## _wp04149 - 1. Summary of Statistics

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---

### Introduction and scope
- Study period: December 1995–December 2000.
- Sample: a large panel of more than 100 banks from Argentina.
- Objective: examine the effects of bank consolidation on bank performance in Argentina using methodology similar to Demsetz and Strahan (1994).
- Performance measures analyzed: returns (accounting measures) and insolvency risk (including Z-ROA/Z-ROE measures referenced elsewhere in the document).

### Key findings on consolidation and performance
- Overall conclusion: consolidation had a beneficial effect on bank performance in Argentina over the sample period.
- Returns:
  - A merger increases a bank’s return on equity by 4.53 percentage points.
  - A merger increases risk-adjusted return on equity by 0.30 points.
  - A privatization increases return on equity by 23.1 percentage points.
  - A privatization increases risk-adjusted return on equity by 2.3 points.
  - A bank acquisition reduces return on equity by 2.62 percentage points.
  - Bank acquisitions do not seem to have any significant effect on risk-adjusted return.
- Insolvency risk:
  - A merger reduces a bank’s insolvency risk by 0.22 point.
  - A privatization reduces a bank’s insolvency risk by 0.51 point.
  - Bank acquisitions seemed to have no impact on insolvency risk.

### Context: Argentine banking sector evolution and structural drivers
- Historical and policy milestones:
  - Bonex Plan announced January 1, 1990 (rescheduling of domestic-currency CDs into ten-year dollar-denominated bonds, "BONEX").
  - Convertibility Plan introduced March 1991 (currency board fixing exchange rate at one to one with the U.S. dollar, deregulation, trade liberalization, privatization).
- Monetary and financial indicators:
  - Ratio of broad money to GDP: 25 percent of GDP in 1980; less than 6 percent in 1990; rose to 20 percent by late 1994.
  - Deposits fell by about 18 percent between November 1994 and March 1995.
  - Share of peso deposits in total deposits dropped from 49 percent in late 1994 to 44 percent when re-intermediation started.
- Market structure shifts:
  - Large banks (assets > 1 percent of market) increased their market share in assets from 71 percent to 85 percent during the analyzed period.
  - Small banks (assets ≤ 1 percent of market) saw market share drop from 29 percent to 15 percent.
  - The share of system assets controlled by foreign institutions increased from 18 percent in 1994 to almost 50 percent by the end of 1999.
- Crisis and policy responses:
  - Tequila crisis (Mexican crisis onset) led to bank runs and capital flight in Argentina; reforms and a new IMF-supported program helped restore confidence by mid-1995.
  - Government and central bank interventions included liquidity support (lowering reserve requirements on DCDs and FCDs), rediscount and repo facilities, creation of a trust fund for provincial bank restructuring and privatization, a trust fund for bank capitalization, and a new deposit insurance scheme covering DCDs and FCDs up to specified ARG$ amounts.

### Consolidation trends and structural change (1998 figure highlights)
- Number of small banks fell from 105 to 66 (a 37 percent loss).
- Number of large banks did not shift materially, fluctuating around an average of 22.
- Number of the largest large banks (each bank asset > 5 percent of total assets) jumped from 4 to 7, that jump occurring in 1998.
- Overall structural change in the Argentine banking system during the period:
  - Reduced the number of banks by 27 percent.
  - Increased the amount of assets in the banking system by 20 percent.
  - Left the number of branches largely the same.
- Small banks were often “swallowed up or closing”; large banks and the largest large banks drove the measured changes.

### Data, sample, and dependent variables
- Data coverage: December 1995 to December 2000.
- Data source: monthly balance sheet data for more than 100 Argentine banks; each balance sheet reports more than 100 items.
- Unbalanced panel: total number of banks = 98; total observations = 4,742.
- Balanced panel (banks with observations from December 1995 to December 2000): number of banks = 50; observations = 3,947.
- Dependent/primary performance measures used:
  - ROE (return on equity)
  - ROA (return on assets)
  - Z-ROE (ROE adjusted for return variance)
  - Z-ROA (banking-industry insolvency-risk measure constructed using De Nicoló (2000) framework)

