## 1. Sustainability of Corporate Debt in the LA-5: Weak Tail Analysis

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---

### I. Introduction
- Purpose: develop a specialized method to capture macro-financial linkages to predict solvency risk of individual firms.
- Method: extend the bottom-up default analysis (BuDA) of Duan, Miao, and Chan-Lau (2015) and link it with Vacisek’s (1987, 2002) portfolio credit risk model to estimate effects on bank loan provisions and capital requirements.
- Application: five large Latin American economies (Brazil, Chile, Colombia, Mexico, and Peru — LA-5) at end-April 2016.
- Structure: Section II — overview of corporate debt developments in LA-5; Section III — BuDA methodology; Section IV — application to LA-5; Section V — conclusions.

### II. Recent Corporate Debt Developments: LA-5 Countries

H3: A. Financial Ratio Analysis
- Macro backdrop:
  - Average corporate debt among LA-5 rose by about 14 percent of GDP between 2009 and 2015, double the 7 percent rate observed over 2003–2009.
- Sample:
  - Constructed sample of 1,121 publicly traded non-financial firms from Bloomberg LLC used in BuDA exercise.
- Debt level changes:
  - Total stock of debt for sample firms, measured in constant dollar terms, rose by 167 percent in the post-crisis period 2009–2015.
  - Weighted debt-to-asset ratio rose to 47 percent from 33 percent (a 14 percentage point increase).
  - Country increases in total debt (2009–2015): Brazil 185 percent, Chile 120 percent, Mexico 108 percent.
- Sector contributions to debt increase (share of increase by end-2015):
  - Oil, gas, and coal: 21 percent.
  - Utilities: 6¼ percent.
  - Metals and mining, telecommunications, consumer products: about 5½ percent each.
- Bank exposure:
  - In 2015, banks’ corporate loan shares of total assets: Brazil and Mexico roughly 22 percent; Peru 45 percent (of banking system total assets).
  - Correlation between market PDs of bank and corporate sectors rises to close to 0.9 during episodes of economic distress (rolling 24 month correlation).
- Debt sustainability indicators (comparative 2007 vs 2015 patterns; median and debt concentration comments):
  - Debt-to-asset ratio:
    - For extreme weak-tail firms, median rose to 52 percent from 44 percent (2007→2015).
    - Extreme weak-tail firms comprised one out of five firms but accounted for 60 percent of total debt in 2015, up from 40 percent in 2007.
  - Profitability (return on assets):
    - Declined 2007–2015; least profitable firms were also the most indebted.
    - Within extreme weak tail, share of total debt rose eight-fold to 42 percent at end-2015.
  - Revenue growth and cash buffers:
    - Decline in profitability accompanied by decline in revenue growth, most acute in construction and utilities.
    - Cash-to-debt ratios improved marginally: cumulative share of debt held by extreme and moderately cash-strapped firms down to 34 percent in 2015, 2 percentage points below 2007.
  - Subsector migration:
    - Commodity subsector: in 2007, 77 percent of debt was in strong tail; by 2015, about same share shifted to worst performing weak tail.
    - Construction subsector: shifted from 74 percent of subsector debt in strong tail (2007) to 70 percent in weak tail (2015).

