1. CAS Seminar on Ratemaking
2005 Ratemaking Seminar
CAS Seminar on Ratemaking
Basic Techniques for an
Overall Indication
(INT-1)
March 13, 2006
Salt Lake City, Utah
Presented by:
Brian Donlan, FCAS, MAAA & Gavin Lienemann, FCAS, MAAA
Welcome to “Basic Techniques for an Overall Rate Level Indication”.
Today we will be presenting some basic ratemaking concepts and applying them to the calculation of an overall rate level indication. We will be covering a great deal of material and will be moving fairly quickly. Please stop us if you have any questions or need some further explanation.

2. Basic Techniques Overall Rate Level Indication (INT-1)
2005 Ratemaking Seminar
Basic Techniques Overall Rate Level Indication (INT-1)
Basic Ratemaking Equation and Its Considerations:
Organization of Data
Premium Adjustments
Loss Adjustments
Expense Considerations
Other Considerations
Today we are going to discuss the basic ratemaking equations and its considerations, specifically:
The organization of the data
Premium adjustments
Loss Adjustments
Expenses
We will walk through a simplified ratemaking example to allow you to see how these concepts are applied.

3. ORGANIZATION OF DATA I. CALENDAR YEAR DATA II. POLICY YEAR DATA
2005 Ratemaking Seminar
ORGANIZATION OF DATA
I. CALENDAR YEAR DATA
(standard accounting year)
II. POLICY YEAR DATA
III. ACCIDENT YEAR DATA
These are the three main methods of organizing data. I will describe each method in the next few slides.

4. ORGANIZATION OF DATA I. CALENDAR YEAR DATA
2005 Ratemaking Seminar
ORGANIZATION OF DATA
I. CALENDAR YEAR DATA
Premium and Loss transactions that occur during the year.
Loss = Payments + change in reserves during year
Matches financial statements
Data available quickly, least time lag in development
Never changes after it is calculated at the end of a year.
Premium and Loss transactions DO NOT match
Reserve changes from prior years can distort the reliability of the data for ratemaking and management purposes.

5. ORGANIZATION OF DATA II. POLICY YEAR DATA
2005 Ratemaking Seminar
ORGANIZATION OF DATA
II. POLICY YEAR DATA
Premium and Loss transactions on policies with effective dates (new or renewal) during the year.
Loss = Payments + Reserves
Premium and Loss transactions DO match
Transactions from policies effective in prior years do not distort the data for ratemaking
Data with the greatest time lag (not available until one term after end of the year.)
Exact ultimate losses cannot be finalized until all losses settled.

6. ORGANIZATION OF DATA III. ACCIDENT YEAR DATA
2005 Ratemaking Seminar
ORGANIZATION OF DATA
III. ACCIDENT YEAR DATA
Loss transactions for accidents occurring during the year. Premium transaction during the same 12 months.
Loss = Payments + Reserves
Premium and Loss transactions generally match
Transactions from accidents occurring in prior years do not distort the data for ratemaking
Data with slight time lag
Exact ultimate losses cannot be finalized until all losses settled.

7. Basic Ratemaking Equation:
2005 Ratemaking Seminar
Basic Ratemaking Equation:
Future Premiums =
Future Losses +
Future Expenses +
Underwriting Profit and Contingency Provision
The important element to remember here is that rates are estimates of FUTURE costs.
The estimates of the future premium, losses and expenses are based upon past observations of company experience, competitors, the economy, and the world in general. Ratemaking bridges the past to the future.
In the following slides we will discuss how the bridging occurs in more detail.

8. BASIC RATEMAKING METHODS
2005 Ratemaking Seminar
BASIC RATEMAKING METHODS
Loss Ratio Method
develops indicated rate change (A)
A = Experience LR / Target LR
Pure Premium (PP) Method
PP = Loss / Exposure Units
develops indicated rate per unit of exposure (R)
R = [PP + FE] / [1-VER-Profit Ratio]
There are two general pricing methodologies – LR and PP. When consistently applied to a common set of data, it can be shown that these 2 methodologies will result in identical rates.
In general, the PP method is used to set rates for a new line or product or when there are no existing rates. The loss ratio method is used to calculate the needed change in existing rates.
NOTE: THE TWO METHODS PRODUCE IDENTICAL RESULTS
WHEN IDENTICAL DATA AND ASSUMPTIONS ARE USED.