### Summary statistics (selected from Table 1)
- ROE (in percent): Mean = 4.04; Standard Deviation = 1.90
- ROA (in percent): Mean = 0.61; Standard Deviation = 0.35
- Crisk (basis points): Mean = 612.75; Standard Deviation = 175.64
- Emi (index): Mean = 110.58; Standard Deviation = 8.68
- Repo (in percent): Mean = 36.09; Standard Deviation = 5.91
- M3res: Mean = 3.03; Standard Deviation = 0.15
- Shaset: Mean = 0.01; Standard Deviation = 0.02
- NPL/Loan (in percent): Mean = 8.03; Standard Deviation = 1.56
- Lev (in percent): Mean = 905.46; Standard Deviation = 183.58
- Govbond: Mean = 0.29; Standard Deviation = 0.03
- Rsloan: Mean = 0.10; Standard Deviation = 0.01
- Aloan: Mean = 0.08; Standard Deviation = 0.01
- Dsfloan: Mean = 0.12; Standard Deviation = 0.02
- Ploan: Mean = 0.03; Standard Deviation = 0.01
- Perloan: Mean = 0.11; Standard Deviation = 0.01

### Econometric methodology (overview)
- Baseline bank-return generating model: r_it = α + x’_it β + u_it, estimated with fixed effects and GLS to account for heteroscedasticity; bank returns measured primarily by ROE.
- Alternative specification: include factors f_t from factor analysis — model r_it = α + f’_t δ + x’_it β + u_it (two-step: factor analysis then GLS).
- Risk-adjusted returns tested via Sharpe-like ratio: r_it / σ^2_it = α + x’_it β + u_it; σ^2_it estimated by individual GARCH(1,1) for each bank.
- Unit-root behavior: Dickey-Fuller tests showed unit roots for many macro series (except production index); differencing applied where appropriate.
- Causality: Granger-causality tests show weak evidence for causality between degree of bank consolidation and dependent variables.
- Panels: results checked on unbalanced panel and on balanced subset of 50 banks.

### Key regression findings (selected coefficients and significance)
- From Table 3 (Feasible GLS with unit root correction; Dependent variable: ROE; Unbalanced panel; No. obs. 4,742):
  - Ch_shaset = 7.363* (t = 4.14) and alternative 7.170* (t = 4.06)
  - Ch_Crisk = -2.699* (t = -2.80)
  - Ch_Div1 = -5.516* (t = -3.26)
  - Ch_lev = -5.67* (t = -5.01) and alternative -5.480* (t = -4.87)
  - Ch_aloan = 18.242* (t = 1.97)
  - Ch_dsfloan = 13.707* (t = 2.29)
  - DMerger = 4.53* (t = 9.54)
  - DAcqui = -2.615* (t = -2.51)
  - DPrivat = 23.077* (t = 11.20)
  - DDisapp = -4.47* (t = -7.64)
- From Table 5 (Feasible GLS with unit root correction; Dependent variable: Z-ROE; Unbalanced panel; No. obs. 4,372):
  - Ch_shaset = 0.65* (t = 4.93)
  - Ch_Crisk = -0.24* (t = -2.97)
  - Emi = 0.01* (t = 2.62)
  - Ch_Div1 = -0.48* (t = -3.77)
  - Ch_lev = -0.44* (t = -5.85)
  - Ch_aloan = 2.05* (t = 2.09)
  - Ch_dsfloan = 1.86* (t = 2.94)
  - DMerger = 0.30* (t = 5.18)
  - DAcqui = 0.15 (t = 0.74) [not significant]
  - DPrivat = 2.26* (t = 2.26)
  - DDisapp = 1.02 (t = 1.23) [not significant]
  - Log likelihood = -5,410.10 (one-step); -5,414.40 (principal component)

