1. Use of a DFA Model to Evaluate Reinsurance Programs
Presentation Title
Use of a DFA Model to Evaluate Reinsurance Programs
Case Study
1999 CAS Seminar on Financial Risk Management April 12-13, 1999 Denver, Colorado
Friday, March 31, 2017
Presented by: Robert F. Conger, FCAS Tillinghast – Towers Perrin

2. Discussion Outline
The Challenge: How Much Reinsurance to Buy, and What Mix?
Conceptual Framework
Methodological Approach
Case Study: XYZ Insurance
Key Issues

3. 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 

5. 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?

7. Conceptual Framework

8. 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.

9. Components of a reinsurance program can be compared to each other, and to other alternatives, by viewing reinsurance as “rented” capital
Gross Capital Requirement
Reinsurance
Reduction in Required Capital
Net Capital Requirement
Expected Ceded Premium
Cost of Reinsurance
Ceding Commission
Expected Ceded Losses
Cost of Reinsurance
Reduction in Required Capital
Cost of “Rented” Reinsurance Capital =
Is reinsurance a cost effective source of capital? It adds value when this cost of capital is below the cost of alternatives

10. Important considerations include time horizon reporting interval
Reinsurance strategy alternatives can be compared using an Asset/Liability Efficient Frontier (ALEF) framework
Presentation Title 0%
10%
20%
30%
40%
50%
0.0%
0.5%
1.0%
1.5%
2.0%
Level of Risk
Expected Return M N A G H J O B Q I D C K E L F R P
Friday, March 31, 2017
Each point is a strategy as to Assets, Liabilities, Reinsurance and Capital Structure
For example, Strategy C could be a $1-million occurrence retention and a 15% allocation to stocks
Strategy K is superior to C because it offers a higher expected return for the same level of risk
Expected return and level of risk metrics can be customized to fit the perspective of the client
But the choice of performance and risk metrics can have an impact on the relative ranking of strategies
Important considerations include
time horizon
reporting interval
single period vs. cumulative volatility
maximum tolerable period volatility
STAT vs. GAAP measures
We prefer to look at performance in terms of change in the economic value of the company (or business) and to look at risk as “below target risk”, a measure designed to focus on downside risk.

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

12. Methodological Approach

13. Year 1 Financial Results
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 dividends
Corporate Elements
Starting Balance Sheet
Reinsurance Program
Investment Strategy
Capital Structure
Tax Calculator
Financial Calculator
Non-Insurance Income
Affiliate Results
Line of Business B
Balance Sheet
Income Statement
GAAP
Statutory
Economic
Year 1 Financial Results
Line of Business C
. . .
Line of Business Z
Analyzer
Measures of
Risk
Return
Capital Requirements

14. Identify Key Reasons to Buy Reinsurance
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
Offer new insurance products
Allow discounting of reserves
Current reinsurance price is below cost
Etc.
Define Risk Measures that capture the key objectives of the reinsurance program

15. The Risk Measures must be customized to the specific company
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

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%

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
Cost of Reinsurance
Expected Ceded Premium
Ceding Commission
Ceding 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.

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
Dimensions of Risk-Capital Constraints
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
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%”

20. Case Study: XYZ Insurance

21. Presentation Title
As a first step, XYZ identified the highest cost components of the reinsurance program
Top 15 Programs by Normative Net Annual Cost 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
Friday, March 31, 2017 $

22. XYZ measured each component’s contribution to reducing insolvency risk, and translated that into a reduction in required capital $

23. Some program elements appear to add significant value; others may be inefficient

24. In evaluating strategy alternatives, the focus was narrowed to the three least efficient programs
Casualty Working XS
No Change
Double Retention
Treble Retention
Work Comp Working XS
No Change
Double Retention
Treble Retention
Aviation XS
No Change
Double Retention
Treble Retention
Strategy A B C D E F G
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
12%
11% G F E
Expected Return D C B A
10%
0.9%
1.0%
1.1%
Below Target Risk

26. Key Issues

27. 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.