## Annex 1.1 IMF Global Stress Test (GST) Scenarios

## Source details

**Canonical URL:** [Annex 1.1 IMF Global Stress Test (GST) Scenarios](https://www.imf.org/-/media/files/publications/gfsr/2025/october/english/ch1annex.pdf)

## Other formats

- [Markdown version](/-/media/files/publications/gfsr/2025/october/english/ch1annex.pdf.md)
- [Structured JSON version](/-/media/files/publications/gfsr/2025/october/english/ch1annex.pdf.json)

---

### Purpose and scope
- Details the macrofinancial scenario used in the October 2025 GFSR Global Stress Tests.
- Focus of related analysis: “Higher Capital Ratios Strengthen Global Banks but the Weak Tail of Banks Remains Substantial.”
- Preparers and related sections:
  - GST annex prepared by Xiaodan Ding, Srobona Mitra, and Silvia Ramirez.
  - NBFI definitions prepared by Silvia Ramirez.
  - Banks–NBFI stress test section prepared by John Caparusso, Xiaodan Ding, Mindaugas Leika, and Srobona Mitra.

### Stress scenarios and key modelling assumptions
- Two components of analysis:
  - Sensitivity analysis: does not assume further shocks beyond immediate NBFI drawdowns.
  - Scenario analysis: adds the NBFI stress impact to GST results from the global stagflationary scenario.
- Common shock assumptions for both analyses:
  - Stress leads to an inability of NBFIs to refinance their debt.
  - Followed by a significant drawdown—up to 100 percent—of existing credit and liquidity facilities provided by banks to NBFIs.
  - Solvency analysis assumes reassessment of credit risk of the entire NBFI loan portfolio, including credit lines drawn during stress.
- Liquidity analysis:
  - Compares NBFI-driven outflows to available liquid assets using less-strict and more-strict definitions of liquid assets.
  - Identifies banks that would face a funding gap.

### Data coverage, cut-offs, and samples
- Jurisdictions covered: United States and European Union (plus Norway, Liechtenstein, and Iceland in EBA data).
- Cut-off dates:
  - US sensitivity analysis: Q2 2025; scenario analysis (GST sample): Q4 2024.
  - EU: Q2 2024; with exposures to NBFIs increased to match aggregate Q4 2024 data.
- Sample sizes and consolidation:
  - US sensitivity analysis: operating company level, reduced sample of 362 entities with available data and exposure to NBFIs.
  - US scenario analysis (GST sample): consolidated holding company level.
  - EU: 109 entities plus data for all other banks (aggregated) as reported by EBA; consolidated (cross-border, banking group level only).

### Data sources and proxies
- United States:
  - Regulatory: FRB Y-9C reports for scenario analysis; FFIEC Call Report for sensitivity analysis and liquidity stress.
  - Available: loans to NBFIs by type; liquidity data (cash and reserves at banks; aggregate data on unencumbered securities); funding ratios; capital components; RWAs for credit risk.
  - Missing: RWAs for NBFI loans; exposures to NBFIs by instrument granularity; Credit conversion factors (CCFs); off-balance sheet exposures to GSEs.
- European Union (EBA + additional countries):
  - Regulatory: EBA Transparency exercise and EBA website reports.
  - Available/proxies: loans and debt securities as proxy for loans to NBFIs; proxy for off-balance sheet commitments; cash and reserves at banks; securities; capital components; RWAs for credit risk; EBA data on asset encumbrance.
  - Missing: RWAs for NBFI loans; exposures to NBFIs by instrument granularity; CCFs; bank-by-bank asset encumbrance; data for exposures to NBFIs belonging to own group.
- Core data issues:
  - Publicly available data on banks’ exposures to NBFIs is sparse and varies across jurisdictions.
  - Data limitations require multiple assumptions and sensitivity tests.

### Key parameter values and baseline assumptions
- Starting point for risk-weight density: 20 percent.
- Starting Credit Conversion factor: 50 percent.
- Stress assumption for NBFI exposures:
  - Risk weights increase to 50 percent on all NBFI exposures.
  - Credit Conversion factor increases to 100 percent.
- Drawdown rates assumed in sensitivity tests: 50 and 100 percent.
- For the US sample at end-2023: share of loans provided by banks to NBFIs that were credit lines: 81 percent, with an average utilization rate of 40 percent.
- EU/EA supervisory assessments: banks’ exposure to NBFIs is close to 10 percent of total assets, with loans making up nearly half.

### Analytical approach and calculation steps (US and EU differences)
- Overall logic:
  - Assess solvency impact by increasing risk weights on NBFI exposures (including off-balance sheet credit lines migrating on-balance sheet when drawn).
  - Assess liquidity impact by calculating potential outflows from NBFI drawdowns and comparing to available liquid assets.
  - For scenario analysis, add the impact of higher risk-weighted assets from NBFI stress to the GST stagflationary scenario results to assess additional banks weakened by NBFI stress.
- US-specific approach:
  - Sensitivity analysis uses solo (non-consolidated) data to include a broader set of banks, including smaller institutions.
  - Step 1: Outflow calculations for each bank j in the sample (notational formula reported in source).
  - Step 2: Treatment of irrevocable vs. cancelable credit lines:
    - Data do not identify irrevocable vs. cancelable lines; the analysis assumes all credit lines—both irrevocable and cancelable—are gradually utilized and, in the worst-case scenario, reach 100 percent drawdown.
  - Use aggregated unused commitments to NBFIs to expand sample; sensitivity test drawdown rates of 50 and 100 percent.
- EU-specific approach:
  - Uses consolidated (cross-border, banking group level) data for significant institutions reported to EBA.
  - Off-balance sheet exposures scaled proportional to share of loans to NBFIs and increased to match aggregate EBA numbers.
  - Asset encumbrance ratios used as reported by EBA per country.

### Sources of uncertainty and limitations highlighted
- Key uncertainties:
  - Risk weight densities across banks.
  - Credit conversion factors (CCFs).
  - Off-balance-sheet exposures to NBFIs.
  - Asset encumbrance at the bank level.
  - Granularity of exposures by instrument (loans, derivatives, repos/reverse repos, securities, equity instruments).
  - Distinction between irrevocable and cancelable commitments.
- Data limitations lead to reliance on proxies, assumptions, and sensitivity ranges rather than precise loss estimates.
- The analysis does not estimate credit losses from banks’ exposures due to insufficient information; instead, it assumes rating downgrades and/or declines in NBFI financial performance lead to higher risk weights.

### Analytical outputs and intended use
- Outputs used to:
  - Identify banks that could face funding gaps due to NBFI stress.
  - Estimate reduction in CET1 ratios driven by higher risk-weighted assets from NBFI exposures (via risk-weight reassessment and migration of off-balance sheet items).
  - Assess additional number of GST-sample banks weakened when NBFI stress is added to the global stagflationary scenario.
- Comparative notes:
  - Approach differs from FRB 2025 exploratory analysis by not estimating credit losses directly and by estimating liquidity impacts using immediately available liquidity (cash, balances at banks, unencumbered securities).

