1. Estimating Reserve Ranges: Practical Suggestions Richard E. Sherman, FCAS, MAAA Richard E. Sherman & Associates, Inc.

2. A Range of Reasonable Estimates ASOP 36 defines it as “a range of estimates that could be produced by appropriate actuarial methods or alternative sets of assumptions that the actuary judges to be reasonable.” P&C Practice Note, p. 33 ASOP 36 defines it as “a range of estimates that could be produced by appropriate actuarial methods or alternative sets of assumptions that the actuary judges to be reasonable.” P&C Practice Note, p. 33

3. 1) A Comfortable Range Paid projection $9 M Incurred projection $11 M Born Ferg projection $10 M Selected range $9 M - $11 M %-age range +/- 10%

4. 2) A Range with 2 Adjusted Projections Paid projection $7 M Incurred projection $14 M Born Ferg projection $11 M Berq Sher adj paid $9 M Berq Sher adj inc’d $11 M Selected range $9M - $11 M %-age range +/- 10%

5. 3) All Projections Much Too Low Paid projection $6 M Incurred projection $7 M Born Ferg projection $6 M Adjusted paid proj. $8 M Adjusted inc’d proj. $7 M Adj. Born Ferg proj. $7 M Selected range $6M - $8M Should range be: $9M - $11M ???

6. 4) Too Large a Range? Paid projection: $4 M Paid projection: $4 M Incurred projection: $16 M Incurred projection: $16 M Adjusted paid proj.: $6 M Adjusted paid proj.: $6 M Adjusted incurred proj.: $14 M Adjusted incurred proj.: $14 M Born Ferg proj.: $10 M Born Ferg proj.: $10 M Selected range: $6 M - $ 14 M Selected range: $6 M - $ 14 M Disturbing +/- 40% range Disturbing +/- 40% range “Can’t you do better than that?” “Can’t you do better than that?”

7. 5) Too Good to Be True Paid projection: $10 M Paid projection: $10 M Incurred projection: $10 M Incurred projection: $10 M BornFerg projection: $10 M BornFerg projection: $10 M FreqSev projection: $10 M FreqSev projection: $10 M No changes in settlement rates or adequacy level of reserves No changes in settlement rates or adequacy level of reserves HELP!!!! HELP!!!!

8. Ranges & Actuarial Opinions: A Regulatory Perspective Nicole Elliott, ACAS, MAAA Texas Dept of Insurance

9. Type of AOS Review Point46754% Range14517% Point & Range24829% Total859

10. What Types of Ranges are Regulators Seeing? Not discussed in Report Methods considered proprietary Used actuarial judgment - common % +/- a point estimate - common Scenario testing Statistical distributions - rare

11. Possible Help Possible Help Use PLDFs to derive projections of future incremental paids. Assume 6% underlying inflation & derive alternative projections of incremental paids based on 3% & 9% inflation. Use PLDFs to derive projections of future incremental paids. Assume 6% underlying inflation & derive alternative projections of incremental paids based on 3% & 9% inflation. Run a simulation based on mean LDFs and std dev of LDFs, reflecting correlation between the LDFs in successive DYs. Run a simulation based on mean LDFs and std dev of LDFs, reflecting correlation between the LDFs in successive DYs.

12. Cold Showers for Confident Actuaries Review your own track record of past estimates & how they have developed. Review your own track record of past estimates & how they have developed. Cover up the latest 2 diagonals and estimate LDFs based on prior factors. Then compare your projections with actual LDFs. Cover up the latest 2 diagonals and estimate LDFs based on prior factors. Then compare your projections with actual LDFs. Dig up an old rate filing you did 3-5 years ago & compare the projected rates/pure premiums with the ultimates in your latest filing. Dig up an old rate filing you did 3-5 years ago & compare the projected rates/pure premiums with the ultimates in your latest filing.

13. More Cold Showers Review Schedule P—Parts 2 & 3 by AY and calculate %-age favorable/ adverse development of previously carried reserves. Review Schedule P—Parts 2 & 3 by AY and calculate %-age favorable/ adverse development of previously carried reserves. Run a Monte Carlo simulation (using @RISK or Crystal Ball software) to get a feel for the probability distribution of future payments. Run a Monte Carlo simulation (using @RISK or Crystal Ball software) to get a feel for the probability distribution of future payments.

14. Become a High Roller at Monte Carlo Simulation Level 1—Poisson for # of claims; lognormal or pareto for claim size [Process Risk] Level 1—Poisson for # of claims; lognormal or pareto for claim size [Process Risk] Level 2—Add a probability distribution for the uncertainty of lambda for Poisson and for the mean & std dev for lognormal [Parameter Risk] Level 2—Add a probability distribution for the uncertainty of lambda for Poisson and for the mean & std dev for lognormal [Parameter Risk] Level 3—Dream up models from an alternative universe and assign each model a probability of representing reality. Simulate at all 3 levels. [Model Risk] Level 3—Dream up models from an alternative universe and assign each model a probability of representing reality. Simulate at all 3 levels. [Model Risk]

15. Encountering Reality: Industry Runoff Statistics 2,500 P/C Insurers 2,500 P/C Insurers Schedule P – Parts 2 & 3 Schedule P – Parts 2 & 3 Focus on distribution of individual company results Focus on distribution of individual company results Findings never presented on 9/11/01 at CLRS by Kevin Wick of PwC. Findings never presented on 9/11/01 at CLRS by Kevin Wick of PwC.

