## Appendix I: A Selected Literature Review

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### I. Introduction: scope and motivation
- Context: Post-GFC low bank profitability and implications for financial stability.
- Objectives:
  - Investigate theoretical and empirical relationships between bank profitability and financial stability, accounting for bank business models and types of non-interest income (NII).
  - Examine determinants of banking risks and profitability, capturing bank business models, structural and cyclical conditions, and policies.
- Sample and period used in empirical analysis:
  - 431 publicly traded banks.
  - Sample period: 2004 to 2017.

### II. Stylized theoretical model — key structure and predictions
- Balance sheet and definitions:
  - Assets: L (loans), N_r (retail-based NII assets), N_m (market-based NII assets).
  - Liabilities: D (deposits), E (equity); A = L + N_r + N_m = D + E.
  - Capital constraint: E = e A, where e is the reciprocal of leverage ratio.
  - NII share s defined as ratio of NII to operating income.
- Production and returns:
  - Retail-based NII uses Cobb-Douglas production N_r^α L^{1−α}.
  - Returns r̃_i ~ N(r_i, σ_i^2), i = L, m, r (assumed mutually independent for baseline).
- Risk measures defined:
  - Expected Default Frequency (EDF): EDF ≡ 1 − q = Prob(π̃ + e < 0).
  - Value-at-Risk (VaR): Prob(|Loss| ≥ VaR) = Prob(−π̃ − e ≥ VaR) = 0.05 (VaR is 95th percentile of equity loss).
- Optimal allocations and comparative statics:
  - Optimal N_r* and N_m* depend on LTA ratio l and parameter k = (α r_r / (c_r + r_m − c_m))^{1/(1−α)} > 0.
  - Corner solution if l ≥ 1/(1+k): n_r* = 1 − l, n_m* = 0.
  - Interior solution if l < 1/(1+k): n_r* = k l, n_m* = 1 − l − k l.
- Propositions and lemmas:
  - Proposition 1: ∂EDF/∂μ_π* < 0 and ∂VaR/∂μ_π* < 0.
  - Lemma 1: ∂(n_r*/n_m*)/∂l ≥ 0.
  - Proposition 2: If l ≤ l̄, ∂EDF/∂s > 0 and ∂VaR/∂s > 0. Threshold l̄ given by:
    - l̄ = (1 + k) σ_m^2 (1 − x)^2 σ_L^2 + (1 + k)^2 σ_m^2 + k^2 α σ_r^2 < 1/(1 + k).
  - Proposition 3: ∂μ_π*/∂x < 0, ∂μ_π*/∂c_f < 0, ∂μ_π*/∂r_D < 0.
  - Extended model with charter value v:
    - Proposition 4: ∂EDF'/∂v < 0 and ∂VaR'/∂v < 0.
    - Proposition 5: ∂EDF'/∂e < 0 and ∂VaR'/∂e < 0.

### III. Empirical design — variables, measures, and methodology
- Key variables and measures:
  - Profitability: ROAA, ROAE, risk-adjusted ROAA, risk-adjusted ROAE, price-to-book ratio (Price/Book Ratio).
  - Idiosyncratic risk: historical VaR (5 percent annualized daily equity return), Moody’s EDF (one-year ahead).
  - Systemic risk: ΔCoVaR (5th percentile ΔCoVaR used).
  - Business model metrics: NII share (%), Loan-to-Asset ratio (LTA, l), deposit-to-liability ratio, asset-to-equity (leverage) ratio.
  - Bank characteristics: Tier 1 ratio (%), problem loans ratio (%), cost-to-income (%), cost of funds (%), Lerner Index (%).
  - Policy and cyclical variables: 3-month short-term interest rates, central bank claims on financial institutions, government structural balance / potential GDP, GDP growth.
- ΔCoVaR state variables include:
  - Interest rates, term spreads, liquidity spreads, credit risk (Moody’s Baa − 10-year Treasury spread), market returns and volatility.
- Empirical method:
  - Dynamic panel regressions using Arellano-Bover/Blundell-Bond system estimator with robust standard errors.
  - Baseline specification: Y_{k,j,t} = δ Y_{k,j,t−1} + ϑ_k + φ′ X_{k,j,t} + Λ′ M_{j,t} + ε_{k,j,t}.
  - Two main groups of estimations:
    - Determinants of financial stability (VaR, EDF, ΔCoVaR).
    - Determinants of profitability (ROAA, ROAE, Price/Book, risk-adjusted measures).

### IV. Stylized facts from data (2004–2017)
- Profitability dynamics:
  - ROAA, ROAE, and Price/Book Ratio declined sharply during the 2007-2009 GFC.
  - U.S. banks recovered faster post-crisis than European banks; European banks experienced another decline during 2012-2014.
  - None of the profitability measures returned to pre-crisis levels in the sample period.
- Risk dynamics:
  - Elevated systemic and idiosyncratic risks during the GFC and European Sovereign Debt Crisis.
  - U.S. banks show higher contribution to systemic risk (ΔCoVaR) on average.
  - Idiosyncratic risks: U.S. banks elevated during 2007-2009, Europe overtook during 2012-2014.
- Business-model and balance-sheet facts:
  - U.S. banks: higher LTA and deposit-to-liability ratios on average (2004–2017).
  - GSIBs: lowest LTA ratios; average asset sizes: U.S. banks $53 billion, European banks $274 billion, GSIBs $1710 billion.
  - NII share declined since the crisis then stabilized.
  - European banks exhibit higher leverage and problem loan ratios than U.S. banks and GSIBs.
  - Tier 1 ratios rose markedly since the crisis.
  - Lerner index indicates higher pricing power for U.S. banks.

