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1CLRS Basic Track II
Basic Track II
2000 CLRS
September 2000
Minneapolis, Minnesota
2CLRS Basic Track II
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
3CLRS Basic Track II
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
4CLRS Basic Track II
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
5CLRS Basic Track II
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
6CLRS Basic Track II
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
7CLRS Basic Track II
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
8CLRS Basic Track II
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
9CLRS Basic Track II
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.
10CLRS Basic Track II
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.
11CLRS Basic Track II
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
12CLRS Basic Track II
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
13CLRS Basic Track II
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.
14CLRS Basic Track II
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
15CLRS Basic Track II
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
16CLRS Basic Track II
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.
17CLRS Basic Track II
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
18CLRS Basic Track II
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%
19CLRS Basic Track II
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
20CLRS Basic Track II
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
21CLRS Basic Track II
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
22CLRS Basic Track II
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.
23CLRS Basic Track II
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%
24CLRS Basic Track II
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%
25CLRS Basic Track II
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
26CLRS Basic Track II
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
27CLRS Basic Track II
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.
28CLRS Basic Track II
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
29CLRS Basic Track II
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
30CLRS Basic Track II
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%
31CLRS Basic Track II
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%
32CLRS Basic Track II
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