1. Experience Rating for Excess Of Loss Contracts 2004 CAS Ratemaking Seminar
March 11-12, 2004
Elliot Burn
Wyndham Franklin Plaza Hotel
Philadelphia, PA

2. Overview Introduction Basic Steps of Burning Cost Method
Loss and Premium Adjustments
Calculating the Loss Cost & Rate
Potential Problems with Burning Cost Method
Alternate Method – Curve Fitting
Potential Problems with Curve Fitting
Advanced Contract Features
Annual Aggregate Deductibles
Reinstatement Provisions

3. Introduction

4. Introduction How does experience rating work?
Trended losses to a layer are aggregated and developed to “ultimate.”
Ultimate losses are compared to on-level premium to create loss costs.
Loss costs are loaded for profit and expense to determine final rate.
What is the assumption of experience rating?
Historical experience, adjusted properly, is a predictor of future experience.

5. Basic Steps of Burning Cost Method

6. Basic Steps of Burning Cost Method
Trend individual loss amounts.
Cap at policy limits(?)
Distribute individual loss amounts to the layer(s).
Aggregate layer experience by historical treaty period.
Apply excess loss development factors.
Apply rate changes and exposure trend to on-level the subject premium.
Divide losses by on-level premium to derive historical loss cost.
Load loss cost for expenses and profit to calculate the final rate.

7. Summary Exhibit– Our Goal

8. Loss Adjustments

9. Loss Adjustments
Example: Assume you are trying to obtain a loss cost for the layer $100,000 xs $100,000.

10. Loss Adjustments Step 1: Trend losses. What are some sources of trend?
Actual company data, when sufficient experience is available.
External data, such as statistical bureaus or the US Government.

11. Loss Adjustments Sources of Trend Using External Data
Bureau of Labor Statistics – US Department of Labor (BLS)
Consumer Price Indices (CPI)
Wholesale Price Indices (WPI)
Average Weekly Gross Earnings by Industry
Office of Business Economics – US Department of Commerce (OBE)
National Income and Products Accounts (NIP)
Average Per Capita Earnings by Industry
Average Per Capita Income and Product
National Council on Compensation Insurance
Workers Compensation law amendment rate level changes
American Appraisal Company Construction Cost Index
Boeckh Construction Cost Index
A.M. Best Aggregates and Averages

12. “Correct” Method: Trend only portion of loss above policy limit…
Loss Adjustments
Step 1: Trend losses.
Is this correct?
“Correct” Method: Trend only portion of loss above policy limit…
171,046

13. Note that this loss isn’t capped…
Loss Adjustments
Step 2: Cap Losses at Policy Limits.
Note that this loss isn’t capped…

14. Loss Adjustments
Steps 3 & 4: Distribute individual loss amounts to each layer and aggregate layer experience by historical treaty period.

15. Loss Adjustments Loss Development Analysis
Adjust historical losses to an expected ULTIMATE value
Reflects revisions to claim values as claims are settled
Reflects IBNR reporting
Reflects development on reported claims
Key Factors for Consideration
Observation of historical patterns
Incurred and paid developments
Development period

16. Loss Adjustments
Loss Development Analysis

17. Loss Adjustments Loss Development Analysis
Often, excess loss dev’t factors are not very credible.
What are some other options?

18. Are these the only sources??
Loss Adjustments
Are these the only sources??
Sources of Excess LDF’s
Insurance Services Organization (ISO)
Lines of Business: General Liability, Auto Liability, Medical Professional Liability
Advantages: Homogenous data, numerous layers
Disadvantages: Lack of credible high hazard/high layer data (for GL & AL), Medical Professional Liability data represents small portion of market share
Reinsurance Association of America (RAA)
Lines of Business: General Liability, Auto Liability, Medical Professional Liability, and Workers Compensation
Advantages: Represents all data being reinsured, more credible high layer data
Disadvantages: Net of retrocessions, may include some mass torts (e.g. breast implants), losses excess of company retentions

19. Here we are using ISO GL factors…
Loss Adjustments
Here we are using ISO GL factors…
Step 5: Apply excess loss development factors.

20. Premium Adjustments

21. Premium Adjustments Two Types of Premium Adjustments: Rate Level
Premium (Exposure) Trend

22. Premium Adjustments – Rate Level Current Rate Level Adjustment – Common Techniques
Extension of Exposures
Re-rate each exposure (policy)
Requires extensive detail and mechanization
Most accurate method
Parallelogram Method
Easier method
Specific policy information not required
Assumes even distribution of policies written throughout the year

23. Premium Adjustments – Rate Level Extension of Exposures Method
Quick Example:
2003 Earned Exposures
Premium at Current Rates
Current Rates

24. Premium Adjustments – Rate Level Parallelogram Method
Quick Example:

25. Premium Adjustments – Rate Level Calculation of On-Level Factor - Parallelogram Method

26. Premium Adjustments – Exposure Trend
What is the purpose of Exposure Trend?
To project the premium level which will exist during the period being priced. The exposure trend will not account for shifts of business.
Must adjust for items such as:
Average car model year or price group
Average home value
Sales
Payroll
Don’t we already account for this in the rate level adjustment?!?