16. 5 Year Hindsight Comparisons Use latest ultimates less cumulative paid from 5 years ago. Use latest ultimates less cumulative paid from 5 years ago. Compile %-age of insurers where hindsight reserve was within +/- 5%, etc. Compile %-age of insurers where hindsight reserve was within +/- 5%, etc.

17. All Lines of Business 5 Year Hindsight Reserve: %-age of Insurers Within 5% 20% Between 5% & 10% 14% Between 10% & 25% 37% More than 25% 29%

18. Private Passenger Auto Liability 5 Year Hindsight Reserve: %-age of Insurers Within 5% 15% Between 5% & 10% 19% Between 10% & 25% 44% More than 25% 22%

19. Workers Compensation or CMP 5 Year Hindsight Reserve: %-age of Insurers Within 5% 18% Between 5% & 10% 14% Between 10% & 25% 37% More than 25% 31%

20. Other Liability Occurrence 5 Year Hindsight Reserve: %-age of Insurers Within 5% 12% Between 5% & 10% 10% Between 10% & 25% 29% More than 25% 49%

21. Med Mal Claims Made 5 Year Hindsight Reserve: %-age of Insurers Within 5% 11% Between 5% & 10% 6% Between 10% & 25% 15% More than 25% 68%

22. By Size of All Lines Reserves 5 Year Hindsight Reserve: Total Reserve < $ 1 M Total Reserve $10-50 M Total Reserve > $500 M Within 5% 12%17%30% Between 5% & 10% 5%16%15% Between 10% & 25% 20%37%45% More than 25%63%30%10%

23. Consult Hindsight Deviation Profiles for the Reserve Size and LOBs Being Analyzed May cause you to widen your judgmental feel for the size of the range from your analysis. May cause you to widen your judgmental feel for the size of the range from your analysis. Suppose a new part were added to Schedule P to display the %-age hindsight error in stated reserves? A downside: It would make it easier for outsiders to derive quick and dirty estimates of future development. Suppose a new part were added to Schedule P to display the %-age hindsight error in stated reserves? A downside: It would make it easier for outsiders to derive quick and dirty estimates of future development.

24. Future Payments Can Be Fickle Even if the chosen model explains past development well, it may not explain much of future development. Even if the chosen model explains past development well, it may not explain much of future development. Industry runoff results show disturbingly high %-age of insurers with reserve development %-ages greater than 10% and greater than 25%. Unanticipated major influences can cause dramatic movements in ultimates. Industry runoff results show disturbingly high %-age of insurers with reserve development %-ages greater than 10% and greater than 25%. Unanticipated major influences can cause dramatic movements in ultimates.

25. Edgy Reasonableness Is a reserve estimate still reasonable if every one of numerous key assumptions are chosen at the low end of the range of reasonable values for each assumption? At the high end? Is a reserve estimate still reasonable if every one of numerous key assumptions are chosen at the low end of the range of reasonable values for each assumption? At the high end?

26. Trend, Cycle or Noise? AY DY 2 DY 3 DY 4 20031.3741.0621.031 20041.4241.0551.029 20051.4561.049 20061.474

27. Trend, Cycle or Noise? Usually not possible to determine whether data is following a trend, a cyclical pattern, or just fluctuating randomly in a column. Usually not possible to determine whether data is following a trend, a cyclical pattern, or just fluctuating randomly in a column. Simulation exercise. Start with a given mean LDF and std dev and generate a series of four LDFs for DY 2. Compile simulation results of what %-age of the time the data will show a clear trend, even though there is no real trend. Simulation exercise. Start with a given mean LDF and std dev and generate a series of four LDFs for DY 2. Compile simulation results of what %-age of the time the data will show a clear trend, even though there is no real trend.

28. Trend, Cycle or Noise? Choose a series of four underlying distributions for the four LDFs for DY 2, where the means are dropping steadily. From simulation, what %- age of the time will a trend line fitted to the data have an upward slope, in spite of the actual downward trend present in the assumptions? Choose a series of four underlying distributions for the four LDFs for DY 2, where the means are dropping steadily. From simulation, what %- age of the time will a trend line fitted to the data have an upward slope, in spite of the actual downward trend present in the assumptions?

29. Can Actuarial Judgment Overcome Low Credibility? Problem: Credibility of LDFs drops rapidly for the most mature DYs. Culminates in reliance on only one LDF at the tip of the triangle. Suggestion: Apply methods that pull in incremental data prior to the triangle to raise the credibility of the LDFs at or near the tip.

30. Dead on Arrival (DOA) Data Standard Triangle Diagonals Only Area (DOA)

31. Going Out on a BerqSher Limb? Problem: Adjusted triangle resulting from a BerqSher method produces strange progressions of incremental paids or incurreds. Suggestion: Take only Y% of each indicated adjustment. Solve for the Y% that produces the most reasonable adjusted triangle. For example, Y = 60% or 130%.

32. Bias Inherent in Trimming LDFs Problem: Often, relying on the Avg X Hi Lo can result in tossing out most of the large adverse development while only removing small favorable developments from the historical factors. Suggestion: Try smoothing the historical data using moving averages over successive DYs instead. Less bias?

33. CONCLUSIONS Actual variability of future payout >> What you think it is. Actual variability of future payout >> What you think it is. Actual variability >> low and high estimates in your range. Actual variability >> low and high estimates in your range. Do more homework before making selections. Do more homework before making selections. Help your audience appreciate how large the real degree of variability is, while retaining their confidence in your professional abilities. Help your audience appreciate how large the real degree of variability is, while retaining their confidence in your professional abilities.