## 1. Technical Note on Asset Valuation Models

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### Overview and modeling approach
- Purpose:
  - Provide a direct measure of asset price misalignment based on economic and corporate fundamentals, excluding—to the extent possible—market price–based measures.
  - Be tractable and applicable to many international markets.
- Models developed for the October 2019 GFSR:
  - Several major advanced and emerging equity markets.
  - US option-implied equity volatility index (VIX).
  - US and euro-area corporate bond spreads.
  - Emerging market foreign-currency denominated sovereign bond spreads.
- Preparation and caveats:
  - Prepared by Sergei Antoshin, Andrea Deghi, Rohit Goel, Thomas Piontek, and Akihiko Yokoyama.
  - Staff tested models for robustness and selected best-performing variables; approaches subject to limitations and uncertainty from factor selection and alternative specifications.
  - Country-specific equity models use extreme bound analysis; final model-implied valuation = weighted average of fitted estimates, weights = respective regression R^2.

### Global equity markets — Dividend Discount Model (DDM) framework
- Theoretical formulation (key equations and definitions preserved):
  - Standard DDM: Pt = Dt+1 / (kt − E{gt})  (equation (2))
    - Dt+1 is the dividend at time t+1.
    - kt is the cost of capital.
    - E{gt} is the dividend’s anticipated steady-state growth rate.
  - Cost of capital decomposition: kt = Yt + θt  (equation (3))
    - Yt is the long-term interest rate.
    - θt is the equity risk premium.
  - Long-term interest decomposition: Yt = E{rt^sh} + ρt  (equation (5))
    - E{rt^sh} is the expected path of the short-term rate.
    - ρt is the term premium.
  - Assuming E{rt^sh} ~ E{gt} yields Pt = Dt+1 / (ρt + θt)  (equation (6))
- Empirical specification:
  - Pt = β0 + β1 Et + β2 θt + β3 It + εt  (equation (7))
    - Et = expected future earnings (proxy for Dt+1 and E{gt}).
    - θt proxy: standard deviation (across analysts) of earnings forecasts (12 and 18 months).
    - It = either Yt (long-term interest rate) or ρt (term premium); choose based on sign, stability, and R^2.
- Empirical proxies and diagnostics:
  - Expected earnings Et: weighted average forecasts of earnings over the next 12 and 18 months from IBES.
  - Term-premium proxies: 4- and 5-factor ACM term premiums or term spreads (long-term yields minus 3-month yield).
  - Stationarity and cointegration tests (Durbin Watson, Dicky and Fuller, Johansen) and other robustness tests performed.

### Equity model estimation results (sample and fit)
- Markets estimated (monthly data): China, Brazil, euro area, Germany, India, Japan, United Kingdom, United States. These account for over 70 percent of global equity market capitalization.
- Overall performance:
  - Average R^2 across countries: 80 percent.
- Online Annex Table 1.2 — key statistics (As of September 2019) — selected country-level figures (preserved exactly):
  - United States
    - Sample Start: Jan 31, 1990
    - Sample End: Sep 30, 2019
    - Monthly Observations: 357
    - Minimum R^2: 92%
    - Maximum R^2: 93%
    - Average R^2: 93%
    - Standard Error: 1.0
    - Misalignment, Last Month (%): 15.1
    - Historical Volatility: 4.2
    - Misalignment, Last Month Divided by Historical Volatility: 3.6
    - Misalignment, Last Quarter Divided by Historical Volatility: 2.6
  - Euro Area
    - Sample Start: Nov 30, 1999
    - Sample End: Sep 30, 2019
    - Monthly Observations: 239
    - Minimum R^2: 51%
    - Maximum R^2: 54%
    - Average R^2: 53%
    - Standard Error: -0.2
    - Misalignment, Last Month (%): -2.5
    - Historical Volatility: 5.6
    - Misalignment, Last Month Divided by Historical Volatility: -0.4
    - Misalignment, Last Quarter Divided by Historical Volatility: -0.5
  - Germany
    - Sample Start: Aug 31, 1990
    - Sample End: Sep 30, 2019
    - Monthly Observations: 350
    - Minimum R^2: 88%
    - Maximum R^2: 89%
    - Average R^2: 89%
    - Standard Error: 0.1
    - Misalignment, Last Month (%): 1.6
    - Historical Volatility: 5.9
    - Misalignment, Last Month Divided by Historical Volatility: 0.3
    - Misalignment, Last Quarter Divided by Historical Volatility: 0.3
  - Japan
    - Sample Start: Jan 31, 1990
    - Sample End: Sep 30, 2019
    - Monthly Observations: 357
    - Minimum R^2: 42%
    - Maximum R^2: 48%
    - Average R^2: 45%
    - Standard Error: 1.1
    - Misalignment, Last Month (%): 22.7
    - Historical Volatility: 6.2
    - Misalignment, Last Month Divided by Historical Volatility: 3.7
    - Misalignment, Last Quarter Divided by Historical Volatility: -0.1
  - United Kingdom
    - Sample Start: Jan 30, 1990
    - Sample End: Sep 30, 2019
    - Monthly Observations: 357
    - Minimum R^2: 73%
    - Maximum R^2: 79%
    - Average R^2: 75%
    - Standard Error: 0.0
    - Misalignment, Last Month (%): 0.2
    - Historical Volatility: 4.4
    - Misalignment, Last Month Divided by Historical Volatility: 0.0
    - Misalignment, Last Quarter Divided by Historical Volatility: 2.9
  - China
    - Sample Start: Nov 30, 1995
    - Sample End: Sep 30, 2019
    - Monthly Observations: 287
    - Minimum R^2: 80%
    - Maximum R^2: 82%
    - Average R^2: 81%
    - Standard Error: 0.1
    - Misalignment, Last Month (%): 3.1
    - Historical Volatility: 10.4
    - Misalignment, Last Month Divided by Historical Volatility: 0.3
    - Misalignment, Last Quarter Divided by Historical Volatility: 0.1
  - Brazil
    - Sample Start: Nov 30, 1999
    - Sample End: Sep 30, 2019
    - Monthly Observations: 239
    - Minimum R^2: 91%
    - Maximum R^2: 93%
    - Average R^2: 92%
    - Standard Error: 0.0
    - Misalignment, Last Month (%): -0.1
    - Historical Volatility: 7.0
    - Misalignment, Last Month Divided by Historical Volatility: 0.0
    - Misalignment, Last Quarter Divided by Historical Volatility: -0.2
  - India
    - Sample Start: Apr 30, 1996
    - Sample End: Sep 30, 2019
    - Monthly Observations: 282
    - Minimum R^2: 96%
    - Maximum R^2: 96%
    - Average R^2: 96%
    - Standard Error: 0.2
    - Misalignment, Last Month (%): 3.6
    - Historical Volatility: 7.8
    - Misalignment, Last Month Divided by Historical Volatility: 0.5
    - Misalignment, Last Quarter Divided by Historical Volatility: 0.6
- Additional output:
  - Historical misalignments by country shown in Figure 1.1 with generally narrow confidence intervals closely aligned with fitted values.