H3: Key table highlights (Table 1 excerpts and definitions)
- Sample total debt (memorial context): sector totals reported in millions USD converted at constant 2012 exchange rates.
- Indicator definitions and thresholds:
  - Effective interest rate: interest expense in current year in percent of the average of total debt outstanding in the current and previous year.
  - Short-term liability ratio: liabilities and current portion of long-term debt coming due within 12 months in percent of total liabilities.
  - Weak/strong tail classification:
    - Weak tail: firms with risk above the median.
    - Strong tail: firms with risk below or equal to the median.
    - Weak tail subcategories:
      - Extreme: top 20th risk percentile range.
      - Moderate: next 15th risk percentile range.
      - Low: next 15th risk percentile range.
    - Percentile ranges described in notes: extreme concern include the 0-99th/1-20th percentiles; moderate concern 65-79/21-35th; low concern 50-64/35-50th. (Table note preserved as in source.)
- Selected median indicator values and debt shares (representative figures from Table 1 for All Non-financial corporates):
  - Debt to asset ratio, 2015: medians by segment — Extreme: 0.52 ; Moderate: 0.38 ; Low: 0.31 ; Strong: 0.11 ; cumulative share of total debt (Extreme .. Strong): 60.6, 12.6, 18.1, 8.8 ; Total sector (mil USD): 1,159.1
  - Debt to asset ratio, 2007: medians — Extreme: 0.44 ; Moderate: 0.31 ; Low: 0.24 ; Strong: 0.08 ; cumulative share of total debt: 39.6, 20.6, 17.9, 21.9 ; Total sector (mil USD): 279.7
  - Effective interest rate (percent), 2015: medians — Extreme: 23.80 ; Moderate: 11.75 ; Low: 8.59 ; Strong: 4.64 ; cumulative share of total debt: 5.7, 11.0, 9.1, 74.2 ; Total sector (mil USD): 1,140.2
  - Effective interest rate (percent), 2007: medians — Extreme: 32.04 ; Moderate: 13.34 ; Low: 10.36 ; Strong: 6.18 ; cumulative debt shares: 6.5, 9.4, 25.8, 58.3 ; Total sector (mil USD): 227.8
  - Short-term liability ratio, 2015: medians — Extreme: 0.85 ; Moderate: 0.64 ; Low: 0.50 ; Strong: 0.29 ; cumulative debt shares: 2.9, 4.5, 4.0, 88.6 ; Total sector (mil USD): 1,159.8
  - Return on assets (percent), 2015: medians — Extreme: -9.36 ; Moderate: -0.73 ; Low: 1.51 ; Strong: 5.45 ; cumulative debt shares: 42.0, 13.9, 11.2, 32.9 ; Total sector (mil USD): 1,160.7
  - Cash to debt ratio, 2015: medians — Extreme: 0.03 ; Moderate: 0.11 ; Low: 0.19 ; Strong: 0.56 ; cumulative debt shares: 8.2, 25.6, 32.4, 33.9 ; Total sector (mil USD): 1,160.8
  - Note: table contains sectoral breakdowns (Commodity producers, Utilities, Consumer/Retail, Telecommunications & Media, Construction) with analogous medians and debt shares (table preserved as presented).

H3: B. Debt-at-Risk
- Definition: debt-at-risk = debt of firms with interest coverage ratio lower than two (benchmark threshold = 2).
- 2013–2015 changes:
  - Debt-at-risk increased in all LA-5 countries over the two-year period, especially in Brazil, Colombia, and Chile (left panel of Figure 4).
- Liquidity-adjusted assessment:
  - Allowing use of cash on hand plus earnings to meet interest expenses reduces debt-at-risk substantially; Chile’s debt-at-risk actually declined under this estimate.
  - Conclusion: despite increased debt, LA-5 firms accumulated sufficient cash buffers, improving resilience to shocks.

### III. The Bottom-Up Default Analysis (BuDA) Methodology: An Overview
- Motivation:
  - Financial ratios are static, accounting-based, backward-looking, and largely independent of macroeconomic outlook; BuDA aims to capture dynamic macro-financial drivers of corporate solvency risk.
- Conceptual approach:
  - Firm-level PDs directly affected by macroeconomic and financial conditions (real economy influences probability of default).
  - Link projected changes in firm PDs to bank provisioning and capital needs via Vacisek’s portfolio credit risk model.
  - Facilitates what-if scenario analysis to inform policymakers on the nexus between corporate solvency and banking sector buffer needs.
- Four-step conceptual procedure:
  - Specify a macroeconomic scenario.
  - Forecast economy-wide and firm specific risk factors under the specified macroeconomic scenario.
  - Use risk factors as inputs in a forward intensity model to yield the projected PDs of the firm.
  - Use projected PDs as inputs in the credit portfolio module to assess creditor banks’ provisions and capital needs associated with the default risk of the firm.

### Step 1–3: Scenario, Risk-Factor Forecasting, and PD Projection
- Step 1: "Specify a macroeconomic scenario."
- Step 2: "Forecast economy-wide and firm specific risk factors under the specified macroeconomic scenario."
- Step 3: "Use risk factors as inputs in a forward intensity model to yield the projected PDs of the firm."
- Overview:
  - BuDA projects firm-level PDs using a forward intensity model under a specified macroeconomic scenario.

