Transcript Loss Reserving: Is It Broken? What Can Be Done Better? CAS Annual Meeting November 15-16, 2004 Chuck Emma, Pinnacle Tom Ryan, Milliman John J.

Loss Reserving: Is It Broken?
What Can Be Done Better?
CAS Annual Meeting
November 15-16, 2004
Chuck Emma, Pinnacle
Tom Ryan, Milliman
John J. Kollar, ISO
Some Criticisms
• “Actuaries are signing off on reserves
that turn out to be wildly inaccurate.”
Standard & Poors
• “Are actuaries to blame for the huge
shortfalls in reserves…?” Insurance Day
• “Are actuaries hiding the bad news?”
National Underwriter
ISO Study of Loss and Loss
Adjustment Expense Reserves
A. Industry
B. R&D
CAS Annual Meeting
November 15-16, 2004
John J. Kollar, ISO
Industry Loss Reserve Analysis
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•
•
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More than 900 insurer groups
Year-ended 12/31/03
Schedule P data compiled by A. M. Best
More than 95% of LLAE reserves for
studied lines
• PRELIMINARY RESULTS
Lines studied
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•
•
PP Auto Liability
HO/Farmowners
Com. Auto Liability
Other & Products Liab.
Claims-Made
• Other Liab. Occurrence
• Com. Multi-Peril
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•
•
•
Med Mal Occurrence
Med Mal Claims-Made
Products Occurrence
Reinsurance (NonProportional Liability)
• Workers Comp
Some Key Points
• All indications are PRELIMINARY; we have
not yet selected final LDFs & ranges
• Excludes reserves for environmental and
asbestos (E&A) claims
– Possibly $30B to $50B deficient
• No adjustment has yet been made for further
development of 9/11 losses
– Estimated insured losses: $20B to $30B
– U.S. net insured losses: $8B to $12B
• Adjustments have been made for other major
catastrophes
Methodologies
• Paid link-ratio technique
• Case-incurred link-ratio technique
• Consistent with 2001 ISO study
Factors affecting analysis
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Data quality
Development factors
Tail factors
Professional judgment
Conventions
• Each deficiency/redundancy expressed
as percentage of indicated
undiscounted reserve as estimated by
ISO
– Positive percentages indicate deficiencies
– Negative percentages indicate
redundancies
Preliminary Summary Indications
of Reserve Deficiencies
Paid
Case Incurred
• Lines Studied
• All Other Lines
• Total – all lines
+ 7%
+ 5%
+ 7%
+ 9%
+ 5%
+ 8%
• In Dollars
$30B
$34B
Note: excludes E & A
Perspective (Preliminary)
• Reserve adequacy has improved for 2
consecutive years
– Reserves are 7 to 9 percentage points
more adequate at year-end 2003 than at
year-end 2001
Preliminary Indications by Line
• Lines with significant deficiencies
Paid
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•
•
•
•
Other Liability Occurrence
Products Occurrence
Com. Multi-Peril
Workers Comp
Reinsurance (Non-Prop.)
+11%
+ 1%
+ 6%
+14%
+29%
Case Inc.
+ 3%
+13%
+ 9%
+21%
+30%
Preliminary Indications by Line
• Other Lines
Paid
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•
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•
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Priv. Pass. Auto Liability
Homeowners/Farmowners
Commercial Auto Liability
Claims Made Other & Prod.
Medical Malpractice – Occ.
Medical Malpractice – C-M.
- 3%
- 7%
- 4%
- 5%
0%
- 2%
Case Inc.
- 6%
- 7%
+ 2%
- 7%
+ 8%
- 1%
LALAE Ratios: Accident Year vs. Calendar Year
Reserve adequacy deteriorated for at least 7
years but then improved in 2002 & 2003.
%
90
85
80
75
70
65
60
95
96
97
98
Accident Year
99
00
01
Calendar Year
02
03
Loss Reserve Changes vs. Industry
Profitability, All Lines
Changes in reserves are
correlated with profitability.
