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Financial Risk Management

Financial Risk Management. Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html. Risk. Business Risk Operational Risk Financial Risk credit risk market risk liquidity risk Legal Risk. Crouhy, Galai, Mark, Risk Management, McGraw Hill, 2000.

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Financial Risk Management

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

  2. Risk • Business Risk • Operational Risk • Financial Risk • credit risk • market risk • liquidity risk • Legal Risk FRM-1

  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 FRM-1

  4. Derivatives 1993-1995 ($ million) • Shova Shell, Japan 1,580 • Kashima Oil, Japan 1,450 • Metallgesellschaft 1,340 • Barings, U.K. 1,330 • Codelco, Chile 200 • Procter & Gamble, US 157 FRM-1

  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 FRM-1

  6. Public Funds ($ million) • Orange County 1,640 • San Diego 357 • West Virginia 279 • Florida State Treasury 200 • Cuyahoga County 137 • Texas State 55 FRM-1

  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 FRM-1

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

  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 FRM-1

  10. FRM-1

  11. Risk Management andRisk Measurement FRM-1

  12. Basic Statistics • Certainty and uncertainty • Probabilities, distribution, PDF, CDF • Mean, variance • Multivariable distributions • Covariance, correlation, beta • Quantile FRM-1

  13. A 100 km. B 100 km/hr 50 km/hr 1 – 100 2 – 50 3 – 50 (100+50+50)/3 = 66.67 km/hr. FRM-1

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

  15. Probabilities Certainty Uncertainty Probabilities FRM-1

  16. Probabilities Mean Variance FRM-1

  17. 30% 30% 10% 10% 20% Probabilities 0.3 0.2 0.1 1 2 3 4 5 FRM-1

  18. Probabilities 0.3 0.2 0.1 1 2 3 4 5 FRM-1

  19. Probabilities FRM-1

  20. Probabilities FRM-1

  21. Sample Estimates Sometimes one can use weights FRM-1

  22. Normal Distribution N(, ) FRM-1

  23.  Normal Distribution N(, ) FRM-1

  24. Normal Distribution 1%  quantile FRM-1

  25. Lognormal Distribution FRM-1

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

  27. Correlation -1    1  = 0 independent  = 1 perfectly positively correlated  = -1 perfectly negatively correlated FRM-1

  28. Properties FRM-1

  29. Time Aggregation Assuming normality FRM-1

  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: FRM-1

  31. A rf B  Portfolio 2(A+B) = 2(A) + 2(B) + 2(A)(B) FRM-1

  32. ¥$£ £¥ $¥ £$¥ $£¥ £$  £ $ FRM-1

  33. 2 12  John Zerolis "Triangulating Risk", Risk v.9 n.12, Dec. 1996 1 FRM-1

  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. FRM-1

  35. 0.125 0.25 0.5 0.375 0.5 0.5 0.375 0.25 0.125 Binomial Tree 1.0 FRM-1

  36. FRM-1

  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? FRM-1

  38. Example 1 Score Probability 1 1/6 2 1/6 3 1/6 4 1/6 5 1/6 6 1/6 Fair price is 3.5 NIS. Assume that we can play the game for 3 NIS only. FRM-1

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

  40. Example All combinations: 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5 2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 6,6 36 combinations with equal probabilities FRM-1

  41. Example All combinations: 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5 2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 6,6 4 out of 36 give $5, probability = 1/9 FRM-1

  42. Additional information: the first die gives 4. All combinations: 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5 2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 6,6 1 out of 9 give $5, probability = 1/9 FRM-1

  43. Additional information: the first die gives 4. All combinations: 1,1 2,1 3,1 4,1 5,1 6,1 1,2 2,2 3,2 4,2 5,2 6,2 1,3 2,3 3,3 4,3 5,3 6,3 1,4 2,4 3,4 4,4 5,4 6,4 1,5 2,5 3,5 4,5 5,5 6,5 1,6 2,6 3,6 4,6 5,6 6,6 4 out of 24 give $5, probability = 1/6 FRM-1

  44. Example 1 -2 -1 0 1 2 3 FRM-1

  45. Example 1 1 2 3 4 5 6 we pay 1 2 3 4 5 6 7 6 NIS. 2 3 4 5 6 7 8 3 4 5 6 7 8 9 4 5 6 7 8 9 10 5 6 7 8 9 10 11 6 7 8 9 10 11 12 FRM-1

  46. P&L 1 2 3 4 5 6 1 -4 -3 -2 -1 0 1 2 -3 -2 -1 0 1 2 3 -2 -1 0 1 2 3 4 -1 0 1 2 3 4 5 0 1 2 3 4 5 61 2 3 4 5 6 FRM-1

  47. Example 1 (2 cubes) FRM-1

  48. Example 1 (5 cubes) FRM-1

  49. $4 $2 Breakfast 50% 50% FRM-1

  50. $11 $5 Lunch 50% 50% FRM-1

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