A Guide to IMF Stress Testing
Chapter

Chapter 8. Systemic Bank Risk in Brazil: A Comprehensive Simulation of Correlated Market, Credit, Sovereign, and Interbank Risks

Author(s):
Li Ong
Published Date:
December 2014
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Author(s)
Theodore Barnhill Jr and Marcos Souto This chapter was previously published as Barnhill and Souto (2009). The authors would like to thank Mathias Drehmann, Andrew Powell, Til Schuermann, and participants in the GEFRI Conference on Modeling and Managing Sovereign and Systemic Risk (Washington, 2006) and in the Conference on the Integration of Market and Credit Risk, sponsored by the Bank for International Settlements, the Bundesbank, and the Journal of Banking and Finance (Berlin, Integration of Market and Credit Risk, sponsored by the Bank for International Settlements, the Bundesbank, and the Journal of Banking and Finance (Berlin, chapter and suggested important areas for future work.

In this study, we present a comprehensive forward-looking portfolio simulation methodology for assessing the correlated impacts of market risk, private sector and sovereign credit risk, and interbank default risk. In order to produce better integrated risk assessment for banks and systemic risk assessments for financial systems, we argue that reasonably detailed modeling of bank asset and liability structures, loan portfolio credit quality, and loan concentrations by sector, region, and type, as well as a number of financial and economic environment risk drivers, is required. Sovereign and interbank default risks are increasingly important in the current economic environment, and their inclusion is an important model extension. This extended model is demonstrated through an application to both individual Brazilian banks (i.e., 28 of the largest banks) and groups of banks (i.e., the Brazilian banking system) as of December 2004. Our results also show that a commonly used approach of aggregating all banks into one single bank for purposes of undertaking a systemic banking system risk assessment results in a misestimation of both the probability and cost of systemic banking system failures. Our analysis also indicates that, in the event of a sovereign default, the Government of Brazil would face constrained debt management alternatives. We conclude that such forward-looking risk assessment methodologies for assessing multiple correlated risks, combined with the targeted collection of specific types of data on bank portfolios, have the potential to better quantify overall bank and banking system risk levels, which can assist bank management, bank regulators, sovereigns, rating agencies, and investors to make better informed and proactive risk management and investment decisions.

Method Summary

Method Summary
OverviewMonte Carlo simulations are conducted over a selected time period, with each bank balance sheet account updated accordingly for correlated underlying stochastic processes governing interest rates, equity market indices, and exchange rates.
ApplicationThe method enables a forward-looking risk assessment of the impact of multiple correlated risks.
Nature of approachSimulation based.
Data requirementsDetailed data on banks’ balance sheets and portfolios, including transition probabilities from one credit risk category to another.
StrengthsThe method enables the assessment of various correlated risks (market risk and private sector credit risk, including sovereign and interbank default risks) to produce an overall bank risk assessment.
Weaknesses
  • The method is based on normally distributed stochastic shocks. It is particularly important to properly account for fat tail and skewness in the distribution during crisis periods. An attempt to include stochastic volatilities improved simulation results somewhat. Still more research is warranted to further refine simulated distributions.

  • Market and credit risk are integrated through a capital asset pricing model (CAPM) formulation and a distributional analysis of the loans-to-value ratio. In addition to the limitations of the CAPM model that are well documented in the literature, this formulation also requires market data to estimate the asset’s beta, which can prove to be difficult in countries where equity markets are thin and sensitive to the time period used.

  • This method is very data intensive, and simulations may take a significant amount of time to run.

ToolValueCalc Global Portfolio and Credit Risk software, copyright FinSoft, Inc. (1996-2005).

Bear Stearns, Lehman Brothers, American International Group (AIG), Fannie Mae, Freddie Mac, Wachovia, Citigroup, Washington Mutual, and a substantial number of other global financial institutions experienced correlated financial problems during the 2007-08 period. The inability to anticipate these problems and adopt proactive measures to minimize their impact on the global financial system and economy has imposed trillions of dollars of losses on investors and taxpayers. The need for improvements and innovation in risk modeling is apparent.

Financial institutions hold portfolios of debt, equity, and derivative securities that face a variety of correlated risks, including (1) asset and liability structure and loan portfolio concentration risk;1 (2) credit risk on business, consumer, sovereign, and interbank loans and other transactions; (3) interest rate risk; (4) interest rate spread risk; (5) foreign exchange risk; and (6) equity price. The current practice is to undertake market and credit risk assessments separately (e.g., Basel Committee on Banking Supervision, 1988, 1996, 2001). Combining such separate risk measures into one overall portfolio risk measure is not easily accomplished (see, e.g., Jarrow and Turnbull, 2000; and Barnhill and Maxwell, 2002). The absence of reliable overall portfolio risk measures creates problems for determining capital adequacy requirements, capital-at-risk measures, hedging strategies, and so forth.

At any future time, individuals, businesses, banks, groups of banks, and sovereign will all face the same financial and economic environment (for better or worse). There is every reason to expect that the credit quality (default probability) for each of the above entities is nonzero, stochastic, and correlated with future financial and economic environment conditions (e.g., default rates will go up during periods of economic stress). There is also reason to believe that bank market risk is driven systematically by the same future financial and economic conditions. Barnhill, Papapanagiotou, and Schumacher (2003) and Barnhill, Papapanagiotou, and Souto (2004) have shown that banks with high credit risk and concentrated portfolios have a high risk of failure during periods of financial stress.

We present and apply a methodology2 in this chapter that is capable of capturing all the correlated risks mentioned here in a comprehensive way. Banks’ balance sheets and portfolios are modeled with a substantial amount of details that we have not seen in any other methodology, to the best of our knowledge. For example, the loans portfolio of a bank is considered to be distributed across different regions for consumer loans and industry sectors for business loans. The initial distribution of the credit quality of the loan portfolio is assumed to be that reported by the bank. Systematic changes in the credit quality of these business and consumer loans are driven by stochastic economic factors relevant for their sector and region, which are then modeled as correlated stochastic variables. Borrower-specific risk factors are also modeled as independent random events. Loans are priced using different spreads, consistent with their simulated loan-to-value ratios and credit quality. We will discuss the features of the loan credit risk assessment methodology with more detail later.3

In this chapter, we further extend this methodology for assessing the correlated impacts of market risk and private sector credit risk to include sovereign and interbank default risk and produce one overall bank risk assessment. In the current economic environment, we believe that sovereign risk is a significant factor that should be considered in bank and systemic banking system risk assessments. In a further significant innovation, financial and economic environment variables are modeled with stochastic volatilities and correlations. This framework produces simulated distributions of future bank financial performance measures (returns, capital ratios, etc.) that reflect the collective impact of all of the modeled correlated variables. The simulated distributions allow the estimation of the probability and cost of various potential future events, such as bank failures or multiple bank failures, which reflect all of the modeled correlated risks. By modeling multiple banks simultaneously, we also provide a methodology for assessing the probability of multiple bank failures occurring at the same time period.

We incorporate systemic risk through different channels. First, banks are directly interdependent through a nexus of financial interbank contracts. One insolvent bank might become unable to honor its contracts, provoking financial distress in its counterparts (e.g., Rochet and Tirole, 1986; and Elsinger, Lehar, and Summer, 2003). When simulating the banks simultaneously, we assumed that if one bank fails, it will default on its interbank obligations, with some recovery rate. Second, banks’ assets have some degree of correlation, as banks might invest in the same industries or geographical regions. If a shock affects one or more particular industry (or geographical region), then banks with exposure to that industry (or geographical region) will be systematically affected (e.g., Lehar, 2003; Acharya, 2009). By modeling the banks’ portfolios as distributed across geographic regions and industry sectors, we can capture underlying correlations among portfolios of banks that lend to similar regions or industries. Third, a downward business cycle may cause companies’ distress, rendering many loans delinquent and causing banks to further reduce business lending. This can deepen the business cycle, worsening the financial crises and affecting more banks (e.g., Gorton, 1988). We capture this effect, to some extent, through the simulation of the macro-economic environment under which banks operate. In the course of a Monte Carlo simulation, it is possible to obtain a combination of macroeconomic factors that would be consistent with a downward business cycle. Fourth, correlated interest rate, exchange rate, and equity price risk (i.e., market risk) also may have an impact on multiple banks simultaneously.4 We explicitly incorporate the correlation between these variables in the simulation. Fifth, various factors including bank lending policies, the efficiency of the legal system in resolving loan defaults, and the aggregate level of defaults can have a substantial impact on bank risk through variations in the recovery rates on defaulted loans. We model recovery rates as distributed according to a beta distribution. Finally, sovereign defaults may simultaneously impose direct losses on banks through a reduction in the market value of their government securities and indirect losses brought about by economic and contract disruptions that incrementally increase the default rates on private sector loans. Although the characterization of a sovereign default event may be a difficult task, we assume that the government may impose some losses on the market value of its securities, with significant impact on banks’ assets. This channel is of particular importance when analyzing Brazilian banks, as they hold a massive amount of government securities in their portfolios, sometimes above 80 percent of their total assets.

In this study, we model government default in a relatively simplistic way, as a very large “corporate borrower” whose known default probability is systematically related to returns on the Brazilian equity market index plus an idiosyncratic component. The impact of interbank exposure is modeled in a second step after the Monte Carlo simulations are done and the initial bank risk assessments completed.5 It is important to keep in mind the significance of modeling all of the correlated risks above. In particular during times of economic stress, it is likely that default losses on private sector loans will increase, market volatility and risk will also likely increase, and so will the risk of sovereign default. Thus, should a sovereign default occur, it will likely be at a time when many banks are already being adversely affected by other risk factors. This is just the time when the failure of several banks could, through interbank credit defaults, precipitate a number of additional bank defaults and a systemic banking crisis.

We simulate bank risk at different levels: (1) for individual banks; (2) for individual aggregated groups of banks; and (3) simultaneously for three aggregated groups of banks. For our individual bank risk assessments, we simulate 28 of the largest Brazilian banks for two different cases: (1) the Government of Brazil (GOB) is assumed to never default; and (2) GOB can default on its debt with a 4.5 percent probability, which is consistent with the average default probability of countries rated by Fitch in the same grade as Brazil (B rating), as of December 2004.6

Our analysis, as of December 2004, finds that most Brazilian banks have a low risk of failure so long as the government does not default.7 However, in the event of a sovereign default, a number of Brazilian banks face potential solvency problems and could, if customers lose confidence, face liquidity problems as well. This highlights the danger of concentrated lending to an entity that has a nonzero probability of default.

