Introduction To Reinsurance Reserving

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Introduction To Reinsurance Reserving
Atlanta, Georgia September 11, 2006
Anita Sathe, ACAS, ASA Deloitte Consulting
LLP Christopher Bozman, FCAS, MAAA Towers
Perrin Tillinghast Michael Angelina, ACAS, MAAA
Endurance Specialty Holdings
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Agenda

• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
  affect Loss Reserving
• Other Considerations Development Methods
• Other Reserving Methods

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Agenda

• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
  affect Loss Reserving
• Other Considerations Development Methods
• Other Reserving Methods

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Reinsurance Contract Types

• Type of policies
• Mechanics of cession

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Reinsurance Contract Types Type of Policies

• Treaty Reinsurance
• Covers a book or class of business
• Automatic reinsurance
• Insured/policies are unknown at inception but
  become known subsequently
• Typical Uses
• Provide stability
• Increase aggregate capacity
• Facultative Reinsurance
• Covers a specific individual risk
• The reinsurer retains the right to accept or
  reject each risk
• The one insured/policy is known to the reinsurer
  at inception
• Typical uses
• Unique exposures
• Hazardous exposures
• Provide line capacity

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Reinsurance Contract Types Type of Policies

• Finite Reinsurance
• Non-traditional treaty reinsurance
• Transfers a limited amount of risk
• Involves profit sharing elements
• Typical uses
• Surplus relief
• Smoothing results

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Reinsurance Contract Types Mechanics of cession

• Two mechanics of cession
• Pro Rata reinsurance
• Proportional sharing of premiums and losses
• Excess of loss reinsurance
• Losses in excess of a given dollar retention are
  covered
• Applicable to both treaty and facultative
  reinsurance

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Reinsurance Contract Types Mechanics of cession

• Pro Rata reinsurance
• Quota Share
• Fixed percentage of premium losses shared
• Dollar amount ceded varies by size of risk
• E.g. QS Reinsurance with 25 retention.Total
  Premiums 1,000,000Total Losses 700,000

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Reinsurance Contract Types Mechanics of cession

• Pro Rata reinsurance
• Surplus Share
• Fixed amount (line) of losses ceded
• Percentage shared varies by size of risk
• E.g. Surplus share 200,000 xs of 150,000

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Reinsurance Contract Types Mechanics of cession

• Excess Reinsurance
• Per risk
• Applies to property risks
• Limit applies separately to each risk (e.g.
  building)
• Per occurrence
• Typically applies to liability covers
• Limit applies to total loss for an occurrence
  regardless of number of risks or policies
  involved
• Aggregate excess
• Can apply to both property and liability covers
• Limits and retentions stated in terms of loss
  ratio bands
• Reinsurers relative participation is NOT
  pre-determined, but depends on the size of the
  loss or loss ratio

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Reinsurance Contract Types Mechanics of cession

• Excess Reinsurance
• E.g. XOL 3,000,000 xs of 400,000

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Agenda

• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
  affect Loss Reserving
• Other Considerations Development Methods
• Other Reserving Methods

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Data Grouping Dimensions

• Accident Year vs. Underwriting Year
• or Losses Occurring vs. Risks Attaching
• Casualty vs. Property
• Treaty vs. Facultative
• Excess of Loss vs. Proportional
• Broker vs. Direct

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Data Grouping Dimensions

• Accident Year vs. Underwriting Year
• AY allows for easiest application of standard
  techniques
• Premium fixed as of December 31
• Population of claims fixed at December 31 as
  well, though many may be unknown
• May not always be an option for reinsurance
• Underwriting year includes experience on all
  treaties written during the year
• Underwriting Year is often used in reinsurance,
  especially for proportional contracts
• UY can cover two policy years and three calendar
  years for losses. Current UY as of 12 months is
  incomplete

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Incomplete Underwriting Year

• UY 2001 includes all treaties written by the
  reinsurer in 2001
• Risks Attaching and/or Policies Incepting
• UY 2001 can span two years and three accident
  years
• At 12/31/2001, UY 2001 is incomplete
• Standard development methods derived from the
  past UYs will overstate the development of UY
  2001.
• Historical development after 12 months includes
  exposures yet to be earned
• Provision for these losses should not be included
  in reserves at the 12/31/2001 accounting date.

