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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)