1. May-00 Risk Management Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html Value-at-Risk (VaR)

2. VaRMay-2000 slide 2 Risk F Business Risk F Financial Risk – market risk – credit risk – liquidity risk F Operational Risk F Legal Risk

3. VaRMay-2000 slide 3 How much can we lose? Everything correct, but useless answer. How much can we lose realistically?

4. VaRMay-2000 slide 4 Derivatives 1993-1995 ($ million) F Shova Shell, Japan1,580 F Kashima Oil, Japan1,450 F Metallgesellschaft1,340 F Barings, U.K.1,330 F Codelco, Chile200 F Procter & Gamble, US157

5. VaRMay-2000 slide 5 Barings F February 26, 1995 F 233 year old bank F 28 year old Nick Leeson F $1,300,000,000 loss F bought by ING for $1.5

6. VaRMay-2000 slide 6 Public Funds ($ million) F Orange County1,640 F San Diego357 F West Virginia279 F Florida State Treasury200 F Cuyahoga County137 F Texas State55

7. VaRMay-2000 slide 7 Orange County F Bob Citron, the county treasures F $7.5B portfolio (schools, cities) F borrowed $12.5B, invested in 5yr. notes F interest rates increased F reported at cost - big mistake! F realized loss of $1.64B

8. VaRMay-2000 slide 8 F Barings$1.3B F Bank Negara, Malaysia 92$3B F Banesto, Spain$4.7B F Credit Lyonnais$10B F S&L, U.S.A.$150B F Japan$500B Financial Losses

9. VaRMay-2000 slide 9 Metallgesellshaft F 14th largest industrial group F 58,000 employees F offered long term oil contracts F hedge by long-term forward contracts F short term contracts were used (rolling hedge) F 1993 price fell from $20 to $15 F $1B margin call in cash

10. VaRMay-2000 slide 10

11. VaRMay-2000 slide 11 What is the current Risk? duration, convexity volatility delta, gamma, vega rating target zone F Bonds F Stocks F Options F Credit F Forex F Total?

12. VaRMay-2000 slide 12 Standard Approach

13. VaRMay-2000 slide 13 Modern Approach Financial Institution

14. VaRMay-2000 slide 14 Risk Management F Risk measurement F Reporting to board F Limits monitoring F Diversification, reinsurance F Vetting F Reporting to regulators F Decision making based on risk

15. VaRMay-2000 slide 15 Who manages risk? Citibank Bank of England CIBC J. P. Morgan Bankers Trust AIG General Re Swiss Re Aetna Zurich Nike Sony Dell Computers Philip Morris Ford Motor

16. VaRMay-2000 slide 16 Regulators F BIS F FSA F SEC F ISDA F FASB F Bank of Israel F Galai’s committee

17. VaRMay-2000 slide 17 Basic Steps in RM process F Identify risks F Data base (market + position) F Risk measurement F Regulators F Risk Management F Reporting F Strategic decisions

18. VaRMay-2000 slide 18 Building a RM system F Initial study of risks F Decision, Risk Manager F Risk measurement system F Responsibilities and structure F Testing F Active Risk Management F Staff training and maintenance

19. VaRMay-2000 slide 19 Risk Management and Risk Measurement

20. VaRMay-2000 slide 20 Risk Management System F Predict future F Identify business opportunities F Be always right! Risk Management System Can F Predict loss, given event F Identify most dangerous scenarios F Recommend how to change risk profile Can NOT

21. VaRMay-2000 slide 21 Tool, not rule!

22. VaRMay-2000 slide 22 Definition VaR is defined as the predicted worst-case loss at a specific confidence level (e.g. 99%) over a certain period of time.

23. VaRMay-2000 slide 23 Profit/Loss VaR 1% VaR 1%

24. VaRMay-2000 slide 24 Meaning of VaR A portfolio manager has a daily VaR equal $1M at 99% confidence level. This means that there is only one chance in 100 that a daily loss bigger than $1M occurs, 1% VaR under normal market conditions.

25. VaRMay-2000 slide 25 History of VaR F 80’s - major US banks - proprietary F 93 G-30 recommendations F 94 - RiskMetrics by J.P.Morgan F 98 - Basel F SEC, FSA, ISDA, pension funds, dealers F Widely used and misused!

26. VaRMay-2000 slide 26 Risk Management Structure Market data Current position Risk Mapping Valuation Value-at-Risk Reporting and Risk Management

27. VaRMay-2000 slide 27 interest rates and dollar are NOT independent Value Interest Rate dollar

28. VaRMay-2000 slide 28 Risk Measuring Software F CATS, CARMA F Algorithmics, Risk Watch F Infinity F J.P. Morgan, FourFifteen F FEA, Outlook F Reuters, Sailfish F Kamacura F Bankers Trust, RAROC F INSSINC, Orchestra

29. VaRMay-2000 slide 29 Qualitative Requirements F An independent risk management unit F Board of directors involvement F Internal model as an integral part F Internal controller and risk model F Backtesting F Stress test

30. VaRMay-2000 slide 30 Quantitative Requirements F 99% confidence interval F 10 business days horizon F At least one year of historic data F Data base revised at least every quarter F All types of risk exposure F Derivatives

