## Appendix II: Sensitivity Analysis

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### Overview and key context
- Purpose of paper: (i) analyze effects of economic shocks on U.S. nonfinancial corporates (income, balance sheets, aggregate losses) and (ii) propose a tractable stress-testing framework for nonfinancial corporates.
- Sample: company-level data of 755 U.S. domiciled nonfinancial corporates with aggregate indebtedness of over $6 trillion.
- Coverage: sample encompasses nearly two-thirds of total non-financial corporate borrowing by U.S. entities.
- Initial universe and final sample: initial set ~2,000 firms; firms with complete data for stress tests = 755.
- Markets represented: 524 borrowers in the bond market, 306 borrowers in the leveraged loan market, and 75 active in both markets.

### Stylized facts on corporate indebtedness and leveraged finance
- Aggregate and macro metrics:
  - Nonfinancial corporations in the U.S. have added over $4 trillion in debt since the end of 2010, bringing total corporate indebtedness to around $10 trillion or 46 percent of GDP at the end of 2019.
  - The volume of leveraged loans in particular more than doubled between 2010 and 2020.
  - At the end of 2019, outstanding volume of high-yield bonds in the U.S. stood at $1.3 trillion while the volume of leveraged loans was estimated at $1.1.
  - S&P Global Ratings: share of sub-investment grade instruments in overall nonfinancial corporate debt stood at 34 percent at the beginning of 2019.
  - Of the $5.9 trillion investment-grade bond market, BBB-rated firms accounted for around 50 percent in 2019.
- Sector concentrations:
  - As of 2019, the nonfinancial corporate sectors with the highest debt levels were technology ($900 million), utilities ($855 million), and telecommunications ($753 million).
  - Sectors with highest volumes of speculative-grade debt: media and entertainment ($420 billion), high technology ($308 billion), and health care ($244 billion).
- Sample-level totals and composition:
  - Total outstanding debt for firms in the stress test sample amounted to $6.2 trillion at the end of 2019.
  - This compares with overall debt of the U.S. corporate sector of $10.1 trillion.
  - Investment grade rated debt accounts for 60 percent of total outstanding debt in the sample; BBB-rated debt alone represents 38 percent of total debt in the sample.
  - Software and IT, media and entertainment, utilities, and energy sectors account for $2.9 trillion (around 46 percent of total outstanding debt in the sample).
- Leverage and profitability:
  - Definition of leveraged firms: debt-to-EBITDA ratio greater than 5.
  - Number of leveraged companies in the sample: 241.
  - Median debt-to-assets of less leveraged firms rose to 34.8 percent in 2019; still about 20 percentage points lower than median for leveraged firms.
  - Median net revenue-to-assets (return on assets) for leveraged firms dropped below 4 percent in 2019.
  - Non-cash assets accounted for about 55 percent of U.S. nonfinancial corporates’ total assets at end-2019; cash and deposits accounted for about 3½ percent of total assets.

### Market structure and covenant deterioration
- Leveraged finance instruments: high-yield bonds and leveraged loans (including loans of non-investment grade companies, loans with spreads > LIBOR +125, and certain secured loans per S&P LCD definition).
- Characteristics favoring leveraged loans:
  - First-lien senior-secured status; generally floating rates (versus fixed coupons for high-yield bonds).
  - Popularity of collateralized loan obligations (CLOs) increased demand for leveraged loans.
- Market size and measurement:
  - Common leveraged loans market size estimate: $1.1 trillion (based on S&P LCD / LLI definition); alternative broader estimate cited up to $2.2 trillion.
- Covenant erosion:
  - In 2019 nearly 90 percent of leveraged loans were issued without maintenance covenants.
  - 43 percent of leveraged loans issued in the first half of 2019 included some sort of EBITDA add-back.
- Implications:
  - Longer “runways” before distress, increased information asymmetries, more difficult-to-anticipate defaults, and lower recovery rates when defaults occur.

### Stress-testing framework: definitions and metrics
- Two complementary metrics:
  - Net equity position (solvency metric)
    - Current net equity position = starting net equity position + cumulative retained earnings.
    - Algebraic formulation: K_t = K_0 + sum_{j=1..t} [(R_j − E_j)(1−τ_j) − D_j].
    - Interest expenditures I_t depend on outstanding debt and prevailing effective interest rates; changes in interest rates Δi_t apply to fraction α^F_t of prior-period outstanding debt D_{t−1}.
    - Firms assumed to roll over maturing bond debt through issuance of new bonds of same nominal amount; outstanding loan debt amortized linearly over remaining maturity.
    - Tax rate τ_t assumed constant at firm’s most recent effective rate; negative profits produce negative tax payments carried forward.
    - Dividends: assumed paid at rate of 50 percent when after-tax profits are positive; zero otherwise.
    - Expenditures E_t are accounting expenditures (including non-cash items such as depreciation).
  - Net cash position / liquidity need (liquidity metric)
    - Current net cash position = starting net cash position + cumulative net cash inflows.
    - Net liquidity need L_t = L_0 + sum_{j=1..t} [ (R_j − E_j^cash)(1−τ_j) − D_j ] + sum_{j=1..t} A_j.
    - Focus in tests: (i) cover net revenue shortages (expenditures > revenues) driven by macro scenario and (ii) contractual debt obligations (maturing debt and amortizations), abstracting from new debt issuance inflows.
    - Tests assume firms do not engage in asset sales for liquidity.
    - Net liquidity need interpreted as amount of cash that would need to be borrowed to continue operations; absence implies cash buffers exhaust and default/bankruptcy risk.
- Relationship between measures:
  - When cash inflows from potential debt issuance are not considered, measures of net cash position and net liquidity needs are identical in the stress tests.

### Modeling of key P&L and balance-sheet components under scenarios
- Three components linked to macro scenarios: (i) gross revenues, (ii) interest expenditure, (iii) other (non-interest) expenditures.
- Gross revenues:
  - Modeled (revenue-to-asset ratio) via sector-adjusted regression: r_{i,t}^s = a_0 + (β_0 + β_s) X_t + μ_i + ε_{i,t}.
  - X_t is vector of macroeconomic and financial variables; β_s captures sector-specific elasticities.
  - Real GDP growth strongly related to revenue-to-asset ratio for most sectors.
  - Oil prices important for energy and utilities revenues.
- Interest expenditures:
  - Directly linked to interest rate path in scenarios.
  - Prevailing interest rate applied to portion of debt subject to repricing or variable rates and to new debt issued in the period.
  - Corporate spread shocks scaled by firms’ credit ratings (normalized scaling to BBB spread = 1).
- Non-interest expenditures:
  - Modeled to react to revenue changes with elasticity α_a in [0,1]: Δe_t = α_a Δr_t.
  - α_a = 0 implies no cost reduction possible; α_a = 1 implies perfect offset (net revenue acyclical).
  - Baseline specification uses α_a = 0.5.
  - Sensitivity analysis for different α_a values reported.