### IV. Use projected PDs as inputs in the credit portfolio module to assess creditor banks’ provisions and capital needs

H3: Methodology overview and building blocks
- BuDA jointly developed by RMI-CRI, NUS and the IMF (Duan, Miao and Chan-Lau, 2015).
- Main building blocks:
  - Macroeconomic scenarios (baseline and alternatives, typically including downside scenarios).
  - Forecasting of predetermined risk factors (economy-wide and firm-specific).
  - PD projection using the Duan-Sun-Wang (DSW) forward-intensity model.
  - Aggregation and decomposition of PDs by sector or economy.
  - Use of projected PDs as inputs into a credit portfolio model to estimate banks’ provisions and economic capital.

H3: Macroeconomic scenarios (LA-5 implementation details)
- Scenarios must capture economic and financial variables relevant to corporate default risk.
- Typical analysis compares a baseline scenario and alternative scenarios (upside and downside); supervisors commonly emphasize downside scenarios.
- LA-5 case study: starting point April 2016 with projection period through end-2017.
- Baseline assumptions (April 2016): subdued global demand, slowdown/rebalancing in China, lower commodity prices, tightened global financial conditions; Latin America & Caribbean projected to decline by 0.5 percent in 2016.
- Distress scenario design for LA-5:
  - Commodity prices fall to the bottom 25th percentile of empirical distribution (2000 Q1–2017 Q4 baseline forecasts).
  - Implies quarterly price decline of 15½ percent starting at end-2016; oil price bottom USD 19.3 per barrel; metal price index to 51.7 (2005 = 100) by end-2017.
  - Domestic variables (GDP and exchange rate) under distress estimated via country-specific VARs.
  - Assumes no feedback from LA-5 to global variables (no spillovers to rest of world).

H3: Risk factors used by BuDA
- Economy-wide (common) risk factors:
  - Return of domestic stock market index (Current level).
  - Short-term domestic interest rate (Current level).
- Firm-specific risk factors:
  - Liquidity = (cash + short-term investments) / total assets (Trend and level; level is 12-month average; trend = current minus 12-month average).
  - Profitability = net income / total assets (Trend and level).
  - Volatility-adjusted leverage (Distance-to-default, DTD) (Trend and level).
  - Size = ln(market capitalization / median market capitalization) (Trend and level).
  - Market mis-valuation = market cap + total liabilities / total assets (Current).
  - Idiosyncratic volatility = standard deviation of residuals from regressing firm equity returns on domestic market index returns (Current).
- Notes:
  - Median refers to average median PD value of sample non-financial firms across 1000 simulations.
  - Currency denomination mix in corporate debt not modeled separately; total debt considered and currency mismatch effects captured indirectly via market movements.

H3: PD estimation using DSW forward-intensity model
- Inputs: forecasted risk factors from scenario-specific mappings.
- DSW projects PDs for horizons ranging from one-month to five-years ahead.
- PDs can be aggregated economy-wide, by sector, or ad-hoc groups and decomposed into macro drivers.
- Model performance: for a one-year default prediction horizon, AUROC of BuDA’s PD forward intensity model is in the range of 85 percent to 91 percent (RMI-NUS, 2015).
- DSW features:
  - Models default and non-default exits (e.g., M&A, delisting) separately via two independent Poisson processes with forward intensities.
  - Forward intensities are exponentials of affine functions of risk factors.
  - Calibration uses credit events and exit data from CRI database.
  - Simulation framework: random shocks in risk factor forecasts yield multiple PD paths; analysis uses average median PD over 1000 simulations.

H3: Banks’ provisions and capital needs (credit portfolio modeling)
- Stylized creditor bank assumptions:
  - Banks homogeneous, identical granular corporate loan portfolio.
  - Each loan has unit value, identical PD equal to average median PD in scenario, and loss given default (LGD) = 40 percent.
- Loss distribution:
  - Single-factor Vasicek/KM V-style model: obligor asset value standard normal; default threshold from PD via inverse normal.
  - Asset value decomposition: systematic factor S and idiosyncratic shock; asset correlation ρ common across obligors.
- Asset correlation calibration:
  - Basel formula linking PD to asset correlation (equation (12) in source), producing a negative relationship between PDs and asset correlations.
  - Implication: PD down -> asset correlation up -> provisions down, capital up; PD up -> asset correlation down -> provisions up, capital down.
- Provisions and economic capital definitions:
  - Provisions = expected loss of the portfolio.
  - Economic capital = unexpected loss = VaR(99.5 percent) − expected loss.
- Implementation specifics:
  - Stylized portfolio of 10 000 loans and 5000 simulations used for loss distributions.
  - Initial provisions and capital set to end-2015 observed values from IMF FSIs, scaled to corporate loan share.
  - Loss distribution uses backward-looking 12-month average of median PD for through-the-cycle parameter smoothing.

