1CLRS Basic Track I

Basic Track I

1998 CLRS

September 28, 1998

Philadelphia, Pennsylvania

2CLRS Basic Track I

Introduction

Topics Covered» CAS Statement of Principles

– Definitions

– Principles

– Considerations

» Data Needs and Organization» Basic Reserving Techniques

– Paid Loss Development Method

– Incurred Loss Development Method

3CLRS Basic Track I

Statement of Principles

CAS Statement of Principles Regarding Property & Casualty Loss & Loss Adjustment Expense Reserves» 3 Sections» Adopted May 1988» Actuary should also be familar

with standards of practice.

4CLRS Basic Track I

LOSS RESERVEDefinition: Amount necessary to

settle unpaid claims

Characteristic: Estimated liability

Importance: Accurate evaluation of financial condition & underwriting income

Definitions

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Definitions

Accounting Aspects of Loss Reserves

Assets Liabilities

Surplus

Balance Sheet

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Definitions

Carried Loss ReserveThe amount shown in a published

statement or an internal statement of financial considition.

Indicated Loss ReserveThe amount that results from the

application of a particular loss reserving method.

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Definitions

Loss Adjustment Expenses (LAE) are sum of:» Allocated Loss Adjustment

Expenses (ALAE)– Defense, litigation and medical cost

containment expenses. Does not include claims adjusters fees.

» Unallocated Loss Adjustment Expenses (ULAE)

– All expenses not included above, including claims adjusters fee, and company overhead.

8CLRS Basic Track I

Definitions

Prior to 1998 the NAIC considered as ALAE all expenses that could be allocated to an individual claim. This could include adjusters fees. This led to inconsistencies between insurers.

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Definitions

Elements of a Loss Reserve» IBNR» Claims in Transit» Formula Reserve/Case Reserve» Development on Known Claims» Reopened Claims Reserve

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Life Cycle of a Claim Reserve

8/1/96 Accident entered into records as $1,000 Formula Reserve

7/11/96 Accident reported

Claims in Transit

10/5/96Individual reserveestablished

$10,000 Case Reserve

1/1/97Estimate revised

$25,000 Case Reserve

8/18/97Settlement agreed

$30,000 Case Reserve

8/25/97Payment sent

$30,000 Case Reserve

9/2/97Claim draft clears

Closed

4/2/96Accident occurs

Pure IBNR

11CLRS Basic Track I

Four Guiding Principles

Principle 1: Actuarially Sound Loss Reserves

A provision for the unpaid amount required to settle all claims, whether reported or not, for which liability may exist on a particular accounting date.

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Four Guiding Principles

Principle 2: Actuarially Sound LAE Reserve

A provision for the unpaid amount required to investigate, defend and effect the settlement of all claims, whether reported or not, for which LAE liability exists on a particular accounting date.

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Four Guiding Principles

Principle 3: Uncertainty Inherent in Reserves

Implies that a range of reserves can be actuarially sound.

Exists because true value of the liability for loss or LAE at any accounting date can be known only when all attendant claims have been settled.

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Four Guiding Principles

Principle 4: Most appropriate reserve within a range of actuarially sound estimates

Depends on:– the relative likelihood of estimates

within the range

– financial reporting context in which the reserve will be presented

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Principles

“Actuarially Sound” Characteristics» For a defined group of claims» As of a given valuation date» Based on estimates derived from

reasonable assumptions & appropriate actuarial methods

Guiding principles apply to» statutory balance sheets» statements of opinion» reports to shareholders or securities

regulators

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Considerations:Data Organization

Accident Date» The date on which the loss

occurred. Report Date

» The date on which the loss is first reported to the insurer.

Recorded Date» The date on which the loss is first

entered into the statistical records of the insurer.

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Considerations:Data Organization

Accounting Date» Defines a group of claims for

which liability may exist.» All claims incurred on or before

the accounting date. Valuation Date

» Defines the time period for which transactions are included when evaluating the existing liability.

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Accuracy is often improved by subdividing experience into groups exhibiting similar characteristics.

Considerations:Homogeneity

Automobile

Bodily InjuryProperty Damage

PIPMedical Payments

UM-BIUM-PD

CollisionOther Than Collision

Liability Physical Damage

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Considerations:Credibility

A measure of the predictive value that is attached to a body of data.

A group of claims should be large enough to be statistically reliable.» May be a point at which

partitioning will divide the data into groups too small to provide credible development patterns.

