Modeling Bank Risk Levels and Capital Requirements In Brazil

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Modeling Bank Risk Levels and Capital
Requirements In Brazil

• Theodore M. Barnhill
• barnhill_at_gwu.edu
• Robert Savickas
• Marcos Rietti Souto
• Department of Finance, The George Washington
  University
• Benjamin Tabak
• The Central Bank of Brazil

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Synopsis 1

• This work has been supported by the Globalization
  Center at The George Washington University and
  Banco Central Do Brasil.
• We implement an integrated market and credit risk
  simulation model for assessing the risk of single
  and multiple bank failures (i.e. systemic risk),
  and assessing capital adequacy.
• We are not aware of other portfolio analytical
  models that can deal effectively with the
  integrated market and credit risk issues required
  to complete a systemic bank risk analysis of this
  type.
• The work is ongoing and the reported results are
  of a preliminary nature.

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Synopsis 2

• After calibrating the model using an extensive
  Brazilian database we demonstrate a capacity to
  model closely Brazilian bank loan credit
  transition probabilities and defaults.
• This strong credit risk analytical capability
  supports the belief that reasonable Brazilian
  bank failure rate simulations are possible.

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Synopsis 3

• Simulations of up to three hypothetical banks
  portfolios simultaneously indicate that high
  initial bank capital ratios, and very wide
  interest rate spreads on loans produce low bank
  failure probabilities and low systemic bank risk
  for selected hypothetical banks.
• These results are conditioned on the assumption
  that the Brazilian Government does not default on
  its debts.

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Synopsis 4

• If smaller, and internationally more typical,
  interest rate spreads are assumed then both
  inter-bank credit risk and loan portfolio credit
  risk are shown to substantially increase
  simulated bank default rates and multiple bank
  default rates.

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Synopsis 5

• This model can be extended in at least five
  directions
• model more than three banks simultaneously
• model stochastic updates for volatilities and
  correlations
• develop a methodology for explicitly modeling the
  credit risk of consumers loans
• include derivative security exposure in the
  analysis, and
• model the risk of a correlated government default
  (Barnhill and Kopits, 2003) and its impact on
  banks.

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Importance of Risk Assessments

• Forward-looking risk assessment methodologies
  provide a tool to identify potential risks before
  they materialize.
• They also allow an evaluation of the risk impact
  of potential changes in a banks asset/liability
  portfolio composition (credit quality, sector
  concentration, geographical concentration,
  maturity, currency, etc.) as well as its capital
  ratio.
• This allows banks and regulators to make
  appropriate adjustments to a variety of variables
  on a bank by bank basis.

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Overview of Current Methods 1

• Many institutions hold portfolios of debt,
  equity, and derivative securities which face a
  variety of correlated risks including
• Credit,
• Market,
• Interest rate
• Interest rate spread,
• Foreign exchange rate,
• Equity price, Real Estate Price, etc.

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Overview of Current Methods 2

• Typically market and credit risk are modeled
  separately and added in ad hoc ways (e.g. Basel).
  We believe that this practice results in the
  misestimation of overall portfolio risk (Barnhill
  and Gleason (2000)).

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Integrated Portfolio VaR Assessments

• are accomplished by
• Simulating the future financial environment (e.g.
  1 year) as a set of correlated stochastic
  variables (interest rates, exchange rate, equity
  indices, real estate indices, etc.).
• Simulating the correlated evolution of the credit
  rating (and potential default) for each security
  in the portfolio as a function of the simulated
  financial environment.
• Revaluing each security as a function of the
  simulated financial environment and credit
  ratings.
• Recalculating the total portfolio value and other
  variables (e.g. capital ratio) under the
  simulated conditions.
• Repeating the simulation a large number of times.
• Analyzing the distribution of simulated portfolio
  values (capital ratios) etc.to determine risk
  levels.

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Modeling the Financial Environment

• Simulating Interest Rates (Hull and White, 1994).
• Simulating Credit Spreads (Stochastic Lognormal
  Spread).
• Simulating Equity Indices, Real Estate Price
  Indices, and FX Rates (Geometric Brownian
  Motion).
• Simulating Multiple Correlated Stochastic
  Variables (Hull, 1997).

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Modeling Credit Risk

• Credit risk methodologies estimate the
  probability of financial assets migrating to
  different risk categories (e.g. AAA, ...,
  default) over a pre-set horizon
• The values of the financial assets are then
  typically estimated for each possible future risk
  category using forward rates from the term
  structure for each risk class as well as default
  recovery rates

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ValueCalc Credit Risk Simulation Methodology 1

• The conceptual basis is the Contingent Claims
  analytical framework (Black, Scholes, Merton)
  where credit risk is a function of a firms
• debt-to-value ratio and
• volatility of firm value.

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ValueCalc Credit Risk Simulation Methodology 2

• ValueCalc utilizes the following methodology to
  simulate credit rating transitions
• simulate the return on sector equity market price
  indices (e.g. autos, etc.)
• using either a one-factor or multi-factor model
  simulate the return on equity for each firm
  included in the portfolio
• calculate each firms market value of equity
• calculate each firms debt ratio (i.e. total
  liabilities/total liabilities market value of
  equity)
• map simulated debt ratios into simulated credit
  ratings for each firm.