### Sensitivity framing and accounting distinctions
- Appendix II provides a range for potential losses based on all plausible cases to account for uncertainty in firms’ behavioral responses under stress.
- Key accounting distinction:
  - Equity position changes linked to the income statement and include non-cash costs (e.g., depreciation, valuation changes).
  - Liquidity (cash) position changes linked to cash accounts and exclude non-cash items; initial non-interest expenditure e_{t0} is adjusted to obtain e_{t0}^{cash}.
  - Cash-position measures computed both including and excluding firms’ capex as a sensitivity analysis.

### Stress test scenarios
- Two scenarios following the 2020 U.S. FSAP risk assessment:
  - Baseline: based on IMF’s June 2020 Update of the World Economic Outlook (WEO); embeds contemporaneous assessment of COVID-19 impact and implied a sharp contraction in 2020Q2.
    - Baseline lockdown output losses in 2020Q2 are estimated to be less than 15 percent relative to a ‘normal’ period.
  - Alternative (more adverse): assumes a second wave of COVID-19 infections at end-2020 with another lockdown in 2021Q1.
    - Assumes output losses of about 25 percent during any lockdown period relative to a ‘normal’ period.
    - Implies the U.S. economy operates at 75 percent of the pre-COVID-19 level in 2020Q2 and in 2021Q1, producing a “W-shaped” output path.
- The two scenarios serve as lower and upper bounds of FSAP severity; other FSAP sensitivity scenarios lie between them.

### A. Solvency stress—firms falling into negative equity
- Measurement approach:
  - Quantifies number of firms that could fall into negative equity each year; outstanding debt and initial end-2019 equity market valuation of those firms are reported as upper-bound proxies for potential losses.
  - Differentiates leveraged firms (debt-to-EBITDA > 5) from the rest.
- Baseline scenario results:
  - Number of companies with negative equity reaches 5.6 percent of all firms in the sample in 2020.
  - Around three quarters of firms with negative equity are leveraged corporates.
  - Share of companies with negative equity increases moderately from just under 1 percent in 2023 to 1.5 percent in 2025.
  - Initial (end-2019) equity value of corporates with negative equity in 2020: $136 billion (almost all from leveraged firms).
  - Fresh capital injections required to keep these corporates’ equity positive: $51 billion.
  - Outstanding debt of companies with negative equity in 2020: $400 billion ($334 billion by leveraged firms).
- Alternative scenario results:
  - Number of firms with negative equity in 2020 increases to more than 11 percent.
  - More than 60 percent of those firms are leveraged.
  - Number of firms with negative equity remains elevated in 2021 (4.8 percent) and only returns to pre-shock levels in 2022 and beyond.
  - Initial (end-2019) equity value of corporates with negative equity in 2020: $260 billion.
  - Fresh capital injections required: $231 billion.
  - Outstanding debt of companies with negative equity in 2020: $675 billion ($480 billion by leveraged firms).
- Sector concentration: firms with negative equity concentrated in capital goods, auto, energy, and IT sectors.

### B. Liquidity needs and net cash position—overview
- Liquidity metric purpose: quantify refinancing needs to finance continuing operations (banks and nonbank financial institutions as providers).
- Three cash-position metrics computed:
  1. Contractual financing needs: initial cash position plus debt rollovers (independent of scenario).
  2. Dynamic financing needs (lower bound): contractual needs plus scenario-dependent cash shortfall, assuming investment spending is halted (excludes capex).
  3. Dynamic financing needs (upper bound): same as (2) but assumes firms maintain investment at 2019 levels (includes capex).
- Interpretation: actual financing needs likely between metrics (2) and (3); halting capex is rare in practice, so (3) is an upper bound.

### Contractual financing needs (results)
- Aggregate contractual financing needs in 2020 (based on end-2019 cash buffers and debt rollovers): $831 billion.
- $831 billion is roughly equivalent to 12 percent of the current stock of outstanding debt.
- Cumulative financing required to cover all debt rollover needs over 2020-25: $3.2 trillion.
  - Implied: almost half of total outstanding debt would need to be refinanced by 2025.
- Amortization profile:
  - Leveraged firms account for about 40 percent of total amortizations despite representing less than a third of the sample.
  - Normalized by asset size, leveraged corporates account for over two third of aggregate debt amortizations.

### Dynamic financing needs (results)
- Excluding capex (lower bound) — financing needs in 2020:
  - Baseline: $1.4 trillion.
  - Alternative: $2 trillion.
- Including capex at 2019 levels (upper bound) — financing needs in 2020:
  - Baseline: $2.2 trillion.
  - Alternative: $2.8 trillion.
- Sectoral concentration (2020):
  - Energy sector accounts for about a quarter of all sectors’ financing needs in 2020.
  - Energy financing needs range from around $360 billion (baseline excluding capex) to $700 billion (alternative including capex).
  - Auto and durable goods, utilities, and IT also have large needs; together these sectors account for around 41-43 percent of corporate financing needs in 2020.
  - Sectors with relatively small liquidity needs (~1 percent of total): pharmaceuticals and biotech, real estate, professional services.

### Financing needs of solvent companies versus insolvent ones
- Most estimated financing needs relate to firms maintaining positive equity through the stress horizon:
  - Baseline scenario, dynamic financing needs excluding capex in 2020:
    - Firms with positive net equity: $1.4 trillion.
    - Firms with negative net equity: $44 billion.
  - If firms maintain capex at 2019 levels in 2020:
    - Firms with positive net equity: $2.2 trillion.
    - Firms with negative net equity: $60 billion.
- Implication: only a small proportion of aggregate financing needs accrue to companies with negative equity; these insolvent firms would likely not have access to new finance.
  - Combined outstanding debt of firms with negative equity that might not have access to new financing: about $130‒300 billion, equivalent to 2‒5 percent of total outstanding debt in the sample.

