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8/8/2019 VIP Conger
1/25
Use of a DFA Model to EvaluateReinsurance Programs
Case Study
Presented by:Robert F. Conger, FCASTillinghast Towers Perrin
1999 CAS Seminar on Financial Risk ManagementApril 12-13, 1999Denver, Colorado
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Discussion Outline
s The Challenge: How Much Reinsurance to Buy, and What Mix?
s Conceptual Framework
s Methodological Approach
s Case Study: XYZ Insurance
s Key Issues
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Given the behavior of todays insurance and financial markets, manyproperty/casualty insurers are re-evaluating their reinsurance programs
Buy less reinsurance?
s We have excess capital
s Keep net premiums up
s Eliminate unnecessaryexpenses and transactioncosts
s Why share profits?
s Maximize investable assets
Buy more reinsurance?s Regulatory and rating
agency pressure
s Its cheap
s Everyone else is grabbing
this deal
s Let the reinsurers share the
coming unprofitable resultss Predictions of future
catastrophes and mass
torts
s Support the higher limits
were selling
s We cant lose on this latest
reinsurance proposal
s Better safe than sorry
Buy different protection?s Securitization
s Non-P/C reinsurers (e.g.,
Life/Health for workers
compensation)
s Contingent debt/equity
capital
s CAT futuress Blended products that go
beyond traditional hazard
risk
Chief FinancialOfficer
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The design of a reinsurance program involves complex issues, and ismaterial to most insurers bottom lines
s Despite favorable market conditions, reinsurance is still a significant cost
item for many insurers
s Reinsurance decisions are becoming more challenging
u Benefits have always been difficult to evaluate in relation to costs
How does reduction in underwriting volatility affect capital andreturn requirements?
u Decisions are often made at the program level, but need to be placedin overall enterprise context
Need to avoid inefficient reinsurance activity
u Proliferation of reinsurance products expands alternatives to consider
u Alternatives to reinsurance products are becoming available, but addfurther to complexity of analysis
Securitization of risk Contingent debt/equity capital
s Reinsurance price volatility creates short-term tactical opportunities thatcan be more effectively played against a long-term strategy baseline
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Case Study: Reinsurance Strategy for XYZ Insurance
s Large multi-line company, organized into business units
s Reinsurance purchasing occurs at corporate and business unit level
u Corporate buys major treaties covering enterprise
u Business units buy additional coverage to protect their results
s Study focuses on three questions:
u Which elements of the reinsurance program add value over the long
term?
u Which elements are good tactical buys today, due to marketconditions?
u How can the program be restructured to create more value?
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Components of a reinsurance program can be compared to each other, andto other alternatives, by viewing reinsurance as rented capital
s Is reinsurance a cost effective source of capital? It adds value when thiscost of capital is below the cost of alternatives
GrossCapital
Requirement
Cost of RentedReinsurance
Capital
=Cost of Reinsurance
Reduction in Required Capital
Reinsurance
Net CapitalRequirement
Reduction in
RequiredCapital
ExpectedCeded
PremiumCeding
Commission
Expected CededLosses
Cost ofReinsurance
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Reinsurance strategy alternatives can be compared using anAsset/Liability Efficient Frontier (ALEF ) framework
0%
10%
20%
30%
40%
50%
0.0% 0.5% 1.0% 1.5% 2.0%
Level of Risk
ExpectedRetu
rn
M
N
A
G
H
J
O
B
Q
I
D
C
K
E
L
F
R
P
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Either conceptual framework begs several questions
s How to quantify an insurers projected financial results and the potential
for variability in these future results?u Gross of reinsurance
u Net of reinsurance(for each alternative reinsurance program)
s How to measure the Cost of a Reinsurance program and its effect on
an insurers Expected Returns?s How to translate the potential for variability in future results into a
usable and meaningful measure ofRisk?
s What is an insurers Required Capital?
u With no reinsurance
u With current reinsurance
u With alternative reinsurance portfolios
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To quantify projected financial results, XYZ constructed a comprehensivemulti-year model
Line of Business A
Business volumeBusinesscharacteristics
Pricing
Claims
Paid andReserved
Expenses
Cash flow pattern
Reserving patterns
PolicyholderdividendsLine of BusinessB
Line of BusinessC
. . .
Line of BusinessZ
Starting BalanceSheet
FinancialCalculator
Balance Sheet
IncomeStatement
GAAP
Statutory
Economic
Year 1Financial Results
Measures of
Risk
Return
Capital Requirements
Analyzer
ReinsuranceProgram
InvestmentStrategy
CapitalStructure
TaxCalculator
Non-InsuranceIncome
AffiliateResults
Corporate Elements
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Modeled financial outcomes are translated into Risk Measures specific tothe insurer
s Control variability of reportedfinancial results
s Reduce capital needs
u Long-term
u Finance growthu Satisfy regulatory or rating
agency constraints
s Support pricing of primary products
s Offer new insurance products
s
Allow discounting of reservess Current reinsurance price is below
cost
s Etc.