When assessing the systemic risk of the Brazilian financial system, we use different approaches, with the intention of illustrating the importance of modeling the banks individually and simultaneously, as operating under the same macroeconomic environment. We first consider a single bank that is a combination of all 28 banks (these banks represent approximately 75 percent of the banking system total assets and are the banks for which we managed to gather the best available data to carry out this exercise). Subsequently, we simulate three aggregate banks simultaneously and include the risk component associated with interbank default (interbank propagation channel). Our results show that aggregating the banks into one single bank underestimates the cost associated with a systemic risk crisis, when compared with the three-bank simultaneous simulation case. Our analysis also highlights the danger of modeling the financial system as one single financial institution and not accounting for the differential risk characteristics of various banks and for the interbank risk channel, through which a systemic crisis may propagate.

The remainder of this chapter proceeds as follows: Section 1 provides an abbreviated description of the portfolio simulation model we use to undertake the various integrated risk assessments.8 In Section 2, we present and discuss the risk assessments for Brazilian banks and the Brazilian banking system. Concluding remarks and final comments are given in Section 3.

1. An Integrated Model of Correlated Market, Credit, Sovereign, and Interbank Risk in an Environment with Stochastic Volatilities and Correlations

An integrated analysis of correlated market risk and private sector, sovereign, and interbank default risk on both individual banks (i.e., 28 of the largest Brazilian banks) and groups of banks (i.e., the Brazilian banking system) requires a powerful and flexible forward-looking risk assessment methodology.9

We propose that it is possible to identify a set of correlated financial and economic variables, for example, sector equity returns and regional unemployment rates,10 which systematically affect the credit quality and produce correlated default rates among various groups of borrowers (e.g., businesses in various sectors and individuals in various regions). We also model many uncorrelated borrower-specific risk factors. We find such detailed individual borrower and portfolio modeling necessary to assess the risk level of portfolios of loans with varying credit quality distributed across various sectors and regions. In particular, it allows for explicit modeling of loan portfolio concentration and diversification impacts on bank risk levels.

We further propose that the identified set of correlated financial and economic variables can include ones that have systematic impacts on the market values of securities, loans, and other assets. Examples of such variables are interest rates, interest rate spreads, foreign exchange (FX) rates, equity index returns, and commodity prices. Also, a significant innovation in this chapter is that financial and economic environment variables are modeled with stochastic volatilities and correlations.

The structure of the systemic bank risk simulation model is as follows:

  • Simulate the future financial environment (e.g., monthly steps for one year) as a set of correlated stochastic variables that systematically affect each bank’s market risk (interest rates, interest rate spreads, FX rates) and credit risk (sector equity returns, regional real estate prices, regional unemployment rates, etc.).

  • Simulate the correlated evolution of the credit rating (default) for each borrower in each bank’s loan portfolio as a function of the simulated financial environment.

  • Simulate the correlated evolution of the credit rating (default) for the Government of Brazil as a function of the simulated financial environment.

  • Revalue each asset and liability in each bank’s balance sheet as a function of the simulated financial environment and credit ratings. Note that for each run of the simulation, the simulated value of each bank’s assets and liabilities reflects correlated market and credit risk.

  • Estimate each bank’s pretax income, operating costs, taxes, and aftertax income over the simulation period.

  • Calculate financial performance measures for each bank (e.g., economic capital ratio, rate of return on assets) under the simulated conditions. Estimate whether the bank will fail.

  • Estimate each bank’s potential losses on defaulted interbank loans.

  • Recalculate financial performance measures for each bank (e.g., economic capital ratio, rate of return on assets) under the simulated conditions. Reestimate whether each bank will fail.

  • Repeat the simulation a large number of times.

  • Analyze the distributions of simulated bank financial performance mealures (e.g., economic capital ratio) to determine individual bank and banking system systemic risk levels.11

When modeling the macro-financial environment under which banks operate, we use the Hull and White extended Vasicek model (Hull and White, 1990, 1993, 1994) to model stochastic risk-free (e.g., U.S. Treasury) interest rates. Once the risk-free term structure has been estimated, then the AA term structure is modeled as a stochastic lognormal spread over the risk-free interest rate, the A term structure is modeled as a stochastic spread over AA, and so on. The mean value of these simulated credit spreads is set approximately equal to the forward rates implied by the initial term structures for various credit qualities (e.g., AA). This procedure ensures that all simulated credit spreads12 are always positive and that the simulated risky term structures are approximately arbitrage free.13

The model utilized to simulate the value of the equity market indices and FX rate (S) assumes that (S) follows a geometric Brownian motion where the expected growth rate (m) and volatility (σ) are constant (Hull, 2008).

In the current portfolio risk assessment model, the equity indices and FX rate returns are simulated as stochastic variables correlated with the future risk-free interest rate and interest rate spreads. Error terms are drawn from univariate normal distributions and decomposed using the Cholesky factorization. In this particular study, a total of 22 independent random variables (see Table 8.1 for a list of the variables used) are used to describe the macro-financial environment underlying banks’ operations.

Table 8.1Data Description and Sources
AnalysisDataData Sources
Estimation of initial volatilities and correlations for financial and economic environment simulationBrazilian short-term domestic nominal interest rateCentral Bank of Brazil (CBB) Web site
U.S. nominal interest rateFED St. Louis Web site
Brazilian FX rateCBB Web site
GoldCBB Web site
OilInternational Monetary Fund Commodity Prices Database
Brazilian CPI levelCBB Web site
Ibovespa (the broad Brazilian equity market index)DataStream
Ten business sector equity indices (basic industry, construction material, chemicals, cyclical services, food production, food retail, forest and paper, telecommunications, and utilities)DataStream
Unemployment rates for five big cities in Brazil (Recife, Belo Horizonte, Salvador, Rio de Janeiro and Sao Paulo, and Porto Alegre)Brazilian Institute of Geography and Statistics Web site
Estimation of bank-by-bank interest rate spreads by credit rating categoryBank-by-bank net interest marginBankscope
Default rates by credit rating (for 2 of the largest Brazilian banks)1Barnhill, Souto, and Tabak (2006)
Bank-by-bank average interest rate spread for business and customers’ loansCBB Web site
Estimation of betas and firm-specific riskStock prices for 543 Brazilian companies listed in the Brazilian Stock ExchangeDataStream
Price indices for 9 business sector equity indices (basic industry, construction material, chemicals, cyclical services, food production, food retail, forest and paper, telecommunications, and utilities)DataStream
Estimation of debt ratio ranges for businesses in various credit rating categoriesDebt-to-value ratios for 543 companies listed in the Brazilian Stock ExchangeDataStream
Borrowers’ credit ratings1Bank loan ratings for 543 Brazilian companies listed in the Brazilian Stock Exchange, as assigned by Brazilian banksBarnhill, Souto, and Tabak (2006)
Bank-by-bank balance sheet dataBank-by-bank balance sheet data for 28 of the largest Brazilian banksCBB Web site and Bankscope
Bank-by-bank balance sheet maturity structureBank-by-bank asset and liability maturity structures for 28 of the largest Brazilian banksCBB Web site
Bank-by-bank portfolio compositionBank-by-bank business loan portfolio distribution by 9 business sector equity indices (basic industry, construction material, chemicals, cyclical services, food production, food retail, forest and paper, telecommunications, and utilities) and customers’ loan portfolio distribution by five geographical regions (South, Southeast, Middle-West, North, and Northeast)CBB Web site
Bank-by-bank distributions of loan credit ratingsBank-by-bank business loan portfolio distribution by credit qualityCBB
Bank-by-bank credit ratingBank-by-bank credit rating (for the ones among the 28 of the largest Brazilian banks for which this information was available)Standard and Poor’s, Moody’s, and Fitch Web sites
Source: Authors.Note: CPI = Consumer price index; FX = foreign exchange.

This information is protected by Brazilian law and cannot be disclosed. Data for financial and economic variables were available monthly for the period 1999–2004.

Source: Authors.Note: CPI = Consumer price index; FX = foreign exchange.

This information is protected by Brazilian law and cannot be disclosed. Data for financial and economic variables were available monthly for the period 1999–2004.

Variances and covariances are updated for each simulation time step via the following model:

where vtN(0,1),σij,t is the covariance between variables i and j, and λ is the decay factor.14 Initial variances and covariances at the start of each simulation run are estimated as the average realized variances and covariances over the entire January 2003 to December 2004 period. Similar to modeling stochastic returns, volatility shocks also are decomposed via Cholesky factorization and thus are affected by the correlation structure of the state variables.

Barnhill and Souto (2008a) show that the decay factor λ can be changed appropriately, so as to increase the probability mass of index returns in the tails of the simulated distributions. They further show that simulated volatilities and correlations match reasonably well the evolution of historical values. This model is implemented to simulate the credit transition matrix for Brazilian bank loans, and it is shown that this methodology has the potential to improve simulated transition probabilities as compared with the constant volatility case. In particular, it increases the simulated probability of default in lower credit risk categories to values closer to observed historical levels.

A. Modeling banks’ assets, liabilities, and income

Banks’ Balance Sheets

Banks’ balance sheets are modeled with some degree of detail. On the liabilities side, we have (1) domestic funding, which includes interbank, demand, savings, and fixed deposits, NCDs, and repos; (2) foreign funding (in foreign currency); (3) debt; (4) non-interest-bearing liabilities; (5) capital and reserves; and (6) equity. Domestic and foreign funding and debt can be broken down, in the simulation framework, in up to three different maturities15 and then properly linked to different correlated stochastic interest rates (domestic or foreign) and foreign exchange rates. As we shall see, some asset accounts also can be modeled through multiple maturities, and this structure allows us to incorporate asset and liability maturity and currency mismatches (i.e., market risk) as a component of banks’ integrated risk assessments.

On the asset side, the main accounts are (1) money (cash and gold reserves); (2) GOB securities; (3) business loans; (4) consumer loans; (5) foreign loans; (6) equity investments; (7) real estate investments; and (8) non-interest-earning assets. Money and non-interest-earning assets are not updated in the course of the simulations (we thus assume that the bank does not change the amount of money and non-interest-earning assets it holds, over the course of the simulation). Because they are usually the main risk elements in any bank’s portfolio, loans are modeled in more detail. Absent other information, loans (which usually comprise the biggest fraction of most banks’ portfolios) typically are modeled as bonds. We allocate business and consumer loans separately across eight credit risk categories defined by Banco Central do Brasil (AA,…, H). In the case of business loans, we also distribute them across 9 business sectors, whereas loans to individuals are distributed across six regions.16 This breakdown is important for capturing the portfolio diversification or concentration aspects of the risk analysis as well as the integrating of market and credit risk. In total, we use approximately 450 stylized securities to model each bank. Although a larger number of currencies and securities easily could have been modeled, we believe that this number is adequate to capture statistically much of the impact of bank asset and liability portfolio maturity, currency, credit quality, and sector and region concentration characteristics.