### Appendix II — GARCH(1,1) variance estimation and Z-ROA results
- The time series of variances is estimated for each bank using a GARCH (1,1) model.
- Table 6 (Feasible GLS Estimates with Unit Root Correction: Dependent Variable: Z-ROA, Unbalanced Panel; No. obs.: 4,372) — selected estimated coefficients:
  - Const.: 0.414*  (2.56)  and 0.488*  (11.11)
  - Ch_Crisk: -0.171*  (-2.33)
  - Ch_repo: 0.015*  (1.99)
  - Ch_Factor1: 1.12e-08*  (3.18)
  - Ch_shaset: 0.598*  (4.57)  and 0.591*  (4.56)
  - Ch_Div1: -0.635*  (-5.46)  and -0.632*  (-5.41)
  - Ch_lev: -0.587*  (-8.02)  and -0.589*  (-8.08)
  - Ch_dsfloan: 1.367*  (2.21)  and 1.399*  (2.26)
  - DMerger: 0.224*  (9.54)  and 0.217*  (9.04)
  - DAcqui: -0.094  (-1.62)  and -0.108  (-1.86)
  - DPrivat: 0.511*  (10.91)  and 0.509*  (10.92)
  - DDisapp: -0.319*  (-8.91)  and -0.326*  (-9.06)
- The null hypothesis that bank consolidation has no effect on a bank’s solvency is rejected at the 5 percent level in the unbalanced panel specifications, implying bank consolidation significantly reduces solvency risk.
- Balanced-panel estimations weaken some results: balancing removes many banks with lower performance (those that benefit most from consolidation), increasing average returns in the sample and weakening the measured correlation between returns and consolidation.

### Interpretation, robustness, and substantive conclusions
- Bank consolidation (measured as a bank’s share of total banking-industry assets, Shaset) is positively and significantly associated with higher ROE and higher risk-adjusted returns (Z-ROE) in the primary (unbalanced) specifications.
- Mergers and privatizations are associated with improved returns (DMerger and DPrivat positive and significant); acquisitions and bank disappearance are associated with lower returns (DAcqui and DDisapp negative and significant for ROE).
- Among macroeconomic risk factors, country risk (Crisk) is the most significant negative influence on ROE, Z-ROE, and Z-ROA.
- Among bank-specific risk factors, leverage (Lev) and loan-portfolio concentration/diversification (Div1) are significant determinants of performance and insolvency risk.
- Granger-causality tests provide weak evidence of causality from consolidation to performance; consolidation is treated as largely exogenous in main specifications.
- Overall inference: consolidation across the Argentine banking system during December 1995–December 2000 increased measured banking-sector performance (both raw ROE and risk-adjusted returns), with the consolidation process driven largely by large banks acquiring or absorbing smaller banks.

*Source: _wp04149 - 1. Summary of Statistics (PDF chapter).*

### 1. Summary of Statistics ...............................................................................................

### _wp04149 - 1. Summary of Statistics

### Introduction and scope
- Study period: December 1995–December 2000.
- Sample: a large panel of more than 100 banks from Argentina.
- Objective: examine the effects of bank consolidation on bank performance in Argentina using methodology similar to Demsetz and Strahan (1994).
- Performance measures analyzed: returns (accounting measures) and insolvency risk (including Z-ROA/Z-ROE measures referenced elsewhere in the document).

### Key findings on consolidation and performance
- Overall conclusion: consolidation had a beneficial effect on bank performance in Argentina over the sample period.
- Returns:
  - A merger increases a bank’s return on equity by 4.53 percentage points.
  - A merger increases risk-adjusted return on equity by 0.30 points.
  - A privatization increases return on equity by 23.1 percentage points.
  - A privatization increases risk-adjusted return on equity by 2.3 points.
  - A bank acquisition reduces return on equity by 2.62 percentage points.
  - Bank acquisitions do not seem to have any significant effect on risk-adjusted return.
- Insolvency risk:
  - A merger reduces a bank’s insolvency risk by 0.22 point.
  - A privatization reduces a bank’s insolvency risk by 0.51 point.
  - Bank acquisitions seemed to have no impact on insolvency risk.