H3: LA-5 case study: key findings and numeric results
- PD dynamics under baseline:
  - Median PDs decline across LA-5 in the sample period due to improving economic activity under baseline.
  - Notable declines in Brazil and Colombia toward end of sample.
- PD dynamics under distress:
  - Heterogeneous responses across LA-5:
    - Brazil, Chile, Peru: PDs increase rapidly to levels not observed since early 2000.
    - Colombia and Mexico: muted PD response.
  - Drivers (2017 median PD contributions):
    - Peru: decline in metal prices primary driver.
    - Chile: nominal exchange rate depreciation plus high foreign-currency debt.
    - Brazil: commodity price decline’s effect on GDP growth given fragile recovery.
    - Colombia: GDP growth remains positive in distress due to policy framework and flexible exchange rate—limited PD increase.
    - Mexico: negligible PD reaction as domestic and external demand largely unchanged; diversified corporate sector.
- Bank provisions and economic capital (Table 3; values are in percent of GDP):
  - Baseline scenario (2015 vs 2016–17):
    - Brazil: Provisions 1.3 → 1.9; Economic capital 3.7 → 3.7
    - Chile: Provisions 1.4 → 1.3; Economic capital 7.6 → 8.5
    - Colombia: Provisions 1.2 → 0.8; Economic capital 4.7 → 3.8
    - Mexico: Provisions 0.4 → 0.3; Economic capital 2.3 → 3.0
    - Peru: Provisions 0.6 → 0.6; Economic capital 4.4 → 4.0
  - Distress scenario (2015 vs 2016–17):
    - Brazil: Provisions 1.3 → 2.0; Economic capital 3.7 → 4.9
    - Chile: Provisions 1.4 → 2.7; Economic capital 7.6 → 12.3
    - Colombia: Provisions 1.2 → 1.0; Economic capital 4.7 → 3.9
    - Mexico: Provisions 0.4 → 0.4; Economic capital 2.3 → 2.2
    - Peru: Provisions 0.6 → 0.9; Economic capital 4.4 → 5.7
- Interpretation highlights:
  - Under baseline, declining PDs generally reduce provisions; however, Basel-implied higher asset correlations can raise economic capital even when provisions fall (observed in Chile, Mexico, Peru).
  - Under distress, Brazil, Chile, and Peru require both higher provisions and higher capital buffers relative to 2015; Chile’s required provisions could be twice end-2015 levels.
  - Estimated increases relative to GDP under distress: provisions up by about 1 percent of GDP in Brazil and Chile, and by ¼ percent of GDP in Peru; economic capital up by 1½ percent and ½ percent of GDP respectively in Brazil and Peru.
  - Mexico shows a counterintuitive decline in economic capital under distress due to the negative PD–asset correlation relationship; diversification mitigates bank sector vulnerability.

H3: Caveats, limitations, and implementation notes
- BuDA applies to publicly listed firms; results do not represent risks of loans to unlisted firms or consumer loans.
- Market-based model accuracy depends on market prices reflecting fundamentals (illiquidity or manipulation can distort PDs).
- Homogeneous/stylized bank portfolio assumption is a simplification; actual bank portfolios differ.
- Use of Basel formula for asset correlation is a shortcut; Basel relationship can offset economic capital needs as PDs rise.
- Provisions and economic capital estimates are approximations; better loan-portfolio data and scenario-specific asset correlation behavior would improve accuracy.
- BuDA can be extended to include privately held firms in future work (reference to Duan et al., 2014).

