Commentary on the New Hazard Groups

1. June 18, 2007 Commentary on the New Hazard Groups CAS Spring Meeting Jose Couret Orlando

2. Outline • Motivation • Gauging the Improvement • Excess Loss Factors by Class • Conclusion

3. Motivation

4. Motivation Development of New Hazard Groups • Old Hazard Group Mapping • Until recently, hundreds of class codes were condensed into 4 hazard groups--of which hazard groups II and III contained 95% of the exposure. • New Hazard Group Mapping • The number of hazard groups has increased to seven (from four) under NCCI’s B-1403 filing. • The new hazard groups are a significant improvement.

5. Motivation An ELF is a Weighted Average of the ELFs by Injury Type

6. Gauging the Improvement

7. Gauging the ImprovementDiscussion • A key element of the excess percentage is the frequency of loss by injury type. Fatalities and permanent disabilities cost more than other injury types; so when they have high relative frequency, more of the claims cost arises from large losses. • Relative Frequency = claim count for the injury type divided by the claim count for temporary total. • Relative frequency for the more serious injury types should increase as one moves from a lower hazard group to a higher hazard group. • Fatal • Permanent Total • Major Permanent Partial

8. Gauging the ImprovementRelative Frequency by Hazard Group and Injury Type Note: Undeveloped, adjusted to Countrywide Level

9. Gauging the ImprovementRelative Frequency by Hazard Group and Injury Type Classes Formerly in Hazard Group II Note: Undeveloped, adjusted to Countrywide Level

10. Gauging the ImprovementRelative Frequency by Hazard Group and Injury Type Classes Formerly in Hazard Group III Note: Undeveloped, adjusted to Countrywide Level

11. Gauging the ImprovementFatal Frequencies– Within and Between Hazard Groups Hazard Group means are very different. Is the variation within hazard groups significant?

12. Gauging the ImprovementPT Frequencies– Within and Between Hazard Groups

13. Gauging the ImprovementMajor Frequencies– Within and Between Hazard Groups

14. Gauging the ImprovementPerformance Testing with A Holdout Sample • For each injury type, calculated relative frequency for the even reports (2, 4, 6) and used these to predict the odd reports (3, 5, 7). Discarded greenest year of data (first report). • Estimates are expressed as relativities to the all-class relative frequencies. • Three methods used to predict holdout period outcome: • No hazard group method • Old 4-hazard group method • New 7-hazard group method • Note: statistical procedure used to eliminate state differentials.

15. Gauging the ImprovementPerformance Testing with A Holdout Sample Fatal Claims Approx 7x greater Hold-out period relativities we are trying to predict. Clearly, predictions based on new 7-HG averages from even years more closely track holdout period results. New 7-HG predictions yield lowest sum of squared errors.

16. Gauging the ImprovementPerformance Testing with A Holdout Sample Permanent Total claims New 7-HG predictions yield lowest sum of squared errors.

17. Gauging the ImprovementPerformance Testing with A Holdout Sample Major Permanent Partial Claims New 7-HG predictions yield lowest sum of squared errors.

18. Gauging the ImprovementComments • Testing suggests that the new hazard groups are superior to the old. • There is great value in having seven sets of benchmark excess loss factors that do not “cross over”. • New hazard groups are still sufficiently heterogeneous for a correlated credibility approach to add value. Even then, the hazard group estimate can serve as the complement of credibility. • May be impractical for bureaus to support ELFs by class. Individual insurers can derive their own credits and debits to adjust hazard group ELFs to class level.

19. Excess Loss Factors by Class

20. Excess Loss Factors by ClassRelative Permanent Total (PT) Frequency by Class Code

21. Excess Loss Factors by Class Sample State, $4m XS $1M

22. Excess Loss Factors by Class Sample State, $5m XS $5M

23. Excess Loss Factors by ClassCredibility Procedure Yields Modest Reduction in Sum of Squared Errors Sum of Squared Prediction Errors by Injury Type

24. Excess Loss Factors by ClassQuintiles Test • Utilizing a variation on NCCI’s “Quintiles Test” to measure model performance • Approach used to test Experience Rating Plan • Hazard grouping approximation works best when all classes in a Hazard Group • have the same relative frequency of injuries • same composition of loss by injury type • Our goal: determine if by-class approach improves prediction of injury type relative frequency.

25. Excess Loss Factors by Class Quintiles Test Methodology • Discard greenest year of data (first report) • For each injury type, calculated relative frequency relativities (to the hazard group average)from the even reports (2, 4, 6). • Used these to predict the odd reports (3, 5, 7) • Classes within a HG are sorted by credibility-weighted relativity and aggregated into five groups of roughly equal size. • Groupings were created so that the number of TT claim counts in each quintile is roughly equal. • The lowest 20% of the class relativities belong to the risks in the first quintile, the next 20% to the second quintile, etc.

26. Excess Loss Factors by Class Observations Hazard Group D, Permanent Total Claims Column (2), what we are trying to predict, represents the average relative frequency for the classes in the quintile divided by the corresponding estimate for all of HG D. For example, the relative frequency of PT claims (as a ratio to TT) for the classes within the first quintile was about half of the HG average. Upwardly sloping relativities are desirable; indicate the credibility procedure tended to identify class difference in relative PT frequency.

27. Excess Loss Factors by Class Observations (continued) • Goal is to predict the Column (2) frequency relativity for each quintile. Column (3) is a prediction based on the HG average. All entries equal to unity – by assumption every quintile has the HG D relative frequency for PT claims. • The predictions in Column (4) are based on raw class relativities observed for the even years. For example, the classes in the fifth quintile had an even-year relative PT frequency that was 215% of the HG average. • The Column (5) predictions were derived using the multi-dimensional credibility procedure. • Again, the quintiles are ranked by credibility weighted class relativity, not raw relativity.

28. Excess Loss Factors by Class Observations (continued) Hazard Group D, Permanent Total Claims Approx 3x greater Actual Odd year relativities we are trying to predict. Classes in highest quintile 3x more likely to have a PT claim Flat relativities significantly underestimate PT frequency for classes in higher quintiles and overestimate lower quintiles Prediction based on Even years gives too much credibility to historical experience There is significant variability of PT frequency within Hazard Group D

29. Excess Loss Factors by Class Sum of Squared Prediction Errors by Hazard Group and Injury Type Supports severity differentials by hazard group for permanent partial losses. Thinking in R2 terms, the class relativities could be said to "explain" 98% of the "between quintiles” variance for PT/HG D. This is not actually a regression, but the statistic is still impressive by real-life actuarial standards. The use of class relativities dramatically improves the class frequency by injury type estimation.

30. Conclusion

31. Conclusion • The new hazard groups are superior to the old. • There is great value in having excess loss factors that do not “cross over”. • A correlated credibility approach can be used to calculate indicated credits/debits to the hazard group ELFs. The actual credit/debit must incorporate underwriting judgment.