## Annex 1. Economies of Scale and Scope in Banks

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---

### Evidence on economies of scale and scope
- Evidence is described as inconclusive:
  - Early studies: economies of scale limited to relatively small banks; no evidence beyond US$10 billion to US$50 billion in assets.
  - More recent studies: find economies of scale for large banks; information technology and scalable market-based operations may have increased optimal bank size.
- Cost-economy estimates (preserve numeric values exactly):
  - Kovner, Vickery, and Zhou (2013) estimate total value of cost economies in U.S. banking system for banks over US$50 billion in assets: between US$16 billion and US$45 billion a year, corresponding to 0.1 to 0.25 percent of GDP (or 0.1 to 0.25 percent of total U.S. bank holding companies assets per year).
- Diversification-adjusted estimates and implications:
  - Wheelock and Wilson (2012) and Hughes and Mester (2013): 1 percent increase in bank size increases costs by only 0.95 percent for both small and large banks.
  - Implication reported: cost of splitting the four largest U.S. banks so each manages not more than $1 trillion in assets would be over US$70 billion a year; making banks even smaller would cost more.

### Caveats and interpretation
- Assumptions behind cost estimates:
  - Estimates assume large banks’ higher risk tolerance is socially optimal and that social value of market-based activities equals that of traditional lending.
- Agency costs and returns to scope:
  - Negative returns to scope when banks move into market-based activities appear driven by agency costs, not technology.
  - Evidence of negative returns to scope: lower market valuations, higher risk, lower risk-adjusted returns — suggesting potential costs for shareholders and other stakeholders including taxpayers.
  - Counterpoint noted: market-based activities may create surplus for bank customers; in that case returns to scope may still be positive from a social welfare perspective.

### Policy-relevant implications summarized in the annex
- Economies of scale and scope may exist for large banks, but:
  - Magnitudes reported suggest cost economies are nontrivial but limited relative to GDP and total banking assets.
  - Potential gains from scale need to be weighed against increased systemic risk associated with large banks (as discussed in the main analysis).
- Relevance for policy tools:
  - The modest size of estimated economies of scale supports the feasibility of policy tools (e.g., capital surcharges, activity restrictions, resolvability measures) that may reduce bank size or complexity without imposing prohibitive economic costs — subject to caveats about assumptions and distributional effects noted above.

*Source: _sdn1404 - Annex 1. Economies of Scale and Scope in Banks (page 24)*

### Annex 1. Economies of Scale and Scope in Banks .................................................................24

### Annex 1. Economies of Scale and Scope in Banks

### Document location and context
- Appears on page 24 in the source PDF.
- Listed immediately before:
  - "Annex 2. Corporate Governance Challenges in Large Banks" (page 25)
  - "Annex 3. The Sample of Banks and Summary Statistics" (page 26)
  - "Annex 4. Estimating Systemic Risk" (page 28)
  - "References" (page 29)

### Notes on available content
- The supplied content unit contains only the annex title and its placement in the table of contents; no substantive findings, data, projections, analysis, or policy recommendations from Annex 1 are present in the provided text.
- No numeric results, methodological details, or recommendations from Annex 1 are available in the provided excerpt.

*Source: _sdn1404 - Annex 1. Economies of Scale and Scope in Banks (page 24)*

### EXECUTIVE SUMMARY

### _sdn1404 - EXECUTIVE SUMMARY

### Background and context
- Large banks grew substantially in size and became more involved in market-based activities since the late 1990s; information technology and deregulation are identified as key drivers.
- Banking systems became more global and interconnected; large banks increased in size, complexity, and market-based operations (proprietary trading, market-making, securitized holdings, security dealing, custodian services, advisory, hedging).
- The analysis uses a comprehensive global sample of publicly traded banks with assets of at least US$10 billion (sample: 370 banks from 52 countries).