Use of supplementary data sources

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Considerations:Emergence

Patterns

The delay between the occurrence of a claim & when it is recorded on the company’s books.» Property claims reported quickly» Reporting of liability claims is

substantially delayed

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Considerations:Settlement Patterns

The length of time that it normally takes for reported claims to be settled (or closed)

Affects the choice of reserving methods» Lines which settle quickly,

generally are less subject to reserve uncertainty.

» The amount of settlement often varies considerably from the original estimate

22CLRS Basic Track I

Considerations:Emergence/Settlement

Emergence (E) vs. settlement (S)

A E S

A E S

Products Liability

Workers Compensation

Automobile Bodily Injury

A

A E S

E S

Collision

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Other Considerations

Factors Affecting Loss Reserves» Internal or Operational

– Reinsurance programs– Claims handling practices– Business growth– Case reserve adequacy– Mix of business– Underwriting– Organizational changes– Contract changes– Structured settlements– Portfolio characteristics

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Other Considerations

Factors Affecting Loss Reserves» External or Environmental

– Society

– Regulation

– Judiciary

– Seasonality

– Residual Market

– Inflation

– Economy

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Terminology

Case Reserves» Claim reported but not yet paid» Assigned a value by a claims

adjuster or by formula

Bulk + IBNR reserves include:» Reserves for claims not yet

reported (pure IBNR)» Claims in transit» Development on known claims» Reserves for reopened claims

26CLRS Basic Track I

Terminology

Reserves = Outstanding

= Liabilities = Unpaid

= Case Reserves +IBNR Incurred losses may have

various meanings! Ultimate Losses (incl. IBNR) Reported Losses (excl. IBNR)

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Definitions

Loss Development The financial activity on claims from the time they occur to the time they are ….eventually settled and paid. Triangles

Compiled to measure the changes in cumulative claim activity over time in order to estimate patterns of future activity.

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Paid Loss Development Method (LDM)

The losses are sorted by the year in which the accident occurred

The losses are summed at the end of each year

Losses paid to date are shown on the most recent diagonal

The data are organized in this way to highlight historical patterns

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Paid LDM:Compilation of

Triangle

Actuarial Configuration

The goal is to estimate the total amount that will ultimately be paid

Cumulative Paid Losses ($000 Omitted) Final Accident Development Stage in Months Total

Year 12 24 36 48 60 72 Cost

1992 3,780 6,671 8,156 9,205 9,990 10,508 ???1993 4,212 7,541 9,351 10,639 11,536 ???1994 4,901 8,864 10,987 12,458 ???1995 5,708 10,268 12,699 ???1996 6,093 11,172 ???1997 6,962 ???

30CLRS Basic Track I

Paid RTR Development

Factors

From the end of the accident year (at 12 months) to the end of the following year (at 24 months), paid losses for 1993 accident-year grew 79%. During the next year (from 24 to 36 months), paid losses experienced an additional 24% growth (or development) and so forth.

Report-to-report development (RTR) factors are also known as:

Age -to-Age factors

Link ratios

Evaluation Interval in MonthsAccident 72 to

Year 12-24 24-36 36-48 48-60 60-72 Ultimate1992 1.765 1.223 1.129 1.085 1.052 ???1993 1.790 1.240 1.138 1.084 1994 1.809 1.240 1.134 1995 1.799 1.237 1996 1.834 1997

Sample Calculation for Accident Year 1993:

12-to-24 Months 1.790 = 7,541 / 4,212

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Paid LDM:RTR Factors

Evaluation Interval in MonthsAccident 72 to

Year 12-24 24-36 36-48 48-60 60-72 Ultimate1992 1.765 1.223 1.129 1.085 1.052 ???1993 1.790 1.240 1.138 1.084 1994 1.809 1.240 1.134 1995 1.799 1.237 1996 1.834 1997

Simple Average - All Years1.799 1.235 1.134 1.085 1.052

Simple Average - Latest 3 Years1.814 1.239 1.134 XXX XXX

Simple Average - Excluding High & Low1.799 1.238 1.134 XXX XXX

Weighted Average - All Years1.803 1.235 1.134 1.085 1.052

Selected RTR Factors1.800 1.235 1.134 1.085 1.052 1.070

32CLRS Basic Track I

Paid LDM:Issues to Consider

Issues to Consider

Have there been any changes which might make the older years irrelevant?

Are the more recent years better predictors of the future?

Are there outlier points that need to be ignored or adjusted?

Examples

There are more motorcycle losses in the oldest year; Typical P&C no longer insures motorcycles.

Typical P&C has begun writing more business in state X.

In one year, there were bad ice storms at the end of December. Late reporting caused unusually high development in the next year.