### Context: Argentine banking sector evolution and structural drivers
- Historical and policy milestones:
  - Bonex Plan announced January 1, 1990 (rescheduling of domestic-currency CDs into ten-year dollar-denominated bonds, "BONEX").
  - Convertibility Plan introduced March 1991 (currency board fixing exchange rate at one to one with the U.S. dollar, deregulation, trade liberalization, privatization).
- Monetary and financial indicators:
  - Ratio of broad money to GDP: 25 percent of GDP in 1980; less than 6 percent in 1990; rose to 20 percent by late 1994.
  - Deposits fell by about 18 percent between November 1994 and March 1995.
  - Share of peso deposits in total deposits dropped from 49 percent in late 1994 to 44 percent when re-intermediation started.
- Market structure shifts:
  - Large banks (assets > 1 percent of market) increased their market share in assets from 71 percent to 85 percent during the analyzed period.
  - Small banks (assets ≤ 1 percent of market) saw market share drop from 29 percent to 15 percent.
  - The share of system assets controlled by foreign institutions increased from 18 percent in 1994 to almost 50 percent by the end of 1999.
- Crisis and policy responses:
  - Tequila crisis (Mexican crisis onset) led to bank runs and capital flight in Argentina; reforms and a new IMF-supported program helped restore confidence by mid-1995.
  - Government and central bank interventions included liquidity support (lowering reserve requirements on DCDs and FCDs), rediscount and repo facilities, creation of a trust fund for provincial bank restructuring and privatization, a trust fund for bank capitalization, and a new deposit insurance scheme covering DCDs and FCDs up to specified ARG$ amounts (details in the source).

### Interpretation and comparative literature notes
- The Argentine experience may differ from mature-market consolidation dynamics because consolidation in emerging markets is often crisis- and privatization-driven.
- Prior literature:
  - Mixed evidence in mature markets on consolidation’s effects on risk and performance (selected studies cited in the source).
  - Recent emerging market studies referenced suggest consolidation increases banking risk with limited impact on competition, though outcomes may depend on drivers of consolidation (crisis/privatization vs. corporate behavior).
- This study’s contribution: provides empirical evidence from Argentina showing consolidation—particularly mergers and privatizations—was associated with higher returns and lower insolvency risk over the December 1995–December 2000 period, while acquisitions showed weaker or negative return effects and no discernible risk impact.

*Source: _wp04149 - 1. Summary of Statistics (PDF chapter).*

### 1998. Figure 1.D shows that during the analyzed period, the number of small banks fell from

### _wp04149 - 1998. Figure 1.D shows that during the analyzed period, the number of small banks fell from

### Consolidation trends and structural change
- Number of small banks fell from 105 to 66 (a 37 percent loss).
- Number of large banks did not shift materially, fluctuating around an average of 22.
- Number of the largest large banks (each bank asset > 5 percent of total assets) jumped from 4 to 7, that jump occurring in 1998.
- Overall structural change in the Argentine banking system during the period:
  - Reduced the number of banks by 27 percent.
  - Increased the amount of assets in the banking system by 20 percent.
  - Left the number of branches largely the same.
- Small banks were often “swallowed up or closing”; large banks and the largest large banks drove the measured changes.

### Data and sample
- Data coverage: December 1995 to December 2000.
- Data source: monthly balance sheet data for more than 100 Argentine banks; each balance sheet reports more than 100 items.
- Unbalanced panel: total number of banks = 98; total observations = 4,742.
- Balanced panel (banks with observations from December 1995 to December 2000): number of banks = 50; observations = 3,947.
- Dependent/primary performance measures used:
  - ROE (return on equity)
  - ROA (return on assets)
  - Z-ROE (ROE adjusted for return variance)
  - Z-ROA (banking-industry insolvency-risk measure constructed using De Nicoló (2000) framework)

### Summary statistics (Table 1)
- ROE (in percent): Mean = 4.04; Standard Deviation = 1.90
- ROA (in percent): Mean = 0.61; Standard Deviation = 0.35
- Crisk (basis points): Mean = 612.75; Standard Deviation = 175.64
- Emi (index): Mean = 110.58; Standard Deviation = 8.68
- Repo (in percent): Mean = 36.09; Standard Deviation = 5.91
- M3res: Mean = 3.03; Standard Deviation = 0.15
- Shaset: Mean = 0.01; Standard Deviation = 0.02
- NPL/Loan (in percent): Mean = 8.03; Standard Deviation = 1.56
- Lev (in percent): Mean = 905.46; Standard Deviation = 183.58
- Govbond: Mean = 0.29; Standard Deviation = 0.03
- Rsloan: Mean = 0.10; Standard Deviation = 0.01
- Aloan: Mean = 0.08; Standard Deviation = 0.01
- Dsfloan: Mean = 0.12; Standard Deviation = 0.02
- Ploan: Mean = 0.03; Standard Deviation = 0.01
- Perloan: Mean = 0.11; Standard Deviation = 0.01