### Descriptive facts about large banks
- Large banks, relative to small banks, on average have:
  - Lower capital (measured by risk-weighted capital ratios and a simple leverage ratio).
  - Less-stable funding (lower share of deposits in total liabilities).
  - Greater involvement in market-based activities (lower loans/assets; higher noninterest income share).
  - Greater organizational complexity (more subsidiaries; number of subsidiaries expressed as log(1 + number of subsidiaries)).
- Correlations among these dimensions are reported (sample, end-2011; banks with assets > US$10 billion). Selected correlation coefficients from Table 2:
  - Log(Assets) with Tier 1 ratio: -0.21***
  - Log(Assets) with Deposits/Assets: -0.49***
  - Log(Assets) with Loans/Assets: -0.29***
  - Log(Assets) with Noninterest income: 0.39***
  - Log(Assets) with Log(Subsidiaries): 0.70***
  - Leverage correlations include: Leverage with Tier 1 ratio: -0.41***; Leverage with Log(Assets): 0.36***.
- Notes on measures and examples:
  - Assets are in log billions of U.S. dollars (log assets = 2 corresponds to US$7.4 billion; log assets = 5 corresponds to US$148 billion).
  - Funding fragility is defined as deposits from other banks, other deposits, and short-term borrowing as a fraction of total deposits plus money market and short-term funding.

### Empirical strategy and risk measures
- Research question: Are large banks riskier or do they create more systemic risk than small banks, and which bank characteristics (size, capital, funding stability, market-based activities, organizational complexity) drive risk?
- Two dimensions of risk analyzed:
  - Individual bank risk: measured via bank stock returns during the 2007–08 financial crisis (July 2007 to December 2008).
  - Systemic risk contribution: measured by SRISK (based on Brownlees and Engle (2012) and Acharya, Engle, and Richardson (2012)); captures contribution to system-wide distress and incorporates return correlations and bank size.
- Pre-crisis (2006) bank characteristics used as regressors: log assets; Tier 1 ratio and leverage ratio; deposits share and funding fragility index; loans/assets and noninterest income share; log(number of subsidiaries).
- Sample note: the period to end-2008 is chosen to abstract from policy interventions; robustness checks consider July 2007–July 2008.

### Main empirical findings
- Large banks, on average, create more individual and systemic risk than smaller banks, especially when they have:
  - Insufficient capital.
  - Unstable funding.
- Additional findings:
  - Large banks create more systemic risk (but are not individually riskier) when they engage more in market-based activities.
  - Large banks create more systemic risk (but are not individually riskier) when they are more organizationally complex.
- Implications of these empirical patterns:
  - The combination of lower capital, fragile funding, greater market-based activities, and higher complexity suggests a distinct and potentially more fragile business model for large banks.
  - Failures of large banks tend to be more disruptive: they generate liquidity stress in the banking system, their scale- and scope-driven activities are not easily replaced by small banks, and the marginal cost of taxpayer support may increase with required volume.

### Policy implications and recommendations
- Traditional micro-prudential regulation (focused on individual bank risk) may be insufficient for large, systemically important banks; systemic externalities call for additional measures.
- Empirical findings support elements of Basel III:
  - Strengthening bank capital and liquidity requirements.
  - Capital surcharges on systemically important banks that reflect size and complexity (Basel: additional loss absorbency requirement for global systemically important banks; a capital surcharge of up to 2.5%).
  - Basel G-SIB surcharge: finalized as part of Basel III; phase-in period 2016–19.
- Measures to address market-based activities and complexity:
  - Limit risky trading activities (consistent with the Volcker Rule, Vickers, Liikanen proposals).
  - Enhance resolvability (living wills) to facilitate orderly resolution of complex banks and provide ex ante incentives to reduce complexity.
  - Consider measures that explicitly target bank activities and organizational complexity within a macro-prudential framework, because these dimensions raise systemic risk without necessarily increasing individual bank risk.
- Country and regional policy initiatives summarized (status and dates preserved):
  - United States: Volcker Rule — prohibition of proprietary trading within the bank holding company. Part of the U.S. Dodd-Frank Act; implementation beginning in 2015 through 2018.
  - United Kingdom: Vickers Report — ring-fencing retail operations in a separate entity. Part of the Financial Services (Banking Reform) Act 2013, passed by Parliament on December 18, 2013. Final regulations expected to be fully implemented by 2019.
  - European Union: Liikanen Report — prohibition of proprietary trading and supervisory powers to separ ate some high-risk trading activities into a separate legal entity (“subsidiarization”). Legislative proposals: proprietary trading ban would apply as of January 1, 2017 and effective separation of other trading activities would apply as of July 1, 2018.
  - Basel Committee’s Fundamental Review of the Trading Book — increase of capital charges (and other measures to reduce regulatory arbitrage) on assets in the bank’s trading book (in consultation).
- Additional policy levers discussed in the literature and paper:
  - Reduce “too-big-to-fail” subsidies (Farhi and Tirole, 2012; Stein, 2013).
  - Improve bank resolution (Claessens et al., 2011), including contingent capital or bail-in capital.

