EXPOSURE RATING – UNIQUE APPLICATIONS: UMBRELLA PRICING ADEQUACY

1. EXPOSURE RATING – UNIQUE APPLICATIONS: UMBRELLA PRICING ADEQUACY Halina Smosna Endurance Reinsurance Corp of America CARe June 1 & 2, 2006

2. This is what your client tells you: • We now have more seasoned UWs with a consistent, controlled approach to risk selection & pricing • We’ve shifted our portfolio to smaller to medium sized accounts • We no longer write lead Umbrella for Truckers • We’ve improved our pricing; have stronger factors • We can now price monitor accurately • We re-rate the primary using an ISO vendor product • We have higher attachment points than historically • We are providing lower limits than historically • We’ve fine tuned our UW philosophy • The risk profile of our book has completely changed

3. INFORMATION AVAILABLE FROM CLIENT • Umbrella Loss Development Triangles • Premium • Excess Factors; i.e.: • 1xP (as a percent of P) • 4x1xp (as a percent of 1xP or P) • 5x5xp (as a percent of 5xP or 1xP or P) • 1xP Rating basis: Re-rated vs. Charged • Price Monitoring

4. Issues with standard umbrella pricing approaches • Experience approach • Loss development and experience is often volatile • Change in mix of business is not considered • Long tail nature makes it particularly tough to evaluate underwriting changes • Good price monitoring is often available only for recent years • Analyzing client excess factors • Approach involves comparison of client umbrella factors to a benchmark – either ISO or factors from other umbrella carriers • When comparing to other carrier’s rates, doesn’t always consider differences in judgment credits used • Doesn’t consider whether client hazard group (ISO ILF table) assignments are appropriate • Doesn’t reflect adequacy of primary premium actually used in rating • Difficult to appropriately analyze programs using 1xP auto unit rates • Rarely explicitly considers impact of minimum premiums

5. Proposed Solution • Audit your client • Capture detailed pricing information on a wide sample of in-force accounts • Data captured can also be used to review client rate changes. • Determine projected loss ratio on accounts sampled at audit based on the following: • Final umbrella premium charged by client, including full impact of minimum premiums and judgment credits. • ISO curves and table weighting selected by auditor • Evaluation of adequacy of primary premium on account by account basis

6. Overview of Method • Beautiful in its simplicity….on an account by account basis determine: • Umbrella Loss Ratio = Umbrella Loss Cost/Umbrella Premium • Umbrella Loss Cost = Primary Loss Cost * (Umbrella Loss Cost as a % of Primary) • Primary Loss Cost (for GL and CCA) = Primary Premium * Gross loss Ratio • Sample Calculation for one account:

7. Overview of Method • An audit sample:

8. Proceed with Caution when using ISO Mixed Exponential Curves

9. Proceed with Caution when using ISO Mixed Exponential curves • Previous slide highlights issues with using Mixed Exponential (M/E) above $1M • Not a lot of data above $1M • M/E fits data closely up to $1M, but excess of $1 million tail appears to thin • M/E 4x1 and 5x5 factors are inconsistent, for example, Premops 2 4x1 factors are lower than Premops 1 • Similar problems exist with more recent ISO truncated pareto curves. • Do not recommend using M/E for the account audit sample approach

10. Audit Data Capture

11. Audit Data capture – additional info if you want to Price Monitor the sample Capture all the data from the previous slides on the expiring policy as well Additionally, capture the predominant GL exposure base – both the units and the base (sales; square footage, etc) You are already capturing the CCA exposures – i.e., vehicle counts by type of vehicle Capturing the exposure base, such as sales, forces the UW to make sure that renewal and expiring exposure units are on the same basis

12. Audit Data Capture – How to use this info to determine client pricing adequacy • The spreadsheet – AL section:

13. Audit Data Capture – How to use this info to determine client pricing adequacy • The spreadsheet – GL section:

14. First some important assumptions: • What is the Gross Loss Ratio for the Underlying? Examples of possible selected loss ratios

15. Things to consider when selecting the Gross Loss Ratio: • On a supported book of Umbrella business analyze the client’s GL and CCA data triangles to derive the GL and CCA Gross Loss Ratios • On an unsupported (or supported) book of Umbrella business; if the client re-rates the primary get their LCMs and average credits. • On an unsupported book of business where the client rates 1xP off of Charged Premium determining the Gross Loss Ratio is a challenge. Find out who the predominant underlying carriers are and make a conservative assumption!

