1999 Casualty Loss Reserve Seminar A Basic Model for DFA Robert J. Walling, III Miller, Herbers, Lehmann, & Associates Inc. Charles C. Emma Miller, Herbers, Lehmann, & Associates Inc.

Overview 1Description of Model - Rob 2Demonstration of Model - Chuck 3Use of Model - You (the audience)

Objectives of this DFA Model Develop a financial model for a U. S. property-liability insurer that is: Realistic enough to be useable Simple enough to be understood

Caveats Any model is a simplified version of reality This model deals with quantifiable risk only –Examples of excluded items: A line of business being socialized Management fraud Devastating meteor strike

Key Risks for U.S. Property- Liability Insurers Underwriting –Aging Phenomenon –Jurisdictional Risk –Loss Development Catastrophes Investment –Asset Value –Investment Income

Specifics Provisions of Model Six separate, but interrelated modules InvestmentsCatastrophes UnderwritingTaxation Interest rate generatorLoss reserve development Two lines of business For each line of business –New business –1st renewals –2nd and subsequent renewals

What Does This Model Do? Simulates results for the next 5 years Generates financial statements Balance sheet Statutory GAAP Operating statement IRIS results Indicates expected values and distribution of results for any value selected

What Information is Required? Underwriting data Premiums and exposures, by line, state and age Renewal patterns Projected growth rates Loss development patterns Loss frequency and severity Reinsurance program Investment data Statutory and market asset values by asset class Maturity and coupon rates for bonds Beta for equity portfolio

Primary Risks Reflected Pricing Loss reserve development Catastrophe Investment

Components of Pricing Risk Random variation –Loss frequency and severity Inflation affects severity –Correlated with short term interest rates –Line of business specific Jurisdictional risk Underwriting cycle

Jurisdictional Risk State specific Range of rate changes established Narrower range in more restrictive states Time lag for implementing rate change Longer in more restrictive states Increases take longer to implement than decreases

Underwriting Cycle Four phases Immature hardMature hard Immature softMature soft Each phase has different supply-demand function Probability distribution for moving to different phase next period

Loss Development Risk Initial reserve levels based on actuarial analysis, not statement values Still subject to random variation Inflation also affects reserve development –Initial reserves reflect specific inflation rate –Changes in inflation rate affect development

Catastrophe Risk Poisson distribution for number of catastrophes Each catastrophe assigned to a geographic focal point Based on focal point, size of catastrophe is determined based on a lognormal distribution Contagion factor is used to distribute catastrophe to nearby states Losses distributed based on market share by state

Investment Risk Bonds Market values calculated based on term structure of interest rates Includes provision for default Equities - 3 step approach 1Initial market return: Short term interest rate + market risk premium of 8.5% 2Adjusted market return: Initial market return - 4 times change in short term rates 3Final return includes random component (mean = 0, standard deviation = 15%)

Interest Rate Generator Cox-Ingersoll-Ross one factor model

How to Obtain this Model Access the Miller, Herbers, Lehmann homepage ( Click on DFA Model to obtain DynaMo3 You need to have Excel to run this model This model is compatible for those wanting to incorporate the features of that program

How to Learn More about this Model CAS Limited Attendance Seminar on DFA October 4-5, 1999 San Francisco Explanation of types and history of DFA Discussion of common DFA issues Hands-on workshop using DynaMo3 Supervised use of model on participant provided data

How Does DynaMo3 Operate? Runs in Excel ver. 97 Statistical Features offered by Excel Add-ins Basics are Already Resident The Rest is up to You (e.g., parameter selection and output customization)

Worksheet Components I. Inputs General - Interest rates, economic parameters By Line Inputs Premiums - exposures, rates, bus. retention, expenses Exposures - geographical and historical distributions Losses - historical losses, counts, severities, triangles Market condition parameters - cycle position, demand curve Investments - bonds by maturity, reinvestment strategies, stock betas Reinsurance - Stop loss, catastrophe reinsurance

