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
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
ORGANIZATION OF DATA
I. CALENDAR YEAR DATA
(standard accounting year)
II. POLICY YEAR DATA
III. ACCIDENT YEAR DATA
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.
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.
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.
Basic Ratemaking Equation:
Future Premiums =
Future Losses +
Future Expenses +
Underwriting Profit and Contingency Provision
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]
NOTE: THE TWO METHODS PRODUCE IDENTICAL RESULTS
WHEN IDENTICAL DATA AND ASSUMPTIONS ARE USED.
LOSS RATIO METHODOLOGY
Fixed Expense Approach
INDICATED (needed) RATE LEVEL CHANGE
=
Projected Experience Loss + Fixed Expense Ratio
1.0
Expected (Target) Loss + Fixed Expense Ratio
For Example:
90.3% - 1.0 = + 17.9%
76.6%
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
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
A.
EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1)
(2)
(3)
(4)
2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trended Premium @ 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) - 1.0. . . . . . . . . . . . . . .
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
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.
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
CURRENT RATE LEVEL ADJUSTMENT
Extension of Exposures Method
2005 Earned Exposures
Class 1
1,500
1,995
2,700
Territory 1
Territory 2
Territory 3
Class 2
2,260
3,010
2,500
Current Rates
Class 1
$150
$175
$220
Territory 1
Territory 2
Territory 3
Class 2
$300
$350
$440
Premium @ Current Rates
Territory 1
Territory 2
Territory 3
Statewide total
Class 1
$225,000
$349,125
$594,000
Class 2
$678,000
$1,053,500
$1,100,000
$3,999,625
CURRENT RATE LEVEL ADJUSTMENT
Parallelogram Method
A
B
1/04
1/05
1/06
1/07
1/08
Rate Change History
Date
Change
Rate Index
From 1/1/04 to 6/30/05
None
1.000
A
7/1/05
+ 12%
1.12
(1 * 1.12)
B
CURRENT RATE LEVEL ADJUSTMENT
Calculation of On-Level Factor - Parallelogram Method
I. Rate Index for 2005:
Area
Percent
of 2005
Rate
Index
A
B
87.5
12.5
1.000
1.120
100.0
1.015
TOTAL
II. On-Level Factor for 2005:
(1) Current Index
(2) 2005 Index
(3) On-Level Factor (1) / (2)
1.120
1.015
1.103
(4) 2005 Earned Premium
$3,690,000
(5) 2005 Earned Premium @ Current Rate Level
$4,070,070
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
A.
EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1)
(2)
(3)
(4)
2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690
Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.103
Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trended Premium @ 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) - 1.0 . . . . . . . . . . . . . . .
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
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.
Premium Adjustments
Premium Trend – Determination of Trend Period
• Annual Policies. Rates to be revised as of JANUARY 1, 2007
• EXPERIENCE PERIOD: ACCIDENT YEAR 2005
2005
Experience
Period
2006
2007
Policies
Effective
2008
<COVERAGE PROVIDED>
Avg. Earned
Date is 7/1/05
Avg. Earned Date under
Revised Rates is 1/1/2008
TREND PERIOD is 2.50 Years
PREMIUM ADJUSTMENTS
Premium Trend Example
Year
Average
Premium
@CRL
Annual
Change
2001
1,000
-
2002
1,020
2.0%
2003
1,040
2.0%
2004
1,061
2.0%
2005
1,082
2.0%
Annual Trend = 2.0%
Total Trend Factor = 1.02 ^ 2.5 = 1.051
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
A.
EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1)
(2)
(3)
(4)
2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trended Premium @ 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: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . .
(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) - 1.0 . . . . . . . . . . . . . . .
