Bornhuetter-Ferguson: Initial Expected Losses Working Party

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Bornhuetter-Ferguson Initial Expected Losses
Working Party

• Co-Chair Jeff Carlson FCAS, MAAA
• Towers Perrin (Tillinghast)
• Co-Chair Chris Olson FCAS, MAAA
• St. Paul Travelers
• 2005 CLRS Boston, MA
• Session 5 Report of the Bornhuetter-Ferguson
  Initial Expected Losses Working Party

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Rationale

• Bornhuetter-Ferguson is one of the most heavily
  relied upon reserving methods
• Can be thought of as a credibility weighted
  estimate of chain-ladder indication and initial
  expected losses
• Much written about chain-ladder method,
  relatively little about initial expected losses

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Rationale (continued)

• Seminal paper for the method simply says that if
  the expected loss ratio cannot be selected with
  much accuracy, a high ratio should be used.
• It can be argued that over-reliance on (possibly
  flawed) initial expected loss estimates
  contributed to the underestimation of reserves in
  recent years

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Rationale (continued)

• Goal of this working party is to publish a paper
  to provide guidance for practitioners and
  education for students
• Initial expected losses can be applicable to
  methods beyond Born-Ferg

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Working Party Scope

• Have not engaged in primary research
• Want to leverage initial expected loss approaches
  already in use, whether documented or not
• Many smart people using Bornhuetter-Ferguson
  method, probably many very good IEL approaches
  already exist

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Tasks Completed To-Date

• Have completed surveying the workplaces of
  working party members. Received 14 responses
  from a variety of actuaries, representing many
  companies/individuals
• Have identified and summarized relevant published
  literature. Identified 24 items to summarize of
  which 7 were deemed to be of high importance.
• Have laid the groundwork for evaluating various
  options for IEL development

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Workplace Surveys
Identified methods grouped into -BFIEL
obtained from information in the triangle -BFIEL
obtained from outside source -Other
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BFIEL Obtained from Triangle
Method Observations Price (or
exposure)/Trend Rollforward 13 Stanard-Buhlmann /C
ape Cod 6 Average of LDF methods 6 Historical
average of ultimates/loss costs 6 Frequency/Sever
ity 5 Least Squares Regression/Simulation 4
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BFIEL Obtained from Outside Source
Method Observations Pricing
Indication 8 Industry loss ratio/loss
costs 8 Corporate Plan 3 Underwriter loss
ratio 2 Competitor loss ratio 2
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BFIEL Other
Method Observations Benktander
3 method adjusts BFIEL arrived at via other
means by giving more weight to LDF
indication. Prior Selected Ultimate 6 Experien
ce Rating Results 3
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Summary of Published Literature High Importance
Articles

• The Actuary and IBNR, Bornhuetter and Ferguson
• Discussions of The Actuary and IBNR by Cooper
  and White
• Estimating Salvage and Subrogation
  Reserves-Adapting the Bornhuetter-Ferguson
  Approach, Grace

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Summary of Published Literature High Importance
Articles (contd)

• Using Best Practices to Determine a Best Reserve
  Estimate, Struzzieri and Hussian
• Balancing Development and Trend in Loss Reserve
  Analysis, Gluck
• Credible Claims Reserves Benktander Method,
  Mack

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Examples of Methods to be Shown

• Price Trend Rollforward Several versions
  varying the point at which losses are rolled
  forward from
• Stanard-Buhlmann/Cape Cod Original and Glucks
  version
• Benktander
• Frequency/Severity
• Least Squares Regression
• Excess Ratio of 1st dollar expected losses
• Graces Method for Salvage and Subrogation

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Bases for Initial Expected Losses

• Basis source information from which the initial
  expected losses are measured
• Comparable to an exposure basis for pricing an
  insurance risk

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Commonly Used Bases

• Ultimate loss estimate from another source
• From prior analyses
• From other projection methods
• From more mature exposure years
• Premiums
• Exposures (e.g. payroll, car years)
• Ultimate claim counts
• A related group of losses
• Estimate of industry losses
• Estimate of primary layer losses
• Estimate of losses of a related coverage

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The Basis is Converted to the IEL
Basis Conversion Statistic
Ultimate loss estimate from another source None needed
Premiums Expected loss ratio
Exposures Expected pure premium
Ultimate claim counts Expected claim severity
Estimate of industry losses Expected market share
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A particular approach can be evaluated based on
the quality of the basis and the conversion
statistic

• Both the basis and the conversion statistic can
  be judged on several criteria
• Availability
• Accuracy
• Uncertainty/ Variability
• Expected correlation to losses

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IEL approaches can be categorized by Basis and
Source
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Proposed BFIEL Principles

• The purpose of estimating initial expected losses
  is to provide a (better?) predictor of future
  loss development that is not based directly on
  the current paid and outstanding losses.
• If the estimate of initial expected losses is
  developed from past loss history and pricing and
  loss trend assumptions, then the estimate should
  be revised as the loss history develops and
  changes and/or the pricing and loss trend
  assumptions change.

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Proposed BFIEL Principles (contd)

• The reliance to be placed on a loss projection
  based on an estimate of initial expected losses,
  relative to the reliance on loss projections
  based on other approaches, depends on the level
  of confidence in the estimate. For example, an
  estimate based upon past loss experience,
  modified by robust pricing and trend information,
  should be relied upon more so than an estimate
  obtained from a business plan with no rigorous
  supporting rationale.

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ISSUES

• Many methods seem to use the link-ratio method to
  improve the BFIEL. Is this a good thing to do?
• There seems to be a lot of actuaries that use
  their prior selected ultimates as their BFIEL for
  periods more than a year or two old. Is this
  really your expected loss ratio?

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BF IEL Working Party

• Questions?