### Econometric methodology (overview)
- Baseline bank-return generating model: r_it = α + x’_it β + u_it, estimated with fixed effects and GLS to account for heteroscedasticity; bank returns measured primarily by ROE.
- Alternative specification: include factors f_t from factor analysis — model r_it = α + f’_t δ + x’_it β + u_it (two-step: factor analysis then GLS).
- Risk-adjusted returns tested via Sharpe-like ratio: r_it / σ^2_it = α + x’_it β + u_it; σ^2_it estimated by individual GARCH(1,1) for each bank.
- Unit-root behavior: Dickey-Fuller tests showed unit roots for many macro series (except production index); differencing applied where appropriate.
- Causality: Granger-causality tests show weak evidence for causality between degree of bank consolidation and dependent variables.
- Panels: results checked on unbalanced panel and on balanced subset of 50 banks.

### Key regression findings (selected coefficients and significance; significance at 5 percent level indicated by *)
- Table 3 (Feasible GLS with unit root correction; Dependent variable: ROE, unbalanced panel; No. obs. 4,742)
  - Ch_shaset = 7.363* (t = 4.14) and alternative specification Ch_shaset = 7.170* (t = 4.06)
  - Ch_Crisk = -2.699* (t = -2.80)
  - Emi = 0.028 (t = 1.49) [not significant at 5% in this column]
  - Ch_repo = 0.173 (t = 1.81)
  - Ch_Div1 = -5.516* (t = -3.26)
  - Ch_NPL = -0.047 (t = -0.42)
  - Ch_lev = -5.67* (t = -5.01) and alternative -5.480* (t = -4.87)
  - Ch_Govbond = 6.064 (t = 1.75)
  - Ch_rsloan = 20.461 (t = 0.95)
  - Ch_aloan = 18.242* (t = 1.97)
  - Ch_dsfloan = 13.707* (t = 2.29)
  - DMerger = 4.53* (t = 9.54)
  - DAcqui = -2.615* (t = -2.51)
  - DPrivat = 23.077* (t = 11.20)
  - DDisapp = -4.47* (t = -7.64)

- Table 5 (Feasible GLS with unit root correction; Dependent variable: Z-ROE (Sharpe ratio), unbalanced panel; No. obs. 4,372)
  - Ch_shaset = 0.65* (t = 4.93) (one-step and principal-component columns)
  - Ch_Crisk = -0.24* (t = -2.97)
  - Emi = 0.01* (t = 2.62)
  - Ch_repo = 0.01 (t = 1.22)
  - Ch_M3res = -0.10 (t = -0.50)
  - Sdroehat = -0.13 (t = -1.73) and -0.15 (t = -1.81)
  - Ch_Div1 = -0.48* (t = -3.77)
  - Ch_lev = -0.44* (t = -5.85)
  - Ch_aloan = 2.05* (t = 2.09)
  - Ch_dsfloan = 1.86* (t = 2.94)
  - Ch_ploan dropped due to collinearity
  - DMerger = 0.30* (t = 5.18)
  - DAcqui = 0.15 (t = 0.74) [not significant]
  - DPrivat = 2.26* (t = 2.26)
  - DDisapp = 1.02 (t = 1.23) [not significant]
  - Log likelihood = -5,410.10 (one-step); -5,414.40 (principal component)

- Additional robustness checks:
  - Table 4 (GLS without unit root correction) yields qualitatively similar results on consolidation effects though some coefficient signs and t-statistics differ and are noted as inflated in that specification.
  - Two-step regression following Demsetz and Strahan (1995) produced very similar results (not reported in full).