3,690
1.103
1.051
4,278
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
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
Accident Year Loss Development Analysis
INCURRED METHOD - Recognizes SYSTEMATIC inaccuracy of case reserves
INCURRED LOSSES & ALAE
Adjusted for Deductibles and Cats, (000’s)
ACCIDENT
YEAR
2000
2001
2002
2003
2004
2005
12 mos
1,200
1,300
1,400
1,500
1,600
1,900
Reported as of:
24 mos
36 mos
1,488
1,548
1,755
1,843
1,708
1,691
1,800
1,836
1,968
48 mos
1,548
1,843
1,691
Age to Age Development Factor =
Incurred Loss @ Later Report Period divided by Loss @ Prior Report Period
AY 2003 12 mos TO 24 mos Factor = $1,800 / $1,500 = 1.20
Accident Year Loss Development Analysis
INCURRED AGE-TO-AGE FACTORS
ACCIDENT
YEAR
12-24 mos
24-36 mos
36-48 mos
2000
2001
2002
2003
2004
1.24
1.35
1.22
1.20
1.23
1.04
1.05
0.99
1.02
1.00
1.00
1.00
Average
1.248
1.025
1.000
Selected
1.248
1.025
1.000
x
Cumulative
Age-to-Age Factors
1.279
x
1.025
1.000
LOSS DEVELOPMENT ANALYSIS
(1)
Accident
Year
2002
Incurred Loss
& ALAE @ 12/05
1,691
(2)
Cumulative
Age to Ultimate
Factor
1.000
(3)
Estimated
Ultimate Loss
(1) * (2)
1,691
2003
1,836
1.000
1,836
2004
1,968
1.025
2,017
2005
1,900
1.279
2,430
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
A.
EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1)
(2)
(3)
(4)
2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . .
3,690
1.103
1.051
4,278
(5) Accident Year 2005 Ultimate Losses & ALAE . . . . . . . . . . . . . . . . . . 2,430
(6) Unallocated Loss Adjustment Expense (ULAE) Factor. . . . . . . . . . .
(7) Annual Loss Trend ___% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . .
(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) - 1.0 . . . . . . . . . . . . . . .
EXPENSE ANALYSIS
Unallocated Loss Adjustment Expense
Countrywide Figures
(in $ millions)
Year
Incurred
Losses & ALAE
Unallocated
Loss
Adjustment
Expenses
ULAE to
Losses & ALAE
Ratio
2003
2004
2005
$61,200
79,000
82,300
$6,500
7,800
8,300
10.6%
9.9%
10.1%
Estimated Future ULAE Percentage
as a percentage of Incurred Losses & ALAE
10.0%
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
A.
EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1)
(2)
(3)
(4)
2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . .
3,690
1.103
1.051
4,278
(5) Accident Year 2005 Ultimate Losses & ALAE . . . . . . . . . . . . . . . . . . 2,430
(6) Unallocated Loss Adjustment Expense (ULAE) Factor. . . . . . . . . . . 1.10
(7) Annual Loss Trend ___% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . .
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8) . . . . . . . . . . .
(10) Expected Catastrophe Loss & LAE for Projection Period. . . . . . . . .
(11) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(12) Fixed Expenses = (1) * (11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0. . . . . . . . . . . . . . .
31
LOSS ADJUSTMENTS
Loss Trend Analysis
 Project to the loss level predicted to exist during pricing period

Data Issues
• Separate Claim frequency and Severity Trends?
• Internal Vs. External Data ?
• Paid, Incurred, Reported data ?
• Calendar Vs. Accident year ?
• Length of Historical period ?
• Credibility ?
• Extrapolations of Historical Data? (Least Squares Regression,
Time Series, Econometric Models)
LOSS TREND ANALYSIS
Calendar
Year
1998
1999
2000
2001
2002
2003
2004
2005
Paid Losses Earned Exposures
($ 000’s) (000’s)
Premium
1,212
13.0
1,356
13.2
1,496
13.3
1,726
13.4
1,730
13.6
1,839
13.7
1,984
13.8
2,108
14.0
Pure
$ 93.23
$102.73
$112.48
$128.81
$127.21
$134.23
$143.75
$150.57
Annual Trend based on Least Squares (exponential )
6.6%
Most Recent Annual Change (150.57 / 143.75)
4.7%
Other Possible Trend Sources
C.P.I. Medical Care Index
C.P.I. Auto Body Work Index
C.P.I. Home Maintenance & Repair Index
3 - 4%
4 - 5%
3 - 4%
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
A.
EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1)
(2)
(3)
(4)
2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . .
3,690
1.103
1.051
4,278
(5) Accident Year 2005 Ultimate Losses & ALAE . . . . . . . . . . . . . . . . . . 2,430
(6) Unallocated Loss Adjustment Expense (ULAE) Factor. . . . . . . . . . . 1.10
(7) Annual Loss Trend _5.0__% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . . 1.13
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8) . . . . . . . . . . . . 3,020
(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) - 1.0. . . . . . . . . . . . . . .
LOSS ADJUSTMENTS
CATASTROPHES
 Catastrophes should be eliminated from losses
 Average provision should be used as a loss loading
Example:
(1) Expected Annual Catastrophe Loss & ALAE
for Projection Period
394
(2) Projected Premium
4,278
(3) Catastrophe Load (1) / (2)
9.21%
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
A.
EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1)
(2)
(3)
(4)
2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . .
3,690
1.103
1.051
4,278
(5) Accident Year 2005 Ultimate Losses & ALAE . . . . . . . . . . . . . . . . . . 2,430
(6) Unallocated Loss Adjustment Expense (ULAE) Factor. . . . . . . . . . . 1.10
(7) Annual Loss Trend _5.0__% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . . 1.13
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8) . . . . . . . . . . . . 3,020
(10) Expected Catastrophe Loss & LAE for Projection Period. . . . . . . . . 394
(11) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(12) Fixed Expenses = (1) * (11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0. . . . . . . . . . . . . . .
UNDERWRITING EXPENSES
 Commissions and premium taxes vary directly with premiums
 Other acquisition and general expenses are “fixed”
• Not really fixed
• Vary with inflation
EXPENSE ANALYSIS
Direct Expenses
Other Than Loss Adjustment
Countrywide Figures
(In $ Millions)
2003
Written Premium
Commissions
2004
2005
Selected
$
%
$
%
$
%
107,400
100
121,600
100
142,400
100
19,200
15.5
22,100
15.5
15.5
16,647 15.5
%
Other
Acquisition
6,229
5.8
4,700
5.8
5,300
5.8
5.8
Administrative
6,874
6.4
6,200
6.4
8,200
6.4
6.4
3,652
3.4
4,100
3.4
4,900
3.4
3.4
Taxes, Licenses
& Fees
DEVELOPMENT of
EXPECTED LOSS RATIO &
FIXED EXPENSE RATIO
Total
Commissions
Variable
Fixed
15.5%
15.5%
Other Acquisition
5.8
0.0
5.8
General
6.4
0.0
6.4
Taxes, Licenses & Fees
3.4
3.4
0.0
Profit & Contingency
4.0
4.0
0.0
Other Costs *
0.5
0.5
0.0
35.6%
23.4%
12.2%
TOTAL
TARGET Loss, LAE & Fixed Expense Ratio = 100.0% - 23.4% = 76.6%
* Policyholder Dividends, Involuntary Market Costs, Guaranty Fund Assessments, Etc. (if allowable)
0.0%
RATE INDICATION WORKSHEET
Loss Ratio Methodology - Fixed Expense Approach
A.
EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . . 90.3%
(1)
(2)
(3)
(4)
2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . .
3,690
1.103
1.051
4,278
(5) Accident Year 2005 Ultimate Losses & ALAE . . . . . . . . . . . . . . . . . . 2,430
(6) Unallocated Loss Adjustment Expense (ULAE) Factor. . . . . . . . . . . 1.10
(7) Annual Loss Trend _5.0__% Trend Period: 2.5 years
(8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . . 1.13
(9) Trended Ultimate Losses and LAE = (5) * (6) * (8) . . . . . . . . . . . . 3,020
(10) Expected Catastrophe Loss & LAE for Projection Period. . . . . . . . . 394
(11) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .12.2%
(12) Fixed Expenses = (1) * (11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .76.6%
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0. . . . . . . . . . . . . . . +17.9%
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
BASIC RATEMAKING TECHNIQUES
Suggested Readings
Foundations in Casualty Actuarial Science,
Ratemaking by Charles L. McClenahan, Chapter 2, pages 25-90.
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