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

Keep net premiums up

Eliminate unnecessary
expenses and transaction
costs

Why share profits?

Maximize investable assets
 Non-P/C reinsurers (e.g.,
pressure
 It’s cheap
Life/Health for workers
 Everyone else is grabbing this
compensation)
 Contingent debt/equity capital
deal
 Let the reinsurers share the
 CAT futures
 Blended products that go
coming unprofitable results
 Predictions of future
catastrophes and mass torts
 Support the higher limits we’re
selling
beyond traditional hazard risk


 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?
6
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
 Loss reserve adequacy
 Reinsurance choices
Therefore, the “right” choice of
reinsurance for XYZ Insurance will
be different than for any other
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
Reduction in
Required Capital
Reinsurance
Gross
Capital
Requirement
Net Capital
Requirement
Cost of
Reinsurance
Expected
Ceded
Premium
Ceding
Commission
Expected Ceded
Losses
Cost of “Rented”
Reinsurance Capital
=
Cost of Reinsurance
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%
Expected Return
L
30%
J
I
H
20%
G
N
R
Q
O
P
F
K
C
D
E
B
A
M
10%
0%
0.0%
0.5%
1.0%
1.5%
2.0%
Level of Risk
10
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
11
Methodological Approach
To quantify projected financial results, XYZ constructed a comprehensive multi-year
model
Line of Business A
Corporate Elements
•Business volume
•Business characteristics
•Pricing
Starting Balance
Sheet
Reinsurance
Program
Investment
Strategy
Capital
Structure
Tax
Calculator
Non-Insurance
Income
Affiliate
Results
•Claims
• Paid and Reserved
•Expenses
•Cash flow pattern
•Reserving patterns
•Policyholder dividends
Line of Business B
Financial
Calculator
Year 1
Financial Results
Line of Business C
•Balance Sheet
...
Line of Business Z
•Income Statement
GAAP
Statutory
Economic
Analyzer
Measures of
•Risk
•Return
•Capital Requirements
13
Modeled financial outcomes are translated into “Risk Measures” specific to the insurer
Identify Key Reasons to
Buy Reinsurance
 Control variability of reported financial
results
 Reduce capital needs
 Long-term
 Finance growth
 Satisfy regulatory or rating agency
constraints
 Support pricing of primary products
Define Risk
Measures that
capture the key
objectives of the
reinsurance
program
 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
Operating Profit
Unfunded obligations
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
distributions have the same
expected return of 13%, and the
same standard deviation
 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%
Probability
 These two return probability
 The top return distribution is
Prabability
preferable: more upside and
less downside
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
 Implicit expectations
 Conceptual model of reinsurance pricing
Cost of
Reinsurance
Expected Ceded
Premium
Ceding
Ceding Commission
Commission
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
Time Period and Form of Threshold
Measurement Basis
Perspective
Examples:

Likelihood of occurrence

Expected excess severity above threshold

Expected excess over threshold

Loss from single event or risk factor

Annual accounting result

Results over multi-period planning horizon

Experience on runoff basis

Statutory

GAAP

Economic

Absolute result

Result relative to peers

Result versus rating agency or regulatory norm

Result relative to investor expectations
“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
22
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%
23
In evaluating strategy alternatives, the focus was narrowed to the three least efficient
programs
Strategy
Casualty
Working XS
Work Comp
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
24
Each strategy was evaluated in terms of its impact on risk and return
Expected Return
12%
11%
E
D
F
G
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
27
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
29
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.
30