### V. Empirical findings — determinants of risks and profitability
- Hypotheses tested:
  - Hypothesis 1: Low profitability associated with high idiosyncratic risks and higher contribution to systemic risks.
  - Hypothesis 2: High NII share associated with high idiosyncratic and systemic risks for less retail-oriented banks.
  - Hypothesis 3: High leverage associated with high idiosyncratic and systemic risks.
  - Hypothesis 4: High NPL ratio, funding, and operating costs associated with low profitability.
- Selected quantitative findings (reported exactly as in source):
  - Sample observations for VaR regressions range around 3,833–3,922; Hansen p-Values reported (e.g., 0.4590, 0.2060, 0.4140, 0.1130, 0.4190, 0.513).
  - Idiosyncratic risk (VaR) key coefficients:
    - ROAA (%) coefficients: −0.841***, −1.024***, −1.036***.
    - Price-to-Book Ratio (%) coefficients: −0.00917***, −0.0117***, −0.0112***.
    - Non-Interest Income Share (%) examples: 0.0120*, 0.0127*, 0.0215**.
    - Interaction NII Share (%) × Loan-to-Asset Ratio (%): −0.000227*, −0.000344***.
    - Tier 1 Ratio (%): −0.0598***, −0.107***.
    - Problem Loans Ratio (%): 0.0434**, 0.0479**, 0.0542***.
    - Real GDP growth rate (%): −0.229*** to −0.284***.
    - Short-term interest rate (%): 0.116*** to 0.226***.
    - Lerner Index (%) examples: −0.0302***, −0.0444***.
    - Deposit-to-Liability Ratio (%) examples: −0.0122**, −0.00983*.
    - Leverage Ratio example: 0.0317***.
    - Weekly Delta CoVaR coefficient: L0.266*** to L0.351***.
    - Interpretation given: A one standard deviation increase in ROAA is associated with a 0.64 percentage point decrease in VaR (about a quarter of median VaR 2.57 percent). A one standard deviation rise in Price-to-Book associated with 0.59 percentage point decline in VaR.
  - Idiosyncratic risk (EDF) key coefficients:
    - ROAA (%) negative and significant: −0.218*** to −0.231***.
    - Price-to-Book Ratio (%) negative and significant (e.g., −0.0000882**).
    - NII Share (%) generally positive; interaction NII×LTA negative.
    - Problem Loans Ratio (%) positive: 0.00303*** to 0.00366***.
    - Real GDP growth rate (%) negative: −0.00608*** to −0.00817***.
    - Short-term interest rate (%) positive: 0.00438***.
  - Systemic risk (ΔCoVaR) key coefficients:
    - ROAA (%) negative: −0.370***, −0.220***, −0.263***.
    - Price-to-Book Ratio (%) negative: −0.00502***, −0.00292***, −0.00348***.
    - NII Share (%) positive: 0.0432***, 0.0446***, 0.0420***.
    - Interaction NII×LTA negative and significant: −0.000659***, −0.000617***.
    - Tier 1 Ratio (%) often negative: e.g., −0.0677***.
    - Problem Loans Ratio (%) sometimes negative or small for ΔCoVaR: e.g., −0.0267***.
    - Lerner Index (%) positive in some specs: 0.0156*, 0.0186***.
    - Deposit-to-Liability Ratio (%) negative: −0.0328***, −0.0249***.
    - Leverage Ratio positive in some specs: 0.00945*, 0.0279*.
  - Determinants of profitability (selected):
    - Problem Loans Ratio (%) negatively associated with profitability; example: coefficient −0.0199** on ROAA.
      - Quantified example: "A one standard deviation decrease in the problem loan ratio is associated with a 0.1 percentage point increase in the ROAA, which is more than ten percent of the median value of ROAA (0.83 percent)."
    - Cost-to-Income (%) negatively associated: −0.0290***.
    - Cost of Funds (%) negatively associated: e.g., −0.139*** in one specification.
    - Real GDP growth rate (%) positively associated: e.g., 0.0591***; 0.955*** in some ROAE specs.

### VI. Policy-relevant conclusions and implications
- Main messages:
  - Profitability and charter value (price-to-book) are negatively associated with both idiosyncratic and systemic risks across 2004–2017.
  - The source of profitability matters: over-reliance on market-based NII, leverage, and wholesale funding is associated with higher idiosyncratic risk and higher contribution to systemic risk.
  - Interaction effect: High NII share increases risks for less retail-oriented banks (low LTA); retail-oriented banks can obtain diversification benefits from NII.
  - Competition effects: Low competition (higher Lerner index) is associated with lower idiosyncratic risk but higher contribution to systemic risk.
- Policy recommendations:
  - Assess not only levels of profitability but also the source and sustainability of bank profitability in macroprudential stress tests and systemic-risk assessments.
  - Distinguish retail-based versus market-based NII in supervision and regulation.
  - Monitor leverage, funding structure (retail vs. wholesale), and NII composition for prudential calibration.
  - Consider competition-policy interactions: balance consolidation-related efficiency gains against potential increases in systemic vulnerability; facilitate entry rather than raising entry barriers.
  - Ensure effective and timely implementation of the Basel III framework and well calibrated macro-prudential tools to limit excessive reliance on wholesale funding and leverage.

### VII. Key quantitative relationships and thresholds (as presented)
- Sample size and period reiterated:
  - 431 publicly traded banks, 2004 to 2017.
- Regularity and parameter notes:
  - VaR implicitly defined via Φ(...)-0.05=0 (5 percent tail).
  - Model regularity condition example: average empirical problem loan ratio x is less than 5%.
- Directional comparative statics preserved:
  - ∂EDF/∂μ_π* < 0 and ∂VaR/∂μ_π* < 0.
  - ∂EDF/∂e < 0 and ∂VaR/∂e < 0.
  - ∂μ_π*/∂x < 0, ∂μ_π*/∂c_f < 0, ∂μ_π*/∂r_D < 0.
  - If l ≤ l̄, ∂EDF/∂s > 0 and ∂VaR/∂s > 0, with l̄ characterized analytically in model terms.