### Complementary short-term analysis in light of COVID-19 (Box 1 summary)
- Context and methodology:
  - Framework adapted to assess short-term liquidity needs (next ~12 months) given sharp revenue shock and U.S. government liquidity support.
  - Real GDP losses from the June 2020 WEO Update were mapped into sectoral losses for 18 sectors.
  - Assumptions:
    - Gross revenue flows fall sharply in the near term and start recovering in 2020Q3.
    - Companies can reduce non-interest expenditures in the near-term by one-half of the decline in gross revenues.
    - Nonfinancial corporates eligible for Fed liquidity support are those with investment-grade (BBB-rated or higher) as of March 22, 2020.
- Short-term liquidity findings:
  - Among investment-grade firms, the energy sector has the largest share of estimated liquidity needs.
    - Energy sector total outstanding debt: US$580 billion.
    - Energy accounts for 10 percent of investment grade loans and bonds.
    - Energy accounts for almost 70 percent of total investment grade firms’ liquidity needs through 2020.
    - If energy firms were unable to issue debt, over 80 percent of the outstanding debt stock would hit a binding liquidity constraint by year-end.
  - Other sectors (investment-grade) estimated liquidity needs amount to US$290 billion by end-2020.
    - If these firms maintain pre-crisis investment levels and include outstanding debt that needs to be rolled over through end-2020, their financing needs rise to US$610 billion.
  - High-yield (non-investment-grade) firms:
    - Non-investment grade firms’ stock of outstanding bond debt is more than 4½ times smaller than investment-grade stock.
    - Around 15 percent of the debt of non-investment grade non-energy firms (US$485 billion) are estimated to have negative equity by end-2020.
    - Debt issuance needs by the remaining high-yield firms (those ending 2020 with positive equity) are estimated at an additional US$90 billion during 2020 (US$140 billion if maintaining pre-crisis investment spending).

### Stress-test outcomes and financial-stability implications (Box 1)
- Share of firms projected to fall into negative equity:
  - Baseline scenario: about 5 percent of firms.
  - Alternative (adverse) scenario: about 11 percent of firms.
- Corresponding outstanding debt at risk of default for firms falling into negative equity:
  - Baseline scenario: $400 billion.
  - Alternative scenario: $675 billion.
- Potential equity valuation losses for equity holders:
  - Baseline scenario: around $136 billion.
  - Alternative scenario: around $272 billion.
- Leveraged firms (debt-to-EBITDA > 5):
  - Represent 32 percent of firms in sample; account for 33 percent of outstanding debt.
  - Account for the largest share of companies falling into distress (62 to 74 percent depending on scenario).
- Implications for financial institutions:
  - Aggregate potential losses on corporate debt estimated to range from $400 billion (baseline) to $675 billion (alternative); only a fraction would be borne by banks.
  - Banks’ direct exposure:
    - Bank loans to the corporate sector amounted to $1 trillion at end-2019.
    - Bank holdings of corporate bonds about $650 billion.
    - Combined exposures represent less than 10 percent of bank assets.
    - Common equity Tier 1 (CET1) capital for the 34 banks analyzed amounted to $1.2 trillion in 2020Q1; Tier 1 capital amounted to $1.4 trillion.
  - Nonbank financial institutions have larger direct exposures and would likely absorb the lion’s share of losses:
    - Mutual funds’ holdings of corporate bonds: $2.3 trillion (13 percent of assets); corporate equities almost $12 trillion (68 percent of assets).
    - Pension funds: $7.7 trillion (32 percent of assets) in corporate exposures.
    - Exchange-traded funds: $4 trillion (92 percent of assets).
    - Life-insurers: $3.8 trillion (45 percent of assets).
    - Closed-end funds: corporate sector exposure represents 65 percent of assets.
  - Illustrative exposure-at-risk if 11 percent of corporates fall into negative equity and default:
    - Mutual funds: $1.6 trillion at risk.
    - Pension funds: $850 billion at risk.
    - Life-insurers: $425 billion at risk.
    - Banks: about $200 billion at risk.
  - Expected losses would be smaller than these exposures at risk, depending on recovery rates.

### Potential implications for activity and the real economy (Box 1)
- Aggregate activity metrics:
  - Aggregate investment spending by firms in sample in 2019: $686 billion.
  - Aggregate investment of nonfinancial corporates (flow of funds): about $2.1 trillion.
  - Corporate capital consumption allowance: about $1.7 trillion.
  - Revenue from gross sales of firms in sample in 2019: $8.7 trillion.
  - Total gross output of nonfinancial private sector in national accounts: around $30 trillion.
  - Aggregate wage bill for corporates in sample: about $1.9 trillion.
  - Total wage and salary income in national accounts: about $6.8 trillion (nonfinancial private sector).
- Share of activity at risk from firms projected to fall into negative equity:
  - Capex spending at risk (baseline): close to 8 percent of total capex in sample (13 percent in adverse scenario).
  - Gross sales corresponding to firms projected to fall into negative equity:
    - Baseline: about 7 percent of total gross sales in 2020 (9 percent cumulatively over 2020-25).
    - Adverse: 11 percent of total gross sales in 2020 (12 percent cumulatively over 2020-25).
  - Wage bill for firms that fall into negative equity (for which data are available):
    - Baseline: about 6 percent of aggregate wage bill in 2020 (9 percent cumulatively over 2020-25).
    - Adverse: 11 percent of aggregate wage bill in 2020 (17 percent cumulatively over 2020-25).
- Distressed firms may reduce investment and operations, cutting output and employment and potentially creating a feedback loop that exacerbates the downturn and affects both bank and nonbank institutions.

### Sensitivity of expenditures in response to changes in revenue (elasticity α_a)
- Definition and range:
  - The elasticity α_a determines how non-interest expenses react to changes in revenues.
  - α_a can vary from 0 to 1.
    - α_a = 0: firms are unable to reduce any costs in response to changes in revenue.
    - α_a = 1: firms can reduce costs to perfectly offset any reduction in revenue.
- Main patterns:
  - Potential losses increase as α_a decreases.
  - For low values of α_a:
    - Share of companies with negative equity in 2020 ranges from about 15 percent (baseline scenario) to about 28 percent (adverse/alternative scenario).
    - This compares with 5.6 percent (baseline) and 11.1 percent (alternative) when using the central case α_a = 0.5.
    - Corresponding outstanding debt at risk for low α_a ranges from around $890 billion (baseline) to around $1.4 trillion (alternative).
  - When α_a ≈ 1:
    - Only 1 percent of the firms in the sample fall into negative equity in 2020.
    - Corresponding amount of debt at risk is less than $50 billion.
  - Behavior for α_a < 0.8:
    - Potential losses start increasing rapidly and vary almost linearly as α_a decreases from 0.8 toward 0.

