Z Swiss Re Investors, Inc. Z Using DFA to Allocate Capital: Extending the Traditional Approach Dan...

Z

Swiss Re Investors, Inc.

ZUsing DFA to Allocate Capital:

Extending the Traditional ApproachDan Isaac & Stephen Philbrick

2000 Casualty Loss Reserve Seminar:September 19, 2000

Z2

Note to CLRS Participants

Some changes have been made to this presentation subsequent to the CLRS on September 19.

Additional informational slides has been added to both supplement the original presented output and to improve the overall flow.

There have been no substantive changes to the conclusions.

Also, please review the notes attached to some of the slides to achieve a fuller understanding of that particular slide.

Z3

Agenda

Introduction to Capital Allocation

Introduction to DFA Introduction to CUFFS, a sample Insurance Company Extending Traditional Capital Allocation Approaches using

DFA Shapley Illustration Conclusions

Why is Capital Allocated Controversies Metrics and Issues Associated with the Metrics Traditional Capital Allocation Approach

Z4

Capital

Capital Allocation vs. Capital Adequacy

This presentation only address issues relating to Capital Allocations

Z5

Introduction to Capital AllocationIntroduction to Capital Allocation

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Why Allocate Capital?

“The underlying economic point of view taken is that of a reinsurer considering a new contract. The reinsurer has committed surplus to support the variability of his existing book; the new contract will require additional surplus to support its variability.” (Kreps, Reinsurer Risk Loads from Marginal Surplus Requirements)

Z7

Why Allocate Capital?

• to compare managerial performance across business units

• to provide a risk indicator for regulators and other stakeholders

• and to develop a common basis for major decisions, including investment and underwriting strategies, and setting the corporate structure

Capital allocation serves three primary purposes:

(Mulvey, Belfatti and Madsen, Integrated Financial Risk Management: Capital Allocation Issues 1999)

Z8

Capital Allocation is Controversial

“In this paper we have demonstrated that meaningful allocation is a mathematical impossibility…” (Bass & Khury, 1992 Discussion Papers on Insurer Financial Solvency)

“A policy written with a monoline automobile insurance company with $100 million of surplus is not as well protected as a policy written with a large multiline insurance company with $100 million allocated to its automobile line of business”(Charles McClenahan, as quoted by Glenn Meyers, Contingencies, September/October 2000)

“I agree with Chuck’s statement.” Glenn Meyers

Z9

Yet Even the Detractors Note:

“In other words, surplus allocation may be useful as a management tool to help improve the overall return on equity that is of interest to investor-owners…” (Bass & Khury, 1992 Discussion Papers on Insurer Financial Solvency)

“But I also agree with the idea of using capital allocation as an internal management tool…” (Glenn Meyers, Contingencies, September/October 2000)

Z10

Limits of Use

“Furthermore, even greater care must be taken to make sure that such attempts, aimed at the internal management of the enterprise, are not inadvertently extended beyond its natural limited application, to the arena of rate regulation as the sole measure of the soundness of rates.” (Bass & Khury, 1992 Discussion Papers on Insurer Financial Solvency)

Z11

METRICS:

• Statutory Surplus

• Economic Value

• RBC Ratio etc.

• Probability of Ruin (Value at Risk)

• Variance

• Standard Deviation

• Semi-Variance

• Shortfall Measures (Expected Policyholder Deficit, Tail Value at Risk)

Sample Metrics & Allocation Methods

ALLOCATION METHODS:• First-In Marginal Contribution (Standalone)

• Last-In Marginal Contribution (Marginal)

• Shapley Values

Combine Risk Variable and Risk Function• RISK VARIABLE:

• RISK FUNCTION:

Z12

Application of Metrics Issues

Additivity Parameter Risk/Process Risk (CAPM)

Scope

Time Frame Liability versus Assets

Symmetry Not All Failures Are Created Equal

Z13

Traditional Approach to Capital Allocation

No Existing Reserves

One Year of New Business

No Asset Risk

Full Recognition of Ultimate Results at the End of the Year

Z14

Possible Extensions Using DFA

Existing Reserves:

Include existing reserves in addition to one year of new business in capital allocation process

Existing Reserves:


Multiple Years of New

Business:

Allow multiple years of new business to

be written instead of one year of new

business


Business:



business

Asset Returns:

Allow for volatile asset returns, and allocate capital to

assets

Asset Returns:


assets

Introduction to DFAIntroduction to DFA

Z

Z16

Introduction to DFA

Dynamic: Reflects the year-to-year variability and interaction of measurable financial risks.

Financial: Projects 1000 or more sets of probabilistic financial statements (GAAP, Statutory, Economic).

Analysis: Allows a thorough assessment of both risk and reward, thereby aiding in the evaluation and identification of opportunities to improve expected financial results and/or reduce financial variability.