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Incomplete Underwriting Year
1/1/2001
1/1/2002
1/1/2003
1/1/2004
Sample Time Line
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Data Grouping Dimensions

• Casualty vs. Property
• Casualty business generally has a longer
  development tail
• Line of business (LOB) detail is often not
  available to the reinsurer, but if it is you
  might want to further subdivide by LOB as
  different LOBs may develop differently

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Data Grouping Dimensions

• Treaty vs. Facultative
• These display different development patterns, all
  else equal

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Data Grouping Dimensions

• Excess of Loss vs. Proportional
• Can be more important to split than line of
  business
• Different development patterns
• Possible reserve adequacy mix
• Excess of Loss - Case reserves generally reviewed
  by reinsurer claim dept and ACRs established
• Proportional - Case reserves booked as reported
  by ceding company without reinsurer review
• Split Excess by layer - low, high, catastrophe

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Data Grouping Dimensions

• Broker vs. Direct
• Reinsurers obtain business either directly from
  cedant or through broker (or both)
• Data flowing through broker may create additional
  reporting lag and result in different development
  patterns

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Agenda

• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
  affect Loss Reserving
• Other Considerations Development Methods
• Other Reserving Methods

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Differences Between Primary and Reinsurance

• Reporting Lag/Development Lag
• Data
• Increased Variability
• Tailor-Made or Atypical Contracts or Features
• Accumulation of Issues

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Differences Between Primary and Reinsurance

• Reporting Lag/Development Lag
• Primary losses develop faster than reinsurance
  losses due to time lag for data to reach
  reinsurer
• Proportional business Accounts not due to
  reinsurer until 30-90 days after quarter close
• It is possible that losses booked by ceding
  company in calendar year X will be realized and
  booked by reinsurer in calendar year X1
• Excess business Reporting lag compounds with
  development lag
• Reinsurer not notified immediately of the loss
• The losses do not hit the reinsurers data
  until they exceed the threshold established in
  the Excess reinsurance contract

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Differences Between Primary and Reinsurance

• Reporting Lag/Development Lag
• Excess business Reporting lag compounds with
  development lag
• Example
• 400,000 excess of 100,000 per risk cover
• Loss occurs in Year 1, reserved for 25,000
• Year 3 - reserve increased to 50,000, reinsurer
  verbally notified that loss MAY eventually reach
  their contract
• Year 5, reserve increased to 150,000, reinsurer
  incurs loss 4 years after the primary company

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Primary vs. Reinsurer
Reproduction of RAA 2001 Historical Loss
Development Study Graph Primary Company Data
Source A.M. Best Company
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Differences Between Primary and Reinsurance

• Reporting Lag/Development Lag
• Premium Estimates
• Needed in reinsurance more than for primary
  insurance
• Reserves must be set against premium earned as of
  the accounting date
• Reporting lag can cause large earned premium
  amounts to be unreported to the reinsurer as of
  the accounting date
• Creates a need to estimate premium and losses
  associated with this premium

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Differences Between Primary and Reinsurance

• Data
• Quantity
• The infinite detail of primary company data is
  often lost when reported to reinsurers as data
  gets collapsed along several dimensions
• Accident dates not reported
• Lines of business not reported
• Industry benchmarks by line of business or
  accident year can thus be difficult to use
• Quality affected by varied quantity
• Some ceding companies report more detail to
  reinsurers than do others
• As reinsurance data for reserving is organized at
  the level of common detail in terms of reported
  data fields, this has an impact on the quality of
  the analysis

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Differences Between Primary and Reinsurance

• Increased Variability
• Primary insurers purchase reinsurance (among
  other reasons) to make their results less
  variable (i.e. from catastrophes)
• Reinsurer data is subject to this reinsured
  variation
• Depending on the type of reinsurance cover,
  reinsurer data may BE this variation

