Brazil Central Bank Seminar Modeling Systemic Bank Risk In Brazil Theodore M. Barnhill, Jr....

Brazil Central Bank Seminar

Modeling Systemic Bank Risk In Brazil

Theodore M. Barnhill, Jr.

Professor, and Chairman Department of Finance,

The George Washington University


Outline• Summary of Earlier Work on Integrated Market and Credit

Risk Assessments

• Modeling Business Loan Credit Risk in Brazil– A simulation model calibrated with Brazilian data comes close to

matching the credit transition probabilities produced by the Credit Risk Bureau

• Modeling Systemic Bank Risk In Brazil– Preliminary simulation risk studies for hypothetical Brazilian

Banks demonstrates a low risk of failure, even with significant credit risk, due to wide interest rate spreads


Overview of Current Methods • 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.

• 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.


Overview of Current Methods

At the May 4, 2000 conference on bank structure and competition of the Federal Reserve Bank of Chicago, Federal Reserve Board Chairman Alan Greenspan noted that “…the present practice of modeling market risk separately from credit risk, a simplification made for expediency, is certainly questionable in times of extraordinary market stress. Under extreme conditions, discontinuous jumps in market valuations raise the specter of insolvency, and market risk becomes

indistinct from credit risk.”


Overview of Current Methods • 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 bank’s 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 identify potential risks before they materialize and make appropriate adjustments on a bank by bank basis.


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 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


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)


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


Table 2.Moody’s Transition Matrixes Adjusted for Withdrawn Ratings

(1920 -1996)As a benchmark for the simulated transition probabilities, Moody’s historicaltransition probabilities are reported (Carty and Lieberman, 1996).

Probability of Rating after One YearInitialRating

Aaa Aa A Baa Ba B Caa-C Default

Aaa 92.28% 6.43% 1.03% 0.24% 0.02% 0.00% 0.00% 0.00%Aa 1.28% 91.68% 6.09% 0.70% 0.17% 0.02% 0.00% 0.06%A 0.07% 2.45% 91.59% 4.97% 0.67% 0.11% 0.02% 0.13%Baa 0.03% 0.26% 4.19% 89.41% 5.07% 0.66% 0.07% 0.30%Ba 0.01% 0.09% 0.43% 5.09% 87.23% 5.47% 0.45% 1.23%B 0.00% 0.04% 0.15% 0.67% 6.47% 85.32% 3.44% 3.90%Caa-C 0.00% 0.02% 0.04% 0.37% 1.38% 5.80% 78.78% 13.60%


ValueCalc Credit Risk Simulation Methodology

• The conceptual basis is the Contingent Claims Analytical framework (Black, Scholes, Merton) where credit risk is a function of a firm’s:– Debt to Value ratio– Volatility of firm value


ValueCalc Credit Risk Simulation Methodology

• ValueCalc utilizes the following methodology to simulate bond 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 firm’s market value of equity– Calculate each firm’s debt ratio (i.e. total liabilities/total

liabilities + market value of equity)– Map simulated debt ratios into simulated credit ratings for

each firm


Simulating the Return on Equity Indices and FX Rates

whereS = asset spot price; S is assumed to follow

geometric Brownian motion

Rm = the return on the equity index

S S S t t

e x p

2

2

R


Simulating the Equity Return of a Firm• Once the sector equity return (Rm) is simulated, the return on

equity for the individual firms are simulated using a one-factor model (multi-factor models could be used):

Ki = RF + Betai (Rm - RF) + iz

Ki = The return on equity for the firmi,

RF = the risk-free interest rate, Betai = the systematic risk of firmi,

Rm = the simulated return on the sector equity index,i = The firm specific volatility in return on

equity,

z = a Wiener process with z being related to t by the function z = t.


Table 6.Equity Return Volatility’s for High Volatility Firms

by Bond Rating Category

HighVolatility

Firms withBond’sRated

Mean Beta 1993-98 Mean Firm SpecificEquity Return Volatility

1993-1998

Aaa 0.682 0.31662Aa 0.757 0.36305A 0.864 0.41215Baa 0.994 0.50702Ba 1.131 0.72888B 1.314 0.72663Caa 1.301 0.95351

1993 1994 1995 1996 1997 1998S&P 500Volatility

0.059 0.107 0.050 0.107 0.158 0.230


Model Viability• The viability of the model for U.S. Bond Portfolios has been

demonstrated (Barnhill and Maxwell, JBF, 2001).

– 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


• Market risk is not likely to cause a bank with a high credit quality, well-diversified portfolio to fail.

• Higher market risk significantly increases bank risk levels, particularly so for banks with higher credit risk and more concentrated portfolios.

