Use of a DFA Model to Evaluate
Reinsurance Programs
Case Study
1999 CAS Seminar on Financial Risk Management
April 12-13, 1999
Denver, Colorado
Presented by:
Robert F. Conger, FCAS
Tillinghast – Towers Perrin
Discussion Outline
The Challenge: How Much Reinsurance to Buy, and What Mix?
Conceptual Framework
Methodological Approach
Case Study: XYZ Insurance
Key Issues
2
The Challenge: How Much Reinsurance to Buy,
and What Mix?
Given the behavior of today’s insurance and financial markets, many property/casualty
insurers are re-evaluating their reinsurance programs
Buy less reinsurance? Buy more reinsurance? Buy different protection?
We have excess capital Regulatory and rating agency Securitization
pressure Non-P/C reinsurers (e.g.,
Keep net premiums up
It’s cheap Life/Health for workers
Eliminate unnecessary
expenses and transaction Everyone else is grabbing this compensation)
costs deal Contingent debt/equity capital
Why share profits? Let the reinsurers share the CAT futures
coming unprofitable results Blended products that go
Maximize investable assets
Predictions of future beyond traditional hazard risk
catastrophes and mass torts
Support the higher limits we’re
selling
We can’t lose on this latest
reinsurance proposal
Better safe than sorry
Chief Financial Officer
4
The design of a reinsurance program involves complex issues, and is material to most
insurers’ bottom lines
Despite favorable market conditions, reinsurance is still a significant cost item for
many insurers
Reinsurance decisions are becoming more challenging
Benefits have always been difficult to evaluate in relation to costs
How does reduction in underwriting volatility affect capital and return
requirements?
Decisions are often made at the program level, but need to be placed in overall
enterprise context
Need to avoid inefficient reinsurance activity
Proliferation of reinsurance products expands alternatives to consider
Alternatives to reinsurance products are becoming available, but add further to
complexity of analysis
Securitization of risk
Contingent debt/equity capital
Reinsurance price volatility creates short-term tactical opportunities that can be
more effectively played against a long-term strategy baseline
5
Case Study: Reinsurance Strategy for XYZ Insurance
Large multi-line company, organized into business units
Reinsurance purchasing occurs at corporate and business unit level
Corporate buys major treaties covering enterprise
Business units buy additional coverage to protect their results
Study focuses on three questions:
Which elements of the reinsurance program add value over the long term?
Which elements are good tactical buys today, due to market conditions?
How can the program be restructured to create more value?
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Conceptual Framework
The answers to reinsurance questions must be specific to XYZ Insurance
Compared to XYZ Insurance, no other insurance company has exactly the same
Volume and mix of business
Profitability history and outlook
Exposure to large claims, mass torts, and catastrophes
Investment strategy and performance
Capital amount and structure Therefore, the “right” choice of
reinsurance for XYZ Insurance will
Loss reserve adequacy be different than for any other
Reinsurance choices company . . . And may be different
next year than this year.
Risk appetite/aversion
Corporate affiliates
Corporate structure
Stakeholder expectations
Rating agency and regulatory considerations
8
Components of a reinsurance program can be compared to each other, and to other
alternatives, by viewing reinsurance as “rented” capital
Reinsurance Reduction in
Required Capital
Gross
Capital
Requirement Net Capital
Requirement
Cost of
Reinsurance
Expected
Ceded Ceding
Premium Commission
Expected Ceded
Losses
Cost of “Rented” Cost of Reinsurance
Reinsurance Capital
=
Reduction in Required Capital
Is reinsurance a cost effective source of capital? It adds value when this cost of
capital is below the cost of alternatives
9
Reinsurance strategy alternatives can be compared using an
Asset/Liability Efficient Frontier (ALEF) framework
50%
40%
L
F
Expected Return
30% K
J I R
H Q C
O
N D
20% G P E
B
A
M
10%
0%
0.0% 0.5% 1.0% 1.5% 2.0%
Level of Risk
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Either conceptual framework begs several questions
How to quantify an insurer’s projected financial results and the potential for
variability in these future results?