### Liquidity impact — data, metric, and failure rule
- Data and key variables:
  - Source of bank-level liquidity variables: FFIEC Call Reports.
  - Narrow vs broad liquidity definition parameter:
    - A is scenario parameter.
    - For the narrow (stricter) definition of liquidity we assume A=0 (only cash and balances at banks available for liquidity purposes).
    - If A=1, banks are also using unencumbered securities to meet liquidity outflows.
  - Only Level 1 assets (based on accounting classification) were included in liquidity calculations.
- Net liquidity position (NLP) calculation (symbolic equation preserved): NLPj = (liquidity components from Call Reports) + A * (unencumbered securities term) * (TOOOd... term) − (outflow term).
- Failure rule:
  - Bank is illiquid if NLP is <0.
- Analysis constraints:
  - Makes no assumption about the time horizon of outflows.
  - Lacks data on inflows (majority of banks, apart from G-SIBs, do not report or are not subject to LCR requirements and reporting).
  - Does not assume deposit withdrawal from banks and is based on individual bank liquidity position (ignores systemwide redistribution of liquidity).

### Liquidity assembly and scaling (EU specifics)
- EU data sources for exposures:
  - EBA transparency exercise: “Gross carrying amount on Loans and advances (including at amortized cost and fair value) - by exposure” for “Financial corporations other than credit institutions”.
  - Only performing loans included when calculating additional risk weights (share of NPLs in loans to NBFIs is 0.6 percent of all loans to NBFIs as of Q2 2024).
  - “Gross carrying amount on Debt securities (including at amortized cost and fair value) - by exposure” for “Financial corporations other than credit institutions”; only performing securities included (share of NPLs in debt securities is 0.5 percent as of Q2 2024).
- For the EU test, debt securities were excluded from the simulated performing exposure because they constitute about 1 percent of total exposure to NBFIs in terms of assets.
- Off-balance-sheet aggregation and scaling:
  - Initial aggregate off-balance-sheet estimate: EUR Bn 632.
  - EBA published aggregate off-balance-sheet (Q4 2024): EUR Bn 950.
  - IMF estimate is approximately 51 percent lower than EBA’s number.
  - To correct for the difference, each bank’s off-balance-sheet exposure was multiplied by the difference ratio (scaling factor derived from EUR Bn 632 vs EUR Bn 950).
- Final NLP equation for EU banks (structure preserved): NLPj = (cash and short-term items terms) + A * (unencumbered securities and other elements aggregated) * (1 − A Ecccc...) − outflow term.
- Only Level 1 assets included in calculations.

### Limitations and exclusions in liquidity analysis
- No assumption on outflow timing and no inflow data for most banks.
- Analysis excludes systemwide liquidity redistribution.
- Many smaller banks are not subject to LCR reporting, limiting granularity.

### Findings — sample-level liquidity characteristics
- Table excerpts (select columns preserved as in source):
  - Sample of 14 banks (with NLP<0 under broad liquidity metrics): 19 30 17 60 62 222 −2.4 102 21
  - Sample of 362 banks: 13 15 7 77 190 308 −3.2 80 3
- Interpretation:
  - In the United States, banks that fail the liquidity test tend to have higher dependence on non-core funding, a lower share of short-term investments, a higher loan-to-deposit ratio, and a higher ratio of unused commitments to total assets. These are mostly smaller banks in the sample.
  - In the European Union, banks do not face major liquidity challenges because market liquidity remains abundant under the ECB’s monetary policy framework and banks can pledge credit claims as collateral to the ECB. Aggregate country-level AE ratios may mask significant differences across banks and may understate liquidity due to encumbrance practices.

### Cross-validation and concentration
- EBA risk assessment note: banks’ off-balance sheet exposure is uneven and concentrated among largest banks.
- IMF validated the proxy assumption (share of loan portfolios to NBFIs as proxy for share of off-balance-sheet exposures to NBFIs) using U.S. data and found a strong correlation.

### Interaction with solvency analysis
- Liquidity analysis is separate from solvency impact estimation but informs the broader scenario exercise.
- Solvency analysis (Step 4) uses same data sources to estimate RWA and CET1 impacts from higher credit line utilization; it:
  - Focuses only on RWAs (not on potential credit losses).
  - Excludes derivatives, equity positions, and other exposures to NBFIs.
  - Does not simulate deposit outflows but assumes NBFIs’ use of credit lines leads to 100 percent outflow to other financial institutions.

### Key quantitative assumptions used across liquidity/solvency scenario
- Credit conversion factors (CCFs) for existing unused credit facilities: CCF assumed = 50%.
- Utilization of credit lines: assumed 100 percent draw-down.
- RWAs for existing on-balance-sheet loans:
  - Shock to drawdown leads to an increase in RWAs for simulated drawdown plus change due to one-notch downgrade in securitization exposures or secured lines.
  - If average exposure is rated A and downgraded to BBB, delta in risk-weight requirement = 30 percent (assumption similar to FRB).
  - Final RWD of exposures set as 50 and 100 percent (shocks as 30 and 80 percent respectively).
  - 휕휕j (assumed change in RWAs due to one-notch downgrade) set as 30 and 80 percent because NBFIs face liquidity issues and are likely downgraded by at least one notch.

### Macro-result of combined GST incorporation
- Incorporation steps:
  - Matching individual banks using ISIN codes to the GST sample.
  - Applying country average impact to banks with missing data.
  - Imposing additional capital impact on sample banks over the GST adverse scenario horizon and updating the weak bank list based on GST criteria.
- Reported scenario outcome:
  - The share of weak banks in the Advanced Economies (the U.S. and EU) increases from about 20 percent in the GST adverse scenario to 24 percent, with the additional weak banks coming from Europe.
  - In the U.S., banks exposed to additional NBFI risks are already considered weak in the GST adverse scenario.

### Additional observations
- U.S. banks that fail the narrow liquidity test also show a high impact on solvency; only a few of the weakest banks have a high share of non-core funding relative to total funding, making them more vulnerable to hypothetical funding outflows.
- EU banks benefit from ECB collateral frameworks (e.g., pledging credit claims), but aggregate metrics may conceal bank-level encumbrance patterns.
- Off-balance-sheet exposure to NBFIs is concentrated among the largest banks per EBA.
- Correlation between NBFI off-balance-sheet exposures and loans to NBFIs in the U.S. is significant (used to validate proxy).

*Source: Annex 1.1, Annexes 1.2 and 1.3 text from ch1annex - Annex 1.1 IMF Global Stress Test (GST) Scenarios (October 2025).*

### Annex 1.1 IMF Global Stress Test (GST) Scenarios

### Annex 1.1 IMF Global Stress Test (GST) Scenarios

### Purpose and scope
- Details the macrofinancial scenario used in the October 2025 GFSR Global Stress Tests.
- Focus of related analysis: “Higher Capital Ratios Strengthen Global Banks but the Weak Tail of Banks Remains Substantial.”
- Related sections and preparers:
  - GST annex prepared by Xiaodan Ding, Srobona Mitra, and Silvia Ramirez.
  - NBFI definitions prepared by Silvia Ramirez.
  - Banks–NBFI stress test section prepared by John Caparusso, Xiaodan Ding, Mindaugas Leika, and Srobona Mitra.