### Broader implications and uncertainties
- There may be economies of scale and scope in large banks, so optimal bank size is uncertain; explanations for large-bank characteristics include:
  - Economies of scale (diversification, comparative advantage in market-based activities).
  - Too-big-to-fail subsidies (lower cost of debt leading to more leverage and risk-taking).
  - Managerial empire-building and corporate governance shortcomings.
- The paper focuses narrowly on whether large banks are riskier or create more systemic risk and on policy responses; it does not settle the optimal bank size question.
- The paper recognizes that the financial crisis had multiple causes beyond systemic risk from large banks (inefficiencies in certain markets, credit/leverage cycle). It also notes the analysis does not explicitly consider cross-border bank activities, though larger banks with more subsidiaries contribute disproportionately to systemic risk (consistent with conjectures about cross-border risks).

*Source: IMF Executive Summary (._sdn1404 - EXECUTIVE SUMMARY)._*

### 2008. Global sample of stock exchange listed banks, excluding banks with assets below US$10 billion. Column

### _sdn1404 - 2008. Global sample of stock exchange listed banks, excluding banks with assets below US$10 billion. Column

### Individual bank risk: regressions and key statistics
- Dependent variable: Returns July 2007 – Dec 2008 (see regression columns reported).
- Selected regression coefficients (from Table 3 and accompanying text):
  - Return in 2006: 0.0208, 0.0207, -0.165, 0.00256 (standard errors in parentheses in source).
  - Log Assets($): -2.698*, -4.160***, -1.495, -5.238***.
  - Tier 1 Ratio: 1.055, 1.234, 5.400**.
  - Deposits/Assets: 58.64**, 57.15***, 49.17*.
  - Loans/Assets: -50.40***, -47.20***, -21.63, -41.39**.
  - Noninterest Income: 2.501, -2.061, -19.84, -13.52.
  - Log Subsidiaries: 2.176*, 0.760.
  - Leverage (in Column 4): -0.622**.
  - Funding Fragility (in one specification): -20.60**.
  - Observations: 302, 302, 115, 359.
  - R-squared: 0.421, 0.425, 0.531, 0.362.
- Economic magnitudes reported in text:
  - Average bank stock return during the crisis: -45 percent.
  - For every fivefold increase in assets, stock returns would have been 7 percentage points lower.
  - For every 20 percentage point increase in the fraction of funding from deposits, stock returns would have been 12 percentage points higher.
  - An increase in capital ratios for large banks by 2.5 percentage points would imply an increase in stock returns of 13 percentage points.
  - Average stock return for large banks: -55 percent.