31. VaRMay-2000 slide 31 Types of Assets and Risks F Real projects - cashflow versus financing F Fixed Income F Optionality F Credit exposure F Legal, operational, authorities

32. VaRMay-2000 slide 32 Risk Factors There are many bonds, stocks and currencies. The idea is to choose a small set of relevant economic factors and to map everything on these factors. F Exchange rates F Interest rates (for each maturity and indexation) F Spreads F Stock indices

33. VaRMay-2000 slide 33 How to measure VaR F Historical Simulations F Variance-Covariance F Monte Carlo F Analytical Methods

34. VaRMay-2000 slide 34 Historical Simulations F Fix current portfolio. F Pretend that market changes are similar to those observed in the past. F Calculate P&L (profit-loss). F Find the lowest quantile.

35. VaRMay-2000 slide 35 Example 4.00 4.20 4.10 4.15 Assume we have $1 and our main currency is SHEKEL. Today $1=4.30. Historical data: 4.30*4.20/4.00 = 4.515 4.30*4.20/4.20 = 4.30 4.10*4.10/4.20 = 4.198 4.15*4.15/4.10 = 4.352 P&L 0.215 0 -0.112 0.052

36. VaRMay-2000 slide 36 today USD NIS 2000 100 -120 2001 200 100 2002-300 -20 2003 20 30

37. VaRMay-2000 slide 37 today Changes in IR USD: +1%+1% +1% +1% NIS: +1% 0% -1% -1%

38. VaRMay-2000 slide 38 Returns year 1% of worst cases

39. VaRMay-2000 slide 39 Profit/Loss VaR 1% VaR 1%

40. VaRMay-2000 slide 40 Weights Since old observations can be less relevant, there is a technique that assigns decreasing weights to older observations. Typically the decrease is exponential. See RiskMetrics Technical Document for details.

41. VaRMay-2000 slide 41 Variance Covariance F Means and covariances of market factors F Mean and standard deviation of the portfolio F Delta or Delta-Gamma approximation F VaR 1% =  P – 2.33  P F Based on the normality assumption!

42. VaRMay-2000 slide 42  Variance-Covariance 2.33   -2.33  1%

43. VaRMay-2000 slide 43 Monte Carlo

44. VaRMay-2000 slide 44 Monte Carlo F Distribution of market factors F Simulation of a large number of events F P&L for each scenario F Order the results F VaR = lowest quantile

45. VaRMay-2000 slide 45 Monte Carlo Simulation

46. VaRMay-2000 slide 46 Real Projects Most daily returns are invisible. Proper financing should be based on risk exposure of each specific project. Note that accounting standards not always reflect financial risk properly.

47. VaRMay-2000 slide 47 Example F You are going to invest in Japan. F Take a loan in Yen. F Financial statements will reflect your investment according to the exchange rate at the day of investment and your liability will be linked to yen. F Actually there is no currency risk.

48. VaRMay-2000 slide 48 Airline company F fuel - oil prices and $ F purchasing airplanes - $ and Euro F salaries - NIS, some $ F tickets $ F marketing - different currencies F payments to airports for services

49. VaRMay-2000 slide 49 Airline company F loans F equity F callable bonds

50. VaRMay-2000 slide 50 Airline company Base currency - by major stockholder. Time horizon - by time of possible price change. Earnings at risk, not value at risk, since there is too much optionality in setting prices. One can create a one year cashflow forecast and measure its sensitivity to different market events.

51. VaRMay-2000 slide 51 Reporting Division of VaR by business units, areas of activity, counterparty, currency. Performance measurement - RAROC (Risk Adjusted Return On Capital).

52. VaRMay-2000 slide 52 How VaR is used F Internal Risk Management F Reporting F Regulators

53. VaRMay-2000 slide 53 Backtesting Verification of Risk Management models. Comparison if the model’s forecast VaR with the actual outcome - P&L. Exception occurs when actual loss exceeds VaR. After exception - explanation and action.

54. VaRMay-2000 slide 54 Backtesting Green zone - up to 4 exceptions Yellow zone - 5-9 exceptions Red zone - 10 exceptions or more OK increasing k intervention

55. VaRMay-2000 slide 55 Stress Designed to estimate potential losses in abnormal markets. Extreme events Fat tails Central questions: How much we can lose in a certain scenario? What event could cause a big loss?

56. VaRMay-2000 slide 56 Unifying Approach F One number F Based on Statistics F Portfolio Theory F Verification F Widely Accepted F Easy Comparison

57. VaRMay-2000 slide 57 Board of Directors (Basle, September 1998) F periodic discussions with management concerning the effectiveness of the internal control system F a timely review of evaluations of internal controls made by management, internal and external auditors  periodic efforts to ensure that management has promptly followed up on recommendations and concerns expressed by auditors and supervisory authorities on internal control weaknesses  a periodic review of the appropriateness of the bank’s strategy and risk limits.

58. VaRMay-2000 slide 58 Open Questions F Risks related to cashflow F Non-traded assets F Credit information F Global Database F Liquidity problem

59. VaRMay-2000 slide 59 Issues Specific to Israel F Indexation F Exchange Band F Shallow Markets