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

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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

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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

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ISO Study of Loss and Loss Adjustment Expense
ReservesA. IndustryB. RD

• CAS Annual Meeting
• November 15-16, 2004
• John J. Kollar, ISO

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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

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Lines studied

• 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

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Some Key Points

• All indications are PRELIMINARY we have not yet
  selected final LDFs ranges
• Excludes reserves for environmental and asbestos
  (EA) 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

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Methodologies

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

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Factors affecting analysis

• Data quality
• Development factors
• Tail factors
• Professional judgment

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Conventions

• Each deficiency/redundancy expressed as
  percentage of indicated undiscounted reserve as
  estimated by ISO
• Positive percentages indicate deficiencies
• Negative percentages indicate redundancies

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Preliminary Summary Indications of Reserve
Deficiencies

• Paid Case Incurred
• Lines Studied 7 9
• All Other Lines 5 5
• Total all lines 7 8
• In Dollars 30B 34B
• Note excludes E A

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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

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Preliminary Indications by Line

• Lines with significant deficiencies
• Paid Case Inc.
• Other Liability Occurrence 11 3
• Products Occurrence 1 13
• Com. Multi-Peril 6 9
• Workers Comp 14 21
• Reinsurance (Non-Prop.) 29 30

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Preliminary Indications by Line

• Other Lines
• 
  Paid Case 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

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

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Loss Reserve Changes vs. Industry Profitability,
All Lines
Changes in reserves are correlated with
profitability.
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Indicated Reserve Deficiencies vs. Industry
Profitability
Since 1997, changes in estimated
deficiencies have mirrored changes in overall
profitability.

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Retrospective Estimated Deficiencies Economic
Discount, All Studied Lines

Even when discounted, reserves may not be
adequate.
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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

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Pers. Auto Incurred LALAE Development from 15 to
Ultimate for Voluntary DE Risks
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Pers. Auto Liab. Paid Bodily Injury LALAE
Development from 15 to Ult. for PA Risks
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Other Liability Full Coverage Bodily Injury Loss
Development from 15 to Ultimate
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Com. Auto BI Liability Development from 15 to
Ultimate in Tort States for Trucks, Tractors
Trailers
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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.

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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.

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Possible Stochastic Model(s)

• Reserve f(Age, AY, Size)e
• Age or valuation or lag
• AY (accident year)
• Size is reflected in a BF/Cape Cod formula.
• The error term, e, could depend on accident year,
  age and size.
• Lognormal distribution?
• Correlation of es between (age,AY) cells?

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Uses of Stochastic Model(s)

• Test hypothesis that an insurers data is
  described by a clusters 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 ????.

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Confidence Intervals for Reserves

• Given distribution of es 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!

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What do You Think?