### VIII. Appendix tables and robustness checks — selected statistics and coefficients
- Appendix Table 3 (Macroeconomic Variables) definitions: GDP growth (IMF WEO), Interest rate (3 month) (OECD), Government bond yield (10 year) (Haver Analytics), General government balance (IMF WEO), Central bank claims (IMF MFS, Haver Analytics).
- Appendix Table 4 (Summary statistics, selected):
  - Cost of Funds (%) — N = 4,846; mean = 1.473; p50 = 1.146; sd = 1.113; min = 0.047; max = 67.374.
  - Cost-to-Income (%) — N = 5,304; mean = 65.40; p50 = 63.98; sd = 17.88; min = 25.27; max = 347.1.
  - Price-to-Book Ratio (%) — N = 4,838; mean = 139.11; p50 = 128.16; sd = 68.67; min = 12.51; max = 515.4.
  - ROAA (%) — N = 5,268; mean = 0.71; p50 = 0.81; sd = 1.08; min = -6.02; max = 224.067.
  - ROAE (%) — N = 5,241; mean = 7.23; p50 = 8.37; sd = 21.11; min = -114.74; max = 242.03.
  - Tier 1 Ratio (%) — N = 5,099; mean = 13.40; p50 = 12.60; sd = 4.43; min = 1.49; max = 150.77.
  - Problem Loans Ratio (%) — N = 5,134; mean = 2.79; p50 = 1.37; sd = 5.46; min = 0.30; max = 40.39.
  - Loan-to-Asset Ratio (%) — N = 5,306; mean = 65.72; p50 = 68.59; sd = 15.08; min = 10.00; max = 192.24.
  - Non-Interest Income Share (%) — N = 5,216; mean = 28.66; p50 = 25.18; sd = 18.77; min = 0.39; max = 225.7.
  - Deposit-to-Liability Ratio (%) — N = 5,377; mean = 77.71; p50 = 78.38; sd = 19.84; min = 20.99; max = 99.36.
  - Leverage Ratio — N = 5,401; mean = 12.09; p50 = 10.64; sd = 6.09; min = 1.83; max = 169.01.
  - Lerner Index (%) — N = 5,115; mean = 26.59; p50 = 27.41; sd = 11.93; min = -58.00; max = 56.56.
  - Delta CoVaR (95%) of Weekly Loss (%) — N = 4,710; mean = 1.62; p50 = 1.27; sd = 2.19; min = -4.257; max = 10.50.
  - VaR (95%) of Daily Loss (%) — N = 4,722; mean = 3.11; p50 = 2.56; sd = 9.19; min = 0.10; max = 12.71.
  - Expected Default Frequency (%) — N = 3,669; mean = 0.76; p50 = 0.39; sd = 0.17; min = 0.01; max = 98.25.
  - logit(EDF) — N = 3,669; mean = -5.469; p50 = -5.544; sd = 0.967; min = -8.527; max = -1.091.
- Appendix IV robustness (selected static panel coefficients reproduced exactly as printed):
  - Static panel ROAA (%) L coefficients: -0.214*** (0.00552); -0.264*** (0.00628); -0.284*** (0.00635); -0.176* (0.00968); -0.467*** (0.00895); -0.500*** (0.00968).
  - Non-Interest Income Share (%) L coefficients: 0.00893** (0.000414); 0.00789 (0.000533); 0.0137*** (0.000442); 0.0171* (0.000915); 0.0222** (0.000920); 0.0390*** (0.000748).
  - NII×LTA L coefficients: -0.000198*** (7.23e-05); -0.000174** (8.77e-05); -0.000212*** (8.14e-05); -0.000264* (0.0000160); -0.000584*** (0.0000129).
  - Real GDP Growth Rate (%) examples: -0.00491*** (0.00151); -0.00562*** (0.00144); -0.00580*** (0.00142).
  - Tier 1 Ratio (%) L examples: -0.00288 (0.00109); -0.00500 (0.000862); -0.107*** (0.00228); -0.0709** (0.00201).
  - Problem Loans Ratio (%) L examples: 0.0776*** (0.000857); 0.0760*** (0.000972); 0.0752*** (0.000898).
  - Observations across static specifications: 3,086; 3,128; 3,133; 4,062; 4,113; 4,184; 5,052; 5,034; 5,108.
- Robustness for profitability regressions (selected coefficients reproduced exactly):
  - Real GDP Growth Rate (%) coefficients: 0.100*** (0.00235); 1.702*** (0.395); 0.0948*** (0.00182).
  - Problem Loans Ratio (%) L coefficients: -0.0421*** (0.000798); -0.541*** (0.141); -0.0379*** (0.000688).
  - Cost-to-Income (%) L coefficients: -0.00756*** (0.000185); -0.0806*** (0.00211); -0.00518*** (0.000156).
  - Cost of Funds (%) L coefficients: -0.103* (0.00548); -0.260*** (0.00614); -0.187*** (0.00491).
  - Appendix Table 9 dynamic panel pre-tax profitability examples:
    - Problem Loans Ratio (%) coefficients: -0.000598*** (0.000137); -0.00165 (0.000811); -0.00108 (0.000664); -0.00199*** (0.000730).
    - Cost-to-Income (%) coefficients: -0.000418*** (5.26e-05); -0.00130** (0.000589); -0.00162*** (0.000341); -0.00215*** (0.000374).
    - Hansen p-Values reported: 0.0931; 0.0388; 0.234; 0.225.

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### Appendix I: A Selected Literature Review ............................................................................. 3

### Appendix I: A Selected Literature Review

### Appendix index and page references
- Appendix I: A Selected Literature Review ............................................................................. 34
- Appendix II: Proofs of Propositions and Lemmas .................................................................. 36
- Appendix III: Data Sources and Definitions ........................................................................... 42
- Appendix IV: Robustness Checks .......................................................................................... 45

### Document organization (major components)
- Literature review material is contained in Appendix I (page 34).
- Analytical derivations and formal results are contained in Appendix II (page 36).
- Empirical inputs, definitions, and data provenance are contained in Appendix III (page 42).
- Sensitivity analyses and checks are contained in Appendix IV (page 45).

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### References .............................................................................................................

### wp1905 - References

### I. Introduction: scope and motivation
- Context: Post-GFC low bank profitability and implications for financial stability.
- Objectives:
  - Investigate theoretical and empirical relationships between bank profitability and financial stability, accounting for bank business models and types of non-interest income (NII).
  - Examine determinants of banking risks and profitability, capturing bank business models, structural and cyclical conditions, and policies.
- Sample and period used in empirical analysis:
  - 431 publicly traded banks.
  - Sample period: 2004 to 2017.