Worksheet Components II. Random Variable Generators Interest Rate (and Inflation Rate) Random Generator Payment Pattern Random Generator Underwriting Cycle Generator Catastrophe Loss Generator

Worksheet Components III. Calculators Lines of Business - By Line and Total Lines - Direct (Gross), Ceded, Net - Prior, New, 1st Renewals, Later Renewals Investment Distribution Asset Classes- Details of bonds by class, stocks Tax Calculator

Worksheet Components IV. Outputs The Basics - Balance Sheets, Statutory and GAAP - Income Statements - By Line Loss Ratio Analysis - Simulation Data - Customized Outputs by Trial Using Excel Functionality Anything Else the User Pre-Selects - Loss Ratios by LOB - Interest Rates - Catastrophic Losses and Counts

XYZ Insurance Company Basic Characteristics Two Line, Two State Company - Approximate 50/50 HO and WC ($45MM total ‘98) - 50/50 IL and FL - 5% growth plans $40MM in Statutory Surplus at 12/98 Conservative Investment Distribution - 96% US Gov. Bonds, 3% Stocks, 1% Cash

XYZ Insurance Company Company Behavior / Strategies Positive cashflows reinvested in proportion to current portfolio distribution Negative cashflows result in sold assets in proportion to current portfolio distribution Rate changes depend on market growth plans and a rate adequacy factor

XYZ Insurance Company Global Assumptions / A-Priori Expectations Mature Soft Market for Both LOB’s Long Term Interest Rate = 6.0% Initial Short Term Rate = 4.91% Resultant Inflation Expectations –HO Severity Inflation = 4.0% –WC Severity Inflation = 6.0% Zero Frequency Trend for Both LOB’s

XYZ Insurance Company More A-Priori Expectations U/W Expense Ratios= 29.0% of NEP L/R Expectations –HO = 70.0% (+ 8% CAT load) –WC = 75.0% –So, Combined A-Priori Ratio = 107.0% (approx.)

XYZ Insurance Company Let’s Try Four Different Runs...

XYZ Insurance Company 1. Base Case Run Run the company under its currently described condition (a perceived mature soft market and growth strategy of 5%)

XYZ Insurance Company 1. Base Case Run: Results Mean 2003 Surplus51,915 CV 2003 Surplus 10.3% 2003 Net Earned Premium 83,807 Avg. 5 Year HMP L/R 76.9% Avg. 5 Year WC L/R 74.2% Minimum Surplus40,999 Maximum Surplus61,133

XYZ Insurance Company 2. Change Reinsurance Program Purchase Catastrophic Reinsurance attaching at $5MM (instead of $3MM) per occurrence and $25MM with same limit

XYZ Insurance Company 2. Change Reinsurance Program: Results Mean 2003 Surplus51,725 CV 2003 Surplus 11.0% 2003 Net Earned Premium 84,035 Avg. 5 Year HMP L/R 77.2% Avg. 5 Year WC L/R 74.2% Minimum Surplus40,490 Maximum Surplus61,726

XYZ Insurance Company 3. Impose FL Rate Regulatory Restrictions Freeze FL rates for five years for both LOB’s

XYZ Insurance Company 3. Impose FL Rate Regulatory Restrictions: Results Mean 2003 Surplus50,296 CV 2003 Surplus 10.8% 2003 Net Earned Premium 83,155 Avg. 5 Year HMP L/R 77.5% Avg. 5 Year WC L/R 75.4% Minimum Surplus38,999 Maximum Surplus58,685

XYZ Insurance Company 4. Change Our Market Perception Revise our current market perception to be an immature-hard, and increase growth plans to 10% annually

XYZ Insurance Company 4. Change Our Market Perception: Results Mean 2003 Surplus41,141 CV 2003 Surplus 17.1% 2003 Net Earned Premium 104,633 Avg. 5 Year HMP L/R 80.4% Avg. 5 Year WC L/R 75.9% Minimum Surplus30,702 Maximum Surplus54,310

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