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

Estimating Reserve Ranges: Estimating Reserve Ranges: Practical SuggestionsPractical Suggestions

Richard E. Sherman, Richard E. Sherman, FCAS, MAAAFCAS, MAAA

Richard E. Sherman & Associates, Inc.Richard E. Sherman & Associates, Inc.

A Range of Reasonable EstimatesA Range of Reasonable Estimates

ASOP 36 defines it as “a range of ASOP 36 defines it as “a range of estimates that estimates that could be could be producedproduced by appropriate by appropriate actuarial methods or alternative actuarial methods or alternative sets of assumptions that the sets of assumptions that the actuary judges to be actuary judges to be reasonable.” reasonable.” P&C Practice Note, p. P&C Practice Note, p. 3333

1) A Comfortable Range1) A Comfortable Range

Paid projectionPaid projection $9 M$9 M

Incurred projectionIncurred projection $11 M$11 M

Born Ferg projectionBorn Ferg projection $10 M$10 M

Selected rangeSelected range $9 M - $11 M$9 M - $11 M

%-age range%-age range +/- 10%+/- 10%

2) A Range with 2 Adjusted Projections2) A Range with 2 Adjusted Projections

Paid projectionPaid projection $7 M$7 MIncurred projectionIncurred projection $14 M$14 MBorn Ferg projectionBorn Ferg projection $11 M$11 MBerq Sher adj paidBerq Sher adj paid $9 M$9 MBerq Sher adj inc’dBerq Sher adj inc’d $11 M$11 MSelected rangeSelected range $9M - $11 M$9M - $11 M%-age range%-age range +/- 10%+/- 10%

3) All Projections Much Too Low3) All Projections Much Too Low

Paid projectionPaid projection $6 M$6 MIncurred projectionIncurred projection $7 M$7 MBorn Ferg projectionBorn Ferg projection $6 M$6 MAdjusted paid proj.Adjusted paid proj. $8 M$8 MAdjusted inc’d proj.Adjusted inc’d proj. $7 M$7 MAdj. Born Ferg proj.Adj. Born Ferg proj. $7 M$7 MSelected rangeSelected range $6M - $8M$6M - $8MShould range be:Should range be: $9M - $11M ???$9M - $11M ???

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

5) Too Good to Be True5) 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 No changes in settlement rates or

adequacy level of reservesadequacy level of reserves HELP!!!!HELP!!!!

Ranges & Actuarial Opinions: A Regulatory Perspective

Nicole Elliott, ACAS, MAAA

Texas Dept of Insurance

Type of AOS Review

Point 467 54%

Range 145 17%

Point & Range 248 29%

Total 859

What Types of Ranges are Regulators Seeing?

Not discussed in ReportMethods considered proprietaryUsed actuarial judgment - common% +/- a point estimate - commonScenario testingStatistical distributions - rare

Possible HelpPossible Help

Use PLDFs to derive projections of future Use PLDFs to derive projections of future incremental paids. Assume 6% underlying incremental paids. Assume 6% underlying inflation & derive alternative projections of inflation & derive alternative projections of incremental paids based on 3% & 9% incremental paids based on 3% & 9% inflation.inflation.

Run a simulation based on mean LDFs and Run a simulation based on mean LDFs and std dev of LDFs, reflecting correlation std dev of LDFs, reflecting correlation between the LDFs in successive DYs.between the LDFs in successive DYs.

Cold Showers Cold Showers for Confident Actuariesfor Confident Actuaries

Review your own track record of past Review your own track record of past estimates & how they have developed.estimates & how they have developed.

Cover up the latest 2 diagonals and Cover up the latest 2 diagonals and estimate LDFs based on prior factors. Then estimate LDFs based on prior factors. Then compare your projections with actual compare your projections with actual LDFs.LDFs.

Dig up an old rate filing you did 3-5 years Dig up an old rate filing you did 3-5 years ago & compare the projected rates/pure ago & compare the projected rates/pure premiums with the ultimates in your latest premiums with the ultimates in your latest filing.filing.

More Cold ShowersMore Cold Showers

Review Schedule P—Parts 2 & 3 by Review Schedule P—Parts 2 & 3 by AY and calculate %-age favorable/ AY and calculate %-age favorable/ adverse development of previously adverse development of previously carried reserves.carried reserves.