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Primary Experience Gross of Reinsurance
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Primary Experience Net of Reinsurance
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Reinsurance Experience
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Differences Between Primary and Reinsurance

• Tailor-made or Atypical Contracts or Features
• Many (possibly large) reinsurance contracts have
  features that affect the way their experience
  will develop relative to other contracts with
  which they would otherwise be grouped
• Examples Stop loss arrangements, loss
  corridors, sunset clauses, etc

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Differences Between Primary and Reinsurance

• Accumulation of Issues
• Each primary insurer faces issues (e.g. changes
  in reserve adequacy, settlement patterns, etc.)
• Issues affect companys loss reserving data, and
  reserving analyst has tools to neutralize the
  effects
• Reinsurance loss reserving data is an
  accumulation of primary data each of which may
  have these issues
• Adds a further complication to the reinsurance
  loss reserving process

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Agenda

• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
  affect Loss Reserving
• Other Considerations Development Methods
• Other Reserving Methods

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Applications, Complications, and Considerations

• Application of Projection Methods
• Loss Development Method
• Loss Ratio Method
• Bornhuetter-Ferguson Method
• Other Methods

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Applications, Complications and Considerations

• Complications
• parameter uncertainty
• Volatility in report-to-report (RTR) factors
• Result can be very leveraged by tail factor
  selection
• Loss trend factors
• Expected loss ratios
• data constraints
• Line of business definition
• Claim count information often lacking
• Other considerations
• qualitative information
• Often lack information on claims and underwriting
  changes at cedant level

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Loss Development Method Assumptions

• Assumes the relative change in a given years
  reported loss ALAE from one evaluation to the
  next will be similar to the relative change in
  prior years reported loss ALAE at similar
  evaluation points
• RTR factors measure change in reported loss
  ALAE at successive evaluations
• tail factor allows for development beyond the
  observed experience
• Assumes the relative adequacy of the companys
  case reserves has been consistent over time
• Assumes no material changes in the rate claims
  are paid or reported

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Loss Development Method Suggestions for Tail
Factors

• Industry benchmarks
• RAA for excess
• Reinsurance industry data going back 40 years
• Available for treaty vs. facultative and by
  attachment range
• Primary sources lagged for pro-rata
• ISO
• A.M. Best
• NCCI
• Curve fitting
• Compare to benchmarks for reasonability

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Loss Development MethodHow to deal with
variability in Historical Development

• Refine data
• Line of business mix
• At the very least need to split property vs.
  casualty pro-rata vs. excess
• Treaty vs. facultative
• Development patterns may differ
• Attachment points/limits
• Need to understand attachment points on from
  ground up (FGU) basis
• How are attachment points/limits changing over
  time
• Assess whether or not data is still credible
  after making refinements

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Loss Development MethodHow to deal with
variability in Historical Development

• Adjust for unique situations and claims
• Commutations
• Remove from analysis, otherwise projections will
  be distorted
• Treat any finite contracts separately
• E.g. aggregate stop loss covers will not
  develop similarly to per occurrence excess
• Be watchful of traditional contracts with
  finite features
• Annual aggregate deductibles, loss corridors
• Asbestos, pollution, mass tort claims should be
  subdivided and reviewed separately
• If these claims are included in development data,
  the tail factor will be overstated for more
  recent periods
• Segregate cats, 9/11 losses, other large/unusual
  losses

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Loss Development MethodHow to deal with
variability in Historical Development

• Supplement with benchmarks
• Utilize benchmark (or weighting of benchmarks)
  that is most appropriate for the book of business
  being analyzed. Consider
• Nature of underlying exposure (e.g. products
  versus premises)
• Attachment points/limits
• Actual historical development
• Ceding company profile
• Insolvent ceding companies will cause reporting
  delays

