DFA and Reinsurance Structuring

1
DFA and Reinsurance Structuring Presented by
Joseph W. Wallen, FCAS General Re Capital
Consultants CAS Ratemaking Seminar March 9-10,
2000


General Reinsurance
2
Topics

• I. How Are We Using DFA?
• II. Using DFA to Evaluate Reinsurance Structure
• III. Reinsurance Applications
• The Business Managers View
• The CFOs View
• IV. Conclusion

3
How Are We Using DFA?
4
How Do We Use DFA Models for Clients in the
Reinsurance Context?

• As business consultants to our clients we use
  DFA to
• Evaluate appropriate retentions
• Evaluate and choose optimal reinsurance
  structures
• Independent appraisal of different reinsurance
  proposals
• As a part of the General Re team we use DFA
  to
• Design effective reinsurance programs for
  reinsurance clients
• Help General Re model the underwriting risk it is
  taking
• e.g., mix of business questions

5
Why Use DFA to Evaluate Reinsurance Structure?

• Traditionally evaluated using intuition/rules
  of thumb
• Retentions as a percent of PHS
• Assumptions about riskiness of certain
  lines/layers
• DFA Can
• Confirm traditional rules of thumb
• Add quantitative analysis to the process
• Expand the evaluation criteria to include other
  items
• e.g. asset allocation issues
• Incorporate additional factors
• Between line correlations/diversification
• Asset/Liability correlations

6
Using DFA to Evaluate Reinsurance Structure
7
Steps Involved in Evaluating Reinsurance
Structures
Determine Risk/Return Metrics
Decompose AY Risk Into Line/Layer
Additional Considerations
Generate R/I Opportunity Set and Generate DFA
Output
Evaluate DFA Output versus Risk/Return Metrics
8
What Are Some Steps in Evaluating Reinsurance
Structure?

• Step 1 - Determine Management Objectives for
  Reinsurance
• Depends on who answers the question
• Business Unit/Underwriting Manager
• Incentive compensation based
• Possibly based on U/W Income or Combined Ratio
• Other qualitative issues
• CFO
• Enterprise decisions
• Public vs. Mutual company issues
• More focused on balance sheet/income statement
• Capital adequacy

9
What Are the Steps in Evaluating Reinsurance
Structure?

• Step 2 - Determine Appropriate Metrics and
  Constraints
• How do they measure risk?
• Uncertainty (e.g. Standard Deviation)
• Loss (e.g., Value at Risk or Surplus Decline)
• Mean Excess Loss
• What return metric is used to evaluate
  reinsurance?
• Dont pre-suppose one correct method
• Different business models
• Loss Ratios/Combined Ratios
• Accident Year/Calendar Year
• Book Income
• Total Return
• Earnings Per Share

10
What Are the Steps in Evaluating Reinsurance
Structure?

• Step 3 - Decompose Accident Year results by
  Line/Layer
• Reinsurance generally starts with impact on
  Accident Year
• Additional impact on other items
• Investment Income
• Reserves
• Examine how U/W results covary with Lines/Layers
• Will indicate where the u/w risk is
• Might lead to the relative value of reinsured
  lines/ layers
• Still need to evaluate in the context of DFA Model

11
What Are the Steps in Evaluating Reinsurance
Structure?

• Step 4 - Create Set of Reinsurance Choices
• Need to be reasonable and defined
• Unlike asset allocation issues
• Generally looking at discrete choices
• Based on examination of losses by layer in
  previous step
• Evaluate where reinsurance dollars are best
  allocated

12
What Are the Steps in Evaluating Reinsurance
Structure?

• Step 5 - Evaluate Alternative Reinsurance
  Structures Using
• the DFA Model
• Based on original risk/return metrics
• Need to consider additional evaluation criteria
  outside the DFA Model
• claims
• underwriting
• financial strength
• production of business

13
The Underwriting Managers Perspective
14
Examples of Evaluating Reinsurance Structure

• Example 1 - The Underwriting Managers
  Perspective
• Senior management mandates
• Target 95 Combined Ratio
• Maximize underwriting profit dollars
• Measure on an annual basis for accident year
• Managers objectives
• Grow business
• Maximize bonus
• Minimize underwriting risk
• Probability of CR gt 105, lt 5