### Stress scenarios and key modelling assumptions
- Two components of analysis: sensitivity analysis and scenario analysis (Figure A1.3.1).
  - Sensitivity analysis: does not assume further shocks beyond immediate NBFI drawdowns.
  - Scenario analysis: adds the NBFI stress impact to GST results from the global stagflationary scenario.
- Common shock assumptions for both analyses:
  - Stress leads to an inability of NBFIs to refinance their debt.
  - Followed by a significant drawdown—up to 100 percent—of existing credit and liquidity facilities provided by banks to NBFIs.
  - Solvency analysis assumes reassessment of credit risk of the entire NBFI loan portfolio, including credit lines drawn during stress.
- Liquidity analysis:
  - Compares NBFI-driven outflows to available liquid assets using less-strict and more-strict definitions of liquid assets.
  - Identifies banks that would face a funding gap.

### Data coverage, cut-offs, and samples
- Jurisdictions covered: United States and European Union (plus Norway, Liechtenstein, and Iceland in EBA data).
- Cut-off dates:
  - US sensitivity analysis: Q2 2025; scenario analysis (GST sample): Q4 2024.
  - EU: Q2 2024; with exposures to NBFIs increased to match aggregate Q4 2024 data.
- Sample sizes and consolidation:
  - US sensitivity analysis: operating company level, reduced sample of 362 entities with available data and exposure to NBFIs.
  - US scenario analysis (GST sample): consolidated holding company level.
  - EU: 109 entities plus data for all other banks (aggregated) as reported by EBA; consolidated (cross-border, banking group level only).

### Data sources and proxies
- United States:
  - Regulatory: FRB Y-9C reports for scenario analysis; FFIEC Call Report for sensitivity analysis and liquidity stress.
  - Available: loans to NBFIs by type; liquidity data (cash and reserves at banks; aggregate data on unencumbered securities); funding ratios; capital components; RWAs for credit risk.
  - Missing: RWAs for NBFI loans; exposures to NBFIs by instrument granularity; Credit conversion factors (CCFs); off-balance sheet exposures to GSEs.
- European Union (EBA + additional countries):
  - Regulatory: EBA Transparency exercise and EBA website reports.
  - Available/proxies: loans and debt securities as proxy for loans to NBFIs; proxy for off-balance sheet commitments; cash and reserves at banks; securities; capital components; RWAs for credit risk; EBA data on asset encumbrance.
  - Missing: RWAs for NBFI loans; exposures to NBFIs by instrument granularity; CCFs; bank-by-bank asset encumbrance; data for exposures to NBFIs belonging to own group.
- Core data issues noted:
  - Publicly available data on banks’ exposures to NBFIs is sparse and varies across jurisdictions.
  - Data limitations require multiple assumptions and sensitivity tests.

### Key parameter values and baseline assumptions (preserve exact values)
- Starting point for risk-weight density: 20 percent.
- Starting Credit Conversion factor: 50 percent.
- Stress assumption for NBFI exposures:
  - Risk weights increase to 50 percent on all NBFI exposures.
  - Credit Conversion factor increases to 100 percent.
- Drawdown rates assumed in sensitivity tests: 50 and 100 percent.
- For the US sample at end-2023: share of loans provided by banks to NBFIs that were credit lines: 81 percent, with an average utilization rate of 40 percent.
- EU/EA supervisory assessments indicate banks’ exposure to NBFIs is close to 10 percent of total assets, with loans making up nearly half.

### Analytical approach and calculation steps (US and EU differences)
- Overall logic:
  - Assess solvency impact by increasing risk weights on NBFI exposures (including off-balance sheet credit lines migrating on-balance sheet when drawn).
  - Assess liquidity impact by calculating potential outflows from NBFI drawdowns and comparing to available liquid assets.
  - For scenario analysis, add the impact of higher risk-weighted assets from NBFI stress to the GST stagflationary scenario results to assess additional banks weakened by NBFI stress.
- US-specific approach:
  - Sensitivity analysis uses solo (non-consolidated) data to include a broader set of banks, including smaller institutions.
  - Step 1: Outflow calculations for each bank j in the sample (notational formula reported in source).
  - Step 2: Treatment of irrevocable vs. cancelable credit lines:
    - Data do not identify irrevocable vs. cancelable lines; the analysis assumes all credit lines—both irrevocable and cancelable—are gradually utilized and, in the worst-case scenario, reach 100 percent drawdown.
  - Use aggregated unused commitments to NBFIs to expand sample; sensitivity test drawdown rates of 50 and 100 percent.
- EU-specific approach:
  - Uses consolidated (cross-border, banking group level) data for significant institutions reported to EBA.
  - Off-balance sheet exposures scaled proportional to share of loans to NBFIs and increased to match aggregate EBA numbers.
  - Asset encumbrance ratios used as reported by EBA per country.

### Sources of uncertainty and limitations highlighted
- Key uncertainties:
  - Risk weight densities across banks.
  - Credit conversion factors (CCFs).
  - Off-balance sheet exposures to NBFIs.
  - Asset encumbrance at the bank level.
  - Granularity of exposures by instrument (loans, derivatives, repos/reverse repos, securities, equity instruments).
  - Distinction between irrevocable and cancelable commitments.
- Data limitations lead to reliance on proxies, assumptions, and sensitivity ranges rather than precise loss estimates.
- The analysis does not estimate credit losses from banks’ exposures due to insufficient information; instead, it assumes rating downgrades and/or declines in NBFI financial performance lead to higher risk weights.

### Analytical outputs and intended use
- Outputs used to:
  - Identify banks that could face funding gaps due to NBFI stress.
  - Estimate reduction in CET1 ratios driven by higher risk-weighted assets from NBFI exposures (via risk-weight reassessment and migration of off-balance sheet items).
  - Assess additional number of GST-sample banks weakened when NBFI stress is added to the global stagflationary scenario.
- Comparative notes:
  - Approach differs from FRB 2025 exploratory analysis by not estimating credit losses directly and by estimating liquidity impacts using immediately available liquidity (cash, balances at banks, unencumbered securities).

*Source: Annex 1.1, Annexes 1.2 and 1.3 text from ch1annex - Annex 1.1 IMF Global Stress Test (GST) Scenarios (October 2025).*

### 14. Step 3. Liquidity impact. We use data from FFIEC Call Reports to obtain the following variables:

### 14. Step 3. Liquidity impact

### Data and key variables
- Source of bank-level liquidity variables: FFIEC Call Reports.
- Narrow vs broad liquidity definition parameter:
  - A is scenario parameter.
  - For the narrow (stricter) definition of liquidity we assume A=0 (only cash and balances at banks available for liquidity purposes).
  - If A=1, banks are also using unencumbered securities to meet liquidity outflows.
- Only Level 1 assets (based on accounting classification) were included in liquidity calculations.

### Liquidity position metric and failure rule
- Net liquidity position (NLP) calculation (symbolic equation preserved in source): NLPj = (liquidity components from Call Reports) + A * (unencumbered securities term) * (TOOOd... term) minus (outflow term).
- Bank is illiquid if NLP is <0.
- The analysis:
  - Makes no assumption about the time horizon of outflows.
  - Lacks data on inflows (majority of banks, apart from G-SIBs, do not report or are not subject to LCR requirements and reporting).
  - Does not assume deposit withdrawal from banks and is based on individual bank liquidity position (i.e., ignores systemwide redistribution of liquidity).