*Source: IMF working paper "Sustainability of Corporate Debt in the LA-5: Weak Tail Analysis" (content unit wp17133).*

### 1. Sustainability of Corporate Debt in the LA-5: Weak Tail Analysis ......................................9

### 1. Sustainability of Corporate Debt in the LA-5: Weak Tail Analysis

### I. Introduction
- Purpose: develop a specialized method to capture macro-financial linkages to predict solvency risk of individual firms.
- Method: extend the bottom-up default analysis (BuDA) of Duan, Miao, and Chan-Lau (2015) and link it with Vacisek’s (1987, 2002) portfolio credit risk model to estimate effects on bank loan provisions and capital requirements.
- Application: five large Latin American economies (Brazil, Chile, Colombia, Mexico, and Peru — LA-5) at end-April 2016.
- Structure: Section II — overview of corporate debt developments in LA-5; Section III — BuDA methodology; Section IV — application to LA-5; Section V — conclusions.

### II. Recent Corporate Debt Developments: LA-5 Countries

H3: A. Financial Ratio Analysis
- Macro backdrop:
  - Average corporate debt among LA-5 rose by about 14 percent of GDP between 2009 and 2015, double the 7 percent rate observed over 2003–2009.
- Sample:
  - Constructed sample of 1,121 publicly traded non-financial firms from Bloomberg LLC used in BuDA exercise.
- Debt level changes:
  - Total stock of debt for sample firms, measured in constant dollar terms, rose by 167 percent in the post-crisis period 2009–2015.
  - Weighted debt-to-asset ratio rose to 47 percent from 33 percent (a 14 percentage point increase).
  - Country increases in total debt (2009–2015): Brazil 185 percent, Chile 120 percent, Mexico 108 percent.
- Sector contributions to debt increase (share of increase by end-2015):
  - Oil, gas, and coal: 21 percent.
  - Utilities: 6¼ percent.
  - Metals and mining, telecommunications, consumer products: about 5½ percent each.
- Bank exposure:
  - In 2015, banks’ corporate loan shares of total assets: Brazil and Mexico roughly 22 percent; Peru 45 percent (of banking system total assets).
  - Correlation between market PDs of bank and corporate sectors rises to close to 0.9 during episodes of economic distress (rolling 24 month correlation).
- Debt sustainability indicators (comparative 2007 vs 2015 patterns; median and debt concentration comments):
  - Debt-to-asset ratio:
    - For extreme weak-tail firms, median rose to 52 percent from 44 percent (2007→2015).
    - Extreme weak-tail firms comprised one out of five firms but accounted for 60 percent of total debt in 2015, up from 40 percent in 2007.
  - Profitability (return on assets):
    - Declined 2007–2015; least profitable firms were also the most indebted.
    - Within extreme weak tail, share of total debt rose eight-fold to 42 percent at end-2015.
  - Revenue growth and cash buffers:
    - Decline in profitability accompanied by decline in revenue growth, most acute in construction and utilities.
    - Cash-to-debt ratios improved marginally: cumulative share of debt held by extreme and moderately cash-strapped firms down to 34 percent in 2015, 2 percentage points below 2007.
  - Subsector migration:
    - Commodity subsector: in 2007, 77 percent of debt was in strong tail; by 2015, about same share shifted to worst performing weak tail.
    - Construction subsector: shifted from 74 percent of subsector debt in strong tail (2007) to 70 percent in weak tail (2015).