### Key findings on individual bank risk (text summary)
- Size per se is an independent factor that drives individual bank risk (Columns 1 and 2).
- Among large banks only (over US$50 billion in assets), size per se ceases to be an independent risk factor; risk is driven by insufficient capital (Column 3).
- Insufficient capital is also a risk factor for investment banks (Column 4).
- Nondepository (or unstable) funding is associated with more bank risk (Columns 1-3). Large banks have less depository funding, compounding their risk.
- Market-based activities do not add to individual bank risk; evidence (via loans-to-assets ratio) suggests more market-based activities may have improved bank performance during the crisis (Columns 1 and 2). This result is driven by a subset of U.S. banks with large exposure to mortgage loans; when restricting to large banks, the result is no longer significant (Column 3).
- Organizational complexity does not appear to be an important driver of individual bank risk (borderline significant in Column 2; not significant in Column 4).

### Systemic risk (SRISK): definition, components, and measurement
- SRISK is defined as a bank’s contribution to the deterioration of the capitalization of the financial system as a whole during a crisis.
- Computed as the dollar value of capital shortfall that a bank is expected to suffer when the U.S. financial stock index falls by 40 percent over six months, expressed in billions of U.S. dollars.
- SRISK is determined by:
  - Bank stock volatility during periods of distress;
  - The covariance of bank stock with the market during periods of distress (distinguishes systemic from individual risk);
  - Bank leverage;
  - Bank size.
- Estimation details:
  - SRISK estimated over July 2007 to December 2008 (stock market data from January 2000 to December 2012 used to estimate underlying pricing model).
  - Annex 4 and accompanying working paper (Laeven, Ratnovski, and Tong, 2013) provide methodological details.
- Table 4: Banks with the Highest SRISK during the 2007–08 Financial Crisis (global sample of stock exchange-listed banks)
  1. Royal Bank of Scotland — United Kingdom
  2. Deutsche Bank — Germany
  3. Barclays — United Kingdom
  4. BNP Paribas — France
  5. Credit Agricole — France
  6. Citigroup — United States
  7. JPMorgan Chase — United States
  8. UBS — Switzerland
  9. ING Groep — Netherlands
  10. Bank of America — United States

### Determinants of systemic risk: regression results and economic magnitudes
- Summary of main empirical results (Table 5 and text):
  - In simple regressions (Columns 1–3), bank size and organizational complexity are significant predictors of SRISK.
  - An increase in the number of subsidiaries by 5 from its average of 30 implies an increase in SRISK of US$3 billion (50 percent of its average of US$6 billion).
  - Including interactions of structural variables with bank size (Columns 4–6) yields:
    - Large banks contribute more to systemic risk when they have less capital.
    - Large banks contribute more to systemic risk when they have fewer deposits.
    - Large banks contribute more to systemic risk when they engage more in market-based activities (measured by noninterest income share or loans/assets).
- Representative regression coefficients/highlights from Table 5 (preserve numeric values exactly):
  - SRISK in 2006: 0.902***, 0.449**, 0.966***, 0.659***, 0.598***, 0.474**.
  - Log Assets($): 5.368***, 14.54***, 5.582***, 8.054***, 24.80***, 28.76***.
  - Tier 1 Ratio: -0.423, -2.303, 2.653***, 3.271***, 3.320***.
  - Deposits/Assets (various columns): 3.115, -13.47, 0.365, -1.586, 27.32**.
  - Loans/Assets (various columns): -4.114, -12.49, 0.993, 4.678, 62.28***, 55.76***.
  - Noninterest Income (various columns): -7.586*, -10.52, -4.055, -54.84***, -10.90***, -9.551**.
  - Log Subsidiaries: 1.917**, 1.249**, 1.981**, 1.862**, 1.786***.
  - Interaction terms:
    - Log Assets * Tier 1 Ratio: -0.880***, -1.090***, -1.120***.
    - Log Assets * Noninterest Income: 13.28***.
    - Log Assets * Loans/Assets: -16.61***, -14.62***.
    - Log Assets * Deposits/Assets: -8.042**.
  - Observations: 285, 110, 338, 285, 285, 285.
  - R-squared: 0.840, 0.905, 0.846, 0.869, 0.871, 0.877.
- Economic examples cited in text (exact values preserved):
  - For a large bank with a size of US$100 billion, increasing the Tier 1 capital ratio from 7 to 11 percent would decrease SRISK by US$14 billion.
  - For a small bank with a size of US$10 billion, a similar increase in bank capital would decrease SRISK by US$7 billion.
  - Average SRISK: US$6 billion.
  - An increase in the fraction of loans in total assets from 48 to 68 percent would decrease SRISK by US$5 billion more for the large bank compared to the small bank.
  - An increase in the fraction of deposits in total assets from 48 to 80 percent would decrease SRISK by US$5 billion more for the large bank compared to the small bank.
- Comparison of drivers:
  - Capital ratios matter, particularly for large banks.
  - Large banks that rely on less-stable funding contribute disproportionately to systemic risk.
  - Market-based activities: banks that engage more in market-based activities did not have high individual risk (and may have performed better individually), but large market-oriented banks contributed more to systemic risk — they are more likely to fail together, increasing systemwide externalities.