9. LOSS RATIO METHODOLOGY Fixed Expense Approach
2005 Ratemaking Seminar
LOSS RATIO METHODOLOGY Fixed Expense Approach
INDICATED (needed) RATE LEVEL CHANGE =
Projected Experience Loss + Fixed Expense Ratio
Expected (Target) Loss + Fixed Expense Ratio
- 1.0
Today we will focus on the Loss Ratio methodology. This is a quick example of how the calculation works.
For Example: 90.3%
76.6%
- 1.0 = %

10. 2005 Ratemaking Seminar
LOSS RATIO METHODOLOGY Experience Loss + Fixed Expense Ratio Projection
Premium Adjustments
Adjust to Current Rate Level
Premium Trend
Loss Adjustments
Loss Development
Loss Trend
Catastrophe Adjustments

11. RATE INDICATION WORKSHEET
2005 Ratemaking Seminar
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
EXPERIENCE Loss + Fixed Expense Ratio = ( ) / (4)
(1) Earned Premium
(2) Current Rate Level Factor
(3) Premium Trend Factor
(4) Trended Current Rate Level = (1)*(2)*(3)
(5) Accident Year 2005 Ultimate Losses & ALAE
(6) Unallocated Loss Adjustment Expense (ULAE) Factor
(7) Annual Loss Trend ___% Trend Period:
(8) Exponential Trend Factor [1.0 + (7)] ** Trend Period
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8)
Expected Catastrophe Loss & LAE for Projection Period
(11) Fixed Expense Ratio (FER)
(12) Fixed Expenses = (1) * (11)
We will be coming back to this exhibit throughout the presentation. This details the specific elements and calculations that go into the calculation of the overall rate level indication. We will be filling in the various elements as we discuss them.
B. EXPECTED (Target) Loss + Fixed Expense Ratio
C. INDICATED RATE LEVEL CHANGE = (A / B)

12. Sample Rate Level Indication Assumptions
2005 Ratemaking Seminar
Sample Rate Level Indication Assumptions
Annual Policies. Rates to be revised as of JANUARY 1, 2007
Loss Ratio Methodology
EXPERIENCE PERIOD: ACCIDENT YEAR 2005
2005 Earned Premium $3,690,000
Reported Incurred Losses as of 12/31/05: $1,900,000

13. Current Rate Level Adjustment
2005 Ratemaking Seminar
PREMIUM ADJUSTMENTS
Current Rate Level Adjustment
Loss Ratio Method analyzes the appropriateness of the CURRENT RATES for use in the future.
CRL adjustment reflects rate changes NOT already included in historical recorded premium.

14. Current Rate Level Adjustment - Common Techniques
2005 Ratemaking Seminar
PREMIUM ADJUSTMENTS
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

15. CURRENT RATE LEVEL ADJUSTMENT Extension of Exposures Method
2005 Ratemaking Seminar
CURRENT RATE LEVEL ADJUSTMENT Extension of Exposures Method
2005 Earned Exposures
Class Class 2
Territory , ,260
Territory , ,010
Territory , ,500
Current Rates
Class Class 2
Territory $ $300
Territory $ $350
Territory $ $440
Current Rates
Class Class 2
Territory $225, $678,000
Territory $349, $1,053,500
Territory $594, $1,100,000
Statewide total $3,999,625

16. CURRENT RATE LEVEL ADJUSTMENT
2005 Ratemaking Seminar
CURRENT RATE LEVEL ADJUSTMENT
Parallelogram Method A B
1/ / / / /08
Rate Change History
Date Change Rate Index
From 1/1/04 to 6/30/05 None A
7/1/ % B
(1 * 1.12)

17. CURRENT RATE LEVEL ADJUSTMENT
2005 Ratemaking Seminar
CURRENT RATE LEVEL ADJUSTMENT
Calculation of On-Level Factor - Parallelogram Method
I. Rate Index for 2005:
Percent Rate
Area of Index A B
TOTAL
II. On-Level Factor for 2005:
(1) Current Index
(2) Index
(3) On-Level Factor (1) / (2)
(4) Earned Premium $3,690,000
(5) Earned Current Rate Level $4,070,070

18. RATE INDICATION WORKSHEET
2005 Ratemaking Seminar
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
EXPERIENCE Loss + Fixed Expense Ratio = ( ) / (4)
(1) Earned Premium ,690
Current Rate Level Factor
(3) Premium Trend Factor
(4) Trended Current Rate Level = (1)*(2)*(3)
(5) Accident Year 2005 Ultimate Losses & ALAE
(6) Unallocated Loss Adjustment Expense (ULAE) Factor
(7) Annual Loss Trend ___% Trend Period:
(8) Exponential Trend Factor [1.0 + (7)] ** Trend Period
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8)
(10) Expected Catastrophe Loss & LAE for Projection Period
(11) Fixed Expense Ratio (FER)
(12) Fixed Expenses = (1) * (11)
B. EXPECTED (Target) Loss + Fixed Expense Ratio
C. INDICATED RATE LEVEL CHANGE = (A / B)

