Estimating Reserve Ranges: Practical Suggestions

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Estimating Reserve Ranges Practical Suggestions

• Richard E. Sherman,
• FCAS, MAAA
• Richard E. Sherman Associates, Inc.

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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. PC
  Practice Note, p. 33

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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
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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 incd 11 M
Selected range 9M - 11 M
-age range /- 10
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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 incd proj. 7 M
Adj. Born Ferg proj. 7 M
Selected range 6M - 8M
Should range be 9M - 11M ???
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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
• Cant you do better than that?

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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!!!!

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Possible Help

• Simply present a minimum realistic range of /-
  5 or /- 10.
• Run a Monte Carlo simulation and pick the 30
  70 confidence level reserves as your range.

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More 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.

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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.

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More Cold Showers

• Review Schedule PParts 2 3 by AY and calculate
  -age favorable/ adverse development of
  ultimates.
• Run a Monte Carlo simulation to get a feel for
  the probability distribution of future payments.

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Become a High Roller at Monte Carlo Simulation

• Level 1Poisson for of claims lognormal or
  pareto for claim size Process Risk
• Level 2Add a probability distribution for the
  uncertainty of lambda for Poisson and for the
  mean std dev for lognormal Parameter Risk
• Level 3Dream up models from an alternative
  universe and assign each model a probability of
  representing reality. Simulate at all 3 levels.
  Model Risk

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Encountering RealityIndustry Runoff Statistics

• 2,500 P/C Insurers
• Schedule P Parts 2 3
• Focus on distribution of individual company
  results
• Excluded insurers with booked reserves lt 1 M.
• Findings never presented on 9/11/01 at CLRS by
  Kevin Wick of PwC.

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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.

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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
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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
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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
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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
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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
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By Size of All Lines Reserves
5 Year Hindsight Reserve Total Reserve lt 1 M Total Reserve 10-50 M Total Reserve gt 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
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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.

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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.

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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?

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Trend, Cycle or Noise?
AY DY 2 DY 3 DY 4
2003 1.374 1.062 1.031
2004 1.424 1.055 1.029
2005 1.456 1.049
2006 1.474
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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 it isnt real.

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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?

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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.

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

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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?

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Common WC Reserving Concerns

• Chronic gradual stair-stepping.
• Case reserves typically have entrenched downward
  biases, yet actuaries often give credence to
  incurred for the most mature AYs in selecting a
  tail.

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WC Reserving Pitfall A

• WC payout consists of two radically different
  distributions
• short term payments and
• lifetime payments to permanently disabled
  claimants.
• Unless you have 30 DYs of experience, you
  are likely to base projections on 1) even though
  most of the gross reserve is due to 2).

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Short Term v. Lifetime WC Payments
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WC Reserving Pitfall B

• 4 - 5 Medical component of CPI
• 8 - 10 Average rate of medical cost escalation
  for WC
• Basket of services keeps shifting to more
  expensive ones.

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WC Reserving Pitfall C

• Case reserve reflects current annual incremental
  paid, inflated up to the claimants expected year
  of death.
• Problem Additional costs for claimants outliving
  their life expectancy will significantly exceed
  the reduced costs from claimants who die
  earlydue to the compounding of medical inflation.

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WC Reserving Pitfall D

• Leaving the paid tail unchanged even though
  retentions have risen dramatically.

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CONCLUSIONS

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