### Outputs reported
- Number of banks with NLP <0.
- Their share in terms of total assets.
- Share of liquidity gap of banks with negative liquidity position in terms of TA.

### Additional methodological notes (EU sample)
- Data sources for EU exposures:
  - EBA transparency exercise: “Gross carrying amount on Loans and advances (including at amortized cost and fair value) - by exposure” for “Financial corporations other than credit institutions”.
  - Only performing loans included when calculating additional risk weights (share of NPLs in loans to NBFIs is 0.6 percent of all loans to NBFIs as of Q2 2024).
  - “Gross carrying amount on Debt securities (including at amortized cost and fair value) - by exposure” for “Financial corporations other than credit institutions”; only performing securities included (share of NPLs in debt securities is 0.5 percent as of Q2 2024).
- For the EU test, debt securities were excluded from the simulated performing exposure because they constitute about 1 percent of total exposure to NBFIs in terms of assets.
- Off-balance-sheet aggregation and scaling:
  - Initial aggregate off-balance-sheet estimate: EUR Bn 632.
  - EBA published aggregate off-balance-sheet (Q4 2024): EUR Bn 950.
  - IMF estimate is approximately 51 percent lower than EBA’s number.
  - To correct for the difference, each bank’s off-balance-sheet exposure was multiplied by the difference ratio (scaling factor derived from EUR Bn 632 vs EUR Bn 950).

### Step 3 (EU) — Liquidity data assembly
- Final NLP equation for EU banks preserves the structure in the source: NLPj = (cash and short-term items terms) + A * (unencumbered securities and other elements aggregated) * (1 − A Ecccc...) − outflow term.
- Only Level 1 assets included in calculations.

### Limitations and exclusions in liquidity analysis
- No assumption on outflow timing and no inflow data for most banks.
- Analysis excludes systemwide liquidity redistribution.
- Many smaller banks are not subject to LCR reporting, limiting granularity.

### Findings — sample-level liquidity characteristics (Table A1.3.2 excerpt)
- Table values for select liquidity/funding metrics (columns preserved as in source):
  - Sample of 14 banks (with NLP<0 under broad liquidity metrics): 19 30 17 60 62 222 -2.4 102 21
  - Sample of 362 banks: 13 15 7 77 190 308 -3.2 80 3
- Interpretation in source:
  - In the United States, banks that fail the liquidity test tend to have higher dependence on non-core funding, a lower share of short-term investments, a higher loan-to-deposit ratio, and a higher ratio of unused commitments to total assets. These are mostly smaller banks in the sample.
  - In the European Union, banks do not face major liquidity challenges because market liquidity remains abundant under the ECB’s monetary policy framework and banks can pledge credit claims as collateral to the ECB. Aggregate country-level AE ratios may mask significant differences across banks and may understate liquidity due to encumbrance practices.

### Cross-validation and concentration
- EBA risk assessment note: banks’ off-balance sheet exposure is uneven and concentrated among largest banks.
- The IMF validated the proxy assumption (share of loan portfolios to NBFIs as proxy for share of off-balance-sheet exposures to NBFIs) using U.S. data and found a strong correlation.

### Interaction with solvency analysis (context for liquidity step)
- The liquidity analysis is separate from solvency impact estimation but informs the broader scenario exercise.
- The solvency analysis (Step 4) uses same data sources to estimate RWA and CET1 impacts from higher credit line utilization; it:
  - Focuses only on RWAs (not on potential credit losses).
  - Excludes derivatives, equity positions, and other exposures to NBFIs.
  - Does not simulate deposit outflows but assumes NBFIs’ use of credit lines leads to 100 percent outflow to other financial institutions.

### Key quantitative assumptions used across liquidity/solvency scenario
- Credit conversion factors (CCFs) for existing unused credit facilities: CCF assumed = 50%.
- Utilization of credit lines: assumed 100 percent draw-down.
- RWAs for existing on-balance-sheet loans:
  - Shock to drawdown leads to an increase in RWAs for simulated drawdown plus change due to one-notch downgrade in securitization exposures or secured lines.
  - If average exposure is rated A and downgraded to BBB, delta in risk-weight requirement = 30 percent (assumption similar to FRB).
  - Final RWD of exposures set as 50 and 100 percent (shocks as 30 and 80 percent respectively).
  - 휕휕j (assumed change in RWAs due to one-notch downgrade) set as 30 and 80 percent because NBFIs face liquidity issues and are likely downgraded by at least one notch.

### Macro-result of combined GST incorporation
- The combined solvency impact on U.S. and EU banks from the NBFI shock (focused on RWA effect) was incorporated into the GST stress test results by:
  - Matching individual banks using ISIN codes to the GST sample.
  - Applying country average impact to banks with missing data.
  - Imposing additional capital impact on sample banks over the GST adverse scenario horizon and updating the weak bank list based on GST criteria.
- Scenario outcome reported in source:
  - The share of weak banks in the Advanced Economies (the U.S. and EU) increases from about 20 percent in the GST adverse scenario to 24 percent, with the additional weak banks coming from Europe.
  - In the U.S., banks exposed to additional NBFI risks are already considered weak in the GST adverse scenario.

### Additional observations highlighted in the source
- U.S. banks that fail the narrow liquidity test also show a high impact on solvency; only a few of the weakest banks have a high share of non-core funding relative to total funding, making them more vulnerable to hypothetical funding outflows.
- EU banks benefit from ECB collateral frameworks (e.g., pledging credit claims), but aggregate metrics may conceal bank-level encumbrance patterns.
- Off-balance-sheet exposure to NBFIs is concentrated among the largest banks per EBA.
- Correlation between NBFI off-balance-sheet exposures and loans to NBFIs in the U.S. is significant (used to validate proxy).

*Source: Global Financial Stability Report Chapter 1, Online Annex (excerpts: “14. Step 3. Liquidity impact.”).*

### 4. The  analytical  sample  combines  SEC  Form  N-PORT  filings  from  the  2025Q2  submission  cycle—

### ch1annex - 4. The  analytical  sample  combines  SEC  Form  N-PORT  filings  from  the  2025Q2  submission  cycle—

### Analytical sample and descriptive statistics
- Sample construction:
  - Combines SEC Form N-PORT filings from the 2025Q2 submission cycle (reporting portfolio holdings and exposures for 2025Q1) with historical Lipper fund-flow statistics.
  - Includes funds classified by Lipper as Mutual Funds in the Bond asset category.
  - Limited to the intersection of these sources: U.S.-domiciled bond mutual funds (regardless of investment objective). Foreign funds not subject to N-PORT filing requirements are excluded by construction.
- Table A2.4.2 — General sample statistics:
  - Sample size: 1235 bond mutual funds
- Top 3 bond fund types (US Mutual Fund Objective) by count:
  - Core Bond Funds 12.6%
  - High Yield Funds 6.4%
  - Short Investment Grade Debt Funds 6.2%
- Top 3 bond fund types (US Mutual Fund Objective) by total assets:
  - Core Bond Funds 41.2%
  - Multi-Sector Income Funds 13.4%
  - Short Investment Grade Debt Funds 5.2%
- Assets, Liabilities, and Treasury Holdings (Sum (bn); Weighted Average (bn); Weighted Median (bn); Weighted (5th, 95th) percentile (bn)):
  - Total assets: 4894.3; 114.8; 30.2; (1.1, 410.3)
  - Total liabilities: 696.1; 31.3; 1.1; (0.0, 163.1)
  - Treasury Holdings: 1126.7; 31.6; 5.8; (0.0, 166.7)
- Note: Fund type reflects a fund’s US Mutual Fund Objective as reported by Lipper. Weighting of average, median and 5th and 95th percentile is based on funds’ total assets.