16. Calculations – CCA – Page 1 • Primary Auto Premium: $36,000 • Premium Type: Manual • Gross Loss Ratio for Premium Type: 60% • Primary CCA Loss Cost = $36,000 * 0.60 = $21,600

17. Calculations – CCA – Page 2 • Umbrella Attachment point = 1M • Umbrella Attachment point + Umbrella Limit = 11M • Limited Expected Value (LEV) at Umbrella Attachment point = 16,946 • LEV at Umbrella Attachment point + Umbrella Limit = 22,392 • Use your CCA distribution by vehicle type to determine your LEVs

18. Calculations – CCA – Page 3 • Umbrella Loss Cost as a % of Primary • (LEV@11M – LEV@1M) / (LEV@1M) • (22,392 – 16,946) / (16,946) = 32.1% • Umbrella Loss Cost • (Umbrella Loss Cost as a % of Primary) * (Umbrella Primary Loss Cost) • (0.321) * (21,600) = 6,941

19. What if client uses Unit rates for CCA? • Can estimate Primary CCA Premium by making assumptions regarding the primary rates by vehicle type. • The following is a rough example: • Simply apply your vehicle count by vehicle type distribution to those assumptions.

20. Calculations – GL – Page 1 • Primary GL Premium: $89,000 • Premium Type: Actual Charged • Gross Loss Ratio for Premium Type: 70% • Primary GL Loss Cost = $89,000 * 0.70 = $62,300

21. Calculations – GL – Page 2 • Umbrella Attachment point = 1M • Umbrella Attachment point + Umbrella Limit = 11M • Limited Expected Value (LEV) at Umbrella Attachment point = 27,830 • LEV at Umbrella Attachment point + Umbrella Limit = 38,034 • Use your GL distribution to Tables 1,2,3,A,B,C to determine your LEVs

22. Calculations – GL - Page 3 • Umbrella Loss Cost as a % of Primary • (LEV@11M – LEV@1M) / (LEV@1M) • (38,034 – 27,830) / (27,830) = 36.7% • Umbrella Loss Cost • (Umbrella Loss Cost as a % of Primary) * (Umbrella Primary Loss Cost) • (0.367) * (62,300) = 22,842

23. Now the Final Answer……….. • CCA Estimated Umbrella Loss Cost = $6,941 • GL Estimated Umbrella Loss Cost = $22,842 • Total Estimated Umbrella Loss Cost = $29,783 • Umbrella Charged Premium = $41,118 • Umbrella Loss Ratio for Policy XYZ = $29,783/$41,118 = 72.4%

24. Comments • At a typical 2 day audit including lost time on meet & greet, etc., you should be able to capture required info on at least 30 accounts and then derive the loss ratio from the sample • UWs can easily get comfortable with data capture if an actuary cannot attend the audit • Maintain a running database from annual audits. If there are no significant changes in excess factors, you can bring forward your loss ratio from prior years’ samples with trend and on-leveling

25. Sensitivities • Can be difficult to get precise distribution to GL Tables 1,2,3,A,B,C. Results are sensitive to Table distribution • Gross Loss Ratio selection drives results. On an unsupported Umbrella book may be difficult to determine the Gross Loss ratio • Composition of audit sample • Sometimes one well or poorly priced large policy can unduly impact the results • Audit samples often reflect larger and tougher accounts, which may not be representative of the book.