### II. Stylized theoretical model — key structure and predictions
- Balance sheet notation and definitions:
  - Assets: L (loans), N_r (retail-based NII assets), N_m (market-based NII assets).
  - Liabilities: D (deposits), E (equity); A = L + N_r + N_m = D + E.
  - Capital constraint: E = e A, where e is the reciprocal of leverage ratio.
  - NII share s defined as ratio of NII to operating income.
- Profit function and retail complementarity:
  - Retail-based NII uses Cobb-Douglas production N_r^α L^{1−α} creating complementarity between lending and retail NII.
  - Returns r̃_i ~ N(r_i, σ_i^2), i = L, m, r (assumed mutually independent for baseline).
- Risk definitions:
  - Expected Default Frequency proxy (EDF): EDF ≡ 1 − q = Prob(π̃ + e < 0).
  - Value-at-Risk (VaR): Prob(|Loss| ≥ VaR) = Prob(−π̃ − e ≥ VaR) = 0.05 (VaR is 95th percentile of equity loss).
- Main model solutions and comparative statics:
  - Optimal N_r* and N_m* depend on LTA ratio l and parameter k = (α r_r / (c_r + r_m − c_m))^{1/(1−α)} > 0.
  - Corner solution if l ≥ 1/(1+k): n_r* = 1 − l, n_m* = 0.
  - Interior solution if l < 1/(1+k): n_r* = k l, n_m* = 1 − l − k l.
- Propositions (analytical predictions):
  - Proposition 1: ∂EDF/∂μ_π* < 0 and ∂VaR/∂μ_π* < 0 (idiosyncratic risks decrease in expected ROA μ_π*).
  - Lemma 1: ∂(n_r*/n_m*)/∂l ≥ 0 (retail NII intensity relative to market NII increases with LTA ratio).
  - Proposition 2: If l ≤ l̄ (threshold), ∂EDF/∂s > 0 and ∂VaR/∂s > 0 (when LTA is below threshold, higher NII share s increases VaR and EDF). Threshold l̄ given by:
    - l̄ = (1 + k) σ_m^2 (1 − x)^2 σ_L^2 + (1 + k)^2 σ_m^2 + k^2 α σ_r^2 < 1/(1 + k)  (expression as in text).
  - Proposition 3: ∂μ_π*/∂x < 0, ∂μ_π*/∂c_f < 0, ∂μ_π*/∂r_D < 0 (expected profits decrease in problem loan ratio x, operating cost c_f, and funding cost r_D).
  - Extended model with charter value v (price-to-book = Price/Book Ratio):
    - Proposition 4: ∂EDF'/∂v < 0 and ∂VaR'/∂v < 0 (idiosyncratic risks decrease in price-to-book ratio v).
    - Proposition 5: ∂EDF'/∂e < 0 and ∂VaR'/∂e < 0 (idiosyncratic risks decrease in e = E/A; equivalently increase in leverage 1/e raises risks).

### III. Empirical design — variables, measures, and methodology
- Key variables and measures:
  - Profitability: ROAA, ROAE, risk-adjusted ROAA, risk-adjusted ROAE, price-to-book ratio (Price/Book Ratio).
  - Idiosyncratic risk: historical VaR (5 percent annualized daily equity return), Moody’s EDF (one-year ahead).
  - Systemic risk: ΔCoVaR (5th percentile ΔCoVaR used), estimated via quantile regressions on weekly data (Adrian and Brunnermeier 2016 framework).
  - Bank business models: NII share (%), Loan-to-Asset ratio (LTA, l), deposit-to-liability ratio, asset-to-equity (leverage) ratio.
  - Bank characteristics: Tier 1 ratio (%), problem loans ratio (%), cost-to-income (%), cost of funds (%), Lerner Index (%).
  - Policy and cyclical variables: 3-month short-term interest rates, central bank claims on financial institutions (IMF IFS), government structural balance / potential GDP, GDP growth.
- ΔCoVaR state variables (examples used):
  - Interest rates (change in 3-month German and 3-month T-bill rates).
  - Term structure (change in 10-year minus 3-month spreads).
  - Liquidity risk (changes in 3-month Euribor minus 3-month Germany yields; changes in LIBOR vs secondary market T-bill rates).
  - Credit risk (change in Moody’s Baa − 10-year Treasury spread).
  - Market returns (Euro Stoxx 50, S&P 500), market volatility (VIX), and excess financial vs real estate sector returns.
- Empirical method:
  - Dynamic panel regressions using Arellano-Bover/Blundell-Bond system estimator with robust standard errors.
  - Baseline specification: Y_{k,j,t} = δ Y_{k,j,t−1} + ϑ_k + φ′ X_{k,j,t} + Λ′ M_{j,t} + ε_{k,j,t}, where Y is risk or profitability, X is bank-specific variables, M is policy/cyclical variables, and ϑ_k bank fixed effects.
  - Two groups of estimations:
    - Determinants of financial stability (VaR, EDF, ΔCoVaR): include profitability, NII share, NII × LTA interaction, problem loans, leverage, Lerner index, deposit-to-liability ratio, policy controls.
    - Determinants of profitability: include problem loans ratio, cost-to-income, cost of funds, policy controls; profitability measures as dependent variables.

### IV. Stylized facts from data (2004–2017)
- Profitability dynamics:
  - ROAA, ROAE, and Price/Book Ratio declined sharply during the 2007-2009 GFC.
  - U.S. banks recovered faster post-crisis than European banks; European banks experienced another decline during the 2012-2014 European Sovereign Debt Crisis.
  - None of the profitability measures returned to pre-crisis levels in the sample period.
- Risk dynamics:
  - Elevated systemic and idiosyncratic risks during GFC and European Sovereign Debt Crisis.
  - U.S. banks show higher contribution to systemic risk (ΔCoVaR) compared with European banks on average.
  - Idiosyncratic risks (VaR, EDF): U.S. banks elevated during 2007-2009, Europe overtook during 2012-2014.
- Bank business model stylized facts:
  - U.S. banks: higher LTA and deposit-to-liability ratios on average (2004–2017).
  - GSIBs: lowest LTA ratios; average asset sizes: U.S. banks $53 billion, European banks $274 billion, GSIBs $1710 billion.
  - NII share declined since the crisis then stabilized.
  - European banks exhibit higher leverage and problem loan ratios than U.S. banks and GSIBs.
  - Tier 1 ratios rose markedly since the crisis.
  - Lerner index indicates higher pricing power for U.S. banks.

