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CAS Seminar on Ratemaking. Basic Techniques for an Overall Rate Level Indication (INT-2) March 7, 2002 The Tampa Marriott Waterside Tampa, Florida Presented by: Charles Parsons, FCAS, MAAA & Linda Torkelson, FCAS, MAAA. Basic Techniques Overall Rate Level Indication (INT-2).

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Cas seminar on ratemaking

CAS Seminar on Ratemaking

Basic Techniques for an Overall

Rate Level Indication

(INT-2)

March 7, 2002

The Tampa Marriott Waterside

Tampa, Florida

Presented by:

Charles Parsons, FCAS, MAAA & Linda Torkelson, FCAS, MAAA


Basic techniques overall rate level indication int 2

Basic TechniquesOverall Rate Level Indication (INT-2)

Basic Ratemaking Equation and Its Considerations:

  • Organization of Data

  • Premium Adjustments

  • Loss Adjustments

  • Expense Considerations

  • Other Considerations


Basic ratemaking equation

Basic Ratemaking Equation:

Future Premiums=

Future Losses +

Future Expenses +

Underwriting Profit and Contingency Provision


Basic ratemaking methods

BASIC RATEMAKING METHODS

  • Pure Premium (PP) Method

    • PP = Loss / Exposure Units

    • develops indicated rate per unit of exposure (R)

    • R = [PP + FE] / [1-VER-Profit Ratio]

  • Loss Ratio Method

    • develops indicated rate change (A)

    • A = Experience LR / Target LR

NOTE: THE TWO METHODS PRODUCE IDENTICAL RESULTS

WHEN IDENTICAL DATA AND ASSUMPTIONS ARE USED.


Organization of data

ORGANIZATION OF DATA

I. CALENDAR YEAR DATA

(standard accounting year)

II. POLICY YEAR DATA

III. ACCIDENT YEAR DATA


Organization of data1

ORGANIZATION OF DATA

I. CALENDAR YEAR DATA

Premium and Loss transactions that occur during the year.

Loss = Payments + change in reserves duringyear

  • 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 data2

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 data3

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.


Sample rate level indication assumptions

SAMPLE RATE LEVEL INDICATIONASSUMPTIONS

  • Annual Policies. Rates to be revised as of JANUARY 1, 2002

  • Loss Ratio Methodology

  • EXPERIENCE PERIOD: ACCIDENT YEAR 2000

    • 2000 Earned Premium $3,690,000

    • Reported Incurred Losses as of 12/31/00: $1,700,000

2000 2001 2002 2003

Experience Policies

Period Effective

<COVERAGE PROVIDED>

Avg. Accident Avg.. Accident Date under

Date is 7/1/00 Revised Rates is 1/1/2003

TREND PERIOD is 2.50 Years


Loss ratio methodology fixed expense approach

LOSSRATIOMETHODOLOGYFixed Expense Approach

INDICATED (needed) RATE LEVEL CHANGE =

Projected Experience Loss + Fixed Expense Ratio

Expected (Target) Loss + Fixed Expense Ratio

- 1.0

For Example:76.5%

74.7%

- 1.0 = + 2.4%


Loss ratio methodology experience loss fixed expense ratio projection

LOSSRATIOMETHODOLOGYExperience Loss + Fixed Expense Ratio Projection

  • Premium Adjustments

    • Adjust to Current Rate Level

    • Premium Trend

    • Coverage Drift

  • Loss Adjustments

    • Loss Development

    • Loss Trend

    • Deductible Adjustments

    • Catastrophe Adjustments


Cas seminar on ratemaking

RATE INDICATION WORKSHEET

Loss Ratio Methodology - Fixed Expense Approach

  • A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 11) / (4). . . . . . . . . . . . .

    • (1) 2000 Earned Premium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (2) Current Rate Level Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (3) Premium Trend Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (4) Trended Premium @ Current Rate Level = (1)*(2)*(3).. . . . . . . . . .

