Experience Rating for Excess Of Loss
Contracts
2004 CAS Ratemaking Seminar
March 11-12, 2004
Elliot Burn
Wyndham Franklin Plaza Hotel
Philadelphia, PA
1
Overview


Introduction
Basic Steps of Burning Cost Method




Alternate Method – Curve Fitting


Loss and Premium Adjustments
Calculating the Loss Cost & Rate
Potential Problems with Burning Cost Method
Potential Problems with Curve Fitting
Advanced Contract Features


Annual Aggregate Deductibles
Reinstatement Provisions
2
Introduction
3
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.
4
Basic Steps of Burning
Cost Method
5
Basic Steps of Burning Cost Method
1.
2.
3.
4.
5.
6.
7.
8.
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.
6
Summary Exhibit– Our Goal
7
Loss Adjustments
8
Loss Adjustments
Example: Assume you are trying to obtain a loss cost for
the layer $100,000 xs $100,000.
9
Loss Adjustments
Step 1: Trend losses.
 What are some sources of trend?
Actual company data, when sufficient experience is
available.
2. External data, such as statistical bureaus or the US
Government.
1.
10
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 Council on Compensation Insurance




National Income and Products Accounts (NIP)
Average Per Capita Earnings by Industry
Average Per Capita Income and Product
Workers Compensation law amendment rate level changes
American Appraisal Company Construction Cost Index
Boeckh Construction Cost Index
A.M. Best Aggregates and Averages
11
Loss Adjustments
Step 1: Trend losses.
Is this
correct?
171,046
“Correct”
Method:
Trend only
portion of
loss above
policy
limit…
12
Loss Adjustments
Step 2: Cap Losses at Policy Limits.
Note that
this loss
isn’t
capped…
13
Loss Adjustments
Steps 3 & 4: Distribute individual loss amounts to each
layer and aggregate layer experience by historical
treaty period.
14
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
15
Loss Adjustments
Loss Development Analysis
16
Loss Adjustments
Loss Development Analysis
Often, excess loss dev’t factors are not very credible.
 What are some other options?
17
Loss Adjustments
Sources of Excess LDF’s

Insurance Services Organization (ISO)




Are
these
the only
sources?
?
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
18
Loss Adjustments
Step 5: Apply excess loss development factors.
Here we
are using
ISO GL
factors…
19
Premium Adjustments
20
Premium Adjustments
Two Types of Premium Adjustments:
1.
2.
Rate Level
Premium (Exposure) Trend
21
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
22
Premium Adjustments – Rate Level
Extension of Exposures Method
Quick Example:
2003 Earned Exposures
Premium at Current Rates
Current Rates
23
Premium Adjustments – Rate Level
Parallelogram Method
Quick Example:
24
Premium Adjustments – Rate Level
Calculation of On-Level Factor - Parallelogram Method
25
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?!?
26
Premium Adjustments
Step 6: Apply rate changes and exposure trend to onlevel the subject premium.
Back to
our
example…
27
Calculating the Loss
Cost & Rate
28
Calculating the Loss Cost & Rate
Step 7: Divide losses by on-level premiums to
derive historical loss costs.
Is that
your
final
answer?!
29
Calculating the Loss Cost & Rate
Three Types of Reinsurer Expenses:
1.
Expenses varying with premium
 Ceding commission paid to the reinsured
 Brokerage fees (where applicable)
 Federal excise taxes (where applicable)
 Profit* (*Not really an “expense”)
2.
Fixed Expenses
 General overhead costs (salaries, real estate)
 Underwriting and claim audit expenses
3.
Expenses varying with Losses
 Reinsurer’s unallocated loss adjustment expenses
30
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%
31
Potential Problems
with
Experience Rating
32
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”
33
Alternate Method –
Curve Fitting
34
Curve Fitting

What is curve fitting?


Assumptions



Estimating a parametric frequency distribution and a parametric severity
distribution from given claim data.
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
35
Curve Fitting

Common Frequency Distributions



Common Severity Distributions




Poisson
Negative Binomial
Gamma
Mixed Exponential
Pareto
Issue: One curve doesn’t necessarily fit all the data.
36
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.
37
Advanced
Contract Features
38
Advanced Contract Features
Annual Aggregate Deductibles
 Reinstatement Provisions

39
Annual Aggregate Deductibles

What is an Annual Aggregate Deductible (AAD)?


Two ways to estimate savings from AAD:
1.
2.

When ceding company retains the 1st X dollar amount of
losses per year.
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.
40
Annual Aggregate Deductibles
Expected Cumulative Loss Distributions
Before AAD
After $1.5M AAD
Losses
start
hitting the
layer here.
41
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.
42
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
43
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
44
Questions?
45
References
1.
2.
3.
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, 1935-1967,”
Proceedings of the Casualty Actuary Society, 1968.
46