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
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 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. PropertyLiability Insurers
• Underwriting
– Aging Phenomenon
– Jurisdictional Risk
– Loss Development
• Catastrophes
• Investment
– Asset Value
– Investment Income
Specifics Provisions of Model
• Six separate, but interrelated modules
Investments
Underwriting
Interest rate generator
Catastrophes
Taxation
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 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
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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 hard
Immature soft
Mature hard
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
Bonds
Market values calculated based on term structure of
interest rates
Includes provision for default
Equities - 3 step approach
1 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 rates
3 Final return includes random component (mean = 0,
standard deviation = 15%)
Interest Rate Generator
Cox-Ingersoll-Ross one factor model
r  a (b  r )t  s r 
r  short term interest rate
a  speed of reversion  .2339
b  long run mean interest rate  .05
s  volatility of interest rate process  .0854
r  annual change in r
t  one year
  random sampling from a standard normal distributi on
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
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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. 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 Surplus
CV 2003 Surplus
2003 Net Earned Premium
Avg. 5 Year HMP L/R
Avg. 5 Year WC L/R
Minimum Surplus
Maximum Surplus
51,915
10.3%
83,807
76.9%
74.2%
40,999
61,133
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 Surplus
CV 2003 Surplus
2003 Net Earned Premium
Avg. 5 Year HMP L/R
Avg. 5 Year WC L/R
Minimum Surplus
Maximum Surplus
51,725
11.0%
84,035
77.2%
74.2%
40,490
61,726
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 Surplus
CV 2003 Surplus
2003 Net Earned Premium
Avg. 5 Year HMP L/R
Avg. 5 Year WC L/R
Minimum Surplus
Maximum Surplus
50,296
10.8%
83,155
77.5%
75.4%
38,999
58,685
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 Surplus
CV 2003 Surplus
2003 Net Earned Premium
Avg. 5 Year HMP L/R
Avg. 5 Year WC L/R
Minimum Surplus
Maximum Surplus
41,141
17.1%
104,633
80.4%
75.9%
30,702
54,310
OK, Now It’s Your Turn ...