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CAS Seminar on Ratemaking
Basic Techniques for anBasic Techniques for an
Overall IndicationOverall Indication (INT-1)(INT-1)
March 13, 2006 Salt Lake City, Utah
Presented by: Presented by:
Brian Donlan, FCAS, MAAA & Gavin Lienemann, Brian Donlan, FCAS, MAAA & Gavin Lienemann, FCAS, MAAAFCAS, MAAA
Basic TechniquesOverall 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 DATAPremium 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 DATAPremium 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 DATALoss 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 RESULTSWHEN IDENTICAL DATA AND ASSUMPTIONS ARE USED.
LOSS RATIO METHODOLOGYFixed Expense Approach
INDICATED (needed) RATE LEVEL CHANGE =INDICATED (needed) RATE LEVEL CHANGE =
Projected Experience Loss + Fixed Expense RatioProjected Experience Loss + Fixed Expense RatioExpected (Target) Loss + Fixed Expense RatioExpected (Target) Loss + Fixed Expense Ratio
- 1.0- 1.0
For Example:For Example: 90.3%90.3%76.6%76.6%
- 1.0 = + 17.9%- 1.0 = + 17.9%
LOSS RATIO METHODOLOGYExperience Loss + Fixed Expense Ratio Projection
Premium Adjustments Adjust to Current Rate
Level Premium Trend
Loss Adjustments Loss Development Loss Trend Catastrophe Adjustments
RATE INDICATION WORKSHEETRATE INDICATION WORKSHEETLoss Ratio Methodology - Fixed Expense ApproachLoss Ratio Methodology - Fixed Expense Approach
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .
A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (2) Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(3) Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (4) 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0. . . . . . . . . . . . . . .
Sample Rate Level IndicationAssumptions
• 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 ADJUSTMENTSPREMIUM 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 ADJUSTMENTSPREMIUM 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 ClassClass 1 Class 22
Territory 1Territory 1 1,500 2,260Territory 2Territory 2 1,995 3,010Territory 3Territory 3 2,700 2,500
Class 1 Class 2Class 1 Class 2
Territory 1Territory 1 $150 $300Territory 2Territory 2 $175 $350Territory 3Territory 3 $220 $440
Class 1 Class 2Class 1 Class 2
Territory 1Territory 1 $225,000 $678,000Territory 2Territory 2 $349,125 $1,053,500Territory 3Territory 3 $594,000 $1,100,000
Current Rates
Premium @ Current Rates
Statewide totalStatewide total $3,999,625
AA BB
1/04 1/05 1/06 1/07 1/08
CURRENT RATE LEVEL ADJUSTMENTCURRENT RATE LEVEL ADJUSTMENT
Parallelogram Method
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 B(1 * 1.12)
CURRENT RATE LEVEL ADJUSTMENTCURRENT RATE LEVEL ADJUSTMENT
Calculation of On-Level Factor - Parallelogram Method
I. Rate Index for 2005:I. Rate Index for 2005:
Percent Rate Area of 2005 Index
A 87.5 1.000 B 12.5 1.120 TOTAL 100.0 1.015
II. On-Level Factor for 2005:II. On-Level Factor for 2005: (1) Current Index 1.120 (2) 2005 Index 1.015 (3) On-Level Factor (1) / (2) 1.103
(4) 2005 Earned Premium $3,690,000
(5) 2005 Earned Premium @ Current Rate Level $4,070,070
RATE INDICATION WORKSHEETRATE INDICATION WORKSHEETLoss Ratio Methodology - Fixed Expense ApproachLoss Ratio Methodology - Fixed Expense Approach
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . .
A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690
(2) Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.103(3) Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
(4) 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0 . . . . . . . . . . . . . . .
PREMIUM ADJUSTMENTSPREMIUM ADJUSTMENTS
Premium Trend
To projectproject 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 except
policy countpolicy count
PREMIUM PREMIUM ADJUSTMENTSADJUSTMENTS
Premium TrendPremium Trend AUTO EXAMPLE - MODEL YEAR RATINGAUTO EXAMPLE - MODEL YEAR RATING
Over time, the average model year and symbol will Over time, the average model year and symbol will “drift” toward newer more expensive vehicles. “drift” toward newer more expensive vehicles.
HOMEOWNERS EXAMPLE - EXPOSURE TRENDHOMEOWNERS EXAMPLE - EXPOSURE TRENDThe exposure unit used in Homeowners is the amount of The exposure unit used in Homeowners is the amount of insurance which is tied to the value of the home.insurance which is tied to the value of the home.
Both of these situations will cause average premium in Both of these situations will cause average premium in the projection period to be higher than in the the projection period to be higher than in the experience period, regardless of any rate activity.experience period, regardless of any rate activity.
