basic track ii

1CLRS Basic Track II

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

– Claim Severity

– Claim Closure Rate

– Adequacy of Case Reserves

– Frequency/Severity Projection

» Importance of Tail Factors


Comparison of LDM Projections

Estimated Ultimate Losses Based on:Accident Paid Incurred Average =

Year LDM LDM SelectedPaid Method Incurred MethodAverage

1994 11,244 11,250 11,247 1995 12,985 12,738 12,862 1996 15,215 14,471 14,843 1997 17,588 16,308 16,948 1998 19,109 17,539 18,324 1999 21,435 20,119 20,777

Total 97,576 92,425 95,001

Ultimate Loss Projections

-5,000

10,00015,00020,00025,000

PaidMethodIncurredMethodAverage


Comparison of Loss Development Methods

Con

Pro

UnderlyingAssumptions

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

Assumptions Sample ProblemsClaims settlement patterns unchanging

Case reserving practices & philosophiesunchanging

No claim processing changes

Policy limits have no impact on lossdevelopment

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


Key Assumptions & Potential Problems

Assumptions Sample ProblemsLoss development unaffected by changingloss cost trends

No change in mix of business

No cyclical loss development

No data anomalies

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 impactedby business underwriting cycles

Catastrophic or unusual losses reflected inloss experience;Unusual claim settlement/reporting delays


Comparison of Estimated Reserves

Estimated Loss Reserves Based on:Accident Paid Incurred Average =

Year LDM LDM SelectedPaid Method Incurred MethodAverage

1994 736 742 739 1995 1,449 1,202 1,326 1996 2,757 2,013 2,385 1997 4,889 3,609 4,249 1998 7,937 6,367 7,152 1999 14,473 13,157 13,815

Total 32,241 27,090 29,666

Components of Selected Reserve @ 12/31/99

-

2,000

4,000

6,000

8,000

10,000

12,000

14,000

16,000

Accident Year

IBNR

Case


Formulas to Derive IBNR Reserves

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

Ultimate Losses

Minus

Paid Losses

Minus

Case Reserves

Ultimate Losses

Minus

Reported Losses

Unpaid Losses

Minus

Case Reserves


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

Cumulative Number of Claims Reported * Final Accident Development Stage in Months # of

Year 12 24 36 48 60 72 Claims

1994 1,428 2,772 2,850 2,866 2,870 2,888 ???1995 1,710 3,032 3,086 3,094 3,110 ???1996 1,358 2,780 2,990 3,000 ???1997 1,510 2,588 2,656 ???1998 1,488 2,604 ???1999 1,604 ???

* The definition of a "reported claim" varies from company to company. Some companies count claims as one per claimant when more than one claim is involved in an incident. Some companies remove claims that close without payment. We assume that Typical P&C Insurance Company counts on a per claimant basis and includes closed claims without payment.


Reported Counts DM:LDF Selected

Evaluation Interval in MonthsAccident 72 to

Year 12-24 24-36 36-48 48-60 60-72 Ultimate1994 1.941 1.028 1.006 1.001 1.006 ???1995 1.773 1.018 1.003 1.005 1996 2.047 1.076 1.003 1997 1.714 1.026 1998 1.750 1999

Simple Average - All Years1.845 1.037 1.004 1.003 1.006

Simple Average - Latest 3 Years1.837 1.040 1.004 XXX XXX

Simple Average - Excluding High & Low1.821 1.027 1.003 XXX XXX

Selected Development Factors1.821 1.037 1.006 1.004 1.006 1.000

Selected Development Factors to Ultimate1.919 1.054 1.016 1.010 1.006 1.000


Reported Counts DM:Projection

Actual Estimated EstimatedClaims Development Ultimate Unreported

Accident Reported Factors to Claims ClaimsYear @ 12/31/99 Ultimate [(2) x (3)] (4) - (2)(1) (2) (3) (4) (5)

1994 2,888 1.000 2,888 01995 3,110 1.006 3,129 19 1996 3,000 1.010 3,030 30 1997 2,656 1.016 2,699 43 1998 2,604 1.054 2,744 140 1999 1,604 1.919 3,078 1,474

Total 15,862 17,568 1,706


Reasonableness 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

Est. Ultimate Losses ($000) Indicated Loss RatioAccident Earned Using: Using:

Year Premium PLDM ILDM Selected PLDM ILDM Selected

1994 18,168 11,244 11,250 11,247 0.619 0.619 0.619 1995 21,995 12,985 12,738 12,862 0.590 0.579 0.585 1996 24,173 15,215 14,471 14,843 0.629 0.599 0.614 1997 25,534 17,588 16,308 16,948 0.689 0.639 0.664 1998 31,341 19,109 17,539 18,324 0.610 0.560 0.585 1999 38,469 21,435 20,119 20,777 0.557 0.523 0.540

Total 159,680 97,576 92,425 95,001 0.611 0.579 0.595


Reasonableness Checks:Ultimate Loss Ratios

Ultimate Loss Ratio

0.500

0.600

0.700

1994 1995 1996 1997 1998 1999

Accident Year

Paid LDM

Incurred LDM

Selected


Reasonableness Checks:Frequency & Severity

Ultimate Claim

Accident Claim Earned Frequency

Year Count Exposures* (2) / (3)

(1) (2) (3) (4)

1994 2,888 102 28.314

1995 3,129 98 31.929

1996 3,030 103 29.417

1997 2,699 105 25.705

1998 2,744 109 25.174

1999 3,078 118 26.085

* Earned exposures are used to measure the underlying

volume or units covered by insurance in each year. For

automobile liability, exposures are typically measured by

the number of cars insured for the year.


Reasonableness Checks:Frequency & Severity

Ultimate Est. Ultimate Losses ($000) Indicated SeverityAccident Claim Using: Using:

Year Count PLDM ILDM Selected PLDM ILDM Selected(1) (2) (3) (4) (5) (6) (7) (8)

1994 2,888 11,244 11,250 11,247 3,893 3,895 3,894 1995 3,129 12,985 12,738 12,862 4,150 4,071 4,111 1996 3,030 15,215 14,471 14,843 5,021 4,776 4,899 1997 2,699 17,588 16,308 16,948 6,516 6,042 6,279 1998 2,744 19,109 17,539 18,324 6,964 6,392 6,678 1999 3,078 21,435 20,119 20,777 6,964 6,536 6,750


Reasonableness Checks: Pure Premium

Values at 12 MonthsEarned Pure

Accident Exposures Reported Premium PercentageYear ('000's) Losses [(2)/(1)] Change

1994 102 9,337 91.5 1995 98 10,540 107.6 17%1996 103 11,875 115.3 7%1997 105 13,343 127.1 10%1998 109 14,469 132.7 4%1999 118 16,561 140.3 6%

Estimated Ultimate ValuesEarned Pure

Accident Exposures Incurred Premium PercentageYear ('000's) LDM [(2)/(1)] Change

1994 102 11,250 110.3 1995 98 12,738 130.0 18%1996 103 14,471 140.5 8%1997 105 16,308 155.3 11%1998 109 17,539 160.9 4%1999 118 20,119 170.5 6%


Reasonableness Checks: Pure Premium

Pure Premium Trends

-

50.0

100.0

150.0

200.0

1994 1995 1996 1997 1998 1999

Ult

imat

e P

ure

P

rem

ium

At 12 Months Additional to Ultimate


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

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

Cumulative Number of Claims Reported * Final Accident Development Stage in Months # of

Year 12 24 36 48 60 72 Claims

1994 1,428 2,772 2,850 2,866 2,870 2,888 ???1995 1,710 3,032 3,086 3,094 3,110 ???1996 1,358 2,780 2,990 3,000 ???1997 1,510 2,588 2,656 ???1998 1,488 2,604 ???1999 1,604 ???

* The definition of a "reported claim" varies from company to company. Some companies count claims as one per claimant when more than one claim is involved in an incident. Some companies remove claims that close without payment. We assume that Typical P&C Insurance Company counts on a per claimant basis and includes closed claims without payment.


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.

Sensitivity Analysis:Rate Level Adequacy

Increases in average premium are primarily due to:Changes in the mix of business.Rate increases.

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.

Accident Earned Earned Average Change fromYear Premium Exposures Premium Prior Year

1994 18,168 102 178.1 1995 21,995 98 224.4 26%1996 24,173 103 234.7 5%1997 25,534 105 243.2 4%1998 31,341 109 287.5 18%1999 38,469 118 326.0 13%


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.

Est. Ultimate Severity Est. Change in SeverityAccident Using: Using:

Year PLDM ILDM Selected PLDM ILDM Selected(1) (3) (4) (5) (6) (7) (8)

1994 3,893 3,895 3,894 1995 4,150 4,071 4,111 7% 5% 6%1996 5,021 4,776 4,899 21% 17% 19%1997 6,516 6,042 6,279 30% 27% 28%1998 6,964 6,392 6,678 7% 6% 6%1999 6,964 6,536 6,750 0% 2% 1%


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.