### US option-implied equity volatility (VIX) fair value model
- Objective:
  - Identify economic and financial drivers affecting market expectations of future US equity volatility.
- Framework and data:
  - Focus: US equity market.
  - Estimation: Ordinary least-squares regression over 16 years of quarterly data with VIX as dependent variable; all series transformed to z-scores.
  - Eleven independent variables grouped into four categories:
    - Macroeconomic fundamentals:
      - Interquartile Range of One-Year Ahead US GDP Forecasts.
      - Interquartile Range of One-Year Ahead US CPI Forecasts.
      - U.S. Unemployment Rate Change (Year-over-Year).
    - Funding and liquidity conditions:
      - TED Spread.
      - Interquartile Range of One-Year Ahead US 3-Month T-Bill Forecasts.
      - Federal Reserve Net Purchases of US Treasuries.
      - Rolling 12-Month Standard Deviation of Citi Global Economic Surprise Index.
    - Corporate performance:
      - Net Income to Assets for S&P 500 firms.
      - Payouts to Net Income for S&P 500 firms.
    - External factors:
      - US Trade Policy Uncertainty Index (Baker, Bloom, Davis).
      - Sentix Euro Area Economic Sentiment Index.
- Results and interpretation:
  - Model fit: provides a good fit for historical VIX values.
  - Drivers: lower macro uncertainty and stronger corporate performance have been important drivers of lower implied equity volatility.
  - 2019 assessment: external factors (trade tensions, global outlook uncertainty) suggest implied volatility should be higher than average 2019 levels; part of the divergence may reflect investor belief that central banks will lean against sharp tightening in financial conditions.
  - Historical note: VIX was also compressed relative to model-fitted VIX in 2017.

*Italic: IMF staff calculations; sources cited in text (Bloomberg Finance L.P.; Thomson Reuters I/B/E/S; Federal Reserve; Haver Analytics; Philadelphia Federal Reserve Survey of Professional Forecasters; S&P Market Intelligence).*

---

### 3. Drivers of Declining Equity Volatility

### Overview and estimation approach for corporate bond spreads
- Conceptual link: corporate bond spreads linked to economic (firm value) factors, uncertainty measures, and leverage following structural-option-pricing intuition (Black and Scholes (1973); Merton (1974)).
- Spread measure: difference between yield on Bloomberg-Barclays corporate bond index and duration-matched Treasury yield.
- Estimation: monthly linear regressions:
  - Corporate Bond Spread_t = α0 + β1 Economic Factor_t + β2 Uncertainty Factor_t + β3 Leverage Factor_t + ε_t
- Variable selection: extreme bound analysis; model-implied spread = weighted average fitted value across specifications, weights = R^2.
- Unit-root and cointegration testing performed.
- Sample periods:
  - United States: January 1995 to July 2019
  - Euro area: January 2004 to July 2019
- Coefficients apply to standardized independent variables.

### Corporate bond spread valuation model — key inputs
- Economic (Firm Value) Factors:
  - Expected GDP Growth Forecast (US and euro area)
  - NFIB Small Business Survey (US)
  - Mean Forecast EPS Growth Long Term (MSCI EMU) (euro area)
  - Industrial Production, Change Year on Year (US and euro area)
  - Unemployment Rate, Change over Six Months (US and euro area)
- Uncertainty factors:
  - Probability of Recession (US and euro area)
  - Standard Deviation of GDP Growth Forecast (US and euro area)
  - EPS Forecast Dispersion (12 months, 18 months, long term)
- Leverage:
  - Corporate Debt to GDP (US and euro area)
- Data sources: Bloomberg Finance L.P.; Consensus Economics; Haver Analytics; Thomson Reuters I/B/E/S; IMF staff calculations.

### Empirical results and diagnostics (selected preserved statistics)
- Sign and interpretation:
  - Economic factors: negative coefficients (better conditions → narrower spreads), except noted 6-month unemployment change nuance.
  - Uncertainty and leverage: positive coefficients (higher uncertainty/leverage → wider spreads).
- Model explanatory power:
  - The share of variation explained by the model is 60–70 percent.
- Selected reported averages (preserved formatting and values):
  - Expected GDP Growth Forecast: Avg. Beta -0.3757%; Avg. Rsq -0.8854% (US IG column formatting in source)
  - NFIB Small Business Survey: Avg. Beta -0.4768%; Avg. Rsq -1.2465% (US)
  - Industrial Production, Change Year on Year: Avg. Beta -0.4258%; Avg. Rsq -1.1858% (US)
  - Unemployment Rate, Change Over Six Months: Avg. Beta 0.4057%; Avg. Rsq 1.1959% (US)
  - Probability of Recession: Avg. Beta 0.3463%; Avg. Rsq 0.9961% (US)
  - Standard Deviation of GDP Growth Forecast: Avg. Beta 0.2460%; Avg. Rsq 0.8862% (US)
  - EPS Forecast Dispersion 12 Months: Avg. Beta 0.6480%; Avg. Rsq 2.3383% (Euro HY column)
  - Corporate Debt to GDP: Avg. Beta 0.1860%; Avg. Rsq 0.5959% (US)
- Misalignment findings:
  - Corporate bond spread misalignments particularly large in the United States, with some misalignment in the euro area.
  - Model spreads more sensitive to economic factors in the United States and to uncertainty factors in the euro area.
  - For US investment-grade corporate bonds in 2019, model-based spreads were wider than actual spreads, driven mainly by higher corporate debt and weaker fundamentals.

### EM hard-currency sovereign spread valuation model — framework and results
- Rationale and coverage:
  - External government debt outstanding in emerging markets rose to $1.3 trillion in 2018 from $0.5 trillion in 2008.
  - Model covers 71 emerging and frontier markets across five regions, quarterly data back almost 25 years to December 1996 (uneven spans).
  - EM hard-currency sovereign spreads based on JP Morgan bond indices; Bloomberg data.
- Estimation: OLS on an unbalanced panel:
  - Spread_it = c + Σ_k β_k * Fundamental_kit (k = 1..K = 7) + Σ_j α_j * GlobalRiskAppetite_t * Rating_j (j = 1..J = 8)
  - K = 7 fundamentals; J = 8 rating buckets (AAA, AA, A, BBB, BB, B, CCC, and below).
- Fundamental determinants included (preserved order):
  1. Domestic Real GDP growth – 1 year forward consensus forecasts
  2. Domestic CPI Inflation – 1 year forward consensus forecasts
  3. Current Account Balance (percent of GDP)
  4. External Debt (percent of GDP)
  5. Net Issuance of Foreign Currency Government Debt (percent of GDP)
  6. Foreign Currency Reserves (percent of GDP)
  7. External Real GDP growth – 1 year forward consensus forecasts
- Global risk appetite proxy:
  - US BBB corporate spread used as global risk appetite factor (alternatives like VIX produced broadly consistent results).
- Empirical findings:
  - Domestic fundamentals: higher real GDP growth and lower inflation reduce spreads; higher reserves and lower external debt compress spreads; coefficients statistically significant with ±2 standard errors shown in figures.
  - Sensitivity to global risk appetite and ratings:
    - Lower-rated issuers are more sensitive to global risk appetite.
    - A 100 basis point increase in the US BBB corporate bond spread could widen spreads of B-rated EM bonds by more than 200 basis points, compared to 50 basis points for A-rated EM issuers.
    - Rolling regressions (last 24 quarters) show sensitivity of EM sovereign spreads to external conditions rose significantly in recent years; impact from global risk appetite rose by more than 60 basis points over the last few years.
  - Misvaluation history and status as of September 2019:
    - EM hard-currency sovereign bonds were highly overvalued before major stress events (Asian crisis 1998; global financial crisis 2008).
    - As of September 2019, median spreads were broadly fair-valued, contrasting with early 2018 when EM foreign-currency bonds were, on average, overvalued.
    - Distributional assessment: almost 90 percent of EMs were overvalued before the global financial crisis, compared to about one-third as of Q3:2019.
  - Robustness: corroborated using alternative measures (residual difference, historical percentile, z-scores); trends consistent across thresholds.

