© English Matthews Brockman 2000
Business Planning in Personal Lines using DFA
A Talk by Mike Brockman
and Karl Murphy
2001 Joint GIRO/CAS Conference
3 – 6 October 2001, Glasgow
© English Matthews Brockman 2000
What is DFA?
“A process for analysing the financial
condition of an insurance enterprise, by
calculating a company’s risk profile through
introducing the uncertainties of the real world
into the management process”
- investigating risk using simulation
© English Matthews Brockman 2000
Traditional Approach to Planning
• Looks at point estimates
• Scenario based only
• Tends not to be holistic in nature
© English Matthews Brockman 2000
Why Use is DFA?
• DFA is a methodology which introduces the
uncertainties of the real world into the
management process
• DFA recognises the fact that in any given
scenario a range of outcomes is possible
• Dynamic in sense of
– Stochastic view of experience
– Dynamic view of strategy
© English Matthews Brockman 2000
Output From a DFA Model
• Varies with nature of the problem
• For a particular business plan obtain a loss
profile
• Need concept of risk (VAR or TVAR?)
• Risk – return measure (e.g. Efficient
frontier)
• Optimal strategies based on risk measure
© English Matthews Brockman 2000
Efficient Frontier Analysis
• Classical efficient
frontier techniques can
be used
• Definition of risk
needs to be determined
• Can assist in deciding
business mix
• Every point is a
strategy
© English Matthews Brockman 2000
How to Build a DFA Model:
The Basic Building Block
Input
Output
Marginal distributions
Correlation /
Dependency
Structure
Deterministic
inputs
© English Matthews Brockman 2000
Base
Module
Simulated
output
variables
with
dependency
structure
Example Underwriting Module
Underwriting Module
Attritional Claims
Underwriting cycle
Cat module
Price Elasticity
Reinsurance
• Each module does not necessarily have only one
output
• Enables accurate modelling of marginal distributions
• Dependencies between modules modelled in the
higher module
• List of submodules is not necessarily complete!
• Each module may represent a segment
© English Matthews Brockman 2000
Business Unit Example
Business Unit
Asset Module
Reserving Module
Underwriting Module
Planning Module
• Modular approach enables replacement of modules
as and when necessary
• All variables from within a module/sub-module
may be made available to model dependency
structures
© English Matthews Brockman 2000
High Level Models
Global DFA Model
Commercial Lines
DFA Model
© English Matthews Brockman 2000
Personal Lines
DFA Model
Other Business area
DFA Model
Business Considerations
in Model Design
•
Business Volumes
- Expenses
- Operational infrastructure
- Solvency and capital requirements
•
Premium Income Levels
-
•
Competition
Insurance cycle
Pricing strategy
Business volume
Extreme Events
- Impacts losses
- Operational infrastructure
- Impacts prices
© English Matthews Brockman 2000
Business Considerations
in Model Design
• Lines of Business
-
Behave differently
Different cycles
Different returns
Different risks
• Economic Factors
-
State of the economy
Inflation
Interest Rates
Stock Market
Litigiousness
© English Matthews Brockman 2000
Financial Management
of your Business
•
•
•
•
•
How do you decide which line of business to grow?
How to you determine the optimal pricing strategy?
How do you measure which strategy is best?
How do you allow for uncertainty?
How do you allow for correlations and dependencies?
© English Matthews Brockman 2000
The Insurance Cycle
Building Block
© English Matthews Brockman 2000
Can the Cycle Be Predicted?
• Lines of business behave differently
• Competition and consolidation
• Information
• Technology
• Barriers to entry
© English Matthews Brockman 2000
Property
Motor
Liability
Acc/Health
1.2
1
.8
Loss Ratio
.6
.4
1.2
1
.8
.6
.4
86
88
90
92
94
96
98
86
88
90
Underwriting Cycle by Class
© English Matthews Brockman 2000
92
94
96
98
Observed Loss Ratio
AR(2)
Sin-Cos
1
Loss Ratio
.9
.8
.7
.6
.5
1985
1987
© English Matthews Brockman 2000
1989
1991
1993
1995
Motor Loss Ratios by Year
1997
1999
2001
Can the Cycle Be Predicted?
• Possibly over short term but uncertain
• Some lines more stable
• Impact of extreme events
• A range of future scenarios
• Could assign probabilities to scenarios
© English Matthews Brockman 2000
Building a Model to Manage Uncertainty
A Simple Example
• How does your future view of the cycle affect your
capital requirements and the probability of ruin?
• How do you choose which line of business to
grow?
© English Matthews Brockman 2000
Model Assumptions
• 2 classes: Motor and Property
• 1000 policies in each class initially
• Initial ave loss £1200 for Motor, £1800 for Property
• Claims frequency 20% for Motor, 15% for Property
• Ave loss ratio 99% for Motor, 98% for Property
• Property more volatile
© English Matthews Brockman 2000
Model Assumptions
• Initial premium approx £500,000 split ~ 50:50
motor/household
• Initial Capital £1,000,000
• Capitalised such that if growth is 5% per annum, the
Board is happy with the level of risk
• Company follows premium levels set by the market
• Assume the company can meet its growth targets
• Simulate over two complete cycles
© English Matthews Brockman 2000
© English Matthews Brockman 2000
© English Matthews Brockman 2000
© English Matthews Brockman 2000
Results from Different Growth Scenarios
Motor
Growth
5%
10%
20%
0%
Extra
Extra*
Property Expected Capital
Growth
Profit
Required
5%
10%
35%
£0.4m
0%
0%
£0.5m
20%
50%
£1.5m
* to maintain risk level
© English Matthews Brockman 2000
Business Planning Model
© English Matthews Brockman 2000