Report on CAS Research Working Parties

1. Report on CAS Research Working Parties Moderator: Donald Mango, FCAS, MAAA CAS Vice President of Research and Development Director of Research and Development, GE ERC 2004 ERM Symposium April 27, 2004

2. Agenda • Working Parties Overview • Correlations and Dependencies WP • Executive Decision Making Using DFA WP • Elicitation and Elucidation of Risk Preferences WP • Q&A throughout

3. What is a “working party”? • Essentially a task force focused on research of a specific topic or solution of a specific problem • Group effort with a single work product • Modeled on GIRO platform where it has been used successfully

4. What can WP’s deliver? • Original Research • Survey papers • Overview of research published to date on a particular topic • Could be used as syllabus material • Compendiums of papers by different authors • Correlation of Risk working party will use this format • Similar approach taken by Reserve Variability WP • Studies of industry experience based on special data calls

5. What are the current working parties? • Correlations and Dependencies Among All Risk Sources • Executive Level Decision Making Using Dynamic Financial Analysis • Elicitation and Elucidation of Risk Preferences • Quantifying Variability in Reserves Estimates • Implication of Fair Value on Asset Allocation (on hold)

6. Report of the Correlation Working Party Glenn Meyers Insurance Services Office, Inc.

7. Charge of the Working Party • ERM requires the quantification of the total risk of an enterprise. One must consider correlation to properly combine the individual risk components. • Considerations • Theoretical • Empirical • Computational

8. Theoretical Considerations • Conclusion – No overriding “theory of correlation.” • We will provide examples of multivariate models that exhibit correlation. • Experts prefer the term “dependencies” rather than correlation. • I find myself reverting the common usage so nonexperts will know what I am talking about.

9. Empirical Considerations • Historical problem – lack of data • One observation per year • If correlation matters, we should be able to find data that exhibits that correlation. • One approach • Create a model that depends on a “driver” for correlation. • Use data from several insurers to parameterize the driver. • Example to follow

10. Computational Considerations • ERM demands the aggregation of segments. • Simulation • Iman Conover and Copulas • Fourier transforms • Faster than simulations, but less flexible and require more setup time.

11. Chapters Written by Individual Authors • Common Shock Models – Glenn Meyers • The Iman-Conover Method – Stephen Mildenhall • Correlation over time – Hans Waszink • Aggregating Bivariate Distributions – David Homer • Dependency in Market Risk – Younju Lee • Modeling Time Series with Non-Constant Correlations – Dan Heyer • Correlations in a General Stochastic Setting – Lijia Guo • 4 CAS Members and 3 non members

12. From Meyers ChapterThe Negative Binomial Distribution • Select a at random from a gamma distribution with mean 1 and variance c. • Select the claim count K at random from a Poisson distribution with mean al • K has a negative binomial distribution with:

13. Multiple Line Parameter Uncertainty • Select b from a distribution with E[b] = 1 and Var[b] = b. • For each line h, multiply each loss by b. • Can calculate r if desired.

14. Multiple Line Parameter UncertaintyA simple, but nontrivial example E[b] = 1 and Var[b] = b

15. Low Volatilityb = 0.01 r= 0.50

16. Low Volatilityb = 0.03 r= 0.75

17. High Volatilityb = 0.01 r= 0.25

18. High Volatilityb = 0.03 r= 0.45

19. About Correlation • There is no direct connection between r and b. • For the same value of b: • Small insurers have large process risk and hence smaller correlation • Large insurers have smaller process risk and hence larger correlations. • Pay attention to the process that generates correlations.

20. Estimating b From Data =0

21. Reliable estimates of b are possible with lots of data. • Real estimates provided by Meyers, Klinker and Lalonde http://www.casact.org/pubs/forum/03sforum/03sf015.pdf

22. Sample CalculationsCommon Shocks to Frequency and Severity Multiply expected claim count by a random shock. Negative binomial count distributions Var[Shock] called covariance generator Multiply scale of claim severity by a random shock. Lognormal severity distributions Var[Shock] called the mixing parameter Look at spreadsheet

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27. Parting Message • Build models of underlying processes. • Common shock model illustrated here • Other chapters build other models • Quantify parameters of models • Use data! (If data will never exist, why worry?) • Express parameters in a form that has intuitive meaning. • Correlation is a consequence of the models.

