2. FRM Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html Financial Risk Management

3. Zvi WienerFRM-1 slide 2 Risk Business Risk Operational Risk Financial Risk  credit risk  market risk  liquidity risk Legal Risk

4. Zvi WienerFRM-1 slide 3 Crouhy, Galai, Mark, Risk Management, McGraw Hill, 2000. Golub, Tilman, Risk Management Approaches for Fixed Income Markets, Wiley, 2000. Jorion, Value at Risk, McGraw Hill, 1997. http://www.gloriamundi.org http://www.riskmetrics.com http://www.bis.org http://www.garp.com

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

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

7. Zvi WienerFRM-1 slide 6 Public Funds ($ million) Orange County1,640 San Diego357 West Virginia279 Florida State Treasury200 Cuyahoga County137 Texas State55

8. Zvi WienerFRM-1 slide 7 Orange County Bob Citron, the county treasures $7.5B portfolio (schools, cities) borrowed $12.5B, invested in 5yr. notes interest rates increased reported at cost - big mistake! realized loss of $1.64B

9. Zvi WienerFRM-1 slide 8 Barings$1.3B Bank Negara, Malaysia 92$3B Banesto, Spain$4.7B Credit Lyonnais$10B S&L, U.S.A.$150B Japan$500B Financial Losses

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

11. Zvi WienerFRM-1 slide 10

12. Zvi WienerFRM-1 slide 11 Risk Management and Risk Measurement

13. Zvi WienerFRM-1 slide 12 Basic Statistics Certainty and uncertainty Probabilities, distribution, PDF, CDF Mean, variance Multivariable distributions Covariance, correlation, beta Quantile

14. Zvi WienerFRM-1 slide 13 A100 km.B 100 km/hr 50 km/hr 1 – 1002 – 503 – 50 (100+50+50)/3 = 66.67 km/hr.

15. Zvi WienerFRM-1 slide 14 1.+40% 2.+10% 3.-50% 4.+20% 1.-2% 2.+1% 3.-1% 4.+1% 1.4*1.1*0.5*1.2 = 0.924 0.98*1.01*0.99*1.01 = 0.9897

16. Zvi WienerFRM-1 slide 15 Probabilities Certainty Uncertainty Probabilities

17. Zvi WienerFRM-1 slide 16 Probabilities Mean Variance

18. Zvi WienerFRM-1 slide 17 Probabilities 1234512345 0.2 0.3 0.1 20% 30% 10%

19. Zvi WienerFRM-1 slide 18 Probabilities 1234512345 0.2 0.3 0.1

20. Zvi WienerFRM-1 slide 19 Probabilities

21. Zvi WienerFRM-1 slide 20 Probabilities

22. Zvi WienerFRM-1 slide 21 Sample Estimates Sometimes one can use weights

23. Zvi WienerFRM-1 slide 22 Normal Distribution N( ,  )

24. Zvi WienerFRM-1 slide 23 Normal Distribution N( ,  )  

25. Zvi WienerFRM-1 slide 24 Normal Distribution  quantile 1%

26. Zvi WienerFRM-1 slide 25 Lognormal Distribution

27. Zvi WienerFRM-1 slide 26 Covariance Shows how two random variables are connected For example: independent move together move in opposite directions covariance(X,Y) =

28. Zvi WienerFRM-1 slide 27 Correlation -1    1  = 0 independent  = 1 perfectly positively correlated  = -1 perfectly negatively correlated

29. Zvi WienerFRM-1 slide 28 Properties

30. Zvi WienerFRM-1 slide 29 Time Aggregation Assuming normality

31. Zvi WienerFRM-1 slide 30 Time Aggregation Assume that yearly parameters of CPI are: mean = 5%, standard deviation (SD) = 2%. Then daily mean and SD of CPI changes are:

32. Zvi WienerFRM-1 slide 31 Portfolio  2 (A+B) =  2 (A) +  2 (B) + 2  (A)  (B)    rfrf A B

33. Zvi WienerFRM-1 slide 32 $ £   $¥  £¥  £$ $  £¥ £  $¥ ¥  $£

34. Zvi WienerFRM-1 slide 33   12 11 22 John Zerolis "Triangulating Risk", Risk v.9 n.12, Dec. 1996

35. Zvi WienerFRM-1 slide 34 Useful Books Duffie D., Dynamic Asset Pricing Theory. Duffie D., Security Markets, Stochastic Models. Shimko D. Finance in Continuous Time, A Primer. Kolb Publishing Company, 1992.