Accident Number of Closed Claims by Development Age UltimateYear 12 24 36 48 60 72 Claims

1994 826 2,131 2,559 2,706 2,795 2,845 2,888

1995 782 2,308 2,738 2,957 3,049 3,129

1996 780 2,146 2,665 2,832 3,030

1997 917 1,980 2,368 2,699

1998 911 1,978 2,744

1999 1,106 3,078

Accident Percentage Closed to Est. Ultimate NumberYear 12 24 36 48 60 72

1994 29% 74% 89% 94% 97% 99%

1995 25% 74% 88% 95% 97%

1996 26% 71% 88% 93%

1997 34% 73% 88%

1998 33% 72%

1999 36%

Example: 29% = 826 / 2,888


Sensitivity Analysis:Case Reserve Adequacy

Accident Case Reserves ($000)Year 12 24 36 48 60 72

1994 5,557 4,176 2,936 1,987 1,245 742

1995 6,328 4,664 3,200 2,051 1,189

1996 6,974 4,968 3,251 1,955

1997 7,635 5,274 3,367

1998 8,376 5,604

1999 9,599

Accident Number of Open ClaimsYear 12 24 36 48 60 72

1994 602 641 291 160 75 43

1995 928 724 348 137 61

1996 578 634 325 168

1997 593 608 288

1998 577 626

1999 498

Accident Average Case Reserve Year 12 24 36 48 60 72

1994 9,231 6,515 10,089 12,419 16,600 17,256

1995 6,819 6,442 9,195 14,971 19,492

1996 12,066 7,836 10,003 11,637

1997 12,875 8,674 11,691

1998 14,516 8,952

1999 19,275


Sensitivity Analysis:Case Reserve Adequacy

In general, we expect increasing numbers:

1. Across the rows because smaller claims settle more quickly; and2. 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 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%.

199419951996199719981999

Average Case Reserve @ 12 Months

0

5000

10000

15000

20000

25000

1994 1995 1996 1997 1998 1999

Actual Fitted-exp


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.

Estimated Ultimate Frequency Estimated Ultimate SeverityAccident Linear Exponential Linear Exponential

Year Actual Fit Fit Actual Fit Fit

1994 28.3 30.6 30.6 3,894 3,740 3,625 1995 31.9 29.4 29.3 4,111 4,347 4,399 1996 29.4 28.1 28.0 4,899 5,051 5,172 1997 25.7 26.9 26.8 6,279 5,870 5,946 1998 25.2 25.6 25.6 6,678 6,821 6,719 1999 ?? 24.4 24.4 ?? 7,927 7,493

R-squared 0.491 0.509 0.954 0.946

Selected for 1999 24.4 7,493


Frequency/Severity Projection Method

Accident Earned Ultimate Ultimate Losses LossesYear Exposures Frequency Severity Estimated @ 12/31/99

1994 102 28.3 3,894 11,247 739 1995 98 31.9 4,111 12,862 1,326 1996 103 29.4 4,899 14,843 2,385 1997 105 25.7 6,279 16,948 4,249 1998 109 25.2 6,678 18,324 7,152 1999 118 24.4 7,493 21,618 14,656

Total 635 95,842 30,507

A Comparison of Loss Ratio Methods for 1999Paid Loss Development Method 55.7%

Incurred Loss Development Method 52.3%

Frequency and Severity Method 56.2%


Selection of Tail Factors

How much difference does the tail factor selection make?

Effect on Estimates Given a 2% Increase in Reported Losses Tail Factor

Reported Estimated Revised UnpaidAccident Losses Selected LDF's Ultimate Earned Loss Losses

Year @ 12/31/99 LDF Age to Ult. Losses Premium Ratio @ 12/31/99

1994 11,250 1.020 1.020 11,475 18,168 63% 967 1995 12,725 1.001 1.021 12,992 21,995 59% 1,456 1996 14,413 1.003 1.024 14,759 24,173 61% 2,301 1997 16,066 1.011 1.035 16,628 25,534 65% 3,929 1998 16,776 1.030 1.066 17,883 31,341 57% 6,711 1999 16,561 1.162 1.239 20,519 38,469 53% 13,557

Total 87,791 94,256 159,680 59% 28,921

Estimated Unpaid Losses Based on Original ILDM 27,090 (Without the 2% Tail Factor Increase)

Increase in Estimated Unpaid Losses Due to Increased Tail Factor 7%


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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