1. © 2005 Towers Perrin Determination of Statistically Optimal Geographical Territory Boundaries Casualty Actuarial Society Seminar on Ratemaking Session PL-7 Klayton N. Southwood March 13, 2006

2. © 2005 Towers Perrin 1 Risk Classification Definition — A grouping of risks with similar risk characteristics so that differences in costs may be recognized Purpose — Means by which data can be gathered so as to measure and quantify a specific risk characteristic’s relation to the propensity for loss Example — Territory classes are a means to gather data so as to measure and quantify geographic risk factors relative to the propensity for loss

3. © 2005 Towers Perrin 2 Homogeneity Definition — A risk classification is homogeneous if all risks in the class have the same or a similar degree of risk with respect to the specific risk factor being measured Purpose — Homogeneity of the class increases the credibility of the loss data generated by the class Example — A territory is considered homogeneous if all risks in the territory represent the same, or approximately the same, level of geographical risk

4. © 2005 Towers Perrin 3 Statistical Test of Homogeneity Within Variance: Based on the squared difference between each zip code pure premium in the cluster and the average pure premium for the specific cluster being tested Between Variance: Based on the squared difference between each cluster’s pure premium and the statewide average pure premium Total Variance = Within Variance + Between Variance Within Variance Percentage = Within Variance divided by Total Variance Goals: Low Percentage of Total Variance Within High Percentage of Total Variance Between

5. © 2005 Towers Perrin 4 Building Blocks

6. © 2005 Towers Perrin 5 Territory Risk Classes

7. © 2005 Towers Perrin 6 Basis to Group Areas County Largely stable over time Broad area ZIP Code Narrowly defined may be beneficial to define territories Useful for online rating Main disadvantage is need to deal with change over time Geo Coding Finest detail Static over time No predefined grouping

8. © 2005 Towers Perrin 7 Loss Index Normalized Pure Premium Normalized Zip Code Pure Premium EQUALS Actual Zip Code Pure Premium TIMES State Ave. Prem. State Ave. Base Zip Ave. Prem. Zip Base ÷

9. © 2005 Towers Perrin 8 Loss Index Econometric Model Population Density Vehicle Density Accidents per Vehicle Injuries per Accident Thefts per Vehicle

10. © 2005 Towers Perrin 9 Credibility 3000 Claims Complement Neighborhood Pure Premium Within Two Miles One Mile Extension

11. © 2005 Towers Perrin 10 Clustering Contiguous v. Non-Contiguous Absolute Dollar Difference Absolute Percentage Difference

12. © 2005 Towers Perrin 11 Homeowners Fire (Contiguous) Texas COVERAGES

13. © 2005 Towers Perrin 12 Homeowners Fire (Non-Contiguous) Texas

14. © 2005 Towers Perrin 13 ISO Public Protection Classifications Texas ©ISO Properties, Inc., 2003

15. © 2005 Towers Perrin 14 Texas Within Territory Variance as a Percentage of Total Variance — Fire (Contiguous)

16. © 2005 Towers Perrin 15 Texas Within Territory Variance as a Percentage of Total Variance — Fire (Non-Contiguous)

17. © 2005 Towers Perrin 16 Homeowners Liability (Contiguous) Texas COVERAGES

18. © 2005 Towers Perrin 17 Texas Within Territory Variance as a Percentage of Total Variance — Liability (Contiguous)

19. © 2005 Towers Perrin 18 Homeowners Theft/Vandalism (Contiguous) Texas COVERAGES

20. © 2005 Towers Perrin 19 Texas Within Territory Variance as a Percentage of Total Variance — Theft/Vandalism (Contiguous)

21. © 2005 Towers Perrin 20 Homeowners Wind and Water (Contiguous) Texas COVERAGES

22. © 2005 Towers Perrin 21 Texas Auto Benchmark Texas AUTO BENCHMARK

23. © 2005 Towers Perrin 22 Indicated Auto Territories — All Coverages (Contiguous) Texas ALL COVERAGES

24. © 2005 Towers Perrin 23 Texas Within Territory Variance as a Percentage of Total Variance — All Coverages (Contiguous)

25. © 2005 Towers Perrin 24 Indicated Auto Territories — All Coverages (Non-Contiguous) Texas

26. © 2005 Towers Perrin 25 Texas Within Territory Variance as a Percentage of Total Variance — All Coverages (Non-Contiguous)

27. © 2005 Towers Perrin 26 Current Auto Territories — All Coverages North Carolina

28. © 2005 Towers Perrin 27 1997 – 1999 Indicated Auto Territories — All Coverages (Contiguous) North Carolina

29. © 2005 Towers Perrin 28 North Carolina Within Territory Variance as a Percentage of Total Variance — All Coverages (Contiguous)

30. © 2005 Towers Perrin 29 North Carolina * 1993 – 1999 for Comprehensive 1997 – 1999* Indicated Auto Territories — All Coverages (Non-Contiguous)

31. © 2005 Towers Perrin 30 North Carolina Within Territory Variance as a Percentage of Total Variance — All Coverages (Non-Contiguous)

32. © 2005 Towers Perrin 31 North Carolina 1997 – 1999 Indicated Auto Territories — Bodily Injury (Contiguous)

33. © 2005 Towers Perrin 32 North Carolina Within Territory Variance as a Percentage of Total Variance — Bodily Injury (Contiguous)

34. © 2005 Towers Perrin 33 North Carolina 1997 – 1999 Indicated Auto Territories — Property Damage (Contiguous)

35. © 2005 Towers Perrin 34 North Carolina Within Territory Variance as a Percentage of Total Variance — Property Damage (Contiguous)

36. © 2005 Towers Perrin 35 North Carolina 1997 – 1999 Indicated Auto Territories — Comprehensive (Contiguous)

37. © 2005 Towers Perrin 36 North Carolina Within Territory Variance as a Percentage of Total Variance — Comprehensive (Contiguous)

38. © 2005 Towers Perrin 37 North Carolina 1997 – 1999 Indicated Auto Territories — Collision (Contiguous)

39. © 2005 Towers Perrin 38 North Carolina Within Territory Variance as a Percentage of Total Variance — Collision (Contiguous)

40. © 2005 Towers Perrin 39 Stability Predictive stability Choice of perils included in data Number of years of data Rating stability Limit movement between zones Use of capping Use of confidence intervals to help analyze changes

41. © 2005 Towers Perrin 40 Predictive Power and Stability Predictive Power – Test #1 1993/1994 v. 1995/1996 Correlation Coefficient Tested Boundaries Based on 1994/1996 Non-Contiguous Better Predictive Power – Test #2 1993/1995 v. 1994/1996 Tested Boundaries Based on 1994/1996 Within Variance Only Marginally Better for 1994/1996 Data Stability 1993/1995 Clusters v. 1994/1996 Clusters Compared Indicated Boundaries and Relativities Little Dislocation

42. © 2005 Towers Perrin 41 Determination of Statistically Optimal Geographical Territory Boundaries 2006 CAS Ratemaking Seminar Klayton N. Southwood