cas seminar on ratemaking basic techniques for an overall indication (int-1) march 13, 2006 salt...

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


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.


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.


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.


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


B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . .


(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) . . . . . . . . . .


(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) . . . . . . . . . . .


(11) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

(12) Fixed Expenses = (1) * (11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0 . . . . . . . . . . . . . . .


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 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%




(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


(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) . . . . . . . . . . .



(12) Fixed Expenses = (1) * (11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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




(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690


(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) . . . . . . . . . . .



(12) Fixed Expenses = (1) * (11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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




(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690


(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) . . . . . . . . . . .



(12) Fixed Expenses = (1) * (11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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%




(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690


(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. . . . . . . . .


(12) Fixed Expenses = (1) * (11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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%




(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690


(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


(12) Fixed Expenses = (1) * (11). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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)


90.3%

B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .76.6%


(1) 2005 Earned Premium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690


(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

cas seminar on ratemaking basic techniques for an overall indication (int-1) march 13, 2006 salt...

Documents