36. Zvi WienerFRM-1 slide 35 Binomial Tree 1.0 0.5 0.25 0.5 0.125 0.375

37. Zvi WienerFRM-1 slide 36

38. Zvi WienerFRM-1 slide 37 Example We will receive n dollars where n is determined by a die. What would be a fair price for participation in this game?

39. Zvi WienerFRM-1 slide 38 Example 1 ScoreProbability 11/6 21/6 31/6 41/6 51/6 61/6 Fair price is 3.5 NIS. Assume that we can play the game for 3 NIS only.

40. Zvi WienerFRM-1 slide 39 Example If there is a pair of dice the mean is doubled. What is the probability to gain $5?

41. Zvi WienerFRM-1 slide 40 Example 1,12,13,14,15,16,1 1,22,23,24,25,26,2 1,32,33,34,35,36,3 1,42,43,44,45,46,4 1,52,53,54,55,56,5 1,62,63,64,65,66,6 All combinations: 36 combinations with equal probabilities

42. Zvi WienerFRM-1 slide 41 Example 1,12,13,14,15,16,1 1,22,23,24,25,26,2 1,32,33,34,35,36,3 1,42,43,44,45,46,4 1,52,53,54,55,56,5 1,62,63,64,65,66,6 All combinations: 4 out of 36 give $5, probability = 1/9

43. Zvi WienerFRM-1 slide 42 All combinations: 1 out of 9 give $5, probability = 1/9 Additional information: the first die gives 4. 1,12,13,14,15,16,1 1,22,23,24,25,26,2 1,32,33,34,35,36,3 1,42,43,44,45,46,4 1,52,53,54,55,56,5 1,62,63,64,65,66,6

44. Zvi WienerFRM-1 slide 43 All combinations: 4 out of 24 give $5, probability = 1/6 Additional information: the first die gives  4. 1,12,13,14,15,16,1 1,22,23,24,25,26,2 1,32,33,34,35,36,3 1,42,43,44,45,46,4 1,52,53,54,55,56,5 1,62,63,64,65,66,6

45. Zvi WienerFRM-1 slide 44 Example 1 -2 -1 0 1 2 3

46. Zvi WienerFRM-1 slide 45 Example 1 123456we pay 12345676 NIS. 2345678 3456789 45678910 567891011 6789101112

47. Zvi WienerFRM-1 slide 46 P&L 123456 1-4-3-2-101 2-3-2-1012 3-2-10123 4-101234 5012345 6123456

48. Zvi WienerFRM-1 slide 47 Example 1 (2 cubes)

49. Zvi WienerFRM-1 slide 48 Example 1 (5 cubes)

50. Zvi WienerFRM-1 slide 49 Breakfast $2 $450%

51. Zvi WienerFRM-1 slide 50 Lunch $5 $1150%

52. Zvi WienerFRM-1 slide 51

53. Zvi WienerFRM-1 slide 52 Lunch Breakfast $2$4 $5$7$9 $11$13$15 50%  = $11  = ?? 50%

54. Zvi WienerFRM-1 slide 53 Correlation  =+1 $2$4 $5$7$9 $11$13$15 Lunch Breakfast 50%  = $11  = $450%

55. Zvi WienerFRM-1 slide 54 Correlation  =-1 $2$4 $5$7$9 $11$13$15 Lunch Breakfast 50%  = $11  = $250%

56. Zvi WienerFRM-1 slide 55 Correlation  =0 $2$4 $5$7$9 $11$13$15 Lunch Breakfast 50%  = $11  = $3.1650%

57. Zvi WienerFRM-1 slide 56 How much can we lose? Everything correct, but useless answer. How much can we lose realistically?

58. Zvi WienerFRM-1 slide 57 What is the current Risk? duration, convexity volatility delta, gamma, vega rating target zone Bonds Stocks Options Credit Forex Total?

59. Zvi WienerFRM-1 slide 58 Standard Approach

60. Zvi WienerFRM-1 slide 59 Modern Approach Financial Institution

61. Zvi WienerFRM-1 slide 60 interest rates and dollar are NOT independent Value Interest Rate dollar