### V. Empirical findings — determinants of risks and profitability
- Hypotheses tested (as derived from theory):
  - Hypothesis 1: Low profitability associated with high idiosyncratic risks (Propositions 1 & 4) and high contribution to systemic risks.
  - Hypothesis 2: High NII share associated with high idiosyncratic and systemic risks for less retail-oriented banks (Proposition 2).
  - Hypothesis 3: High leverage associated with high idiosyncratic and systemic risks (Proposition 5).
  - Hypothesis 4: High NPL ratio, funding, and operating costs associated with low profitability (Proposition 3).
- Key empirical relationships (selected quantitative findings reported exactly as in source):
  - Sample and estimation details: Observations for VaR regressions range around 3,833–3,922; Hansen p-Values reported (e.g., 0.4590, 0.2060, 0.4140, 0.1130, 0.4190, 0.513).
  - Idiosyncratic risk (VaR) results (Table 1 excerpts):
    - ROAA (%) coefficients: −0.841***, −1.024***, −1.036*** (standard errors shown in table).
    - Price-to-Book Ratio (%) coefficients: −0.00917***, −0.0117***, −0.0112***.
    - Non-Interest Income Share (%) coefficients: mixed but e.g., 0.0120*, 0.0127*, 0.0215** in certain specifications.
    - Interaction NII Share (%) × Loan-to-Asset Ratio (%): negative coefficients (e.g., −0.000227*, −0.000344***) indicating NII adverse effects decline with higher LTA.
    - Tier 1 Ratio (%): negative association with VaR (e.g., −0.0598***, −0.107***).
    - Problem Loans Ratio (%) positive association with VaR (e.g., 0.0434**, 0.0479**, 0.0542***).
    - Real GDP growth rate (%) negative association with VaR (e.g., −0.229*** to −0.284***).
    - Short-term interest rate (%) positive association with VaR (e.g., 0.116*** to 0.226***).
    - Lerner Index (%) negative association with VaR in some specifications (e.g., −0.0302***, −0.0444***).
    - Deposit-to-Liability Ratio (%) negative association with VaR (e.g., −0.0122**, −0.00983*).
    - Leverage Ratio associated with higher VaR in some specs (e.g., 0.0317***).
    - Weekly Delta CoVaR = L0.266*** to L0.351*** (positive and significant).
    - Interpretation: A one standard deviation increase in ROAA is associated with a 0.64 percentage point decrease in VaR (about a quarter of median VaR 2.57 percent). A one standard deviation rise in Price-to-Book associated with 0.59 percentage point decline in VaR.
  - Idiosyncratic risk (EDF) results (Table 2 excerpts):
    - ROAA (%) negative and significant (e.g., −0.218*** to −0.231*** across specs).
    - Price-to-Book Ratio (%) negative and significant (e.g., −0.0000882** etc. — refer to table for exact entries).
    - NII Share (%) generally positive association with EDF, with interaction NII×LTA negative (implying retail-oriented banks see diversification benefits).
    - Problem Loans Ratio (%) positive association with EDF (e.g., 0.00303*** to 0.00366***).
    - Real GDP growth rate (%) negative association with EDF (e.g., −0.00608*** to −0.00817***).
    - Short-term interest rate (%) positive association with EDF (e.g., 0.00438***).
  - Systemic risk (ΔCoVaR) results (Table 3 excerpts):
    - ROAA (%) negative association with ΔCoVaR (e.g., −0.370***, −0.220***, −0.263***).
    - Price-to-Book Ratio (%) negative association (e.g., −0.00502***, −0.00292***, −0.00348***).
    - NII Share (%) positive association with ΔCoVaR (e.g., 0.0432***, 0.0446***, 0.0420***).
    - Interaction NII×LTA negative and significant (e.g., −0.000659***, −0.000617***), implying retail orientation mitigates the systemic-risk effect of NII.
    - Tier 1 Ratio (%) mixed but often negative (e.g., −0.0677*** in some specs).
    - Problem Loans Ratio (%) often negative or small (e.g., −0.0267***) for ΔCoVaR — interpretation in text: NPL may be linked more with retail activities and lower beta with market moves.
    - Lerner Index (%) positive association with ΔCoVaR in some specifications (e.g., 0.0156*, 0.0186***).
    - Deposit-to-Liability Ratio (%) negative association with ΔCoVaR (e.g., −0.0328***, −0.0249***).
    - Leverage Ratio positive association with ΔCoVaR in some specs (e.g., 0.00945*, 0.0279*).
- Determinants of profitability (Table 4 excerpts):
  - Problem Loans Ratio (%) negatively associated with profitability measures (e.g., coefficient −0.0199** on ROAA; other entries negative across ROAA, ROAE, Price/Book).
    - Quantified example: "A one standard deviation decrease in the problem loan ratio is associated with a 0.1 percentage point increase in the ROAA, which is more than ten percent of the median value of ROAA (0.83 percent)."
  - Cost-to-Income (%) negatively associated with profitability (e.g., −0.0290***).
  - Cost of Funds (%) negatively associated with profitability (e.g., −0.139*** on one specification).
  - Real GDP growth rate (%) positively associated with profitability (e.g., 0.0591***, 0.955*** in some ROAE specs).
  - Claims growth rate and Log(Assets) coefficients reported as in table (exact figures shown).
  - Robustness: Results robust to different lag specifications, inclusion of year dummies, and static panel regressions.

