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
CLAIM CLOSING PATTERNS
Data Needed
Reported Claims Development Triangle
Closed Claims Development Triangle
Projected Ultimate Claims
Paid Loss Development Triangle
Slide 12
CLAIM CLOSING PATTERNS
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
CLAIM CLOSING PATTERNS
Accident Reported Claims
Year 12 24 36 Ultimate
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
CLAIM CLOSING PATTERNS
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
CLAIM CLOSING PATTERNS
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
CLAIM CLOSING PATTERNS
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
CLAIM CLOSING PATTERNS
Adjusted Paid Loss Development Method
Accident Months of Development
Year 12 24 36 Ultimate
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
CLAIM CLOSING PATTERNS
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
CLAIM CLOSING PATTERNS
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
Year 12 24 36 Ultimate
1995 5,000 8,000 10,000 10,000
1996 5,000 8,000 10,000
1997 5,000 10,000
Accident Closed Claims
Year 12 24 36 Ultimate
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
Year 12 24 36 Ultimate
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
Year 12 24 36 Ultimate
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
CASE RESERVE ADEQUACY
STEP 1: Review Paid-To-Incurred Triangles:
Accident Months of Development
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
CASE RESERVE ADEQUACY
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
CASE RESERVE ADEQUACY
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
CASE RESERVE ADEQUACY
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
CASE RESERVE ADEQUACY
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
CASE RESERVE ADEQUACY
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
CASE RESERVE ADEQUACY
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