*Source: onlineannex11 - 3. Drivers of Declining Equity Volatility (PDF).*

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### 1. Median Market versus the Model

### Implied spreads and distributional overview
- Analysis of residuals between market and model-implied spreads (basis points) and distributional depiction by overvaluation ranges: <–75, –75 to –25, –25 to +25, +25 to +75, >75 (charts and exact frequency bars provided in source).

### Sample and data sources for corporate credit quality analysis
- Firm-level databases used:
  - Bureau van Dijk Orbis; S&P Market Intelligence (CIQ); WIND (China only).
- Effective number of firms with data for 2016:
  - Orbis: about 1,351,667 firms
  - CIQ: 10,097 firms
  - WIND: 10,486 firms
- Firm size groups:
  - Large: assets > 500 million US dollars
  - Medium: assets between 50 million and 500 million
  - Small: assets < 50 million
- Sector classification:
  - Orbis uses NACE codes mapped to 6 major sectors; CIQ and WIND use GICS codes mapped to 10 major industries.

### Measures of corporate credit quality and calibration
- Principal metrics:
  - Debt-at-risk: debt owed by firms with interest coverage ratio (ICR) below 1.
  - Speculative-grade debt: debt owed by firms with implied speculative-grade ratings based on ICR and net debt-to-assets ratio.
- Definitions:
  - Net debt = gross debt minus cash.
  - ICR = EBIT-to-interest expense (EBIT used instead of EBITDA).
  - Thresholds for implied speculative-grade (BB/Ba or lower): ICR below 4.1 AND net debt-to-assets above 25 percent.
  - Maximum success rate in classification using these thresholds: 67.8 percent.
- Credit-rating benchmark statistics (bond samples):
  - Bond samples used for calibration:
    - About 6,600 investment grade bonds from Bloomberg Barclays Global Aggregate Industrial Index.
    - About 2,200 speculative grade bonds from Bloomberg Barclays US and Pan-European High Yield ex. Financials indices.
  - Summary medians and weighted averages (preserved):
    - Medians:
      - IG: EBIT/Interest = 6.8; Net Debt/Assets = 30
      - HY: EBIT/Interest = 2.0; Net Debt/Assets = 42
    - Weighted averages:
      - IG: EBIT/Interest = 7.8; Net Debt/Assets = 31
      - HY: EBIT/Interest = 1.7; Net Debt/Assets = 41
    - Rating-category medians:
      - BBB: EBIT/Interest = 4.8; Net Debt/Assets = 33
      - BB: EBIT/Interest = 2.6; Net Debt/Assets = 38
    - Threshold benchmarks:
      - Mid-point: EBIT/Interest = 3.7; Net Debt/Assets = 36
      - Optimization result: EBIT/Interest = 4.1; Net Debt/Assets = 25
    - Success Rate: 67.8%
    - Memo (Moody’s 2017): EBITA/Interest — Baa = 6.5; Ba = 3.9; mid-point ~ 5.2

### Aggregation to system (country) level — approach and uncertainty
- Sources of uncertainty:
  - Differences across databases, accounting conventions, and lack of full visibility on firm-size distribution in overall corporate sector.
- Aggregation procedure:
  - Aggregate by firm size for each country using individual firm debt as weights.
  - Combine sub-samples from three databases using total debt in databases as weights.
  - Mid-size and small firms combined into SME group; SMEs’ debt = sum; credit metric = average of components.
- Four estimates of the share of large firms in the overall corporate sector:
  - High estimate: based on sample’s distribution (skewed toward large firms) — more optimistic.
  - Low estimate: assumes sample fully captures large firms and remainder are SMEs — more pessimistic.
  - Central estimate: large firms’ debt = total corporate bonds + half of total loans.
  - Average estimate: average of low and high estimates.
- Example aggregate average from sample-level debt-at-risk (2016, across countries; share of debt at firms with EBIT-to-interest below 1) — preserved values:
  - Average (system): 25%
  - Average (sample): 19%
  - Average (Orbis): 34%
  - Average (CIQ): 22%
  - Average (WIND): 16%
  - Average (Large firms sub-sample): 34%
  - Average (SME sub-sample): 44%

### Scenario analysis: baseline updates, adverse scenario design, and projections
- Data vintages:
  - Orbis: coverage fairly good through 2016–17.
  - CIQ and WIND: nearly complete through 2018.
  - Estimates for 2017–19 use historical and baseline GDP growth and a constant interest rate on debt through 2019.
- Adverse scenario design:
  - Calibrated to emulate half the severity of the global financial crisis (GFC).
  - During the GFC, GDP growth in these major economies declined, on average, by about 3 standard deviations; adverse scenario assumes cumulative GDP growth decline of 1.4 standard deviations in 2020–21.
- Adverse scenario GDP growth outcomes (shock = 1.4 standard deviations; GDP growth in percent; cumulative decline from baseline in percentage points) — preserved table:
  - China: GDP Growth in 2020 = 4.6; in 2021 = 3.1; Cumulative Decline from Baseline = 4.1
  - France: 2020 = 0.2; 2021 = -0.8; Cumulative Decline = 3.2
  - Germany: 2020 = -0.9; 2021 = -2.4; Cumulative Decline = 6.5
  - Italy: 2020 = -1.5; 2021 = -2.9; Cumulative Decline = 5.8
  - Japan: 2020 = -0.5; 2021 = -1.9; Cumulative Decline = 3.4
  - Spain: 2020 = 0.4; 2021 = -1.4; Cumulative Decline = 4.6
  - United Kingdom: 2020 = 0.1; 2021 = -1.1; Cumulative Decline = 4.0
  - United States: 2020 = 1.3; 2021 = 0.2; Cumulative Decline = 2.4
- Projecting firm outcomes:
  - EBIT and interest projected through 2021 at firm level; assets, cash, debt assumed constant.
  - Declines in EBIT modeled via regressions of EBIT-to-assets on GDP growth by country, sector, and firm size for each database.
  - Modeled declines in EBIT are similar to but somewhat less severe than half actual GFC declines (quartile comparisons in source).
- Interest-rate shock calibration:
  - Interest rate on debt for each firm assumed to rise to half the level observed during the GFC.
  - Modeled interest-rate increases compared to historical GFC increases and to corporate bond spread model for the United States.
- Adverse scenario for interest (US firms; increase in the interest rate by 2021 in basis points) — Model versus Historical, by data source (preserved values):
  - Orbis:
    - Large: Model = 63; History = 65
    - Medium: Model = 77; History = 75
    - Small: Model = 101; History = 54
    - All: Model = 65; History = 63
  - CIQ:
    - Large: Model = 68; History = 60
    - Medium: Model = 77; History = 99
    - Small: Model = 67; History = 136
    - All: Model = 68; History = 60
  - Interpretation: modeled increases for large and medium firms similar on average to corporate-spread-model findings; increase for small firms greater in the model than model-implied results for aggregate bond indices.