South African Banks Barnhill, Papapanagiotou, and

Schumacher, (Journal of Financial Markets, Institutions and Instruments,

2002) show that:


South African Banks– The credit quality of the bank’s loan portfolio is

the most important risk factor. Banks with high credit risk and concentrated portfolios are shown to have a significant risk of failure during periods of low volatility and a high risk of failure during periods of financial stress.

– All of these factors have potentially very important implications for bank capital requirements.


Modeling Business Loan Credit Risk in Brazil

By:

Theodore M. Barnhill, Jr.

Benjamin Tabak,

Marcos Souto

November 2002


Beta estimation

• In Brazil it is difficult to estimate betas for lower credit quality firms as infrequent trading generally pushes betas down.

• In theory results should be just the opposite with betas rising for lower credit quality firms.


Beta estimation

• Another approach that we tried was to deleverage betas for the highest credit rating (more liquid firms) and releverage them for lower credit rating firms.

• This approach produced betas that increase for lower credit rating firms, but in the extreme these betas were outside the observed range for Brazil


Final Beta estimation

• Betas collected by our own estimation and from Bloomberg and other sources suggest that systematic risk should be in the 0.3 – 1.36 range.

• Betas for the US fall in a similar range• Our approach ended using a similar trend to

that observed for the US with betas increasing as credit quality declines.


Debt to Value Ratio Estimation

• From DataStream we also collected and analyzed data on the debt to value ratios for all publicly traded companies in Brazil.

• As expected the debt to value ratios increased as credit ratings declined.


Debt to Value Ratios, Betas, and Firm Unsystematic Equity Return Risk used in Simulations

AA A B C D E F G+H+Write-offDebt RatiosLower bound 0.27 0.51 0.67 0.775 0.79 0.8 0.848 0.96Target 0.38 0.61 0.815 0.835 0.88 0.89 0.893 0.96Upper bound 0.53 0.78 0.9 0.92 0.9275 0.933 0.95 0.96

beta 0.67 0.85 1 1.1 1.2 1.3 1.36Unsystematic risk 0.379689 0.5492 0.6946 0.705 0.767 0.78 0.722


Uncertainty on credit quality assignments

• Distributional Analysis for Bank credit ratings assignments in the Credit Risk Bureau Data Base. Perhaps a standard methodology could be developed to narrow the dispersion of ratings and improve the usefulness of the credit risk data.

mean 2.71median 225th Percentile 175th Percentile 4Max 9Min 1


Historical Brazilian Credit Transition Matrix

We considered both the system wide and an average of two large bank’s credit transition matrices for the period of 2000-2002.

By reputation these two banks are better in assigning credit ratings than the average of the banking system.


Historical Transition Matrix for the Brazilian Financial System (average of June 2000 to June 2001, and

June 2001 to June 2002)

Value AA A B C D E F G+H+WriteoffAA 0.898 0.0495 0.0295 0.0075 0.009 0.001 0.0015 0.005A 0.069 0.773 0.066 0.045 0.022 0.0045 0.003 0.018B 0.079 0.1025 0.6875 0.047 0.0315 0.014 0.0055 0.033C 0.031 0.085 0.11 0.6405 0.0495 0.0125 0.012 0.0595D 0.038 0.077 0.0595 0.0985 0.498 0.0275 0.028 0.1725E 0.03 0.056 0.0215 0.0275 0.035 0.4885 0.1005 0.241F 0.0155 0.013 0.031 0.019 0.0215 0.026 0.5515 0.322


Historical Transition Matrix for the average of two banks (average of June 2000 to June 2002)

Value AA A B C D E F G+H+WriteoffAA 0.90075 0.06425 0.0205 0.00525 0.00175 0.00025 0.00025 0.00675A 0.119 0.69025 0.1015 0.04725 0.02125 0.003 0.00425 0.014B 0.03275 0.11025 0.71875 0.09225 0.02 0.00475 0.0055 0.01625C 0.03275 0.04175 0.1525 0.6735 0.0465 0.009 0.01325 0.03075D 0.01075 0.0185 0.04 0.05125 0.602 0.039 0.05425 0.18425E 0.00125 0.0775 0.00525 0.00825 0.0405 0.558 0.04025 0.26825F 0.00775 0.006 0.0115 0.0225 0.031 0.076 0.568 0.27625


Simulated Credit Transition Matrix(Equity Market Index Volatility = 39%)