Identify KeyReasons to BuyReinsurance
Define RiskMeasures that
capture the keyobjectives ofthe reinsurance
program
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We have explored several illustrative alternatives to traditional statisticalmeasures of risk and variability
s Different reinsurance programs result in different distributions ofoperating results, and therefore different degrees of risk
s The Risk Measures must be customized to the specific company
TargetReturn Capital
Operating Profit Operating Loss
Unfunded obligations
Below Target Returnmeasure
ExpectedPolicyholder Deficitmeasure
Probability of OperatingResult = X$
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The advantage of Below Target Risk over standard deviation can beillustrated by an example
s These two return probability
distributions have the sameexpected return of 13%,and the same standarddeviation
s Using a target return of 3%(roughly equivalent to azero real return), the top
distribution has a BTR of17.6%; the bottomdistribution has a BTR of27.7%
s The top return distributionis preferable: more upsideand less downside
13%
Probability
Probability
Rate of Return
Pra
bability
Rate of Return
P
rabability
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The Cost of Reinsurance may be modeled several ways
s Current proposals from reinsurers/intermediaries
u Actual
u Hypothetical, based on current market conditions and marketknowledge
s Nature of long-term relationship with reinsurers
u Explicit deal
u Implicit expectations
s Conceptual model of reinsurance pricing
s In the current market, where reinsurers are aggressively seeking top-linegrowth, short term tactical opportunities may lead to differentreinsurance buying decisions than in the long run
The choice of methods will depend on the objectives of the analysis,the expected duration of the reinsurance arrangement, and the natureof information available.
CedingCommission
ExpectedCeded
Premium
Expected CededLosses
Cost ofReinsurance
CedingCommission
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The definition of Required Capital likewise will vary depending oncompany perspective
s Illustrative definitions of required capital with current reinsurance
programu Current capital
u Estimated capital at threshold of specified A.M. Best rating
u Multiple of RBC
u Capital that keeps Expected Policyholder Deficit < x%
s With alternative reinsurance programs, we canu Model the different amount of Required Capital that would produce the
same level of risk, or
u Determine the change in level of risk, given the same amount ofcapital
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While probability of ruin is the simplest form of risk-capital constraint, morecomplex constraints can be defined
Probability Metric
Time Period and Form of Threshold
Measurement Basis
Perspective
s Likelihood of occurrence
s Expected excess severity above threshold
s Expected excess over threshold
s Loss from single event or risk factor
s Annual accounting result
s Results over multi-period planning horizon
s Experience on runoff basis
s Statutorys GAAP
s Economic
s Absolute result
s Result relative to peers
s Result versus rating agency or regulatory norm
s Result relative to investor expectations
Dimensions of Risk-Capital Constraints
Examples: Less than a 1% chance of GAAP operating loss equal to or greaterthan 25% of reported equity
Economic capital sufficient to reduce expected unfundedpolicyholder obligations to less than .25%
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As a first step, XYZ identified the highest cost components of thereinsurance program
Top 15 Programs by Normative Net Annual Cost
0 2 4 6 8 10 12 14 16
Casualty Clash
Special Property QS
Prof Liab XS
Aviation XS
Marine XS
Casualty High XS
Surety QS
Std Property Risk XS
Umbrella QSProperty High Cat
Work Comp Working XS
E&O Program XS
Special Property Fac
Property First Cat
Casualty Working XS
Millions$
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XYZ measured each components contribution to reducing insolvency risk,and translated that into a reduction in required capital
Marginal Reduction in Required Capital
0 20 40 60 80 100 120 140
Casualty Clash
Special Property QS
Prof Liab XS
Aviation XS
Marine XS
Casualty High XS
Surety QS
Std Property Risk XS
Umbrella QS
Property High Cat
Work Comp Working XS
E&O Program XS
Special Property Fac
Property First Cat
Casualty Working XS
Millions$
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Some program elements appear to add significant value; others may beinefficient
Implied Marginal (Normative) Cost of Reinsurance Capital
0.0% 10.0% 20.0% 30.0% 40.0% 50.0% 60.0% 70.0% 80.0%
Casualty Clash
Special Property QS
Prof Liab XS
Aviation XS
Marine XS
Casualty High XS
Surety QS
Std Property Risk XS
Work Comp Working XS
Umbrella QS
Property High Cat
E&O Program XS
Casualty Working XS
Special Property Fac
Property First Cat
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In evaluating strategy alternatives, the focus was narrowed to the threeleast efficient programs
Strategy
A
B
C
D
E
F
G
CasualtyWorking XS
No Change
Double
Retention
Double
Retention
Double
Retention
Treble Retention
Treble Retention
Treble Retention
Work CompWorking XS
No Change
No Change
Double
Retention
Double
Retention
Double
Retention
Treble Retention
Treble Retention
Aviation XS
No Change
No Change
No Change
Double
Retention
Double
Retention
Double
Retention
Treble Retentions 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
10%
11%
12%
0.9% 1.0% 1.1%
Below Target Risk
ExpectedR
et
urn
A
B
D
C
E F
G
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An essential feature of the model is the interaction between its componentsand 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
u Long term patternsu Shocks
u Year-to-year variability
As with the company model itself, inter-relationships betweenelements are an essential feature of the modeling
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Sensitivity testing is an essential step of the process
s Some of the elements to be subjected to sensitivity testing include
u Alternative choices of Risk Measures
u Different definitions of Required Capital
u Selected measure of reinsurance cost
u Modeling time horizon
Years of business
Years of runoffu Parameters used to model reinsurable losses (e.g., size-of-loss
distribution)
u Degree of correlation of results across lines of business and acrossyears
u Base level of company profitability and growth
u Different combinations of reinsurance components
s The objective of the sensitivity testing is to satisfy ourselves that theresults are robust, and not driven by one of the modeling choices
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Of course, modeling does not replace management judgment
s Modeling results will depend on key management perspectives, such as
the choice of Risk Measure
s The final trade-off between risk and return is a matter of preference
But this modeling approach provides strong support to allow making thekey decisions in a well-informed manner.