### Fund-flow scenarios and assumptions
- Flow data and imputation:
  - Fund flow assumptions for the March 2020 and April 2025 scenarios derived from actual fund-level monthly data from LSEG Lipper.
  - Historical flow percentages (as percent of a fund’s assets under management) are applied to each fund’s current size (2025Q1).
  - Missing values or funds not yet operating during historical episodes were imputed using the median flow of peers within the same US mutual fund objective.
- Scenario definitions (Table A1.4.3):
  - April 2025 outflows + 60 bps rate shock
    - Flow assumptions: April 2025 outflows projected to current fund size; extended to funds with missing data on the basis of US mutual fund objective grouping (median of group assigned)
    - Flow statistics: Median; (5th, 95th percentile) = −0.8% (−7.1%, 5.6%)
    - Interest Rate Shock Assumptions (for derivatives): Level shift of curve by +60 basis points
  - March 2020 outflows + 80 bps rate shock
    - Flow assumptions: March 2020 outflows projected to current fund size; extended to funds with missing data on the basis of US mutual fund objective grouping (median of group assigned)
    - Flow statistics: Median; (5th, 95th percentile) = −2.7% (−16.9%, 9.0%)
    - Interest Rate Shock Assumptions (for derivatives): Level shift of curve by +80 basis points
  - 99th pct outflows + 100 bps rate shock
    - Flow assumptions: Each individual fund’s 99th percentile outflow, projected to current fund size; extended to funds with missing data on the basis of US mutual fund objective grouping (median of group assigned)
    - Flow statistics: Median; (5th, 95th percentile) = −9.4% (−40.0%, −2.2%)
    - Interest Rate Shock Assumptions (for derivatives): Level shift of curve by +100 basis points
- Third scenario detail:
  - Assigns to each fund its own 99th percentile of monthly outflows (January 2013 to June 2025) as share of assets under management. For many funds this corresponds to March 2020, but some funds recorded inflows even then. Shorter history for young funds can skew percentile estimates.

### Derivatives pricing and duration assumptions
- Derivatives considered:
  - Only interest-rate derivatives: US Treasury futures and (USD) fixed-float interest-rate swaps.
  - Positions repriced using the linear (DV01) response to the exogenous rate shock; convexity and higher-order effects excluded.
- Duration assumptions for US Treasury Futures and US Dollar Interest Rate Swaps (Table A1.4.4):
  - US Treasury Futures — Contract / Duration assumption:
    - 2-Year: 2.0
    - 5-Year: 4.7
    - 10-Year: 9.0
    - 10-Year Ultra: 9.8
    - Bond: 18.0
    - Bond Ultra: 20.0
    - (additional maturity rows with durations: 5 → 4.5; 6 → 5.4; 7 → 6.1)
  - US Dollar Interest Rate Swaps (fixed-float, all benchmark rates) — Maturity / Duration:
    - 0.5 / 0.5
    - 1 / 1
    - 1.5 / 1.4
    - 2 / 1.9
    - 3 / 2.8
    - 4 / 3.7
    - 5 / 4.5
    - 6 / 5.4
    - 7 / 6.1
    - (longer maturities) 8 / 6.9; 10 / 8.3; 12 / 9.5; 15 / 11.2; 20 / 13.7; 25 / 15.7; 30 / 17.5; 40 / 20.5; 50 / 22.9
  - Parameter values reflect IMF staff judgment informed by recent market conditions and prevailing rate levels.

### Key findings on liquidity pressures and heterogeneity
- Relative contributions to gross liquidity pressures:
  - Liquidity pressures from investor outflows are much larger than those from variation margin calls on interest rate derivatives (Figure A1.4.2).
  - Under the assumptions presented, US bond mutual funds’ gross liquidity pressures from margin calls on interest rate derivatives are dwarfed by the impact of fund outflows.
- Aggregate vs fund-level outcomes:
  - Fund-level heterogeneity means aggregate statistics on flows or margin calls can understate the scale of forced liquidations.
  - Some funds experience inflows in a given scenario while others must sell assets; heterogeneity reflects both sources of pressure and balance-sheet composition.
  - Funds with larger buffers (cash, MMF shares, Treasury bills, commercial paper) tap US Treasury bonds only in more severe scenarios; funds with thinner liquidity cushions may be forced to sell Treasuries even under milder conditions (e.g., the April 2025 flow scenario).
- Figure A1.4.2 (summary metrics displayed):
  - Share of gross liquidity pressures attributed to outflows vs interest rate derivative margin calls:
    - April 2025 outflows + 60 bps rate shock scenario: Outflows 87.7%; Interest Rate Derivative Margin calls 12.3%
    - March 2020 outflows + 80 bps rate shock scenario: Outflows 94.6%; Interest Rate Derivative Margin calls 5.4%
    - 99th pct outflows + 100 bps rate shock scenario: Outflows 96.3%; Interest Rate Derivative Margin calls 3.7%
- Caveat:
  - Liquidity pressures from outflows and margin calls are not strictly additive because some funds may face inflows (outflows) in combination with margin calls (credit), whereby these sources partially cancel out; overlap is indicated as insignificant but the figure is indicative.