### Policy implications (text summary)
- Large banks have less capital, less stable funding, engage more in market-based activities, and are more organizationally complex than small banks; these properties are highly correlated and suggest a distinct, potentially more fragile business model for large banks.
- Large banks create more individual and systemic risk, particularly when they are not well capitalized and have unstable funding.
- Large banks create more systemic risk (but not necessarily more individual risk) when they have more subsidiaries and engage more in market-based activities.
- The analysis recognizes potential trade-offs: while too-big-to-fail subsidies and corporate governance issues may indicate socially excessive scale, economies of scale for large banks complicate policy prescriptions.

*Sources: Bankscope; Datastream; and IMF staff calculations.*

### conclusions as to what the socially optimal banks size is.

### _sdn1404 - conclusions as to what the socially optimal banks size is.

### Traditional vs. Systemic Risk-Based Regulation of Large Banks
- Market failure: when shareholders and managers do not internalize downside of individual risk realizations due to limited liability, they choose on the margin to operate riskier banks — i.e., larger banks, with less capital, and less-stable funding.
- Micro-prudential limitation: a pure micro-prudential approach that focuses on individual bank risk may be insufficient because:
  - The same capital or funding deficiencies create more systemic risk when they occur in large banks.
  - Large banks’ involvement in market-based activities and organizational complexity do not necessarily increase individual bank risk but do increase systemic risk, and therefore may be invisible to traditional micro-prudential regulation.
- Policy implications validated by the analysis:
  - More stringent capital and liquidity standards for large banks (macro-prudential reasons), consistent with imposing capital surcharges on systemically important banks as in Basel III.
  - Address market-based activities through higher capital surcharges (Fundamental Review of the Trading Book) and minimal haircuts (Financial Stability Board work on repo markets).
  - Consider a small, fixed (not risk-based) capital surcharge on all trading assets to reduce incentives for low-margin, high-scale “tail risk” strategies.
  - Use living wills to facilitate orderly resolution of complex banks and provide incentives to reduce organizational complexity.

### Policy Tools
- Capital surcharges:
  - Supported as a cornerstone of the Basel III framework and advocated by policymakers (IMF, 2010) and academics.
  - Confirmed by the analysis to be a powerful tool to reduce systemic risk by:
    - Reducing likelihood of bank failure (lower individual risk).
    - Reducing impact of a bank’s failure on the financial system and broader economy (lower systemic risk) via increased loss absorption capacity.
  - Indirect effect: capital surcharges that reduce bank size can mitigate externalities from unstable funding and market-based activities.
- Costs of higher capital:
  - Three types of cost highlighted:
    1. Impact on bank lending and the real economy — general view: effect is modest in steady state (Kashyap, Stein, and Hanson, 2010; Admati and Hellwig, 2013); but costs may be substantial if banks cut lending (Aiyar, Calomiris, and Wieladek, 2014). Suggestion: phase in tighter capital requirements over time, backloaded to when economic growth accelerates.
    2. Loss of economies of scale and scope if banks reduce size in response to surcharges — these costs are likely modest (see Annex 1).
    3. Potential re-distribution of risk within the financial system — risk could shift to unregulated parts of the financial system or to smaller banks, necessitating additional measures.
- Contingent capital:
  - Regulatory requirements for issuance of hybrid debt instruments that convert into equity during distress are proposed to facilitate recapitalization when capital is scarce.
- Activity restrictions vs. price-based tools:
  - Examples: Volcker rule, Vickers, Liikanen proposals.
  - Literature suggests these tools are difficult to calibrate; presence of economies of scale and scope complicates determining optimal scope of bank activities.
  - Under uncertainty, price-based tools (properly designed capital surcharges) may be preferred (Weitzman, 1974 logic).
  - Specific restrictions on well-identified risky trading activities with little economic value (e.g., proprietary carry trade in collateralized debt or sovereign bonds) might be warranted.
- Complementary measures to correct market failures:
  - Better resolution regimes (living wills; resolution regime for global systemically important financial institutions per Financial Stability Board, 2011).
  - Better corporate governance mechanisms to reduce organizational complexity and high-powered incentives encouraging excessive risk-taking.