### Methodological notes and assumptions
- Use net debt rather than gross debt due to increased cash holdings post-GFC.
- ICR-based implied rating thresholds established empirically via optimization; chosen thresholds (ICR < 4.1 and net debt/assets > 25 percent) have maximum success rate 67.8 percent.
- Central estimate for large firms’ share: large firms’ debt = total corporate bonds + half of total loans (half of loans chosen in absence of loan-level data by firm size).
- Scenario interest-rate adjustments assume gradual translation of bond-yield changes into interest expense (annual changes in corporate bond yields take from 5 to 14 years to be fully reflected in interest expense based on average maturities of major bond indices).

*Source: onlineannex11 - 1. Median Market versus the Model (PDF chapter).*

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### 3. Technical Note on Investment Fund Stress Testing

### Objectives and approach
- Objective: assess whether fixed-income funds could meet severe but plausible redemption increases by disposing exclusively of liquid assets.
- Steps:
  - Quantify volumes of liquid assets of individual funds using alternative liquidity concepts.
  - Calibrate sizes of funds’ redemption shocks per specified procedure.
  - Compute liquidity shortfalls = max(0, redemption shock − liquidity buffers) for each fund and liquidity concept.
  - Aggregate shortfalls:
    - Across all funds (asset-weighted).
    - Across funds with positive shortfalls.
- Interpretation:
  - Average shortfall across all funds = ex-ante liquidity risk investors accept when purchasing fund shares.
  - Average shortfall across funds with positive shortfalls = ex-post risk for investors locked in shares of funds suffering shortfalls.

### Data, sample, and adjustments
- Sample: 1,760 funds from 34 jurisdictions.
- Selection criteria:
  - Data availability.
  - Minimum size of $1 billion from Morningstar Direct database.
- Time period: January 2000 to June 2019.
- Monthly series used:
  - Fund sizes in home currency and US dollars.
  - Net redemptions (historical fund-level).
  - Fractions invested in debt by credit rating (reported and Morningstar-calculated).
  - Asset allocations and fixed-income portfolio breakdowns (cash, sovereign, corporate, municipal, securitized, derivatives).
  - Positions in preferred stock and agency mortgage-backed securities treated per adjustments.
- Data adjustments:
  - Preferred stock considered equity; corporate debt positions adjusted accordingly.
  - Agency mortgage-backed securities removed from securitized assets and treated separately.
  - Merge rating-quality data by using Morningstar-calculated data for periods after December 2016 when available, fund-reported otherwise.

### Liquidity shocks, aggregation, and metrics
- Redemption shocks:
  - Defined as the worst percentile of each fund’s individual monthly net outflows over 2000–2019.
  - Redemptions exceeding in absolute value 50 percent of the previous month’s NAV are dropped as outliers.
- Aggregation: individual fund shortfalls aggregated asset-weighted; final metrics converted to quarterly frequency.
- Three liquidity metrics used:
  - High-Quality Liquid Assets (HQLA).
  - Alternative High-Quality Liquid Assets (AQLA).
  - Narrow liquidity (cash position).

### HQLA computation (Basel III haircuts preserved)
- Haircuts by asset class and rating grade (columns preserved):
  - Sovereign Debt: AAA 0; AA 0; A 15; BBB 50; BB 100; B 100; Below B 100; Unrated 100
  - Corporate Debt: AAA 15; AA 15; A 50; BBB 50; BB 100; B 100; Below B 100; Unrated 100
  - Equity: 50
  - Residential Mortgage: 25, 25, 100
  - Cash: 0
  - Municipal Debt: AAA 50; AA 50; A 50; BBB 50; BB 100; B 100; Below B 100; Unrated 100
- Haircuts deducted from portfolio components and aggregated to HQLA.

### AQLA and narrow liquidity
- AQLA rationale: broader concept recognizing additional liquid assets via netting of short-funded positions and allowing certain short positions to be maintained during stress.
- AQLA adjustments:
  - Balance short positions against other portfolio components; exclude short positions in liquid assets used to finance long positions.
  - Curtail individual long positions in liquid assets exceeding total portfolio value.
  - Maintain short positions during redemption stress (analogous to credit lines).
  - Implementation order: adjustments begin with most liquid components, then less liquid.
- Formal adjusted portfolio component computation preserved:
  - x̂_i = {
    x_i + min(−x_i, ∑ x_nn≠i) − ∑ max(x̂_j − x_j,0)_{j=1}^{i−1}  if x_i < 0
    x_i  if  0 ≤ x_i ≤ 1
    x_i + min(0, ∑ x_nn≠i) − ∑ min(x̂_j − x_j,0)_{j=1}^{i−1}  if x_i > 1
    }
  - x̂_i = adjusted portfolio component (fraction of portfolio); x_i = unadjusted component; indices n and i denote portfolio components and liquidity rank.
- Narrow liquidity: cash buffer cleaned using same methodology to generate cash liquidity buffer.
- Section prepared by Frank Hespeler.

*This section was prepared by Frank Hespeler.*

### 1. Technical Note on Asset Valuation Models

### 1. Technical Note on Asset Valuation Models

### Overview
- Purpose of models:
  - Provide a direct measure of asset price misalignment based on economic and corporate fundamentals, excluding—to the extent possible—market price–based measures.
  - Be tractable and applicable to many international markets.
- Models developed for the October 2019 GFSR:
  - Several major advanced and emerging equity markets.
  - US option-implied equity volatility index (VIX).
  - US and euro-area corporate bond spreads.
  - Emerging market foreign-currency denominated sovereign bond spreads.
- Prepared by: Sergei Antoshin, Andrea Deghi, Rohit Goel, Thomas Piontek, and Akihiko Yokoyama.
- Modeling approach notes:
  - Staff tested models for robustness and selected best-performing variables, but the approaches are subject to limitations and uncertainty arising from factor selection and alternative specifications.
  - Country-specific equity models use extreme bound analysis to evaluate sensitivity to alternative variable selections; final model-implied valuation corresponds to a weighted average of fitted estimates, weights equal to respective regression R^2.

### Global Equity Markets — Dividend Discount Model (DDM) framework
- Theoretical formulation:
  - Standard DDM: Pt = Dt+1 / (kt − E{gt})  (equation (2))
    - Dt+1 is the dividend at time t+1.
    - kt is the cost of capital.
    - E{gt} is the dividend’s anticipated steady-state growth rate.
  - Cost of capital decomposition: kt = Yt + θt  (equation (3))
    - Yt is the long-term interest rate.
    - θt is the equity risk premium.
  - Long-term interest decomposition: Yt = E{rt^sh} + ρt  (equation (5))
    - E{rt^sh} is the expected path of the short-term rate.
    - ρt is the term premium.
  - Assuming E{rt^sh} ~ E{gt} yields Pt = Dt+1 / (ρt + θt)  (equation (6))
    - Price is a function of expected dividends, plus equity and term premia.
- Empirical estimation specification:
  - Pt = β0 + β1 Et + β2 θt + β3 It + εt  (equation (7))
    - Et = expected future earnings (proxy for Dt+1 and E{gt}).
    - It = either Yt (long-term interest rate) or ρt (term premium).
    - εt is the misalignment (positive = overvaluation, negative = undervaluation).
- Empirical proxies used:
  - Expected earnings Et: weighted average (across analysts) forecasts of earnings over the next 12 and 18 months from IBES.
  - Equity risk premium θt proxy: standard deviation (across analysts) of earnings forecasts over the next 12 months and 18 months from IBES (following Durham (2013)).
  - Interest rate Yt: yield on general government bonds with different maturities.
  - Term premium ρt proxies: 4- and 5-factor model term premiums (Adrian, Crump and Moench (2013)) or term spreads (long-term yields minus 3-month yield).
- Variable selection rule:
  - Choose Yt versus ρt based on sign and stability of coefficients and goodness of fit (R^2). Term spreads outperformed interest rates for the United States and the euro area; ACM term premiums perform similarly to term spreads in those cases.
- Robustness and diagnostics:
  - Stationarity and cointegration tests (Durbin Watson, Dicky and Fuller, Johansen) and other robustness tests were performed.

