Using the Public-Access DFA Model: A Case Study

Richard Gorvett, FCAS, Ph.D.

The College of Insurance

Thomas Hettinger, ACAS

Miller, Rapp, Herbers & Terry, Inc.

Robert Walling, ACAS

Miller, Rapp, Herbers & Terry, Inc.

CAS Seminar on Dynamic Financial Analysis

July, 1998

Outline of Our Case Study

• Description of the MRH&T Public-Access DFA Model

• Description of the Company

• Information Requested From the Company

• Initial Findings

• Presentation to Company Management

• Reaction of Company Management: Their Concerns and Our Responses

• Future Model Enhancements

• Conclusions

DynaMo:The Public-Access DFA Model

• Developed by Miller, Rapp, Herbers & Terry, Inc. (with Academic Assistance)

• Freely Available -- Encourages Industry Input

• www.mrht.com

• Excel and @Risk

• Stochastic Simulation– Specify Inputs– Select Outputs

U/WInputs

Investment& Economic

Inputs

U/W GeneratorPayment Patterns

U/W Cycle

CatastropheGenerator

InvestmentGenerator

U/WCashflows

InvestmentCashflows

TaxOutputs

& SimulationResults

DynaMo

Interest RateGenerator

Risks Modeled

Underwriting

• Pricing– Claim Frequency and Severity (Non-Cat.)

• Inflation

• Aging Phenomenon

– Jurisdictional– Underwriting Cycle

• New Business Penalty

• Loss Reserve Development

• Catastrophes

Risks Modeled

Financial

• Interest Rates– Cox-Ingersoll-Ross

• dr = a(b-r)dt + sr0.5dz

– Mean-Reverting; Rate-Sensitive Volatility

• Inflation– General (CPI): Function of Simulated Interest Rate– Line of Business: Function of Simulated CPI

• Equity Market Performance

Outputs Available

• 5-year Projections

• Balance Sheets

• Income Statements

• Loss Ratio Reports

• IRIS Tests

• Others as Needed– Select Any Cell of Spreadsheet– Graphs and Histograms

Model Uses

Internal

• Strategic Planning• Ratemaking• Reinsurance• Valuation / M&A• Market Simulation

and Competitive Analysis

• Asset / Liability Management

External

• External Ratings• Communication

with Financial Markets

• Regulatory / Risk-Based Capital

• Capital Planning / Securitization

Description of Case Company

We applied DynaMo to an actual insurance company having the following attributes:

• Mid-size Property-Liability Insurer

• Writes Nationally

• In Business for More than Twenty Years

• Multi-line

Lines of Business

• Private Passenger Auto

• Homeowners

• Commercial Auto

• Commercial Multiple Peril

• Workers Compensation

• Others

Reinsurance Contracts

• Excess-of-Loss

• Quota Share

• Catastrophe

• Aggregate Stop Loss

Data Requested From Company

• Annual Statements• Expense Data

– IEE– Future Plans

• Historical Loss Data– Actuarial Analysis– Direct, Ceded, and Net

• Historical Premium Data– By Renewal Category Where Possible

• Reinsurance Program

Data Requested From Company

• Underwriting Data -- by Line of Business– New and Renewal Exposures Written– Renewal Ratios– Projected Growth Rates– Exposure Distribution– Policy Limit Profile

• Asset data– Statutory and Market Values, by Asset Type– Coupon and Dividend Rates– Equity Betas

The DFA Process

• Review Company

• Gather Data

• Modify Base Model to Best Reflect ABC’s Structure– Group and Ungroup Lines of Business– Unique Reinsurance?– Unique Assets?– Other

The DFA Process (cont.)

• Enter Data

• Run Model– How Many Simulations?

• Review Results– Graphs– Exhibits

The DFA Process (cont.)

• Check for Reasonableness– Premiums– Losses– Asset Values– Compare Modeled Latest Two Years to Actual– Loss Ratios– ...

The DFA Process (cont.)

• Re-parameterize Model– Frequencies– Severities– Interest Rates– Other

• Accept or Reject– What Criteria?

The DFA Process (Cont.)