%
35
30
25
20
15
10
5
0
-5
'73
'76
'79
'82
'85
'88
'91
'94
'97
Change in LLAE Reserves / Paid LLAE
GAAP Return on Average Net Worth
'00
'03
Indicated Reserve Deficiencies vs. Industry
Profitability
Since 1997, changes in estimated deficiencies
have mirrored changes in overall profitability.
%
20
15
10
5
0
-5
-10
-15
95
96
97
98
Paid Link Ratio
GAAP Return on Average Net Worth
99
00
01
02
Case-Incurred Link Ratio
03
Retrospective Estimated Deficiencies &
Economic Discount, All Studied Lines
%
Even when discounted,
reserves may not be adequate.
25
15
5
-5
-15
95
96
97
98
Paid Link Ratio
Compound Discount Factors
99
00
01
02
03
Case-Incurred Link Ratio
ISO Industry Loss Reserve
Analysis
• Final, More complete analysis, as well as
methodology and selections for each line, in
Loss and Loss Adjustment Expense
Reserves at Year-End 2003: Technical
Analysis
• Separate analysis of loss adjustment
expenses in:
Loss and Loss Adjustment Expense
Reserves at Year-End 2003:
ALAE Supplement
Pers. Auto Incurred L&ALAE Development
from 15 to Ultimate for Voluntary DE Risks
1.5
1.431
1.4
1.347
1.3
1.2
1.084
1.1
1.0
0.9
0.857
0.8
Total Limits BI
Total Limits PD
UM BI (15K/30K)
PIP
Pers. Auto Liab. Paid Bodily Injury L&ALAE
Development from 15 to Ult. for PA Risks
13
12.023
12
11
10
9
8.000
8
7
7.278
6.203
6.522
6.688
20K/40K
25K/50K
7.278
6
5
15K/30K
50K/100K 100K/300K 250K/500K
Total
Limits
Other Liability Full Coverage Bodily Injury
Loss Development from 15 to Ultimate
12
10.878
Excess
Basic Limits
10
8.987
8
7.529
6
4.951
4
3.134
2.385
2
2.107
1.537
0
Owners,
Landlords &
Tenants
Manufacturers &
Contractors
Manually-Rated
Completed
Operations
A-Rated
Completed
Operations
Com. Auto BI Liability Development from
15 to Ultimate in Tort States for Trucks,
Tractors & Trailers
3.0
2.514
2.5
2.0
1.572
1.5
1.0
0.5
0.0
Total Limits Indemnity
Allocated Loss Adjustment
Expenses
Research on Loss Reserving
• Within each Schedule P Line, loss
development varies by state, coverage,
limits, sub-line, ALAE, etc.
• Loss development patterns can vary by
insurer. No surprise!
• Find clusters of insurer loss
development patterns by ?.
– Each cluster would consist of multiple
insurers.
• Fit a stochastic model to each cluster.
Data Being Analyzed
• Schedule P by insurer
• ISO ratemaking data by insurer
– Identity of individual insurer data is
protected.
– Individual insurer data will be clustered.
Possible Stochastic Model(s)
Reserve = f(Age, AY, Size)∙ε
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Age or valuation or lag
AY (accident year)
Size is reflected in a BF/Cape Cod formula.
The error term, ε, could depend on accident
year, age and size.
– Lognormal distribution?
– Correlation of ε’s between (age,AY) cells?
Uses of Stochastic Model(s)
• Test hypothesis that an insurer’s data is
described by a cluster’s model.
• If data is consistent with (fails to reject
hypothesis) a model for one cluster, consider
using it.
• If data is consistent with models for several
clusters, use weighted average of models
with weights determined by Bayes’ Theorem.
• If data is not consistent with models for any
cluster, then ????.
Confidence Intervals for Reserves
• Given distribution of ε’s for each age
and accident year, we want to find the
distribution of a sum of (age, accident
year) cells.
– All future ages in an accident year
– For all accident years
• Correlation matters!
What do You Think?