### Equity model estimation results (sample and fit)
- Markets estimated (monthly data): China, Brazil, euro area, Germany, India, Japan, United Kingdom, United States. These account for over 70 percent of global equity market capitalization.
- Overall performance:
  - Average R^2 across countries: 80 percent.
- Online Annex Table 1.2 — key statistics (As of September 2019):
  - United States
    - Sample Start: Jan 31, 1990
    - Sample End: Sep 30, 2019
    - Monthly Observations: 357
    - Minimum R^2: 92%
    - Maximum R^2: 93%
    - Average R^2: 93%
    - Standard Error: 1.0
    - Misalignment, Last Month (%): 15.1
    - Historical Volatility: 4.2
    - Misalignment, Last Month Divided by Historical Volatility: 3.6
    - Misalignment, Last Quarter Divided by Historical Volatility: 2.6
  - Euro Area
    - Sample Start: Nov 30, 1999
    - Sample End: Sep 30, 2019
    - Monthly Observations: 239
    - Minimum R^2: 51%
    - Maximum R^2: 54%
    - Average R^2: 53%
    - Standard Error: -0.2
    - Misalignment, Last Month (%): -2.5
    - Historical Volatility: 5.6
    - Misalignment, Last Month Divided by Historical Volatility: -0.4
    - Misalignment, Last Quarter Divided by Historical Volatility: -0.5
  - Germany
    - Sample Start: Aug 31, 1990
    - Sample End: Sep 30, 2019
    - Monthly Observations: 350
    - Minimum R^2: 88%
    - Maximum R^2: 89%
    - Average R^2: 89%
    - Standard Error: 0.1
    - Misalignment, Last Month (%): 1.6
    - Historical Volatility: 5.9
    - Misalignment, Last Month Divided by Historical Volatility: 0.3
    - Misalignment, Last Quarter Divided by Historical Volatility: 0.3
  - Japan
    - Sample Start: Jan 31, 1990
    - Sample End: Sep 30, 2019
    - Monthly Observations: 357
    - Minimum R^2: 42%
    - Maximum R^2: 48%
    - Average R^2: 45%
    - Standard Error: 1.1
    - Misalignment, Last Month (%): 22.7
    - Historical Volatility: 6.2
    - Misalignment, Last Month Divided by Historical Volatility: 3.7
    - Misalignment, Last Quarter Divided by Historical Volatility: -0.1
  - United Kingdom
    - Sample Start: Jan 30, 1990
    - Sample End: Sep 30, 2019
    - Monthly Observations: 357
    - Minimum R^2: 73%
    - Maximum R^2: 79%
    - Average R^2: 75%
    - Standard Error: 0.0
    - Misalignment, Last Month (%): 0.2
    - Historical Volatility: 4.4
    - Misalignment, Last Month Divided by Historical Volatility: 0.0
    - Misalignment, Last Quarter Divided by Historical Volatility: 2.9
  - China
    - Sample Start: Nov 30, 1995
    - Sample End: Sep 30, 2019
    - Monthly Observations: 287
    - Minimum R^2: 80%
    - Maximum R^2: 82%
    - Average R^2: 81%
    - Standard Error: 0.1
    - Misalignment, Last Month (%): 3.1
    - Historical Volatility: 10.4
    - Misalignment, Last Month Divided by Historical Volatility: 0.3
    - Misalignment, Last Quarter Divided by Historical Volatility: 0.1
  - Brazil
    - Sample Start: Nov 30, 1999
    - Sample End: Sep 30, 2019
    - Monthly Observations: 239
    - Minimum R^2: 91%
    - Maximum R^2: 93%
    - Average R^2: 92%
    - Standard Error: 0.0
    - Misalignment, Last Month (%): -0.1
    - Historical Volatility: 7.0
    - Misalignment, Last Month Divided by Historical Volatility: 0.0
    - Misalignment, Last Quarter Divided by Historical Volatility: -0.2
  - India
    - Sample Start: Apr 30, 1996
    - Sample End: Sep 30, 2019
    - Monthly Observations: 282
    - Minimum R^2: 96%
    - Maximum R^2: 96%
    - Average R^2: 96%
    - Standard Error: 0.2
    - Misalignment, Last Month (%): 3.6
    - Historical Volatility: 7.8
    - Misalignment, Last Month Divided by Historical Volatility: 0.5
    - Misalignment, Last Quarter Divided by Historical Volatility: 0.6
- Additional outputs:
  - Historical misalignments by country are shown in Figure 1.1, with generally narrow confidence intervals closely aligned with fitted values.

### US Option-Implied Equity Market Volatility (VIX) fair value model
- Context and motivation:
  - Despite heightened policy uncertainty and rising global geopolitical risks, option-implied equity market volatility in the US has been relatively muted, with occasional short-lived spikes.
  - The VIX fair value model aims to identify economic and financial drivers affecting market expectations of future US equity volatility.
- Framework and data:
  - Focus: US equity market (US accounts for over one-third of global equity market and heavily dominates implied volatility trading).
  - Estimation: Ordinary least-squares regression run over 16 years of quarterly data with VIX as the dependent variable.
  - All data series transformed to z-scores.
  - Eleven independent variables grouped into four categories (Online Annex Table 1.3):
    - Macroeconomic fundamentals:
      - Interquartile Range of One-Year Ahead US GDP Forecasts.
      - Interquartile Range of One-Year Ahead US CPI Forecasts.
      - U.S. Unemployment Rate Change (Year-over-Year).
      - Rationale: Dispersion of forecasts proxies macroeconomic uncertainty; changes in unemployment proxy economic conditions.
    - Funding and liquidity conditions:
      - TED Spread (difference between 3-month US Treasury bill yield and 3-month US dollar LIBOR).
      - Interquartile Range of One-Year Ahead US 3-Month T-Bill Forecasts.
      - Federal Reserve Net Purchases of US Treasuries.
      - Rolling 12-Month Standard Deviation of Citi Global Economic Surprise Index.
      - Rationale: Funding stress and monetary accommodation affect volatility.
    - Corporate performance:
      - Net Income to Assets for S&P 500 firms.
      - Payouts to Net Income for S&P 500 firms.
      - Rationale: Corporate fundamentals and payouts can smooth valuations and compress volatility.
    - External factors:
      - US Trade Policy Uncertainty Index (Baker, Bloom, Davis).
      - Sentix Euro Area Economic Sentiment Index.
      - Rationale: Geopolitical tensions and foreign economic uncertainty can raise volatility.
- Results and interpretation:
  - Model fit:
    - The model provides a good fit for historical VIX values (Figure 1.2, panel 1).
  - Drivers:
    - Lower uncertainty about macroeconomic outcomes and stronger corporate performance have been important drivers of lower implied equity volatility (Figure 1.2, panel 2).
    - Net shareholder payouts and corporate performance contributed to steady investor earnings expectations and compressed volatility.
  - 2019 assessment:
    - External factors such as trade tensions and uncertainty about the global economic outlook suggest implied volatility should be higher than the average levels for 2019 (Figure 1.2, panel 3).
    - Part of the divergence between actual VIX and model-fitted VIX may reflect investor belief that central banks will lean against sharp tightening in financial conditions, implicitly providing insurance against significant declines in stock prices.
  - Historical notes:
    - The VIX index was also compressed relative to the model-fitted VIX in 2017; prior discussion in the October 2017 GFSR provides details on the model calibration for that period.

