1. FRM5 Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html Value-at-Risk (VaR)

2. Zvi WienerFRM5-VaR slide 2 Risk Business Risk Financial Risk market risk credit risk liquidity risk Operational Risk Legal Risk

3. Zvi WienerFRM5-VaR slide 3 How much can we lose? Everything correct, but useless answer. How much can we lose realistically?

4. Zvi WienerFRM5-VaR slide 4 What is the current Risk? duration, convexity volatility delta, gamma, vega rating target zone Bonds Stocks Options Credit Forex Total?

5. Zvi WienerFRM5-VaR slide 5 Standard Approach

6. Zvi WienerFRM5-VaR slide 6 Modern Approach Financial Institution

7. Zvi WienerFRM5-VaR slide 7 Definition VaR is defined as the predicted worst-case loss at a specific confidence level (e.g. 99%) over a certain period of time.

8. Zvi WienerFRM5-VaR slide 8 Profit/Loss VaR 1% VaR 1%

9. Zvi WienerFRM5-VaR slide 9 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.

10. Zvi WienerFRM5-VaR slide 10 Main Ideas A few well known risk factors Historical data + economic views Diversification effects Testability Easy to communicate

11. Zvi WienerFRM5-VaR slide 11 History of VaR 80’s - major US banks - proprietary 93 G-30 recommendations 94 - RiskMetrics by J.P.Morgan 98 - Basel SEC, FSA, ISDA, pension funds, dealers Widely used and misused!

12. Zvi WienerFRM5-VaR slide 12 Risk Management Structure Market data Current position Risk Mapping Valuation Value-at-Risk Reporting and Risk Management

13. Zvi WienerFRM5-VaR slide 13 interest rates and dollar are NOT independent Value Interest Rate dollar

14. Zvi WienerFRM5-VaR slide 14 Risk Measuring Programs CATS, CARMA$400K/yr Algorithmics, Risk Watch>$1M Infinity>$1M J.P. Morgan, FourFifteen$25K/yr FEA, Outlook$18K Reuters, Sailfish? Theoretics, TARGA$75K Bankers Trust, RAROC$50K/run INSSINC, Orchestra$25-75K

15. Zvi WienerFRM5-VaR slide 15 Why Capital Requirements Government Protection Debt financing In Israel this is not binding! But it will be!! Traded assets constitute a small portion 339-9, 339-10 defines who must use VaR

16. Zvi WienerFRM5-VaR slide 16 Unifying Approach One number Based on Statistics Portfolio Theory Verification Widely Accepted Easy Comparison

17. Zvi WienerFRM5-VaR slide 17 Capital Requirements Minimal required capital Supervision factor, 3  k  4

18. Zvi WienerFRM5-VaR slide 18 Qualitative Requirements An independent risk management unit Board of directors involvement Internal model as an integral part Internal controller and risk model Backtesting Stress test

19. Zvi WienerFRM5-VaR slide 19 Quantitative Requirements 99% confidence interval 10 business days horizon At least one year of historic data Data base revised at least every quarter All types of risk exposure Derivatives

20. Zvi WienerFRM5-VaR slide 20 Types of Assets and Risks Real projects - cashflow versus financing Fixed Income Optionality Credit exposure Legal, operational, authorities

21. Zvi WienerFRM5-VaR slide 21 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. Exchange rates Interest rates (for each maturity and indexation) Spreads Stock indices

22. Zvi WienerFRM5-VaR slide 22 How to measure VaR Historical Simulations Variance-Covariance Monte Carlo Analytical Methods Parametric versus non-parametric approaches

23. Zvi WienerFRM5-VaR slide 23 Historical Simulations Fix current portfolio. Pretend that market changes are similar to those observed in the past. Calculate P&L (profit-loss). Find the lowest quantile.

24. Zvi WienerFRM5-VaR slide 24 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 4.30*4.10/4.20 = 4.198 4.30*4.15/4.10 = 4.352 P&L 0.215 0 -0.112 0.052

25. Zvi WienerFRM5-VaR slide 25 today USD NIS 2000 100 -120 2001 200 100 2002-300 -20 2003 20 30

26. Zvi WienerFRM5-VaR slide 26 today Changes in IR USD: +1%+1% +1% +1% NIS: +1% 0% -1% -1%

27. Zvi WienerFRM5-VaR slide 27 Returns year 1% of worst cases

28. Zvi WienerFRM5-VaR slide 28 Profit/Loss VaR 1% VaR 1%

29. Zvi WienerFRM5-VaR slide 29 Variance Covariance Means and covariances of market factors Mean and standard deviation of the portfolio Delta or Delta-Gamma approximation VaR 1% =  P – 2.33  P Based on the normality assumption!