Z17

Introduction to DFA

Optimization & Valuation

• Financial Statements- Economic- GAAP- Statutory

• Financial Strategies• Define Strategic Asset Allocation

TMFIRMCashflow

Statements

Income

Statements

Balance

Sheets

Combining the asset and liability simulations and their interactions creates a robust set of a thousand or more prospective year-by-year financial statements to enhance decision-making.

Economic& Asset

Simulation

By Currency• Inflation• GDP• Interest Rates• Asset class returns• Etc.

Liability &Business

Simulation

By Line of Business• Amount and timing of:

reserves and future losses

• Reinsurance structure• Expenses• Business Plan• Etc.

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Introduction to CUFFS Insurance Company Introduction to CUFFS Insurance Company

Z19

0%

10%

20%

30%

40%

1 2 3 4 5 6 7 8 9 10

Existing Reserves Run-off Pattern

52%

10%

2%

17%

19%

Workers Comp

Auto Liability

Property

General Liability

All Other

CUFFS Insurance Company: Existing Reserves

Existing Reserves (by line)

Duration: 2.5

Z20

Financial Conditions• Existing Reserves $ 5,263

million

• Unearned Premium $ 1,729 million

Cash Out Flows

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

1 2 3 4 5 6 7 8 9 10

Expenses

Unearned Premium

Existing Reserves

CUFFS Insurance Company: Run-off Cash Flows

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Losses and Expenses Paid less Premiums Collected

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

1 2 3 4 5 6 7 8 9 10

Net Cash Flow

Financial Conditions• Invested Assets $ 9,867

million

• Statutory Surplus $ 3,755 million

Duration: 2.7

CUFFS Insurance Company: Run-off Cash Flows

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0%

10%

20%

30%

40%

1 2 3 4 5 6 7 8 9 10

Accident Year Payment Pattern

23%

9%

2%

48%

18%

Workers Comp

Auto Liability

Property

General Liability

All Other

Written Premium (by line)

Duration: 2.0

CUFFS Insurance Company: Business Plan

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60%

65%

70%

75%

80%

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Accident Year

Loss Ratios

• Mean Loss Ratio: 75.2%

• Premium Growth Rate: 1.2%

0

1000

2000

3000

4000

5000

Net

Ear

ned

Pre

miu

m

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004

Year

Earned Premium--- Budget ---

--- Budget ---

CUFFS Insurance Company: Premium Growth & Loss Ratio

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CUFFS Insurance Company: Asset Portfolio Summary

Invested Assets

Asset Mix24%

18%

3%

11%

8%6%

10%

Cash

Treasuries

Corporates

Common Stocks

Municipals

Mortgage Backed

Other

0%10%20%30%40%50%

1-5 Yrs 5-10 Yrs 10-30 Yrs

Maturity Distribution

Fixed Income

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Extending Traditional Capital Allocation Approaches using DFAExtending Traditional Capital Allocation Approaches using DFA

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Use Standard Deviation of Statutory Surplus at the end of the time horizon as the Risk Measure

Allocating Capital based on the Marginal Impact of a particular variable (e.g. Difference between With and Without Workers Comp)

Excluded Business is assumed to be Completely Reinsured

Capital Allocation Methodology

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Existing Reserves:


Existing Reserves:



Business:



business


Business:



business

Asset Returns:


assets

Asset Returns:


assets

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Existing Reserves Clearly can be Very Risky (e.g. Asbestos Reserves) Driven by many of the same factors as the New Business Need to address both “How Much” and “How Long”

- Especially important for Pricing Long-Term Lines


Existing Reserves:


Existing Reserves:



Business:



business


Business:



business

Asset Returns:


assets

Asset Returns:


assets

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WC - Res

WC - New

AL - Res

AL - New

Prop - Res

Prop - New

GL - Res

GL - New

Capital Allocation Based onNew Business and Existing

Reserves

WC

WC

AL

AL

Prop

Prop

GL

GL

Other

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Distribution of Written PremiumDistribution of Existing

Reserves

WC

AL

Prop

GL

Capital Allocation Based onNew Business

Existing Reserves

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New Business versus Reserves

Existing Reserves

Different Risk Characteristics

- New Property Business can be very Risky because of Catastrophe exposure

- Largely Eliminated in the Property Reserves

Split by line varies dramatically

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Workers Comp Property

Reserves New Business

Risk Allocation by Line

Existing Reserves

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Multiple Years of New Business Companies do not Close at the End of One Year Some Risks take longer than One Year to Develop

(e.g. Pollution)


Existing Reserves:


Existing Reserves:



Business:



business


Business:



business

Asset Returns:


assets

Asset Returns:


assets

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Multiple Years of New Business

WC - Res WC - Res

WC - New WC - New

AL - Res AL - Res

AL - NewAL - New

Prop - Res

Prop - Res

Prop - NewProp - New

GL - Res

GL - Res

GL - New

GL - New

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

1-Year 5-Year

Other

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Time Diversification changes Impact of Different Risk Factors

