1. De-Mystifying Reinsurance Pricing STRIMA Conference Baton Rouge, LA September 26, 2006 Presented by Michael Petrocik, FCAS, MAAA Chief Actuarial Officer – Specialty Markets Munich Reinsurance America, Inc.

2. 2 Actuarial Concepts3 Comparison of Pricing Methods19 Experience Rating21 Exposure Rating27 Final Steps32 Agenda

3. 3 Actuarial Concepts Three Important Actuarial Pricing Concepts:  Loss development  Trending  Credibility

4. 4 Loss Development Loss development is the process of estimating the ultimate value of a body of losses, based on the amount of reported or paid loss at a given point in time.  The difference between the ultimate amount of losses and the reported amount is called IBNR (Incurred but not reported) Excess loss development estimates the ultimate value of losses in a specific excess layer. This process is much more difficult than ground-up development because…  Excess losses take much longer to reach maturity  Excess losses are much less frequent

5. 5 Ground-Up Loss Development General Liability Ground-Up Reported Loss Development $5 Million Policy Limit 12 Months 24 Months 36 Months 48 Months 60 Months 72 Months 84 Months Ult Loss 199910,00017,00020,40028,56031,41634,55836,28543,543 20009,00017,10022,23026,67628,01029,13036,704 200112,00019,20026,88034,94440,18654,265 20028,00012,00019,20021,12031,502 200311,00019,80029,70055,581 200412,00020,40053,120 200513,00057,602

6. 6 Ground-Up Loss Development Age-to-Age Ratios 12-24 24-36 36-48 48-60 60-72 72-84 19991.7001.2001.4001.100 1.050 20001.9001.3001.2001.0501.040 20011.6001.4001.3001.150 20021.5001.6001.100 20031.8001.500 20041.700 Avg A-A1.7021.3911.2551.1051.0721.0501.200 Ult Factors4.4312.6041.8711.4921.3501.2601.200 % of Ult22.6%38.4%53.4%67.0%74.1%79.4%83.3%

7. 7 Excess Loss Development General Liability Excess Reported Loss Development $4 Mil xs $1 Mil Layer 12 Months 24 Months 36 Months 48 Months 60 Months 72 Months 84 Months Ult. Loss 19991,0002,7003,5106,1437,985 9,18314,693 2000001,5001,950 2,7305,023 20011,5001,8004,3207,77614,77429,319 20026001,8005,4009,18028,367 200301,5003,75019,705 20042,0005,80072,208 20051,00033,199

8. 8 Excess Loss Development Age-to-Age Ratios 12-24 24-36 36-48 48-60 60-72 72-84 19992.7001.3001.7501.3001.0001.150 20001.3001.0001.400 20011.2002.4001.8001.900 20023.000 1.700 20032.500 20042.900 Avg A-A2.6672.3691.7011.5571.0791.1501.600 Ult Factors33.19912.4505.2553.0901.9841.8401.600 % of Ult3.0%8.0%19.0%32.4%50.4%54.3%62.5%

9. 9 Loss Development Comparison General Liability Percents of Ultimate Ground-UpExcess AgeDevelopment 1222.6%3.0% 2438.4%8.0% 3653.4%19.0% 4867.0%32.4% 6074.1%50.4% 7279.4%54.3% 8483.3%62.5%

10. 10 Trending Trending is the process of adjusting past years data to the conditions that will exist in the year being forecast.  Most forms of trending are an adjustment for inflation There are two purposes for trending past experience years: 1.To restate the past as it would look if those events occurred during the upcoming policy year 2.To put each of the past years on an equal basis in order to assist in comparing them

11. 11 Trending There are three types of trend adjustments that are typically done during an actuarial analysis.  Exposure trend – units that are denominated in dollars are adjusted for subsequent inflation in that item  Loss severity trend – losses are adjusted for changes in the average size of similar type claims  Loss frequency trend – the number of claims is adjusted based upon changes in how often a claim occurs

12. 12 Trend versus Development Losses are adjusted by both loss development factors and trend factors. Don’t each of these steps do the same thing? No. Both processes are necessary to get a full forecast of the upcoming year’s claims because…  Development takes the amount of known losses at a point in time to their final, full (historical) value  Trending restates the historical value of losses at cost levels expected to exist in the upcoming policy year

13. 13 Leveraged Trend Inflation (trend) affects different layers in very different ways. It is kindest to the ground-up layer and harshest to the excess layer. The increased effect on the excess layer is referred to as “leveraged trend.” Leveraged trend is due to the interplay of limits and attachment points on claim values. Let’s look at an example.

14. 14 Leveraged Trend Policy Limit$1,000,000 Attachment Point$100,000 Inflation Rate20% Before Inflation After Inflation TotalGround UpExcessTotalGround UpExcess 50,000 060,000 0 95,000 0114,000100,00014,000 250,000100,000150,000300,000100,000200,000

15. 15 Leveraged Trend Claims Size

16. 16 Leveraged Trend Now let’s look at the inflation rate for each layer. BeforeAfterInflation Total Claim395,000474,00020.0% Ground-Up Layer245,000260,0006.1% Excess Layer150,000214,00042.7%

17. 17 Credibility Credibility is the process of assessing the predictive reliability of a body of data used in experience rating. The credibility process assigns a value between 0% and 100% to the experience rating.  This value is used as a weight on the experience rate result when calculating the final loss pick.  The remainder, or complement of credibility, is usually assigned to an exposure rating estimate.

