Use of a DFA Model to Evaluate Reinsurance Programs Case Study Presented by: Robert F. Conger, FCAS...
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Transcript of Use of a DFA Model to Evaluate Reinsurance Programs Case Study Presented by: Robert F. Conger, FCAS...
Use of a DFA Model to Evaluate Reinsurance Programs
Case Study
Presented by:Robert F. Conger, FCASTillinghast – Towers Perrin
1999 CAS Seminar on Financial Risk ManagementApril 12-13, 1999Denver, Colorado
2
Discussion Outline
The Challenge: How Much Reinsurance to Buy, and What Mix?
Conceptual Framework
Methodological Approach
Case Study: XYZ Insurance
Key Issues
The Challenge: How Much Reinsurance to Buy,and What Mix?
4
Given the behavior of today’s insurance and financial markets, many property/casualty insurers are re-evaluating their reinsurance programs
Buy less reinsurance?
We have excess capital
Keep net premiums up
Eliminate unnecessary expenses and transaction costs
Why share profits?
Maximize investable assets
Buy more reinsurance? Regulatory and rating
agency pressure It’s cheap Everyone else is grabbing
this deal Let the reinsurers share the
coming unprofitable results Predictions of future
catastrophes and mass
torts Support the higher limits
we’re selling We can’t lose on this latest
reinsurance proposal Better safe than sorry
Buy different protection? Securitization Non-P/C reinsurers (e.g.,
Life/Health for workers
compensation) Contingent debt/equity
capital CAT futures Blended products that go
beyond traditional hazard
risk
Chief Financial Officer
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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
6
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?
Conceptual Framework
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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
Risk appetite/aversion
Corporate affiliates
Corporate structure
Stakeholder expectations
Rating agency and regulatory considerations
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.
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Components of a reinsurance program can be compared to each other, and to other alternatives, by viewing reinsurance as “rented” capital
Is reinsurance a cost effective source of capital? It adds value when this cost of capital is below the cost of alternatives
Gross Capital
Requirement
Cost of “Rented” Reinsurance
Capital
=Cost of Reinsurance
Reduction in Required Capital
Reinsurance
Net Capital Requirement
Reduction in Required Capital
ExpectedCeded
PremiumCeding
Commission
Expected Ceded Losses
Cost of Reinsurance
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Reinsurance strategy alternatives can be compared using an Asset/Liability Efficient Frontier (ALEF) framework
0%
10%
20%
30%
40%
50%
0.0% 0.5% 1.0% 1.5% 2.0%
Level of Risk
Ex
pe
cte
d R
etu
rn
M
N
A
G
H
J
O
B
Q
I
D
C
K
E
L
F
R
P
11
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
Methodological Approach
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To quantify projected financial results, XYZ constructed a comprehensive multi-year model
Line of Business A
•Business volume
•Business characteristics
•Pricing
•Claims
•Paid and Reserved
•Expenses
•Cash flow pattern
•Reserving patterns
•Policyholder dividendsLine of Business B
Line of Business C
. . .
Line of Business Z
Starting Balance Sheet
Financial Calculator
•Balance Sheet
•Income Statement
GAAP
Statutory
Economic
Year 1Financial Results
Measures of
•Risk
•Return
•Capital Requirements
Analyzer
Reinsurance Program
Investment Strategy
Capital Structure
TaxCalculator
Non-Insurance Income
AffiliateResults
Corporate Elements
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Modeled financial outcomes are translated into “Risk Measures” specific to the insurer
Control variability of reported financial results
Reduce capital needs Long-term Finance growth Satisfy regulatory or rating
agency constraints
Support pricing of primary products
Offer new insurance products
Allow discounting of reserves
Current reinsurance price is below cost
Etc.
Identify Key Reasons to Buy
Reinsurance
Define Risk Measures that
capture the key objectives of
the reinsurance program
15
We have explored several illustrative alternatives to traditional statistical measures of risk and variability
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
Target Return Capital
Operating Profit Operating Loss
Unfunded obligations
“Below Target Return” measure
“Expected Policyholder Deficit” measure
Probability of Operating Result = X$
16
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
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
13%
Pro
bab
ility
Pro
bab
ility
Rate of Return
Pra
bab
ility
Rate of Return
Pra
bab
ility
17
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
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
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.
Ceding Commission
Expected Ceded
Premium
Expected Ceded Losses
Cost of Reinsurance
Ceding Commission
18
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
19
While probability of ruin is the simplest form of risk-capital constraint, more complex constraints can be defined
Probability Metric
Time Period and Form of Threshold
Measurement Basis
Perspective
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
Dimensions of Risk-Capital Constraints
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%”
Case Study: XYZ Insurance
21
As a first step, XYZ identified the highest cost components of the reinsurance 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 QS
Property High Cat
Work Comp Working XS
E&O Program XS
Special Property Fac
Property First Cat
Casualty Working XS
Millions$
22
XYZ measured each component’s 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 be inefficient
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
24
In evaluating strategy alternatives, the focus was narrowed to the three least efficient programs
Strategy
A
B
C
D
E
F
G
Casualty Working XS
No Change
Double
Retention
Double
Retention
Double
Retention
Treble Retention
Treble Retention
Treble Retention
Work Comp Working 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 Retention The same framework can be used to evaluate alternative programs, in
addition to changes to the existing program structure
25
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
Ex
pe
cte
d R
etu
rn
A
B
D
C
E F G
Key Issues
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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
28
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
29
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
30
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.