Value AA A B C D E F G-HAA 0.9035 0.0965 0 0 0 0 0 0A 0.114 0.79625 0.08925 0.0005 0 0 0 0B 0.004 0.0495 0.75325 0.1 0.031 0.0155 0.0345 0.01225C 0.0015 0.027 0.126 0.68625 0.04875 0.02225 0.05475 0.0335D 0.00025 0.007 0.0445 0.01475 0.61475 0.04875 0.0885 0.1815E 0 0.00575 0.03775 0.0125 0.0085 0.56175 0.10475 0.269F 0 0.00225 0.02325 0.01225 0.0075 0.073 0.60375 0.278G-H 0 0 0 0 0 0 0 1


Delta Simulated Credit Transition Probabilities Vs. Historical 2001-2002

Value AA A B C D E F G-H

AA 0.00275 0.03225 -0.0205 -0.00525 -0.00175 -0.00025 -0.00025 -0.00675A -0.005 0.106 -0.01225 -0.04675 -0.02125 -0.003 -0.00425 -0.014B -0.02875 -0.06075 0.0345 0.00775 0.011 0.01075 0.029 -0.004C -0.03125 -0.01475 -0.0265 0.01275 0.00225 0.01325 0.0415 0.00275D -0.0105 -0.0115 0.0045 -0.0365 0.01275 0.00975 0.03425 -0.00275E -0.00125 -0.07175 0.0325 0.00425 -0.032 0.00375 0.0645 0.00075F -0.00775 -0.00375 0.01175 -0.01025 -0.0235 -0.003 0.03575 0.00175G-H 0 0 0 0 0 0 0 0.2035


Mean Absolute Delta Simulated Credit Transition Probabilities Vs. Historical 2001-2002

mean 0.01865178625th Percentile 0.003937550th Percentile 0.0112575th Percentile 0.0295625Maximum 0.106Minimum 0.00025


Modeling Bank Risk In Brazil:Current Assumptions

• The risk of the Brazilian Government Defaulting on its financial obligations is not treated.

• Credit Risk on Consumer Loans can be modeled as if they are business loans.

• The volatilities and correlations of the financial market variables are estimated using th RiskMetrics Exponentially Weighted Moving Average method.


Modeling Bank Risk In Brazil:Current Assumptions

• The yield on Government loans as of June 30, 2002 was 17.77%

• The average yield on Business loans was 38.28%,

• The average yield on consumer loans was 60.57%

• A portfolio of about 500 securities is adequate to approximate the statistical characteristics of much larger bank portfolios.


Bank Loan Distribution (Higher Risk)Total AA A B C D E F G-H

Ibovespa 0.2059 0.0126 0.0465 0.0152 0.0073 0.0033 0.0000 0.0448 0.0750

Banks 0.0000 0.0046 0.0000 0.0000 0.0000 0.0009 0.0000 0.0000 0.0004

BasicInd 0.0071 0.0000 0.0022 0.0049 0.0000 0.0000 0.0000 0.0000 0.0000

Beverage 0.0048 0.0046 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 0.0000

Chemistry 0.0266 0.0059 0.0161 0.0034 0.0000 0.0000 0.0003 0.0000 0.0007

GenInd 0.0388 0.0200 0.0105 0.0024 0.0009 0.0003 0.0000 0.0003 0.0042

Metal 0.0678 0.0201 0.0416 0.0038 0.0015 0.0000 0.0004 0.0000 0.0000

Mining 0.0343 0.0341 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Oil_Sec 0.0050 0.0033 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0017

Paper 0.0245 0.0103 0.0070 0.0004 0.0000 0.0000 0.0000 0.0060 0.0006

TeleWire 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Textile 0.0178 0.0000 0.0050 0.0095 0.0000 0.0000 0.0008 0.0000 0.0024

Tobacco 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Utility 0.0885 0.0663 0.0200 0.0016 0.0000 0.0000 0.0000 0.0000 0.0000

Region 1 North 0.0136 0.0004 0.0035 0.0017 0.0022 0.0023 0.0003 0.0006 0.0025

Region 2 North-East 0.0854 0.0025 0.0218 0.0110 0.0139 0.0142 0.0019 0.0038 0.0160

Region 3 Central-West 0.0385 0.0011 0.0098 0.0049 0.0063 0.0064 0.0008 0.0017 0.0072

Region 4 South-East 0.2331 0.0069 0.0594 0.0299 0.0380 0.0387 0.0051 0.0103 0.0436

Region 5 South 0.1084 0.0032 0.0276 0.0139 0.0177 0.0180 0.0024 0.0048 0.0203

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Total 1.0000 0.1961 0.2709 0.1025 0.0879 0.0839 0.0121 0.0722 0.1745