Unlike state variable returns that are estimated for each time step in each simulation path, all balance sheet accounts are recalculated only at the end of each simulation period.17 In Table 8.2, we present some descriptive statistics on the stylized balance sheet for 28 Brazilian banks. These data were obtained from Bankscope and the Web site of the Brazilian central bank.18

Table 8.2Brazilian Banks Balance Sheets—Main Statistics
Balance Sheet ItemsMin.MedianSDMax.
Capital and liabilities
Public funding
Domestic funding26.0%59.8%17.9%85.2%
Foreign funding0.9%7.3%12.7%54.5%
Capital and other liabilities0.0%0.0%0.0%0.0%
Non-interest-bearing3.9%12.2%12.4%50.2%
Equity and reserves less impairments5.0%10.1%7.4%38.4%
Debt0.0%0.0%1.3%4.0%
Total100.0%100.0%0.0%100.0%
Assets
Money0.0%1.3%2.1%9.4%
Gold0.0%0.0%0.0%0.0%
Domestic risk-free loans25.0%54.2%18.3%90.5%
Domestic business loans1.0%21.2%13.9%55.6%
Domestic individual loans0.0%3.5%11.3%57.0%
Foreign loans0.0%0.0%0.0%0.0%
Equity investments0.0%0.4%0.8%3.8%
Real estate investments0.0%1.1%1.2%3.6%
Other assets2.5%10.6%9.1%44.4%
Total100.0%100.0%0.0%100.0%
Net interest margin0.0270.0750.0420.203
Net noninterest income/total assets−0.080−0.0320.0310.040
Sources: Bankscope and Central Bank of Brazil Web site.Note: This table provides statistics on the stylized balance sheets used in the simulation to describe the main assets and liabilities accounts for Brazilian banks, as of December 2004.
Sources: Bankscope and Central Bank of Brazil Web site.Note: This table provides statistics on the stylized balance sheets used in the simulation to describe the main assets and liabilities accounts for Brazilian banks, as of December 2004.

Banks’ Operating Expenses, Taxes, and Income

In addition to the bank’s assets and liabilities, we also model net noninterest income. Net noninterest income is defined as fee income plus other noninterest income minus operating expenses. We use historical information to estimate the ratio of noninterest income to total assets, and at the end of each simulation period, we calculate how much the bank will have spent on operations. This amount is then deducted from the bank’s simulated net interest income plus (minus) capital gains (losses) to estimate pretax income. We also estimate taxes paid by banks as an assumed percentage of taxable income over the simulation period. Aftertax income is estimated as pretax income less estimated taxes.

Banks in Brazil operate with very high net interest margins. During the period under analysis, information from Banco Central do Brasil indicates that the spreads between the average yield on bank business loans (consumer loans) and government securities were approximately 20 percent (40 percent). Considering all loans (government, business, and consumer) information from Bankscope (see Table 8.2), the median net interest margin for the 28 Brazilian banks analyzed in this study was 7.5 percent.

Brazilian banks also have high operating expense ratios. Information from Bankscope indicates that the median ratio of net noninterest income to total assets for the 28 Brazilian banks analyzed in this study was -3.2 percent.

B. Modeling bank loan portfolio credit risk

The methodology used to model business loan credit transition probabilities and defaults starts with an extensive empirical analysis of all publicly traded companies in Brazil and all bank loans made to those firms by all Brazilian banks.19 The purpose of this analysis is to identify typical debt-to-value ratios, beta coefficients, and firm-specific equity return volatilities for Brazilian firms with various bank-assigned credit ratings. The results are found in Table 8.3.

Table 8.3Debt Ratios, Betas, and Unsystematic Risk Used in the Portfolio Simulation Risk Assessments1
AAABCDEFDefault
Debt-to-value ratios
Lower bound0.2700.4570.6600.7450.7850.7980.8020.960
Target0.4050.6200.8100.8380.8900.9020.8940.960
Upper bound0.5160.7060.8650.9170.9220.9350.9400.960
Beta0.670.851.001.101.201.301.36
Unsystematic risk0.380.550.690.710.770.780.72
Source: Authors.Note: This table provides results for distributional analysis of equity return risk characteristics, debt-to-value ratios, and internal bank credit ratings for all publicly traded Brazilian companies. 1. See Barnhill, Souto, and Tabak (2003).

See Barnhill, Souto, and Tabak (2003).

Source: Authors.Note: This table provides results for distributional analysis of equity return risk characteristics, debt-to-value ratios, and internal bank credit ratings for all publicly traded Brazilian companies. 1. See Barnhill, Souto, and Tabak (2003).

See Barnhill, Souto, and Tabak (2003).

As expected, typical debt ratios increase as company bank loan ratings decline.20 For simulation runs reported later in this study, we assume that debt ratios start at the midpoint between the maximum and minimum values for the assumed initial credit rating category. Credit ratings are generally assumed to change when simulated debt ratios cross the min—max boundaries set for the initial credit rating.21 We use this information to develop stylized firms for each credit rating (i.e., target debt-to-value ratio and assumed beta and firm-specific risk factors). For each run of the simulation, the return on each borrowing firm’s equity is estimated as a function of the simulated return on an equity market index plus a firm-specific random change. This simulated equity return allows the estimation of a new debt-to-value ratio and credit rating (including default22) for each firm in the bank’s loan portfolio.23 Using a metric proposed by Jafry and Schuermann (2004), Barnhill and Souto (2008a) report simulated Brazilian bank loan credit transition probability matrices that are very similar to historical Brazilian credit transition matrices.

After simulating the loans’ future credit rating, we calculated their values using the simulated term structure of interest rates appropriate for each risk class. If the loan is simulated to default, the recovery rate (representing the present value of all future recoveries) on the loan is set at either the higher (45 percent) or lower (15 percent) level discussed earlier. If the loan is denominated in a foreign currency, then its numeraire currency value is calculated by multiplying the simulated loan value by the simulated foreign exchange rate that by construction is also a correlated stochastic variable.

C. Modeling bank capital ratios

The previous analysis allows the market value of the bank’s assets, liabilities, equity, and capital ratio to be calculated for each simulation run:

where MVEt is the simulated market value of the bank’s equity at time t; Ai,t is the simulated market value of the ith asset at time t, which represents the simulated financial environment variables (e.g., interest rates, exchange rates, equity prices); and, where appropriate, the simulated credit rating of the borrower, Li,t, is the simulated market value of the ith liability at time t, which represents the simulated financial environment variables (e.g., interest rates, exchange rates). The bank’s asset level is also adjusted to reflect bank net interest income, operating costs, and taxes over the simulation period.

The final outcome of the model after many simulation runs is an estimated distribution of the bank’s capital-to-asset ratio, characterized by a mean, a standard deviation, a maximum, and a minimum value, as well as a value-at-risk measure indicating how frequently the bank’s capital-to-asset ratio falls below a certain threshold (e.g., 3 percent), which is used to estimate the bank’s default probability. Declines in the capital ratio (i.e., potential losses) under each simulation run are estimated as the difference between the initial bank capital and the simulated capital ratio.24

where CapitalRatiot is the simulated bank capital ratio at time t.

D. Modeling sovereign risk

The Government of Brazil is modeled as a large business borrower with an assumed debt-to-value ratio and an assumed market value of equity.25 The government’s market value of equity is assumed to be systematically related to returns on the Brazilian equity market index and to also have an idiosyncratic component. On each run of the simulation, we estimate a new market value of equity and debt-to-value ratio for the GOB, and if this value exceeds some critical level, then the GOB is assumed to default. The initial debt-to-value ratio, beta, and idiosyncratic risk components are selected to produce a targeted average sovereign default rate of 4.5 percent. The simulated sovereign defaults thus are systematically related to returns on the Brazilian equity market (and other correlated state variables), which also are systematically related to simulated defaults on private sector loans. Through this mechanism, we end up modeling correlated sovereign and private sector loan defaults,26 which also are correlated with simulated financial and economic variables (e.g., equity returns, interest rates, foreign exchange rates).

E. Modeling interbank default risk

The potential impact of interbank defaults is modeled in a second step after the initial Monte Carlo simulation bank risk assessments are completed.27 For this purpose, we first aggregate the 28 banks into three groups according to their individual risk characteristics and then simulate the three groups simultaneously,28 under the same financial/macroeconomic scenarios. Given that we do not have precise information on interbank borrower or lender identities (we have info only on aggregate interbank lending for each bank), we assume interbank lending from one bank to be proportional to the other three aggregate banks’ total assets. We then assume, in a second lance, that if one bank falls below a 3 percent capital ratio,29 it becomes incapable of honoring its interbank obligations and defaults on them. Only 50 percent of these interbank obligations are assumed to be recovered, with subsequent impact on other banks’ capital ratios. Eventually, one bank’s failure can induce other banks to become insolvent as well, depending on the size of interbank exposure, combined with other factors, as mentioned earlier. It is important to keep in mind the significance of modeling all of the correlated risks above. In particular, during times of economic stress, it is likely that default losses on private sector loans will increase, market volatility and risk will also likely increase, and so will the risk of sovereign default. Thus, should a sovereign default occur, it will likely be at a time when many banks are already being adversely affected by other risk factors. This is just the time when the failure of several banks could, through interbank credit defaults, precipitate a number of additional bank defaults and a systemic banking crisis.

F. Modeling systemic bank risk

Finally, we assess the systemic risk of the Brazilian financial system, in different ways. We first consider a single bank that is a combination of all 28 banks,30 and then we simulate the three aggregate banks simultaneously and include potential correlated interbank default losses (interbank propagation channel). Our results show that aggregating the banks into one single bank underestimates the cost associated with a systemic risk crisis, when compared with the three-bank simultaneous simulation case. The analysis highlights the danger of modeling the financial system as one single financial institution and not accounting for the differential risk characteristics of various banks and for the interbank channel, through which a systemic crisis may propagate.