Premium AdjustmentsPremium Trend – Determination of Trend Period
• Annual Policies. Rates to be revised as of JANUARY 1, 2007
• EXPERIENCE PERIOD: ACCIDENT YEAR 2005
2005 2006 2007 2008 Experience Policies Period Effective
<COVERAGE PROVIDED> Avg. Earned Avg. Earned Date under Date is 7/1/05 Revised Rates is 1/1/2008
TREND PERIOD is 2.50 Years
PREMIUM ADJUSTMENTSPREMIUM ADJUSTMENTS
Premium Trend Example
Annual Trend = 2.0%Annual Trend = 2.0%Total Trend Factor = 1.02 ^ 2.5 = 1.051Total Trend Factor = 1.02 ^ 2.5 = 1.051
Year
Average Premium
@CRLAnnual Change
2001 1,000 -
2002 1,020 2.0%
2003 1,040 2.0%
2004 1,061 2.0%
2005 1,082 2.0%
RATE INDICATION WORKSHEETRATE INDICATION WORKSHEETLoss Ratio Methodology - Fixed Expense ApproachLoss Ratio Methodology - Fixed Expense Approach
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .
A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690
(2) Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.103(3) Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.051(4) Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . . 4,278
(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)] ** 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0 . . . . . . . . . . . . . . .
LOSS RATIO METHODOLOGYExperience 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 ADJUSTMENTSLOSS ADJUSTMENTSLoss 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 AnalysisAccident Year Loss Development Analysis
INCURRED METHOD - Recognizes SYSTEMATIC inaccuracy of case reserves
INCURRED LOSSES & ALAEAdjusted for Deductibles and Cats, (000’s) ACCIDENT Reported as of: YEAR 12 mos 24 mos 36 mos 48 mos 2000 1,200 1,488 1,548 1,548 2001 1,300 1,755 1,843 1,843 2002 1,400 1,708 1,691 1,691 2003 1,500 1,800 1,836 2004 1,600 1,968 2005 1,9001,900
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 = 1.201.20
Accident Year Loss Development AnalysisAccident Year Loss Development Analysis
INCURRED AGE-TO-AGE FACTORS
ACCIDENT YEAR 12-24 mos 24-36 mos 36-48 mos
2000 1.24 1.04 1.00 2001 1.35 1.05 1.00 2002 1.22 0.99 1.00 2003 1.201.20 1.02 2004 1.23
Average 1.248 1.025
1.000
Selected 1.248 1.025
1.000
x xCumulative
Age-to-Age Factors 1.279 1.0251.000
LOSS DEVELOPMENT ANALYSISLOSS DEVELOPMENT ANALYSIS
(1)(1) (2) (2) (3) (3)CumulativeCumulative EstimatedEstimated
AccidentAccident Incurred LossIncurred Loss Age to UltimateAge to Ultimate Ultimate LossUltimate Loss YearYear & ALAE @ 12/05& ALAE @ 12/05 FactorFactor (1) * (2)(1) * (2) 2002 1,691 1.000 1,691
2003 1,836 1.000 1,836
2004 1,968 1.025 2,017
2005 1,9001,900 1.279 2,4302,430
RATE INDICATION WORKSHEETRATE INDICATION WORKSHEETLoss Ratio Methodology - Fixed Expense ApproachLoss Ratio Methodology - Fixed Expense Approach
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .
A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690
(2) Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.103(3) Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.051(4) Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . . 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0 . . . . . . . . . . . . . . .
EXPENSE ANALYSISEXPENSE ANALYSIS
Unallocated Loss Adjustment ExpenseUnallocated Loss Adjustment Expense
Countrywide FiguresCountrywide Figures(in $ millions)(in $ millions)
Unallocatedllocated LossLoss ULAELAE toto
IncurredIncurred AdjustmentAdjustment Losses & ALAELosses & ALAEYearYear Losses & ALAELosses & ALAE ExpensesExpenses RatioRatio 2003 $61,200 $6,500 10.6%2004 79,000 7,800 9.9%2005 82,300 8,300 10.1%
Estimated Future ULAE Percentage 10.0%as a percentage of Incurred Losses & ALAE
31
RATE INDICATION WORKSHEETRATE INDICATION WORKSHEETLoss Ratio Methodology - Fixed Expense ApproachLoss Ratio Methodology - Fixed Expense Approach
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .
A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690
(2) Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.103(3) Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.051(4) Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . . 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0. . . . . . . . . . . . . . .