### Interpretation and substantive conclusions
- Bank consolidation (measured as a bank’s share of total banking-industry assets, Shaset) is positively and significantly associated with higher ROE and higher risk-adjusted returns (Z-ROE).
- Mergers and privatizations are associated with improved returns (DMerger and DPrivat positive and significant); acquisitions and bank disappearance are associated with lower returns (DAcqui and DDisapp negative and significant for ROE).
- Higher country risk and higher leverage reduce ROE and Z-ROE (Ch_Crisk negative; Ch_lev negative).
- Loan-concentration measures (Ch_Div1) negatively affect performance measures.
- Some bank-specific loan-category changes (Ch_aloan, Ch_dsfloan) show positive associations with Z-ROE in the regressions where they are significant.
- Granger-causality tests provide weak evidence of causality from consolidation to performance; consolidation may be treated as largely exogenous in the main specifications.
- Overall inference: consolidation across the Argentine banking system during December 1995–December 2000 increased measured banking-sector performance (both raw ROE and risk-adjusted returns), with the consolidation process driven largely by large banks acquiring or absorbing smaller banks.

*Source: IMF working paper content unit _wp04149 (figures, tables, and text excerpts provided).*

### Appendix II. The time series of variances is estimated for each bank using a GARCH (1,1)

### _wp04149 - Appendix II. The time series of variances is estimated for each bank using a GARCH (1,1)

### Estimation results and robustness checks
- The time series of variances is estimated for each bank using a GARCH (1,1) model.
- Results in Table 6 are consistent, overall, with those in Table 3:
  - The macroeconomic variable of country risk and the bank-specific variable of leverage have negative and significant effects on Z-ROA.
  - Dummy variables (except for the acquisition dummy) are significant; estimated coefficients support a relation between bank consolidation and solvency risk.
  - The null hypothesis that bank consolidation has no effect on a bank’s solvency is rejected at the 5 percent level, implying bank consolidation significantly reduces solvency risk.
- When model (1) is estimated with unit root correction on the balanced panel:
  - Results are significantly weaker.
  - The estimated coefficient for ch_shaset is positive, but the consolidation variable has no significant effect on bank returns.
  - Only country risk and the bank merger dummy variable tend to be significant for different specifications.
- When model (3) for Z-ROA is estimated on the balanced panel:
  - A positive but insignificant effect of bank consolidation on bank insolvency is found.
  - More risk factor variables become significant (country risk, portfolio diversification, leverage, and the merger and acquisition dummies), with expected signs.
  - The significance of dummy variables offers indirect evidence of a positive effect of bank consolidation on bank returns.

### Balanced vs. unbalanced panel issues
- By balancing the panel, the sample loses 49 percent of the banks and 38 percent of the observations.
- Balancing tends to remove many of the banks with lower performance measures (the banks that benefit most from consolidation), which:
  - Increases average bank returns in the sample while the bank consolidation variable remains constant.
  - Weakens the correlation between bank returns and bank consolidation.
- Conclusion: a major effect of bank consolidation is the disappearance of small and weak banks from the sample; elimination of weak banks is part of the consolidation process.

### Key statistics from Table 6 (Feasible GLS Estimates with Unit Root Correction: Dependent Variable: Z-ROA, Unbalanced Panel)
- Const.: 0.414*  (2.56)  and 0.488*  (11.11)
- Ch_Crisk: -0.171*  (-2.33)
- Emi: (0.00)2  (1.25)
- Ch_repo: 0.015*  (1.99)
- Ch_M3res: -0.038  (-0.19)
- Ch_Factor1: 1.12e-08*  (3.18)
- Ch_shaset: 0.598*  (4.57)  and 0.591*  (4.56)
- Ch_Div1: -0.635*  (-5.46)  and -0.632*  (-5.41)
- Ch_NPL: -0.004  (-0.55)  and -0.004  (-0.62)
- Ch_lev: -0.587*  (-8.02)  and -0.589*  (-8.08)
- Ch_Govbond: 0.376  (1.51)  and 0.363  (1.46)
- Ch_rsloan: 1.677  (1.33)  and -1.657  (-1.31)
- Ch_aloan: 0.96  (1.43)  and 0.875  (1.29)
- Ch_dsfloan: 1.367*  (2.21)  and 1.399*  (2.26)
- Ch_ploan: 3.123  (1.76)  and 3.222  (1.833)
- Ch_peloan: -0.679  (-0.98)  and -0.737  (-1.06)
- DMerger: 0.224*  (9.54)  and 0.217*  (9.04)
- DAcqui: -0.094  (-1.62)  and -0.108  (-1.86)
- DPrivat: 0.511*  (10.91)  and 0.509*  (10.92)
- DDisapp: -0.319*  (-8.91)  and -0.326*  (-9.06)
- No. obs.: 4,372
- Note: * Significant at the 5 percent level. T-statistics in parenthesis.

