Ratemaking Actuarial 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

Ratemaking Process In a stable world: Calculate amount needed: To pay claims To pay expenses Add these together to find the rate Terminology Gross 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 World Loss reserves Case reserves Incurred But Not Reported (IBNR) Inflation Other time dependent factors (auto insurance) Traffic density Law enforcement efforts Legal rules governing loss settlements Trending adjusts for time dependent factors Severity = average loss Frequency = number of claims per exposure

Risk Classification For 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

Ratemaking Methods Judgment 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 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

Other Factors in Ratemaking Investment 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 No filing required

Development of Data Collection 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

Ratemaking Adjustment of statistics Loss development factors Trending Linear Exponential Territorial relativities Class relativities

Example 1998 Incurred Losses = $10,000,000 Trend Factors Frequency = 1.02 Severity = 1.04 Rates for coverage in effect for 2002 Number of years of trending = 4 Trended incurred losses = 10,000,000x(1.02) 4 x(1.04) 4 = 12,662,923 Earned exposures for 1998 = 20,000 Pure premium = 12,662,923/20,000 =

Rate Filings Schedule 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