1 METODOLOGÍAS Y PRÁCTICAS EN RESERVAS TÉCNICAS PARA SEGUROS DE SALUD Y SEGUROS GENERALES LIMA – 31 DE MAYO, 2007 APESEG Presentado por: APESEG & Milliman, Inc. Basic Methods for Evaluating Reserves Basic Methods for Evaluating Reserves

2 LOSS RESERVING METHODS In practice, many methods estimate Ultimate Losses Loss Reserves are Obtained By Subtraction Estimated Ultimate Losses - Paid to date Losses = Total Reserve - Case Reserve = IBNR Reserve

3 LOSS RESERVING METHODS Expected Loss (Loss Ratio) Loss Development (Chain Ladder) Tail Factors Inflation Adjustments Bornhuetter-Ferguson Generalized Cape Cod Many, many others available

4 BASIC METHODS – BASEBALL EXAMPLE Given the following information, how many homeruns will Sammy Sosa finish with in the 2007 season? 2004 total homeruns: total homeruns: total homeruns: : 20 homeruns through 40 games of the 160 game season

5 BASIC METHODS – BASEBALL EXAMPLE How many homeruns will Sammy Sosa finish with in the 2007 season?

6 BASIC METHODS – BASEBALL EXAMPLE How many homeruns will Sammy Sosa finish with in the 2007 season? Based on the prior 3 years, the Expected Value would be 40 homeruns.

7 BASIC METHODS – BASEBALL EXAMPLE How many homeruns will Sammy Sosa finish with in the 2007 season?

8 BASIC METHODS – BASEBALL EXAMPLE How many homeruns will Sammy Sosa finish with in the 2007 season?

9 BASIC METHODS – BASEBALL EXAMPLE How many homeruns will Sammy Sosa finish with in the 2007 season? What is the Bornhuetter-Ferguson (B-F) Method? Named after paper written by Ron Bornhuetter and Ron Ferguson published in the Casualty Actuarial Society Proceedings Compromise between the Expected Loss and Loss Development Methods.

10 BASIC METHODS – BASEBALL EXAMPLE How many homeruns will Sammy Sosa finish with in the 2007 season? What data is needed for the B-F Method? Expected Ultimate Value (40) Factor to Project Actual Data to Ultimate (4.000) Actual Data to Date (20)

11 BASIC METHODS – BASEBALL EXAMPLE How many homeruns will Sammy Sosa finish with in the 2007 season? B-F Projection: Ultimate Value = (Expected Value*IBNR Factor)+(Inc. to Date) IBNR Factor = (1.000/LDF) = (1.000/4.000) =.75 (In Other Words, 75% of the season is left to be played) Ultimate Value = (40 *.75) + 20 = 50

12 How many homeruns will Sammy Sosa finish with in the 2007 season? Expected Value Method Games 0-40Games 41-80Games Games Home Runs10 Home Runs10 Home Runs10 Home Runs Development Projection Method Games 0-40Games 41-80Games Games Home Runs20 Home Runs20 Home Runs20 Home Runs Bornhuetter-Ferguson Method Games 0-40Games 41-80Games Games Home Runs10 Home Runs10 Home Runs10 Home Runs BASIC METHODS – BASEBALL EXAMPLE

13 How many homeruns will Sammy Sosa finish with in the 2007 season? BASIC METHODS – BASEBALL EXAMPLE

14 Comparison of Methods BASIC METHODS – BASEBALL EXAMPLE If Actual 10 After 40 Games If Actual 20 After 40 Games If Actual 5 After 40 Games

15 LOSS RESERVING METHODS Each Method is Based on Idealized Model of Reality Models have Implicit Assumptions Such Assumptions are Rarely Satisfied No single method or Formula will work Use multiple methods Use judgment in selecting values Actuary to test Assumptions Review Diagnostics Possibly Use Additional Methods to Adjust Data

16 LOSS RATIO METHODS Problem. I know the earned premium, but how do I estimate the Expected Loss Ratio? Use Pricing Assumptions Use Available Industry Information Useful when Company does not have relevant information to analyze New Business Small Volume Late Reporting of Losses (e.g., high excess of loss). x Earned Premium Expected Loss Ratio E(LR) = Ultimate Losses

17 EXPECTED LOSS RATIO METHOD

18 EXPECTED LOSS METHOD EXAMPLE

19 DEVELOPMENT METHOD Also Called the Chain Ladder Method and the Completion Factor Method Data Triangles Paid Loss Incurred Loss Claim Counts

20 TRIANGLE EXAMPLE

21 TRIANGLE EXAMPLE

22 LOSS DEVELOPMENT METHOD EXAMPLE

23 TAIL FACTORS Previous Example Showed Development to 60 Months Suppose Process is Not Complete Curve Fits Industry Information Paid to Incurred Ratios Judgment

24 LOSS DEVELOPMENT METHOD EXAMPLE

25 LOSS DEVELOPMENT METHOD EXAMPLE

26 IMPORTANCE OF TAIL FACTOR

27 IMPORTANCE OF TAIL FACTOR

28 PAYMENT/REPORTING PATTERNS

29 EXAMPLE PAYMENT PATTERNS

30 EMERGENCE AND SETTLEMENT PATTERNS

31 BRINGING RESULTS TOGETHER Make Tentative Selections Loss Development Factors Tail Factors Expected Loss Ratios Generalized Cape Cod Trend and Decay Weights for Various Methods

32 BRINGING RESULTS TOGETHER

33 BRINGING RESULTS TOGETHER

34 BRINGING RESULTS TOGETHER Check Ultimate Losses for Reasonableness by Reviewing additional Diagnostics Ultimate Loss Ratios Frequency and Severity Percent of Total Loss by Year Paid, Case Reserve, IBNR Ratios of Ceded Reserves to Total Reserves Average Hindsight Outstanding Cost Per Open Claim Many Others Sensitivity Test Reasonable Ranges for Key Selections

35 BRINGING RESULTS TOGETHER

36 BRINGING RESULTS TOGETHER

37 BRINGING RESULTS TOGETHER

38 BRINGING RESULTS TOGETHER

39 BASIC METHODS REVIEW Basic Methods Expected Loss Loss Development Bornhuetter-Ferguson Cape Cod Reasonability and Sensitivity of Estimates Tail Factor Selection Review of resulting Ultimate Loss Ratios, Claim Severities and Frequencies, and other Diagnostics Sensitivity of Results to Key Assumptions Loss Adjustment Expenses Documentation