18. 18 Credibility Credibility is generally defined in terms of a number of expected claims or an amount of exposure. Although based on statistical tests, credibility always includes a significant amount of judgment.  Many important factors can’t be quantitatively evaluated, like data quality.  The relative value of the exposure rating estimate must also be judgmentally considered.

19. 19 Methods Used to Price Reinsurance Experience Rating  Also known as “loss rating”  Price based on past claims experience Exposure Rating  Price base on present hazard complexion of the risk  Natural catastrophe and terrorism models use exposure methods

20. 20 Comparison of Methods Experience Rating  Generally, the preferred method  Price based on past history of claims  Greater reliance on client’s experience Exposure Rating  Typically used to supplement data that is not fully credible  Price based on current hazard composition of risk  Greater reliance on industry experience

21. 21 Experience Rating Experience rating bases the loss estimate on the client’s past history of losses within the layer being reinsured. Experience rating works best in situations where there are multiple claims expected in a single year.  High layers and smaller coverages are challenging to rate. Before analyzing, experience must be adjusted, if there have been changes in the claims environment (tort caps and immunities). Natural catastrophe losses are not experience rated.

22. 22 Experience Rating Data Exposure Information – for each line of business, exposure units are needed for each year of history, as well as an estimate for the upcoming year. Common exposure units:  Auto – power units (number of vehicles)  Workers Comp – payroll  Property – total insured values  General Liability – net operating expenditures (NOE), population, police, students  Professional Liability – NOE, population, students, doctors, occupied beds

23. 23 Experience Rating Data Subject Premium – if premium is calculated for the reinsured layer, it can be used in lieu of exposures.  If so, premium is needed for each historical year, as well as the prospective year  Using premium is most typical in workers’ compensation  When using premium, a history of rate changes is also required so that past premium can be adjusted to current rate levels.

24. 24 Experience Rating Data Loss Information – the key component of any experience rating analysis is accurate, detailed loss information.  Losses are needed for each year being analyzed, in line of business detail.  Reinsurers look to get information on all past losses. At a minimum, all losses of at least half the attachment point are necessary.  Losses should be evaluated as recently as possible.  If possible, annual evaluations of each loss should be submitted. This allows the reinsurer to create loss development factors unique to the risk.

25. 25 Experience Rating Data Loss Information Detail  Line of business  Paid and outstanding amounts  Allocated loss adjustment expenses separate from loss  Occurrence dates  Policy limit  Brief claim description of large losses  Policy effective date, if policies are issued on various dates  Catastrophe losses identified

26. 26 Experience Rating Steps 1.Adjust past exposure units for inflation, if necessary 2.Adjust past loss experience for claims inflation (trending) 3.Calculate how much of each trended claim falls into the layer being priced 4.Develop claims in layer to ultimate value 5.Calculate ratio of losses to (trended) exposures 6.Select appropriate average loss ratio 7.Apply selected loss ratio to prospective exposures to yield expected losses

27. 27 Exposure Rating Rather than use past history, exposure rating evaluates the current loss complexion of the risk.  Detailed profiles of the current exposures insured define the loss complexion. Exposure rating is typically used to supplement places where experience rating is not fully credible. Exposure rating estimates losses in excess layers based upon relativities to lower layers.  Relativities are applied to the experience rated estimate of a low (ground-up) layer.

28. 28 Exposure Rating Curves Exposure rating relies upon loss severity curves which describe the amount of losses expected at any given limit. Loss severity curves are based on statistical fits to claims experience for broad classes of business, rather than the client’s actual experience. Profile information is used to fine tune curves.

29. 29 Exposure Rating Curves Sample Casualty Curve Limit% of LossesIncrementalRelativity 250,00060.0% 100.0% 500,00070.0%10.0%16.7% 1,000,00080.0%10.0%16.7% 2,000,00090.0%10.0%16.7% 3,000,00095.0%5.0%8.3% 4,000,00098.0%3.0%5.0% 5,000,000100.0%2.0%3.3%

30. 30 Exposure Rating Data The key exposure rating data are profiles of the insured exposures of each line of business.  Auto – vehicles by weight class  Workers’ comp – payrolls by class of business  Property – total insured values by location  Also, distributions of construction types, occupancies and protection classes  General and professional liability – exposures by class or hazard type (low, medium and high hazard)  Policy limit distribution, if various limits apply

31. 31 Exposure Rating Steps 1.Calculate loss estimate for base layer. 2.Select appropriate curve for line of business. 3.Adjust curve to applicable limit(s). 4.Modify curve based on profile of line of business. 5.Calculate relativity for the layer being priced. 6.Multiply base layer losses by relativity to yield losses for layer.

32. 32 Final Steps Expenses – costs other than claim payments  Allowances for reinsurer expenses are added to final loss pick.  Must include reinsurer’s expenses as well as any external expenses (commission, TPA).  Usually a combination of percentage charges (commission, taxes) and flat dollar amounts (overhead). Reinsurer’s margin – return for capital used  Margins are based on target combined ratios or returns on equity.  Target margins reflect riskiness and cash flow dynamics.

33. Thank you very much for your attention. Michael Petrocik, FCAS, MAAA Munich Reinsurance America, Inc. © Copyright 2006 Munich Reinsurance America, Inc. All rights reserved. The Munich Re America name is a mark owned by Munich Reinsurance America, Inc. The material in this presentation is provided for your information only, and is not permitted to be further distributed without the express written permission of Munich Reinsurance America. This material is not intended to be legal, underwriting, financial, or any other type of professional advice. Examples given are for illustrative purposes only.