2. Simulation Results

Our risk assessments relate to three sets of Monte Carlo simulations:31 (1) individual banks, with no government default; (2) individual banks, with government default; and (3) systemic banking system risk. In the first and second sets of simulations, we wish to compare individual bank risk with and without sovereign default risk. We also compare the risk assessment produced by our portfolio simulations with the bank credit ratings provided by Moody’s and Standard & Poor’s. Using the risk assessments from the second set of simulations, we group banks into three risk categories and construct three aggregate banks. In the third set of simulations, we undertake a risk analysis for a single aggregate bank and subsequently a simultaneous risk analysis for three aggregate banks with different risk levels to assess systemic banking system risk (i.e., the likelihood of multiple banks defaulting), reflecting market, credit, sovereign, and interbank risk. These correlated market and credit risk assessments are based on analyses of the output from 2,000 simulation runs.

A. Individual banks, no government default

The first set of our simulations comprises all 28 banks, simulated individually, assuming that the GOB will never default on its domestic debt over the simulation horizon (one year).32 Simulation results for selected banks from this group are presented in Table 8.4, and a few comments are in order. First, reported value-at-risk (VaR) levels indicate the percentage of time that simulated bank capital ratios fall above a certain threshold. For example, Bank 20 VaR at the 99 percent confidence level is 0.147, indicating that 1 percent of the time, the simulated capital ratio for Bank 20 fell below 0.147. Second, with a few exceptions, Brazilian banks are well capitalized. For example, Bank 12 has a 0.252 capital ratio, and Bank 6 has a 0.382 capital ratio. Banks with capital ratios below 0.07 are Bank 5 (0.059), Bank 14 (0.062), Bank 16 (0.065), Bank 21 (0.067), and Bank 23 (0.063). Third, in general, if we do not factor government default into the simulations, Brazilian banks are profitable and have an increasing capital ratio on average over the one-year simulation period. None of the banks produces simulated capital ratios that would indicate significant default risk problems over a one-year time step. Even the minimum simulated capital ratios are well above the 3 percent level that we have set as the critical bank capital level at which banks begin to default, although in several cases the simulated capital ratios are below a 0.08 capital ratio on an economic capital basis (e.g., Bank 5 with minimum capital ratio of 0.004, Bank 7 with 0.040, and Bank 21 with 0.046, among others). Finally, simulated capital ratios have a small standard deviation for all banks, ranging from 0.001 (Banks 14, 19, and 21) to 0.008 (Bank 5 and Bank 24). Given the substantial amount of government securities held by these banks, this result is not surprising at all. Bank 9 holds a more modest fraction of government securities. However, the credit quality of its portfolio is fairly high, with a corresponding small default rate.

Table 8.4Simulated Capital Ratios: Individual Banks, No Government Default
VaR Levels
BankInitialMeanSDMaximumMinimum99%95%90%
Bank 10.1890.2010.0040.2140.1830.1910.1950.197
Bank 20.1410.1440.0050.1620.1240.1310.1360.138
Bank 30.0830.0890.0040.0970.0580.0770.0820.084
Bank 40.1490.1610.0050.1730.1360.1450.1520.155
Bank 50.0590.0680.0080.0880.0040.0470.0540.058
Bank 60.3820.3710.0030.3800.3620.3650.3670.368
Bank 70.0730.0720.0040.0910.0400.0590.0650.067
Bank 80.0960.1110.0040.1260.0930.1000.1040.106
Bank 90.1840.2240.0050.2460.2040.2110.2160.218
Bank 100.0910.0960.0070.1230.0590.0780.0840.087
Bank 110.0910.1070.0030.1190.0970.1000.1020.104
Bank 120.2520.2480.0040.2600.2310.2380.2410.242
Bank 130.1320.1490.0070.1880.1270.1340.1380.140
Bank 140.0620.0730.0010.0800.0680.0700.0710.071
Bank 150.1030.1500.0040.1680.1360.1430.1450.146
Bank 160.0650.0690.0020.0780.0600.0630.0650.066
Bank 170.0940.1060.0060.1340.0850.0900.0960.098
Bank 180.2000.2340.0050.2470.2130.2220.2260.229
Bank 190.2010.2000.0010.2060.1960.1970.1980.199
Bank 200.1740.1630.0070.1900.1250.1470.1520.155
Bank 210.0670.0660.0040.0740.0460.0550.0590.061
Bank 220.0730.0780.0010.0800.0750.0760.0770.077
Bank 230.0630.1210.0050.1520.0980.1070.1130.115
Bank 240.1390.1560.0080.1860.1220.1360.1430.146
Bank 250.0920.1010.0030.1130.0890.0930.0960.097
Bank 260.1610.1670.0030.1810.1560.1600.1620.163
Bank 270.2060.2070.0040.2250.1890.1960.1990.201
Bank 280.0900.1020.0020.1120.0940.0970.0990.100
Source: Authors.Note: VaR = value at risk. The table uses 2,000 simulated capital ratios and assumes that the Government of Brazil does not default on its domestic debt. Reported VaR capital ratio levels indicate the percentage of time that simulated values fall below a certain threshold. The assumed recovery rate on defaulted private sector loans is 45 percent in these simulations.
Source: Authors.Note: VaR = value at risk. The table uses 2,000 simulated capital ratios and assumes that the Government of Brazil does not default on its domestic debt. Reported VaR capital ratio levels indicate the percentage of time that simulated values fall below a certain threshold. The assumed recovery rate on defaulted private sector loans is 45 percent in these simulations.

B. Individual banks, government default

Given that Brazilian banks hold a significant amount of GOB debt, it is very important to assess the impact of correlated sovereign risk on banks’ default probabilities.33 For this exercise, we propose to model government default in a relatively simplistic way, which we claim can still provide reasonable insights on banks’ exposure to sovereign risk. In particular, in the current study we model the GOB as if it were a large corporate borrower, subject to systematic and idiosyncratic risk factors. When determining these parameters, we need to be able to reproduce reasonably closely the rate at which a sovereign country like Brazil is expected to default, given its current credit rating. We also wish to capture appropriately the correlations between market risk, private sector loan defaults, and sovereign defaults.

The definition of government default itself is neither simple nor consensual. Fitch defines default as a failure to make timely payment of principal and/or interest on either (1) rated foreign currency debt or (2) other material foreign currency debt obligations, such as Paris or London Club liabilities. For the present study, using the model discussed earlier, we chose to produce GOB average default rates that are comparable to the average default rates of countries’ sovereign debt rated at the same risk level as Brazil (B). We assume the GOB to have a default probability of 4.5 percent on foreign currency loans, consistent with Klaar, Rawkins, and Riley (2004). An important issue in the event of a sovereign default on its foreign debt is the government’s willingness or ability to honor its domestic debt obligations. Although the government may want to expand its monetary base in order to repay domestic loans, this practice has well-known nocive effects on the economy, which might eventually spill over into the banking system. It is also possible that the government may force debt holders to change their contracts for something that has a lower market value than the original ones. In any instance, even if the government does not fully default on its domestic debt, the banks ultimately may incur market value losses. To be able to model this explicitly is not an easy task. No one knows for sure which set of actions will be taken by the government during such events. There are innumerous possible outcomes for banks, each of which will affect banks’ portfolios differently. Given this limitation, we propose to construct a matrix of some potential government default implications that will provoke additional losses on banks’ portfolios, through two different channels. The first channel incorporates losses directly on the government securities, by assuming that banks may lose 0 percent, 10 percent, or 25 percent of the market value of their government securities. Such losses may result from increases in required market interest rates and interest rate spreads, because the government may defer payment of the debt or may force banks to change the terms of the debt in ways that reduce its value.

In addition, government default events usually are associated with major disruptions in the whole economy, affecting all sectors, and banks’ borrowers may become incapable of repaying some of their debts. We conjecture that these events will affect firms with different creditworthiness differently. That is, we assume that firms with higher credit quality are better prepared to handle these crisis events. The way we capture the differential impact of a sovereign default is by imposing an increase on the default rate on private sector loans in different credit categories. We assume three different scenarios: (1) businesses and individuals have a zero increment to their default rates; (2) businesses and individuals in each credit risk category have an increase in their default rates equal to the average default of that credit risk category; and (3) businesses and individuals in each credit risk category have an increase in their default rates equal to two times the average default of that credit risk category.

The combination of all these possible outcomes leads to nine potential government and private sector incremental loan loss scenarios banks may face in the event of a government default. Although these scenarios are far from exhausting the innumerous possibilities, they do provide a reasonable range for incremental bank loan losses. As indicated earlier, in cases where we assess systemic banking system risk, we will evaluate these nine potential loan loss scenarios for two assumed private sector defaulted loan recovery rates (15 percent and 45 percent).

In Tables 8.5 to 8.7, we report the average simulated bank default rate, the associated average cost to bring banks’ capital ratio back to a 0.08 level (estimated only for the times when the bank defaults), and the 99 percent VaR capital level (banks have 1 percent probability of having their capital ratios fall below this level). Given that banks hold a significant amount of government securities, bank default rates start to appear significant only when there is some degree of losses on government securities. For example, if banks lose an average of 10 percent in the market value of their government debt, then 6 banks (e.g., Bank 5 and Bank 16) will have a default rate of around 4 percent to 5 percent. If banks lose 25 percent of the market value of their government securities, then 15 banks (e.g., Bank 3, Bank 8, Bank 10) will have a default rate of around 4 percent to 6 percent. In either of these cases (i.e., 10 percent or 25 percent loss rates), the bank failures would result from a sovereign default and thus would be highly correlated and could precipitate a systemic banking system problem. Interestingly, some banks will not default at all (e.g., Bank 1 and Bank 2), even in the worst case scenario that we analyze in this chapter (losing 25 percent of the market value of government securities and suffering incremental defaults on business and individual loans equal to twice their average historical default rates). Either these banks are highly capitalized, and thus capable of absorbing larger losses on their government securities, or they have a balance between government, business, and consumer loans that allow them to diversify the risk of a potential government default, along with a high net interest margin stemming from large interest rate spreads on business and consumer loans. The average cost (as percentage of total assets) to bring the banks back to a 0.08 capital level whenever they default is usually high. For example, if the GOB defaults and the banks lose 25 percent of the market value of their government securities, this “bailout” cost ranges from 0.055 of total assets (Bank 13) to 0.278 (Bank 22). Again, the large amount of government securities held by Brazilian banks make them quite vulnerable in the event of a sovereign default resulting in very high potential bank bailout costs. The simulated 99 percent VaR capital ratios just reinforce the size of the losses these banks could face in the event of government default. If banks lose 25 percent of the market value of government securities, capital ratios may range from 0.248 (Bank 6) to −0.199 (Bank 22).