Gross of reinsurance
Net of reinsurance
(for each alternative reinsurance program)
How to measure the Cost of a Reinsurance program and its effect on an insurer’s
Expected Returns?
How to translate “the potential for variability” in future results into a usable and
meaningful measure of Risk?
What is an insurer’s Required Capital?
With no reinsurance
With current reinsurance
With alternative reinsurance portfolios
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Methodological Approach
To quantify projected financial results, XYZ constructed a comprehensive multi-year
model
Line of Business A
Corporate Elements
•Business volume
•Business characteristics Starting Balance Reinsurance Investment
Sheet Program Strategy
•Pricing
•Claims
Capital Tax
• Paid and Reserved Structure Calculator
•Expenses
•Cash flow pattern Non-Insurance Affiliate
•Reserving patterns Financial Income Results
Calculator
•Policyholder dividends
Line of Business B Year 1
Financial Results
Line of Business C
•Balance Sheet
... GAAP
•Income Statement
Statutory
Line of Business Z
Economic
Measures of
Analyzer
•Risk
•Return
•Capital Requirements
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Modeled financial outcomes are translated into “Risk Measures” specific to the insurer
Identify Key Reasons to
Buy Reinsurance
Control variability of reported financial
results
Define Risk
Reduce capital needs
Measures that
Long-term
capture the key
Finance growth
objectives of the
Satisfy regulatory or rating agency
constraints reinsurance
program
Support pricing of primary products
Offer new insurance products
Allow discounting of reserves
Current reinsurance price is below
cost
Etc.
14
We have explored several illustrative alternatives to traditional statistical measures of
risk and variability
Probability of Operating Result = X$
“Below Target Return” measure
“Expected Policyholder
Deficit” measure
Target Return
Capital Unfunded obligations
Operating Profit Operating Loss
Different reinsurance programs result in different distributions of operating results,
and therefore different degrees of “risk”
The Risk Measures must be customized to the specific company
15
The advantage of Below Target Risk over standard deviation can be illustrated by
an example
These two return probability
distributions have the same
expected return of 13%, and the
same standard deviation
Probability
Using a target return of 3%
(roughly equivalent to a zero
real return), the top distribution
has a BTR of 17.6%; the bottom
distribution has a BTR of 27.7%
The top return distribution is
preferable: more upside and
less downside
Prabability
Rate of Return
13%
16
The Cost of Reinsurance may be modeled several ways
Current proposals from reinsurers/intermediaries
Actual
Hypothetical, based on current market conditions and market knowledge
Nature of long-term relationship with reinsurers
Explicit deal Cost of
Reinsurance
Implicit expectations Expected Ceded
Premium Ceding Commission
Ceding
Commission
Conceptual model of reinsurance pricing Expected Ceded
Losses
The choice of methods will depend on the objectives of the analysis, the
expected duration of the reinsurance arrangement, and the nature of information
available.