*Italic: IMF staff calculations; sources cited in text (Bloomberg Finance L.P.; Thomson Reuters I/B/E/S; Federal Reserve; Haver Analytics; Philadelphia Federal Reserve Survey of Professional Forecasters; S&P Market Intelligence).*

### 3. Drivers of Declining Equity Volatility

### 3. Drivers of Declining Equity Volatility

### Overview and model approach
- The analysis links corporate bond spread behavior to three groups of explanatory variables: economic (firm value) factors, uncertainty measures, and leverage metrics, following a structural-option-pricing intuition (Black and Scholes (1973); Merton (1974)).
- Corporate bond spreads are measured as the difference between the yield on the Bloomberg-Barclays corporate bond index and the duration-matched Treasury yield.
- The primary estimation approach for corporate spreads uses monthly linear regressions of the form:
  - Corporate Bond Spread_t = α0 + β1 Economic Factor_t + β2 Uncertainty Factor_t + β3 Leverage Factor_t + ε_t
- Factor selection employed extreme bound analysis to choose robust variables from a wide range of macro and financial candidates.
- Model-implied spread is the weighted average fitted value across model specifications, with weights equal to the R^2 from each regression.
- The model variables are tested for unit roots and Johansen cointegration; sample periods:
  - United States: January 1995 to July 2019
  - Euro area: January 2004 to July 2019
- Note: coefficients reported apply to standardized independent variables.

### Corporate bond spread valuation model (US and euro area): key model inputs
- Economic (Firm Value) Factors:
  - Expected GDP Growth Forecast (US and euro area)
  - NFIB Small Business Survey (US)
  - Mean Forecast EPS Growth Long Term (MSCI EMU) (euro area)
  - Industrial Production, Change Year on Year (US and euro area)
  - Unemployment Rate, Change over Six Months (US and euro area)
- Uncertainty:
  - Probability of Recession (US and euro area)
  - Standard Deviation of GDP Growth Forecast (US and euro area)
  - EPS Forecast Dispersion 12 Months, 18 Months, and Long Term (various)
- Leverage:
  - Corporate Debt to GDP (US and euro area)
- Data sources: Bloomberg Finance L.P.; Consensus Economics; Haver Analytics; Thomson Reuters I/B/E/S; IMF staff calculations.

### Corporate model empirical results and diagnostics
- Sign and interpretation of coefficients:
  - Economic factors: coefficients are negative (better economic conditions → narrower spreads) with an exception for the 6-month change in unemployment rate discussed in notes.
  - Uncertainty and leverage factors: coefficients are positive (higher uncertainty or leverage → wider spreads).
- Model explanatory power:
  - The share of variation explained by the model is 60–70 percent.
- Summary statistics (selected reported averages):
  - Expected GDP Growth Forecast: Avg. Beta -0.3757%; Avg. Rsq -0.8854% (US IG column formatting in source)
  - NFIB Small Business Survey: Avg. Beta -0.4768%; Avg. Rsq -1.2465% (US)
  - Industrial Production, Change Year on Year: Avg. Beta -0.4258%; Avg. Rsq -1.1858% (US)
  - Unemployment Rate, Change Over Six Months: Avg. Beta 0.4057%; Avg. Rsq 1.1959% (US)
  - Probability of Recession: Avg. Beta 0.3463%; Avg. Rsq 0.9961% (US)
  - Standard Deviation of GDP Growth Forecast: Avg. Beta 0.2460%; Avg. Rsq 0.8862% (US)
  - EPS Forecast Dispersion 12 Months: Avg. Beta 0.6480%; Avg. Rsq 2.3383% (Euro HY column)
  - Corporate Debt to GDP: Avg. Beta 0.1860%; Avg. Rsq 0.5959% (US)
- Misalignment findings:
  - Corporate bond spread misalignments are particularly large in the United States, with some misalignment in the euro area.
  - Model spreads are more sensitive to economic factors in the United States and to uncertainty factors in the euro area.
  - For US investment-grade corporate bonds in 2019, model-based spreads were wider than actual spreads, driven mainly by higher levels of corporate debt and weaker economic fundamentals.

### EM hard-currency sovereign spread valuation model: framework and data
- Rationale:
  - Foreign-currency bond markets are an important external funding source for emerging market borrowers; mis-pricing can pose risks to investors and issuers.
  - External government debt outstanding in emerging markets increased to $1.3 trillion in 2018 from $0.5 trillion in 2008.
- Coverage and data:
  - Model covers 71 emerging and frontier markets across five major regions, with quarterly data spanning back almost 25 years to December 1996 (time span is uneven across countries due to staggered EMBIG index entries).
  - EM hard-currency sovereign spreads are based on JP Morgan bond indices; data sourced from Bloomberg.
- Estimation approach:
  - Given data limitations, panel estimation is used: an OLS model on an unbalanced panel.
  - Model form:
    - Spread_it = c + Σ_k β_k * Fundamental_kit (k = 1..K = 7) + Σ_j α_j * GlobalRiskAppetite_t * Rating_j (j = 1..J = 8)
  - K = 7 fundamental factors; J = 8 rating buckets (AAA, AA, A, BBB, BB, B, CCC, and below).
- Fundamental determinants included:
  1. Domestic Real GDP growth – 1 year forward consensus forecasts
  2. Domestic CPI Inflation – 1 year forward consensus forecasts
  3. Current Account Balance (percent of GDP)
  4. External Debt (percent of GDP)
  5. Net Issuance of Foreign Currency Government Debt (percent of GDP)
  6. Foreign Currency Reserves (percent of GDP)
  7. External Real GDP growth – 1 year forward consensus forecasts
- Global risk appetite proxy:
  - The US BBB corporate spread is used as the global risk appetite factor (alternative measures such as the VIX Index produced broadly consistent results).