27. Premium Adjustments
Step 6: Apply rate changes and exposure trend to on-level the subject premium.
Back to our example…

28. Calculating the Loss Cost & Rate

29. Calculating the Loss Cost & Rate
Step 7: Divide losses by on-level premiums to derive historical loss costs.
Is that your final answer?!

30. Calculating the Loss Cost & Rate
Three Types of Reinsurer Expenses:
Expenses varying with premium
Ceding commission paid to the reinsured
Brokerage fees (where applicable)
Federal excise taxes (where applicable)
Profit* (*Not really an “expense”)
Fixed Expenses
General overhead costs (salaries, real estate)
Underwriting and claim audit expenses
Expenses varying with Losses
Reinsurer’s unallocated loss adjustment expenses

31. Calculating the Loss Cost & Rate
Step 8: Load selected loss cost for expenses to calculate the final premium. Divide by subject premium to determine rate.
Premium = [Expected Loss x (1+ULAE) + Fixed Expenses]
(1 – Variable Expense %)(1-Profit Load)
Back to our Example…
ULAE = 5%
Fixed Expenses = 10,000
Variable Expense % = 12%
Expected Loss = 1.1% x40,000,000 = 440,000
Profit Load = 5%
Premium = [440,000 x(1+0.05)+10,000] = 564,593
(1– 0.12)(1-0.05)
Rate=Premium/Subject Premium=564,593/40,000,000=1.4%

32. Potential Problems with Experience Rating

33. Potential Problems with Experience Rating
Presence or absence of a few large claims drives the indicated rates.
Order of application of development, trend, and capping makes a difference.
Trending individual claims past policy limits.
Impact of current policy limit profile vs. historicals.
History not reflective of current situation: reserving practices, type of business, coverage, etc.
“Free cover”

34. Alternate Method – Curve Fitting

35. Curve Fitting What is curve fitting? Assumptions
Estimating a parametric frequency distribution and a parametric severity distribution from given claim data.
Assumptions
That a curve fit to the loss data after appropriate adjustments is an appropriate estimator of future loss.
Frequency and severity are independent.
What data is required?
Large Loss Listing with Policy Limits, Excess of a Truncation Point
Historical & Prospective Exposure Base
On-Leveling Factors

36. Curve Fitting Common Frequency Distributions
Poisson
Negative Binomial
Common Severity Distributions
Gamma
Mixed Exponential
Pareto
Issue: One curve doesn’t necessarily fit all the data.
Choose truncation point carefully. Interested in the tail of the distribution.

37. Potential Problems with Curve Fitting
Individual claims either need to be developed to ultimate (which is difficult to do) or are assumed to be at ultimate (not always a good assumption).
Don’t use aggregate LDF’s to develop individual losses.
How do you determine the # of IBNR claims?
One loss distribution often doesn’t fit all of the data.

38. Advanced Contract Features

39. Advanced Contract Features
Annual Aggregate Deductibles
Reinstatement Provisions

40. Annual Aggregate Deductibles
What is an Annual Aggregate Deductible (AAD)?
When ceding company retains the 1st X dollar amount of losses per year.
Two ways to estimate savings from AAD:
Estimate directly from experience rating if set at sufficiently low level.
Better approach: use an aggregate distribution model.
Important Point: Adding an AAD to a contract doesn’t proportionately decrease the expected losses.

41. Annual Aggregate Deductibles
Expected Cumulative Loss Distributions
Before AAD After $1.5M AAD
Losses start hitting the layer here.

42. Reinstatement Provisions
What is a Reinstatement Provision?
It puts a limit on either the number of occurrences or the aggregate losses that will be paid under a contract.
Free or paid
“Pro-rata as to amount” or “pro-rata as to time”
Reinstatement provisions are typically found on high excess layers, where loss tends to be either 0 or a full limit loss.
Want to use an aggregate distribution model to determine the expected # of reinstatements and the total expected reinstatement premium.

43. Reinstatement Provisions
Example of “Pro-Rata as to Amount” Reinstatement
Occurrence Limit: $10,000,000
Annual Premium: $3,000,000
Reinstatement Provision: 110%, pro-rata as to amount
Actual Loss Amount: $5,000,000
Reinstatement Premium = $3,000,000 x 1.10 x 5/10 =
$1,650,000

44. Advanced Contract Features
Other
Advanced Contract Features
Other Aggregate Contract Features
Stop-Loss
Multi-Year
Adjustable Features
Swing-Rated Premiums
Sliding Scale Commissions
Profit Commissions
Loss Corridors
Loss Caps

45. Questions?

46. References
Clark, David R. “Basics of Reinsurance Pricing,” CAS Study Note,1996.
McClenahan, Charles L. “Ratemaking,” Foundations of Casualty Actuarial Science, 1996.
Masterson, N.E. “Economic Factors in Liability and Property Insurance Claim Costs, ,” Proceedings of the Casualty Actuary Society, 1968.