1998 casualty loss reserve seminar intermediate track iii- techniques

1998 CASUALTY LOSS RESERVE SEMINAR

Intermediate Track III- Techniques

SEPTEMBER 28, 1998

INTRODUCTION

The Ideal Situation

Loss reserve data should contain a long stable history of homogeneous claim experience, where no significant operational changes

materially affect either the mix of business or the handling of claims, and there should be

sufficient number of claims to produce credible loss patterns.

Slide 1

INTRODUCTION

The RealityVirtually All Elements of “The Ideal” are Periodically Violated:

1. The Mix Changes

2. Claim Handling Changes: Payments Accelerate / Decelerate Case Reserves are Strengthened / Weakened

3. The Environment Changes: New Causative Agents Impact Loss Costs Society’s Attitudes Change Court Decisions Change “The Rules” Changes in the Economy Affect Claim Inflation

Slide 2

INTRODUCTION

This Session Will Discuss

1. The potential impact of mix changes. (Slides 4-10)

2. Changes in claim closing patterns. (Slides 11-21)

3. Changes in case reserve adequacy. (Slides 22-31)

4. Tail factor selection. (Slides 32-37)

Slide 3

CHANGE IN MIX

Cumulative Paid Losses (Combined)

Accident Months of Development Year 12 24 36+ .

1994 $2,000 $4,000 $5,000

1995 $2,000 $4,000 $5,000

1996 $2,000 $4,000

1997 $2,000

Slide 4

CHANGE IN MIX

Cumulative Paid Losses (by Type of Claim)

Each of % of Months of Development

1994-1996 Total 12 24 36+

Category A (75%) $1,500 $1,800 $2,000

Category B (25%) $500 $2,200 $3,000 $2,000 $4,000 $5,000

1997

Category A (25%) $500

Category B (75%) $1,500

$2,000

Slide 5

CHANGE IN MIX

Cumulative Paid Losses (by Type of Claim)

Each of Months of Development

1994-1996 12 24 36+

Category A $1,500 $1,800 $2,000

Category B $500 $2,200 $3,000

$2,000 $4,000 $5,000

1997 If Forecasting By Claim Category

Category A $500 $600 $700

Category B $1,500 $6,600 $9,000

$2,000 $7,200 $9,700

1997 If Ignoring Claim Category

Combined $2,000 $4,000 $5,000

Slide 6

CHANGE IN MIX

Key Principle

Always Search for Subdivisions of Data Related to Possible

Causes of Variable Loss Development

Slide 7

CHANGE IN MIX

Suggested Subdivisions of Data Include

Primary: 1. Geographic: Laws Vary, Regional Office May Use Different . Claims Personnel, Degree of Litigiousness Varies 2. New Products Versus Old 3. Subline or Coverage 4. Deductibles or Policy Limits 5. Type of Loss Payment (e.g. Medical vs. Indemnity)

Reinsurance: 1. Attachment Point 2. Production Source 3. Line or Subline Slide 8

CHANGE IN MIX How Do You Decide?Ask:1. Underwriters2. Claims Department3. Agents4. Actuaries

The Key:

Learn as Much as Possible About the Book of Business You are Evaluating. What it has been historically What it is becoming

Slide 9

CHANGE IN MIXWhat Should be Done if Mix Change Includes New Business for

Which You Have Insufficient Data?

1. Seek Alternative Sources of Data. For example, perhaps a general . liability book formerly comprised solely of “OL&T” exposures, but in . recent years began adding “M&C” risks Possible Solution: Relate ISO development patterns for M&C to OL&T . and modify development factors for your evaluation.

2. Discuss Potential Impacts With Claims, Underwriting, and Other . Actuaries. Discuss how the change might affect:

Length of the tail

Frequency

Severity

Loss Ratios

Slide 10

CLAIM CLOSING PATTERNS

How Can Changes In Payment Patterns Be Recognized?

Look at Settlement Rates for the Most Recent Accident Years

Ask the Claims Department About Changes in:

- Opening and Closing Practices

- The Claims Handling Environment

- Levels of Staffing, Reorganizations

- Definition of a Claim (e.g. Multiple Claimants)