### Main conclusions and quantified effects
- Sample and period: a large panel of more than 100 banks from Argentina, December 1995 to December 2000.
- Overall finding: a positive and significant effect of bank consolidation on bank performance:
  - Bank returns increase with consolidation, and insolvency risk is reduced.
- Specific quantified effects:
  - A merger increases a bank’s return on equity and risk-adjusted return on equity by 4.53 percentage points and 0.30 points, respectively.
  - A privatization increases return on equity and risk-adjusted return on equity by 23.1 percentage points and 2.3 points, respectively.
  - An acquisition reduces return on equity by 2.62 percentage points.
  - Acquisitions have no significant effect on risk-adjusted return.
  - A bank’s insolvency risk is reduced significantly through:
    - Mergers: 0.22 point reduction.
    - Privatizations: 0.51 point reduction.
  - Acquisitions appear to have no impact on insolvency risk.
- Among macroeconomic risk factors, country risk is the most significant.
- Among bank-specific risk factors, leverage and loan portfolio diversification are the most significant.

### Appendix I — Data definitions (selected)
- Variables preceded by Ch indicate first differences to control for unit root characteristics.
- Dependent variables: ROE, Z-ROE, Z-ROA.
- Macro-risk factors:
  - Country Risk (Crisk): an increase is expected to affect ROE, Z-ROE, and Z-ROA negatively.
  - Industrial Production (Emi): industrial production index; proxy for GDP growth; increase expected to enhance performance.
  - Central Bank Reserves (M3res): ratio between M3 and central bank international reserves; trend increases reflect higher risk.
  - Liquid Funds Available (Repo): ratio of liquid fund over total deposit; expected positive effect.
  - Factor 1: constructed using a factor model to reduce number of aggregate macroeconomic risk factors.
- Bank-specific risk factors:
  - Loan Portfolio Diversification (Div1): Herfindahl-Hirschman Index across loan types; a fall implies greater diversification and improved performance.
  - NonPerforming Loan (NPL): ratio of nonperforming loans over total loans; reduction expected to improve performance.
  - Leverage (Lev): ratio between a bank’s liability and a bank’s equity; higher leverage expected to reduce Z-ROA, increase ROE, and leave Z-ROE unaffected in equilibrium.
  - Government Bonds Holdings (Govbond): bank’s government bond holdings; ambiguous effects depending on country risk changes.
  - Loan-type ratios: Rsloan (Mortgage), Aloan (Overdraft loans), Dsfloan (Discount papers), Ploan (Loans with real collateral), Perloan (Personal loans).
  - Dummies: Dmerger (1 once merger takes place), Dacqui (1 once acquisition takes place), Dprivat (1 once a public bank becomes private), Ddisapp (1 before the bank disappears).

### Appendix II — Z-ROA definition
- Let K represent the equity asset ratio and r represent return on assets. Then,
  - Prob( r ≤ -K ) = ∫_{-∞}^{-K} ƒ(r) dr.
- Using Chebishev’s inequality,
  - Prob (r ≤ -K ) ≤ σ^2 / ( μ+ K )^2 = 1 / (Z-ROA)^2,
  - where Z-ROA = (μ + K)/σ.
- Notes:
  - (i) Z- ROA: A higher value implies lower insolvency risk.
  - (ii) Z-ROA measures the number of standard deviations that returns have to fall in order to deplete equity.

*Content derived from _wp04149 - Appendix II. The time series of variances is estimated for each bank using a GARCH (1,1).*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/wp/2004/_wp04149.pdf_