Bank Loan Distribution (Lower Risk)Total AA A B C D E F G-H

Ibovespa 0.2555 0.1044 0.0527 0.0630 0.0091 0.0136 0.0056 0.0024 0.0049

Banks 0.0023 0.0023 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

BasicInd 0.0009 0.0000 0.0002 0.0007 0.0000 0.0000 0.0000 0.0000 0.0000

Beverage 0.0027 0.0024 0.0000 0.0000 0.0000 0.0000 0.0003 0.0000 0.0000

Chemistry 0.0412 0.0372 0.0020 0.0014 0.0000 0.0000 0.0000 0.0000 0.0006

GenInd 0.0656 0.0160 0.0432 0.0019 0.0030 0.0010 0.0000 0.0000 0.0005

Metal 0.0917 0.0350 0.0545 0.0012 0.0000 0.0000 0.0010 0.0000 0.0000

Mining 0.0060 0.0058 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Oil_Sec 0.0185 0.0185 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Paper 0.0348 0.0243 0.0095 0.0006 0.0000 0.0000 0.0000 0.0003 0.0002

TeleWire 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Textile 0.0209 0.0016 0.0060 0.0123 0.0000 0.0000 0.0003 0.0001 0.0006

Tobacco 0.0090 0.0090 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Utility 0.1942 0.1404 0.0500 0.0010 0.0028 0.0000 0.0000 0.0000 0.0000

Region 1 North 0.0045 0.0001 0.0010 0.0014 0.0003 0.0004 0.0002 0.0001 0.0010

Region 2 North-East 0.0138 0.0003 0.0030 0.0042 0.0009 0.0011 0.0006 0.0004 0.0032

Region 3 Central-West 0.0175 0.0004 0.0038 0.0054 0.0011 0.0014 0.0008 0.0006 0.0040

Region 4 South-East 0.1637 0.0038 0.0354 0.0504 0.0107 0.0132 0.0071 0.0052 0.0378

Region 5 South 0.0571 0.0013 0.0123 0.0176 0.0037 0.0046 0.0025 0.0018 0.0132

0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

Total 1.0000 0.4028 0.2737 0.1611 0.0317 0.0353 0.0184 0.0110 0.0661


Hypothetical Banks Capital Ratios(Initial Cap Ratio Approximately .15

Mean Simulated Rates of Return on Equity over 25%)

Credit Risk Lower Higher HigherRecovery Rate 30% 30% 15%

Capitalization Ratio

Cumulative Probability



0.01 .00% .00% 0.05%0.05 .00% .00% 0.10%0.1 0.30% .65% 1.45%0.15 2.00% 5.30% 6.90%0.2 14.55% 26.40% 30.30%0.25 52.05% 68.10% 73.55%0.3 91.60% 96.20% 97.30%0.34 99.30% 99.95% 100.00%0.35 99.80% 99.95%0.36 99.95% 100.00%0.37 100.00%


Hypothetical Banks Capital Ratios

Relative Frequency For Hypothetical Bank 2 Capital Ratios(15% Assumed Recovery Rate, Higher Credit Risk)

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

xxx

xxx Relative Frequency


Current Extensions to the Model• The simulation risk model has been extended so as to assess

the risk of correlated failures among a group of financial institutions.

• The model has also been extended to estimate the risk of government financial distress (not for Brazil).

• We are well advanced toward creating a model for simulating consumer loan loss rates,

• We also are well advanced toward modeling both stochastic volatility and correlation structures using a methodology suggested by Engel (2000)


Conclusions

• With appropriate calibration, using A large Brazilian data set, our simulation model produces credit transition and default probabilities that are close to the ones reported by the Credit Risk Bureau.

• Using this credit risk modeling capability, along with better data on credit risk spreads, default recovery rates, and more detailed bank asset and liability structures we believe that reasonable estimates of bank and multiple bank failure rates are possible.

• Very preliminary simulation risk studies for hypothetical Brazilian banks demonstrates a low risk of failure, even with significant credit risk, due to wide interest rate spreads. This conclusion is conditioned on the assumption that the government of Brazil will not default on it debt.


Conclusions• This type of portfolio simulation risk analysis points out the importance of

regulators considering a variety of factor in assessing bank risk levels, including:

– Financial environment volatility,

– Portfolio credit risk,

– Portfolio diversification,

– Asset and liability maturity and currency mismatches,

– Interest rate spreads,

– Capital levels.

– Inter-bank credit exposures

• All of these factors should, and can, be handled in one overall systemic risk assessment.

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Brazil Central Bank Seminar Modeling Systemic Bank Risk In Brazil Theodore M. Barnhill, Jr....

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