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July 13 - 14, 1998 Boston, Massachusetts

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

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July 13 - 14, 1998 Boston, Massachusetts

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

  2. 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. 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. OVERVIEW OF COMPANY Direct Written Premium (000s) 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

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

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

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

  8. 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

  9. INPUTS • Economic • Assets • Premium • Losses • Expenses • Reinsurance

  10. ECONOMIC ASSUMPTIONS GDP is autoregressive model Yi = a + b Yi -1+ c Yi -2 + d (Li -1- Si-1) + f (Li -2- Si-2) + g (Si -1 ) + ei where Yi = GDP change in period i; Li = long-term interest rates; Si = short-term interest rates; and ei = random error term.

  11. 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 )

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

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

  15. SMALL LOSS RATIO: PROPERTY (1) (2) (3) (4) (5) Ultimate Losses Direct Small Accident Direct on Large Catastrophe Earned Loss Ratio YearLossesClaims Losses Premium [(1)-(2)-(3)]/(4) 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%

  16. SMALL LOSS RATIOS where l/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. LARGE LOSS ASSUMPTIONS: GENERAL LIABILITY Projected Accident Projected Average Year Frequency Cost (000S) 1987 0.00 -- 1988 0.00 -- 1989 0.11 $ 700 1990 0.10 1,000 1991 0.00 -- 1992 0.10 1,000 1993 0.11 800 1994 0.33 1,000 1995 0.23 900 1996 0.37 1,100 High 0.35 Selected $1,200 Middle 0.30 Low 0.225

  18. SELECTED LARGE LOSSASSUMPTIONS Expected Expected Severity Line Frequency (000s) Property 0.15 $1,000 Workers’ Compensation 0.05 1,500 Commercial Auto 0.25 700 Personal Auto 0.01 600

  19. SELECTED CATASTROPHEASSUMPTIONS Probability Amount Probability Amount 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

  20. SUMMARY OF LOSS RATIOASSUMPTIONS (1) (2) (3) (4) Direct Small Large Catastrophe Loss Loss Loss Loss Ratio LineRatioRatioRatio(1)+(2)+(3) 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%

  21. SUMMARY OF LAE RATIOASSUMPTIONS ALAE/Loss ULAE/Loss Line Ratio Ratio 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%

  22. EXPENSES Commissions 17.3% of GWP Premium Taxes 2.7% of GWP

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

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

  25. EXCESS OF LOSSREINSURANCE PREMIUM 1997 Ceded Premium Line (000s) Property $ 360 General Liability 1,440 Workers’ Compensation 600 Commercial Auto 360 Personal Auto 2

  26. 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)))

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

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

  29. STATUTORY RESULTS Net After-Tax Income 1997 1998 1999 Surplus 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 86,912 5% -10,998 -11,201 -12,089 101,731 10% -8,020 -8,213 -9,118 106,444 25% -2,754 -3,012 -3,887 114,765 50% 2,213 2,070 1,137 122,115 75% 6,992 6,612 5,698 128,275 90% 10,720 10,529 9,628 136,349 95% 12,952 12,689 11,754 136,981 99% 16,341 16,028 15,117 142,560 (Max)100% 22,616 22,327 21,472 147,783 Plan 4,000 4,500 5,000 131,500 P{x>Plan} 38% 35% 28% 15%

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

  31. GENERAL LIABILITY LARGE CLAIMS Expected Number Probability of Last of Large ClaimsThree Year’s Results 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%

  32. FIXED EXPENSES • Inflationary Impact on Salaries

  33. OBJECTIVE #3 Identify key drivers of results.

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

  35. 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

  36. KEY DRIVERS Net Income Net Income Impact Impact of if 10% Probability 90th Percentile Average Worse Than of 10% Adverse 1997 Expected Worse Than Deviation VariableValue(thousands) Expected(millions) 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

  37. KEY DRIVERS Net Income Net Income Impact Impact of if 10% Probability 90th Percentile Average Worse Than of 10% Adverse 1997 Expected Worse Than Deviation VariableValue(thousands) Expected(millions) 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

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