    • (5) Accident Year 2000 Ultimate Losses. . . . . . . . . . . . . . . . . . . . . . . . . .

    • (6) Allocated Loss Adjustment Expense (ALAE) Factor. . . . . . . . . . . . . .

    • (7) Annual Loss Trend ____% Trend Period: 2.5 years

    • (8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . . .

    • (9)Trended Ultimate Losses and ALAE = (5) * (6) * (8). . . . . . . . . . . .

    • (10) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (11)Fixed Expenses = (1) * (10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

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


Cas seminar on ratemaking

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.


Cas seminar on ratemaking

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

CURRENT RATE LEVEL ADJUSTMENTExtension of Exposures Method

2000 Earned Exposures

Class 1 Class 2

Territory 1 1,500 2,260

Territory 2 1,995 3,010

Territory 3 2,700 2,500

Current Rates

Class 1 Class 2

Territory 1 $150 $300

Territory 2 $175 $350

Territory 3 $220 $440

Premium @ Current Rates

Class 1 Class 2

Territory 1 $225,000 $678,000

Territory 2 $349,125 $1,053,500

Territory 3 $594,000 $1,100,000

Statewide total $3,999,625


Cas seminar on ratemaking

CURRENT RATE LEVEL ADJUSTMENT

Parallelogram Method

A

B C

1/99 1/00 1/01 1/02 1/03

Rate Change History

DateChangeRate Index

From 1/1/99 to 12/31/00None1.000 A

1/1/00- 5%0.950 B

(1 * 0.95)

7/1/00+ 2%0.969 C

(1 * 0.95 * 1.02)

1/1/01+ 4%1.008 Current

(1 * 0.95 * 1.02 * 1.04)


Cas seminar on ratemaking

CURRENT RATE LEVEL ADJUSTMENT

Calculation of On-Level Factor - Parallelogram Method

I. Rate Index for 2000:

Percent Rate

Areaof 2000Index

A 50.0 1.000

B 37.5 0.950

C 12.5 0.969

TOTAL 100.0 0.977

II. On-Level Factor for 2000:

(1) Current Index 1.008

(2) 2000 Index 0.977

(3) On-Level Factor (1) / (2) 1.032

(4) 2000 Earned Premium $3,690,000

(5)2000 Earned Premium @ Current Rate Level $3,808,080


Cas seminar on ratemaking

RATE INDICATION WORKSHEET

Loss Ratio Methodology - Fixed Expense Approach

  • A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 11) / (4). . . . . . . . . . . . .

    • (1) 2000 Earned Premium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690

    • (2) Current Rate Level Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.032

    • (3) Premium Trend Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (4) Trended Premium @ Current Rate Level = (1)*(2)*(3).. . . . . . . . . .

    • (5) Accident Year 2000 Ultimate Losses. . . . . . . . . . . . . . . . . . . . . . . . . .

    • (6) Allocated Loss Adjustment Expense (ALAE) Factor. . . . . . . . . . . . . .

    • (7) Annual Loss Trend _5.0__% Trend Period: 2.5 years

    • (8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . . .

    • (9)Trended Ultimate Losses and ALAE = (5) * (6) * (8). . . . . . . . . . . .

    • (10) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (11)Fixed Expenses = (1) * (10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

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


Cas seminar on ratemaking

PREMIUM ADJUSTMENTS

Premium Trend

  • To project the premium level which will exist during the period being priced due to underlying inflation sensitive exposures.

  • Must adjust for items such as:

    • Average car model year or price group

    • Average home value

    • Any item that would impact future premium or both premium and losses in the future except policy count


Cas seminar on ratemaking

PREMIUM ADJUSTMENTS

Premium Trend / Coverage Drift

  • 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.


Cas seminar on ratemaking

PREMIUM ADJUSTMENTS

Auto Premium Trend Example

Annual Trend = 0.975 / 0.954 - 1 = 2.2%

Total Trend Factor = 1.022 ^ 2.5 = 1.056


Cas seminar on ratemaking

RATE INDICATION WORKSHEET

Loss Ratio Methodology - Fixed Expense Approach

  • A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 11) / (4). . . . . . . . . . . . .

