1. 0 July 13 - 14, 1998 Boston, Massachusetts Presented by: Susan E. Witcraft Milliman & Robertson, Inc. Addressing Three Questions Regarding an Insurance Company’s Operations

2. 1 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.

3. 2 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?

4. 3 OVERVIEW OF COMPANY Line199719981999 Property$64,889$65,668$68,951 General Liability31,00031,00031,000 Workers’ Compensation21,58621,58621,586 Commercial Auto38,63838,63838,638 Personal Auto57,01860,63664,435 Direct Written Premium (000s)

5. 4 MODEL USED Asset Accounting Economic Scenarios Liability Scenarios Loss/Cat Expense Other Liability Accounting Financial Statements Report Generator

6. 5 RISKS MODELED l Economy l Investment Yields & Returns l Premium l Losses l Fixed Expenses l Statutory Assessments

7. 6 RISKS NOT MODELED l Mass Torts l Loss Payment Patterns l Reserve Strengthening l LAE Ratios l Reinsurance Pricing l Illiquid Assets l Reduction in Best’s Rating l Credit Risk

8. 7 DATA l Management’s Three-Year Financial Plan l Five Years of Statutory Annual Statements l Company’s Analysis of Direct Ultimate Losses and LAE l Corresponding Payment Triangles and Earned Premium l Paid & Incurred Development Triangles of Individual Large Losses l Probability Distributions of Catastrophe Losses l Policy Limits Profiles l List of Large Catastrophe Losses for the Past 10 Years

9. 8 INPUTS l Economic l Assets l Premium l Losses l Expenses l Reinsurance

10. 9 ECONOMIC ASSUMPTIONS where Y i = GDP change in period i ; L i = long-term interest rates; S i = short-term interest rates; and e i = random error term. Y i = a + b Y i -1 + c Y i -2 + d (L i -1 - S i-1 ) + f (L i -2 - S i-2 ) + g (S i -1 ) + e i GDP is autoregressive model

11. 10 ECONOMIC ASSUMPTIONS Remaining system of equations is recursive I i =  (Y i, I i-1... I i-4, Y i-1... Y i- 4, e i ) S i =  (I i, S i-1, S i-2, e i ) L i =  (S i, L i-1, L i-2, S i-1, S i- 2, e i ) SP i =  (L i, Y i+1, Y i, I i, e i ) D i =  (D i-1, SP i-1, SP i- 2 )

12. 11 ASSET ASSUMPTIONS l Book, Acquisition & Par Values of Bonds by Coupon and Maturity l Book, Acquisition & Market Values of Other Asset Classes l Investment Strategy

13. 12 PREMIUM ASSUMPTIONS Growth Personal Lines  N(0.05, 0.025) Commercial Lines  N(0, 0.025) Percent Earned in Year Percent Collected in Year

14. 13 LOSS ASSUMPTIONS l Small Losses l Large Claims (xs $500,000) l Catastrophe Losses (xs $2 Million)

15. 14 SMALL LOSS RATIO: PROPERTY 1987$13,172$ 0$ 0$31,89341.3% 198813,6540037,40836.5% 198918,9041,929038,58044.0% 199023,9523,870043,00246.7% 199129,3526,1742,46047,03846.7% 199224,4844,356046,45943.3% 199327,0865,561049,42743.6% 199441,80612,0599,75053,59746.4% 199533,6186,401060,24745.2% 199635,4667,012062,33045.7% Selected43% (1)(2)(3)(4)(5) UltimateLossesDirectSmall AccidentDirecton LargeCatastropheEarnedLoss Ratio YearLossesClaimsLossesPremium[(1)-(2)-(3)]/(4)

16. 15 SMALL LOSS RATIOS wherel/r= loss ratio j = year x = line of business k= specific line of business being modeled I= interest rate a,b,c,d, and f = constants e= Normal random variable

17. 16 LARGE LOSS ASSUMPTIONS: GENERAL LIABILITY 19870.00-- 19880.00-- 19890.11$ 700 19900.101,000 19910.00-- 19920.101,000 19930.11800 19940.331,000 19950.23900 19960.371,100 High0.35Selected $1,200 Middle0.30 Low0.225 Projected AccidentProjectedAverage YearFrequencyCost (000S)

18. 17 SELECTED LARGE LOSS ASSUMPTIONS Property0.15$1,000 Workers’ Compensation0.051,500 Commercial Auto0.25700 Personal Auto0.01600 Expected ExpectedSeverity LineFrequency(000s)

19. 18 SELECTED CATASTROPHE ASSUMPTIONS 0.5%$200 3.0%130 1.5%110 1.5%90 1.5%70 2.5%60 2.5%50 2.5%44 2.5%38 2.5%32 2.5%26 2.5%$20 5.0%18 5.0%16 5.0%14 5.0%12 5.0%10 9.5%9 10.0%8 10.0%7 10.0%6 10.0%5 Expected Number/Year 0.25 Probability Amount