### Corporate Debt-at-Risk sensitivity analysis — measuring the effects of higher US tariffs
- Scope and approach:
  - Estimates additional costs from increased US tariffs for countries’ export sectors and translates those into broader corporate sector impacts and effects on corporate revenues and EBIT under alternative pass-through assumptions.
  - Domestic policy responses are not incorporated.
- Notation and key formulae:
  - Additional costs for a country’s export sector: TTC_{c,x} = AT_c * XShare_{c,US} * XShareTariffed_{c}
    - (Symbolic notation preserved from source: TTC_{c,xiii…} = AT_c * XXShare_c_US * XXShare_c_ixii…)
  - Broader corporate impact factoring in share of exporting corporates proxied by goods exports as percent of GDP (XG_GDP): XTT_C_c = TTC_{c,x} * XG_GDP
  - For the US, goods imports as percent of GDP (MG_GDP) used to proxy proportion of corporates facing increased tariff costs.
- Pass-through scenarios considered:
  - Scenario A: 100% pass-through of additional tariff costs to consumers (PPT_US = 1)
    - Firms maintain margins; higher prices reduce demand in the importing country.
    - Estimated sensitivity of sales volumes to change in prices from panel regression: ~ -0.11 (a 1 pp rise in prices → sales decline by 0.11%).
    - Effective change on corporate revenues: δrev_c = XTT_C_c * −0.11
  - Scenario B: 0% pass-through; US importers do not pass on costs (PPT_US = 0)
    - US importers and exporting counterparts share increased tariff costs equally (each absorbs 50%).
    - Net impact on EBIT (percent of revenue) for a country = Implied increase in tariff related costs * 50% * (relevant GDP import share factor as applied in examples).
- Table A1.5.1 — Estimated change in revenues due to higher prices from a 100% pass-through (selected country rows):
  - Bangladesh: Implied increase in tariff related costs 6.1% ; General sensitivity of revenues to price increases −0.11 ; Effective change on revenues −0.7%
  - Brazil: 3.2% ; −0.11 ; −0.3%
  - Canada: 15.3% ; −0.11 ; −1.7%
  - Chile: 3.3% ; −0.11 ; −0.4%
  - China: 3.2% ; −0.11 ; −0.3%
  - Colombia: 0.9% ; −0.11 ; −0.1%
  - France: 1.9% ; −0.11 ; −0.2%
  - Germany: 2.2% ; −0.11 ; −0.2%
  - India: 1.3% ; −0.11 ; −0.1%
  - Japan: 4.1% ; −0.11 ; −0.5%
  - Malaysia: 0.9% ; −0.11 ; −0.1%
  - Mexico: 6.3% ; −0.11 ; −0.7%
  - Philippines: 1.6% ; −0.11 ; −0.2%
  - South Africa: 0.9% ; −0.11 ; −0.1%
  - Korea: 3.2% ; −0.11 ; −0.4%
  - Spain: 1.0% ; −0.11 ; −0.1%
  - Turkey: 0.9% ; −0.11 ; −0.1%
  - United Kingdom: 1.5% ; −0.11 ; −0.2%
  - United States: 3.4% ; −0.11 ; −0.4%
  - Vietnam: 1.9% ; −0.11 ; −0.2%
  - Sources: Center for Global Development’s US Tariff Tracker, The Budget Lab at Yale, IMF’s World Economic Outlook database, and IMF Staff estimates
  - Note: Additional effective tariffs calculated relative to January 20, 2025, and as of July 12th, 2025. For the US, the implied increase in tariff related costs is the simple average of countries in the sample and is only marginally higher than estimates for additional import tariffs faced by US consumers by The Budget Lab at Yale. The general sensitivity of revenues to price increases corresponds to the coefficient for change in CPI under specification 3.
- Regression analysis used to estimate sensitivity (Table A1.5.2 — specification 3 shown as primary for periods of rising inflation):
  - DV: Real GDP growth using country financial conditions, and during periods of rising inflation (3)
    - Real GDP growth, lagged: 0.275***
    - Change in CPI: −0.114***
    - Lagged CPI: 0.0689***
    - Country aggregate Z-scores, lagged: −0.919***
    - Change in country aggregate Z-scores: −3.042***
    - Constant: 2.819***
    - Observations: 602
    - Number of countries: 43
    - *** p<0.01, ** p<0.05, * p<0.1
  - Sources: Bloomberg Finance L.P.; Haver Analytics; national data sources; and IMF staff calculations
  - Note: All data are in annual frequency and the country sample maps countries included in IMF’s Financial Conditions Index framework.
- Table A1.5.3 — Estimated change in EBIT due to absorption of higher tariff costs (0% pass-through, 50% absorption by corporates; selected country rows):
  - Bangladesh: Implied increase in tariff related costs 6.1% ; Absorption 50% ; Net impact on EBIT −3.0%
  - Brazil: 3.2% ; 50% ; −1.6%
  - Canada: 15.3% ; 50% ; −7.7%
  - Chile: 3.3% ; 50% ; −1.7%
  - China: 3.2% ; 50% ; −1.6%
  - Colombia: 0.9% ; 50% ; −0.5%
  - France: 1.9% ; 50% ; −1.0%
  - Germany: 2.2% ; 50% ; −1.1%
  - India: 1.3% ; 50% ; −0.7%
  - Japan: 4.1% ; 50% ; −2.1%
  - Malaysia: 0.9% ; 50% ; −0.5%
  - Mexico: 6.3% ; 50% ; −3.2%
  - Philippines: 1.6% ; 50% ; −0.8%
  - South Africa: 0.9% ; 50% ; −0.5%
  - Korea: 3.2% ; 50% ; −1.6%
  - Spain: 1.0% ; 50% ; −0.5%
  - Turkey: 0.9% ; 50% ; −0.4%
  - United Kingdom: 1.5% ; 50% ; −0.7%
  - Vietnam: 1.9% ; 50% ; −0.9%
  - United States: 3.4% ; 50% ; −1.7%
  - Sources and notes: same as Table A1.5.1

### Additional observations and limitations
- Exercise limitations and interpretive caveats:
  - Interest-rate derivatives margin calls are small relative to outflow-generated liquidity pressures.
  - Fund-level heterogeneity implies aggregate measures can understate forced liquidation risk; liquidity cushions matter.
  - Derivatives repricing excludes convexity and higher-order effects.
  - Scenario severity for 99th percentile outflows may be skewed for younger funds with shorter histories.
  - For the corporate sensitivity analysis, domestic policy responses and detailed country- or product-level controls are not incorporated; results present first-round effects on revenue and EBIT and potential contribution to stagflationary pressures.
- Empirical takeaway on tariffs:
  - Under 100% pass-through, a country with a 10% sectoral additional cost would see an effective revenue impact of −1.1% (10% * −0.11).
  - Under 0% pass-through with 50% absorption, corporates face larger direct hits to EBIT (country-specific percentages shown in Table A1.5.3).

*Source: Global Financial Stability Report Chapter 1 Online Annex (IMF | October 2025).*

### 12. Owing to higher longer-term interest rates and strong borrowing during the period of low interest

### ch1annex - 12. Owing to higher longer-term interest rates and strong borrowing during the period of low interest

### Corporate debt refinancing and interest burden
- Average coupon on debt maturing in 2025–26 is estimated around 3.5%.
- About 40 percent of this maturing debt is currently servicing a fixed rate.
- Given current yields on ~5%, refinancing of this debt by corporates would be more expensive by about 150bps.
- The refinancing implication is an additional interest expense of ~60bps higher than existing effective interest rates.

### Assessment sample and data vintage
- Firm-level analysis imposed higher tariff and interest costs on Q1 2025 data.
- The firm-level sample covered about 13,200 firms across a group of 20 countries, of which 11 are emerging market economies.
- Firms with total assets greater than USD 500 million in Q1 2025 are classified as large; the remaining 6,000 firms are classified as small and medium firms.

### Sensitivity analysis and Interest Coverage Ratios (ICRs)
- The sensitivity exercise imposes higher tariff and interest costs under two scenarios:
  - Scenario 1: 100% pass-through & 60bps increase in effective interest rates.
  - Scenario 2: 0% pass-through & 60bps increase in effective interest rates.
- Median global corporate ICRs (by scenario) as reported in the figures:
  - Global corporate median ICRs: 3.3; 2.6; 2.5
  - By firm size (large): 3.6; 2.9; 2.8
  - By firm size (small & medium): 2.5; 2.0; 1.8
- Findings:
  - Median ICRs show a notable deterioration regardless of pass-through level.
  - Small and medium sized firms show greater sensitivity in ICR deterioration than large firms.
  - Median ICRs would worsen further for small and medium firms if countries where corporates operate at [lower leverage with structurally low interst rates] are excluded.
  - The simple sensitivity analysis may bias median ICR estimates because it does not distinguish firms’ market power based on size.