Slide 11


Data Needed

Reported Claims Development Triangle

Closed Claims Development Triangle

Projected Ultimate Claims

Paid Loss Development Triangle

Slide 12


Unadjusted Paid Loss Development Method

Accident Months of Development

Year 12 24 36 Ultimate

1995 $1,000 $4,000 $6,000 $6,000

1996 $1,000 $3,500 $5,250

1997 $750 $4,223

12-24 24-36 36-Ult

Age - Age 3.75 1.50 1.00

Age - Ultimate 5.63 1.50 1.00

Slide 13


Accident Reported Claims


1995 500 900 1,000 1,000

1996 480 880 980

1997 450 900

Accident Closed Claims

Year 12 24 36

1995 250 810 1,000

1996 240 704

1997 180

Slide 14


Accident Closed / Reported

Year 12 24 36

1995 50.0% 90.0% 100.0%

1996 50.0% 80.0%

1997 40.0%

Accident Closed / Ultimate

Year 12 24 36

1995 25.0% 81.0% 100.0%

1996 24.5% 71.8%

1997 20.0%

Slide 15


Accident Closing Percent

Year 12 24 36

1995 20.0% 71.8% 100.0%

1996 20.0% 71.8%

1997 20.0%

Accident Adjusted Closed Claims

Year 12 24 36

1995 200 718* 1,000

1996 196 704

1997 180

* 718 = 71.8% x 1,000

Slide 16

CLAIM CLOSING PATTERNS - AY 1995

Actual Adjusted Actual Adjusted

Closed Closed Paid Paid

Age Claims Claims Losses Losses

0 0 0 $0 $0

12 250 200 $1,000 ?

24 810 718 $4,000 ?

36 1,000 1,000 $6,000 ?

Slide 17


Linear Interpolation of Adjusted Paid Losses

AY = 1995 200 - 0

@ 12 Months 250 - 0 x (1,000 - 0) + 0 = 800

AY = 1995 718 - 250

@ 24 Months 810 - 250 x (4,000 - 1,000) + 1,000 = 3,507

AY = 1996 196 - 0

@ 12 Months 240 - 0 x (1,000 - 0) + 0 = 817

Slide 18


Adjusted Paid Loss Development Method



1995 $800 $3,507 $6,000 $6,000

1996 817 3,500 5,985

1997 750 5,550

12-24 24-36 36-Ult

Age - Age 4.33 1.71 1.00

Age - Ultimate 7.40 1.71 1.00

Slide 19


Impact of Adjustment

Accident Revised Original

Year Forecast Forecast Difference

1995 $6,000 $6,000 $0

1996 5,985 5,250 735

1997 5,550 4,223 1,327

Total $17,535 $15,473 $2,062

Slide 20


Step 1: Review Closing Rates to Determine Whether There Has Been a Change

Step 2: Seek Independent Confirmation That Change Occurred

Step 3: Restate Historical Closed Claims Using Current Closing Rates

Step 4: Restate Historical Paid Losses Using Restated Closed Claims

Step 5: Apply Standard Loss Development Method To Restated Paid Losses

Slide 21

CASE RESERVE ADEQUACY

Claim Data

Accident Reported Claims


1995 5,000 8,000 10,000 10,000

1996 5,000 8,000 10,000

1997 5,000 10,000

Accident Closed Claims


1995 1,000 6,000 10,000 10,000

1996 1,000 6,000 10,000

1997 1,000 10,000

Slide 22

CASE RESERVE ADEQUACYLoss Data

Accident Incurred Losses ($000) Projected


1995 $10,000 $40,000 $50,000 $50,000

1996 $10,000 $45,000 $56,250

1997 $10,417 $55,340

Accident Paid Losses ($000) Projected


1995 $2,000 $24,000 $50,000 $50,000

1996 $2,500 $30,000 $62,500

1997 $3,125 $78,125

The Issue: What Is Driving The Divergence?

Slide 23


STEP 1: Review Paid-To-Incurred Triangles:


Year 12 24 36 .

1995 20% 60% 100%

1996 25% 67%

1997 30%

Does the Change in These Ratios Portray a Speed-Up in Payments, a Decrease in Case Reserve Adequacy, or Both?

Slide 24


STEP 2: Review Settlement Rates (No. Closed/No. Reported)

Accident Settlement Rate

Year 12 24 36 .

1995 20% 75% 100%

1996 20% 75%

1997 20%

Observation: The settlement rates appear to be consistent.

Slide 25


STEP 3: Review Trends in Average Paid Claims Versus Trends in Average Case Reserves

Accident Average Paid Average Case Reserves

Year 12 24 12 24 .

1995 $2,000 $4,000 $2,000 $8,000 1996 $2,500 $5,000 $1,875 $7,500

1997 $3,125 $1,823

Trend 25% 25% -4.5% -6.3%

Observations: Case reserve trend is much lower than paid trend.

Slide 26


STEP 4: Review Potential Reasons For Observed Trends

Is the book shifting to a lower severity mix?

Have policy limits and/or reinsurance retentions kept pace with claims inflation?

Has anything material changed in the handling of claims?

- Turnover in claim department staff

- Changes in philosophy

If you conclude there has been case reserve weakening (or . strengthening), the data should be adjusted. Slides 28-30 give . one approach.