20. 19 SUMMARY OF LOSS RATIO ASSUMPTIONS Property43.0%15.0%8.7%66.7% General Liability25.0%36.0%0.0%61.0% Workers’ Compensation67.5%7.5%0.0%75.0% Commercial Auto45.0%17.5%0.0%62.5% Personal Auto68.0%0.6%0.0%68.6% (1)(2)(3)(4) Direct SmallLargeCatastropheLoss LossLossLossRatio LineRatioRatioRatio(1)+(2)+(3)

21. 20 SUMMARY OF LAE RATIO ASSUMPTIONS Property10.5%6.0% General Liability15.0%5.0% Workers’ Compensation8.0%4.5% Commercial Auto8.5%7.0% Personal Auto8.0%7.0% ALAE/LossULAE/Loss LineRatioRatio

22. 21 EXPENSES Commissions17.3% of GWP Premium Taxes 2.7% of GWP

23. 22 STATUTORY ASSESSMENTS 95%0.5% 3%1.0% 1%2.0% 1%5.0% Statutory Assessments/ Direct Written ProbabilityPremium

24. 23 EXCESS OF LOSS REINSURANCE l Attachment Point  $5 Million - General Liability  $1 Million - All Other Lines l No Deductible, Maximum, or Ceding Commission

25. 24 EXCESS OF LOSS REINSURANCE PREMIUM Property$ 360 General Liability1,440 Workers’ Compensation600 Commercial Auto360 Personal Auto2 1997 Ceded Premium Line(000s)

26. 25 QUOTA SHARE REINSURANCE l General Liability Only l Cede 75% of Premium + Losses l Commission = Min(0.4, Max(0.18,0.25+0.8(0.55-l/r)))

27. 26 CATASTROPHE REINSURANCE l $50 Million Excess of $10 Million l 2 Reinstatements at 5% Rate On Line l $4.5 Million Initial Premium

28. 27 Evaluate the likelihood that actual results will equal or exceed those in the company’s plan. OBJECTIVE #1

29. 28 STATUTORY RESULTS Mean$2,020$1,740$ 855$120,852 Probability (Min) 0%$-40,231$-40,456$-41,342$ 64,729 1%-21,02621,32022,11686,912 5%-10,998-11,201-12,089101,731 10%-8,020-8,213-9,118106,444 25%-2,754-3,012-3,887114,765 50%2,2132,0701,137122,115 75%6,9926,6125,698128,275 90%10,72010,5299,628136,349 95%12,95212,68911,754136,981 99%16,34116,02815,117142,560 (Max)100%22,61622,32721,472147,783 Plan4,0004,5005,000131,500 P{x>Plan}38%35%28%15% Net After-Tax Income 199719981999Surplus

30. 29 Identify differences in assumptions between us and the company. OBJECTIVE #2

31. 30 GENERAL LIABILITY LARGE CLAIMS Company:6.00.1% M&R Low:7.21.3% M&R Middle:9.217.4% M&R High:10.746.0% Expected NumberProbability of Last of Large ClaimsThree Year’s Results

32. 31 FIXED EXPENSES l Inflationary Impact on Salaries

33. 32 Identify key drivers of results. OBJECTIVE #3

34. 33 l List Independent Variables l Use t-Test to Determine Statistical Significance l Calculate Impact on Income at 90th Percentile APPROACH

35. 34 LIST OF VARIABLES TESTED l Gross Written Premium  Commercial Lines  Personal Lines l Underwriting Expense Deviation l Statutory Assessments l Number of Catastrophes l Size of Each Catastrophe l Small Loss Ratio  Property  Commercial Auto  General Liability  Workers’ Compensation  Personal Auto l Number of Large Claims  Property  Commercial Auto  General Liability  Workers’ Compensation  Personal Auto l Average Cost of Large Claims  Property  Commercial Auto  General Liability  Workers’ Compensation  Personal Auto l Inflation l Short and Long Term Rates

36. 35 KEY DRIVERS Small Loss Ratio - General Liability25.0%$ 77516%$-1.0 Commercial Auto45.0%1,73919%-2.6 Personal Auto68.0%3,8773%-2.8 Workers’ Compensation67.5%1,45722%-2.6 Property43.0%2,79015%-4.0 Net Income ImpactImpact of if 10%Probability90th Percentile AverageWorse Thanof 10%Adverse 1997ExpectedWorse ThanDeviation VariableValue(thousands)Expected(millions)

37. 36 KEY DRIVERS Number of Large Claims - Property9.7$ 97036%$-3.3 General Liability9.31,11634%-4.4 Commercial Auto9.767931%-2.3 Workers’ Compensation1.116530%-2.9 Number of Catastrophes0.2514125%-2.5 Underwriting Expenses (Deviation from Expected) 0%N/AN/A-2.8 Net Income ImpactImpact of if 10%Probability90th Percentile AverageWorse Thanof 10%Adverse 1997ExpectedWorse ThanDeviation VariableValue(thousands)Expected(millions)