1. 1 QUANTITATIVE RISK MANAGEMENT AT ABN AMRO Jan Sijbrand January 14th, 2000

2. 2 Quantitative methods in banking I.Risk and Capital Reserves II. Modelling Financial Instruments

3. 3 I. Risk and Capital Reserves A bank (like any company) aims to earn money in return for taking risk. But: Taking risk may result occasionally in experiencing losses. In the extreme, banks may default. Bank default will have large impact on economy:  Depositors lose their money  Firms lack source of financing for investments

4. 4 Therefore: Bank is required by Central Bank to hold Capital. Level of required capital is set so as to make bank default extremely unlikely. Sources of bank capital:  Equity capital  Reserves  Subordinated loans

5. 5 Required capital ABN AMRO (1998, millions EURO) Credit risk - on balance13.474 Credit risk - off balance 3.137 Market risk 651 Actual capital22.612

6. 6 What is Market risk?  The possibility to gain or lose on an exposure to market prices  Profit may result from –bid/offer spreads –commissions and fees –trading profits (?) The banks’ own Capital protects against losses. The profit should provide a return on this capital.

7. 7 The value at Risk concept 1) Register current risk position accurately 2) Calculate the effect of market price movements (profit/loss) from one day to the next during the last thousand days 3) Present all these daily results in a histogram

8. 8 The Value at Risk distribution: Market Risk 1% VatR 0 * Expected result (average): zero * With 99% certainty no greater loss than VatR * Bid/Ask spread etc. have to compensate for taking this risk

9. 9 What is Credit risk? “Potential drop in the value of an asset because a debtor may not fulfill its obligations” AssetDebtor LoanCustomer BondIssuer Derivative transactionCounterparty with positive MtM

10. 10 Credit Losses (1) Source: S&P Ratings Performance 1997

11. 11 Credit Losses (2) Average

12. 12 Distribution of Credit Losses  Non-symmetric (skewed) –Large probability of small losses –Small probability of large losses  Long, fat tail  Non-normal distribution

13. 13 Credit Losses = Unexpected credit losses Expected credit losses + Amount one expects to loseDeviation from expected credit losses  “ Cost of doing business”  Not risk, because expected  Unanticipated losses  risk  Capital as protection

14. 14 Loss distribution Expected Loss Unexpected Loss 

15. 15 Risk/Reward for Credit exposures:  Reward comes in the form of interest margin (interest on loan minus funding rate)  This income needs to cover –the Expected Losses fully; –a Return on the Economic Capital (say 20%)

16. 16 Economic capital Capital needed to sustain potential credit losses with probability (=confidence level) Can be calculated for:  portfolio of assets  incremental assets  line of business Also called Value-at-Risk (VatR)

17. 17 Portfolio models for Credit risk Determine:  Expected credit losses  Probability distribution of credit losses  potential unexpected credit losses Examples: CreditMetrics, KVM, CreditPortfolioView, CreditRisk+

18. 18 Main ingredients of Portfolio Models  Probability of default (credit quality) of debtors  Estimated exposure at default for assets  Loss rate given default for assets  Extent of diversification / concentration of portfolio (default correlation's)

19. 19 One-Year default probabilities per rating Source: S&P

20. 20 Exposure at default Forecast of amount owed at time of default  Different from current exposure  Forecast depends on asset type: –loan facility: nominal amount, or  estimated outstanding for committed but (partly) undrawn line –derivative: estimated positive market value –bond: nominal amount

21. 21 Loss rate given default Percentage of exposure at default which one expects to lose Depends on  seniority of claim on debtor  type, quality and quantity of collateral

22. 22 Historic bond recovery SeniorityAverage Senior secured 58.52 Senior unsecured 49.60 Subordinated 35.30 Total 43.77 Source: S&P “Ratings Performance 1997”. Data from 1981 - 1997. Recovery as % of par.

23. 23 Default correlation Likelihood of simultaneous defaults of multiple obligors Depends on e.g.:  geographic diversification  diversification over industry sectors  state of the economy

24. 24 Estimating correlations Bond credit spreads Equity returns Industry and country factors Factor models (CreditMetrics, KMV) Default correlations

25. 25 Loss Distribution +Economic capital Expected loss Economic capital 

26. 26 Conclusion on Credit risk and capital Modelling credit risk on a portfolio basis presents many challenging modelling questions: - Estimating default probabilities - Estimating default correlations - Assessing effect of economic cycles - Optimization of risk/return Results may substantially change approach towards taking and managing credit risk in banking industry.

27. 27 II. Financial Instruments: Model risk  Mismatch: model and reality  Interesting questions: –How severe is model risk for pricing/hedging of derivatives, market risk evaluation of a portfolio (VaR), etc? –For example: Do we need to model a stochastic interest rate for a convertible?  Need for quantification of model risk!

28. 28 Managing Model risk  Models for derivatives are developed by commercial line in the dealing room (“frontoffice”)  Independent validation by Risk Management  One of the tests: Hedge Performance Measurement  Model reserve where necessary

29. 29 Hedge performance measurement  Derivative:  Hedge instruments:  Hedge ratios:  Consider the hedged portfolio:  Uncertainty tomorrow  hedge errors:

30. 30 Hedge performance measurement  Different hedge strategies (choice of and )  different hedge errors.  Different models (predict )  different hedge errors.  Estimate density of hedge errors (risk profile).

31. 31 Application Dollar/Yen  Model: Black-Scholes (for FX)  Hedge strategy: Black-Scholes delta hedge  Model risk profile vs. empirical risk profile  Test criteria of interest (e.g. VaR or variance).  Could interpret test-statistic as first quantification of model risk

32. 32 Application Dollar/Yen -.7-.6-.5-.4-.3-.2-.10.1.2.3.4.5.6.7 10 20 30 40 50 Density Model based risk profile -.7-.6-.5-.4-.3-.2-.10.1.2.3.4.5.6.7 10 20 Density Empirical risk profile

33. 33 Model reserves Uncertainty in hedge error (up to 99%) may be covered by a VaR-style capital reserve.

34. 34 Summary The impact of quantitative methods on bank risk management  Market risk:Capital Adequacy Reserve based on Historical Simulation.  Credit risk:Modelling reserves likely to be Monte-Carlo based. Correlations still difficult to estimate.  Model risk:Ad hoc and sometimes quite complex.