### Sensitivity using historically estimated industry elasticities
- Method:
  - Stress tests rerun using historically estimated α_a for each industry (annual data 2000-19).
- Comparative results:
  - Number of firms falling into negative equity is smaller when using historical α_a versus central case α_a = 0.5.
    - Baseline: 5.6 percent fall into negative equity using α_a = 0.5, versus about 3.7 percent using historical α_a.
  - Expected losses for debt and equity holders are larger in all scenarios when assuming α_a = 0.5 compared with historical α_a.
- Interpretative note:
  - Using a slightly more conservative α_a than the historical average over 2000-19 is considered more prudent given uncertainty about firm behavior under severe stress.

### Sensitivity to the dividend payout rate
- Parametrization and range:
  - Central case assumes dividends paid out of positive after-tax profits with a factor of 0.5 (i.e., 50 percent of net after-tax profits).
  - Dividend payout rate can vary from 0 to 1.
    - 0: all positive after-tax profits retained.
    - 1: 100 percent payout.
  - When net after-tax profits are negative, the dividend parameter is set to zero.
- Impact on 2020 results:
  - Number of firms falling into negative equity in 2020 and potential debt and equity losses are unaffected by the dividend payout rate.
    - Reason: firms that go from positive equity in 2019 to negative equity in 2020 record negative net after-tax profit in 2020, and firms with negative profits do not pay dividends.
- Impact on subsequent years (2021 onwards) and cumulative horizon:
  - Dividend payout rate affects capital accumulation and therefore resilience in later years.
  - Most losses occur in 2020, so cumulative sensitivity is small.
  - Numerical examples (cumulative over 2020-25) — Alternative scenario:
    - Cumulative number of firms with negative equity: 151 firms when dividend payout rate = 0; 154 firms when dividend payout rate = 1 (difference of 3 firms).
    - Estimated outstanding debt at risk (cumulative over 2020-25): $1.15 trillion when payout = 0; $1.18 trillion when payout = 1.
  - Baseline scenario:
    - Estimated outstanding debt at risk (cumulative over 2020-25): $772 billion when payout = 0; $774 billion when payout = 1.
    - Difference in cumulative number of firms with negative equity over 2020-25 is one additional firm when payout = 1 relative to payout = 0.

### Overall sensitivity conclusions and prudential implication
- Elasticity α_a is a key driver of stress-test outcomes:
  - Lower α_a (less ability to cut costs) materially increases numbers of firms with negative equity and amounts of debt at risk.
  - α_a values in the historical sectoral range (roughly 0.2 to 0.7 for most industries) imply outcomes not far from the central case, but losses rise rapidly as α_a falls below 0.8.
- Dividend payout rate has limited quantitative effect on stress-test outcomes:
  - Minimal impact because primary losses occur in 2020 when dividend policy does not affect firms that record losses.
  - Small differences over 2020-25 arise from reduced capital accumulation when payout rates are higher.
- Prudential implication:
  - Using a slightly more conservative α_a than the historical average is justifiable given uncertainty about firm behavior under severe stress.

_Italic: Source: IMF staff calculations and stress test analysis as presented in Appendix II of the referenced IMF working paper._

### Appendix I:  Relationship Between Equity and Liquidity Positions and Historical Credit

### Appendix I:  Relationship Between Equity and Liquidity Positions and Historical Credit

### Downgrades and Defaults
- Downgrades and Defaults ....................................................................................................... 36

*Source: wpiea2020238-print-pdf - Appendix I:  Relationship Between Equity and Liquidity Positions and Historical Credit*

### Appendix II: Sensitivity Analysis ......................................................................................

### Appendix II: Sensitivity Analysis

### Overview and Key Context
- Purpose of paper: (i) analyze effects of economic shocks on U.S. nonfinancial corporates (income, balance sheets, aggregate losses) and (ii) propose a tractable stress-testing framework for nonfinancial corporates.
- Sample: company-level data of 755 U.S. domiciled nonfinancial corporates with aggregate indebtedness of over $6 trillion.
- Coverage: sample encompasses nearly two-thirds of total non-financial corporate borrowing by U.S. entities.
- Initial universe and final sample: initial set ~2,000 firms; firms with complete data for stress tests = 755.
- Markets represented: 524 borrowers in the bond market, 306 borrowers in the leveraged loan market, and 75 active in both markets.

### Stylized Facts on Corporate Indebtedness and Leveraged Finance
- Aggregate and macro metrics:
  - Nonfinancial corporations in the U.S. have added over $4 trillion in debt since the end of 2010, bringing total corporate indebtedness to around $10 trillion or 46 percent of GDP at the end of 2019.
  - The volume of leveraged loans in particular more than doubled between 2010 and 2020.
  - At the end of 2019, outstanding volume of high-yield bonds in the U.S. stood at $1.3 trillion while the volume of leveraged loans was estimated at $1.1.
  - S&P Global Ratings: share of sub-investment grade instruments in overall nonfinancial corporate debt stood at 34 percent at the beginning of 2019.
  - Of the $5.9 trillion investment-grade bond market, BBB-rated firms accounted for around 50 percent in 2019.
- Sector concentrations (as stated in source):
  - As of 2019, the nonfinancial corporate sectors with the highest debt levels were technology ($900 million), utilities ($855 million), and telecommunications ($753 million).
  - Sectors with highest volumes of speculative-grade debt: media and entertainment ($420 billion), high technology ($308 billion), and health care ($244 billion).
- Sample-level debt composition and totals:
  - Total outstanding debt for firms in the stress test sample amounted to $6.2 trillion at the end of 2019.
  - This compares with overall debt of the U.S. corporate sector of $10.1 trillion.
  - Investment grade rated debt accounts for 60 percent of total outstanding debt in the sample; BBB-rated debt alone represents 38 percent of total debt in the sample.
  - Software and IT, media and entertainment, utilities, and energy sectors account for $2.9 trillion (around 46 percent of total outstanding debt in the sample).
- Leverage and profitability patterns:
  - Definition of leveraged firms: debt-to-EBITDA ratio greater than 5.
  - Number of leveraged companies in the sample: 241.
  - Median debt-to-assets of less leveraged firms rose to 34.8 percent in 2019; still about 20 percentage points lower than median for leveraged firms.
  - Median net revenue-to-assets (return on assets) for leveraged firms dropped below 4 percent in 2019.
  - Non-cash assets accounted for about 55 percent of U.S. nonfinancial corporates’ total assets at end-2019; cash and deposits accounted for about 3½ percent of total assets.

