2 8.0; Bank 3 4.6; Bank 4 2.5; Bank 5 5.5.
  - Impact on CAR (in percent) relative to pre-shock CAR (15.1; 17.6; 14.5; 15.7; 14.5; 13.3):
    - NPLs increase by 100 percent: All Banks -1.2; Bank 1 -1.5; Bank 2 -0.8; Bank 3 -1.1; Bank 4 -1.3; Bank 5 -2.5.
    - NPLs increase by 200 percent: All Banks -2.4; Bank 1 -3.0; Bank 2 -1.7; Bank 3 -2.2; Bank 4 -2.6; Bank 5 -4.9.
    - NPLs increase by 400 percent: All Banks -3.6; Bank 1 -4.6; Bank 2 -2.6; Bank 3 -3.3; Bank 4 -3.9; Bank 5 -7.3.
    - 10 percent of performing loans become NPLs: All Banks -2.3; Bank 1 -1.7; Bank 2 -1.6; Bank 3 -2.7; Bank 4 -3.0; Bank 5 -2.0.
    - 20 percent of performing loans become NPLs: All Banks -4.6; Bank 1 -3.4; Bank 2 -3.3; Bank 3 -5.5; Bank 4 -6.0; Bank 5 -3.9.
    - 40 percent of performing loans become NPLs: All Banks -9.3; Bank 1 -6.9; Bank 2 -6.5; Bank 3 -11.1; Bank 4 -12.1; Bank 5 -7.8.
- Observations from the example (text):
  - Algebraic relationship: larger increases in NPLs mechanically produce larger decreases in CARs.
  - Result: CARs deteriorate as shocks increase and can fall below required capitalization, sometimes significantly (illustrated by Bank 5 in Scenario 2 falling by 9.3 percentage points to 4 percent).

### Scenario 2 (illustrative ad hoc shock to banking system vs individual banks)
- Aggregate vs individual outcomes (Table 7 excerpt):
  - Example where aggregate outcome masks heterogeneity:
    - Bank 5 CAR declined by 9.3 percentage points to 4 percent (column 6, rows 41 and 40).
    - Bank 2 capitalization fell by 3.4 percentage points to 11.2 percent (column 3, rows 41 and 40), below the required minimum 12 percent.
  - Under/over-provisioning and post-shock capitalization shown with exact figures:
    - Post-shock New CARs (in percent) under the 400 percent across loan classifications shock: All Banks 10.4; Bank 1 11.7; Bank 2 11.2; Bank 3 11.2; Bank 4 9.6; Bank 5 4.0.
    - Impact on CAR (in percent): All Banks -4.7; Bank 1 -5.9; Bank 2 -3.4; Bank 3 -4.5; Bank 4 -5.0; Bank 5 -9.3.

### Key weaknesses of ad hoc and extreme shocks (summary of findings)
- Any assumption of 100 percent provisioning following a shock:
  - Would significantly overstate additional provisions required and thus underestimate resulting capitalization.
  - Loan quality typically moves progressively through classifications with graduating provisioning rates, not straight to loss loans with 100 percent provisioning.
- Aggregated uniform shocks:
  - Mask wide variation in balance sheet soundness across banks.
  - Risk that supervisors base contingency planning on potentially meaningless aggregate stress-test outputs.
- Extremity of shocks:
  - Sufficiently large ad hoc shocks would break any bank or banking system algebraically, producing results that may be uninformative without empirical evidence supporting plausibility of such tail shocks.
  - Lack of quality raw data precludes ability to quantify or justify large shocks, limiting practical supervisory actionability.

