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Estimating Reserve Ranges: Practical Suggestions. Richard E. Sherman, FCAS, MAAA Richard E. Sherman & Associates, Inc. A Range of Reasonable Estimates.
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Estimating Reserve Ranges: Practical Suggestions Richard E. Sherman, FCAS, MAAA Richard E. Sherman & Associates, Inc.
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
4) Too Large a Range? • Paid projection: $4 M • Incurred projection: $16 M • Adjusted paid proj.: $6 M • Adjusted incurred proj.: $14 M • Born Ferg proj.: $10 M • Selected range: $6 M - $ 14 M • Disturbing +/- 40% range • “Can’t you do better than that?”
5) Too Good to Be True • Paid projection: $10 M • Incurred projection: $10 M • BornFerg projection: $10 M • FreqSev projection: $10 M • No changes in settlement rates or adequacy level of reserves • HELP!!!!
Ranges & Actuarial Opinions: A Regulatory Perspective Nicole Elliott, ACAS, MAAA Texas Dept of Insurance
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
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. • Run a simulation based on mean LDFs and std dev of LDFs, reflecting correlation between the LDFs in successive DYs.
Cold Showers for Confident Actuaries • 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. • 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.
More Cold Showers • 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.
Become a High Roller at Monte Carlo Simulation • 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 3—Dream up models from an alternative universe and assign each model a probability of representing reality. Simulate at all 3 levels. [Model Risk]
Encountering Reality:Industry Runoff Statistics • 2,500 P/C Insurers • Schedule P – Parts 2 & 3 • Focus on distribution of individual company results • Findings never presented on 9/11/01 at CLRS by Kevin Wick of PwC.
5 Year Hindsight Comparisons • Use latest ultimates less cumulative paid from 5 years ago. • Compile %-age of insurers where hindsight reserve was within +/- 5%, etc.
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. • 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.
Future Payments Can Be Fickle • 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.
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?
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. • 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.
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?
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.
Dead on Arrival (DOA) Data Diagonals Only Area (DOA) Standard Triangle
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%.
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?
CONCLUSIONS • Actual variability of future payout >> What you think it is. • Actual variability >> low and high estimates in your range. • 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.