15
Evaluating Reinsurance Structure

• Within the DFA Model
• Capture information for all underwriting accounts
• Look at losses by potential reinsurance layer
• Should include correlations between lines
• Decompose accident year underwriting risk by
  line/layer
• Identify areas of greatest risk
• Normalize for expected ceded profit
• Select line/layer combinations of cessions to
  design program
• Compare resulting program to risk/return metrics

16
Where is the underwriting risk?
17
Where is the underwriting risk?
18
Where is the underwriting risk?
Covariance of Layer Loss with U/W Profit
Line
Layer
CAL
GL
PPAL
APD
Grand Total
250 xs 0
(5,056,680)

(1,451,143)

(166,236)


(390,639)


(7,117,259)

250 xs 250
(1,259,468)

(454,840)

(6,391)


0
(1,720,699)

500 xs 500
(1,268,704)

(579,009)

0
0
(1,847,713)

4 xs 1
(568,757)

(805,518)

0
0
(1,374,275)

Total
(8,153,609)

(3,290,510)

(172,627)


(390,639)

(12,059,946)

19
Where is the underwriting risk?
Ratio of Covariance to Ceded Profit Dollars
Line
Layer
CAL
GL
PPAL
APD
Grand Total





250 xs 0
5,360
5,177
662
1,009
3,823





-
7,627
250 xs 250
8,041
7,162
3,908





500 xs 500
7,179
7,849
-
-
7,234





4 xs 1
9,811
19,076
-
-
15,455
20
Evaluating Reinsurance Based on Risk Metrics
Combined Ratio - Worst 25 of Outcomes
115.0
113.0
111.0
109.0
Combined Ratio
107.0
105.0
103.0
101.0
99.0
75
77
79
81
83
85
87
89
91
93
95
97
99
Percentile
Gross Business
1M Retn
250k Retn
500k Retn
21
Underwriting Managers Perspective

• Based on these criteria manager may choose an
  across the board 500k
• retention
• Meets Combined Ratio tolerance
• Cedes approximately 350k annual nominal u/w
  profit
• Also need to examine on an economic basis
• Will increase ceded profits
• Ignores further diversification benefits on
  balance sheet
• Assets and Underwriting not perfectly correlated
• There may be additional natural hedges against
  income uncertainty
• For example
• Ceding a layer/line negatively correlated with
  assets may increase income risk

22
Optimization Results - Efficient Frontier

• Can construct an efficient frontier of
  retentions by line or unit
• Currently done in a brute force fashion via
  simulations
• Requires us to be restrictive in developing our
  opportunity set
• Provides a useful framework for evaluating
  risk/return tradeoff of retention as it impacts
  the underwriting account

23
Reinsurance from the CFOs Perspective
24
Examples of Evaluating Reinsurance Structure

• Example 2 - The CFOs Perspective
• Goal for reinsurance is to
• Reduce likelihood of missing EPS by gt 0.50/share
• Minimize probability of 10 PHS Loss
• Maximize profit/ROE
• Generally want to minimize reinsurance use
• Subject to earnings volatility constraints

25
Evaluating Reinsurance Structure at the
Enterprise Level

• Other factors beyond AY underwriting results
• Asset category risk and return
• Reserve runoff
• Correlations between Liabilities and Assets
• Similar process to the Underwriting Managers
  perspective
• Consider U/W contribution to income/ROE/Capital
  risk
• Reinsurance only affects a portion of risk
  components

26
Where is the return risk?
27
Impact of Reinsurance on EPS

• Traditional Excess of Loss Reinsurance
• Has minimal impact on EPS downside risk except
  at tails
• Diversification of earnings stream
• Leads to use of stop loss if available

28
Impact of Reinsurance on Likelihood of PHS
Decline

• Unlike EPS protection this metric shows real
  value
• Choice depends on risk tolerance
• Places more value on Excess of Loss

29
Conclusion
30
DFA and Reinsurance Structure

• DFA can be useful in evaluating reinsurance
• Identifies areas of risk from underwriting that
  might
• benefit from reinsurance
• Indicates potential value of reinsurance as it
  impacts
• Accident Year results
• Balance Sheet/Earnings
• A tool to evaluate potential structures
• Exploring alternatives such as
• Underwriting risk versus asset risk
• Using reinsurance to change mix of risk across
  balance
• sheet

31

Thank You.