### Scenarios and Distributional Risks
- Benign scenario: large banks shrink, adopt safer business models like smaller banks (more capital, more stable funding, less risky market-based activities) as they lose too-big-to-fail subsidies and market-based economies of scale.
- Adverse scenario: capital surcharges push risk outside large banks into unregulated sectors or smaller banks, creating new systemic risks requiring further measures.

### Implications for the “Too Much Finance” Debate
- Complementary viewpoint: beyond allocative efficiency concerns, systemic risk considerations suggest larger financial systems (higher ratio of domestic credit to GDP) tend to have more large banks and therefore more systemic risk.
- Empirical correlations cited:
  - Correlation between ratio of domestic credit to GDP and market share of large banks (over US$50 billion in assets): 0.75 and 0.71.
- Policy implication: to control systemic risk in large financial systems, regulatory policy needs special attention to the role of large banks.

### Conclusions (Paper-wide)
- Empirical finding: large banks, on average, create more individual and systemic risk than smaller banks.
- Risk amplifiers for large banks: insufficient capital, unstable funding, greater engagement in market-based activities, organizational complexity.
- Drivers of bank size: too-big-to-fail subsidies and empire-building incentives suggest today’s large banks might be too large from a social welfare perspective.
- Uncertainty: literature does not dismiss economies of scale (likely modest), so “optimal” bank size is highly uncertain; outright restrictions on bank size may be imprecise and difficult to implement.
- Recommended regulatory approach: combine micro- and macro-prudential perspectives with tools including capital surcharges on large banks (Basel III) and measures to reduce market-based activities and organizational complexity.

### Annex 1 — Economies of Scale and Scope in Banks
- Evidence on economies of scale is inconclusive:
  - Early studies: economies of scale limited to relatively small banks; no evidence beyond US$10 billion to US$50 billion in assets.
  - More recent studies: find economies of scale for large banks; information technology and scalable market-based operations may have increased optimal bank size.
- Cost-economy estimates:
  - Kovner, Vickery, and Zhou (2013) estimate total value of cost economies in U.S. banking system for banks over US$50 billion in assets: between US$16 billion and US$45 billion a year, corresponding to 0.1 to 0.25 percent of GDP (or 0.1 to 0.25 percent of total U.S. bank holding companies assets per year).
- Diversification-adjusted estimates:
  - Wheelock and Wilson (2012) and Hughes and Mester (2013): 1 percent increase in bank size increases costs by only 0.95 percent for both small and large banks.
  - Implication: cost of splitting the four largest U.S. banks so each manages not more than $1 trillion in assets would be over US$70 billion a year; making banks even smaller would cost more.
- Caveats:
  - Such estimates assume large banks’ higher risk tolerance is socially optimal and that social value of market-based activities equals that of traditional lending.
  - Negative returns to scope when banks move into market-based activities appear driven by agency costs, not technology.
  - Evidence of negative returns to scope: lower market valuations, higher risk, lower risk-adjusted returns — which suggests potential costs for shareholders and other stakeholders including taxpayers.
  - Counterpoint: market-based activities may create surplus for bank customers; in that case returns to scope may still be positive from a social welfare perspective.