### Country heterogeneity and risky debt shares
- The distribution of debt by ICR varies notably across countries and affects vulnerability.
- Some countries show large increases in share of risky debt (debt with ICR below 1) despite smaller-than-average increases in tariff rates.
- For the sample countries, the average increase in tariff costs is estimated at 1% of revenues (based on effective tariff information as of July 12, 2025).
- The analysis highlights that pre-existing high shares of risky debt amplify the impact of additional cost shocks.

### Estimating US dollar exposures — methodology overview
- USD Assets are defined and estimated as:
  - USD Assets = USD Equities + USD Bonds + USD Bank Claims (A1)
- Data sources and choices:
  - Prioritize IMF CPIS data for dollar-denominated equities and debt; use US Treasury TIC data to fill CPIS gaps when necessary.
  - Exclude foreign exchange reserves from private USD asset estimates; when TIC is used, USD-denominated FX reserves are removed via:
    - USD-denominated FX reserves = total FX reserves × USD share in FX reserves (A2)
  - BIS Locational Banking Statistics (LBS) used to estimate USD bank claims, including dollars loans and deposits held by banks and USD deposits held by non-bank sectors.
  - For non-bank USD deposits, aggregate deposit liabilities reported by foreign countries that identify deposits from the country’s non-bank sector (A3).
- Estimating exposures relative to FX market liquidity:
  - US dollar exposures are also measured relative to monthly transaction volume of each local foreign exchange market; FX turnover data are from BIS Triennial Central Bank Survey.

### Estimating USD-denominated liabilities
- USD-denominated liabilities are defined and estimated as:
  - USD-denominated liabilities = debt issuance denominated in USD + loans in USD + bank deposits in USD (A4)
- Data sources:
  - BIS International Debt Securities (IDS) for USD debt issuance in international markets (does not include USD debt issued in domestic markets).
  - BIS LBS for USD loans and USD deposits by counterparty.

### Adjustment for net banking sector and uncaptured exposures
- Net banking sector adjustment:
  - If banks have both USD assets and liabilities, subtract the minimum of bank USD assets and liabilities from both totals to derive exposures with a net banking sector (to avoid double counting and reflect natural hedges).
- Uncaptured exposures:
  - Estimates exclude local USD positions (e.g., Formosa bonds) and therefore may miss institution-level FX mismatches even when economy-level positions appear balanced.

### Results and key quantitative findings on USD exposures
- Estimated “runnable” USD exposures (security investments, loans, deposits) are significantly large in economies where international financial centers and large non-bank financial institutions are located.
- Economies highlighted with disproportionately large USD exposures relative to local FX market size include: Cayman Islands, UK, Luxembourg, Hong Kong SAR, Switzerland, Bermuda; and locations with large non-bank financial institutions such as Japan, Canada, Ireland, Germany, Netherlands, Taiwan Province of China, Korea, France, Norway, Australia.
- USD-denominated corporate bond share in the US as reported in TIC:
  - 82.7% for 2024 June
  - 81.7% for 2023 June

### Implications
- Effective interest rates for corporates will continue to rise as they refinance maturing fixed-rate debt amid higher long-term rates, raising interest burdens and weakening ICRs, particularly for small and medium firms.
- Countries with pre-existing large shares of risky debt are more susceptible to increases in the share of debt with ICR below 1 even when tariff-related cost increases are smaller-than-average.
- Large USD exposures concentrated in certain financial centers and non-bank financial hubs can translate into substantial price impact if hedging flows concentrate in a short period, given exposures may be much larger than the size of local FX markets.

*IMF Global Financial Stability Report — Online Annex (excerpts from Annex 1.5, 1.6, and 1.7).*

### 3.      While largely driven by the compensation for taking on duration risk, the TP estimations based on

### 3.      While largely driven by the compensation for taking on duration risk, the TP estimations based on

### TP versus DTP: conceptual distinction and market microstructure
- TP (term premium) estimates based on government bond yields reflect multiple premium components:
  - Compensation for taking on duration risk (primary driver).
  - Fluctuations that capture changes in the perceived creditworthiness of the sovereign issuer in terms of credit spread risk, which can confound the reading of TP as a gauge of compensation for ‘pure’ interest rate risk—particularly when investors are increasingly attuned to fiscal profligacy and rising bond issuance supply.
- DTP (duration term premium) is constructed from yields for fully collateralized and centrally cleared interest rate swaps:
  - Non-duration premium components (notably credit spread risk related effects) are largely neutralized in swap-based measures.
  - Market microstructure considerations underpin DTP: intermediaries recycle duration risk by temporarily warehousing sovereign bonds for asset owners (pension funds, insurers, sovereign wealth funds)—often via auction participation—while neutralizing ‘pure’ interest rate exposures through pay-fix interest rate swaps.
  - DTP thus provides a cleaner measure of compensation specifically related to taking on duration risk—driven by undiversifiable business cycle risk, financial conditions and market uncertainty—while neutralizing changes in an issuer’s perceived creditworthiness.

### Relation between TP, DTP, and swap spreads
- Under the assumption that short-rate dynamics governing no-arbitrage pricing restrictions are roughly similar across bond and swap markets:
  - The difference between TP and DTP is highly correlated with the 30y swap spread.
  - The wedge between G4 TP and DTP estimates closely corresponds to the level of the G4 swap spread (referenced in Figure 1.9, panels 2 and 3 in the source).

### Model specification (affine no-arbitrage term structure framework)
- Data input:
  - Both TP and DTP are calculated following Adrian et al. (2013) based on zero-coupon rates 푦푦푡 for either government bonds or centrally cleared interest rate swaps. Indices for the G4 jurisdictions and the two instrument types are suppressed in the notation.
- Cross-sectional yield representation:
  - 푦푦푡,푛푛 = −푙푙푙푙푙푙 푃푃푡푡푛푛푛푛 = −1푛푛 (퐴퐴푛푛 + 퐵퐵푛푛′푋푋푡푡) .  (Equation (1) in source)
  - 푦푦푡 capture a set of 푁푁푁푁1 yields that load onto a vector of 퐾퐾푁푁1 state variables 푋푋푡.
  - Loading matrix: 퐵퐵 (dimension consistent with 퐾퐾 and 푁푁), intercept: 퐴퐴 (푁푁푁푁1).
- State dynamics:
  - First-order VAR: 푋푋푡 = 휇휇 + 훷훷푋푋푡−1 + 훺훺푣푣푡, 푣푣푡 ∼ 푖푖.푖푖.푑푑.푁푁(0,퐼퐼).  (Equation (2))
  - Parameters: 휇휇 is 퐾퐾푁푁1 intercept, 훷훷 is 퐾퐾푁푁×퐾퐾 state transition matrix, Ω is 퐾퐾푁푁×퐾퐾 covariance matrix.
- Stochastic discount factor and affine market prices of risk:
  - 푀푀푡+1 = 푒푒푁푁푒푒(−푟푟푡 − 1 2 훬훬푡′ 훬훬푡 − 훬훬푡′푣푣푡), with short rate and market price of risk affine in states:
    - 푟푟푡 = 훿훿0 + 훿훿1′푋푋푡 .  (Equation (3))
    - 훬훬푡 = 휆휆0 + 휆휆1′푋푋푡 .  (Equation (4))
  - Parameter dimensions: 훿훿0 scalar; 훿훿1 is 퐾퐾푁푁1; 휆휆0 is 퐾퐾푁푁1; 휆휆1 is 퐾퐾푁푁×퐾퐾.
- Bond pricing via iterated expectations and exponentially-affine solution:
  - 푃푃푡푛 = 퐸퐸푡[푀푀푡+1 푃푃푡푛−1] with terminal condition 푃푃푡+푛0 = 1, yielding:
    - 푃푃푡푛 = exp(퐴퐴푛 + 퐵퐵푛′푋푋푡).
  - Risk-adjusted parameters under empirical and pricing measures:
    - 휇휇� = 휇휇 − 훺훺휆휆0
    - 휙휙� = 휙휙 − 훺훺휆휆1
  - Difference equations for yield factor loadings:
    - 퐴퐴푛+1 = 퐴퐴푛 + 퐵퐵푛′ 휇휇� + 1 2 퐵퐵푛′ 훺훺 훺훺′ 퐵퐵푛 − 훿훿0 .  (Equation (5))
    - 퐵퐵푛+1 = 퐵퐵푛′ 휙휙� 훿훿1′ .  (Equation (6))