19. PREMIUM ADJUSTMENTS Premium Trend
2005 Ratemaking Seminar
PREMIUM ADJUSTMENTS
Premium Trend
To project the premium level which will exist during the period being priced. The premium trend accounts for shifts of business that will also impact the losses.
Must adjust for items such as:
Average car model year or price group
Average home value
Territorial distribution shift
Any item that would impact future premium or both premium and losses in the future except policy count

20. PREMIUM ADJUSTMENTS Premium Trend AUTO EXAMPLE - MODEL YEAR RATING
2005 Ratemaking Seminar
PREMIUM ADJUSTMENTS
Premium Trend
AUTO EXAMPLE - MODEL YEAR RATING
Over time, the average model year and symbol will “drift” toward newer more expensive vehicles.
HOMEOWNERS EXAMPLE - EXPOSURE TREND
The exposure unit used in Homeowners is the amount of insurance which is tied to the value of the home.
Both of these situations will cause average premium in the projection period to be higher than in the experience period, regardless of any rate activity.

21. Premium Adjustments Premium Trend – Determination of Trend Period
2005 Ratemaking Seminar
Premium Adjustments Premium Trend – Determination of Trend Period
Annual Policies. Rates to be revised as of JANUARY 1, 2007
EXPERIENCE PERIOD: ACCIDENT YEAR 2005
Experience Policies
Period Effective
<COVERAGE PROVIDED>
Avg. Earned Avg. Earned Date under
Date is 7/1/ Revised Rates is 1/1/2008
TREND PERIOD is 2.50 Years

22. PREMIUM ADJUSTMENTS Premium Trend Example Annual Trend = 2.0%
2005 Ratemaking Seminar
PREMIUM ADJUSTMENTS
Premium Trend Example
Year
Average Premium
@CRL
Annual Change
2001
1,000 -
2002
1,020
2.0%
2003
1,040
2004
1,061
2005
1,082
Annual Trend = 2.0%
Total Trend Factor = 1.02 ^ 2.5 = 1.051

23. RATE INDICATION WORKSHEET
2005 Ratemaking Seminar
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
EXPERIENCE Loss + Fixed Expense Ratio = ( ) / (4)
(1) Earned Premium ,690
(2) Current Rate Level Factor
(3) Premium Trend Factor
(4) Trended Current Rate Level = (1)*(2)*(3) ,278
(5) Accident Year 2005 Ultimate Losses & ALAE
(6) Unallocated Loss Adjustment Expense (ULAE) Factor
(7) Annual Loss Trend ___% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] **
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8)
(10) Expected Catastrophe Loss & LAE for Projection Period
(11) Fixed Expense Ratio (FER)
(12) Fixed Expenses = (1) * (11)
B. EXPECTED (Target) Loss + Fixed Expense Ratio
C. INDICATED RATE LEVEL CHANGE = (A / B)

24. 2005 Ratemaking Seminar
LOSS RATIO METHODOLOGY Experience Loss + Fixed Expense Ratio Projection
Loss Adjustments
Loss Development
Loss Adjustment Expenses
Allocated Loss Adjustment Expense (ALAE)
Generally included with loss
Unallocated Loss Adjustment Expense (ULAE)
Generally loaded to Loss & ALAE
Loss Trend
Catastrophe Adjustments

25. Loss Development Analysis
2005 Ratemaking Seminar
LOSS ADJUSTMENTS
Loss Development Analysis
Adjust historical losses to an expected ULTIMATE value
Reflects revisions to claim values as claims are settled
Used with policy and accident year data
Reflects IBNR reporting.
Reflects development on reported claims.
Key Factors for Consideration
Observation of historical patterns
Incurred and Paid developments
Development period

26. Accident Year Loss Development Analysis
2005 Ratemaking Seminar
Accident Year Loss Development Analysis
INCURRED METHOD - Recognizes SYSTEMATIC inaccuracy of case reserves
INCURRED LOSSES & ALAE
Adjusted for Deductibles and Cats, (000’s)
ACCIDENT Reported as of:
YEAR 12 mos mos mos mos
, , , ,548
, , , ,843
, , , ,691
, , ,836
, ,968
,900
Age to Age Development Factor =
Incurred Later Report Period divided by Prior Report Period
AY mos TO 24 mos Factor = $1,800 / $1,500 = 1.20

27. Accident Year Loss Development Analysis
2005 Ratemaking Seminar
Accident Year Loss Development Analysis
INCURRED AGE-TO-AGE FACTORS
ACCIDENT
YEAR mos mos mos
Average
Selected
x x
Cumulative
Age-to-Age Factors

