Finance 431:Property-Liability Insurance

Lecture 6:Ratemaking

RatemakingActuarial functions

Ratemaking

Loss reserving

Data collection and analysis

Profitability analysis

Competitive analysis

Prepare statistical reports

Mergers and acquisitions

Planning

Actuarial services

Staff actuaries

Consulting actuaries

Advisory organizations

ISO (Insurance Services Office)

AAIS (American Association of Insurance Services)

NCCI (National Council of Compensation Insurers)

SAA (Surety Association of America)

Ratemaking Principles

Corporate objectives

Stable

Responsive

Promote loss control

Cover contingencies

Understandable

Regulatory objectives

Rates must be:

Adequate

Not excessive

Not unfairly discriminatory

Which of the following insurance rating practice would be considered unfairly discriminatory?A) To charge higher auto rates for individuals

with poor credit scoresB) To charge males more than females for auto

insuranceC) To charge homeowners who live near the

ocean more for coverageD) To charge drivers in Chicago more for

coverage than drivers in UrbanaE) None of the above

Ratemaking ProcessIn a stable world:

Calculate amount needed:

To pay claims

To pay expenses

Add these together to find

the rate

TerminologyGross rate = total premium

Pure premium = claims

Expense loading = expenses

Profit and contingencies =

return on capital and risk loading

Exposure unit = measure of risk assumed in contract

Written premium = premiums booked

Earned premium = pro-rata portion of premiums exposed to loss

Ratemaking in the Real WorldLoss reserves

Case reservesIncurred But Not Reported (IBNR)

InflationOther time dependent factors (auto insurance)

Traffic densityGas pricesLaw enforcement effortsLegal rules governing loss settlements

Trending adjusts for time dependent factorsSeverity = average lossFrequency = number of claims per exposure

Risk ClassificationFor automobile insurance

Age of driver

Sex and marital status of driver

Type of vehicle

Use of vehicle

Driving record of driver

Mileage driven

Territory where vehicle is garaged

Credit score

Ratemaking MethodsJudgment method

Loss ratio method

Percent rate change = (A-E)/E

A = Actual loss ratio

E = Expected loss ratio

Pure premium method

G = (P+F)/(1-V)

G = Gross premium

P = Pure premium = Frequency x Severity

F = Fixed expenses

V = Variable expenses

Examples

Loss Ratio Method

Actual LR = 66%

Expected LR = 60%

Percent rate change =

(66-60)/60 = +10%

Pure Premium Method

Pure premium = $400

Fixed expenses = $50

Variable expenses = 25%

Gross premium =

(400+50)/(1-.25) = 600

Calculate the gross premium based on the following information:

Loss frequency 10%Loss severity 900Fixed expenses 10Variable expenses 20%

A) 90B) 120C) 125D) 500E) None of the above

Other Factors in RatemakingInvestment Income

Investment income

Realized capital gains

Unrealized capital gains

Profit

Rate Regulation

Statutory standards

Administration

State-made rates

Mandatory bureau membership

Prior approval

File and use

Open competition

Under which rate regulatory law do can insurers change rates without approval?

A) State made ratesB) Mandatory bureau ratesC) Prior approvalD) File and useE) Open competition

Development of DataCollection of statistics

Policy year

Calendar year

Accident year

Calendar year calculations

Earned Premium = Beginning UEP Reserve + Written Premium - Ending UEP Reserve

Incurred Losses =

Paid Losses + Ending Loss Reserve - Beginning Loss Reserve

Calculate the calendar year earned premium for 2007 based on the following information:

Written premium in 2007 $10 millionUnearned premium reserve

12/31/06 2.0 million12/31/07 2.5 million

A) $7.5 millionB) $9.5 millionC) $10.5 millionD) $12 millionE) None of the above

Calculate the calendar year incurred losses for 2007 based on the following information:

Paid losses in 2007 $10 millionLoss reserve

12/31/06 2.0 million12/31/07 2.5 million

A) $7.5 millionB) $9.5 millionC) $10.5 millionD) $12 millionE) None of the above

RatemakingAdjustment of statistics

Loss development factors

Trending

Linear

Exponential

Territorial relativities

Class relativities

Example2004 Incurred Losses = $10,000,000Trend Factors

Frequency = 1.02Severity = 1.04

Rates for coverage in effect for 2008Number of years of trending = 4Trended incurred losses = 10,000,000x(1.02)4x(1.04)4=

12,662,923Earned exposures for 2004 = 20,000Pure premium = 12,662,923/20,000 = 633.15

Rate FilingsSchedule of proposed rates

Percentage change in statewide average rates

Percentage change by territory and class

Statistical support for changes

Investment income calculation

Expense loading data

Explanatory material