### Annex 2 — Corporate Governance Challenges in Large Banks
- Governance model: Anglo-Saxon model focuses governance on ensuring firms operate in shareholders’ interests via boards and incentive contracts; more efficient with concentrated ownership and active takeover markets.
- Constraints on governance effectiveness in banks:
  - Limits on concentration of ownership and takeovers (e.g., U.S. regulation limits nonbank ownership of banks to no more than 10 percent of voting stock) reduce shareholder influence.
  - High leverage means shareholders may have aggressive risk preferences misaligned with other stakeholders (depositors, creditors, government).
  - Trading activities manufacture “tail risks” hard to quantify in normal times, making oversight and fiduciary duty assessment difficult.
  - Expanding control to other stakeholders (creditors, government) is not a panacea due to risks of directed or affiliated lending undermining credit quality.
- Complexity and transparency:
  - Large banks tend to be more leveraged, more complex, and engage more in trading activities, complicating corporate governance.
  - Analyst forecast dispersion (standard deviation of EPS forecasts divided by absolute mean EPS forecast) is larger for large banks and has grown since the crisis, suggesting increased complexity and/or lower transparency.
- Table A1 (median values reported):
  - Average forecast dispersion:
    - 2006 Large Banks: 5.8  [126]
    - 2006 Small Banks: 4.1  [105]
    - 2011 Large Banks: 7.6  [131]
    - 2011 Small Banks: 6.0  [61]
  - Notes: Large banks = assets in excess of US$50 billion. Small banks = assets between US$10 billion and US$50 billion. Number of banks reported in square brackets.

*Source: _sdn1404 - conclusions as to what the socially optimal banks size is.*

### Annex 3. The Sample of Banks and Summary Statistics

### Annex 3. The Sample of Banks and Summary Statistics

### Sample construction and coverage
- Start: sample of publicly traded financial institutions in Bankscope with data on equity returns and total assets at the end of 2006.
- Exclusions:
  - Financial institutions that are not publicly traded (because measures of systemic risk are based on equity returns).
  - Financial institutions that disappear before the end of the sample period in December 2008.
- Resulting counts reported in the text:
  - "This gives 1,721 financial institutions."
  - After focusing on deposit-taking institutions (commercial banks and bank holding companies) and excluding nonbank financial institutions, "reducing the sample to 1,343 institutions."
- Tables referenced:
  - Table A2 reports the number of banks per country and the number of large banks (with assets in excess of US$50 billion) in the sample.
  - Table A3 reports descriptive statistics for the main variables in the empirical analysis.

### Table A2 — Number of Banks in the Sample, by Country (selected entries)
- Total reported in table: "Total                       1,250                       137"
- Selected country rows (Country — Number of Banks — Of which: Large Banks):
  - Argentina: 6 — 0
  - Australia: 8 — 5
  - Austria: 6 — 3
  - Bahrain: 4 — 0
  - Belgium: 4 — 3
  - Brazil: 16 — 2
  - Canada: 15 — 6
  - China: 9 — 5
  - Denmark: 40 — 1
  - France: 11 — 4
  - Germany: 13 — 7
  - Greece: 12 — 3
  - Hong Kong SAR: 11 — 2
  - India: 25 — 2
  - Indonesia: 26 — 0
  - Italy: 20 — 6
  - Japan: 101 — 21
  - Korea, Rep. of: 9 — 5
  - Mexico: 5 — 0
  - Netherlands: 6 — 3
  - Poland: 14 — 0
  - Portugal: 5 — 2
  - Russian: 7 — 0
  - Saudi Arabia: 8 — 0
  - Singapore: 7 — 3
  - South Africa: 10 — 4
  - Spain: 13 — 5
  - Sweden: 4 — 3
  - Switzerland: 15 — 2
  - Turkey: 14 — 1
  - United Kingdom: 13 — 8
  - United States: 639 — 28