### Market Structure and Covenant Deterioration
- Leveraged finance instruments: high-yield bonds and leveraged loans (including loans of non-investment grade companies, loans with spreads > LIBOR +125, and certain secured loans per S&P LCD definition).
- Characteristics favoring leveraged loans:
  - First-lien senior-secured status; generally floating rates (versus fixed coupons for high-yield bonds).
  - Popularity of collateralized loan obligations (CLOs) increased demand for leveraged loans.
- Market sizes and measurement notes:
  - Common leveraged loans market size estimate: $1.1 trillion (based on S&P LCD / LLI definition); alternative broader estimate cited up to $2.2 trillion.
- Covenant erosion:
  - In 2019 nearly 90 percent of leveraged loans were issued without maintenance covenants.
  - 43 percent of leveraged loans issued in the first half of 2019 included some sort of EBITDA add-back.
- Implications of covenant erosion and collateral dilution:
  - Longer “runways” before distress, increased information asymmetries, more difficult-to-anticipate defaults, and lower recovery rates when defaults occur.

### Stress-Testing Framework: Definitions and Metrics
- Two complementary metrics:
  - Net equity position (solvency metric)
    - Current net equity position = starting net equity position + cumulative retained earnings.
    - Algebraic formulation (as in source): K_t = K_0 + sum_{j=1..t} [(R_j − E_j)(1−τ_j) − D_j].
    - Interest expenditures I_t depend on outstanding debt and prevailing effective interest rates; changes in interest rates Δi_t apply to fraction α^F_t of prior-period outstanding debt D_{t−1}.
    - Firms assumed to roll over maturing bond debt through issuance of new bonds of same nominal amount; outstanding loan debt amortized linearly over remaining maturity.
    - Tax rate τ_t assumed constant at firm’s most recent effective rate; negative profits produce negative tax payments carried forward.
    - Dividends: assumed paid at rate of 50 percent when after-tax profits are positive; zero otherwise.
    - Expenditures E_t are accounting expenditures (including non-cash items such as depreciation).
  - Net cash position / liquidity need (liquidity metric)
    - Current net cash position = starting net cash position + cumulative net cash inflows.
    - Net liquidity need L_t = L_0 + sum_{j=1..t} [ (R_j − E_j^cash)(1−τ_j) − D_j ] + sum_{j=1..t} A_j
      - where L_0 is initial cash position; R_t gross revenues; E_t^cash cash-basis expenditures; A_t debt amortization at time t.
    - Focus in tests: two net cash inflow needs — (i) cover net revenue shortages (expenditures > revenues) driven by macro scenario and (ii) contractual debt obligations (maturing debt and amortizations), abstracting from new debt issuance inflows.
    - Tests assume firms do not engage in asset sales for liquidity (given illiquid nature of non-cash assets).
    - Net liquidity need interpreted as amount of cash that would need to be borrowed (bond, loan, or equity) to continue operations; absence of such borrowing implies cash buffers exhaust and default/bankruptcy risk.
- Relationship between measures:
  - When cash inflows from potential debt issuance are not considered, measures of net cash position and net liquidity needs are identical in the stress tests.

### Modeling of Key P&L and Balance Sheet Components under Scenarios
- Three components linked to macro scenarios: (i) gross revenues, (ii) interest expenditure, (iii) other (non-interest) expenditures.
- Gross revenues
  - Modeled (revenue-to-asset ratio) via sector-adjusted regression:
    - r_{i,t}^s = a_0 + (β_0 + β_s) X_t + μ_i + ε_{i,t}
  - X_t is vector of macroeconomic and financial variables from scenarios; β_s captures sector-specific elasticities.
  - Real GDP growth is strongly related to revenue-to-asset ratio for most sectors.
  - Oil prices important driver for energy and utilities revenues.
- Interest expenditures
  - Directly linked to interest rate path in scenarios.
  - Prevailing interest rate applied to portion of debt subject to repricing or variable rates and to new debt issued in the period.
  - Corporate spread shocks scaled by firms’ credit ratings (illustrated via a normalized scaling to BBB spread = 1).
- Non-interest expenditures
  - Modeled to react to revenue changes with elasticity α_a in [0,1]:
    - Δe_t = α_a Δr_t
  - α_a = 0 implies no cost reduction possible; α_a = 1 implies perfect offset (net revenue acyclical).
  - Baseline specification uses α_a = 0.5.
  - Sensitivity analysis for different α_a values reported (see Appendix II reference).

### Sensitivity and Assumptions Noted
- Dividend payout sensitivity: sensitivity analysis varying dividend payout rates from 0 to 100 percent included (results show very little sensitivity; dividend payouts matter only when firms have positive after-tax profits).
- Firms assumed to aim to roll over maturing bond debt at same nominal amount; loan amortization modeled linearly.
- Tax treatment: negative tax payments treated symmetrically (added to net equity when negative).
- Asset sales and other uses of proceeds (share buybacks, M&A) are not envisaged in stress tests.
- Capex: cash expenditures may include or exclude capex; both cases considered in stress tests.

*Source: Appendix II: Sensitivity Analysis, wpiea2020238-print-pdf*

### Appendix II. The sensitivity analysis also includes results using the historically estimated 훼훼

### Appendix II. The sensitivity analysis also includes results using the historically estimated 훼훼푎푎 for each industry including in our stress tests.

### Sensitivity framing and accounting distinctions
- Appendix II provides a range for potential losses based on all plausible cases to account for uncertainty in firms’ behavioral responses under stress.
- Key accounting distinction:
  - Equity position changes are linked to the income statement (P&L) and include non-cash costs (e.g., depreciation, valuation changes).
  - Liquidity (cash) position changes are linked to cash accounts and exclude non-cash items; initial non-interest expenditure e푡0 is adjusted to obtain e푡0cash.
  - Cash-position measures are computed both including and excluding firms’ capex as a sensitivity analysis.