H3: Key table highlights (Table 1 excerpts and definitions)
- Sample total debt (memorial context): sector totals reported in millions USD converted at constant 2012 exchange rates.
- Indicator definitions and thresholds:
  - Effective interest rate: interest expense in current year in percent of the average of total debt outstanding in the current and previous year.
  - Short-term liability ratio: liabilities and current portion of long-term debt coming due within 12 months in percent of total liabilities.
  - Weak/strong tail classification:
    - Weak tail: firms with risk above the median.
    - Strong tail: firms with risk below or equal to the median.
    - Weak tail subcategories:
      - Extreme: top 20th risk percentile range.
      - Moderate: next 15th risk percentile range.
      - Low: next 15th risk percentile range.
    - Percentile ranges described in notes: extreme concern include the 0-99th/1-20th percentiles; moderate concern 65-79/21-35th; low concern 50-64/35-50th. (Table note preserved as in source.)
- Selected median indicator values and debt shares (representative figures from Table 1 for All Non-financial corporates):
  - Debt to asset ratio, 2015: medians by segment — Extreme: 0.52 ; Moderate: 0.38 ; Low: 0.31 ; Strong: 0.11 ; cumulative share of total debt (Extreme .. Strong): 60.6, 12.6, 18.1, 8.8 ; Total sector (mil USD): 1,159.1
  - Debt to asset ratio, 2007: medians — Extreme: 0.44 ; Moderate: 0.31 ; Low: 0.24 ; Strong: 0.08 ; cumulative share of total debt: 39.6, 20.6, 17.9, 21.9 ; Total sector (mil USD): 279.7
  - Effective interest rate (percent), 2015: medians — Extreme: 23.80 ; Moderate: 11.75 ; Low: 8.59 ; Strong: 4.64 ; cumulative share of total debt: 5.7, 11.0, 9.1, 74.2 ; Total sector (mil USD): 1,140.2
  - Effective interest rate (percent), 2007: medians — Extreme: 32.04 ; Moderate: 13.34 ; Low: 10.36 ; Strong: 6.18 ; cumulative debt shares: 6.5, 9.4, 25.8, 58.3 ; Total sector (mil USD): 227.8
  - Short-term liability ratio, 2015: medians — Extreme: 0.85 ; Moderate: 0.64 ; Low: 0.50 ; Strong: 0.29 ; cumulative debt shares: 2.9, 4.5, 4.0, 88.6 ; Total sector (mil USD): 1,159.8
  - Return on assets (percent), 2015: medians — Extreme: -9.36 ; Moderate: -0.73 ; Low: 1.51 ; Strong: 5.45 ; cumulative debt shares: 42.0, 13.9, 11.2, 32.9 ; Total sector (mil USD): 1,160.7
  - Cash to debt ratio, 2015: medians — Extreme: 0.03 ; Moderate: 0.11 ; Low: 0.19 ; Strong: 0.56 ; cumulative debt shares: 8.2, 25.6, 32.4, 33.9 ; Total sector (mil USD): 1,160.8
  - Note: table contains sectoral breakdowns (Commodity producers, Utilities, Consumer/Retail, Telecommunications & Media, Construction) with analogous medians and debt shares (table preserved as presented).

H3: B. Debt-at-Risk
- Definition: debt-at-risk = debt of firms with interest coverage ratio lower than two (benchmark threshold = 2).
- 2013–2015 changes:
  - Debt-at-risk increased in all LA-5 countries over the two-year period, especially in Brazil, Colombia, and Chile (left panel of Figure 4).
- Liquidity-adjusted assessment:
  - Allowing use of cash on hand plus earnings to meet interest expenses reduces debt-at-risk substantially; Chile’s debt-at-risk actually declined under this estimate.
  - Conclusion: despite increased debt, LA-5 firms accumulated sufficient cash buffers, improving resilience to shocks.

### III. The Bottom-Up Default Analysis (BuDA) Methodology: An Overview
- Motivation:
  - Financial ratios are static, accounting-based, backward-looking, and largely independent of macroeconomic outlook; BuDA aims to capture dynamic macro-financial drivers of corporate solvency risk.
- Conceptual approach:
  - Firm-level PDs directly affected by macroeconomic and financial conditions (real economy influences probability of default).
  - Link projected changes in firm PDs to bank provisioning and capital needs via Vacisek’s portfolio credit risk model.
  - Facilitates what-if scenario analysis to inform policymakers on the nexus between corporate solvency and banking sector buffer needs.
- Four-step conceptual procedure (illustrated in Figure 5 in source):
  - The source describes BuDA as a four-step procedure; the paper extends BuDA with portfolio credit risk modeling to translate PD changes into bank buffer needs.

*Source: IMF working paper "Sustainability of Corporate Debt in the LA-5: Weak Tail Analysis" (content unit wp17133).*

### 1. Specify a macroeconomic scenario.

### 1. Specify a macroeconomic scenario.

### Overview
- This content unit outlines the initial steps required to project firm-level probabilities of default (PDs) using a forward intensity model under a specified macroeconomic scenario.

### Step 1: Specify a macroeconomic scenario
- "Specify a macroeconomic scenario."

### Step 2: Forecast economy-wide and firm specific risk factors under the specified macroeconomic scenario
- "Forecast economy-wide and firm specific risk factors under the specified 
macroeconomic scenario."

### Step 3: Use risk factors as inputs in a forward intensity model to yield the projected PDs of the firm
- "Use risk factors as inputs in a forward intensity model to yield the projected PDs of 
the firm."