### Table A3 — Descriptive Statistics of Regression Variables (as reported)
- Variable — Observations — Mean — Standard Deviation — Minimum — Maximum
  - Return — 368 — -45.4227.76 — -99.1854.43
  - SRISK — 346 — 5.7017.26 — -9.0769.43
  - Log(Assets) — 373 — 3.891.36 — 2.31 — 7.64
  - Tier 1 Ratio — 310 — 10.144.34 — 3.68 — 48.47
  - Deposits/Assets — 356 — 0.63 — 0.21 — 0.00 — 0.94
  - Loans/Assets — 370 — 0.56 — 0.17 — 0.00 — 0.92
  - Noninterest — 373 — 0.38 — 0.23 — -0.55 — 1.10
  - Log(Subsidiaries) — 373 — 3.51 — 1.75 — 0.00 — 8.30
  - Leverage — 373 — 15.70 — 7.40 — 1.04 — 53.97
  - Funding Fragility — 371 — 0.21 — 0.23 — 0.00 — 1.00

### Analyst forecast notes (footnotes)
- Forecasts: "We use forecasts made in December of the year from the Institutional Broker Estimate System dataset."
- Restriction: analysis restricted "to banks with at least three analysts so as to reduce the impact of small analyst numbers on forecast dispersion."
- Statistical note: "Medians equality test suggests that the dispersion of analyst forecasts is significantly different in large versus small banks at the 5 percent level in both 2006 and 2011."

### Treatment of numeric outliers
- For the purpose of analysis, each systemic risk measure is winsorized "at its 1st and 99th percentiles to remove the influence of outliers."

### SRISK methodology (Annex 4 summary relevant to the sample)
- Main measure: SRISK, based on Brownlees and Engle (2012) and Acharya, Engle, and Richardson (2012).
- Focus period: "the crisis period from the middle of 2007 to the end of 2008."
- SRISK interpretation: "measures the expected capital shortage faced by a financial firm during a period of system distress when the market declines substantially."
- SRISK formula components:
  - k is the minimum fraction of capital (ratio of total assets) each firm needs to hold; "We set k equal to the prudential capital ratio of 8 percent."
  - Di,t is the book value of debt (total liabilities); Ei,t is the market value of equity.
  - SRISK is not restricted at zero in this study: "Note that we do not restrict SRISK at zero, allowing it to take on negative values."
- MES (marginal expected shortfall):
  - Definition: "MES is defined as the tail expectation of the firm’s equity return conditional on a market decline."
  - Market proxy: "We take the daily return on the S&P 500 index as a proxy for the market return."
  - Parameters:
    - h = one day (t measured in days).
    - C = –2 percent, so that "MES is the one-day loss expected if market returns are less than –2 percent."
  - Estimation sample for return model: "daily data over the period from January 2000 to December 2012."
  - Crisis-period MES: computed as "the average of the predicted values for MES over the period from July 1, 2007 to December 31, 2008."
- Long-run MES approximation:
  - Parameter settings: "We set h in |tht C + equal to 180 days and 180|tt C + equal to –40 percent, and use the following approximation to compute long-run MES, where 1|tt C + is –2 percent."
  - The paper provides an exponential approximation formula linking short-run and long-run MES (as shown in the source).
- SRISK computation:
  - Return model estimated using daily data from January 2000 to December 2012 (same as for MES).
  - SRISK computed using the average of predicted MES values over July 1, 2007 to December 31, 2008.
  - Transformation: "In our analysis, we take the negative value of SRISK to translate it into an increasing measure of systemic risk."
  - Units and returns: "All stock returns are computed in local currency terms. SRISK is expressed in billions of U.S. dollars."

*Source: _sdn1404 - Annex 3. The Sample of Banks and Summary Statistics*

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_Source: https://www.imf.org/-/media/websites/imf/imported-full-text-pdf/external/pubs/ft/sdn/2014/_sdn1404.pdf_