Ratemaking

1. 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

2. Corporate objectives Stable Responsive Promote loss control Cover contingencies Understandable Regulatory objectives Rates must be: Adequate Not excessive Not unfairly discriminatory Ratemaking Principles

3. In a stable world: Calculate amount needed: To pay claims To pay expenses Add these together to find the rate Terminology Gross Rate = Pure Premium + Expense Loading + P&C Provision Pure Premium = Claims & Loss Adjustment Expense Expense loading = Production & Operating Expenses Profit and contingencies (P&C) = Return on Capital and Risk Loading Exposure unit = Measure of loss exposure assumed by insurer Written premium = premiums booked Earned premium = pro-rata portion of premiums exposed to loss Ratemaking Process

4. Ratemaking in the Real World Loss reserves Case reserves Incurred But Not Reported (IBNR) Inflation (Economic & Non-Economic) 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 Exposure if inflation sensitive

5. 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

6. 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-Q) G = Gross premium P = Pure premium F = Fixed expenses V = Variable expenses Q = Profit & Contingency

7. Loss Ratio Method Actual LR = 75% Expected LR = 68% Percent rate change = (75-68)/68 = +10.3% Pure Premium Method Pure premium = $400 Fixed expenses = $50 Variable expenses = 25% Profit & Contingency = -2% Gross premium = (400+50)/(1-.25+.02) = 584 Examples

8. Investment Profit Sources: Investment income Realized capital gains Unrealized capital gains Earned By: Loss Reserve Unearned Premium Reserve Amount Varies by Length of Payout Pattern Rate Regulation Statutory standards Administration State-made rates Mandatory bureau membership Prior Approval File and Use/Use and File No filing required Other Factors in Ratemaking

9. 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 Development of Data

10. Adjustment of statistics Loss development factors Current Rate Level Trending Linear Exponential Econometric Territorial relativities Class relativities Ratemaking

11. Example – Pure Premium Method 1999 Incurred Losses = $10,000,000 Trend Factors Frequency = 1.02 Severity = 1.04 Rates for coverage in effect for 2003 Number of years of trending = 4 Trended incurred losses = 10,000,000x(1.02)4x(1.04)4= 12,662,923 Earned exposures for 1999 = 20,000 Pure premium = 12,662,923/20,000 = 633.15

12. Example – Loss Ratio Method Trended incurred losses = 12,662,923 1999 Earned Premium = 13,698,630 +13% Rate Change in 2001 1999 “On-Level” Earned Premium = 15,479,452 Actual Loss Ratio = 12,662,923/15,479,452 = 0.818 Indicated Rate Change = (0.818-0.73)/0.73 = +12.1%

13. 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