### EM model empirical results and diagnostics
- Domestic fundamentals:
  - Higher real GDP growth and lower inflation reduce sovereign spreads.
  - Higher reserves and lower external debt compress spreads.
  - Coefficients plotted with ±2 standard errors and are all statistically significant in the reported figures.
- Sensitivity to global risk appetite and ratings:
  - Lower-rated issuers are more sensitive to global risk appetite.
  - A 100 basis point increase in the US BBB corporate bond spread could widen spreads of B-rated EM bonds by more than 200 basis points, compared to 50 basis points for A-rated EM issuers.
  - Rolling regressions (last 24 quarters) show the sensitivity of EM sovereign spreads to external conditions has risen significantly in recent years.
  - The impact from global risk appetite rose by more than 60 basis points over the last few years (illustrated by differences between colored lines in source figure).
- Misvaluation history and status as of September 2019:
  - EM hard-currency sovereign bonds were highly overvalued (spreads too tight) before major stress events such as the Asian crisis (1998) and the global financial crisis (2008).
  - Overvaluation can persist but corrections can be swift, causing abrupt tightening of funding conditions.
  - As of September 2019, median spreads were broadly fair-valued, contrasting with early 2018 when EM foreign-currency bonds were, on average, overvalued.
  - Distributional assessment: almost 90 percent of EMs were overvalued before the global financial crisis, compared to about one-third as of Q3:2019.
- Robustness:
  - Results are corroborated using alternative measures of overvaluation: residual difference between market and model-implied spreads, historical percentile, and z-scores; trends remain consistent with other thresholds.

*Source: onlineannex11 - 3. Drivers of Declining Equity Volatility (PDF).*

### 1. Median Market versus the Model

### 1. Median Market versus the Model

### Implied spreads and distributional overview
- The document contains an analysis of the residual between market and model-implied spreads (basis points), and a distributional depiction of countries by the extent of overvaluation (percent), classifying observations by ranges: <–75, –75 to –25, –25 to +25, +25 to +75, >75 (undervalued → fair valued → overvalued). (Charts and exact frequency bars are provided in the source.)

### Sample and data sources for corporate credit quality analysis
- Three firm-level databases are used: Bureau van Dijk Orbis; S&P Market Intelligence (CIQ); WIND (for Chinese firms only).
- Effective number of firms with data for 2016:
  - Orbis: about 1,351,667 firms
  - CIQ: 10,097 firms
  - WIND: 10,486 firms
- Firms are grouped by asset size:
  - Large: assets exceeding 500 million US dollars
  - Medium: assets between 50 million and 500 million
  - Small: assets below 50 million
- Sector classification:
  - Orbis uses NACE codes mapped to 6 major sectors
  - CIQ and WIND use GICS codes mapped to 10 major industries

### Measures of corporate credit quality
- Two principal metrics:
  - Debt-at-risk: debt owed by firms with interest coverage ratio (ICR) below 1.
  - Speculative-grade debt: debt owed by firms with implied speculative-grade ratings based on ICR and net debt-to-assets ratio.
- Definitions and calculations:
  - Net debt = gross debt minus cash.
  - ICR = EBIT-to-interest expense (EBIT used instead of EBITDA).
  - Thresholds for implied speculative-grade (BB/Ba or lower) established empirically: ICR below 4.1 AND net debt-to-assets above 25 percent.
  - The maximum success rate in classification using these thresholds is 67.8 percent.

### Credit-rating benchmark statistics (based on bond samples)
- Samples used to calibrate thresholds:
  - About 6,600 investment grade bonds from the Bloomberg Barclays Global Aggregate Industrial Index.
  - About 2,200 speculative grade bonds from Bloomberg Barclays US and Pan-European High Yield ex. Financials indices.
  - Bond-level data: credit ratings, EBIT, interest expense, debt, cash from Bloomberg.
- Summary statistics (medians and weighted averages):
  - Medians:
    - IG: EBIT/Interest = 6.8; Net Debt/Assets = 30
    - HY: EBIT/Interest = 2.0; Net Debt/Assets = 42
  - Weighted averages:
    - IG: EBIT/Interest = 7.8; Net Debt/Assets = 31
    - HY: EBIT/Interest = 1.7; Net Debt/Assets = 41
  - Rating-category medians:
    - BBB: EBIT/Interest = 4.8; Net Debt/Assets = 33
    - BB: EBIT/Interest = 2.6; Net Debt/Assets = 38
  - Threshold benchmarks:
    - Mid-point: EBIT/Interest = 3.7; Net Debt/Assets = 36
    - Optimization result: EBIT/Interest = 4.1; Net Debt/Assets = 25
  - Success Rate: 67.8%
  - Memo (Moody’s 2017): EBITA/Interest — Baa = 6.5; Ba = 3.9; mid-point ~ 5.2

### Extrapolation to system (country) level — approach and uncertainty
- Sources of uncertainty:
  - Differences in results across the three databases (coverage, accounting conventions).
  - Lack of visibility on the “true” distribution of firms by size in the overall corporate sector.
- Aggregation procedure:
  - Results aggregated by firm size for each country using individual firm debt as weights.
  - Overall sample results for each country and firm size obtained by aggregating sub-samples from the three databases using total debt in the databases as weights.
  - Mid-size and small firms combined into one SME group; SMEs’ debt is the sum and credit metric is the average of components for mid-size and small firms.
- Four estimates of the share of large firms in the overall corporate sector:
  - High estimate: based on sample’s distribution (skewed toward large firms) — more optimistic credit-quality picture.
  - Low estimate: assumes sample fully captures large firms and the remainder of the sector consists of SMEs — more pessimistic.
  - Central estimate: large firms’ debt = total corporate bonds + half of total loans.
  - Average estimate: average of low and high estimates.
- Example aggregate average from sample-level debt-at-risk (2016, across countries; share of debt at firms with EBIT-to-interest below 1):
  - Average (system): 25%
  - Average (sample): 19%
  - Average (Orbis): 34%
  - Average (CIQ): 22%
  - Average (WIND): 16%
  - Average (Large firms sub-sample): 34%
  - Average (SME sub-sample): 44%
  - (Full table with country-level breakdowns by source and firm size is in the source.)

### Scenario analysis: baseline updates, adverse scenario design, and projections
- Data vintage coverage:
  - Orbis: coverage fairly good through 2016–17.
  - CIQ and WIND: nearly complete samples through 2018.
  - Estimates for 2017–19 use historical and baseline GDP growth and a constant interest rate on debt through 2019.
- Adverse scenario design:
  - Calibrated to emulate half the severity of the global financial crisis (GFC).
  - During the GFC, GDP growth in these major economies declined, on average, by about 3 standard deviations; adverse scenario assumes a cumulative GDP growth decline of 1.4 standard deviations in 2020–21.
- Adverse scenario GDP growth outcomes (shock = 1.4 standard deviations; GDP growth in percent; cumulative decline from baseline in percentage points):
  - China: GDP Growth in 2020 = 4.6; in 2021 = 3.1; Cumulative Decline from Baseline = 4.1
  - France: 2020 = 0.2; 2021 = -0.8; Cumulative Decline = 3.2
  - Germany: 2020 = -0.9; 2021 = -2.4; Cumulative Decline = 6.5
  - Italy: 2020 = -1.5; 2021 = -2.9; Cumulative Decline = 5.8
  - Japan: 2020 = -0.5; 2021 = -1.9; Cumulative Decline = 3.4
  - Spain: 2020 = 0.4; 2021 = -1.4; Cumulative Decline = 4.6
  - United Kingdom: 2020 = 0.1; 2021 = -1.1; Cumulative Decline = 4.0
  - United States: 2020 = 1.3; 2021 = 0.2; Cumulative Decline = 2.4
- Projecting firm outcomes under the adverse scenario:
  - EBIT and interest are projected through 2021 at the firm level.
  - Balance-sheet items (assets, cash, debt) are assumed constant.
  - Declines in EBIT are modeled via regressions of EBIT-to-assets on GDP growth by country, sector, and firm size for each database.
  - Modeled declines in EBIT are, on aggregate, similar to but somewhat less severe than half the actual declines in EBIT during the GFC (quartile comparisons are provided in the source).
- Interest-rate shock calibration:
  - The interest rate on debt for each firm is assumed to rise to half the level observed during the GFC.
  - Modeled interest-rate increases are compared to historical increases observed during the GFC and to the corporate bond spread model for the United States.
- Adverse scenario for interest (US firms; increase in the interest rate by 2021 in basis points) — Model versus Historical, by data source:
  - Orbis:
    - Large: Model = 63; History = 65
    - Medium: Model = 77; History = 75
    - Small: Model = 101; History = 54
    - All: Model = 65; History = 63
  - CIQ:
    - Large: Model = 68; History = 60
    - Medium: Model = 77; History = 99
    - Small: Model = 67; History = 136
    - All: Model = 68; History = 60
  - Interpretation: modeled increases for large and medium firms are similar, on average, to the corporate-spread-model findings; the increase for small firms is greater in the model than the model-implied results for aggregate bond indices.

