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© English Matthews Brockman 2000
© 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
InputOutput
BaseModule
Marginal distributions
Correlation / Dependency
Structure
Deterministic inputs
Simulated output
variables with
dependency structure
© English Matthews Brockman 2000
Example Underwriting Module
A ttrit io n a l C la im s U n d e rw rit in g cyc le C a t m od u le P rice E la s tic ity R e in su ra n ce
U n d e rw rit in g M o d u le
• 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
A sse t M od u le R e se rv in g M o d u le U n d e rw rit in g M o d u le P la nn in g M od u le
B u s in ess U n it
• 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
C o m m e rc ia l L in esD F A M o d e l
P e rso n a l L in esD F A M o d e l
O th er B u sin e ss a reaD F A M o d e l
G lo b a l D F A M o d e l
© English Matthews Brockman 2000
Business Considerationsin 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 Considerationsin 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 Managementof 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
Lo
ss R
atio
Underwriting Cycle by Class
Property
.4
.6
.8
1
1.2
Motor
Liability
86 88 90 92 94 96 98
.4
.6
.8
1
1.2
Acc/Health
86 88 90 92 94 96 98
© English Matthews Brockman 2000
Loss
Rat
io
Motor Loss Ratios by Year
Observed Loss Ratio Sin-Cos AR(2)
1985 1987 1989 1991 1993 1995 1997 1999 2001
.5
.6
.7
.8
.9
1
© English Matthews Brockman 2000
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, theBoard 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
Property Growth
Extra Expected
Profit
Extra* Capital
Required5% 5%10% 10% 35% £0.4m20% 0% 0% £0.5m0% 20% 50% £1.5m
* to maintain risk level
© English Matthews Brockman 2000
Business Planning Model