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Paid LDM:Application

! Evaluation Interval in Months72 to

12-24 24-36 36-48 48-60 60-72 Ultimate

RTRs 1.800 1.235 1.134 1.085 1.052 1.070

Cumulative Paid Losses ($000 Omitted) Final Accident Development Stage in Months Total

Year 12 24 36 48 60 72 Cost1992 3,780 6,671 8,156 9,205 9,990 10,508 11,244 1993 4,212 7,541 9,351 10,639 11,536 12,136 12,985 1994 4,901 8,864 10,987 12,458 13,157 14,220 15,215 1995 5,708 10,268 12,699 14,401 15,625 16,437 17,588 1996 6,093 11,172 13,797 15,646 16,976 17,859 19,109 1997 6,992 12,532 15,477 17,550 19,042 20,032 21,435

Sample Calculations for Accident Year 1996:

At 24 Months: 12,532 = 6,962 x 1.800At 36 Months: 15,477 = 12,532 x 1.235

or 15,477 = 6,962 x 1.800 x 1,235

Cumulative Development Factors12 to Ult 24 to Ult 36 to Ult 48 to Ult 60 to Ult 72 to Ult

3.082 1.712 1.386 1.222 1.126 1.070

34CLRS Basic Track I

Paid LDM:Projections &

Reserves

Loss Reserve Estimate @ 12/31/97 = $32.307 million

Actual Cumulative Estimated Actual EstimatedPaid Selected Development Ultimate Paid Loss

Accident Losses RTR Factors to Losses Losses ReservesYear @ 12/31/97 Factors Ultimate [(2) x (4)] @ 12/31/97 {(5) - (6)}(1) (2) (3) (4) (5) (6) (7)

1992 10,508 1.070 1.070 11,244 10,508 736 1993 11,536 1.052 1.126 12,990 11,536 1,454 1994 12,458 1.085 1.222 15,224 12,458 2,766 1995 12,699 1.134 1.386 17,601 12,699 4,902 1996 11,172 1.235 1.712 19,126 11,172 7,954 1997 6,962 1.800 3.082 21,457 6,962 14,495

Total 65,335 97,642 65,335 32,307

35CLRS Basic Track I

Incurred LDM:Compilation of

Triangle

Case Reserves ($000 Omitted)Accident Development Stage in Months

Year 12 24 36 48 60 721992 5,557 4,176 2,936 1,987 1,245 7421993 6,328 4,664 3,200 2,051 1,1891994 6,974 4,968 3,251 1,9551995 7,635 5,274 3,3671996 8,376 5,6041997 9,599

Cumulative Reported Losses* ($000 Omitted) FinalAccident Development Stage in Months Total

Year 12 24 36 48 60 72 Cost1992 9,337 10,847 11,092 11,192 11,235 11,250 ???1993 10,540 12,205 12,551 12,690 12,725 ???1994 11,875 13,832 14,238 14,413 ???1995 13,343 15,542 16,066 ???1996 14,469 16,776 ???1997 16,561 ???

* = paid losses + case reserves

36CLRS Basic Track I

Incurred LDM:RTR Factors

SelectedEvaluation Interval in Months

Accident 72 toYear 12-24 24-36 36-48 48-60 60-72 Ultimate1992 1.162 1.023 1.009 1.004 1.001 ???1993 1.158 1.028 1.011 1.003 1994 1.165 1.029 1.012 1995 1.165 1.034 1996 1.159 1997

Simple Average - All Years1.162 1.029 1.011 1.004 1.001

Simple Average - Latest 3 Years1.163 1.030 1.011 XXX XXX

Simple Average - Excluding High & Low1.162 1.029 1.011 XXX XXX

Weighted Average - All Years1.162 1.030 1.011 1.003 1.001

Selected RTR Development Factors1.162 1.030 1.011 1.003 1.001 1.000

37CLRS Basic Track I

Incurred LDM:Projections &

Reserves

Actual Estimated Actual EstimatedReported Development Ultimate Paid Loss

Accident Losses Factors to Losses Losses ReservesYear @ 12/31/97 Ultimate [(2) x (3)] @ 12/31/97 {(4) - (5)}(1) (2) (3) (4) (5) (6)

1992 11,250 1.000 11,250 10,508 742 1993 12,725 1.001 12,738 11,536 1,202 1994 14,413 1.004 14,471 12,458 2,013 1995 16,066 1.015 16,307 12,699 3,608 1996 16,776 1.045 17,531 11,172 6,359 1997 16,561 1.214 20,105 6,962 13,143

Total 87,791 92,402 65,335 27,067