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1. Introduction
2. Definitions of risk - outline
3. Risk in Terms of Distributions (1)
4. Distributional properties (1)
5. Distributional properties (2)
6. Distributional properties (3)
7. Distributional properties and utility
8. Example (1)
9. Example (2)
10. Example (3)
11. Distributional characteristics:impact on port.choice
12. First order stochastic dominance (1)
13. First order stochastic dominance (2)
14. Comparing the probability distribution functions
15. Example of first order stochastic dominance
16. First order stochastic dominance (3)
17. Second order stochastic dominance (1)
18. Second order stochastic dominance (2)
19. Difference between distribution functions
20. Integrating the difference
21. Second order stochastic dominance (3)
22. Summary of part 1
23. Axiomatic approach
24. Definition of risk (1)
25. Definition of risk (2)
26. Risk measure
27. Risk measure - single number benefits
28. Risk measure Rho (1)
29. Risk measure Rho (2)
30. Translation invariance
31. Sub - additivity
32. Positive homogeneity
33. Monotonicity
34. Relevance
35. Coherent risk measures
36. Current method for measuring risk
37. VaR method
38. The VaR measure satisfies the...
39. VaR and sub - additivity (1)
40. VaR and sub - additivity (2)
41. VaR and sub - additivity (3)
42. VaR and sub - additivity (4)
43. VaR and sub - additivity (5)
44. VaR and sub - additivity (6)
45. VaR and sub - additivity (7)
46. TailVaR
47. Worst conditional expectation
48. TailVaR versus WCE
49. Summary part 2
50. Risk in terms of utility (1)
51. Rothschild - Stiglitz Theorem on risk
52. Example
53. Law of iterated expectations
54. Back to Rothschild - Stiglitz Theorem
55. Rothschild - Stiglitz Theorem
56. Less risky portfolios have smaller variance
57. Two - fund separation
58. Two - fund separation follows from Stiglitz theorem
59. Summary of part 3
60. Conclusions

Topics Covered

• Distributional properties of risk
• Variance
• Risk aversion and variance aversion
• First order stochastic dominance
• Second order stochastic dominance
• Axiomatic approach to risk measures
• Risk as a choice variable
• Acceptable and non-acceptable risk
• Single-dimensional risk measures
• Risk measure and risk capital
• Coherent risk measurers
• Value-at-Risk (VaR) is not coherent
• TailVaR and worst conditional expectations
• Rothschild/Stiglitz increasing risk
• Conclusions: risk definition depends on context and purpose

Links

Series:

• Quantitative Financial Risk Management

Categories:

• Finance, Accounting & Economics

Talk Citation

Publication History

• Published on October 1, 2007
• Archived on April 4, 2022