### Stress test scenarios
- Two scenarios following the 2020 U.S. FSAP risk assessment:
  - Baseline: based on IMF’s June 2020 Update of the World Economic Outlook (WEO); embeds contemporaneous assessment of COVID-19 impact and implied a sharp contraction in 2020Q2.
    - Baseline lockdown output losses in 2020Q2 are estimated to be less than 15 percent relative to a ‘normal’ period.
  - Alternative (more adverse): assumes a second wave of COVID-19 infections at end-2020 with another lockdown in 2021Q1.
    - Assumes output losses of about 25 percent during any lockdown period relative to a ‘normal’ period.
    - Implies the U.S. economy operates at 75 percent of the pre-COVID-19 level in 2020Q2 and in 2021Q1, producing a “W-shaped” output path.
- The two scenarios serve as lower and upper bounds of FSAP severity; other FSAP sensitivity scenarios lie between them.

### A. Solvency stress—firms falling into negative equity
- Measurement approach:
  - Quantifies number of firms that could fall into negative equity each year; outstanding debt and initial end-2019 equity market valuation of those firms are reported as upper-bound proxies for potential losses.
  - Differentiates leveraged firms (debt-to-EBITDA > 5) from the rest.
- Baseline scenario results:
  - Number of companies with negative equity reaches 5.6 percent of all firms in the sample in 2020.
  - Around three quarters of firms with negative equity are leveraged corporates.
  - Share of companies with negative equity increases moderately from just under 1 percent in 2023 to 1.5 percent in 2025.
  - Initial (end-2019) equity value of corporates with negative equity in 2020: $136 billion (almost all from leveraged firms).
  - Fresh capital injections required to keep these corporates’ equity positive: $51 billion.
  - Outstanding debt of companies with negative equity in 2020: $400 billion ($334 billion by leveraged firms).
- Alternative scenario results:
  - Number of firms with negative equity in 2020 increases to more than 11 percent.
  - More than 60 percent of those firms are leveraged.
  - Number of firms with negative equity remains elevated in 2021 (4.8 percent) and only returns to pre-shock levels in 2022 and beyond.
  - Initial (end-2019) equity value of corporates with negative equity in 2020: $260 billion.
  - Fresh capital injections required: $231 billion.
  - Outstanding debt of companies with negative equity in 2020: $675 billion ($480 billion by leveraged firms).
- Sector concentration: firms with negative equity concentrated in capital goods, auto, energy, and IT sectors.

### B. Liquidity needs and net cash position—overview
- Liquidity metric purpose: quantify refinancing needs to finance continuing operations (banks and nonbank financial institutions as providers).
- Three cash-position metrics computed:
  1. Contractual financing needs: initial cash position plus debt rollovers (independent of scenario).
  2. Dynamic financing needs (lower bound): contractual needs plus scenario-dependent cash shortfall, assuming investment spending is halted (excludes capex).
  3. Dynamic financing needs (upper bound): same as (2) but assumes firms maintain investment at 2019 levels (includes capex).
- Interpretation: actual financing needs likely between metrics (2) and (3); halting capex is rare in practice, so (3) is an upper bound.

### Contractual financing needs (results)
- Aggregate contractual financing needs in 2020 (based on end-2019 cash buffers and debt rollovers): $831 billion.
- $831 billion is roughly equivalent to 12 percent of the current stock of outstanding debt.
- Cumulative financing required to cover all debt rollover needs over 2020-25: $3.2 trillion.
  - Implied: almost half of total outstanding debt would need to be refinanced by 2025.
- Amortization profile:
  - Leveraged firms account for about 40 percent of total amortizations despite representing less than a third of the sample.
  - Normalized by asset size, leveraged corporates account for over two third of aggregate debt amortizations.

### Dynamic financing needs (results)
- Excluding capex (lower bound):
  - Financing needs in 2020:
    - Baseline: $1.4 trillion.
    - Alternative: $2 trillion.
- Including capex at 2019 levels (upper bound):
  - Financing needs in 2020:
    - Baseline: $2.2 trillion.
    - Alternative: $2.8 trillion.
- Sectoral concentration (2020):
  - Energy sector accounts for about a quarter of all sectors’ financing needs in 2020.
  - Energy financing needs range from around $360 billion (baseline excluding capex) to $700 billion (alternative including capex).
  - Auto and durable goods, utilities, and IT also have large needs; together these sectors account for around 41-43 percent of corporate financing needs in 2020.
  - Sectors with relatively small liquidity needs (~1 percent of total): pharmaceuticals and biotech, real estate, professional services.

### Financing needs of solvent companies versus insolvent ones
- Most estimated financing needs relate to firms maintaining positive equity through the stress horizon:
  - Baseline scenario, dynamic financing needs excluding capex in 2020:
    - Firms with positive net equity: $1.4 trillion.
    - Firms with negative net equity: $44 billion.
  - If firms maintain capex at 2019 levels in 2020:
    - Firms with positive net equity: $2.2 trillion.
    - Firms with negative net equity: $60 billion.
- Implication: only a small proportion of aggregate financing needs accrue to companies with negative equity; these insolvent firms would likely not have access to new finance.
  - Combined outstanding debt of firms with negative equity that might not have access to new financing: about $130‒300 billion, equivalent to 2‒5 percent of total outstanding debt in the sample.

### Complementary short-term analysis in light of COVID-19
- High-frequency stress tests assessed short-term (next ~12 months) liquidity needs given sharp revenue shock and U.S. government liquidity support.
- Key findings:
  - Corporate sector could face significant liquidity needs following sharp revenue falls from COVID-19.
  - Energy sector accounts for a large proportion (70 percent) of liquidity needs of investment-grade corporates (those eligible for Fed liquidity support).
  - Non-investment-grade segment (not eligible for Fed liquidity support) could see a substantial increase in insolvencies, though its liquidity needs are relatively small due to a small share of the corporate bond debt market.

_Italic: Source: IMF staff calculations and stress test analysis as presented in Appendix II of the referenced IMF working paper._

### Box 1: Short-term liquidity needs following the COVID-19 outbreak

### Box 1: Short-term liquidity needs following the COVID-19 outbreak

### Context and methodology
- Rapid spread of COVID-19 in the first quarter of 2020 coincided with a collapse in oil prices, stay-at-home orders, and mandated closures of places of gathering, producing sharp corrections in equity markets and widening corporate spreads.
- U.S. authorities responded with unprecedented fiscal packages and Federal Reserve credit facilities under Section 13(3).
- The annual stress test framework was adapted to assess nonfinancial corporate sector short-term liquidity needs (next 12 months or so) in the context of the shock and government liquidity support.
- Real GDP losses from the June 2020 WEO Update were mapped into sectoral losses for 18 sectors.
- Using contractual details of outstanding debt and assumptions on revenue and expenditure items, corporates’ liquidity (net cash) and solvency (net equity) positions were projected forward; firms’ monthly cash positions account for initial cash, net revenue flows, and bond debt amortization or rollover.
- Assumptions:
  - Gross revenue flows fall sharply in the near term and start recovering in 2020Q3.
  - Impact on revenues varies by industry based on calibrated sensitivity to the economic shutdown by sector.
  - Companies can reduce non-interest expenditures in the near-term by one-half of the decline in gross revenues.
  - Nonfinancial corporates eligible for Fed liquidity support are those with investment-grade (BBB-rated or higher) as of March 22, 2020; the sample is split into investment-grade and non-investment-grade sub-segments.

