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
DynaMo
Catastrophe
Generator
U/W
Inputs
U/W Generator
Payment Patterns
U/W Cycle
U/W
Cashflows
Tax
Interest Rate
Generator
Investment
& Economic
Inputs
Investment
Generator
Investment
Cashflows
Outputs
& Simulation
Results
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
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–
–
–
–
–
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 Distribution
Original Assumptions
0.25
0.15
0.1
0.05
Millions
9. 2
30
5. 0
27
0. 8
24
6. 6
20
2. 4
17
8. 2
13
3. 9
10
.7
69
.5
35
1.3
.9
0
-32
Probability
0.2
Initial Findings - Possible Reasons
Large Growth
Objectives
Surplus Drain
Renewal
Ratio
New Business
Penalty
Initial Findings - Additional
Complications
Growth
Objectives
Unacceptable
Surplus
Drain
Loss Ratio
Deterioration
Devaluation
of Assets
Adverse Reserve
Development
Unusual
Catastrophes
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
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–
–
–
•
•
•
•
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
–
–
–
–
–
–
–
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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
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–
–
–
Actuarial
Investments
Reinsurance
CFO
• Interactive Session
– Q&A
– Laptops for Training and Variation
Suggested Changes
• Our Original Suggestion
– Temper Growth Rate
• ABC’s Suggestion
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–
–
–
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 Distribution
Constrained Growth Assumptions
0.25
0.15
0.1
0.05
Millions
4.8
33
8.1
30
1.4
28
4.7
25
8.0
22
1.3
20
4.6
17
7.8
14
1.1
12
94
.4
0
67
.7
Probability
0.2
Year 2002 Surplus Distribution
Different Reinsurance Assumptions
Increased Stop Loss Max Ceding Amount
0.3
0.2
0.15
0.1
0.05
Millions
0.4
28
2.3
24
4.3
20
6.2
16
8.1
12
90
.1
52
.0
13
.9
-62
.2
-24
.2
0.3
0
-10
Probability
0.25
Year 2002 Surplus Distribution
Different Reinsurance Assumptions
Lowered Stop Loss Attachment Point
0.3
0.2
0.15
0.1
0.05
Millions
8.7
30
2.0
27
5.3
23
8.7
19
2.0
16
5.3
12
88
.6
51
.9
15
.2
.5
-21
.2
0
-58
Probability
0.25
Year 2002 Surplus Distribution
Slightly Constrained Growth, Tightened Underwriting,
and Increased New Business Retention
0.25
0.15
0.1
0.05
Millions
6.2
35
6.2
32
6.2
29
6.2
26
6.3
23
6.3
20
6.3
17
6.3
14
6.4
11
86
.4
0
56
.4
Probability
0.2
ABC’s First Impressions
• Excel/@Risk Platform
• Understandability
• Ability to Modify
ABC’s View on Using the Model
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•
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•
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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