*Source: wp17133 - 1. Specify a macroeconomic scenario.*

### 4. Use projected PDs as inputs in the credit portfolio module to assess creditor banks’

### 4. Use projected PDs as inputs in the credit portfolio module to assess creditor banks’ provisions and capital needs associated with the default risk of the firm.

### Methodology overview
- BuDA (Bottom-Up Default Analysis) jointly developed by RMI-CRI, NUS and the IMF (Duan, Miao and Chan-Lau, 2015).
- Main building blocks:
  - Macroeconomic scenarios (baseline and alternatives, typically including downside scenarios).
  - Forecasting of predetermined risk factors (economy-wide and firm-specific).
  - PD projection using the Duan-Sun-Wang (DSW) forward-intensity model.
  - Aggregation and decomposition of PDs by sector or economy.
  - Use of projected PDs as inputs into a credit portfolio model to estimate banks’ provisions and economic capital.

### Macroeconomic scenarios
- Scenarios must capture economic and financial variables relevant to corporate default risk.
- Typical analysis compares a baseline scenario and alternative scenarios (upside and downside); supervisors commonly emphasize downside scenarios.
- LA-5 case study: starting point April 2016 with projection period through end-2017.
- Baseline assumptions (April 2016): subdued global demand, slowdown/rebalancing in China, lower commodity prices, tightened global financial conditions; Latin America & Caribbean projected to decline by 0.5 percent in 2016.
- Distress scenario design for LA-5:
  - Commodity prices fall to the bottom 25th percentile of empirical distribution (2000 Q1–2017 Q4 baseline forecasts).
  - Implies quarterly price decline of 15½ percent starting at end-2016; oil price bottom USD 19.3 per barrel; metal price index to 51.7 (2005 = 100) by end-2017.
  - Domestic variables (GDP and exchange rate) under distress estimated via country-specific VARs.
  - Assumes no feedback from LA-5 to global variables (no spillovers to rest of world).

### Risk factors used by BuDA
- Economy-wide (common) risk factors:
  - Return of domestic stock market index (Current level).
  - Short-term domestic interest rate (Current level).
- Firm-specific risk factors:
  - Liquidity = (cash + short-term investments) / total assets (Trend and level; level is 12-month average; trend = current minus 12-month average).
  - Profitability = net income / total assets (Trend and level).
  - Volatility-adjusted leverage (Distance-to-default, DTD) (Trend and level).
  - Size = ln(market capitalization / median market capitalization) (Trend and level).
  - Market mis-valuation = market cap + total liabilities / total assets (Current).
  - Idiosyncratic volatility = standard deviation of residuals from regressing firm equity returns on domestic market index returns (Current).
- Notes:
  - Median refers to average median PD value of sample non-financial firms across 1000 simulations.
  - Currency denomination mix in corporate debt not modeled separately; total debt considered and currency mismatch effects captured indirectly via market movements.

### PD estimation using DSW forward-intensity model
- Inputs: forecasted risk factors from scenario-specific mappings.
- DSW projects PDs for horizons ranging from one-month to five-years ahead.
- PDs can be aggregated economy-wide, by sector, or ad-hoc groups and decomposed into macro drivers.
- Model performance: for a one-year default prediction horizon, AUROC of BuDA’s PD forward intensity model is in the range of 85 percent to 91 percent (RMI-NUS, 2015).
- DSW features:
  - Models default and non-default exits (e.g., M&A, delisting) separately via two independent Poisson processes with forward intensities.
  - Forward intensities are exponentials of affine functions of risk factors.
  - Calibration uses credit events and exit data from CRI database.
  - Simulation framework: random shocks in risk factor forecasts yield multiple PD paths; analysis uses average median PD over 1000 simulations.

### Banks’ provisions and capital needs (credit portfolio modeling)
- Stylized creditor bank assumptions:
  - Banks homogeneous, identical granular corporate loan portfolio.
  - Each loan has unit value, identical PD equal to average median PD in scenario, and loss given default (LGD) = 40 percent.
- Loss distribution:
  - Single-factor Vasicek/KM V-style model: obligor asset value standard normal; default threshold from PD via inverse normal.
  - Asset value decomposition: systematic factor S and idiosyncratic shock; asset correlation ρ common across obligors.
- Asset correlation calibration:
  - Basel formula linking PD to asset correlation (equation (12) in source), producing a negative relationship between PDs and asset correlations.
  - Implication: PD down -> asset correlation up -> provisions down, capital up; PD up -> asset correlation down -> provisions up, capital down.
- Provisions and economic capital definitions:
  - Provisions = expected loss of the portfolio.
  - Economic capital = unexpected loss = VaR(99.5 percent) − expected loss.
- Implementation specifics:
  - Stylized portfolio of 10 000 loans and 5000 simulations used for loss distributions.
  - Initial provisions and capital set to end-2015 observed values from IMF FSIs, scaled to corporate loan share.
  - Loss distribution uses backward-looking 12-month average of median PD for through-the-cycle parameter smoothing.