Run a Monte Carlo simulation (using Run a Monte Carlo simulation (using @RISK or Crystal Ball software) to @RISK or Crystal Ball software) to get a feel for the probability get a feel for the probability distribution of future payments.distribution of future payments.

Become a High Roller Become a High Roller at Monte Carlo Simulationat Monte Carlo Simulation

Level 1—Poisson for # of claims; lognormal or Level 1—Poisson for # of claims; lognormal or pareto for claim size [pareto for claim size [Process RiskProcess Risk]]

Level 2—Add a probability distribution for the Level 2—Add a probability distribution for the uncertainty of lambda for Poisson and for the uncertainty of lambda for Poisson and for the mean & std dev for lognormal [mean & std dev for lognormal [Parameter RiskParameter Risk]]

Level 3—Dream up models from an alternative Level 3—Dream up models from an alternative universe and assign each model a probability of universe and assign each model a probability of representing reality. Simulate at all 3 levels. representing reality. Simulate at all 3 levels. [[Model RiskModel Risk] ]

Encountering Reality:Encountering Reality:Industry Runoff StatisticsIndustry Runoff Statistics

2,500 P/C Insurers2,500 P/C Insurers Schedule P – Parts 2 & 3Schedule P – Parts 2 & 3 Focus on distribution of individual Focus on distribution of individual

company resultscompany results Findings never presented on Findings never presented on 9/11/019/11/01

at CLRS by Kevin Wick of PwC.at CLRS by Kevin Wick of PwC.

5 Year Hindsight Comparisons5 Year Hindsight Comparisons

Use latest ultimates less cumulative Use latest ultimates less cumulative paid from 5 years ago.paid from 5 years ago.

Compile %-age of insurers where Compile %-age of insurers where hindsight reserve was within +/- 5%, hindsight reserve was within +/- 5%, etc.etc.

All Lines of BusinessAll Lines of Business

5 Year Hindsight 5 Year Hindsight

Reserve:Reserve:%-age of %-age of InsurersInsurers

Within 5%Within 5% 20%20%

Between 5% & 10%Between 5% & 10% 14%14%

Between 10% & 25%Between 10% & 25% 37%37%

More than 25%More than 25% 29%29%

Private Passenger Auto LiabilityPrivate Passenger Auto Liability




Between 5% & 10%Between 5% & 10% 19%19%

Between 10% & 25%Between 10% & 25% 44%44%


Workers Compensation or CMPWorkers Compensation or CMP




Between 5% & 10%Between 5% & 10% 14%14%

Between 10% & 25%Between 10% & 25% 37%37%


Other Liability OccurrenceOther Liability Occurrence




Between 5% & 10%Between 5% & 10% 10%10%

Between 10% & 25%Between 10% & 25% 29%29%


Med Mal Claims MadeMed Mal Claims Made




Between 5% & 10%Between 5% & 10% 6%6%

Between 10% & 25%Between 10% & 25% 15%15%


By Size of All Lines ReservesBy Size of All Lines Reserves

5 Year 5 Year Hindsight Hindsight

Reserve:Reserve:

Total Total Reserve Reserve < $ 1 M< $ 1 M

Total Total Reserve Reserve $10-50 M$10-50 M

Total Total ReserveReserve> $500 M> $500 M

Within 5%Within 5% 12%12% 17%17% 30%30%

Between Between 5% & 10%5% & 10%

5%5% 16%16% 15%15%

Between Between

10% & 25%10% & 25%20%20% 37%37% 45%45%

More than More than

25%25%63%63% 30%30% 10%10%

Consult Hindsight Deviation Consult Hindsight Deviation Profiles for the Reserve Size and Profiles for the Reserve Size and

LOBs Being AnalyzedLOBs Being Analyzed

May cause you to widen your May cause you to widen your judgmental feel for the size of the judgmental feel for the size of the range from your analysis.range from your analysis.

Suppose a new part were added to Suppose a new part were added to Schedule P to display the %-age Schedule P to display the %-age hindsight error in stated reserves? A hindsight error in stated reserves? A downside: It would make it easier for downside: It would make it easier for outsiders to derive quick and dirty outsiders to derive quick and dirty estimates of future development.estimates of future development.