### Key methodological notes and assumptions
- Use of net debt rather than gross debt is motivated by increased cash holdings in the nonfinancial sector after the global financial crisis.
- The ICR-based implied rating thresholds were established empirically via an optimization maximizing correct classification against bond-level ratings; the chosen thresholds (ICR < 4.1 and net debt/assets > 25 percent) have a maximum success rate of 67.8 percent.
- Central estimate for large firms’ share assumes large firms’ debt = total corporate bonds + half of total loans; half of loans chosen in the absence of loan-level data by firm size.
- Scenario interest-rate adjustments assume gradual translation of bond-yield changes into interest expense (noting that annual changes in corporate bond yields take from 5 to 14 years to be fully reflected in interest expense based on average maturities of major bond indices).

*Source: onlineannex11 - 1. Median Market versus the Model (PDF chapter).*

### 3. Technical Note on Investment Fund Stress

### 3. Technical Note on Investment Fund Stress Testing

### Objectives
- Assess whether fixed-income funds could meet severe but plausible increases in redemption requests by disposing exclusively of liquid assets.
- Steps performed:
  - Quantified volumes of liquid assets of individual funds using alternative liquidity concepts.
  - Calibrated sizes of the funds’ redemption shocks following the specified procedure.
  - For each fund and each liquidity concept, computed liquidity shortfalls as the maximum of zero and the difference between the redemption shock and the liquidity buffers.
  - Computed two aggregate liquidity shortfall measures:
    - Aggregating shortfalls across all funds (asset-weighted).
    - Aggregating shortfalls across funds that had positive shortfalls.
- Interpretation:
  - Average shortfall across all funds quantifies ex-ante liquidity risk investors accept when purchasing shares of fixed-income funds.
  - Average shortfall across funds with positive shortfalls captures ex-post risk of investors locked in shares of funds suffering shortfalls under liquidity stress.

### Data and sample
- Sample: 1,760 funds from 34 jurisdictions.
- Selection criteria:
  - Data availability.
  - Minimum size of $1 billion from the Morningstar Direct database.
- Time period: January 2000 to June 2019.
- Monthly data series used:
  - Fund sizes in home currency and in US dollars.
  - Net redemptions (historical fund-level data).
  - Fractions of funds’ portfolios invested in debt by credit rating (AAA - unrated) in two versions: (i) reported by funds and (ii) calculated by Morningstar on the basis of individual securities’ ratings.
  - Funds’ asset allocations including positions in cash, bonds, equity and other assets.
  - Funds’ fixed income portfolios differentiated by position types, e.g., cash and cash equivalents, sovereign debt, corporate debt, municipal debt, securitized assets and derivatives.
  - Funds’ positions in preferred stock, a senior form for equity, and agency mortgage-backed securities.
- Data adjustments:
  - Corporate debt positions are adjusted for preferred stock positions, which are considered equity.
  - Agency mortgage-backed securities are removed from securitized assets and are used as separate portfolio components.
  - The two types of rating quality data are merged into a single metric by using Morningstar-calculated data for all periods after December 2016 when available, and fund-reported data otherwise.

### Liquidity shortfalls: shocks and aggregation
- Redemption shocks:
  - Defined as the worst percentile of each fund’s individual monthly net outflows observed over the period 2000 to 2019.
  - Redemptions exceeding in absolute value 50 percent of the previous month’s net asset value of the respective fund are dropped as statistical outliers.
- Aggregation:
  - Individual fund liquidity shortfalls are aggregated across funds on an asset-weighted basis.
  - Final metrics are converted to quarterly frequency due to data availability constraints.

### Liquidity metrics and computation
- Three alternative liquidity metrics used to compute liquidity shortfalls:
  - High-Quality Liquid Assets (HQLA).
  - Alternative High-Quality Liquid Assets (AQLA).
  - Narrow liquidity (cash position of a fund).
- High-Quality Liquid Assets (HQLA):
  - Computation follows Basel III principles for the Liquidity Coverage Ratio.
  - Haircuts model the fraction of assets that cannot be sold at short notice; haircuts depend on asset class and credit quality.
  - Haircuts (Online Annex Table 3.1: Basle III Liquidity Coverage Ratio Haircuts)
    - Rating Grade columns: AAA, AA, A, BBB, BB, B, Below B, Unrated
    - Sovereign Debt: 0, 0, 15, 50, 100, 100, 100, 100
    - Corporate Debt: 15, 15, 50, 50, 100, 100, 100, 100
    - Equity: 50
    - Residential Mortgage: 25, 25, 100
    - Cash: 0
    - Municipal Debt: 50, 50, 50, 50, 100, 100, 100, 100
  - Corresponding haircuts are deducted from respective portfolio components, then aggregated into the HQLA metric.
- Alternative High-Quality Liquid Assets (AQLA):
  - Rationale: funds may have more liquid assets to meet redemptions than HQLA indicates (e.g., funded by short positions that are netted out in HQLA).
  - AQLA corrects by balancing such positions against other (non-liquid) portfolio components.
  - Excludes short positions in liquid assets that are used to finance long positions in other assets.
  - Curtails individual long positions in liquid assets exceeding the value of the entire portfolio.
  - Allows maintaining short positions during redemption stress (analogous to credit lines), providing additional action space for liquidity management.
  - AQLA is a wider liquidity concept than HQLA.
  - Implementation order: adjustments applied starting with short or excess long positions in the most liquid part of the portfolio and then through less liquid parts in order.
  - Formal adjusted portfolio component computation (as presented):
    - x̂_i = {
      x_i + min(−x_i, ∑ x_nn≠i) − ∑ max(x̂_j − x_j,0)_{j=1}^{i−1}  if x_i < 0
      x_i  if  0 ≤ x_i ≤ 1
      x_i + min(0, ∑ x_nn≠i) − ∑ min(x̂_j − x_j,0)_{j=1}^{i−1}  if x_i > 1
      }
    - where x̂_i denotes the adjusted portfolio component (as a fraction of the entire portfolio), x_i is the unadjusted portfolio component, and indices n and i denote the number of portfolio components and the liquidity rank of the specific component respectively.
  - The same methodology is used to clean cash positions reported by funds to generate the cash liquidity buffer for the narrow liquidity concept.

*This section was prepared by Frank Hespeler.*

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_Source: https://www.imf.org/-/media/files/publications/gfsr/2019/october/english/onlineannex11.pdf_