july 13 - 14, 1998 boston, massachusetts
DESCRIPTION
Addressing Three Questions Regarding an Insurance Company’s Operations. July 13 - 14, 1998 Boston, Massachusetts. Presented by: Susan E. Witcraft Milliman & Robertson, Inc. BACKGROUND. - PowerPoint PPT PresentationTRANSCRIPT
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July 13 - 14, 1998July 13 - 14, 1998
Boston, MassachusettsBoston, Massachusetts
Presented by:Presented by:
Susan E. Witcraft Susan E. Witcraft
Milliman & Robertson, Inc.Milliman & Robertson, Inc.
Addressing Three Questions RegardingAddressing Three Questions Regardingan Insurance Company’s Operationsan Insurance Company’s Operations
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BACKGROUND
During each of the past several years, an
insurance company’s actual experience has
been much worse than the plan provided to
its Board.
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QUESTIONS
1. What is the probability that the insurance company will meet or exceed the earnings estimates provided to its Board for the following year?
2. Are the assumptions underlying the earnings estimates overly optimistic, or has the company had a run of bad luck?
3. What elements of the company’s business are its sources of greatest risk?
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OVERVIEW OF COMPANY
Line 1997 1998 1999
Property $64,889 $65,668 $68,951
General Liability 31,000 31,000 31,000
Workers’ Compensation 21,586 21,586 21,586
Commercial Auto 38,638 38,638 38,638
Personal Auto 57,018 60,636 64,435
Direct Written Premium (000s)
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MODEL USED
AssetAccounting
EconomicScenarios
LiabilityScenarios
Loss/Cat
Expense
Other
LiabilityAccounting
FinancialStatements
ReportGenerator
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RISKS MODELED
Economy
Investment Yields & Returns
Premium
Losses
Fixed Expenses
Statutory Assessments
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RISKS NOT MODELED
Mass Torts Loss Payment Patterns Reserve Strengthening LAE Ratios Reinsurance Pricing Illiquid Assets Reduction in Best’s Rating Credit Risk
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DATA
Management’s Three-Year Financial Plan Five Years of Statutory Annual Statements Company’s Analysis of Direct Ultimate Losses and LAE Corresponding Payment Triangles and Earned Premium Paid & Incurred Development Triangles of Individual Large
Losses Probability Distributions of Catastrophe Losses Policy Limits Profiles List of Large Catastrophe Losses for the Past 10 Years
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INPUTS
Economic
Assets
Premium
Losses
Expenses
Reinsurance
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ECONOMIC ASSUMPTIONS
where Yi = GDP change in period i;
Li = long-term interest rates;
Si = short-term interest rates; and
ei = random error term.
Yi = a + b Yi -1 + c Yi -2 + d (Li -1 - Si-1 ) + f (Li -2 - Si-2 )
+ g (Si -1 ) + ei
GDP is autoregressive model
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ECONOMIC ASSUMPTIONS
Remaining system of equations is recursive
Ii = (Yi , Ii-1 . . . Ii-4 , Yi-1 . . . Yi- 4 , ei )
Si = (Ii , Si-1 , Si-2 , ei )
Li = (Si , Li-1 , Li-2 , Si-1 , Si- 2 , ei )
SPi = (Li , Yi+1 , Yi , Ii , ei )
Di = (Di-1 , SPi-1 , SPi- 2 )
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ASSET ASSUMPTIONS
Book, Acquisition & Par Values of Bonds by Coupon and Maturity
Book, Acquisition & Market Values of Other Asset Classes
Investment Strategy
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PREMIUM ASSUMPTIONS
Growth
Personal Lines N(0.05, 0.025)
Commercial Lines N(0, 0.025)
Percent Earned in Year
Percent Collected in Year
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LOSS ASSUMPTIONS
Small Losses
Large Claims (xs $500,000)
Catastrophe Losses (xs $2 Million)
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SMALL LOSS RATIO: PROPERTY
1987 $13,172 $ 0 $ 0 $31,893 41.3%1988 13,654 0 0 37,408 36.5%1989 18,904 1,929 0 38,580 44.0%1990 23,952 3,870 0 43,002 46.7%1991 29,352 6,174 2,460 47,038 46.7%1992 24,484 4,356 0 46,459 43.3%1993 27,086 5,561 0 49,427 43.6%1994 41,806 12,059 9,750 53,597 46.4%1995 33,618 6,401 0 60,247 45.2%1996 35,466 7,012 0 62,330 45.7%
Selected 43%
(1) (2) (3) (4) (5)Ultimate Losses Direct Small
Accident Direct on Large Catastrophe Earned Loss RatioYear Losses Claims Losses Premium [(1)-(2)-(3)]/(4)
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SMALL LOSS RATIOS
where l/r = loss ratioj = yearx = line of businessk = specific line of business being modeledI = interest ratea,b,c,d, and f = constantse = Normal random variable
jjxjxkx
xjxkx
kjkj eifrldrlcrlbarl
)/()/()/(/ ,1,,1,
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LARGE LOSS ASSUMPTIONS: GENERAL LIABILITY
1987 0.00 --1988 0.00 --1989 0.11 $ 7001990 0.10 1,0001991 0.00 --1992 0.10 1,0001993 0.11 8001994 0.33 1,0001995 0.23 9001996 0.37 1,100
High 0.35 Selected $1,200 Middle 0.30 Low 0.225
ProjectedAccident Projected Average
Year Frequency Cost (000S)
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SELECTED LARGE LOSSASSUMPTIONS