### Estimation procedure (three-step OLS, per Adrian et al., 2013)
- Step A: Estimate the VAR to obtain 휇휇, 훷훷, and 훺훺 governing the data-generating process of yield factors (solve equation (2)).
- Step B: Regress excess returns of bonds on lagged factors and contemporaneous factor innovations from step A to obtain exposures to shocks and loadings of bond excess returns on factors (solve equation (3)).
- Step C: Run a cross-sectional regression using results from step B to obtain market prices of risk (equation (4)); recover yield loadings 퐴퐴 and 퐵퐵 from difference equations (5) and (6) to solve equation (1) so that the difference between yield estimates under the pricing and empirical measures recovers TP and DTP estimates, respectively.
- Note: While a full information maximum likelihood could be used, the three-step OLS is the chosen approach here.

### BB: Confidence Ellipsoid Construction (uncertainty quantification for TP/DTP vs projected free float)
- Purpose:
  - To quantify uncertainty around the relationship between TP or DTP and projected bond supply held by private investors (free float), incorporating parameter uncertainty (via non-parametric bootstrapping) and survey-based issuance uncertainty.
- Definitions and setup:
  - Let z ∈ ℝnm×1 denote the stacked vector of projected long-term TP or DTP (e.g., G4 GDP-weighted at the 30-year tenor).
  - Let x ∈ ℝnm×1 denote the corresponding stacked free float values (as a share of outstanding debt), where each 푁푁푖 corresponds to the share of debt to be absorbed by price-sensitive private investors rather than central banks.
  - Postulated bivariate relationship: 푧푧 = 훼훼 + 훽훽T T푇푇 ∙ 푁푁 + 휀휀 .
- Bootstrap and survey-scenario procedure:
  - Estimate 훼훼� and 훽훽̂ from jurisdiction-specific regressions using historical data; denote variance of 훽훽̂ as Σ�훽훽.
  - Non-parametric bootstrap for parameter uncertainty: generate m draws 훽훽(푗푗) ~ i.i.d. N(훽훽̂, Σ�훽훽) and retain 훼훼� as the point estimate.
  - Free float uncertainty from central bank holding surveys: draw n scenarios N(푖푖) ~ i.i.d. N(휇휇푥, 휎휎푥2) with 휇휇푥 and 휎휎푥2 matched to the mean and percentile range of survey responses.
  - Combine dimensions to form an n×m simulation array:
    - 푦푦(푖푖,푗푗) = 훼훼� + 훽훽̂(푗푗) ∙ 푁푁(푗푗) for 푖푖 = 1,...,푛푛, 푗푗 = 1,...,푚푚.
- Confidence ellipsoid summary:
  - The resulting 푧푧(푖푖,푗푗) pairs form a cloud of plausible outcomes.
  - Compute the empirical covariance matrix of these draws and perform an eigen-decomposition to define a two-dimensional 95 percent confidence ellipsoid that captures both parameter uncertainty in the regression and dispersion in survey-based expectations.

---

### Annex 1.8 — Short-Term Rate Sensitivities to Reserves and Dealer Positions (motivation, methodology, and results)
- Motivation:
  - Short-term rates (implementation of monetary policy) are influenced by central bank policy, inflation expectations, macroeconomic conditions, bank reserves, and dealer balance sheet constraints.
  - In floor-type or ample-reserve regimes, policy rates on reserves can anchor market rates.
  - Dealer intermediation in secured short-term markets is balance-sheet intensive; balance-sheet costs influence repo rates as dealers adjust compensation. These pressures intensify under high repo demand or during stress periods (e.g., quarter-ends) when regulatory limits reduce intermediation capacity.
- Methodology:
  - Analyze how reserves and dealer balance sheet usage affect secured rates focusing on SOFR spreads over reverse repurchase agreements (RRP).
  - Estimate rolling-window regressions of the SOFR–RRP spread on reserve balances and primary dealer positions (PDP):
    - 푆푆푆푆푆푆푆푆푆푆푆푆푡 = α + 훽훽1 × 훥훥푅푅푆푆푅푅 푆푆푆푆푅푅푆푆푅푅푡 + 훽훽2 × 훥훥훥훥퐷퐷훥훥 푡 .
  - Definitions:
    - Reserves = total banking sector balances held at the Federal Reserve.
    - PDP proxies dealer balance sheet usage = dealer net positions in credit markets relative to their two-year historical average.
    - All variables expressed as quarter-on-quarter differences.
    - Regressions estimated with a 52-week rolling window (coefficients vary over time).
- Results (summary):
  - Reserves:
    - Consistently exert a negative effect on the SOFR–RRP spread, with magnitude varying over time.
    - Before 2020, rising reserves significantly compressed spreads; after COVID, the effect weakened, reflecting transition from scarce to abundant reserves.
  - Dealer balance sheet effects:
    - More modest and episodic.
    - Following September 2019 repo turmoil, mildly negative coefficients are consistent with greater dealer intermediation narrowing spreads.
    - Post-COVID and again in 2025, dealer coefficients appear to amplify upward pressure on spreads reflecting tighter balance sheet space when intermediating large repo volumes.
  - October 2025 GFSR context:
    - The section “Sovereign Bond Market Function Crucially Depends on NBFIs” highlights 2025 average results: dealers exerted some upward pressure on spreads (likely driven by growing repo demand due to increased issuance and basis trades), while elevated reserve balances acted as a stabilizing force.
- Empirical display (Figure A1.8.1):
  - Presents z-scores of rolling betas (reserves beta — blue line; PDP beta — red line) from regressions of SOFR spreads on reserves and dealer positions.
  - Notes: All variables standardized; differences from previous quarter; rolling window spans 52 weeks; gray areas reflect 95 percent confidence intervals; sample starts in May 2019.

*This content unit was prepared by Johannes S. Kramer and Kleopatra Nikolaou for the Global Financial Stability Report Chapter 1 Online Annex (IMF | October 2025).*

---


_Source: https://www.imf.org/-/media/files/publications/gfsr/2025/october/english/ch1annex.pdf_