### Short-term liquidity findings
- Among investment-grade firms, the energy sector has the largest share of estimated liquidity needs.
  - Energy sector total outstanding debt: US$580 billion.
  - Energy accounts for 10 percent of investment grade loans and bonds.
  - Energy accounts for almost 70 percent of total investment grade firms’ liquidity needs through 2020.
  - If energy firms were unable to issue debt, over 80 percent of the outstanding debt stock would hit a binding liquidity constraint by year-end.
- Other sectors (investment-grade) estimated liquidity needs amount to US$290 billion by end-2020.
  - If these firms maintain pre-crisis investment levels and include outstanding debt that needs to be rolled over through end-2020, their financing needs rise to US$610 billion.
- High-yield (non-investment-grade) firms:
  - Non-investment grade firms’ stock of outstanding bond debt is more than 4½ times smaller than investment-grade stock (resulting liquidity needs are relatively small in aggregate).
  - Around 15 percent of the debt of non-investment grade non-energy firms (US$485 billion) are estimated to have negative equity by end-2020.
  - Debt issuance needs by the remaining high-yield firms (those ending 2020 with positive equity) are estimated at an additional US$90 billion during 2020 (US$140 billion if maintaining pre-crisis investment spending).

### Scenarios and stress-test outcomes
- Share of firms projected to fall into negative equity:
  - Baseline scenario: about 5 percent of firms.
  - Alternative (adverse) scenario: about 11 percent of firms.
- Corresponding outstanding debt at risk of default for firms falling into negative equity:
  - Baseline scenario: $400 billion.
  - Alternative scenario: $675 billion.
- Potential equity valuation losses for equity holders:
  - Baseline scenario: around $136 billion.
  - Alternative scenario: around $272 billion (double the baseline).
- Leveraged firms (debt-to-EBITDA > 5):
  - Represent 32 percent of firms in sample; account for 33 percent of outstanding debt.
  - Account for the largest share of companies falling into distress (62 to 74 percent depending on scenario).
  - Liquidity needs appear moderate given small size and recent extensions to debt maturity profiles, but could face significant challenges under market pressure and funding liquidity strains.

### Implications for financial stability and the financial system
- Aggregate potential losses on corporate debt were estimated to range from $400 billion in the baseline scenario to $675 in the alternative scenario; only a fraction would be borne by banks.
- Banks’ direct exposure:
  - Bank loans to the corporate sector amounted to $1 trillion at end-2019.
  - Bank holdings of corporate bonds about $650 billion.
  - Combined exposures represent less than 10 percent of bank assets.
  - Bank capital buffers cited: Common equity Tier 1 (CET1) capital for the 34 banks analyzed amounted to $1.2 trillion in 2020Q1; Tier 1 capital amounted to $1.4 trillion.
  - Potential losses to the banking system from direct exposure appear a priori contained relative to these buffers.
- Nonbank financial institutions have larger direct exposures and would likely absorb the lion’s share of losses in severe corporate stress:
  - Mutual funds’ holdings of corporate bonds: $2.3 trillion (13 percent of assets); corporate equities almost $12 trillion (68 percent of assets).
  - Pension funds: $7.7 trillion (32 percent of assets) in corporate exposures.
  - Exchange-traded funds: $4 trillion (92 percent of assets).
  - Life-insurers: $3.8 trillion (45 percent of assets).
  - Closed-end funds: corporate sector exposure represents 65 percent of assets.
- Illustrative exposure-at-risk if 11 percent of corporates fall into negative equity and default:
  - Mutual funds: $1.6 trillion at risk.
  - Pension funds: $850 billion at risk.
  - Life-insurers: $425 billion at risk.
  - Banks: about $200 billion at risk.
- Expected losses would be smaller than these exposures at risk, depending on recovery rates.

### Potential implications for activity and the real economy
- Aggregate investment and sales in the sample:
  - Aggregate investment spending by firms in sample in 2019: $686 billion.
  - Aggregate investment of nonfinancial corporates (flow of funds): about $2.1 trillion.
  - Corporate capital consumption allowance: about $1.7 trillion.
  - Revenue from gross sales of firms in sample in 2019: $8.7 trillion.
  - Total gross output of nonfinancial private sector in national accounts: around $30 trillion.
  - Aggregate wage bill for corporates in sample: about $1.9 trillion.
  - Total wage and salary income in national accounts: about $6.8 trillion (nonfinancial private sector).
- Share of activity at risk from firms projected to fall into negative equity:
  - Capex spending at risk (baseline): close to 8 percent of total capex in sample (13 percent in adverse scenario).
  - Gross sales corresponding to firms projected to fall into negative equity:
    - Baseline: about 7 percent of total gross sales in 2020 (9 percent cumulatively over 2020-25).
    - Adverse: 11 percent of total gross sales in 2020 (12 percent cumulatively over 2020-25).
  - Wage bill for firms that fall into negative equity (for which data are available):
    - Baseline: about 6 percent of aggregate wage bill in 2020 (9 percent cumulatively over 2020-25).
    - Adverse: 11 percent of aggregate wage bill in 2020 (17 percent cumulatively over 2020-25).
- Distressed firms may reduce investment and operations, cutting output and employment and potentially creating a feedback loop that exacerbates the downturn and affects both bank and nonbank institutions.

### Conclusion and key takeaways
- A significant number of firms could fall into negative equity under stress: about 5 percent in the baseline and about 11 percent in the alternative scenario.
- Outstanding debt at risk ranges from $400 billion (baseline) to $675 billion (alternative).
- Equity valuation losses estimated at around $136 billion in the baseline and about $272 billion in the alternative.
- Energy sector represents the largest short-term liquidity need among investment-grade firms (US$580 billion outstanding debt; almost 70 percent of investment-grade liquidity needs through 2020).
- Banks’ direct exposures to the corporate sector are limited (less than 10 percent of bank assets) and appear manageable relative to bank capital buffers, while nonbank financial institutions (mutual funds, pension funds, life-insurers, ETFs) carry larger exposures and would likely face the bulk of losses in severe stress.
- Leveraged firms (debt-to-EBITDA > 5), although a smaller share of firms, account for the majority of distress and potential losses.