28. LOSS DEVELOPMENT ANALYSIS
2005 Ratemaking Seminar
LOSS DEVELOPMENT ANALYSIS
(1) (2) (3)
Cumulative Estimated
Accident Incurred Loss Age to Ultimate Ultimate Loss
Year & 12/05 Factor (1) * (2)
, ,691
, ,836
, ,017
, ,430

29. RATE INDICATION WORKSHEET
2005 Ratemaking Seminar
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
EXPERIENCE Loss + Fixed Expense Ratio = ( ) / (4)
(1) Earned Premium ,690
(2) Current Rate Level Factor
(3) Premium Trend Factor
(4) Trended Current Rate Level = (1)*(2)*(3) ,278
(5) Accident Year 2005 Ultimate Losses & ALAE ,430
(6) Unallocated Loss Adjustment Expense (ULAE) Factor
(7) Annual Loss Trend ___% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] **
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8)
(10) Expected Catastrophe Loss & LAE for Projection Period
(11) Fixed Expense Ratio (FER)
(12) Fixed Expenses = (1) * (11)
B. EXPECTED (Target) Loss + Fixed Expense Ratio
C. INDICATED RATE LEVEL CHANGE = (A / B)

30. Unallocated Loss Adjustment Expense
2005 Ratemaking Seminar
EXPENSE ANALYSIS
Unallocated Loss Adjustment Expense
Countrywide Figures
(in $ millions)
Unallocated
Loss ULAE to
Incurred Adjustment Losses & ALAE
Year Losses & ALAE Expenses Ratio
$61, $6, %
, , %
, , %
Estimated Future ULAE Percentage %
as a percentage of Incurred Losses & ALAE

31. RATE INDICATION WORKSHEET
2005 Ratemaking Seminar
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
EXPERIENCE Loss + Fixed Expense Ratio = ( ) / (4)
(1) Earned Premium ,690
(2) Current Rate Level Factor
(3) Premium Trend Factor
(4) Trended Current Rate Level = (1)*(2)*(3) ,278
(5) Accident Year 2005 Ultimate Losses & ALAE ,430
(6) Unallocated Loss Adjustment Expense (ULAE) Factor
(7) Annual Loss Trend ___% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] **
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8)
(10) Expected Catastrophe Loss & LAE for Projection Period
(11) Fixed Expense Ratio (FER)
(12) Fixed Expenses = (1) * (11)
B. EXPECTED (Target) Loss + Fixed Expense Ratio
C. INDICATED RATE LEVEL CHANGE = (A / B)

32. LOSS ADJUSTMENTS Loss Trend Analysis
2005 Ratemaking Seminar
LOSS ADJUSTMENTS
Loss Trend Analysis
Project to the loss level predicted to exist during pricing period
Data Issues
Separate Claim frequency and Severity Trends?
Internal Vs. External Data ?
Paid, Incurred, Reported data ?
Calendar Vs. Accident year ?
Length of Historical period ?
Credibility ?
Extrapolations of Historical Data? (Least Squares Regression, Time Series, Econometric Models)

33. Other Possible Trend Sources
2005 Ratemaking Seminar
LOSS TREND ANALYSIS
Calendar Paid Losses Earned Exposures Pure
Year ($ 000’s) (000’s) Premium
, $
, $102.73
, $112.48
, $128.81
, $127.21
, $134.23
, $143.75
, $150.57
Annual Trend based on Least Squares (exponential ) %
Most Recent Annual Change ( / ) %
Other Possible Trend Sources
C.P.I. Medical Care Index %
C.P.I. Auto Body Work Index %
C.P.I. Home Maintenance & Repair Index %

34. RATE INDICATION WORKSHEET
2005 Ratemaking Seminar
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
EXPERIENCE Loss + Fixed Expense Ratio = ( ) / (4)
(1) Earned Premium ,690
(2) Current Rate Level Factor
(3) Premium Trend Factor
(4) Trended Current Rate Level = (1)*(2)*(3) ,278
(5) Accident Year 2005 Ultimate Losses & ALAE ,430
(6) Unallocated Loss Adjustment Expense (ULAE) Factor
(7) Annual Loss Trend _5.0__% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] **
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8) ,020
(10) Expected Catastrophe Loss & LAE for Projection Period
(11) Fixed Expense Ratio (FER)
(12) Fixed Expenses = (1) * (11)
B. EXPECTED (Target) Loss + Fixed Expense Ratio
C. INDICATED RATE LEVEL CHANGE = (A / B)