    • (1) 2000 Earned Premium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690

    • (2) Current Rate Level Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.032

    • (3) Premium Trend Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.056

    • (4) Trended Premium @ Current Rate Level = (1)*(2)*(3).. . . . . . . . . .4,021

    • (5) Accident Year 2000 Ultimate Losses. . . . . . . . . . . . . . . . . . . . . . . . . .

    • (6) Allocated Loss Adjustment Expense (ALAE) Factor. . . . . . . . . . . . . .

    • (7) Annual Loss Trend ______% Trend Period: 2.5 years

    • (8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . . .

    • (9)Trended Ultimate Losses and ALAE = (5) * (6) * (8). . . . . . . . . . . .

    • (10) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (11)Fixed Expenses = (1) * (10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

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


Cas seminar on ratemaking

LOSS ADJUSTMENTS

DEDUCTIBLES

  • Changes in deductible distort experience

  • Automobile Physical Damage

    • Review each deductible separately, or

    • Adjust to a common basis, or

    • Reflect deductible shift in trend factors

  • Homeowners

    • Add amount of deductible back to each loss


Cas seminar on ratemaking

LOSS ADJUSTMENTS

CATASTROPHES

  • Catastrophes should be eliminated from losses

  • Average provision should be used as a loss loading

  • Provision for catastrophes should be included in the profit load


Cas seminar on ratemaking

LOSS ADJUSTMENTS

Loss Development Analysis

  • Adjust historical losses to an expected ULTIMATE value

  • Reflects revisions to claim values as claims are settled

  • MUST be 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


Cas seminar on ratemaking

Accident Year Loss Development Analysis

INCURRED METHOD - Recognizes SYSTEMATIC inaccuracy of case reserves

INCURRED LOSSES - Adjusted for Deductibles and Cats, (000’s)

ACCIDENTReported as of:

YEAR12 mos24 mos36 mos48 mos60 mos72 mos

1993 1,000 1,230 1,304 1,238 1,212 1,212

1994 1,100 1,320 1,412 1,398 1,356 1,356

1995 1,200 1,488 1,562 1,514 1,498 1,496

1996 1,300 1,756 1,790 1,736 1,726

1997 1,400 1,708 1,810 1,756

1998 1,5001,800 1,926

1999 1,600 1,968

2000 1,800

Age to Age Development Factor =

Incurred Loss @ Later Report Period divided by Loss @ Prior Report Period

AY 1998 12 mos TO 24 mos Factor =$1,800 / $1,500 = 1.20


Cas seminar on ratemaking

Accident Year Loss Development Analysis

INCURRED AGE-TO-AGE FACTORS

ACCIDENT 12 to 24 to 36 to 48 to 60 to

YEAR 24 mos36 mos48 mos60 mos72 mos

1993 1.23 1.06 0.95 0.98 1.00

1994 1.20 1.07 0.99 0.97 1.00

1995 1.24 1.05 0.97 0.99 1.00

1996 1.35 1.02 0.97 0.99

1997 1.22 1.06 0.97

19981.20 1.07

1999 1.23

2 Year Average1.2151.0650.9700.9901.000

3 Year Average1.2171.0500.9700.9831.000

4 Year Average1.2501.0500.9750.9831.000

Middle 3 Last 51.2301.0600.9700.9831.000


Cas seminar on ratemaking

Accident Year Loss Development Analysis

AVERAGEDAGE-TO-AGE FACTORS

12 to 24 to 36 to 48 to 60 to

24 mos36 mos48 mos60 mos72 mos

2 Year Average1.2151.0650.9700.9901.000

3 Year Average1.2171.0500.9700.9831.000

4 Year Average1.2501.0500.9750.9831.000

Middle 3 Last 51.2301.0600.9700.9831.000

Selected Age to Age 1.230 1.055 0.970 0.985 1.000

Factor

x x x x

Cumulative Age to

Ultimate Factor 1.240 1.008 0.955 0.985 1.000


Cas seminar on ratemaking

LOSS DEVELOPMENT ANALYSIS

(1) (2) (3)

