DFA and Reinsurance Structuring

Presented by Joseph W. Wallen, FCASGeneral Re Capital Consultants

CAS Ratemaking SeminarMarch 9-10, 2000

General Reinsurance

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Topics

I. How Are We Using DFA?

II. Using DFA to Evaluate Reinsurance Structure

III. Reinsurance Applications The Business Manager’s View The CFO’s View

IV. Conclusion

How Are We Using DFA?

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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

How Do We Use DFA Models for Clients in the Reinsurance Context?

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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

Why Use DFA to Evaluate Reinsurance Structure?

Using DFA to Evaluate Reinsurance Structure

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Steps Involved in Evaluating Reinsurance Structures

Determine Risk/Return Metrics

Decompose AY Risk

Into Line/Layer

Generate R/I Opportunity Set and

Generate DFA Output

Evaluate DFA Output versus

Risk/Return Metrics

Additional Considerations

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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

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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? Don’t pre-suppose one correct method Different business models Loss Ratios/Combined Ratios

Accident Year/Calendar Year Book Income Total Return Earnings Per Share

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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

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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

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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

The Underwriting Manager’s Perspective

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Examples of Evaluating Reinsurance Structure

Example 1 - The Underwriting Manager’s Perspective

Senior management mandates: Target 95% Combined Ratio Maximize underwriting profit dollars Measure on an annual basis for accident year

Manager’s objectives: Grow business Maximize bonus Minimize underwriting “risk”

Probability of CR > 105%, < 5%

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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

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Where is the underwriting risk?

Allocation of AY U/W Risk by Layer

59%14%

15%

11%

250 xs 0 250 xs 250 500 xs 500 4 xs 1

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Where is the underwriting risk?

Allocation of GL Risk Contribution by Layer - to U/W Results

12%

4%

5%

7%

250 xs 0 250 xs 250 500 xs 500 4 xs 1

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Where is the underwriting risk?

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)

Line

Covariance of Layer Loss with U/W Profit

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Where is the underwriting risk?

Layer CAL GL PPAL APD Grand Total

250 xs 0 5,360

5,177

662

1,009

3,823250 xs 250 8,041

7,162

3,908

-

7,627

500 xs 500 7,179

7,849

-

-

7,234

4 xs 1 9,811

19,076

-

-

15,455

Line

Ratio of Covariance to Ceded Profit Dollars

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Evaluating Reinsurance Based on Risk Metrics

Combined Ratio - Worst 25% of Outcomes

99.0%101.0%103.0%105.0%107.0%109.0%111.0%113.0%115.0%

75%

77%

79%

81%

83%

85%

87%

89%

91%

93%

95%

97%

99%

Percentile

Com

bine

d R

atio

Gross Business 1M Retn 250k Retn 500k Retn

Combined RatioProbability

Greater Than Gross 1M Retn 500k Retn 250k Retn95.0% 54.90% 58.30% 60.20% 61.90%

100.0% 26.40% 26.70% 25.70% 21.90%105.0% 9.50% 8.40% 4.90% 3.30%110.0% 2.40% 1.40% 1.00% 0.10%

Avg U/W Profit (3,948) (4,069) (4,312) (4,468) Tradeoff (vs. Gross) (121) (364) (519)

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Underwriting Manager’s Perspective

Based on these criteria manager may choose an across the board 500kretention 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

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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

E f f i c i e n t F r o n t i e r

-1 , 0 0 0

- 5 0 0

0

5 0 0

1 , 0 0 0

1 , 5 0 0

2 , 0 0 0

87

,00

0

88

,00

0

89

,00

0

90

,00

0

91

,00

0

92

,00

0

S t a n d a r d D e v ia t i o n

Av

er

ag

e

Un

de

rw

riti

ng

Pr

ofi

t/L

os

s

S t a n d a r d D e v i a t i o n R e t a i n e d U n d e r w r i t i n g P r o f i t /L o s s

Reinsurance from the CFO’s Perspective

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Examples of Evaluating Reinsurance Structure

Example 2 - The CFO’s Perspective

Goal for reinsurance is to: Reduce likelihood of missing EPS by > $0.50/share Minimize probability of 10% PHS Loss Maximize profit/ROE

Generally want to minimize reinsurance use Subject to earnings volatility constraints

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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 Manager’s perspective

Consider U/W contribution to income/ROE/Capital risk

Reinsurance only affects a portion of risk components

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Where is the return risk?

Contribution of Risk by Income Category

Underwriting - AY

Asset Returns

Reserves Other

Underwriting - AY Asset Returns Reserves Other

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Impact of Reinsurance on EPS

EPS Protection

0.0%

20.0%

40.0%

60.0%

Missing Earnings Target By at Least

Prob

abili

ty

Gross 42.1% 37.0% 32.2% xs 1M 42.9% 37.3% 31.5% xs 250 42.0% 35.4% 31.0% xs 500 42.9% 36.8% 30.8%

$0.50 $1.00 $1.50

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

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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

Probability of PHS Declining

0.0%

5.0%

10.0%

Probability of PHS Declining by

Prob

abili

ty

Gross 7.9% 2.1% 0.8% xs 1M 8.3% 2.0% 0.5% xs 500 7.2% 1.8% 0.3% xs 250 6.1% 1.1% 0.1%

5% 10% 15%

Conclusion

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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

Thank You.