35. LOSS ADJUSTMENTS CATASTROPHES Example:
2005 Ratemaking Seminar
LOSS ADJUSTMENTS
CATASTROPHES
Catastrophes should be eliminated from losses
Average provision should be used as a loss loading
Example:
Expected Annual Catastrophe Loss & ALAE
for Projection Period 394
(2) Projected Premium 4,278
(3) Catastrophe Load (1) / (2) 9.21%

36. RATE INDICATION WORKSHEET
2005 Ratemaking Seminar
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
EXPERIENCE Loss + Fixed Expense Ratio = ( ) / (4)
(1) Earned Premium ,690
(2) Current Rate Level Factor
(3) Premium Trend Factor
(4) Trended Current Rate Level = (1)*(2)*(3) ,278
(5) Accident Year 2005 Ultimate Losses & ALAE ,430
Unallocated Loss Adjustment Expense (ULAE) Factor
Annual Loss Trend _5.0__% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] **
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8) ,020
(10) Expected Catastrophe Loss & LAE for Projection Period
(11) Fixed Expense Ratio (FER)
(12) Fixed Expenses = (1) * (11)
B. EXPECTED (Target) Loss + Fixed Expense Ratio
C. INDICATED RATE LEVEL CHANGE = (A / B)

37. UNDERWRITING EXPENSES
2005 Ratemaking Seminar
UNDERWRITING EXPENSES
Commissions and premium taxes vary directly with premiums
Other acquisition and general expenses are “fixed”
Not really fixed
Vary with inflation

38. Other Than Loss Adjustment
2005 Ratemaking Seminar
EXPENSE ANALYSIS
Direct Expenses
Other Than Loss Adjustment
Countrywide Figures
(In $ Millions)
Selected
$ % $ % $ % %
Written Premium , , ,
Commissions , , ,
Other
Acquisition , , ,
Administrative , , ,
Taxes, Licenses
& Fees , , ,

39. DEVELOPMENT of EXPECTED LOSS RATIO & FIXED EXPENSE RATIO
2005 Ratemaking Seminar
DEVELOPMENT of
EXPECTED LOSS RATIO &
FIXED EXPENSE RATIO
Total Variable Fixed
Commissions % % %
Other Acquisition
General
Taxes, Licenses & Fees
Profit & Contingency
Other Costs *
TOTAL % % %
TARGET Loss, LAE & Fixed Expense Ratio = % % = 76.6%
* Policyholder Dividends, Involuntary Market Costs, Guaranty Fund Assessments, Etc. (if allowable)

40. RATE INDICATION WORKSHEET
2005 Ratemaking Seminar
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
EXPERIENCE Loss + Fixed Expense Ratio = ( ) / (4)
(1) Earned Premium ,690
(2) Current Rate Level Factor
(3) Premium Trend Factor
(4) Trended Current Rate Level = (1)*(2)*(3) ,278
(5) Accident Year 2005 Ultimate Losses & ALAE ,430
(6) Unallocated Loss Adjustment Expense (ULAE) Factor
(7) Annual Loss Trend _5.0__% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] **
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8) ,020
(10) Expected Catastrophe Loss & LAE for Projection Period
(11) Fixed Expense Ratio (FER) %
(12) Fixed Expenses = (1) * (11)
90.3%
B. EXPECTED (Target) Loss + Fixed Expense Ratio %
C. INDICATED RATE LEVEL CHANGE = (A / B) %

41. OTHER CONSIDERATIONS CREDIBILITY DEDUCTIBLES
2005 Ratemaking Seminar
OTHER CONSIDERATIONS
CREDIBILITY
DEDUCTIBLES
TYPES (Straight, Franchise, Percentage)
Must consider deductibles offered
Will the offerings change; will the mix of change
Deductible relativities based on Loss Elimination Ratios
LIMITS
Basic limits data used for auto indication; Increased limits reviewed separately
Basic limits review emphasizes frequency of loss, not severity

42. BASIC RATEMAKING TECHNIQUES
2005 Ratemaking Seminar
BASIC RATEMAKING TECHNIQUES
Suggested Readings
Foundations in Casualty Actuarial Science,
Ratemaking by Charles L. McClenahan, Chapter 2, pages
Statement of Principles Regarding Property and Casualty
Insurance Ratemaking,
CAS Committee on Ratemaking (1988).
Insurance Operations,
Webb, Harrison and Markham, CPCU Text, Chapters 10 and 11.
Introduction to Ratemaking and Loss Reserving for
Property and Casualty Insurance,
by Robert L. Brown, Chapter 3 - Ratemaking
Trend and Loss Development Factors,
by Charles F. Cook, 1970 Proceedings of the Casualty Actuarial Society