Table 8.5Simulated Capital Ratios: Individual Banks, No Government Default
Losses on Government Loans and Incremental Defaults on Business and Consumer Loans
Bank0%0% + 1 times the average historical default rates0% + 2 times the average historical default rates10%10% + 1 times the average historical default rates10% + 2 times the average historical default rates25%25% + 1 times the average historical default rates25%+2 times the average historical default rates
Bank 10.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 20.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 30.0000.0000.0000.0010.0010.0010.0460.0460.046
Bank 40.0000.0000.0000.0000.0000.0000.0000.0000.002
Bank 50.0000.0000.0010.0380.0450.0480.0480.0480.048
Bank 60.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 70.0000.0000.0000.0470.0470.0470.0470.0470.047
Bank 80.0000.0000.0000.0000.0000.0000.0340.0380.041
Bank 90.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 100.0000.0000.0000.0050.0070.0070.0600.0600.060
Bank 110.0000.0000.0000.0000.0000.0000.0450.0450.045
Bank 120.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 130.0000.0000.0000.0000.0000.0000.0030.0040.005
Bank 140.0000.0000.0000.0500.0500.0500.0500.0500.050
Bank 150.0000.0000.0000.0000.0000.0000.0450.0450.045
Bank 160.0000.0000.0000.0410.0410.0410.0410.0410.041
Bank 170.0000.0000.0000.0000.0000.0000.0340.0350.037
Bank 180.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 190.0000.0000.0000.0000.0000.0000.0490.0490.049
Bank 200.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 210.0000.0000.0000.0500.0500.0500.0500.0500.050
Bank 220.0000.0000.0000.0500.0500.0500.0500.0500.050
Bank 230.0000.0000.0000.0000.0000.0000.0510.0510.051
Bank 240.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 250.0000.0000.0000.0000.0000.0000.0480.0480.048
Bank 260.0000.0000.0000.0000.0000.0000.0000.0000.001
Bank 270.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 280.0000.0000.0000.0000.0000.0000.0460.0460.046
Source: Authors.Note: This table provides statistics and VaR values at different percentage levels, using 2,000 simulated capital ratios, for each of the 28 banks in our Simulation sample, assuming that the GOB does not default on its domestic debt. Reported VaR capital ratio levels indicate the percentage of time that simulated values fall below a certain threshold. For example, Bank 1 VaR at 99 percent level is 0.191, indicating that 1 percent of the time simulated capital ratios for Bank 1 fell below 0.191. The assumed recovery rate on defaulted private sector loans is 45 percent in these simulations.
Source: Authors.Note: This table provides statistics and VaR values at different percentage levels, using 2,000 simulated capital ratios, for each of the 28 banks in our Simulation sample, assuming that the GOB does not default on its domestic debt. Reported VaR capital ratio levels indicate the percentage of time that simulated values fall below a certain threshold. For example, Bank 1 VaR at 99 percent level is 0.191, indicating that 1 percent of the time simulated capital ratios for Bank 1 fell below 0.191. The assumed recovery rate on defaulted private sector loans is 45 percent in these simulations.
Table 8.6Simulated Average “Bailout” Cost: Individual Banks, Government Default
Losses on Government Loans and Incremental Defaults on Business and Consumer Loans
Bank0%0% + 1 times the average historical default rates0% + 2 times the average historical default rates10%10% + 1 times the average historical default rates10% + 2 times the average historical default rates25%25% + 1 times the average historical default rates25% + 2 times the average historical default rates
Bank 10.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 20.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 30.0000.0000.0000.0510.0540.0560.1020.1050.108
Bank 40.0000.0000.0000.0000.0000.0000.0000.0000.052
Bank 50.0000.0000.0530.0640.0680.0740.1630.1700.178
Bank 60.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 70.0000.0000.0000.0770.0780.0800.1970.1980.200
Bank 80.0000.0000.0000.0000.0000.0000.0590.0600.062
Bank 90.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 100.0000.0000.0000.0590.0590.0610.1500.1530.156
Bank 110.0000.0000.0000.0000.0000.0000.0730.0760.076
Bank 120.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 130.0000.0000.0000.0000.0000.0000.0550.0550.055
Bank 140.0000.0000.0000.0610.0610.0610.1730.1730.173
Bank 150.0000.0000.0000.0000.0000.0000.1580.1580.158
Bank 160.0000.0000.0000.0840.0850.0860.2330.2340.234
Bank 170.0000.0000.0000.0000.0000.0000.0600.0620.062
Bank 180.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 190.0000.0000.0000.0000.0000.0000.0830.0830.084
Bank 200.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 210.0000.0000.0000.0880.0910.0940.2390.2430.248
Bank 220.0000.0000.0000.0950.0950.0950.2780.2780.278
Bank 230.0000.0000.0000.0000.0000.0000.0850.0860.087
Bank 240.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 250.0000.0000.0000.0000.0000.0000.0650.0680.070
Bank 260.0000.0000.0000.0000.0000.0000.0000.0000.050
Bank 270.0000.0000.0000.0000.0000.0000.0000.0000.000
Bank 280.0000.0000.0000.0000.0000.0000.1680.1680.168
Source: Authors.Note: Average “bailout” cost is the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to the 0.08 level, whenever they fall below 0.03 (assumed default). We assume various different scenarios. On the business and individuals loans, we assume that (1) businesses and individuals have a zero increment to their default rates; (2) businesses and individuals in each credit risk category have an increase in their default rates equal to the average default of that credit risk category; and (3) businesses and individuals in each credit risk category have an increase in their default rates equal to two times the average default of that credit risk category. The second channel incorporates losses directly on the government securities, by assuming that banks may lose 0 percent, 10 percent, or 25 percent of the market value of their government securities for a variety of reasons. The assumed recovery rate on defaulted private sector loans is 45 percent in these simulations.
Source: Authors.Note: Average “bailout” cost is the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to the 0.08 level, whenever they fall below 0.03 (assumed default). We assume various different scenarios. On the business and individuals loans, we assume that (1) businesses and individuals have a zero increment to their default rates; (2) businesses and individuals in each credit risk category have an increase in their default rates equal to the average default of that credit risk category; and (3) businesses and individuals in each credit risk category have an increase in their default rates equal to two times the average default of that credit risk category. The second channel incorporates losses directly on the government securities, by assuming that banks may lose 0 percent, 10 percent, or 25 percent of the market value of their government securities for a variety of reasons. The assumed recovery rate on defaulted private sector loans is 45 percent in these simulations.
Table 8.7Simulated 99 Percent VaR Capital Ratio: Individual Banks, Government Default
Losses on Government Loans and Incremental Defaults on Business and Consumer Loans
Bank0%0% + 1 times the average historical default rates0%+2 times the average historical default rates10%10% + 1 times the average historical default rates10% + 2 times the average historical default rates25%25% + 1 times the average historical default rates25% + 2 times the average historical default rates
Bank 10.1890.1890.1890.1750.1740.1730.1260.1240.122
Bank 20.1290.1290.1290.1150.1140.1130.0510.0500.050
Bank 30.0850.0850.0840.0510.0480.045−0.026−0.029−0.032
Bank 40.1520.1510.1510.1280.1250.1220.0580.0550.052
Bank 50.0580.0560.0530.0110.005−0.002−0.092−0.100−0.108
Bank 60.3650.3640.3640.3350.3340.3330.2480.2470.245
Bank 70.0650.0640.063−0.001−0.002−0.003−0.121−0.123−0.124
Bank 80.1030.1030.1020.0840.0830.0800.0180.0160.013
Bank 90.2130.2130.2130.2100.2080.2060.1900.1880.186
Bank 100.0770.0770.0770.0400.0380.035−0.081−0.085−0.088
Bank 110.1020.1020.1020.0770.0770.0770.0030.0030.003
Bank 120.2380.2380.2380.2130.2110.2100.1340.1310.129
Bank 130.1320.1320.1320.1080.1070.1060.0380.0360.035
Bank 140.0800.0800.0800.0180.0180.018−0.094−0.094−0.094
Bank 150.1470.1470.1470.0860.0860.086−0.080−0.080−0.080
Bank 160.0670.0670.067−0.006−0.007−0.008−0.156−0.157−0.158
Bank 170.0940.0940.0940.0810.0800.0790.0170.0150.014
Bank 180.2250.2250.2250.2080.2070.2060.1370.1340.132
Bank 190.1960.1960.1960.1350.1350.134−0.005−0.006−0.006
Bank 200.1550.1540.1540.1390.1370.1340.0870.0840.081
Bank 210.0610.0610.060−0.012−0.015−0.019−0.164−0.169−0.173
Bank 220.0760.0760.076−0.016−0.016−0.016−0.199−0.199−0.199
Bank 230.1100.1100.1100.0800.0790.079−0.011−0.012−0.013
Bank 240.1400.1390.1390.1360.1340.1330.1130.1100.107
Bank 250.0950.0950.0950.0730.0710.0690.0100.0070.005
Bank 260.1610.1610.1610.1320.1310.1300.0460.0450.043
Bank 270.1960.1960.1960.1770.1750.1730.1120.1100.107
Bank 280.0920.0920.0920.0400.0400.040−0.095−0.095−0.095
Source: Authors.Note: The 99 percent value-at-risk (VaR) simulated capital ratio is the threshold below which banks’ capital ratio will fall 1 percent of the time. We assume various different scenarios. On the business and individuals loans, we assume that (1) businesses and individuals have a zero increment to their default rates; (2) businesses and individuals in each credit risk category have an increase in their default rates equal to the average default of that credit risk category; and (3) businesses and individuals in each credit risk category have an increase in their default rates equal to two times the average default of that credit risk category. The second channel incorporates losses directly on the government securities, by assuming that banks may lose 0 percent, 10 percent, or 25 percent of the market value of their government securities for a variety of reasons. The assumed recovery rate on defaulted private sector loans is 45 percent in these simulations.
Source: Authors.Note: The 99 percent value-at-risk (VaR) simulated capital ratio is the threshold below which banks’ capital ratio will fall 1 percent of the time. We assume various different scenarios. On the business and individuals loans, we assume that (1) businesses and individuals have a zero increment to their default rates; (2) businesses and individuals in each credit risk category have an increase in their default rates equal to the average default of that credit risk category; and (3) businesses and individuals in each credit risk category have an increase in their default rates equal to two times the average default of that credit risk category. The second channel incorporates losses directly on the government securities, by assuming that banks may lose 0 percent, 10 percent, or 25 percent of the market value of their government securities for a variety of reasons. The assumed recovery rate on defaulted private sector loans is 45 percent in these simulations.