• Modify and Rerun Model

• Sensitivity Test By Changing Parameters

• Determine Plan of Attack

A Second Look at Parameters

• New Business Penalty– Frequencies– Severities

• Interest Rates– Long Term Mean– Volatility

• Underwriting Cycle– Trends in WC and HMP Results

Initial Findings - Areas to Review

• Dispersion of Results

• Probability of Undesirable Results

• Maximum and Minimum

Initial Findings

• Surplus Steadily Decreased Over the 5 Year Period

• Great Variability in Year 2002 Results

• Probability of Negative Surplus

Year 2002 Surplus DistributionOriginal Assumptions

0

0.05

0.1

0.15

0.2

0.25

Millions

Pro

babi

lity

Initial Findings - Possible Reasons

Large GrowthLarge Growth ObjectivesObjectives

RenewalRenewalRatioRatio

New BusinessNew BusinessPenaltyPenalty

Surplus DrainSurplus Drain

Initial Findings - Additional Complications

GrowthGrowthObjectivesObjectives

Loss RatioLoss RatioDeteriorationDeterioration

Adverse ReserveAdverse ReserveDevelopmentDevelopment

UnusualUnusualCatastrophesCatastrophes

DevaluationDevaluationof Assetsof Assets

UnacceptableUnacceptableSurplusSurplusDrainDrain

What Now?

• Leave As Is

• Make Adjustments and Rerun– Critical Variables– Parameters

Critical Variables

• Exposure Changes

• Expense Provisions

• Frequencies and Severities– Initial Selections

– New Business Penalty

• Growth Rates

• Interest Rates– Current

– Long-Run

Critical Variables (cont.)

• Parameter Adjustments– Inflation

– U/W Cycle (Probability of Turning)

– U/W Cycle (Supply and Demand Curves)

– Jurisdictional Risk

• Renewal Ratios

• Reinvestment Allocations

• Stock Betas

• U/W Cycle (Current Position)

Critical Variables (cont.)

• Reinsurance Arrangements– Q/S– XOL– CAT– Stop Loss– Retention– Cost– Commission– Ceding %

Presentation of Initial Findings• Initial Report to Management

– Information about DynaMo and DFA– Results/Simulations for 2 Initial Scenarios

• Meeting With ABC and Authors– Actuarial– Investments– Reinsurance– CFO

• Interactive Session – Q & A– Laptops for Training and Variation

Suggested Changes

• Our Original Suggestion– Temper Growth Rate

• ABC’s Suggestion– Adjusting Growth Unsatisfactory– Renewal Ratio– New Business Penalty (Tighten U/W)– Exposure Distributions

• Our Additional Recommendation– Changing Reinsurance Provisions

Other Changes

• Change Long Term Interest Rate– Tendency of Interest Rates Climbing

(Mean Reverting Property of C-I-R Model)– Higher Investment Return– Lower Future Value of Current Bonds– Higher General Inflation– Higher Claims Inflation– Greater Than Expected Losses

Year 2002 Surplus DistributionConstrained Growth Assumptions

0

0.05

0.1

0.15

0.2

0.25

Millions

Pro

babi

lity

Year 2002 Surplus Distribution Different Reinsurance Assumptions

Increased Stop Loss Max Ceding Amount

0

0.05

0.1

0.15

0.2

0.25

0.3

Millions

Pro

babi

lity

Year 2002 Surplus Distribution Different Reinsurance Assumptions

Lowered Stop Loss Attachment Point

0

0.05

0.1

0.15

0.2

0.25

0.3

Millions

Pro

babi

lity

Year 2002 Surplus Distribution Slightly Constrained Growth, Tightened Underwriting,

and Increased New Business Retention

0

0.05

0.1

0.15

0.2

0.25

Millions

Pro

babi

lity

ABC’s First Impressions

• Excel/@Risk Platform

• Understandability

• Ability to Modify

ABC’s View on Using the Model

• Strategic Planning

• Capital Allocation

• Reinsurance Contract Negotiations

• Internal Communications

• External Communications– Regulators– Rating Agencies– Investment Community

• Other Company Assessment

ABC’s Concerns

• Usability With Other Software– Catastrophe Models– Fixed Income Security Software

• Presenting Results to Senior Management

• Comparing Expected vs. Actual– Project Last Year and Look at Differences

• Enhanced Assets– Callable Bonds– CMO’s

Future Enhancements

• Expand Enterprise-Wide Modeling Capabilities

• Enhancements to Assets– Callable Bonds– Other Options Embedded in Bonds– CMO’s– Foreign Currency Risk– More Sophisticated Reinvestment Abilities

• Add State and/or Regional Detail in U/W Module

Future Enhancements (cont.)

• Enhancement of U/W Cycle Module– Supply/Demand Curves– Impact on Retention Rates– Impact on Jurisdictional Risk

• Additional Correlations Between LoB’s

• Add Tax Carry-Forwards and Carry-Backs

• Additional Outputs– RBC– BCAR– Others

Summary and Conclusions

• The MRH&T Public-Access Model– Publicly Available– Use Encouraged; Comments Welcome– Evolving

• Application of DFA Model to Companies– Model Flexibility is Important– Test the Results; Make Adjustments if Necessary– Listen to the Company