### VI. Policy-relevant conclusions and implications (as stated)
- Main messages:
  - Profitability and charter value (price-to-book) are negatively associated with both idiosyncratic and systemic risks — higher profitability/charter value tends to reduce risk-taking on average across 2004–2017.
  - The source of profitability matters: over-reliance on market-based NII, leverage, and wholesale funding is associated with higher idiosyncratic risk and higher contribution to systemic risk.
  - Interaction effect: High NII share increases risks for less retail-oriented banks (low LTA); retail-oriented banks can obtain diversification benefits from NII through retail-oriented fee activities.
  - Competition effects: Low competition (higher mark-up / higher Lerner index) is associated with lower idiosyncratic risk but higher contribution to systemic risk — implying a trade-off that policymakers should consider regarding consolidation and market power.
- Policy recommendations and implications emphasized:
  - Financial stability authorities should assess not only levels of profitability but also the source and sustainability of bank profitability when evaluating bank resilience to systemic stress and designing macroprudential stress tests.
  - The differing impacts of competition on idiosyncratic vs. systemic risk suggest policymakers should balance efficiency gains from consolidation against potential increases in systemic vulnerability; facilitating entry of new firms rather than raising entry barriers is one suggested approach to preserve competitive environments.
  - Attention to leverage, funding structure (retail vs. wholesale), and NII composition can inform prudential policy and macroprudential calibration.

*Italic source attribution line as provided in original material.*

### conclusion. The details are provided in Appendix IV.

### V. POLICY IMPLICATIONS AND CONCLUSIONS

### Study design and theoretical predictions
- Sample and empirical approach:
  - Panel regression for 431 publicly traded banks from 2004 to 2017.
- Core theoretical predictions from the stylized model:
  - Idiosyncratic risks (VaR of equity prices and EDF) are negatively related to both ROAA and long-term expected profitability (charter value).
  - Profits reduce risks by providing equity buffers and by encouraging prudence and reduced risk-taking.
  - Idiosyncratic risk rises with the share of NII activities when the LTA ratio is below a certain threshold.
  - Idiosyncratic risk increases with the leverage ratio of banks.
  - Profitability decreases as the problem loan ratio, operating costs, and funding costs increase.

### Empirical findings
- Profitability and market valuation:
  - Profitability (ROAA) and the price-to-book ratio are negatively associated with both contribution to systemic risk (ΔCoVaR) and idiosyncratic risk measured by VaR and the EDF of banks.
- Noninterest income (NII) and business models:
  - A high NII share tends to be associated with higher idiosyncratic risk and higher contribution to systemic risk when the LTA ratio is low (i.e., when a bank’s business model is less retail-oriented).
  - Market-based NII activities are generally riskier than retail-based NII activities.
- Competition and systemic risk:
  - Lower competition (high mark-up, higher Lerner index) is associated with lower idiosyncratic risk but higher contribution to systemic risk.
- Funding structure and leverage:
  - High leverage and over-reliance on wholesale funding are associated with higher idiosyncratic risk and higher contribution to systemic risk.
- Determinants of profitability:
  - Asset quality (problem loans ratio), cost efficiency (cost-to-income ratio), and funding costs are important determinants of bank profitability measures (ROAA, ROAE, and risk-adjusted returns) and price-to-book ratio.

### Policy implications and recommendations
- Distinguish NII types in supervision and policy:
  - Make a sharper distinction between retail-based and market-based NII activities in risk assessment and regulation, because market-based NII are generally riskier.
  - Recognize that in a low interest rate environment banks tend to diversify into NII activities, shifting their risk profile.
- Monitor bank consolidation effects:
  - Account for the impact of bank consolidation on competition and systemic risk: mergers and acquisitions can improve firm-level outcomes but may raise contribution to systemic risk through reduced competition (higher Lerner index).
  - Seek the right balance between cost efficiency and a competitive, stable banking environment.
- Evaluate sustainability and sources of profitability:
  - Pay greater attention to the source and sustainability of bank profitability in macro-prudential stress tests and systemic risk analysis.
  - Over-reliance on leverage and wholesale funding undermines financial stability and should be monitored and constrained where necessary.
- Support regulatory frameworks and macro-prudential tools:
  - Ensure effective and timely implementation of the Basel III framework.
  - Use well calibrated macro-prudential tools to keep banks’ reliance on wholesale funding and leverage prudentially manageable.

### Key quantitative relationships and thresholds (as found or derived in the paper)
- Sample size and period:
  - 431 publicly traded banks, 2004 to 2017.
- Regularity and parameter notes referenced in proofs and propositions:
  - VaR defined implicitly via Φ(...)-0.05=0 (5 percent tail).
  - A parameter regularity condition: the problem loan ratio x < 1+ (r_m − c_m) (1−α α k −1) + 1−α α k c_r r_L. The paper notes this assumption is reasonable, as the average value of x observed empirically in the sample is less than 5%.
- Directional comparative statics established analytically and supported empirically:
  - ∂EDF/∂μ_π* < 0 and ∂VaR/∂μ_π* < 0 (idiosyncratic risks fall with higher expected ROA).
  - ∂EDF/∂e < 0 and ∂VaR/∂e < 0 (idiosyncratic risks fall with higher effective equity e, i.e., lower leverage 1/e).
  - ∂μ_π*/∂x < 0, ∂μ_π*/∂c_f < 0, ∂μ_π*/∂r_D < 0 (expected profits fall with problem loan ratio x, cost c_f, and funding cost r_D).
  - When LTA ratio l is below a threshold l̄, higher NII share s leads to higher VaR and EDF: ∂EDF/∂s > 0 and ∂VaR/∂s > 0 if l ≤ l̄. The threshold l̄ is characterized analytically in terms of model variances and parameters.

*Source: Conclusion and Appendix IV details as presented in the provided content unit.*

### Appendix Table 3: Macroeconomic Variables

### Appendix Table 3: Macroeconomic Variables

### Definitions (Data series and sources)
- GDP growth — IMF WEO: Growth of Gross Domestic Product, constant prices
- Interest rate (3 month) — OECD: Short term (3 months) interest rate, money market
- Government bond yield (10 year) — Haver Analytics: 10-Year Government Bond Yield (AVG, %)
- General government balance — IMF WEO: General government structural balance
- Central bank claims — IMF MFS statistics, Haver Analytics: Central Bank Survey, Claims on Other Financial Corporations and Other Depository Corporations

*Source: Appendix Table 3 content from the provided PDF.*

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### Appendix Table 4: Summary Statistics (selected variables)

- Sources: S&P Global Market Intelligence’s SNL database and IMF staff calculations.