Slide 27


STEP 5: Adjust Historical Case Reserves to Current Adequacy Levels

Accident Adjusted Average Case Reserves Year 12 24 36 .

1995 $1,166 $6,000 $0

1996 $1,458 $7,500

1997 $1,823

Examples: $6,000 = $7,500 / 1.25

$1,116 = $1,823 / (1.25 ^ 2)

ASSUME: 25% is the Actual Rate of Claim Inflation

Slide 28


Adjust Paid to Number Adjusted

Formula Incurred = Date + of x Average

Losses Losses Open Case Reserves

AY = 95

@ 12 Months 6,664 = 2,000 + (4,000 x 1.166)

AY = 95

@ 24 Months 36,000 = 24,000 + (2,000 x 6.000)

AY = 96

@ 12 Months 8,332 = 2,500 + (4,000 x 1.458)

Note: All dollar amounts are in thousands.

Slide 29


STEP 6: Project Ultimate Losses Using Adjusted Incurred Losses and Standard Loss Development Method

Accident Adjusted Incurred Losses ($000)

Year 12 24 36 Ultimate .

1995 $6,664 $36,000 $50,000 $50,000

1996 $8,332 $45,000 $62,500

1997 $10,417 $78,125

Slide 30

CASE RESERVE ADJUSTMENT

Comparison of Estimates

Original Original Revised

Accident Incurred Paid Incurred

Year Estimate Estimate Estimate

1995 $50,000 $50,000 $50,000

1996 $56,250 $62,500 $62,500

1997 $55,340 $78,125 $78,125

Slide 31

TAIL FACTORS

The Need For Tail Factors Accident Reported Claims .

Year 96 108 120 132 144

1986 243 247 250 252 253

1987 250 256 261 264

.

Accident Open Claims .

Year 96 108 120 132 144

1986 55 45 35 25 15

1987 60 53 44 31

Accident Incurred Losses .

Year 96 108 120 132 144

1986 341,500 413,200 462,800 495,200 515,000

1987 366,200 443,100 496,300 531,000

IT APPEARS LOSS DEVELOPMENT WILL CONTINUE BEYOND THE ENDPOINT OF THE DATA.

Slide 32

TAIL FACTOR SELECTION METHODS

Techniques To Derive Tail Factors

1. Examine broader data sources: e.g. ISO, NCCI, RAA, Best’s (Caution: Learn . the limitations of such data.)

2. Curve Fitting

3. “Generalized Bondy Method” which assumes that the age-to-age factors are . decaying at a constant rate over time.

Example: Determine a tail factor based on the following observed age-to-age factors (LDFs).

96-108 108-120 120-132 132-144

LDF LDF LDF LDF

1.210 1.120 1.070 1.040

Slide 33

TAIL FACTOR SELECTION Using Generalized Bondy Method To Calculate Tail Factors

(1) (2)=Ln(1) (3)=(2)/(2 prior) (4) Months Actual LDFs Ln(Actual) Decay Ratio Predicted LDFs

96-108 1.210 0.191

108-120 1.120 0.113 0.595

120-132 1.070 0.068 0.597

132-144 1.040 0.039 0.580

144-156 1.024=(1.040)0.600

156-168 1.014=(1.024)0.600

168-180 1.008=(1.014)0.600

Selected Decay Ratio 0.600

Tail Factor (144 months to Ultimate) 1.061=(1.040)1.500

Notes: 1. This method can be misleading when decay rates are unstable. 2. The tail factor is very sensitive to the last selected age-to-age factor.

Slide 34

TAIL FACTORS

When To Use These Different Approaches To Tail Factors

Situation Source

Reinsurance lines RAA Data

Standard Workers Compensation line NCCI

Unusual line where industry data is Curve fitting or Bondy

difficult to obtain, e.g. aviation

Company’s own data is unstable or not Industry Data

credible, or a start-up line

Slide 35

TAIL FACTORS

How Much Tail Can There Be In Development In Reinsured Layers?

Line of Selected Cumulative Age to Ultimate Factors* .

Business 15 Years to Ult. 25 Years to Ult.

W.C. Treaty 1.582 1.149

G.L. Treaty 1.234 1.030

A.L. Treaty 1.021 1.000

* Based on RAA Data.

Slide 36

TAIL FACTORS

Some Examples Of When Development Occurs Beyond 10 Years

LINE REASONS

Products and Issues complex (Who’s liable? How to prove the Pollution/Environmental injury was caused by the product? Date of loss?)

Workers Compensation Occupational Disease

Life pension cases, with escalation clauses in some states

Medical Malpractice Delayed manifestation, with subsequent complex issues

Slide 37

1998 casualty loss reserve seminar intermediate track iii- techniques

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