### A proposed compromise: the “Breaking Point” method (reverse stress testing)
- Concept:
  - A “stressing until it breaks” exercise (reverse stress testing) that estimates amounts of classified loans which would reduce a bank’s CAR to a chosen breaking point (example: 12 percent).
  - Advantages: (i) does not depend heavily on the quality of reported data; (ii) does not require assumptions on size of overall NPL shocks.
  - Must be complemented by on-site supervisory examinations; cannot be used standalone.
- Scenario A: Shock to aggregate NPLs (Table 9)
  - Aggregate breaking point calculations (exact figures):
    - Pre-shock CAR All Banks 15.1 percent (row 3).
    - Pre-shock NPL ratio 5.0 percent (row 7).
    - Breaking point NPL ratio for banking system: 17.5 percent (row 13).
    - Total NPLs at breaking point: 253.4 (row 14).
    - Increase in NPLs: 180.4 (row 16).
    - Rate of increase in NPLs (in percent): 247.1 (row 17).
    - Total provisions that should be held post-shock: 167.5 (row 18).
    - Under/over-provisioning post-shock: -109.0 (row 21).
    - New capital amount required: 421.0 (row 22).
    - New CAR (in percent) after full provisioning: 12.0 (row 23).
  - Interpretation:
    - Breaking point NPL ratio for the banking system is around 17.5 percent, compared to current 5 percent.
    - NPLs would have to increase by almost 250 percent from current levels.
    - Aggregate breaking point is of limited use for on-site examiners because it masks bank-level heterogeneity.
- Scenario B: Shock to loans by classification (Table 10)
  - Method assumptions:
    - A certain percentage of existing performing loans become NPLs for each bank.
    - New NPL amounts remain in same proportions across categories as pre-shock balances.
    - Performing loan balances remain in same proportions as pre-shock.
    - It is assumed that loans are fully provisioned for initially; NPLs increase proportionately across categories; RWA remains the same.
  - Breaking-point NPL ratios (exact figures, column 1–6, row 23):
    - All Banks 18.5; Bank 1 40.5; Bank 2 20.7; Bank 3 17.4; Bank 4 12.7; Bank 5 17.5.
  - Exact numeric example post-shock (selected figures from Table 10):
    - Total NPLs at breaking point (row 24): All Banks 267.7; Bank 1 28.8; Bank 2 79.7; Bank 3 107.0; Bank 4 36.4; Bank 5 15.8.
    - Increase in NPLs (row 31): All Banks 194.7; Bank 1 22.8; Bank 2 59.7; Bank 3 82.0; Bank 4 24.4; Bank 5 5.8.
    - Rate of increase in NPLs (in percent) (row 32): All Banks 266.7; Bank 1 379.3; Bank 2 298.5; Bank 3 328.0; Bank 4 203.7; Bank 5 57.5.
    - Total provisions that should be held (row 33): All Banks 165.2; Bank 1 13.0; Bank 2 41.5; Bank 3 74.6; Bank 4 24.0; Bank 5 12.0.
    - Under/over-provisioning (row 41): All Banks -106.7; Bank 1 -9.6; Bank 2 -27.6; Bank 3 -51.5; Bank 4 -14.0; Bank 5 -4.0.
    - New capital amount required after full provisioning (row 42): All Banks 423.3; Bank 1 20.4; Bank 2 132.4; Bank 3 168.5; Bank 4 66.0; Bank 5 36.0.
    - New CAR (in percent) after full provisioning (row 43): All Banks 12.0; Bank 1 12.0; Bank 2 12.0; Bank 3 12.0; Bank 4 12.0; Bank 5 12.0.
  - Interpretation:
    - Breaking-point NPL ratios vary widely across banks, reflecting balance-sheet composition and relative credit exposure to capital.
    - Example: Bank 1 breaking point ~40.5 percent; Bank 4 breaking point ~12.7 percent—despite both Bank 2 and Bank 4 having pre-shock CAR of 14.5 percent and being fully provisioned, Bank 2 can absorb an NPL ratio up to 20.7 percent while Bank 4 reaches the CAR threshold at 12.7 percent due to larger credit exposure relative to capital.

### Policy and supervisory implications (drawn from text)
- Usefulness and limits of stress testing:
  - Simple stress tests using ad hoc and extreme shocks are flawed and may produce results of limited supervisory utility.
  - Stress tests should not rely solely on ad hoc extreme shocks; they need empirical justification or else produce findings with unclear policy implications.
- Role of the breaking point method:
  - Provides a potentially more informative reverse-testing tool where reporting of NPLs is unreliable.
  - Offers off-site supervisors guidance on which banks to prioritize for on-site inspection.
  - Must be complemented by on-site examination findings and other supervisory information.
- Comprehensive testing:
  - Stress tests should be comprehensive and include other risks, e.g., liquidity risk, not only solvency (credit and market risk).
  - Where data are unavailable or unreliable, sometimes refraining from stress testing may be more prudent than producing misleading results.

*Source: Authors’ calculations and analysis in the provided IMF working paper excerpt.*

---


_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2010/_wp10282.pdf_