1. Workers Compensation Excess of Loss Pricing CAS Reinsurance Pricing Seminar Moshe D. Goldberg, FCAS July 29, 2005

2. Page 2 Workers Compensation Workers Compensation characteristics that cause it to differ from other lines of business – Extremely long tail – Annuity-type benefits – Benefits defined by statute, not by courts - Indemnity and Medical benefits - Benefits, to some degree, vary by state – No policy limits - Essentially unlimited medical coverage!! – True No-Fault system (Or is it?) Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

3. Page 3 WC’s Long Tail Discounting of case reserves prevalent – Explicit (lifetime pension cases) – Implicit (by not inflating projected future payments) Mortality assumptions used in setting reserves Effect of unwinding of discount can be quite large on an excess layer Claims often develop adversely quite late – Family stops taking care of claimant – Back injuries “creep” into the layer Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

4. Page 4 Example of Impact on Reinsurer An injured worker is expected to live 10 years. Weekly indemnity benefits are 500/wk = 26,000/yr Initial stabilizing medical expenses are 150,000 Annual medical expenses are 50,000/yr Initial case reserve = 150k+(26k+50k)*10 = 910k One would expect the loss to the 1Mx1M reinsurer to be zero.

5. Page 5 Implicit Discount Effect Suppose that instead of the ongoing medical expenses being 50k/yr, they are really inflating at 6% per annum. The primary company still books the ongoing medical loss at 500k, implicitly discounting them at 6%/yr. Total undiscounted ongoing medical expenses are really 659k = 50k*(1.06 10 -1)/.06, instead of the booked 500k The total undiscounted loss is 1,069k, and the 1Mx1M reinsurer will see 69k of development Imagine if the time horizon was longer!

6. Page 6 Mortality Assumption Effect Back to the original example (no growth in medical costs), however, instead of a certain 10 year survival, there was a 50% probability of this worker living only 5 years and 50% of living 15 years. Losses paid if the claimant lives 5 years = 530k = 150k+(26k+50k)*5 Losses paid if the claimant lives 15 years =1,290k = 150k+(26k+50k)*15 With 50% probability, the 1Mx1M reinsurer will see 290k development

7. Page 7 Example of “Tail” Development for 1Mx1M layer

8. Page 8 WC Exposure Rating Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

9. Page 9 Exposure Rating Conceptually, exposure rating WC is no different than other lines – Compute overall expected losses – Allocate these losses to the layer being priced by a size-of-loss curve. Practically, WC exposure rating is very different than other lines – Overall expected loss computation is relatively similar – However, the allocation to layer is handled vey differently. Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

10. Page 10 Exposure Rating For lines with policy limits, like GL, the rating bureaus publish ILFs, which are based on size-of-loss curves But WC doesn’t have policy limits. So NOW what do we do? Retrospective Rating’s Excess Loss Factors (ELFs) to the rescue! Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

11. Page 11 Terminology of WC Size-of-loss curves “Injury Type” : Description of the seriousness of a WC injury “Average Cost per Case” : Average severity “Entry Ratio” : Ratio of a number to the ACPC “Hazard Group” : Set of classes with similar severity distributions. Currently there are four HGs, but the NCCI is looking at adding more. “Excess Loss Factor” : Ratio of expected losses in excess of an entry ratio to the overall losses Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

12. Page 12 Injury Types Lost-Time Claim Injury Types – Fatal – Permanent Total (PT) – Major Permanent Partial (PP) – Minor Permanent Partial – Temporary Total (TT) Non-Lost-Time Injury Type – Medical Only Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

13. Page 13 Average Cost per Case These are the average severities by: – State – Hazard Group – Injury Type They are used in computing entry ratios. Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

14. Page 14 Excess Loss Factors (ELFs) ELF(x) = 1 – [LEV(x)/E(X)] = 1 – Loss Elimination Ratio at x The “x” is an entry ratio, so E(X) is, by definition, unity.

15. Page 15 Entry Ratio/ELF Example Injury TypeACPCEntry Ratio @ 1M ELF(1M)Inj Type Weight Fatal250,0004.000.23853% PT1,000,0001.000.567711% Major PP250,0004.000.139544% Minor PP50,00020.000.000116% TT10,000100.000.000021% Med Only5002,000.000.00005%

16. Page 16 Example Suppose we’re pricing the $1M xs $1M layer Expected Loss Ratio = 75% ELF(1M) = 0.13; ELF(2M) = 0.06 Losses in the layer = ELF(1M) – ELF(2M) = 7.0% 7.0% of the total losses are in this 1M xs 1M layer Exposure Loss Cost Rate = 75% * 7.0% = 5.25% This still needs to be discounted and loaded Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

17. Page 17 WC Trends Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

18. Page 18 WC Trends The long tail and unlimited medical benefits add to the difficulty in estimating trends for Workers Compensation. In addition, states can – and do – change the WC benefits, adding to the uncertainty. Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

19. Page 19 Source: NCCI, Inc Used with permission

20. Page 20 Impact of Non-uniform Frequency Trend on Excess of Loss Pricing Exposure Rating – Shape of the distribution changes, with more of the losses coming from larger claims Experience Rating – Measured ground-up severity trend will increase from the reduced frequency of the smaller claims – Assuming uniform trend by size of loss, the measured large loss trend will be lower than the measured ground-up trend – This impact is mitigated by the less-negative frequency trend Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

21. Page 21 Example Two types of claims, small and large. In year 1, small claims have average severity of 100k, while large claims have average severity of 500k. In year 1, there are an equal number of small and large claims, say 50 of each claim Average Severity in year 1 is 300k = (50*100k + 50*500k)/(50+50) Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

22. Page 22 Example, continued In year 2, there are now 40 small claims (frequency trend = -20%), while there are still 50 large claims (0% frequency trend). Total frequency trend = -10% The average severity for each claim type increases 10% – Small claim severity = 110k – Large Claim Severity = 550k But, the measured overall severity is now 354k = (40*110k+50*550k)/(40+50) This is an 18% increase! Moshe D. Goldberg, FCAS CAS Reinsurance Pricing July 29, 2005

23. Page 23 Source: NCCI, Inc. Used with permission

24. Page 24 Source: NCCI, Inc. Used with permission