30. Zvi WienerFRM5-VaR slide 30  Variance-Covariance 2.33   -2.33  1%

31. Zvi WienerFRM5-VaR slide 31 Monte Carlo

32. Zvi WienerFRM5-VaR slide 32 Monte Carlo Distribution of market factors Simulation of a large number of events P&L for each scenario Order the results VaR = lowest quantile

33. Zvi WienerFRM5-VaR slide 33 Monte Carlo Simulation

34. Zvi WienerFRM5-VaR slide 34 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.

35. Zvi WienerFRM5-VaR slide 35 Stock Portfolio Single risk factor or multiple factors Degree of diversification Tracking error Rare events

36. Zvi WienerFRM5-VaR slide 36 Bond Portfolio Duration Convexity Partial duration Key rate duration OAS, OAD Principal component analysis

37. Zvi WienerFRM5-VaR slide 37 Options and other derivatives Greeks Full valuation Credit and legal aspects Collateral as a cushion Hedging strategies Liquidity aspects

38. Zvi WienerFRM5-VaR slide 38 Credit Portfolio rating, scoring credit derivatives reinsurance probability of default recovery ratio

39. Zvi WienerFRM5-VaR slide 39 Reporting Division of VaR by business units, areas of activity, counterparty, currency. Performance measurement - RAROC (Risk Adjusted Return On Capital).

40. Zvi WienerFRM5-VaR slide 40 How VaR is used Internal Risk Management Reporting Regulators

41. Zvi WienerFRM5-VaR slide 41 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.

42. Zvi WienerFRM5-VaR slide 42 Backtesting Green zone - up to 4 exceptions Yellow zone - 5-9 exceptions Red zone - 10 exceptions or more OK increasing k intervention

43. Zvi WienerFRM5-VaR slide 43 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?

44. Zvi WienerFRM5-VaR slide 44 Risk Management Risk measurement Reporting to board Limits monitoring Diversification, reinsurance Vetting Reporting to regulators Decision making based on risk

45. Zvi WienerFRM5-VaR slide 45 Tool, not rule!

46. Zvi WienerFRM5-VaR slide 46 pluto.mscc.huji.ac.il/~mswiener/ Useful Internet sites Regulators Insurance Companies Risk Management in SEC reports Risk Management resources

47. Zvi WienerFRM5-VaR slide 47 How to hedge financial risk? Static hedge Forwardsagreements that fix the price Futures Optionsstatic hedge Dynamic delta or vega hedge, with a variable amount of options held. It is applicable if there is a very liquid market and low transaction costs.

48. Zvi WienerFRM5-VaR slide 48 RMG http://www.riskmetrics.com/ http://www.pictureofrisk.com/ http://www.riskmetrics.com/rm/splash.html rmgaccess

49. Zvi WienerFRM5-VaR slide 49 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

50. Zvi WienerFRM5-VaR slide 50 Consulting Oliver, Wyman and Co. Willis Corroon Richard Scora Ernst and Young Enterprise Advisors Kamakura

51. Zvi WienerFRM5-VaR slide 51 Examples of Risk Reports http://www.pictureofrisk.com http://www.mbrm.com/ http://www.riskmetrics.com/rm/splash.html

52. Zvi WienerFRM5-VaR slide 52 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.

53. Zvi WienerFRM5-VaR slide 53 Example You are going to invest in Japan. Take a loan in Yen. Financial statements will reflect your investment according to the exchange rate at the day of investment and your liability will be linked to yen. Actually there is no currency risk.

54. Zvi WienerFRM5-VaR slide 54 Airline company fuel - oil prices and $ purchasing airplanes - $ and Euro salaries - NIS, some $ tickets $ marketing - different currencies payments to airports for services

55. Zvi WienerFRM5-VaR slide 55 Airline company loans equity callable bonds

56. Zvi WienerFRM5-VaR slide 56 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.

57. Zvi WienerFRM5-VaR slide 57 Issues Specific to Israel Indexation Exchange Band Shallow Markets

58. Zvi WienerFRM5-VaR slide 58 Home assignment Calculate your personal VaR