1999 Casualty Loss Reserve Seminar A Basic Model for DFA Robert J. Walling, III Miller, Herbers,...

1999 Casualty Loss Reserve Seminar

A Basic Model for DFA

Robert J. Walling, III Miller, Herbers, Lehmann, & Associates Inc.

Charles C. EmmaMiller, Herbers, Lehmann, & Associates Inc.

Overview

1 Description of Model - Rob

2 Demonstration of Model - Chuck

3 Use 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 useableSimple 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

Investments Catastrophes

Underwriting Taxation

Interest rate generator Loss 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 yearsGenerates financial statements

Balance sheet StatutoryGAAPOperating statementIRIS 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 ageRenewal patternsProjected growth ratesLoss development patternsLoss frequency and severityReinsurance program

Investment dataStatutory and market asset values by asset classMaturity and coupon rates for bondsBeta 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 specificRange of rate changes established

Narrower range in more restrictive states

Time lag for implementing rate changeLonger in more restrictive statesIncreases take longer to implement than decreases

Underwriting CycleFour phases

Immature hard Mature hardImmature soft Mature 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

BondsMarket values calculated based on term structure of interest ratesIncludes provision for default

Equities - 3 step approach1 Initial market return:

Short term interest rate + market risk premium of 8.5%2 Adjusted market return: Initial market return - 4 times change in short term rates3 Final return includes random component (mean = 0, standard

deviation = 15%)

Interest Rate Generator

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How to Obtain this Model

Access the Miller, Herbers, Lehmann homepage (www.mrht.com)

Click on DFA Model to obtain DynaMo3

You need to have Excel to run this model

This model is compatible with @Risk 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 or @Risk Add-ins

Basics are Already Resident

The Rest is up to You (e.g., parameter selection and output customization)

Worksheet Components

I. InputsGeneral - Interest rates, economic parameters

By Line InputsPremiums - 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


II. Random Variable Generators

Interest Rate (and Inflation Rate) Random Generator

Payment Pattern Random Generator

Underwriting Cycle Generator

Catastrophe Loss Generator


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


IV. OutputsThe 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 CharacteristicsTwo 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


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


Global Assumptions / A-Priori ExpectationsMature 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


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.)


Let’s Try Four Different Runs ...


1. Base Case Run

Run the company under its currently described condition (a perceived mature soft market and growth strategy of 5%)


1. Base Case Run: Results

Mean 2003 Surplus 51,915

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 Surplus 40,999

Maximum Surplus 61,133


2. Change Reinsurance Program

Purchase Catastrophic Reinsurance attaching at $5MM (instead of $3MM) per occurrence and $25MM with same limit


2. Change Reinsurance Program: Results









3. Impose FL Rate Regulatory Restrictions

Freeze FL rates for five years for both LOB’s


3. Impose FL Rate Regulatory Restrictions: Results









4. Change Our Market Perception

Revise our current market perception to be an immature-hard, and increase growth plans to 10% annually


4. Change Our Market Perception: Results








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1999 Casualty Loss Reserve Seminar A Basic Model for DFA Robert J. Walling, III Miller, Herbers,...

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