26. Advantages • Supplements results from other approaches. Please continue to analyze client historical experience and umbrella factors. • This method reflects current pricing and composition of book. • Given long-tail and volatile nature of umbrella, hard to get appropriate experience indication for recent years. This method is very responsive to current underwriting and pricing practices. • Reflects impact of minimum premiums. • Provides quantitative result of underwriting audit. • Results of this method have been in line with our expectations for given types of business

27. Extra credit…. Price Monitoring • Capture same data on expiring and renewal accounts • Additionally, capture expiring and renewal exposures for GL and CCa • For GL capture predominant exposure base in the event of multiple bases

28. Extra credit…. Price Monitoring • The Basic Concept • Umbrella Rate Change = {UMB PremiumR /ExposureR)/LEVR)} / {UMB PremiumE /ExposureE)/LEVE)} • LEV = Limited Expected Value for renewal or expiring layer as a percent of Primary • Subscripts: R = renewal; E = expiring

29. Extra credit…. Price Monitoring • Rate Monitor Spreadsheet – Renewal Info – Same info as in prior exhibits

30. Extra credit…. Price Monitoring • RENEWAL Info – you’ve seen most of this before: • GL Exposure = 1.5M in sales • AL Exposure = 26 vehicles • AL Proxy Exposure = 42,900 (vehicle counts by type * primary rate @1m by type) • Umbrella/GL Loss Cost as a % of Primary = 36.7% • Umbrella/CCA Loss Cost as a % of Primary = 32.1% • Umbrella Premium $41,118 • Umbrella limit = 10M; Attachment Point = 1M

31. Extra credit…. Price Monitoring • Rate Monitor Spreadsheet – Expiring Info

32. Extra credit…. Price Monitoring • EXPIRING Info – you haven’t seen this before: • GL Exposure = 1.25M in sales • AL Exposure = 38 vehicles • AL Proxy Exposure = 86,050 (vehicle counts by type * primary rate @1m by type) • Umbrella/GL Loss Cost as a % of Primary = 43.5% • Umbrella/CCA Loss Cost as a % of Primary = 30.4% • Umbrella Premium $40,000 (approx split GL: $28,480; CCA $11,520) • Umbrella limit = 4M; Attachment Point = 1M

33. Extra credit…. Price Monitoring • The next few slides will take you through the calculations • When actually performing the calculations you may want to isolate the change in Premium vs. the change in Exposure

34. Extra credit…. Price Monitoring STEP1: • Calculate Premium Change: • $41,118/40,000 – 1 = +2.8%

35. Extra credit…. Price Monitoring STEP 2: • Calculate GL Exposure Change: • Calculation adjusts for change in limit, attachment point and ILF curve distribution • (1.50/1.25) * (.367/.435) - 1 = +1.2% • {ExposureR /ExposureE}* {(LEV@11M – LEV@1M) / (LEV@1M)}R / {(LEV@5M – LEV@1M) / (LEV@1M)}E • Subscripts: R = renewal; E = expiring

36. Extra credit…. Price Monitoring STEP 3: • Calculate CCA Exposure Change: • Calculation adjusts for change in limit, attachment point and ILF curve distribution • (42,900/86,050) * (.321/.304) - 1 = -47.3%% • {ExposureR /ExposureE}* {(LEV@11M – LEV@1M) / (LEV@1M)}R / {(LEV@5M – LEV@1M) / (LEV@1M)}E • Subscripts: R = renewal; E = expiring

37. Extra credit…. Price Monitoring STEP 4: • Calculate Weighted Exposure Change: • ((+1.2% * 28,480) + (-47.3% * 11,520) ) / (40,000) • = -12.8%

38. Extra credit…. Price Monitoring STEP 5: • CALCULATE RATE CHANGE: • (1+.028) / (1 - .128) – 1 = +17.8%