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Development by Line of Business
Source RAA Historical Loss Development Study,
2005 Edition.
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Treaty vs. Facultative General Liability
Source RAA Historical Loss Development Study,
2005 Edition.
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Impact of Attachment Points General Liability
Source RAA Historical Loss Development Study,
2005 Edition.
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Loss Development Method

• Application same as for primary business
• Results leveraged
• no claims no IBNR
• large claims large IBNR

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Loss Development Method

• Paid Loss Development Method not very common for
  reinsurance reserving
• Payment pattern is often extremely slow and
  erratic
• may be appropriate for property or low limit
  proportional business (e.g. nonstandard auto
  liability)

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Loss Ratio Method

• Useful for new business or immature years
• Need premium base and a priori expectation
  regarding loss ratio
• Advantage stability
• ultimate loss estimate does not change unless the
  premium or loss ratio are revised
• Potential problem lack of responsiveness
• ignores actual loss experience as it emerges

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Loss Ratio Method

• Ultimate Loss Earned Premium x ELR

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Loss Ratio Method

• Selecting the loss ratio
• historical experience
• paid and incurred loss experience
• LDF projection
• adjusted to appropriate year
• rate changes
• trends
• coverage changes
• underwriting considerations
• underwriting files
• actuarial pricing
• market considerations
• benchmarks (industry results)

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Adjustment for Incomplete Years

• Recent underwriting or policy years may not be
  fully earned as of the evaluation date
• may need to scale back loss development
  projections
• apply ultimate loss ratio to earned premium as of
  evaluation date
• Ensure that resulting IBNR is reasonable
• Ultimate Loss Ratio Ultimate Loss / Ultimate
  Premium
• Ultimate premium
• project development
• seek underwriter input

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Agenda

• Reinsurance Contract Types
• Data Grouping Dimensions
• Differences Between Reinsurance and Primary that
  affect Loss Reserving
• Other Considerations Development Methods
• Other Reserving Methods

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Reserving Methods - Bornhuetter-Ferguson

• Essentially a blend of LDF method and Expected
  Loss method
• begins with an a-priori estimate of expected
  losses
• IELR (Initial Expected Loss Ratio) x Earned
  Premium
• splits a-priori estimate into two pieces
• expected reported losses (IEL x reported)
• expected unreported losses(IBNR) (IEL x
  unreported)
• replaces expected reported losses with actual
  reported (case incurred) losses
• Restated ultimate loss estimate equals
• expected unreported(IBNR) plus actual reported
  (case incurred)

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Bornhuetter-Ferguson Method - an Example
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Bornhuetter-Ferguson Method - an Example (Cont)
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Bornhuetter-Ferguson Method - Advantages

• Allows for smoothing of results
• LDF method understates when case incurred losses
  are small
• overstates if losses large (ELR may understate in
  this instance)
• Incorporates changes in the environment
• attachment point, coverage changes, layer
  restructuring, price strengthening/deterioration
• Balances stability and actual loss emergence
• Estimates IBNR when loss activity is sparse
• ideal for long tailed lines (umbrella, xs
  casualty)
• redundant for short tailed lines (approximates
  LDF method)
• Reflects potential information found in
  underwriting files
• underlying limits profile

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Bornhuetter-Ferguson Method - Disadvantages

• Reporting pattern
• expected percentage reported 1 / LDF
• difficulty in estimating pattern for LDF method
  also applies here
• Initial expected losses
• IBNR is directly related to a-priori estimate
• double the expected losses ----gt double the IBNR
• importance of IELR may be lost in the analysis
• need to step back and determine of total IBNR
  that is loss ratio driven
• Ultimate Premium
• most recent year may be difficult to estimate
• booked premium is probably under-reported due to
  timing lags
• seek underwriting estimate

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Bornhuetter-Ferguson Method -Alternative Sources
of Initial Expected Losses