While having the previously noted limitations, this approach to modeling correlated market, credit, and sovereign risk highlights the danger of the exposure of many Brazilian banks to very high levels of GOB securities. It is true that Brazil has been implementing more responsible fiscal and monetary policies, controlling inflation, and obtaining important positive balance in exports and imports, among other positive indicators. However, Brazil is still an emerging economy, vulnerable to flow of capitals, with a huge stock of debt.34 Thus, government securities are not free of risk, and the correlated risk of government default should be accounted for.

C. Rating Brazilian banks

We will now compare the simulated results obtained in the previous section with rating agency ratings of Brazilian banks’ short-term debt instruments. We will focus our attention on a single output derived from the simulations, including the risk of a sovereign default. In particular, we will look at the 99 percent confidence level capital ratio (99 percent VaR level) for the scenario where in the event of a sovereign default banks lose 10 percent of the market value of their government securities, experience an incremental increase in defaults on their private sector loans equal to twice the average default rate, and have a 45 percent average recovery rate on defaulted private sector loans. This measure embeds both the default probability and the size of associated monetary loss and is consistent with what the rating agencies also utilize for rating banks, businesses, and sovereigns. For this purpose, we will divide our sample of banks into three groups, according to their 99 percent VaR capital level. Group 1 will be composed of banks with 99 percent VaR capital ratios less than 0.07, Group 2 with banks with 99 percent VaR capital ratios between 0.07 and 0.13, and Group 3 with 99 percent VaR capital ratios above 0.13. Given that the 99 percent VaR sets the threshold below which banks’ capital ratio will fall 1 percent of the time, the lower the 99 percent VaR level, the closer the bank is to the assumed critical 0.03 capital ratio level and the higher the probability of default (thus the riskier the bank).

Our ratings are generally consistent with Moody’s and Standard & Poor’s. Out of 16 banks also rated by Moody’s, we had a similar rating on 12 banks. Out of 10 banks also rated by Standard & Poor’s, we had a similar rating on 7 banks. However, out of 18 banks also rated by Fitch, we had a similar rating on only 9 banks.

D. Systemic banking system risk

For assessing systemic banking system risk, we will consider two cases. First, we aggregate the 28 banks into one single bank. Second, we aggregate banks according to their risk rating, in the three groups described earlier. Aggregated balance sheet accounts were obtained by simple addition from all banks in each group, whereas loan credit quality distributions and assets and liability maturity structures were obtained by a weighted average (size of each category relative to total assets, in each bank).

One Single Aggregate Bank

The simulation results for a single aggregate bank are consistent with what we have obtained for individual banks. When we model correlated market and private sector loan credit risk but do not consider government default, simulated capital ratios are comfortably above an assumed 0.08 target capital level, with small standard deviation (0.003). This result is intuitive given the substantial amount of government securities that are collectively held by the 28 banks in our simulation sample. Because the single aggregate bank has a 0.154 initial capital ratio, it does not face solvency problems when a sovereign default imposes market value losses on government securities of 10 percent. However, Table 8.8 indicates that at a 25 percent loss rate on government securities, the default rate on the single aggregate bank may reach 3 percent (3.6 percent) when the assumed average recovery rate on private sector loans is 45 percent (15 percent). The associated cost to bring the single bank’s capital ratio back to a 0.08 level averages 5.7 percent (6.1 percent) of the bank’s total assets. The 99 percent VaR capital ratio also deteriorates substantially. Under the no-government-default assumption, it is 0.147, while it drops to 0.021 (0.016) under the above sovereign default scenario when the average recovery rates on defaulted private sector loans are 45 percent (15 percent).

Table 8.8Simulated Default Probabilities, Bailout Costs, and 99 Percent Capital Ratios: Government Default Risk Considered, All 28 Banks Modeled as a Single Bank
Losses on Government Loans and Incremental Defaults on Business and Consumer Loans
All 28 Banks0%0% + 1 times the average historical default rates0% + 2 times the average historical default rates10%10% + 1 times the average historical default rates10% + 2 times the average historical default rates25%25% + 1 times the average historical default rates25% + 2 times the average historical default rates
45 percent recovery rate on business and customers’ loans
Default probabilities0.0000.0000.0000.0000.0000.0000.0170.0220.030
Bailout cost0.0000.0000.0000.0000.0000.0000.0550.0570.057
99% VaR level0.1430.1430.1430.1100.1080.1050.0270.0240.021
15 percent recovery rate on business and customers’ loans
Default probabilities0.0000.0000.0000.0000.0000.0000.0250.0330.036
Bailout cost0.0000.0000.0000.0000.0000.0000.0580.0590.061
99% VaR level0.1420.1410.1410.1060.1030.1010.0220.0190.016
Source: Authors.Note: This table presents simulated default probabilities on groups of banks; average “bailout cost as the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to 0.08 level, whenever they fall below 0.03 (assumed default); and the 99 percent value-at-risk (VaR) simulated capital ratio as the threshold below which banks’ capital ratio will fall 1 percent of the time. We assume various different scenarios. On the business and individuals loans, we assume that (1) businesses and individuals have a zero increment to their default rates; (2) businesses and individuals in each credit risk category have an increase in their default rates equal to the average default of that credit risk category; and (3) businesses and individuals in each credit risk category have an increase in their default rates equal to two times the average default of that credit risk category. The second channel incorporates losses directly on the government loans, by assuming that banks may lose 0 percent, 10 percent, or 25 percent of the market value of their government loans for a variety of reasons.
Source: Authors.Note: This table presents simulated default probabilities on groups of banks; average “bailout cost as the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to 0.08 level, whenever they fall below 0.03 (assumed default); and the 99 percent value-at-risk (VaR) simulated capital ratio as the threshold below which banks’ capital ratio will fall 1 percent of the time. We assume various different scenarios. On the business and individuals loans, we assume that (1) businesses and individuals have a zero increment to their default rates; (2) businesses and individuals in each credit risk category have an increase in their default rates equal to the average default of that credit risk category; and (3) businesses and individuals in each credit risk category have an increase in their default rates equal to two times the average default of that credit risk category. The second channel incorporates losses directly on the government loans, by assuming that banks may lose 0 percent, 10 percent, or 25 percent of the market value of their government loans for a variety of reasons.

Although used frequently, modeling systemic risk via a single aggregate bank has significant limitations. First, it masks the fact that under certain conditions (e.g., 10 percent loss rate on government securities), a number of individual banks could fail simultaneously.35 Second, this approach does not account for interbank exposures that can trigger sequential failures. Still, the simulated results do show the importance of modeling correlated sovereign risk not only at an individual bank level but also, and perhaps most important, at a systemic level.

Multiple Aggregate Banks

So far we have simulated the banks individually and taken account of correlated market, credit, and sovereign risk. However, we have not taken into account one important channel for propagating a systemic crisis, through interbank credit exposures. For this purpose, we will simulate the three aggregated banks (Groups 1, 2, and 3) simultaneously, under the same financial and economic environment.36 Then we will examine the simulated capital ratios for all three banks to determine whether one or more banks fail. In that event, we will then calculate the default impacts on other banks as the failed banks become incapable of repaying their interbank debts. This exercise will be explained in more detail in the subsection below on simultaneous aggregate banks. Before we get there, however, it is useful to describe the groups separately and to simulate them individually, to have a more precise understanding of their default risk.

Individual Aggregate Banks. Simulated capital ratios, without sovereign risk, show that all three groups of banks are profitable and on average have increasing capital ratios.37 When sovereign risk is considered (Table 8.9), then only Group 3 survives all our simulated scenarios (same as for the individual banks). Group 1 has a small nonzero default probability at a 10 percent loss rate on government securities. Group 2 also has a nonzero default rate when the assumed losses in the market value of government debt increases from 10 percent to 25 percent. Under the scenario of 25 percent average losses on government securities and a 45 percent average recovery rate on defaulted private sector loans, Group 1 defaults at an average rate of 0.048, and Group 2 defaults at rates in the range of 0.1 percent to 1.8 percent. The average cost of “bailing out” these banks is large: for Group 1, it surpasses 12 percent of total assets required to bring its capital ratio back to a 0.08 level. For Group 2, the average bailout cost is around 5 to 6 percent of its total assets. Under the assumption of a lower 15 percent recovery rate on defaulted private sector loans, Group 1’s and Group 2’s default probabilities and bailout costs increase.

Table 8.9Simulated Default Probabilities, Average “Bailout” Cost, and 99 Percent Capital Ratios: Individual Aggregate Banks, Government Default
Losses on Government Loans and Incremental Defaults on Business and Consumer Loans
Aggregate Banks0%0% + 1 times the average historical default rates0% + 2 times the average historical default rates10%10% + 1 times the average historical default rates10% + 2 times the average historical default rates25%25% + 1 times the average historical default rates25% + 2 times the average historical default rates
Recovery rate on defaulted private sector loans = 45%
Default probabilities
Group 10.0000.0000.0000.0010.0010.0010.0480.0480.048
Group 20.0000.0000.0000.0000.0000.0000.0010.0040.018
Group 30.0000.0000.0000.0000.0000.0000.0000.0000.000
Bailout cost
Group 10.0000.0000.0000.0540.0550.0550.1220.1230.124
Group 20.0000.0000.0000.0000.0000.0000.0510.0540.057
Group 30.0000.0000.0000.0000.0000.0000.0000.0000.000
99% VaR level
Group 10.0870.0870.0860.0460.0460.045−0.048−0.049−0.049
Group 20.1320.1300.1260.1090.1030.0960.0450.0350.025
Group 30.2110.2110.2110.1860.1840.1830.1120.1100.108
Recovery rate on defaulted private sector loans = 15%
Default probabilities
Group 10.0000.0000.0000.0020.0020.0020.0480.0480.048
Group 20.0000.0000.0000.0000.0000.0000.0070.0170.034
Group 30.0000.0000.0000.0000.0000.0000.0000.0000.000
Bailout cost
Group 10.0000.0000.0000.0580.0570.0570.1280.1290.130
Group 20.0000.0000.0000.0000.0000.0000.0570.0600.063
Group 30.0000.0000.0000.0000.0000.0000.0000.0000.000
99% VaR level
Group 10.0810.0810.0810.0400.0390.038−0.055−0.056−0.057
Group 20.1250.1230.1190.1030.0950.0860.0340.0240.013
Group 30.2080.2080.2070.1820.1800.1780.1060.1050.103
Source: Authors.Note: This table presents simulated default probabilities on groups of banks; average “bailout” cost as the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to 0.08 level, whenever they fall below 0.03 (assumed default); and the 99 percent value-at-risk (VaR) simulated capital ratio as the threshold below which banks’ capital ratio will fall 1 percent of the time. We assume various different scenarios. On the business and individuals loans, we assume that (1) businesses and individuals have a zero increment to their default rates; (2) businesses and individuals in each credit risk category have an increase in their default rates equal to the average default of that credit risk category; and (3) businesses and individuals in each credit risk category have an increase in their default rates equal to two times the average default of that credit risk category. The second channel incorporates losses directly on the government securities, by assuming that banks may lose 0 percent, 10 percent, or 25 percent of the market value of their government securities for a variety of reasons.
Source: Authors.Note: This table presents simulated default probabilities on groups of banks; average “bailout” cost as the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to 0.08 level, whenever they fall below 0.03 (assumed default); and the 99 percent value-at-risk (VaR) simulated capital ratio as the threshold below which banks’ capital ratio will fall 1 percent of the time. We assume various different scenarios. On the business and individuals loans, we assume that (1) businesses and individuals have a zero increment to their default rates; (2) businesses and individuals in each credit risk category have an increase in their default rates equal to the average default of that credit risk category; and (3) businesses and individuals in each credit risk category have an increase in their default rates equal to two times the average default of that credit risk category. The second channel incorporates losses directly on the government securities, by assuming that banks may lose 0 percent, 10 percent, or 25 percent of the market value of their government securities for a variety of reasons.

