CLOSING THE BOOKS WITH PARTIAL INFORMATION

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CLOSING THE BOOKS WITH PARTIAL INFORMATION

• By Joseph Marker, FCAS, MAAA
• CLRS, Chicago, IL, September 2003

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Closing the Books with Partial information - CLRS
2003

• Outline
• This presentation discusses the setting of Loss
  and LAE reserves when a fresh reserve analysis
  is not available.
• Shows one method in detail.
• Discusses this method in relation to others.
• Shows how method addresses Managements reserving
  issues.

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Closing the Books with Partial information - CLRS
2003

• Importance of Loss and LAE Reserve
• This reserve is
• The largest liability on the balance sheet.
• The balance sheet item with the greatest
  uncertainty.
• Subject to scrutiny at least quarterly.

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Closing the Books with Partial information -
CLRS 2003

• Information Available at Closing
• Often the books are closed with no fresh
  reserve study done in time for the closing, such
  as
• At quarter end, when reviews are not done every
  quarter,
• At quarter end, if a fresh reserve review
  cannot be done in time.
• At monthly intervals, if reviews are done every
  quarter.
• From here on, assume that we are dealing with
  quarterly closings.

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Closing the Books with Partial information - CLRS
2003

• Information Available at Closing
• At closing time, various levels of information
  may be available
• 1. A full reserve review on data as of the
  current quarter, or
• 2. No reserve review, but actual loss
  development through the current quarter, e.g.
• Paid and outstanding loss and loss expense by
  accident year.
• Paid and outstanding claim counts.
• Earned premiums and earned exposures.
• 3. Loss payment and written premium information
  only.
• This discussion assumes that information
  described in (2) is available.

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Closing the Books with Partial information - CLRS
2003

• Example Company XYZ
• Company XYZ is closing its books as of 3/31/2003.
• A full loss reserve review is available as of
  12/31/2002.
• Exhibit 1 shows an example of a Roll Forward
  calculation.
• Method compares expected and actual development
  during the quarter.
• Uses this information to modify the Selected
  Ultimate Loss

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Closing the Books with Partial information - CLRS
2003

• Expected Loss Development Exhibit 1
• Exhibit 1 determines the expected 1st quarter
  development and payments.
• Shows the chain ladder methods (paid and
  incurred) through 12/2002.
• Separates expected development into current
  quarter vs. future.
• Requires the Selected Ultimate Loss by accident
  year as of 12/2002.
• LDF for 1st quarter may need to be interpolated
  from annual factors.

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Closing the Books with Partial information - CLRS
2003

• Expected Loss Development Exhibit 1
• Calculation of 1st Quarter Expected development
• Future development on each accident year equals
• selected ultimate minus developed loss to date
  (12/31/2002)
• The expected proportion developing in 1st quarter
  is given by
• LDF (to quarter end) 1.0 divided by
  LDF (to ultimate) 1.0
• We need to know the proportion of the annual
  development expected in the 1st quarter.

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Closing the Books with Partial information - CLRS
2003

• Expected Loss Development Exhibit 1
• Calculation of 1st Quarter Loss Development
  Factor
• If quarterly LDFs are available, use those.
• If only annual LDFs are available, use
  interpolation.
• Most difficult to assess for the immediate past
  accident year.
• Reference Richard E. Sherman, Extrapolating,
  Smoothing, and Interpolating Development
  Factors, PCAS LXXI (1984), pages 122-155.

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Closing the Books with Partial information - CLRS
2003

• Expected Loss Development Exhibit 1
• Limitations of Exhibit 1
• Uses only the standard age-to-age LDF methods.
• Does not estimate the loss amount for the current
  partial accident year.
• Exhibit 1 can also project claim counts.

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Closing the Books with Partial information - CLRS
2003

• Exhibit 2 Actual Development
• Exhibit 2 brings in the actual paid and developed
  loss for the quarter.
• Differences between actual and expected
  development lead to recalculation of the ultimate
  loss.

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Closing the Books with Partial information - CLRS
2003

• Revising the Selected Ultimate Loss XYZ Company
• Exhibit 2 Roll Forward Loss Adjustment
  Mechanism
• For Incurred Method, Ultimate Loss Previous
  Ultimate Loss plus the difference between Actual
  and Expected 1st Quarter development.
• For Paid Method, use Actual minus Expected
  payments to adjust the loss.
• Key observations about this adjustment mechanism
• For Incurred Method, the Ending IBNR at 3/2003
  depends only on expected development.
• For Paid Method, the Ending Total Reserve depends
  only on the expected payments.

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Closing the Books with Partial information -
CLRS 2003

• Comments on Exhibit 1 Ultimate Loss
• If the tail is lengthening, this procedure
  understates reserves compared to fresh analysis.
• More stable, less responsive than fresh analysis.
• May be used to screen lines of business for
  deeper analysis when actual and expected
  development vary significantly.

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Closing the Books with Partial information - CLRS
2003

• Comments on Exhibit 1 Ultimate Loss
• Management relates well to the concept of
  comparing Actual and Expected development.
• Since IBNR is determined independently of actual
  development, reserve discussions can begin before
  the quarter end.

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Closing the Books with Partial information - CLRS
2003

• Current Accident Year
• We have not discussed setting reserves for the
  current accident year 2003.
• To do this, use exhibits where projections are
  based on
• Bornhuetter-Ferguson methods rather than straight
  LDF methods
• Pricing projections will likely be the key
  information used.
• Common methods for estimating the current
  accident year are
• Fix the loss ratio based on pricing studies
• Using the loss ratio and the projected
  development pattern, adjust the loss ratio by the
  difference between actual and expected emergence.
• Use frequency-severity methods and track claim
  count reporting.

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Closing the Books with Partial information - CLRS
2003

• Current Accident Year
• Calculation is tricky for 2nd and 3rd quarter
  reserves.
• LDFs account for future losses for the entire
  accident year.
• IBNR reserve includes only future development on
  losses with accident dates in the partially
  completed year.

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Closing the Books with Partial information - CLRS
2003

• Summary
• When closing the books without a current reserve
  evaluation, use the actual development to date to
  modify previous reserve estimates.
• Deal with quantities that make sense to
  management, such as
• Actual versus expected development.
• Keep the explanatory exhibits simple and few.
• Use the exhibits to involve other disciplines in
  explaining variances.

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Closing the Books with Partial information - CLRS
2003
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Closing the Books with Partial information - CLRS
2003