Experience Rating for Excess Of Loss Contracts 2004 CAS Ratemaking Seminar March 11-12, 2004 Elliot Burn Wyndham Franklin Plaza Hotel Philadelphia, PA

Overview Introduction Basic Steps of Burning Cost Method Loss and Premium Adjustments Calculating the Loss Cost & Rate Potential Problems with Burning Cost Method Alternate Method – Curve Fitting Potential Problems with Curve Fitting Advanced Contract Features Annual Aggregate Deductibles Reinstatement Provisions

Introduction

Introduction How does experience rating work? Trended losses to a layer are aggregated and developed to “ultimate.” Ultimate losses are compared to on-level premium to create loss costs. Loss costs are loaded for profit and expense to determine final rate. What is the assumption of experience rating? Historical experience, adjusted properly, is a predictor of future experience.

Basic Steps of Burning Cost Method

Basic Steps of Burning Cost Method Trend individual loss amounts. Cap at policy limits(?) Distribute individual loss amounts to the layer(s). Aggregate layer experience by historical treaty period. Apply excess loss development factors. Apply rate changes and exposure trend to on-level the subject premium. Divide losses by on-level premium to derive historical loss cost. Load loss cost for expenses and profit to calculate the final rate.

Summary Exhibit– Our Goal

Loss Adjustments

Loss Adjustments Example: Assume you are trying to obtain a loss cost for the layer $100,000 xs $100,000.

Loss Adjustments Step 1: Trend losses. What are some sources of trend? Actual company data, when sufficient experience is available. External data, such as statistical bureaus or the US Government.

Loss Adjustments Sources of Trend Using External Data Bureau of Labor Statistics – US Department of Labor (BLS) Consumer Price Indices (CPI) Wholesale Price Indices (WPI) Average Weekly Gross Earnings by Industry Office of Business Economics – US Department of Commerce (OBE) National Income and Products Accounts (NIP) Average Per Capita Earnings by Industry Average Per Capita Income and Product National Council on Compensation Insurance Workers Compensation law amendment rate level changes American Appraisal Company Construction Cost Index Boeckh Construction Cost Index A.M. Best Aggregates and Averages

“Correct” Method: Trend only portion of loss above policy limit… Loss Adjustments Step 1: Trend losses. Is this correct? “Correct” Method: Trend only portion of loss above policy limit… 171,046

Note that this loss isn’t capped… Loss Adjustments Step 2: Cap Losses at Policy Limits. Note that this loss isn’t capped…

Loss Adjustments Steps 3 & 4: Distribute individual loss amounts to each layer and aggregate layer experience by historical treaty period.

Loss Adjustments Loss Development Analysis Adjust historical losses to an expected ULTIMATE value Reflects revisions to claim values as claims are settled Reflects IBNR reporting Reflects development on reported claims Key Factors for Consideration Observation of historical patterns Incurred and paid developments Development period

Loss Adjustments Loss Development Analysis

Loss Adjustments Loss Development Analysis Often, excess loss dev’t factors are not very credible. What are some other options?

Are these the only sources?? Loss Adjustments Are these the only sources?? Sources of Excess LDF’s Insurance Services Organization (ISO) Lines of Business: General Liability, Auto Liability, Medical Professional Liability Advantages: Homogenous data, numerous layers Disadvantages: Lack of credible high hazard/high layer data (for GL & AL), Medical Professional Liability data represents small portion of market share Reinsurance Association of America (RAA) Lines of Business: General Liability, Auto Liability, Medical Professional Liability, and Workers Compensation Advantages: Represents all data being reinsured, more credible high layer data Disadvantages: Net of retrocessions, may include some mass torts (e.g. breast implants), losses excess of company retentions

Here we are using ISO GL factors… Loss Adjustments Here we are using ISO GL factors… Step 5: Apply excess loss development factors.

Premium Adjustments

Premium Adjustments Two Types of Premium Adjustments: Rate Level Premium (Exposure) Trend

Premium Adjustments – Rate Level 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

Premium Adjustments – Rate Level Extension of Exposures Method Quick Example: 2003 Earned Exposures Premium at Current Rates Current Rates

Premium Adjustments – Rate Level Parallelogram Method Quick Example:

Premium Adjustments – Rate Level Calculation of On-Level Factor - Parallelogram Method

Premium Adjustments – Exposure Trend What is the purpose of Exposure Trend? To project the premium level which will exist during the period being priced. The exposure trend will not account for shifts of business. Must adjust for items such as: Average car model year or price group Average home value Sales Payroll Don’t we already account for this in the rate level adjustment?!?