### LA-5 case study: key findings and numeric results
- PD dynamics under baseline:
  - Median PDs decline across LA-5 in the sample period due to improving economic activity under baseline.
  - Notable declines in Brazil and Colombia toward end of sample.
- PD dynamics under distress:
  - Heterogeneous responses across LA-5:
    - Brazil, Chile, Peru: PDs increase rapidly to levels not observed since early 2000.
    - Colombia and Mexico: muted PD response.
  - Drivers (2017 median PD contributions):
    - Peru: decline in metal prices primary driver.
    - Chile: nominal exchange rate depreciation plus high foreign-currency debt.
    - Brazil: commodity price decline’s effect on GDP growth given fragile recovery.
    - Colombia: GDP growth remains positive in distress due to policy framework and flexible exchange rate—limited PD increase.
    - Mexico: negligible PD reaction as domestic and external demand largely unchanged; diversified corporate sector.
- Bank provisions and economic capital (Table 3; values are in percent of GDP):
  - Baseline scenario (2015 vs 2016–17):
    - Brazil: Provisions 1.3 → 1.9; Economic capital 3.7 → 3.7
    - Chile: Provisions 1.4 → 1.3; Economic capital 7.6 → 8.5
    - Colombia: Provisions 1.2 → 0.8; Economic capital 4.7 → 3.8
    - Mexico: Provisions 0.4 → 0.3; Economic capital 2.3 → 3.0
    - Peru: Provisions 0.6 → 0.6; Economic capital 4.4 → 4.0
  - Distress scenario (2015 vs 2016–17):
    - Brazil: Provisions 1.3 → 2.0; Economic capital 3.7 → 4.9
    - Chile: Provisions 1.4 → 2.7; Economic capital 7.6 → 12.3
    - Colombia: Provisions 1.2 → 1.0; Economic capital 4.7 → 3.9
    - Mexico: Provisions 0.4 → 0.4; Economic capital 2.3 → 2.2
    - Peru: Provisions 0.6 → 0.9; Economic capital 4.4 → 5.7
- Interpretation highlights:
  - Under baseline, declining PDs generally reduce provisions; however, Basel-implied higher asset correlations can raise economic capital even when provisions fall (observed in Chile, Mexico, Peru).
  - Under distress, Brazil, Chile, and Peru require both higher provisions and higher capital buffers relative to 2015; Chile’s required provisions could be twice end-2015 levels.
  - Estimated increases relative to GDP under distress: provisions up by about 1 percent of GDP in Brazil and Chile, and by ¼ percent of GDP in Peru; economic capital up by 1½ percent and ½ percent of GDP respectively in Brazil and Peru.
  - Mexico shows a counterintuitive decline in economic capital under distress due to the negative PD–asset correlation relationship; diversification mitigates bank sector vulnerability.

### Caveats, limitations, and implementation notes
- BuDA applies to publicly listed firms; results do not represent risks of loans to unlisted firms or consumer loans.
- Market-based model accuracy depends on market prices reflecting fundamentals (illiquidity or manipulation can distort PDs).
- Homogeneous/stylized bank portfolio assumption is a simplification; actual bank portfolios differ.
- Use of Basel formula for asset correlation is a shortcut; Basel relationship can offset economic capital needs as PDs rise.
- Provisions and economic capital estimates are approximations; better loan-portfolio data and scenario-specific asset correlation behavior would improve accuracy.
- BuDA can be extended to include privately held firms in future work (reference to Duan et al., 2014).

*Source: IMF working paper chapter "4. Use projected PDs as inputs in the credit portfolio module to assess creditor banks’ provisions and capital needs associated with the default risk of the firm."*

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_Source: https://www.imf.org/-/media/files/publications/wp/2017/wp17133.pdf_