In the current market, where reinsurers are aggressively seeking top-line growth,
short term tactical opportunities may lead to different reinsurance buying decisions
than in the long run
17
The definition of “Required Capital” likewise will vary depending on company
perspective
Illustrative definitions of required capital with current reinsurance program
Current capital
Estimated capital at threshold of specified A.M. Best rating
Multiple of RBC
Capital that keeps Expected Policyholder Deficit < x%
With alternative reinsurance programs, we can
Model the different amount of Required Capital that would produce the same
level of risk, or
Determine the change in level of risk, given the same amount of capital
18
While probability of ruin is the simplest form of risk-capital constraint, more complex
constraints can be defined
Dimensions of Risk-Capital Constraints
Probability Metric Likelihood of occurrence
Expected excess severity above threshold
Expected excess over threshold
Time Period and Form of Threshold Loss from single event or risk factor
Annual accounting result
Results over multi-period planning horizon
Experience on runoff basis
Measurement Basis Statutory
GAAP
Economic
Perspective Absolute result
Result relative to peers
Result versus rating agency or regulatory norm
Result relative to investor expectations
Examples: “Less than a 1% chance of GAAP operating loss equal to or greater than 25%
of reported equity”
“Economic capital sufficient to reduce expected unfunded policyholder
obligations to less than .25%”
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Case Study: XYZ Insurance
As a first step, XYZ identified the highest cost components of the reinsurance program
Top 15 Programs by Normative Net Annual Cost
Casualty Working XS
Property First Cat
Special Property Fac
E&O Program XS
Work Comp Working XS
Property High Cat
Umbrella QS
Std Property Risk XS
Surety QS
Casualty High XS
Marine XS
Aviation XS
Prof Liab XS
Special Property QS
Casualty Clash
0 2 4 6 8 10 12 14 16
$ Millions
21
XYZ measured each component’s contribution to reducing insolvency risk, and
translated that into a reduction in required capital
Marginal Reduction in Required Capital
Casualty Working XS
Property First Cat
Special Property Fac
E&O Program XS
Work Comp Working XS
Property High Cat
Umbrella QS
Std Property Risk XS
Surety QS
Casualty High XS
Marine XS
Aviation XS
Prof Liab XS
Special Property QS
Casualty Clash
0 20 40 60 80 100 120 140
$ Millions
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Some program elements appear to add significant value; others may be inefficient
Implied Marginal (Normative) Cost of Reinsurance Capital
Property First Cat
Special Property Fac
Casualty Working XS
E&O Program XS
Property High Cat
Umbrella QS
Work Comp Working XS
Std Property Risk XS
Surety QS
Casualty High XS
Marine XS
Aviation XS
Prof Liab XS
Special Property QS
Casualty Clash
0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0%
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In evaluating strategy alternatives, the focus was narrowed to the three least efficient
programs
Casualty Work Comp
Strategy Working XS Working XS Aviation XS
A No Change No Change No Change
B Double Retention No Change No Change
C Double Retention Double Retention No Change
D Double Retention Double Retention Double Retention
E Treble Retention Double Retention Double Retention
F Treble Retention Treble Retention Double Retention
G Treble Retention Treble Retention Treble Retention
The same framework can be used to evaluate alternative programs, in addition
to changes to the existing program structure
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Each strategy was evaluated in terms of its impact on risk and return
12%
Expected Return
11% G
F
E
D
C
B
A
10%
0.9% 1.0% 1.1%
Below Target Risk
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Key Issues
An essential feature of the model is the interaction between its components and
across time
Correlations between lines of business
“Runs” of good or bad years
Relationships between historical and future results
Macro-economic trends over time
Correlations between inflation, equity returns, and interest rates
Relationships between underwriting results and investment results
Relationship between gross-of-reinsurance results and recoveries
Patterns of reserve inadequacy/redundancy
Patterns of variation in cash flow
Influence of past results on future management strategies and actions
Investment strategy dependent on yield curve and/or asset duration
Shareholder dividends dependent on operating results
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The model is run in a wide variety of scenarios over multiple future years
Future inflation rates
Future interest rates and investment returns
Catastrophes
Random large losses
Loss ratio movement
Long term patterns
Shocks
Year-to-year variability
As with the company model itself, inter-relationships between elements are an
essential feature of the modeling
28
Sensitivity testing is an essential step of the process
Some of the elements to be subjected to sensitivity testing include
Alternative choices of Risk Measures
Different definitions of Required Capital
Selected measure of reinsurance cost
Modeling time horizon
Years of business
Years of runoff
Parameters used to model reinsurable losses (e.g., size-of-loss distribution)
Degree of correlation of results across lines of business and across years
Base level of company profitability and growth
Different combinations of reinsurance components
The objective of the sensitivity testing is to satisfy ourselves that the results are
robust, and not driven by one of the modeling choices
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Of course, modeling does not replace management judgment
Modeling results will depend on key management perspectives, such as the choice
of Risk Measure
The final trade-off between risk and return is a matter of preference
But this modeling approach provides strong support to allow making the key
decisions in a well-informed manner.
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