CumulativeEstimated

Accident IncurredAge to Ultimate Ultimate Loss

Year Loss @ 12/00 Factor (1) * (2)

1993 1,212 1.000 1,212

1994 1,356 1.000 1,356

1995 1,496 1.000 1,496

1996 1,726 1.000 1,726

1997 1,756 0.985 1,730

1998 1,926 0.955 1,839

1999 1,968 1.008 1,984

2000 1,800 1.240 2,232


Cas seminar on ratemaking

RATE INDICATION WORKSHEET

Loss Ratio Methodology - Fixed Expense Approach

  • A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 11) / (4). . . . . . . . . . . . .

    • (1) 2000 Earned Premium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690

    • (2) Current Rate Level Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.032

    • (3) Premium Trend Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.056

    • (4) Trended Premium @ Current Rate Level = (1)*(2)*(3).. . . . . . . . . .4,021

    • (5) Accident Year 2000 Ultimate Losses. . . . . . . . . . . . . . . . . . . . . . . . . . 2,232

    • (6) Allocated Loss Adjustment Expense (ALAE) Factor. . . . . . . . . . . . . .

    • (7) Annual Loss Trend ______% Trend Period: 2.5 years

    • (8) Exponential Trend Factor [1.0 + (7)] ** 2.5. . . . . . . . . . . . . . . . . . . . .

    • (9)Trended Ultimate Losses and ALAE = (5) * (6) * (8). . . . . . . . . . . .

    • (10) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (11)Fixed Expenses = (1) * (10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

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


Cas seminar on ratemaking

LOSS ADJUSTMENTS

Loss Trend Analysis

  • Projectto 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)


Cas seminar on ratemaking

LOSS TREND ANALYSIS

Accident Ultimate LossesEarned Exposures Pure

Year($ 000’s)(000’s)Premium

1993 1,212 13.0 $ 93.23

1994 1,356 13.2 $102.73

1995 1,496 13.3 $112.48

1996 1,726 13.4 $128.81

1997 1,730 13.6 $127.21

1998 1,839 13.7 $134.23

1999 1,984 13.8 $143.75

2000 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 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%


Cas seminar on ratemaking

RATE INDICATION WORKSHEET

Loss Ratio Methodology - Fixed Expense Approach

  • A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 11) / (4). . . . . . . . . . . . .

    • (1) 2000 Earned Premium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690

    • (2) Current Rate Level Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.032

    • (3) Premium Trend Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.056

    • (4) Trended Premium @ Current Rate Level = (1)*(2)*(3).. . . . . . . . . .4,021

    • (5) Accident Year 2000 Ultimate Losses. . . . . . . . . . . . . . . . . . . . . . . . . . 2,232

    • (6) Allocated Loss Adjustment Expense (ALAE) Factor. . . . . . . . . . . . . .

    • (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 ALAE = (5) * (6) * (8). . . . . . . . . . . .

    • (10) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (11)Fixed Expenses = (1) * (10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

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


Cas seminar on ratemaking

EXPENSE LOADINGS

  • Loss Adjustment Expenses

    • Allocated

      • With Losses for Auto

      • With Unallocated for Homeowners

    • Unallocated

  • Underwriting Expenses

    • “Fixed”

    • Variable with Premium


Cas seminar on ratemaking

EXPENSE ANALYSIS

Allocated Loss Adjustment Expenses

(If NOT included with losses in loss development section)

Product XYZ

Countrywide Figures

(in $ millions)

Allocated

LossALAEto

IncurredAdjustmentLosses

YearLossesExpensesRatio

1998 $61,200 $6,500 10.6%

1999 79,000 7,800 9.9%

2000 82,300 8,300 10.1%

Estimated Future ALAE Percentage 10.0%

as a percentage of Incurred Losses


Cas seminar on ratemaking

RATE INDICATION WORKSHEET

Loss Ratio Methodology - Fixed Expense Approach

  • A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 11) / (4). . . . . . . . . . . . .