• Loss Ratio Method (incorporates pricing indices)
• Underwriting estimate from pricing study
• by definition it is the a-priori estimate
• verify that parameters for pricing and reserving
  are consistent
• Increased limits factors and direct premium
• may be used if you feel primary companys higher
  limits pricing is inadequate
• should have been incorporated in pricing study
• may also be used for changes in layer and/or
  attachment point
• Stanard-Buhlman estimates
• Frequency/Severity estimates

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Example of change in layer structuringEffect on
IELR
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Stanard-Buhlman Estimate

• Essentially the Bornhuetter-Ferguson estimate
  with on average perfect information
• Uses actual loss ratio indices multiplied by
  average loss ratio
• incorporating loss trend and pricing changes
• Balances the expected average loss ratio so that
• expected reported losses actual reported losses

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Stanard-Buhlman - an Example
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Stanard-Buhlman - an Example (continued)
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Stanard-Buhlman - an Example (continued)
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Stanard-Buhlman - Bornhuetter-Ferguson Method
(continued)
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Frequency Based Method - Basic Steps - Including
Policy Limit Impact

• Estimate the annual number of claims above the
  data limit
• 37.5 claims greater than 150,000
• Use size of loss curves to project the number of
  claims above the reinsurance retention
• 11.3 (of 37.5 claims) greater than 300,000
• Use size-of-loss curves to project average
  severity of claims in reinsurance layer
• 239,751 average severity of claims in 700,000
  excess of 300,000 layer
• Multiply the frequency and the severity
  projections to estimate the total ultimate losses
• Incorporate frequency/severity estimate into
  Bornhuetter-Ferguson method

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Frequency/Severity - Estimate of claim counts
above data limit
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Frequency/Severity - Estimate of claim counts
above data limit (Cont)
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Frequency/Severity - Estimation of excess losses
using pareto distribution
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Frequency/Severity - Bornhuetter-Ferguson Method
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Recap of Methods - Ultimate Loss and ALAE
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Recap of Methods -Ultimate Loss and ALAE Ratios
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Final Selection of UltimatesRules of Thumb

• LDF methods for older, more mature
  accident/policy periods
• look at LDF/ percentage reported to determine
  maturity
• umbrella versus auto physical damage
• Expected Loss techniques for newer, less mature
  accident/policy periods
• most recent or two most recent accident years
• Bornhuetter-Ferguson/ Stanard Buhlman, anywhere
  in between
• requires judgment (GL, umbrella, excess
  casualty)
• Frequency/Severity similar to expected loss
  techniques
• better estimate when loss ratio is
  unstable/unreliable
• high layers, single treaties
• Benchmarks
• IBNR to case O/S ratios loss ratios

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Other Thoughts

• Look for trends, stability, shocks
• are they reasonable ?
• Communicate with the underwriting and claims
  departments
• good fodder for next underwriting audit or
  pricing season
• Gather knowledge on reserving philosophy (level
  of ACRs)
• make adjustments where necessary to benchmarks
• How to handle new lines of business with no
  history
• benchmarks, underwriting files, actuarial pricing
  analysis
• Incomplete underwriting year
• ultimate loss ALAE ratio using ultimate premium
• apply to estimated earned premium look at actual
  case incurred
• Difficult Coverages (Agg XS, deductibles,
  reinstatements)
• requires modeling of underlying exposures

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Other Approaches (Cont)

• Asbestos, Pollution, Other Health Hazards
• Need to handle separately
• Cedant information, industry data, benchmarks
• Results of exposure based modeling techniques
• Large Events / Market Losses (WTC losses)
• Seek input from claims department
• Utilize market information / knowledge
• Property Catastrophes
• Results of models (may need to adjust)
• Underwriter estimates
• Traditional top-down techniques

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Contact Information

• Anita Sathe, ACAS, ASADeloitte Consulting
  LLPPhone [phone]ansathe_at_deloitte.com
• Christopher Bozman, FCAS, MAAATowers Perrin
  TillinghastPhone [phone]Christopher.Boz
  man_at_towersperrin.com
• Michael Angelina, ACAS, MAAAEndurance Specialty
  Holdings, LtdPhone [phone]mangelina_at_end
  urance.bm