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

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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?

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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

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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

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etu

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M

N

A

G

H

J

O

B

Q

I

D

C

K

E

L

F

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P

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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

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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$

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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

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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

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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

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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

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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$

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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

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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

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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

Ex

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B

D

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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

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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 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

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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

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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.