1. Risk Management

2. Risk Management Readings “Beyond Value at Risk” Kevin Dowd Wiley 1998 “Mastering Risk Volume 1 and 2” FT Prentice Hall 2001 “Risk Management for Company Executives” John Smullen FT Prentice Hall 2000

3. Risk Management Readings “The Revolution in Risk Management” Anthony Santomero in “Mastering Finance” FT Prentice Hall 1998 “A Brief History of Downside Risk Measures” David Nawrocki Journal of Investing 1999

4. Lecture Summary The Nature of Risks The Measurement of Risk Attitudes to Risk

5. The Nature of Risk

6. A Story In 1530 Atahuallpa defeated his half brother Huascar to gain control of the Inca Empire He had conquered what he thought was the overwhelming bulk of the civilised world and ruled an Empire some have compared to the Roman Empire in Size He let Francisco Pizarro with 100 soldiers and 60 horsemen meet him at the village of Cajamar which he surrounded with 40,000 troops The Spanish were surrounded but they attacked and killed 6-7,000 within a day. That led to the demise of the Inca Empire

7. Risk Related Thoughts Lightning Strikes The Arrogance of Success Leads to Risk Taking Cultures may be Brittle Other individuals and organisations may see things radically differently Technological Change can have major impacts

8. Risk and Finance

9. Is there a Valuable Distinction Between Risk and Uncertainty ?

10. The Continuum of Risks A Sensible Vision of Outcomes and Their Probabilities - Day to Day Movements in Equities A Sensible Vision of Outcomes but not Their Probabilities - Collapse in Housing Market No Vision of Outcomes or their Probabilities - Chicago Board of Trade 1992

11. The Sources of Risk Market Risk - Interest Rate, Forex, Commodity, Equity, Liquidity Risk (?), etc. Credit Risk - Risk of Counterparty Default Operational Risk - All other Risks

12. Market and Credit Risk Knowledge Of Outcomes Knowledge of Probabilities

13. Operational Risk Knowledge Of Outcomes Knowledge of Probabilities

14. Risk Measurement and Attitudes to Risk

15. Risk Measures and Attitudes to Risk Returns in % terms reflecting distribution from which returns drawn Year12345678910 A1011101111101121011 B5135971296149 E(Ra) = 9.7SD(Ra) = 2.61 E(Rb) = 9.2SD(Rb) = 2.87

16. Consider Data on Last Slide and Evaluate the Nature of the Choice between the two distributions of Returns ?

17. Attitudes to Risk Utility Function - Defined over a probability distribution of returns. Mean and Variance - an approximation see Blake pp 461-468. Time Higher Moments Downside Measures Psychological Issues

18. Real Returns on US Assets 1802-1996

19. Higher Moments r Mr = 1/N (xi –E(xi)) i = 1 N

20. Moments – To what extent is investor utility defined over moments 1 st. Mean 2 nd. Variance 3 rd. Skewness – Degree of Asymmetry 4 th. Kurtosis – Degree of Peakedness

21. Downside Measures Worst Case Value at Risk Lower Downside Moments Extreme Values

22. VAR Definition The Value at Risk (VAR) is the level of expected loss over a given time horizon which will only be exceeded in a specified proportion of instances. J.P.Morgan’s 4.15 Report

23. Definitions and Measures of Risk Likelihood Return a x 0 y

24. Definition of VAR Absolute VAR = (0 - x) Relative VAR = (y - x)

25. Expected Tail Loss When the outturn is worse than the VAR cut-off value what is the average loss Focuses on tail of distribution Better on discontinuous distributions

26. Key Choice Parameters Time Period Confidence Level

27. Time Period Liquidity of Portfolio Regulatory Framework Measurement Technique – Does one Assume Normality How does one deal with portfolio composition Required Data for Testing

28. Confidence Level Risk Management/Capital Requirement Regulatory Requirement (1%) Testing – Higher so more extreme observations Accounting and Comparison

29. Measuring Value at Risk Variance/Covariance Historical Monte Carlo Simulation

30. Issues with Value at Risk and ETL How does it deal with non-normality? How does it deal with financial crises ? How does it deal with shifting parameter values? What types of risk is it best applied to? If distributions are normal VAR and ETL are just a multiples of the standard deviation

31. Risk Measures and Attitudes to Risk Asset AB E(R)9.79.2 SD(R)2.612.87 3 rd.Moment(44.54)(5.25) 4 th. Moment352.96122.61 Worst Case25 Semi-Variance59.296.78 VAR(-0.3)3.2 ETL25

32. Psychological Issues Economic Man Cognitive Dissonance Depends on Situation Too focused on Recent Data

33. Adjusting Expectations Expectation Time A B

34. Definition and Measurement of Risk Distributional Measures of Risk Calculus Based Measures of Risk Some Speciality Measures like Gap Analysis for Particular Risks

35. Calculus Based Measures of Risk

36. Derivative Measures of Risk Underlying Risk Factor Value of Financial Obligation a b

37. Calculus Based Measures of Risk First Derivative measures the rate with which the value of an obligation changes with changes in an Underlying Risk Factor Second Derivative Measure how sensitive is the First Derivative Measure to changes in the Underlying Risk Factor

38. Issues in Relation to Calculus Calculus Based Measures Need to Specify Mathematical Relationship so require a Pricing Model - Bond Valuation, Option Pricing Models Thus difficult to apply to complicated portfolios of obligations Applies to Localised Measurement of Risk An approximation of the function

39. Summary The Nature of Risk The Attitude towards Risk The Measurement of Risk