Another important risk measure, the 99 percent VaR capital level, provides an even more distinct picture. All banks have their 99 percent VaR capital level deteriorate when a sovereign default results in market value losses on government loan. If such losses reach 25 percent of market value, then the 99 percent VaR capital levels for Groups 1, 2, and 3 fall to the range of -0.049 (-0.056), 0.035 (0.024), and 0.11 (0.105), respectively, for the 45 percent (15 percent) assumed recovery rates on defaulted private sector loans.

Simultaneous Aggregate Banks. For assessing systemic risk, we simulate correlated market, credit, and sovereign risk for the three groups of aggregate banks simultaneously, under the same financial and economic environment. Then, in a second analytical step, we introduce the interbank propagation channel by adjusting each group’s simulated capital ratio whenever one of the other two groups’ simulated capital ratios fall below 0.03, using the information on interbank lending and assuming that the groups borrow money from others proportionately to their total assets. For example, Group 1 lends 3.6 percent of its total assets or equivalently R$5,503.60 million. Given that Group 2 has total assets of R$551,250.10 million, and the sum of Group 2 and Group 3 total assets is R$878,571.10 million, we assume that (R$551,250.10/R$878,571.10 =) 0.63 of Group 1’s total interbank lending is lent to Group 2. The remaining (1 – 0.63 =) 0.37 is lent to Group 3.

For estimating the impact of interbank lending, when banks default, we assume interbank lending to be risk free in the first step of the simulation. Subsequently, if a bank fails, then we assume that the other banks will recover 50 percent of the value of the defaulted interbank loans. Obviously, higher recovery rates would certainly diminish the impact of interbank default. We then recalculate simulated total assets and simulated capital ratios, after deducting the defaulted amounts that are not recovered. With new simulated capital ratios, we replicate the same VaR analysis and also estimate default rates and the monetary cost to bring each group’s capital ratios back to a 0.08 capital level. We also estimate the default rates and monetary cost when two banks and three banks default simultaneously. These results are presented in Tables 8.10 and 8.11, which assume a 45 percent and 15 percent recovery rate on defaulted private sector loans, respectively. A few comments are in order.

Table 8.10Systemic Risk: Simultaneously Simulated Aggregate Banks’ Recovery Rate on Defaulted Private Sector Loans = 45 Percent
Incremental Defaults on Business and Consumers’ Loans
Losses on Government Loans+1 times the average historical default rates+2 times the average historical default rates
Probability of Groups 1 and 2 defaulting at the same time (and associated cost given default as a proportion of total assets, in parentheses), to bring both banks’ capital ratios to 0.08
00%0.0000.0000.000
10%0.0000.0000.000
25%0.0160.0210.030
(0.109)(0.110)(0.111)
40%0.0480.0480.048
(0.239)(0.251)(0.258)
50%0.0480.0480.048
(0.358)(0.362)(0.366)
Probability of all groups defaulting at the same time (and associated cost given default as a proportion of total assets, in parentheses), to bring all banks’ capital ratios to 0.08
0%0.0000.0000.000
10%0.0000.0000.000
25%0.0000.0000.000
40%0.0480.0480.048
(0.168)(0.177)(0.182)
50%0.0480.0480.048
(0.271)(0.275)(0.279)
Source: Authors.Note: This table presents simultaneously simulated default probabilities on groups of banks; average “bailout” cost as the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to 0.08 level, whenever they fall below 0.03 (assumed default); and the 99 percent value-at-risk simulated capital ratio as the threshold below which banks’ capital ratio will fall 1 percent of the time.
Source: Authors.Note: This table presents simultaneously simulated default probabilities on groups of banks; average “bailout” cost as the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to 0.08 level, whenever they fall below 0.03 (assumed default); and the 99 percent value-at-risk simulated capital ratio as the threshold below which banks’ capital ratio will fall 1 percent of the time.
Table 8.11Systemic Risk: Simultanesously Simulated Aggregate Bank’s Recovery Rate on Defaulted Private Sector Loans = 15 Percent
Incremental Defaults on Business and Consumers’ Loans
Losses on Government Loans+1 times the average historical default rates+2 times the average historical default rates
Probability of Groups 1 and 2 defaulting at the same time (and associated cost given default as a proportion of total assets, in parentheses), to bring both banks’ capital ratios to 0.08
0%0.0000.0000.000
10%0.0000.0000.000
25%0.0340.0360.039
(0.114)(0.117)(0.119)
40%0.0480.0480.048
(0.259)(0.267)(0.274)
50%0.0480.0480.048
(0.369)(0.373)(0.378)
Probability of all groups defaulting at the same time (and associated cost given default as a proportion of total assets, in parentheses), to bring all banks’ capital ratios to 0.08
0%0.0000.0000.000
10%0.0000.0000.000
25%0.0000.0000.000
40%0.0480.0480.048
(0.183)(0.189)(0.195)
50%0.0480.0480.048
(0.280)(0.284)(0.289)
Source: Authors.Note: This table presents simultaneously simulated default probabilities on groups of banks; average “bailout” cost as the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to 0.08 level, whenever they fall below 0.03 (assumed default); and the 99 percent value-at-risk simulated capital ratio as the threshold below which banks’ capital ratio will fall 1 percent of the time.
Source: Authors.Note: This table presents simultaneously simulated default probabilities on groups of banks; average “bailout” cost as the average capital (as percentage of total assets) necessary to bring banks’ capital ratio back to 0.08 level, whenever they fall below 0.03 (assumed default); and the 99 percent value-at-risk simulated capital ratio as the threshold below which banks’ capital ratio will fall 1 percent of the time.

First, in Table 8.10, as expected, the interbank propagation channel moves from the riskier groups to the less risky groups. Second, because Group 3 is very well capitalized and has the highest credit profile, it defaults only when incurring a much bigger loss on the government securities. Group 3 starts having solvency problems only when a sovereign default imposes a high average loss of 40 percent or more on the market value of government securities. This reveals another nocive facet of banks holding exceedingly large concentrations of government securities. In the event of a sovereign default, the government has constrained debt management alternatives. Should the government take actions that result in a heavy loss on the market value of government securities, then it may trigger a systemic risk default in the financial system. In the particular case of GOB, our analysis suggests that losses on government securities of 10 percent could create significant solvency problems for 5 or 6 out of 28 banks analyzed. Higher loss rates would, of course, create even larger systemic banking system risks. Given that the amount of GOB securities in Brazilian balance sheets is much larger than the amount of business and consumer loans, the impact of incremental defaults on businesses and households has much smaller effects on banks’ default rates and monetary losses. Third, when we integrate the interbank risk into our framework, systemic default rates (i.e., risk of multiple bank failures in the same time period) are smaller compared with the individual banks’ default rates. For example, at a 10 percent loss rate on government securities, there is a zero probability of both Group 1 and Group 2 defaulting simultaneously. At a 25 percent loss rate on government securities, the probability of both Group 1 and Group 2 defaulting at the same time reaches 3.0 percent (3.9 percent) for average recovery rates on private sector loans of 45 percent (15 percent). However, when the systemic event takes place, it is a lot more costly (as a percentage of the assets of the defaulting banks) than previously assessed when simulating all 28 banks as a single bank. We have estimated the average cost to “bail out” the single bank to be 5.5 percent of its total capital under the scenario of a 25 percent average loss on government securities. Under the same scenario, the two riskier groups default at a rate in the range of 1.6 percent to 3.9 percent, with the average cost to bring their capital level back to the 0.08 level equal to over 10 percent of their total assets. A comparison of Tables 8.9 and 8.10, which assume the higher (45 percent) and lower (15 percent) recovery rates on defaulted private sector loans, illustrates the potential significance of this variable on systemic risk levels.

3. Conclusion

We have simulated 28 individual Brazilian banks considering two different scenarios. In one scenario, we access correlated market and business loan credit risk but assume that the Brazilian government will never default on its debt obligations. With few exceptions, Brazilian banks perform very well in these simulations. In a second set of simulations, we model correlated market, credit, and sovereign risk. At a 10 percent loss rate on government securities in the event of a sovereign default, 6 of the 28 banks could fail. At a 25 percent loss rate on government securities, over half of the 28 banks could fail. Banks with more diversified portfolios of government, business, and consumer loans are found to be more profitable on average and to also perform better in the case of a potential government default. These results illustrate the well-known risk of concentrated lending to an entity with a nonzero default rate (e.g., GOB). It also reveals another nocive facet of banks holding exceedingly large concentrations of risky government securities. In the event of a sovereign default, the government has constrained debt management alternatives. Should the government take actions that significantly reduce the market value of government securities, it could trigger a systemic banking system failure. This suggests that the development of global markets for sovereign debt denominated in local currency could have the dual benefits of allowing sovereigns to diversify their borrowing sources and banks to diversify their loan portfolios and default risk.

Our simulations also provide a way of grouping the banks, based on their creditworthiness, under an integrated risk framework. We find that our bank risk categorization is generally consistent with Moody’s and Standard & Poor’s ratings but less so when compared with Fitch ratings.

