Credit Risk Stress Testing

1 Credit Risk Stress Testing Stress Testing Features of Risk Evaluator 1. 1. Introduction Risk Evaluator is a financial tool intended for evaluating market and credit risk of single positions or of large multi-currency portfolios. RiskMetrics and CreditMetrics methodologies of J.P.Morgan Bank and structured Monte Carlo simulation are implemented for about financial instruments including interest rate, foreign exchange and stock instruments, futures and options. Credit Risk of a transaction expresses the uncertainty of future cash flow payments involved by the credit standing of the counterpart to that transaction. The risk to a particular party depends on two factors: changes in market rates, that is market risk and whether or not the counterpart will default prior to the maturity, that is credit risk. The main task in evaluation credit risk is the computation of the credit risk exposure profile showing the notional amount that can be lost when a counterpart default its obligations. The credit risk of a counterpart or of a multi-party portfolio is measured by a single value, called credit Value at Risk (VaR). VaR represents the expected loses (adverse move) of the portfolio value due to credit events at given confidence level and for given credit risk horizon. The resulting Value at Risk is set normally to give a 95% confidence level, that is the actual loss should exceed the Value at Risk figure only in 5% of cases. The risk horizon is set in the most cases to one year, but larger or shorter risk horizons are meaningful too. Risk evaluation software is important for financial institutions due to the BIS/Basle regulations. Risk Evaluator covers the most BIS/Basle requirements for Value at Risk (VaR) calculation. Stress testing provides useful information on the model s range of results, and also allows investigation of the sensitivity of risk estimates to model inputs and critical assumptions. Higher evaluation model transparency can be obtained through changes of input data and exploration of credit risk results. The BIS report describes reported stress testing activities as including: deterioration in credit ratings, changes in default probabilities, deterioration in market spreads, changes of recovery rates, and changes in correlation structures. This study was inspired by [], a publication in RiskMetrics Jourmal, May. It describes briefly the stress testing features of Risk Evaluator 1. outlining stress testing results for major model input factors having influence on credit risk VaR. The study provides examples of the kind of stress testing and sensitivity analysis possible using the Risk Evaluator examining the risk profile of an Eurobond benchmark.. Benchmark Portfolio of Eurobonds Risk Profile The portfolio used in this analysis study is a set of 15 liquid Eurobonds in currencies (BEF, DEM, ESP, EUR, FRF, IEP, ITL and NLG). The portfolio is weighted by bond liquidity. The bonds are assigned to a set of obligors rated from A1 to Ba3 within Moody1 rating system (see Figure 1) group ed in two

groups: A1, A and A3 middle to good quality obligors with % and Ba1, Ba and Ba3 passable obligors with %. The average rating of the portfolio is A3. Figure 1 Running a simulation summary report in Risk Evaluator using EUR as base currency, a one-year risk horizon, and 1 simulation runs provides the risk profile in Table 1. Table 1 Sample Results from a Simulation Summary on the Portfolio Estimated Parameter Result RORAC Expected Portfolio Return 5.9% 1.5% 3.3 3.9% 1.3.3 Percentile Loss.3%...5%.575 We have a 99% confidence that we will not lose more than 3.9% of the expected value of the portfolio at the risk horizon. The RORAC is calculated as the Return/Risk quotient. Risk Evaluator produces correlated credit VaR results grouping obligors into sub -portfolios according to industry sectors and company structures. A sample 5 % risk report from a simulation shows risk estimation results by industry sectors (see Table.). The portfolio VaR is 1.5 % of portfolio expected value (distribution mean). The VaR results by industry sectors are presented in column 3 of Table. The simple uncorrelated sum of VaR of industry sectors produce a higher VaR result of.71 %, so the risk diversification effect is 1.19 %. The risk diversification effect can be explained through following correlation chain: Obligors are assigned to branch indexes on percent basis, branch indexes are bound to branch index correlation matrix that is obtained from historic index series. Obligor correlation is derived from branch index assignments and from branch index correlation matrix. Industry sector correlation is derived from obligor assignments to industry sectors and from obligor correlation.

