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Basic Track II. 2000 CLRS September 2000 Minneapolis, Minnesota. Introduction. Topics Covered Comparison of Results from Paid and Incurred LDMs Reasonableness Checks Ultimate Loss Ratios Frequency/Severity Pure Premium Current Year Sensitivity Analysis Rate Level Adequacy

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Basic Track II

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Basic track ii

Basic Track II

2000 CLRS

September 2000

Minneapolis, Minnesota



  • Topics Covered

    • Comparison of Results from Paid and Incurred LDMs

    • Reasonableness Checks

      • Ultimate Loss Ratios

      • Frequency/Severity

      • Pure Premium

    • Current Year Sensitivity Analysis

      • Rate Level Adequacy

      • Claim Severity

      • Claim Closure Rate

      • Adequacy of Case Reserves

      • Frequency/Severity Projection

    • Importance of Tail Factors

Comparison of ldm projections

Comparison of LDM Projections

Comparison of loss development methods

Comparison of Loss Development Methods



PLDM: No changes in the payment pattern

ILDM: No changes in case reserve adequacy

PLDM: “Hard” data; no estimates involved

ILDM: Uses all the available information


PLDM: May generate large, volatile loss development factors

& take longer to develop to ultimate

ILDM: Uses case reserves, which are estimates, to develop

estimates of ultimate losses


Key assumptions potential problems

Key Assumptions & Potential Problems

Sample Problems


Increasing delays in claim closing rates

Conscious effort to improve case reserve adequacy;

Introduction of new case reserving procedures

Change in data processing;

Revised claim payment recording procedures

Increasing frequency of full policy limits claims;

Changing policy limits

Claims settlement patterns unchanging

Case reserving practices & philosophies


No claim processing changes

Policy limits have no impact on loss


Key assumptions potential problems1

Key Assumptions & Potential Problems

Sample Problems


Surges in inflation;

Increased litigation;

Diminished policy defenses

Changes in reinsurance coverages;

Increased long-tail exposures;

Introduction of new or revised coverages

Claims settlement or reserving impacted

by business underwriting cycles

Catastrophic or unusual losses reflected in

loss experience;

Unusual claim settlement/reporting delays

Loss development unaffected by changing

loss cost trends

No change in mix of business

No cyclical loss development

No data anomalies

Comparison of estimated reserves

Comparison of Estimated Reserves

Formulas to derive ibnr reserves

Formulas to Derive IBNR Reserves

  • Once an estimate of ultimate loss has been obtained, the arithmetic of IBNR is simple.

Unpaid Losses


Case Reserves

Ultimate Losses


Paid Losses


Case Reserves

Ultimate Losses


Reported Losses

Other reserving methods tested

Other Reserving Methods Tested

  • Discussed in subsequent CLRS sessions

    • Expected Loss Technique

    • Bornhuetter-Ferguson Method

    • Severity/Frequency Method

    • Many, many others

  • Note that development method may also be applied to claim counts.

Development method on claim counts

Development Method on Claim Counts

Reported counts dm ldf selected

Reported Counts DM:LDF Selected

Reported counts dm projection

Reported Counts DM:Projection



  • Ultimate losses should be measured for reasonableness against relevant indicators:

    • premium

      • loss ratios

    • exposures or number of policies

      • frequency, pure premium

    • claim counts

      • severity

  • Assumptions & methods should be documented and subjected to sensitivity analysis.

Reasonableness checks ultimate loss ratios

Reasonableness Checks:Ultimate Loss Ratios

Reasonableness checks ultimate loss ratios1

Reasonableness Checks:Ultimate Loss Ratios

Reasonableness checks frequency severity

Reasonableness Checks:Frequency & Severity

Reasonableness checks frequency severity1

Reasonableness Checks:Frequency & Severity

Reasonableness checks pure premium

Reasonableness Checks: Pure Premium

Reasonableness checks pure premium1

Reasonableness Checks: Pure Premium

Sensitivity analysis current year analysis

Sensitivity Analysis:Current Year Analysis

  • Improvements in results may stem from:

    • Higher rates

    • Lower claim frequency

    • Lower claim severity

  • Better results would appear to be present if:

    • Claims were being processed or paid more slowly

    • Case reserves were less adequate

    • Mix of business is different

Sensitivity analysis ratios

Sensitivity Analysis: Ratios

  • Review historical relationships

    • Losses

      • Reported losses to paid

    • Claim counts

      • Settlement rate

      • Ratio of claims closed with no payment to total closed claims

    • Losses and Claim Counts

      • Severities or average values

Sensitivity analysis ratios examples

Sensitivity Analysis: Ratios - Examples

Sensitivity analysis rate level adequacy

Sensitivity Analysis:Rate Level Adequacy

Increases in average premium are primarily due to:

Changes in the mix of business.

Rate increases.

If the changes in average premium in the latest two years are due to rate increases, then that would explain much of the improvement in loss ratios.

If the changes are due to shifts in the mix of business, then the improvement in the loss ratios

may or may not be real. Further investigation would be needed to understand what the shift

was and whether the different business types have varying loss development characteristics.

Sensitivity analysis claim severity

Sensitivity Analysis:Claim Severity

There is no consistent pattern in severity, except that it has generally increased over the years. This is typical, as we expect severity to increase due to inflation.

The very small increase in severity that is forecast for the current year is unusual. In the same year, claim frequency has increased. Perhaps there is an increase in the number of small dollar claims? This would be a good question to ask the Claim Department.

Sensitivity analysis claim closure rate

Sensitivity Analysis:Claim Closure Rate

In the past few years, claims have been closing more rapidly. This would imply that claims are being paid more rapidly and that the paid loss development factor is probably too high. One of the major assumptions of the PLDM (consistent payment patterns) has been violated.

Sensitivity analysis case reserve adequacy

Sensitivity Analysis:Case Reserve Adequacy

Sensitivity analysis case reserve adequacy1

Sensitivity Analysis:Case Reserve Adequacy

In general, we expect increasing numbers:

1. Across the rows because smaller claims settle more quickly; and

2. Down the columns due to inflation.

It is important to understand the company’s case reserving philosophy and procedures to be able to interpret trends in the data. Many changes in case reserve procedures can be monitored by talking to the Claims Department.

Changes in case reserve adequacy affect incurred loss development patterns. For example, if case reserves were less adequate in the current accident year, greater future development would be expected for those accidents than was typical in the past. Use of historical loss development factors in this situation would underestimate future development and lead to inadequate overall reserve estimates.

Sensitivity analysis case reserve adequacy2

Sensitivity Analysis: Case Reserve Adequacy

The fit of the average case reserves @ 12 months implies an annualized trend rate of 19%! This rate is substantially higher than industry trend rates for private passenger automobile liability, which are in the range of 8% to 10%.

Frequency severity projection method

Frequency/Severity Projection Method

A line or another curve can be fitted through actual values for accident years 1994 through 1998. The fitted points for the current year can be used as estimates for the ultimate frequency and severity.

R-squared is a measure of how well a fitted curve matches the data. The value can range from 0 to 1.00, where 1.00 indicates a perfect fit.

Frequency severity projection method1

Frequency/Severity Projection Method

Selection of tail factors

Selection of Tail Factors

  • How much difference does the tail factor selection make?

Selection of tail factors1

Selection of Tail Factors

  • Ultimate losses increase by 2% or $1.8 million.

  • Loss reserves also increase by $1.8 million; however, the 2% increase in the tail factor represents a 7% increase in overall reserve levels!

  • IBNR reserves are increased by an even higher percentage as a result of an increase of 2% in the tail factor

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