Future Payments Can Be FickleFuture Payments Can Be Fickle

Even if the chosen model explains past Even if the chosen model explains past development well, it may not explain development well, it may not explain much of future development.much of future development.

Industry runoff results show disturbingly Industry runoff results show disturbingly high %-age of insurers with reserve high %-age of insurers with reserve development %-ages greater than 10% development %-ages greater than 10% and greater than 25%. and greater than 25%. Unanticipated Unanticipated major influences can cause dramatic major influences can cause dramatic movements in ultimates.movements in ultimates.

Edgy ReasonablenessEdgy Reasonableness

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

Trend, Cycle or Noise?Trend, Cycle or Noise?

AYAY DY 2DY 2 DY 3DY 3 DY 4DY 4

20032003 1.3741.374 1.0621.062 1.0311.031

20042004 1.4241.424 1.0551.055 1.0291.029

20052005 1.4561.456 1.0491.049

20062006 1.4741.474


Usually not possible to determine whether Usually not possible to determine whether data is following a trend, a cyclical data is following a trend, a cyclical pattern, or just fluctuating randomly in a pattern, or just fluctuating randomly in a column.column.

Simulation exercise. Start with a given Simulation exercise. Start with a given mean LDF and std dev and generate mean LDF and std dev and generate a a series of four LDFs for DY 2series of four LDFs for DY 2. Compile . Compile simulation results of what %-age of the simulation results of what %-age of the time the data will show a clear trend, even time the data will show a clear trend, even though there is no real trend.though there is no real trend.


Choose a series of Choose a series of four underlying four underlying distributions for the four LDFs for DY distributions for the four LDFs for DY 22, where the means are dropping , where the means are dropping steadily. From simulation, what %-steadily. From simulation, what %-age of the time will a trend line fitted age of the time will a trend line fitted to the data have an upward slope, in to the data have an upward slope, in spite of the actual downward trend spite of the actual downward trend present in the assumptions? present in the assumptions?

Can Actuarial Judgment Can Actuarial Judgment Overcome Low Credibility?Overcome Low Credibility?

Problem: Credibility of LDFs drops Problem: Credibility of LDFs drops rapidly for the most mature DYs. rapidly for the most mature DYs. Culminates in reliance on only one Culminates in reliance on only one LDF at the tip of the triangle.LDF at the tip of the triangle.

Suggestion: Apply methods that pull Suggestion: Apply methods that pull in incremental data prior to the in incremental data prior to the triangle to raise the credibility of the triangle to raise the credibility of the LDFs at or near the tip.LDFs at or near the tip.

Dead on Arrival (DOA) DataDead on Arrival (DOA) Data

Standard Triangle

DiagonalsOnly Area(DOA)

Going Out on a BerqSher Limb?Going Out on a BerqSher Limb?

Problem: Adjusted triangle resulting Problem: Adjusted triangle resulting from a BerqSher method produces from a BerqSher method produces strange progressions of incremental strange progressions of incremental paids or incurreds.paids or incurreds.

Suggestion: Take only Y% of each Suggestion: Take only Y% of each indicated adjustment. Solve for the Yindicated adjustment. Solve for the Y% that produces the most reasonable % that produces the most reasonable adjusted triangle. For example, Y = adjusted triangle. For example, Y = 60% or 130%.60% or 130%.

Bias Inherent in Trimming LDFsBias Inherent in Trimming LDFs

Problem: Often, relying on the Avg X Hi Lo Problem: Often, relying on the Avg X Hi Lo can result in tossing out most of the large can result in tossing out most of the large adverse development while only removing adverse development while only removing small favorable developments from the small favorable developments from the historical factors.historical factors.

Suggestion: Try smoothing the historical Suggestion: Try smoothing the historical data using moving averages over data using moving averages over successive DYs instead. Less bias?successive DYs instead. Less bias?

CONCLUSIONSCONCLUSIONS

Actual variability of future payout Actual variability of future payout >>>> What you think it is.What you think it is.

Actual variability Actual variability >>>> low and high low and high estimates in your range.estimates in your range.

Do more homework before making Do more homework before making selections.selections.

Help your audience appreciate how large Help your audience appreciate how large the real degree of variability is, while the real degree of variability is, while retaining their confidence in your retaining their confidence in your professional abilities.professional abilities.

Documents

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