3 Table Sample 5 % Risk from a Simulation Report by Industry Sectors Industry Sector VaR VaR (%) Expected Value Financial 53,.7.357% 19,3,99. Transportation 39,97.75.99% 1,35,735. Utilities 5,995.31 3.11% 1,73,19.1 Banks 99,53. 3.1175% 1,3,.51 Industrial 17,.1 1.9% 9,951,1.9 Simple Sum,55,5..71% 75,5,13.3 Portfolio Result 1,19,5.53 1.51% 75,5,13.3 Diversification Effect 95 9.9 1.19% 3. Sensitivity Analysis For a portfolio of bonds, Table 3 summarizes the major model input factors that have an impact on the risk estimates in terms of their effect on the estimate of price volatility and asset return correlation. Risk Evaluator allows construction of stress test scenarios containing specific changes in major model input factors. Following stress testing scenario features are available the whole portfolio: Change transition matrixes based on systematic component and credit year quality. Spreading ratings related spread curves by parallel shifts and long or short end twists. Spreading market risk volatility by parallel shifts and long or short end twists important for evaluation of market driven instruments. Chock or set constant correlation within branch index correlation matrix. A set of stress test scenarios can be related to individual industry sectors: Up or Down grading all counterparts within industry sector. Increase or decrease volumes of counterpart positions within industry sector. Change Exogenous Factor (market dependence) for counterparts, that is change the relation between obligor specific risk and branch index dependence risk within industry sectors. All parameters defining scenarios are stored in scenario tables for later use. The user can change or reload existing scenarios. Credit risk results and corresponding scenario parameters are stored using a relation to allow for scenario and credit risk result reporting. Table 3 Model factors used for stress testing in Risk Evaluator Model Factor Impact on Model Stress Testing in Risk Evaluator Transition and Default Probabilities Volatility of Losses Scenario: Stress Transition Matrixes Spread curves Exposure Volatility Scenario: Spreading spread curves Recovery Rate and Standard Deviation Volatility of Losses Database: Change seniority classes Branch Index Correlation Obligor Correlation Scenario: Set constant correlation Obligor Rating (Industry Sector) Volatility of Losses Scenario: Up/Down grading obligors Obligor Specific Risk (Industry Sector) Obligor Correlation Scenario: Change exogenous factor Obligor Volume (Industry Sector) Obligor s Exposure Scenario: Change obligor s volume

The major model factor can be changed in Risk Evaluator either using the stress test scenarios or manipulating the data in the database. Figure Risk Evaluator Stress Testing Dialog 3.1 Recovery Rate Sensitivity To assess the sensitivity of risk estimates to changes in recovery rate, a set of stress tests were run. The recovery rate was set progressively from to 1% in steps of 1%. The results of each simulation summary were exported to Excel and then summarized to produce the results shown on Figure 3. Figure 3 Percentile Risk vs. Mean Recovery Rate 1 1 1 1 1 3 5 7 9..3 Percentile Loss

5 From this chart we can see the following: All percentile risk measures decrease as recovery rate increases. Sensitivity to recovery rate increases as we consider smaller risk percentiles. 3. Portfolio Correlation Sensitivity In order to investigate the sensitivity to the level of correlation in the portfolio, Risk Evaluator was set to use the Constant Correlation setting on the Advanced Credit Risk Simulation Options Panel. This forces the asset return correlations between every branch index to the same value. The level of constant correlation varied from to 1 in steps of.1, with simulation summary outputs exported to Excel. The results are shown in Figure. We can see the following trends in this data: As the level of asset correlation is increased, all risk percentiles generally increase. Sensitivity to asset correlation increases as we consider larger asset correlation. Figure Percentile Risk vs. Constant Correlation 1 1.1..3..5..7..9 1..3 Percentile Loss. Specific Correlation Scenarios In addition to testing the sensitivity to overall levels of correlation in the portfolio, Risk Evaluator also tests the effect of a change in the specific correlation among a set of industries. This feature is available within the Industries Stress Scenario Panel (Figure 5). Rating up / down grading can be defined separate for every industry sector changing the rating for all obligors assigned to the sector. The volume factor allows to increase or to decrease the exposure for all obligors within the sector. This is used to simulate and to check industry sector balance and diversification strategies. The market dependence parameter is intended to simulate increasing or decreasing the obligor s specific risk part related to branch index dependence part described by obligor s percentile assignments to branch indexes. A zero value means

no index dependence (only specific risk) while a value = 1 forces total index dependence (no specific risk). Figure 5 Risk Evaluator Industries Stress Scenario Panel For the analysis the correlation for each industry was increased progressively from to 1 in steps of.1. The results summarized in figures through 1, show that the most observable effect is in the.3 and.1 percentiles. Figure