We utilize two different approaches to measure systemic risk. First, we aggregate all the banks in one single bank and simulate it individually, with the possibility of government default. Results for this approach show that the financial system might be dragged down by a government default only when the average loss on government securities is 25 percent or higher and that the cost to bail out the system (to bring the average capital ratio to a 0.08 level) is about 5.7 percent of the total assets, under this scenario. In the second approach, we simulate three aggregated groups of banks simultaneously, under the same financial and economic environment. Our results show that if a bank has heavy interbank credit exposure as compared with its initial capital, then correlated interbank default losses may become “the straw that breaks the camel’s back.” We are also able to estimate the very substantial cost of recapitalizing the banking system in the event of a systemic banking system failure. In the particular case of GOB, in the event of government default, losses of 10 percent or higher on government securities could have a significant systemic impact on the banking system. We also find that in extreme events (sovereign defaults), should loan recovery rates on private sector loans be systematically depressed, then banking system systemic risk also increases significantly.

Modeling correlated market, credit, sovereign, and interbank risk is a challenging task. All methodologies which might be used have limitations. In spite of the limitations we have identified, we believe that the portfolio simulation methodology we present in this chapter is able to deal with all of these correlated risks and has the potential to provide important insights into individual bank and systemic banking system risk levels. To the best of our knowledge, no one else has put forward a systematic methodology for assessing correlated market and credit (sovereign, private sector, and interbank) default risk for a financial system. Provided that the required input information is available, we believe that the proposed models can provide useful risk assessment and management information to bank management, bank regulators, sovereigns, rating agencies, and investors.

References

For example, in previous years, there were a number of correlated failures of “agricultural” and “energy” banks in the United States. In the 2007–08 period, it was notable the number of correlated failures of institutions with concentrated exposures to real estate mortgages and mortgage-backed securities.

Based on the work of Barnhill and Maxwell (2002).

The ValueCalc Global Portfolio and Credit Risk software, copyright FinSoft, Inc. (1996-2005), was used to undertake the risk analyses reported in this study.

Several authors have stressed the importance of macroeconomic factors, such as cyclical GDP downturns, interest rate increases, or exchange rate devaluations, on banks’ performance (e.g., Gorton, 1988; and Lindgren, Garcia, and Saal, 1996; among others).

Each simulation run produces a random path over a certain time period (e.g., one year). To minimize computational effort and time, balance sheet accounts are recalculated only at the end of the time period.

According to data provided by the Brazilian Treasury Department, the spread on GOB U.S. dollar-denominated external borrowings averaged over 5 percent during 2004. This is generally consistent with an expected default rate of 4.5 percent.

We note that during the very stressful times of 2007–08, none of the banks that we model in this study failed, consistent with our results.

For a more detailed discussion of the simulation methodologies used in this study see Barnhill and Souto (2008b).

See Table 8.1 for a description of the data used in this study along with respective sources.

In circumstances where banks hold significant mortgage loans, it is useful to model regional real estate prices as a systematic credit risk driver (see Barnhill, Papapanagiotou, and Schumacher, 2003; and Barnhill, Papapanagiotou, and Souto, 2004) that produces correlated changes in the loan-to-value ratio and defaults on mortgage loans in various regions. Given that most Brazilian banks hold very few mortgage loans, we did not model Brazilian real estate prices.

In the present study, the composition of the bank asset and liability portfolio is held constant over the risk horizon (e.g., one year) and is repriced after each run of the simulation using the simulated financial and economic variables and credit qualities of the borrowers. Simulations were run 2,000 times using monthly (i.e., 12) time steps. To infer the potential size of Monte Carlo simulation errors, we simulated some of the banks multiple times. The difference between the maximum and minimum simulated capital ratios over the various simulation run depends on the confidence level considered. At the extremities (e.g., 99th percentile), the variation in simulated capital ratios is typically on the order of 0.1 to 0.2 percent. At the 50th percentile, the variation in simulated capital ratios is on the order of 0.02 to 0.03 percent. The critical capital ratio at which banks are assumed to fail is 3 percent. Given the relatively small size of the above simulation errors, we believe that 2,000 runs are adequate for the purposes of this study.

Considering the large interest rate spreads charged by the banks and the fact that this information was not available to us on a bank-by-bank basis, different credit spreads were estimated for each bank so as to match the historical net interest income of each bank and produce average spreads that are consistent with the reported bank-by-bank interest rate spread (Central Bank of Brazil Web site) and assuming that the credit spread profile across the different credit risk categories was proportional to the expected default rate for each category.

The use of an arbitrage-free interest rate model such as the Hull and White extended Vasicek model (Hull and White, 1990, 1993, 1994)) allows the estimation of an entire term structure of interest rates at the end of each simulation run that is needed to value financial instruments. The volatilities and correlations between the various financial and economic environment variables for this study were estimated from historical Brazilian data.

The optimal decay factor was estimated by minimizing the difference between historical and simulated volatility in the expression (σi,t2σi,t12)+(σi,t2σi,t62)+(σi,t2σi,t122). For more details, please see Barnhill and Souto (2008a).

On the basis of the data we obtained, we categorized the liabilities into the following three maturity groups: < 1 year, between 1 and 3 years, and >3 years. The simulation methodology, however, is flexible enough to handle multiple maturities for both liabilities and assets as well as multiple currency denominations.

The allocation of the 400 stylized business and consumer loans across sectors and regions reflects the amount of the banks lending in the sectors and regions as well as the credit quality of the loans. Sectors and regions with larger amounts of higher credit risk loans (which default at a higher rate) are allocated a larger portion of the available loans. We find that this approach produces more consistent bank risk assessments.

We also specify the time horizon and the time steps over which price paths and balance sheet accounts will be simulated and the number of simulation runs.

It is possible to model a great variety of other financial instruments (e.g., bonds, zero coupon bonds, variable rate loans, forward contracts, swaps, options) within our simulation framework.

For a more detailed discussion of the credit risk modeling methodologies used in this chapter, see Barnhill and Souto (2008b).

We also find that typical betas and firm-specific risk levels increase as a firm’s credit quality decreases. The increasing betas are due in large part to the typically increasing debt-to-value ratios for lower credit-quality companies, which increase the systematic volatility of equity returns. Higher firm-specific risk levels are consistent with firms having a lower credit rating and higher default risk.

Once outside of the assumed debt-to-value range for the initial credit rating, subsequent upgrades (downgrades) occur when the simulated debt-to-value ratio goes below (above) the minimum (maximum) debt-to-value ratios for the sequential rating categories.

The recovery rate on defaulted business and consumer loans (“private sector loans”) is an important risk factor. In the case of Brazil, historically the legal system was viewed as taking an exceptionally long time to resolve loan defaults and bankruptcies, and the recovery rate on defaulted loans was low (e.g., 15 percent). In June 2005, a decade-long effort to modernize Brazil’s bankruptcy laws came into effect. This change is projected to improve the recovery prospects for defaulted Brazilian bank loans (see Eccles, 2005). Thus, for the current study, when we undertake forward-looking risk assessments for Brazilian banks and the banking system, our base case assumption is that the recovery rate on defaulted private sector loans is drawn from a beta distribution with a mean value of 0.45 and a standard deviation of 0.25. However, we will also report simulation results based on an assumed recovery rate of 15 percent to illustrate the potential impacts of a lower recovery rate on systemic banking system risk levels. Although we have not done so in this study, the methodology could be modified to dynamically adjust the assumed recovery rate on defaulted loans to reflect a variety of variables, including end-of-period borrower debt ratios or loan-to-value ratios and banking system total loan default levels.

We were unable to obtain the data required to develop a separate credit risk model for consumer loans. Thus, in this study, we model consumer loans as business loans. For this purpose, we model a systematic risk factor for each region that has the return and volatility characteristics of the Ibovespa stock index but that has correlations with other financial and economic environment variables equal to those of the regional unemployment rates. This model allows us to generate credit transition probabilities and default rates similar to those reported by Brazilian banks and also account for some of the diversification benefits of lending to different types of borrowers (i.e., businesses in various sectors and consumers in various regions).

It is important to note that we are modeling bank’s economic equity capital ratio.

As of December 31, 2008, Standard and Poor’s (S&P) rated 123 sovereigns. Over the previous 12 months, S&P had downgraded 29 sovereigns and upgraded 11 additional ones. At that same date, S&P indicated 2 positive outlooks for upgrades and 26 negative outlooks for downgrades. “These negative trends stem largely from difficulties adjusting to mounting economic pressures” (Cavanaugh, 2009). The recent crisis has evidenced how sovereign risk has become an important risk consideration for banks.

We chose this methodology for modeling the sovereign risk because of simplicity and to save computational time. For more elaborate alternatives to this method of modeling sovereign default risk, which also could be used in this type of systemic bank risk assessment model, see Barnhill and Kopits (2004) and Barnhill (2006).

Each simulation run produces a random path over a certain time period (e.g., one year). To minimize computational effort and time, balance sheet accounts are recalculated only at the end of the time period.

The current version of the ValueCalc programs allows for simulating only three banks simultaneously (for computer memory reasons), although it has the potential to simulate any number of banks simultaneously.

Discussions with bank regulators in several countries indicate that at some low but positive capital ratio, banks start having liquidity and other problems that make it difficult for them to survive. For this study, we assume that banks are likely to fail if their capital ratio (total asset minus total liabilities, over total assets) falls below 3 percent. Our model is, of course, flexible to accommodate other assumptions.

Some international institutions and many central banks create a signage aggregate bank for conducting vulnerability analysis of a country’s banking sector. We believe that this approach has serious limitations in that it masks the fact that many individual banks may be much more risky than the “average aggregate bank.”

Barnhill and Souto (2008b) report a fourth set of simulations that demonstrate that the means and standard deviations of the simulated rates of return on average bank assets and equity are unbiased predictors of historical mean returns and standard deviations of returns.

In fact, as we shall see in the next section, countries at the same sovereign rating as Brazil (B) have a one-year default rate of 4.5 percent on average in the 1994-2004 period, according to Klaar, Rawkins, and Riley (2004).

This study was conducted when Brazil was rated as B. Currently Brazil is being rated as BBB–by most rating agencies. With this higher credit rating (and consequently lower expected sovereign default probability), if this study were to be repeated today, then our bank and systemic banking system risk estimates would be much lower.

Total debt to GDP is around 55 percent, as of December 2004 (Government Financial Statistics, IMF).

Also, we are simulating only 28 Brazilian banks (70 percent of financial system total assets). Including more banks would certainly push the cost for bailing the financial system out to a higher level.

The choice of using three banks as opposed to all 28 banks was made primarily because of memory limitations in the ValueCalc software.

For more detail on these simulations, see Barnhill and Souto (2008b).

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