Selected variables with N, mean, p50, sd, min, max (as printed):

- Cost of Funds (%) — N = 4,846; mean = 1.473; p50 = 1.146; sd = 1.113; min = 0.047; max = 67.374
- Cost-to-Income (%) — N = 5,304; mean = 65.40; p50 = 63.98; sd = 17.88; min = 25.27; max = 347.1
- Price-to-Book Ratio (%) — N = 4,838; mean = 139.11; p50 = 128.16; sd = 68.67; min = 12.51; max = 515.4
- ROAA (%) — N = 5,268; mean = 0.71; p50 = 0.81; sd = 1.08; min = -6.02; max = 224.067
- ROAE (%) — N = 5,241; mean = 7.23; p50 = 8.37; sd = 21.11; min = -114.74; max = 242.03
- Tier 1 Ratio (%) — N = 5,099; mean = 13.40; p50 = 12.60; sd = 4.43; min = 1.49; max = 150.77
- Problem Loans Ratio (%) — N = 5,134; mean = 2.79; p50 = 1.37; sd = 5.46; min = 0.30; max = 40.39
- Loan-to-Asset Ratio (%) — N = 5,306; mean = 65.72; p50 = 68.59; sd = 15.08; min = 10.00; max = 192.24
- Log(Assets) — N = 5,406; mean = 15.83; p50 = 15.24; sd = 2.28; min = 12.32; max = 21.62
- Non-Interest Income Share (%) — N = 5,216; mean = 28.66; p50 = 25.18; sd = 18.77; min = 0.39; max = 225.7
- XL Loan-to-Asset Ratio (%) — N = 5,192; mean = 1,742; p50 = 1,617; sd = 1,015; min = 28.77; max = 14,065
- Deposit-to-Liability Ratio (%) — N = 5,377; mean = 77.71; p50 = 78.38; sd = 19.84; min = 20.99; max = 99.36
- Leverage Ratio — N = 5,401; mean = 12.09; p50 = 10.64; sd = 6.09; min = 1.83; max = 169.01
- Lerner Index (%) — N = 5,115; mean = 26.59; p50 = 27.41; sd = 11.93; min = -58.00; max = 56.56
- ROAA/sd(ROAA) (%) — N = 5,267; mean = 2.68; p50 = 1.20; sd = 0.80; min = -3.06; max = 315.47
- ROAA/sd(ROAE) (%) — N = 5,239; mean = 2.46; p50 = 1.18; sd = 0.76; min = -3.14; max = 415.16
- Gov Structural Balance/Potential GDP (%) — N = 5,992; mean = -4.46; p50 = -3.4? (table shows fragmented entries); sd = -4.258? (table formatting fragmented) — (exact entries preserved only as printed)
- ST Interest Rate (%) — N = 5,966; mean = 1.554; p50 = 0.644; sd = 1.179; min = -0.784; max = 15.82
- Real GDP Growth Rate (%) — N = 5,992; mean = 1.82; p50 = 2.22; sd = 2.13; min = -9.132; max = 225.49
- Claim Growth Rate (%) — N = 5,780; mean = 90.46; p50 = -14.16; sd = 38.15; min = -94.40; max = 6,332
- Delta CoVaR (95%) of Weekly Loss (%) — N = 4,710; mean = 1.62; p50 = 1.27; sd = 2.19; min = -4.257; max = 10.50
- VaR (95%) of Daily Loss (%) — N = 4,722; mean = 3.11; p50 = 2.56; sd = 9.19; min = 0.10; max = 12.71
- Expected Default Frequency (%) — N = 3,669; mean = 0.76; p50 = 0.39; sd = 0.17; min = 0.01; max = 98.25
- logit(EDF) — N = 3,669; mean = -5.469; p50 = -5.544; sd = 0.967; min = -8.527; max = -1.091

*Note: Some table entries were presented with fragmented formatting in the source; numbers above are reproduced exactly as they appear in the provided content.*

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### Appendix IV: Robustness Checks — Static and Dynamic Panel Regressions (selected coefficients and inference)

### Appendix Table 5: Static Panel Regression — Determinants of Risks
- Regression setup: static panel with bank fixed effects and lagged regressors. Robust standard errors in parentheses. Significance: *** p<0.01, ** p<0.05, * p<0.1.
- Selected coefficient estimates (variable = coefficient (standard error) and significance as printed):

- ROAA (%) (dependent in some specifications) = L -0.214*** (0.00552); specification variants: -0.264*** (0.00628); -0.284*** (0.00635); -0.176* (0.00968); -0.467*** (0.00895); -0.500*** (0.00968); 0.000250 (0.00414); 0.00276 (0.00406); -0.00122 (0.00395)

- Non-Interest Income Share (%) = L 0.00893** (0.000414); 0.00789 (0.000533); 0.0137*** (0.000442); 0.0171* (0.000915); -0.00701 (0.000895); 0.0222** (0.000920); 0.0390*** (0.000748); 0.0135 (0.000766); 0.0204*** (0.000766)

- NII Share (%) X Loan-to-Asset Ratio (%) = L -0.000198*** (7.23e-05); -0.000174** (8.77e-05); -0.000212*** (8.14e-05); -0.000264* (0.0000160); 4.18e-05 (0.0000151); -0.000275* (0.0000160); -0.000584*** (0.0000129); -0.000224* (0.0000130); -0.000329** (0.0000134)

- Real GDP Growth Rate (%) = -0.00491*** (0.00151); -0.00562*** (0.00144); -0.00580*** (0.00142); -0.323*** (0.00332); -0.329*** (0.00330); -0.368*** (0.00313); -0.280*** (0.00319); -0.213*** (0.00286); -0.265*** (0.00282)

- ST Interest Rate (%) = -0.000170 (0.00119); 0.01410 (0.00122); 0.00169 (0.00119); 0.00878*** (0.00258); 0.0160*** (0.00191); 0.0186*** (0.00184); 0.00368 (0.00210); -0.00173 (0.00188); 0.00288 (0.00175)