*Source: IMF staff calculations, Box 1, "Short-term liquidity needs following the COVID-19 outbreak."*

### APPENDIX II: SENSITIVITY ANALYSIS

### APPENDIX II: SENSITIVITY ANALYSIS

### Sensitivity of expenditures in response to changes in revenue (elasticity 훼훼_a)
- Definition and range:
  - The elasticity 훼훼_a determines how non-interest expenses react to changes in revenues.
  - 훼훼_a can vary from 0 to 1.
    - 훼훼_a = 0: firms are unable to reduce any costs in response to changes in revenue.
    - 훼훼_a = 1: firms can reduce costs to perfectly offset any reduction in revenue (net non-interest revenues independent of macroeconomic shocks).
- Main patterns:
  - Potential losses increase as 훼훼_a decreases (i.e., lower ability to reduce non-interest costs).
  - For low values of 훼훼_a:
    - Share of companies with negative equity in 2020 ranges from about 15 percent (baseline scenario) to about 28 percent (adverse/alternative scenario).
    - This compares with 5.6 percent (baseline) and 11.1 percent (alternative) when using the central case 훼훼_a = 0.5.
    - Corresponding outstanding debt at risk for low 훼훼_a ranges from around $890 billion (baseline) to around $1.4 trillion (alternative).
  - When 훼훼_a ≈ 1:
    - Only 1 percent of the firms in the sample fall into negative equity in 2020.
    - Corresponding amount of debt at risk is less than $50 billion.
  - Behavior for 훼훼_a < 0.8:
    - Potential losses start increasing rapidly and vary almost linearly as 훼훼_a decreases from 0.8 toward 0.

- Figures and reported metrics (as presented):
  - Number of distressed firms in 2020 (function of 훼훼_a) — baseline and stressed/alternative scenarios.
  - Share of distressed firms in 2020 (percent) — baseline and stressed/alternative scenarios.
  - Outstanding debt of distressed firms in 2020 (Million US$) — baseline and stressed/alternative scenarios.
  - Initial equity of distressed firms in 2020 (Million US$) — baseline and stressed/alternative scenarios.

### Sensitivity using historically estimated industry elasticities
- Method:
  - Stress tests rerun using historically estimated 훼훼_a for each industry (annual data 2000-19).
  - Regression of net revenues (excluding interest expenditure) on macro variables embeds historically observed 훼훼_a at the industry level, assumed constant over time.
- Comparative results:
  - Number of firms falling into negative equity is smaller when using historical 훼훼_a versus central case 훼훼_a = 0.5.
    - Baseline scenario: 5.6 percent fall into negative equity using 훼훼_a = 0.5, versus about 3.7 percent using historical 훼훼_a.
  - Expected losses for debt and equity holders are larger in all scenarios when assuming 훼훼_a = 0.5 compared with historical 훼훼_a.
- Interpretative note:
  - Given uncertainty about firm behavior under a relatively severe stress, using a slightly more conservative 훼훼_a than the historical average over 2000-19 is considered more prudent.

### Sensitivity to the dividend payout rate
- Parametrization and range:
  - Central case assumes dividends paid out of positive after-tax profits with a factor of 0.5 (i.e., 50 percent of net after-tax profits).
  - Dividend payout rate can vary from 0 to 1.
    - 0: all positive after-tax profits retained (build up capital buffers).
    - 1: 100 percent payout; all after-tax profits distributed as dividends.
  - When net after-tax profits are negative, the dividend parameter is set to zero.
- Impact on 2020 results:
  - Number of firms falling into negative equity in 2020 and potential debt and equity losses are unaffected by the dividend payout rate.
    - Reason: firms that go from positive equity in 2019 to negative equity in 2020 do so because they record negative net after-tax profit in 2020, and firms with negative profits do not pay dividends.
- Impact on subsequent years (2021 onwards) and cumulative horizon:
  - Dividend payout rate affects capital accumulation and therefore resilience in later years.
  - Most losses occur in 2020, so cumulative sensitivity is small.
  - Numerical examples (cumulative over 2020-25):
    - Alternative scenario:
      - Cumulative number of firms with negative equity: 151 firms when dividend payout rate = 0; 154 firms when dividend payout rate = 1 (difference of 3 firms).
      - Estimated outstanding debt at risk (cumulative over 2020-25): $1.15 trillion when payout = 0; $1.18 trillion when payout = 1.
    - Baseline scenario:
      - Estimated outstanding debt at risk (cumulative over 2020-25): $772 billion when payout = 0; $774 billion when payout = 1.
      - Difference in cumulative number of firms with negative equity over 2020-25 is one additional firm when payout = 1 relative to payout = 0.
- Figures and reported metrics (as presented):
  - Cumulative number of distressed firms over 2020-25 (function of dividend payout rate) — baseline and stressed/alternative scenarios.
  - Cumulative share of distressed firms over 2020-25 (percent) — baseline and stressed/alternative scenarios.
  - Cumulative outstanding debt of distressed firms over 2020-25 (Billion US$, cumulative) — baseline and stressed/alternative scenarios.
  - Cumulative initial equity of distressed firms over 2020-25 (Billion US$, cumulative) — baseline and stressed/alternative scenarios.

### Overall sensitivity conclusions
- Elasticity 훼훼_a is a key driver of stress-test outcomes:
  - Lower 훼훼_a (less ability to cut costs) materially increases numbers of firms with negative equity and amounts of debt at risk.
  - 훼훼_a values in the historical sectoral range (roughly 0.2 to 0.7 for most industries) imply outcomes not far from the central case, but losses rise rapidly as 훼훼_a falls below 0.8.
- Dividend payout rate has limited quantitative effect on stress-test outcomes:
  - Minimal impact because primary losses occur in 2020 when dividend policy does not affect firms that record losses.
  - Small differences over 2020-25 arise from reduced capital accumulation when payout rates are higher, affecting only a few firms that survive 2020 but deteriorate later.
- Prudential implication:
  - Using a slightly more conservative 훼훼_a than the historical average is justifiable given uncertainty about firm behavior under severe stress.

*Source: IMF staff calculations (APPENDIX II: SENSITIVITY ANALYSIS).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2020/english/wpiea2020238-print-pdf.pdf_