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Model Viability

• Barnhill and Maxwell (JBF, 2001) demonstrated the
  viability of the model for U.S. Bond Portfolios
• Simulated credit rating transition probabilities
  approximate historical patterns
• The model produces reasonable values for bonds
  with credit risk
• The model produces very similar portfolio value
  at risk levels as compared to historical levels.
• The portfolio analysis highlights the importance
  of diversification of credit risk across a number
  of fixed income assets and sectors of the
  economy.
• Portfolios of 15 to 20 bonds have statistical
  characteristics similar to much larger portfolios.

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Modeling Brazilian Banks
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Modeling the Macroeconomic/Financial Environment
1

• Variables employed
• Brazilian short-term interest rate,
• U.S. short-term interest rate,
• foreign exchange rate,
• gold,
• Brazilian c.p.i.,
• oil (Brent crude),
• Brazilian broad equity market index (IBOVESPA),
• 14 Brazilian equity market sectorial indices
  (banks, chemicals, mining, oil, paper,
  telecommunication wireless, textile, tobacco,
  utility, etc)
• 5 seasonally adjusted unemployment rates by
  geographical regions.

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EWMAVolatilities
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EWMA Correlations
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Assumed Spreads on Consumer and Business Loans
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Assumed Business Loan Interest Rate Spreads In
Current Interest Rate Environment
Assumed additional spread on consumer loans 34
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Assumed Business Loan Interest Rate Spreads In
Potential Lower Interest Rate Environment
Assumed additional spread on consumer loans 17
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Brazilian Banks Balance Sheet

• Significant amount of business and consumers
  loans (with wide interest rate spreads
• Large amounts of government loans
• Insignificant exposure to Real Estate

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Loans Credit Rating Distribution

• Assumption Consumers loans are modeled in the
  same way as business loans.
• Brazilian Credit Risk Bureau employs a different
  credit risk rating system than Moodys or
  Standard and Poor.

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Business and Consumers Loans Distribution
Lower Credit Risk
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Business and Consumers Loans Distribution
Higher Credit Risk
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Simulating Credit Transition Matrix 1

• Estimate Betas
• 543 companies
• 12 equity sectors
• Source DataStream
• Problem lack of liquidity
• Approach use monthly observations

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Simulating Credit Transition Matrix 2

• Distribute debt-to-value ratios by credit risk
  category
• Data source DataStream.
• Credit risk category weighted average of those
  assigned by banks in Brazil.
• Distributional Analysis Analyze the distribution
  of company debt-to-value ratios for various
  credit risk categories.

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Simulating Credit Transition Matrix 3

• More on debt-to-value ratios
• Target the firms current and planned future
  debt-to-value ratio.
• The upper and lower bounds represent the values
  of debt ratios at which a company would move to a
  higher/lower credit rating .
• Example (companies in the B credit level) if the
  simulated debt ratios increase to more than 0.90
  then they would fall to credit rating C.
• Conclusion credit risk rating deteriorates as
  systematic and unsystematic components of risk
  increase, and as debt-to-value ratio increases

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Simulating Credit Transition Matrix 4

• Final step
• For each simulation run, estimate returns on
  market index (assumed to follow a GBM) and on
  companies, via CAPM.
• Use returns to estimate a distribution of
  possible future equity market values and debt
  ratios.
• The simulated debt ratios are then mapped into
  the credit ratings as in the previous table.

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Descriptive Statistics
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Single Bank Risk Analysis (12/31/2002)
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Banking System Systemic Risk Analysis

• Systemic risk vs. lower interest rate spread
• Three banks operating simultaneously in the same
  macroeconomic/financial environment.
• Same asset liability structure (with risk-free
  loans).
• Same credit risk exposure (high).
• Different inter-bank exposure.
• Initial capital level 15

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Simulation Results 9

• Systemic risk vs. lower interest rate spread
  (cont.)
• Results
• Probability of a systemic depletion of capital
  increases substantially.
• Inter-bank exposures becomes an issue (the role
  of a cascade failure).

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Extensions

• It is quite possible to extend this analysis in
  at least five directions
• model more than three banks simultaneously
• model stochastic updates for volatilities and
  correlations
• develop a methodology for explicitly modeling the
  credit risk of consumers loans
• model the risk of a correlated government default
  and its impact on banks and
• model correlated derivative security risk
  exposure.

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Conclusions 1

• Our preliminary simulations indicated that the
  risk of the hypothetical banks studied failing is
  small, as is the level of systemic bank risk.
  Further systemic bank risk is not very sensitive
  to the level of inter-bank credit exposures and
  to the credit risk profile of loans held by
  banks. There are at least three potential
  explanations for this result (i) the large
  amount of risk-free loans held by banks (ii)
  the high capital ratios with which the
  hypothetical banks operate and (iii) the large
  interest rate spreads earned by banks, which are
  much larger than the default rates on business
  and consumer loans.

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Conclusions 2

• We found the large interest rate spreads to be
  the most important element on our analysis. When
  we analyze hypothetical banks earning much more
  modest (but perhaps typical) interest rate
  spreads, bank failure risk and systemic bank risk
  increase substantially. Under this circumstance
  both inter-bank credit exposure as well as the
  credit quality of bank loan portfolios become
  important risk factors.

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Conclusions 3

• All the conclusions are our own, and do not
  represent the views of Banco Central do Brasil