7 Financial Percentile Risk vs. Constant Correlation 1 1.1..3..5..7..9 1..3 Percentile Loss Transportation Percentile Risk vs. Constant Correlation 9 7 5 3 1.1..3..5..7..9 1..3 Percentile Loss Figure 7

Figure Utilities Percentile Risk vs. Constant Correlation 5 15 1 5.1..3..5..7..9 1..3 Percentile Loss

9 Figure 9 Banks Percentile Risk vs. Constant Correlation 1 1 1 1 1.1..3..5..7..9 1..3 Percentile Loss Figure 1 Industrial Percentile Risk vs. Constant Correlation 1 1.1..3..5..7..9 1..3 Percentile Loss 5. Transition Probabilities Predictive Stress Testing For the analysis the systematic component was increased progressively from to 1% in steps of 1% as the value of the credit year quality varied from to 3 in steps of.3. Refer to [1] for details on Conditional Transition Matrix. The simulation summary output for systematic component = 5 % and credit year quality variation was exported to Excel. The results are shown in Figure 11.

1 Figure 11 Predictive Risk vs. Credit Year Quality 1 9 7 5 3 1.3..9 1. 1.5 1..1..7 3..3 Percentile Loss. We can see the following trends in this data: As the credit year quality going high, all risk percentiles generally decrease. Sensitivity to year quality decreases as we consider higher quality.. Multi-factor Stress Testing Risk Evaluator allows the user to stress test multiple factors. Figure 1 shows the combined effect of varying recovery rates and constant correlation across the Eurobond portfolio. A set of simulation runs is completed, where the constant correlation varied from.1 to.9 in steps of., and the recovery rates varied from 1% to 9% in steps of %. The results are presented in a 3-D risk profile for the first percentile loss from mean.

11 Figure 1 for Mean 7 5 3 1 1 3 5 7 9 Recovery Rate.1.5.9 Constant Correlation 7. Risk Evaluator Performance Risk Evaluator is characterized by extremely high evaluation speed based on representation of instruments and portfolios by pricing expression trees. Specific instrument objects create pricing expressions trees for every instrument types and for portfolios and other aggregates using mapping to market risk grid points. The pricing expressions are simplified at run time reducing the volume of needed subsequent calculations while exposure creation and Monte Carlo runs. Fast risk evaluation engines perform recursive calculations on pricing trees using specific volatility and covariance algebra. Sample performance results for the analyzed test portfolio and for a large portfolio of 15 positions in 9 currencies are shown in Table. The total valuation time for the 15 position portfolio is 3 seconds including all needed times for loading the positions and the risk data sets from database and the simulation time. The pure simulation time is seconds for 1 runs including pricing tree construction. The simulation time for 1 runs is about 1 minute. The large portfolio needs about 3 minutes for all where the pure simulation for 1 runs consumes only 1 seconds. The performance test was created on a Pentium III / MHz with 1 MB memory using a fast Oracle server.

1 Table Sample Results from a Performance Report Value Date Confidence(%) Currency Date 15.11. 15.11. 95 EUR Test Portfolio Positions Load Counterparts Load Currencies Load 15 5 sec 1 sec 9 1 sec Calculate Var(%) VaR PF Value Total Market Risk 7,31 313,.71 11,33,79. sec Monte Carlo.7 73,51.73 11,3,.3 55 sec Credit Risk 1. 1,11,51.7 75,,13.3 3 sec Large Portfolio Positions Load Counterparts Load Currencies Load 15 9 7 sec sec Calculate Var(%) VaR PF Value Total Market Risk 11.31 3,355,3.3 1,,739,91. 57 sec Monte Carlo 3.,99,1. 1,,73,.9 7 sec Credit Risk 1.,3,39.5 5,375,1.5 11 sec. Summary The Risk Evaluator features to transparently change the major model factors composed in stored scenarios allows for impressive sensitivity and stress testing analysis. Stress test parameter settings and results are written back into database. Simple reporting is possible through clipboard copy and paste to other applications such as Excel or Word. Advanced reporting is performed by Crystal Reporter using stored reporting information in database. The presented features highlight the need to allocate capital based on reasonable model factor stress. Based on an understanding of the model parameter influence on risk results the user can create corresponding confidence intervals around the estimates for risk and economic capital. References [1] Kim, J. (1999) Conditional Transition Matrix Builder: Technical Document [] Rob Fraser() Stress Testing Credit Risk Using CreditManager.5: RiskMetrics Jourmal May