ProjectProject to the loss level predicted to exist during pricing period to the loss level predicted to exist during pricing period
Data IssuesData 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 ADJUSTMENTSLOSS ADJUSTMENTS
Loss Trend Analysis
LOSS TREND ANALYSISLOSS TREND ANALYSIS
CalendarCalendar Paid Losses Earned Exposures PurePaid Losses Earned Exposures Pure YearYear ($ 000’s)($ 000’s) (000’s)(000’s) PremiumPremium
1998 1,212 13.0 $ 93.23 1999 1,356 13.2 $102.73 2000 1,496 13.3 $112.48 2001 1,726 13.4 $128.81 2002 1,730 13.6 $127.21 2003 1,839 13.7 $134.23 2004 1,984 13.8 $143.75 2005 2,108 14.0 $150.57
Annual Trend based on Least Squares (exponential ) 6.6%
Most Recent Annual Change (150.57 / 143.75) 4.7%
Other Possible Trend SourcesOther Possible Trend Sources C.P.I. Medical Care Index 3 - 4%
C.P.I. Auto Body Work Index 4 - 5%
C.P.I. Home Maintenance & Repair Index 3 - 4%
RATE INDICATION WORKSHEETRATE INDICATION WORKSHEETLoss Ratio Methodology - Fixed Expense ApproachLoss Ratio Methodology - Fixed Expense Approach
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .
A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690
(2) Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.103(3) Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.051(4) Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . . 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0. . . . . . . . . . . . . . .
LOSS ADJUSTMENTSLOSS ADJUSTMENTS
CATASTROPHES
Catastrophes should be eliminated from lossesCatastrophes should be eliminated from losses
Average provision should be used as a loss loadingAverage provision should be used as a loss loading
Example:(1) Expected Annual Catastrophe Loss & ALAE for Projection Period
394
(2) Projected Premium4,278
(3) Catastrophe Load (1) / (2)9.21%
RATE INDICATION WORKSHEETRATE INDICATION WORKSHEETLoss Ratio Methodology - Fixed Expense ApproachLoss Ratio Methodology - Fixed Expense Approach
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .
A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690
(2) Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.103(3) Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.051(4) Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . . 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). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0. . . . . . . . . . . . . . .
UNDERWRITING EXPENSESUNDERWRITING EXPENSES
Commissions and premium taxes vary directly with premiumsCommissions and premium taxes vary directly with premiums
Other acquisition and general expenses are “fixed”Other acquisition and general expenses are “fixed”
• Not really fixedNot really fixed
• Vary with inflationVary with inflation
EXPENSE ANALYSISEXPENSE ANALYSISDirect Expenses
Other Than Loss Adjustment
Countrywide Figures (In $ Millions)
2003 2004 20052003 2004 2005 Selected Selected
$ % $ % $ % %$ % $ % $ % %
Written Premium 107,400 100 121,600 100 142,400 100
Commissions 16,647 15.5 19,200 15.5 22,100 15.5 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 Taxes, Licenses
& Fees 3,652 3.4 4,100 3.4 4,900 3.4 3.4
DEVELOPMENT of DEVELOPMENT of EXPECTED LOSS RATIO & EXPECTED LOSS RATIO &
FIXED EXPENSE RATIOFIXED EXPENSE RATIO
Total Variable Fixed
Commissions 15.5% 15.5% 0.0%
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
TOTAL 35.6% 23.4% 12.2%
TARGET Loss, LAE & Fixed Expense Ratio = 100.0% - 23.4% = 76.6%
* Policyholder Dividends, Involuntary Market Costs, Guaranty Fund Assessments, Etc. (if allowable)
RATE INDICATION WORKSHEETRATE INDICATION WORKSHEETLoss Ratio Methodology - Fixed Expense ApproachLoss Ratio Methodology - Fixed Expense Approach
90.3%
B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .76.6%
A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 10+ 12) / (4).. . . . . .
(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690
(2) Current Rate Level Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.103(3) Premium Trend Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.051(4) Trended Premium @ Current Rate Level = (1)*(2)*(3) . . . . . . . . . . 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
C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0. . . . . . . . . . . . . . . +17.9%
OTHER CONSIDERATIONSOTHER CONSIDERATIONS
CREDIBILITY CREDIBILITY
DEDUCTIBLESDEDUCTIBLES
• TYPES (Straight, Franchise, Percentage)TYPES (Straight, Franchise, Percentage)
• Must consider deductibles offeredMust consider deductibles offered
Will the offerings change; will the mix of changeWill the offerings change; will the mix of change
• Deductible relativities based on Loss Elimination Ratios Deductible relativities based on Loss Elimination Ratios
LIMITSLIMITS
• Basic limits data used for auto indication; Increased limits Basic limits data used for auto indication; Increased limits
reviewed separatelyreviewed separately
• Basic limits review emphasizes frequency of loss, not severityBasic limits review emphasizes frequency of loss, not severity
BASIC RATEMAKING TECHNIQUESBASIC RATEMAKING TECHNIQUESSuggested ReadingsSuggested Readings
Foundations in Casualty Actuarial Science, Ratemaking by Charles L. McClenahan, Chapter 2, pages 25-90.
Statement of Principles Regarding Property and CasualtyInsurance 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