28. Working Party:Presenting DFA Results to Decision Makers Nathan Babcock Conning Asset Management

29. Statement of Purpose • “Executive-Level Decision Making Using Dynamic Financial Analysis” • Facilitate effective DFA presentations to senior management • Survey existing presentations • Create tools and documentation

30. Summary of Events • Enroll volunteers • Survey past presentations • Develop graphical template and manual • Create sample dynamic financial analyses and presentations • Write summary report • Review presentations, report, template

31. End Products • Summary report • PowerPoint template for graphs • Paper describing concepts behind template • Three sample presentations (applying template graphs) • Document of presentation guidelines

32. Lessons of the WorkingParty Process • Chairpersons - management responsibilities • Communication with oversight committee • Ability to direct a group of volunteers • Multiple rewrites of the project timeline

33. Working Party Discoveries • WebEx - online presentations- paired with simultaneous teleconference • Hyperlinks- useful in documents, not just Internet- one reading electronically can page within set of {manual, template, report} • Graphics

34. Sample Graph: Profit Distribution Stop Loss

35. Sample Graph: Liability cash flow Practically no chance of paying this much

36. Sample Graph: Hedging Hedge is inexpensive, but useful

37. Working Party:Elicitation and Elucidation of Risk Preferences David Ruhm The Hartford

38. Risk PreferencesWorking Party • Motivation: • Most DFA and Risk Management exercises assume management has a clear, consistent, well-understood, transparent set of risk preferences • Such a set is a prerequisite for many risk analysis efforts, including asset portfolio composition and reinsurance purchasing. • The WP members and others do not believe this to be the case in general

39. Risk PreferencesWorking Party • Goals: • Describe or develop techniques and exercises that can be used to assist company senior management in developing (elicitation) and refining (elucidation) a consistent set of risk preferences. • The Working Party may draw from research in decision theory, prospect theory, and behavioral finance.

40. Risk PreferencesWorking Party • Framework: • Company level assessment (i.e., not riskiness/leverage of individual products sold) supporting planning decisions (product lines). • Provide decision support for the selection of the most desirable prospective portfolio mix. • But moving beyond Markowitz by considering many measures and timeframes. • Consider one-year, two-year, and three-year time horizons • Net Income, both absolute and scaled on PHS • Several likelihood thresholds (1 in 5, 10, 25, 50, 100, 250 years)

41. Risk PreferencesWorking Party • Two Sub-Teams: • Senior Management Silent Auction • Survey Research of Psychology Studies of Preferences • Silent Auction • Attempts to elicit consistent preferences while correcting for framing effects • Give to Sr. Mgmt members, then plot their answers on a single chart

43. Risk PreferencesWorking Party • Behavioral Finance • Non-Bayesian Forecasting: must have a prior before you can apply Bayes' Theorem. Also tend to overweight recent experience. • Herding: need content providers, expressing actual opinions, rather than relativistic participants (what do my peers do?). If all the peers are asking about the other peers, who is putting content in? • Over-reaction: beware of this tendency, which is particularly troubling in this buy-and-hold, non-exchange market. What should the threshold for reaction be? How many bad quarters or years in a row?

44. Risk PreferencesWorking Party • Behavioral Finance • Myopic Loss Aversion: risk premium is a function of time horizon. If you look at returns and results more frequently (shorter time horizon), you will demand a higher risk premium. • Earnings Management: owner's often want unrealistic earnings stability, often at odds with the desired return. • Growth/Decline/Reorganization: Expansion occurs more readily than redeployment and destruction. Function in part of myopic focus on sunk costs and difficulty of exit.

45. Risk PreferencesWorking Party • The Road Ahead • We need a chairperson! • Finalize research summary • Finish Senior Mgmt Silent Auction • Report out later this year

46. Thank you for your attention Questions?