Premium Adjustments Step 6: Apply rate changes and exposure trend to on-level the subject premium. Back to our example…

Calculating the Loss Cost & Rate

Calculating the Loss Cost & Rate Step 7: Divide losses by on-level premiums to derive historical loss costs. Is that your final answer?!

Calculating the Loss Cost & Rate Three Types of Reinsurer Expenses: Expenses varying with premium Ceding commission paid to the reinsured Brokerage fees (where applicable) Federal excise taxes (where applicable) Profit* (*Not really an “expense”) Fixed Expenses General overhead costs (salaries, real estate) Underwriting and claim audit expenses Expenses varying with Losses Reinsurer’s unallocated loss adjustment expenses

Calculating the Loss Cost & Rate Step 8: Load selected loss cost for expenses to calculate the final premium. Divide by subject premium to determine rate. Premium = [Expected Loss x (1+ULAE) + Fixed Expenses] (1 – Variable Expense %)(1-Profit Load) Back to our Example… ULAE = 5% Fixed Expenses = 10,000 Variable Expense % = 12% Expected Loss = 1.1% x40,000,000 = 440,000 Profit Load = 5% Premium = [440,000 x(1+0.05)+10,000] = 564,593 (1– 0.12)(1-0.05) Rate=Premium/Subject Premium=564,593/40,000,000=1.4%

Potential Problems with Experience Rating

Potential Problems with Experience Rating Presence or absence of a few large claims drives the indicated rates. Order of application of development, trend, and capping makes a difference. Trending individual claims past policy limits. Impact of current policy limit profile vs. historicals. History not reflective of current situation: reserving practices, type of business, coverage, etc. “Free cover”

Alternate Method – Curve Fitting

Curve Fitting What is curve fitting? Assumptions Estimating a parametric frequency distribution and a parametric severity distribution from given claim data. Assumptions That a curve fit to the loss data after appropriate adjustments is an appropriate estimator of future loss. Frequency and severity are independent. What data is required? Large Loss Listing with Policy Limits, Excess of a Truncation Point Historical & Prospective Exposure Base On-Leveling Factors

Curve Fitting Common Frequency Distributions Poisson Negative Binomial Common Severity Distributions Gamma Mixed Exponential Pareto Issue: One curve doesn’t necessarily fit all the data. Choose truncation point carefully. Interested in the tail of the distribution.

Potential Problems with Curve Fitting Individual claims either need to be developed to ultimate (which is difficult to do) or are assumed to be at ultimate (not always a good assumption). Don’t use aggregate LDF’s to develop individual losses. How do you determine the # of IBNR claims? One loss distribution often doesn’t fit all of the data.

Advanced Contract Features

Advanced Contract Features Annual Aggregate Deductibles Reinstatement Provisions

Annual Aggregate Deductibles What is an Annual Aggregate Deductible (AAD)? When ceding company retains the 1st X dollar amount of losses per year. Two ways to estimate savings from AAD: Estimate directly from experience rating if set at sufficiently low level. Better approach: use an aggregate distribution model. Important Point: Adding an AAD to a contract doesn’t proportionately decrease the expected losses.

Annual Aggregate Deductibles Expected Cumulative Loss Distributions Before AAD After $1.5M AAD Losses start hitting the layer here.

Reinstatement Provisions What is a Reinstatement Provision? It puts a limit on either the number of occurrences or the aggregate losses that will be paid under a contract. Free or paid “Pro-rata as to amount” or “pro-rata as to time” Reinstatement provisions are typically found on high excess layers, where loss tends to be either 0 or a full limit loss. Want to use an aggregate distribution model to determine the expected # of reinstatements and the total expected reinstatement premium.

Reinstatement Provisions Example of “Pro-Rata as to Amount” Reinstatement Occurrence Limit: $10,000,000 Annual Premium: $3,000,000 Reinstatement Provision: 110%, pro-rata as to amount Actual Loss Amount: $5,000,000 Reinstatement Premium = $3,000,000 x 1.10 x 5/10 = $1,650,000

Advanced Contract Features Other Advanced Contract Features Other Aggregate Contract Features Stop-Loss Multi-Year Adjustable Features Swing-Rated Premiums Sliding Scale Commissions Profit Commissions Loss Corridors Loss Caps

Questions?

References Clark, David R. “Basics of Reinsurance Pricing,” CAS Study Note,1996. McClenahan, Charles L. “Ratemaking,” Foundations of Casualty Actuarial Science, 1996. Masterson, N.E. “Economic Factors in Liability and Property Insurance Claim Costs, 1935-1967,” Proceedings of the Casualty Actuary Society, 1968.