    • (1) 2000 Earned Premium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690

    • (2) Current Rate Level Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.032

    • (3) Premium Trend Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.056

    • (4) Trended Premium @ Current Rate Level = (1)*(2)*(3).. . . . . . . . . .4,021

    • (5) Accident Year 2000 Ultimate Losses. . . . . . . . . . . . . . . . . . . . . . . . . . 2,232

    • (6) Allocated Loss Adjustment Expense (ALAE) 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 ALAE = (5) * (6) * (8). . . . . . . . . . . 2,774

    • (10) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

    • (11)Fixed Expenses = (1) * (10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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

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


Cas seminar on ratemaking

UNDERWRITING EXPENSES

  • Commissions and premium taxes vary directly with premiums

  • Other acquisition and general expenses are “fixed”

    • Not really fixed

    • Vary with inflation


Cas seminar on ratemaking

EXPENSE ANALYSIS

Direct Expenses

Other Than Allocated Loss Adjustment

Product XYZ

Countrywide Figures

(I.E.E. - Insurance Expense Exhibit)

(In $ Millions)

EXPERIENCE PERIOD

1998 1999 2000

$ % $ % $ %

Written Premium 107,400 100 121,600 100 142,400 100

Commissions 16,100 15.0 19,200 15.8 22,100 15.5

Other

Acquisition 4,200 3.9 4,700 3.9 5,300 3.7

Administrative 5,800 5.4 6,200 5.1 8,200 5.8

Unallocated Loss

AdjustmentExpense 6,200 5.8 7,500 6.2 8,200 5.8

Taxes, Licenses

&Fees 3,500 3.3 4,100 3.4 4,900 3.4


Cas seminar on ratemaking

DEVELOPMENT of

EXPECTED LOSS RATIO &

FIXED EXPENSE RATIO

Total VariableFixed

Commissions 15.5%15.5% 0.0%

Other Acquisition 3.81.91.9

Administrative 5.4 0.0 5.4

Unallocated Loss Expenses 6.0 0.0 6.0

Taxes, Licenses & Fees 3.43.4 0.0

Profit & Contingency 4.04.0 0.0

Other Costs * 0.50.5 0.0

TOTAL 38.6%25.3%13.3%

TARGET Loss, ALAE & Fixed Expense Ratio = 100.0% - 25.3% = 74.7%

* Policyholder Dividends, Involuntary Market Costs, Guaranty Fund Assessments, Etc. (if allowable)


Cas seminar on ratemaking

RATE INDICATION WORKSHEET

Loss Ratio Methodology - Fixed Expense Approach

  • A. EXPERIENCE Loss + Fixed Expense Ratio = (9 + 11) / (4). . . . . . . . . . . .

    • (1) 2000 Earned Premium. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3,690

    • (2) Current Rate Level Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.032

    • (3) Premium Trend Factor. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1.056

    • (4) Trended Premium @ Current Rate Level = (1)*(2)*(3).. . . . . . . . . .4,021

    • (5) Accident Year 2000 Ultimate Losses. . . . . . . . . . . . . . . . . . . . . . . . . . 2,232

    • (6) Allocated Loss Adjustment Expense (ALAE) 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 ALAE = (5) * (6) * (8). . . . . . . . . . . 2,774

    • (10) Fixed Expense Ratio (FER). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .13.3%

    • (11)Fixed Expenses = (1) * (10). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491

81.2%

B. EXPECTED (Target) Loss + Fixed Expense Ratio. . . . . . . . . . . . . . . . . . . . .74.7%

C. INDICATED RATE LEVEL CHANGE = (A / B) - 1.0. . . . . . . . . . . . . . ..+8.7%


Cas seminar on ratemaking

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


Cas seminar on ratemaking

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


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