Property 0.15 $1,000Workers’ Compensation 0.05 1,500Commercial Auto 0.25 700Personal Auto 0.01 600
ExpectedExpected Severity
Line Frequency (000s)
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SELECTED CATASTROPHEASSUMPTIONS
0.5% $2003.0% 1301.5% 1101.5% 901.5% 702.5% 602.5% 502.5% 442.5% 382.5% 322.5% 26
2.5% $205.0% 185.0% 165.0% 145.0% 125.0% 109.5% 9
10.0% 810.0% 710.0% 610.0% 5
Expected Number/Year 0.25
Probability Amount Probability Amount
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SUMMARY OF LOSS RATIOASSUMPTIONS
Property 43.0% 15.0% 8.7% 66.7%
General Liability 25.0% 36.0% 0.0% 61.0%
Workers’ Compensation 67.5% 7.5% 0.0% 75.0%
Commercial Auto 45.0% 17.5% 0.0% 62.5%
Personal Auto 68.0% 0.6% 0.0% 68.6%
(1) (2) (3) (4)Direct
Small Large Catastrophe LossLoss Loss Loss Ratio
Line Ratio Ratio Ratio (1)+(2)+(3)
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SUMMARY OF LAE RATIOASSUMPTIONS
Property 10.5% 6.0%General Liability 15.0% 5.0%Workers’ Compensation 8.0% 4.5%Commercial Auto 8.5% 7.0%Personal Auto 8.0% 7.0%
ALAE/Loss ULAE/LossLine Ratio Ratio
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EXPENSES
Commissions 17.3% of GWP
Premium Taxes 2.7% of GWP
))01.0,0()(
5.01(* 11 N
GWPGWPGWP
CPIFEFEt
ttttt
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STATUTORY ASSESSMENTS
95% 0.5%
3% 1.0%
1% 2.0%
1% 5.0%
StatutoryAssessments/Direct Written
Probability Premium
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EXCESS OF LOSS REINSURANCE
Attachment Point $5 Million - General Liability $1 Million - All Other Lines
No Deductible, Maximum, or Ceding Commission
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EXCESS OF LOSSREINSURANCE PREMIUM
Property $ 360General Liability 1,440Workers’ Compensation 600Commercial Auto 360Personal Auto 2
1997 CededPremium
Line (000s)
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QUOTA SHAREREINSURANCE
General Liability Only
Cede 75% of Premium + Losses
Commission = Min(0.4, Max(0.18,0.25+0.8(0.55-l/r)))
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CATASTROPHE REINSURANCE
$50 Million Excess of $10 Million
2 Reinstatements at 5% Rate On Line
$4.5 Million Initial Premium
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Evaluate the likelihood that actual results will
equal or exceed those in the company’s plan.
OBJECTIVE #1
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STATUTORY RESULTS
Mean $2,020 $1,740 $ 855 $120,852
Probability(Min) 0% $-40,231 $-40,456 $-41,342 $ 64,729
1% -21,026 21,320 22,116 86,9125% -10,998 -11,201 -12,089 101,731
10% -8,020 -8,213 -9,118 106,44425% -2,754 -3,012 -3,887 114,76550% 2,213 2,070 1,137 122,11575% 6,992 6,612 5,698 128,27590% 10,720 10,529 9,628 136,34995% 12,952 12,689 11,754 136,98199% 16,341 16,028 15,117 142,560
(Max)100% 22,616 22,327 21,472 147,783
Plan 4,000 4,500 5,000 131,500P{x>Plan} 38% 35% 28% 15%
Net After-Tax Income
1997 1998 1999 Surplus
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Identify differences in assumptions
between us and the company.
OBJECTIVE #2
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GENERAL LIABILITY LARGE CLAIMS
Company: 6.0 0.1%
M&R Low: 7.2 1.3%
M&R Middle: 9.2 17.4%
M&R High: 10.7 46.0%
Expected Number Probability of Lastof Large Claims Three Year’s Results
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FIXED EXPENSES
Inflationary Impact on Salaries
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Identify key drivers of results.
OBJECTIVE #3
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List Independent Variables
Use t-Test to Determine Statistical Significance
Calculate Impact on Income at 90th Percentile
APPROACH
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LIST OF VARIABLES TESTED
Gross Written Premium Commercial Lines Personal Lines
Underwriting Expense Deviation Statutory Assessments Number of Catastrophes Size of Each Catastrophe Small Loss Ratio
Property Commercial Auto General Liability Workers’ Compensation Personal Auto
Number of Large Claims Property Commercial Auto General Liability Workers’ Compensation Personal Auto
Average Cost of Large Claims Property Commercial Auto General Liability Workers’ Compensation Personal Auto
Inflation Short and Long Term Rates
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KEY DRIVERS
Small Loss Ratio -
General Liability 25.0% $ 775 16% $-1.0
Commercial Auto 45.0% 1,739 19% -2.6
Personal Auto 68.0% 3,877 3% -2.8
Workers’ Compensation 67.5% 1,457 22% -2.6
Property 43.0% 2,790 15% -4.0
Net Income Net IncomeImpact Impact ofif 10% Probability 90th Percentile
Average Worse Than of 10% Adverse1997 Expected Worse Than Deviation
Variable Value (thousands) Expected (millions)
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KEY DRIVERS
Number of Large Claims - Property 9.7 $ 970 36% $-3.3 General Liability 9.3 1,116 34% -4.4 Commercial Auto 9.7 679 31% -2.3 Workers’ Compensation 1.1 165 30% -2.9
Number of Catastrophes 0.25 141 25% -2.5
Underwriting Expenses (Deviation from Expected) 0% N/A N/A -2.8
Net Income Net IncomeImpact Impact ofif 10% Probability 90th Percentile
Average Worse Than of 10% Adverse1997 Expected Worse Than Deviation
Variable Value (thousands) Expected (millions)