- Gov Structural Balance/Potential GDP (%) = -0.116*** (0.00126); -0.123*** (0.00125); -0.120*** (0.00122); -0.183*** (0.00191); -0.227*** (0.00203); -0.199*** (0.00175); -0.176*** (0.00181); -0.215*** (0.00176); -0.167*** (0.00169)

- Tier 1 Ratio (%) = L -0.00288 (0.00109); 0.000886 (0.00109); -0.00500 (0.000862); -0.107*** (0.00228); -0.0709** (0.00201); -0.0851*** (0.00192); -0.0468*** (0.00192); -0.0404*** (0.00136); -0.0428*** (0.00154)

- Problem Loans Ratio (%) = L 0.0776*** (0.000857); 0.0760*** (0.000972); 0.0752*** (0.000898); 0.110*** (0.00217); 0.0967*** (0.00197); 0.115*** (0.00196); 0.000355 (0.000825); -0.0201** (0.000914); 0.00426 (0.000804)

- Lerner Index (%) = L -0.0121*** (0.000362); -0.0451*** (0.00116); 0.000905 (0.000548)

- Deposit-to-Liability Ratio (%) = L -0.00341 (0.000300); -0.00271*** (0.000668); -0.00291*** (0.000484)

- Leverage Ratio = L -0.000696 (0.000251); 0.000380 (0.000325); 0.000858*** (0.000177)

- Observations: 3,086; 3,128; 3,133; 4,062; 4,113; 4,184; 5,052; 5,034; 5,108 (as printed across specifications)
- Robust standard errors reported in parentheses. Significance legend repeated: *** p<0.01, ** p<0.05, * p<0.1.

### Appendix Table 6
- Appendix Table 6 presents the dynamic panel regression with year fixed effects (no numeric coefficients printed in the excerpt).

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### Appendix Tables 7–9: Robustness Checks for Determinants of Profitability (selected results)

### Appendix Table 7: Static panel regression with bank fixed effects and lagged regressors (selected coefficients)
- Real GDP Growth Rate (%) — coefficients across specifications: 0.100*** (0.00235); 1.702*** (0.395); 0.0948*** (0.00182); 0.0913*** (0.00154); 2.245** (0.914)
- ST Interest Rate (%) — 0.00124 (0.00250); -0.503 (0.547); 0.125*** (0.00290); 0.159*** (0.00239); 10.40*** (1.771)
- Gov Structural Balance/Potential GDP (%) — 0.0342*** (0.00131); 0.653** (0.271); 0.0392*** (0.00131); 0.0351*** (0.00112); 3.917*** (0.824)
- Claim Growth Rate (%) — 4.09e-05*** (1.08e-05); 0.000205* (0.0000118); 1.77e-05 (1.29e-05); 1.04e-05 (1.12e-05); 0.000280 (0.0000605)
- Problem Loans Ratio (%) = L -0.0421*** (0.000798); -0.541*** (0.141); -0.0379*** (0.000688); -0.0291*** (0.000647); -4.197*** (0.738)
- Cost-to-Income (%) = L -0.00756*** (0.000185); -0.0806*** (0.00211); -0.00518*** (0.000156); -0.00491*** (0.000147); -0.144*** (0.0563)
- Cost of Funds (%) = L -0.103* (0.00548); 0.661 (1.141); -0.260*** (0.00614); -0.187*** (0.00491); -13.87*** (3.478)
- Log(Assets) = L -0.216*** (0.00560); -3.481*** (0.820); -0.209*** (0.00664); -0.270*** (0.00703); -12.40*** (4.516)
- Observations across columns: 4,196; 4,192; 4,196; 4,192; 9,21 (as printed; note formatting fragmentation)
- R-squared values: 0.153; 0.117; 0.204; 0.214; 0.328

### Appendix Table 8
- Appendix Table 8 presents the dynamic panel regression with year fixed effects for profitability (no numeric coefficients printed in the excerpt).

### Appendix Table 9: Dynamic panel regression with pre-tax profitability measures (selected coefficients)
- Problem Loans Ratio (%) — coefficients: -0.000598*** (0.000137); -0.00165 (0.000811); -0.00108 (0.000664); -0.00199*** (0.000730)
- Cost-to-Income (%) — -0.000418*** (5.26e-05); -0.00130** (0.000589); -0.00162*** (0.000341); -0.00215*** (0.000374)
- Cost of Funds (%) — -0.00123*** (0.0000493); 0.0891 (0.130); -0.113** (0.00446); -0.0676 (0.00424)
- Real GDP Growth Rate (%) — 0.0000674*** (0.0000128); 0.00114 (0.000554); 0.00808*** (0.000121); 0.00755*** (0.000136)
- ST Interest Rate (%) — 0.000597* (0.0000325); -0.00689 (0.000984); -0.00161 (0.000309); -0.00287 (0.000303)
- Gov Structural Balance/Potential GDP (%) — 0.000214*** (0.000107); 0.0230** (0.00222); 0.00456 (0.000109); 0.00261** (0.000119)
- Claim Growth Rate (%) — 3.20e-07* (1.93e-07); 5.23e-06 (4.77e-06); 2.31e-06 (1.50e-05); 6.30e-06 (1.51e-05)
- Log(Assets) — -0.000137*** (0.0000294); -0.00742 (0.000586); -0.00250 (0.000213); -0.00377 (0.000254)
- pre-Tax ROAA = L 0.0818 (0.00671)
- pre-Tax ROAE = L 0.0157*** (0.000738)
- pRAROAA = L 0.731*** (0.00332)
- pRAROAE = L 0.683*** (0.00291)
- Observations: 4,351; 4,384; 4,351; 4,384 (as printed)
- Hansen p-Value: 0.0931; 0.0388; 0.234; 0.225

- Robust standard errors in parentheses. Significance legend repeated.

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### Key methodological notes from the appendix
- Robustness checks include static panel regressions with bank fixed effects and lagged regressors, and dynamic panel regressions with year fixed effects.
- Robust standard errors reported in parentheses throughout.
- Significance notation: *** p<0.01, ** p<0.05, * p<0.1.

*Source: wp1905 - Appendix Table 3: Macroeconomic Variables (extracted content from the supplied PDF).*

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_Source: https://www.imf.org/-/media/files/publications/wp/2019/wp1905.pdf_