Loss Reserving: Is It Broken? What Can Be Done Better?

1. Loss Reserving: Is It Broken? What Can Be Done Better? CAS Annual Meeting November 15-16, 2004 Chuck Emma, Pinnacle Tom Ryan, Milliman John J. Kollar, ISO

2. Some Criticisms • “Actuaries are signing off on reserves that turn out to be wildly inaccurate.” Standard & Poors • “Are actuaries to blame for the huge shortfalls in reserves…?” Insurance Day • “Are actuaries hiding the bad news?” National Underwriter

3. ISO Study of Loss and Loss Adjustment Expense ReservesA. IndustryB. R&D CAS Annual Meeting November 15-16, 2004 John J. Kollar, ISO

4. Industry Loss Reserve Analysis • More than 900 insurer groups • Year-ended 12/31/03 • Schedule P data compiled by A. M. Best • More than 95% of LLAE reserves for studied lines • PRELIMINARY RESULTS

5. PP Auto Liability HO/Farmowners Com. Auto Liability Other & Products Liab. Claims-Made Other Liab. Occurrence Com. Multi-Peril Med Mal Occurrence Med Mal Claims-Made Products Occurrence Reinsurance (Non-Proportional Liability) Workers Comp Lines studied

6. Some Key Points • All indications are PRELIMINARY; we have not yet selected final LDFs & ranges • Excludes reserves for environmental and asbestos (E&A) claims • Possibly $30B to $50B deficient • No adjustment has yet been made for further development of 9/11 losses • Estimated insured losses: $20B to $30B • U.S. net insured losses: $8B to $12B • Adjustments have been made for other major catastrophes

7. Methodologies • Paid link-ratio technique • Case-incurred link-ratio technique • Consistent with 2001 ISO study

8. Factors affectinganalysis • Data quality • Development factors • Tail factors • Professional judgment

9. Conventions • Each deficiency/redundancy expressed as percentageof indicated undiscounted reserve as estimated by ISO • Positive percentages indicate deficiencies • Negative percentages indicate redundancies

10. Preliminary Summary Indications of Reserve Deficiencies PaidCase Incurred • Lines Studied + 7% + 9% • All Other Lines + 5% + 5% • Total – all lines + 7% + 8% • In Dollars $30B $34B Note: excludes E & A

11. Perspective (Preliminary) • Reserve adequacy has improved for 2 consecutive years • Reserves are 7 to 9 percentage points more adequate at year-end 2003 than at year-end 2001

12. Preliminary Indications by Line • Lines with significant deficiencies PaidCase Inc. • Other Liability Occurrence +11% + 3% • Products Occurrence + 1% +13% • Com. Multi-Peril + 6% + 9% • Workers Comp +14% +21% • Reinsurance (Non-Prop.) +29% +30%

13. Preliminary Indications by Line • Other Lines PaidCase Inc. • Priv. Pass. Auto Liability - 3% - 6% • Homeowners/Farmowners - 7% - 7% • Commercial Auto Liability - 4% + 2% • Claims Made Other & Prod. - 5% - 7% • Medical Malpractice – Occ. 0% + 8% • Medical Malpractice – C-M. - 2% - 1%

14. LALAE Ratios: Accident Year vs. Calendar Year Reserve adequacy deteriorated for at least 7 years but then improved in 2002 & 2003. %

15. Loss Reserve Changes vs. Industry Profitability, All Lines Changes in reserves are correlated with profitability.

16. Indicated Reserve Deficiencies vs. Industry Profitability Since 1997, changes in estimated deficiencies have mirrored changes in overall profitability. %

17. Retrospective Estimated Deficiencies & Economic Discount, All Studied Lines % Even when discounted, reserves may not be adequate.

18. ISO Industry Loss Reserve Analysis • Final, More complete analysis, as well as methodology and selections for each line, in Loss and Loss Adjustment Expense Reserves at Year-End 2003: Technical Analysis • Separate analysis of loss adjustment expenses in: Loss and Loss Adjustment Expense Reserves at Year-End 2003: ALAE Supplement

19. Pers. Auto Incurred L&ALAE Development from 15 to Ultimate for Voluntary DE Risks

20. Pers. Auto Liab. Paid Bodily Injury L&ALAE Development from 15 to Ult. for PA Risks

21. Other Liability Full Coverage Bodily Injury Loss Development from 15 to Ultimate

22. Com. Auto BI Liability Development from 15 to Ultimate in Tort States for Trucks, Tractors & Trailers

23. Research on Loss Reserving • Within each Schedule P Line, loss development varies by state, coverage, limits, sub-line, ALAE, etc. • Loss development patterns can vary by insurer. No surprise! • Find clusters of insurer loss development patterns by ?. • Each cluster would consist of multiple insurers. • Fit a stochastic model to each cluster.

24. Data Being Analyzed • Schedule P by insurer • ISO ratemaking data by insurer • Identity of individual insurer data is protected. • Individual insurer data will be clustered.

25. Possible Stochastic Model(s) Reserve = f(Age, AY, Size)∙ε • Age or valuation or lag • AY (accident year) • Size is reflected in a BF/Cape Cod formula. • The error term, ε, could depend on accident year, age and size. • Lognormal distribution? • Correlation of ε’s between (age,AY) cells?

26. Uses of Stochastic Model(s) • Test hypothesis that an insurer’s data is described by a cluster’s model. • If data is consistent with (fails to reject hypothesis) a model for one cluster, consider using it. • If data is consistent with models for several clusters, use weighted average of models with weights determined by Bayes’ Theorem. • If data is not consistent with models for any cluster, then ????.

27. Confidence Intervals for Reserves • Given distribution of ε’s for each age and accident year, we want to find the distribution of a sum of (age, accident year) cells. • All future ages in an accident year • For all accident years • Correlation matters!

28. What do You Think?