- Reduces Impact of High Severity Claims (e.g. Property)

- Increases Impact of Inflation Sensitive Lines (e.g. Workers Comp)

Reflects ongoing nature of the company

Reflects wider range of Risks faced by Insurance Companies

- Recognition Delay on Reserves

- Pricing Risk

Multiple Years of New Business

Impact of Expanding the Time Frame

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Asset Returns:

Large Source of Volatility

- Becoming even more so with dropping Premium to Surplus ratios and increasing Equity allocations

Correlated to Liabilities because of Inflation Sensitivity


Existing Reserves:


Existing Reserves:



Business:



business


Business:



business

Asset Returns:


assets

Asset Returns:


assets

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Issue:

- Most allocation methods require a “with” and “without” run

What About Assets?

Concern:

- What should be done for “without” assets?

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Two options on the liability side:

1. Don’t write the business

- New Business only

2. Reinsure the business away

“Without” Assets Definition

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Option #1: Assume some fixed rate of return

Advantages: Easy to understand Most similar to the “without” a line


Disadvantages: What should the fixed rate be? Can’t be achieved in reality

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Disadvantages:

Can lead to nonsensical results

Option #2: Invest everything in lowest risk asset class

Advantages:

Still relatively simple

Achievable alternative


Z40

0%

2%

4%

6%

8%

10%

12%

14%

30%

35%

40%

45%

50%

55%

60%

65%

70%

75%

80%

85%

90%

95%

100%

105%

110%

115%

120%

125%

130%

135%

140%

145%

150%

155%

160%

165%

170%

175%

180%

185%

190%

195%

200%

RBC Ratio

Current Cash


Held Statutory Surplus . Required Regulatory (Risk-Based) Capital

RBC Ratio =.

Z41

Option #3: Determine asset allocation that minimizes risk measure

Advantages:

Eliminates possibility of negative capital allocation


Z42

0%

2%

4%

6%

8%

10%

12%

14%

30%

35%

40%

45%

50%

55%

60%

65%

70%

75%

80%

85%

90%

95%

100%

105%

110%

115%

120%

125%

130%

135%

140%

145%

150%

155%

160%

165%

170%

175%

180%

185%

190%

195%

200%

RBC Ratio

Current Cash Low Risk Portfolio


Held Statutory Surplus . Required Regulatory (Risk-Based) Capital

RBC Ratio =.

Z43

Disadvantages: Much more complex Need a solution for each marginal run Very time consuming, especially for Shapley

values

Option #3: Determine asset allocation that minimizes risk measure

Advantages: Eliminates possibility of negative capital allocation


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WC

AL

Prop

GL

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Without

Asset Returns

Other

Assets

WC

AL

Prop

GL

With

Other

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Considers Indirect Impacts of Operationse.g. Taxes: Impact of Realizing Gains/Losses on

Balance Sheet depends on prior year Gains and Losses

Easier to Consider Multiple Basis for Allocatione.g. Statutory Surplus and RBC Ratio

Can Consider More Complex Transactions Multi-Year Aggregate Reinsurance Contingent Equity

Other Benefits of Using a DFA Model

Z

Shapley ValuesShapley Values

Z47

Shapley Value Introduction

The Marginal “Last-In” allocation method used thus far only evaluates the marginal risk addition to the business as a whole.

The Shapley Value allocation method expands on the Marginal “Last-In” concept by considering all possible permutations of entry.

Shapley Value evenly splits the mutual covariance between the “With” and “Without” marginal scenarios.

Z48

Line of Standalone AllocatedBusiness Capital Capital

A 1,000 548 B 2,000 1,095 C 3,000 1,643 D 4,000 2,191

Sum 10,000 5,477 Total Company 5,477 Ratio 54.8%

Shapley Value Illustration

Z49

Line of Marginal AllocatedBusiness Capital Capital

A 92 163 B 378 668 C 895 1,580 D 1,736 3,066

Sum 3,100 5,477 Total Company 5,477 Ratio 176.7%


Z50

Line of Standalone Allocated AllocatedBusiness Capital Capital Capital

LOB "First-in" "Last-in"A 1,000 548 163 B 2,000 1,095 668 C 3,000 1,643 1,580 D 4,000 2,191 3,066

Sum 10,000 5,477 5,477


Z51

Capital Allocation

-500

1,0001,5002,0002,5003,0003,500

A B C D

LOB

"First-in"

"Last-in"


Z52

Line of Standalone Allocated Allocated AllocatedBusiness Capital Capital Capital Capital

LOB "First-in" "Last-in" ShapleyA 1,000 548 163 345 B 2,000 1,095 668 906 C 3,000 1,643 1,580 1,654 D 4,000 2,191 3,066 2,572

Sum 10,000 5,477 5,477 5,477


Z53

Capital Allocation

-500

1,0001,5002,0002,5003,0003,500

A B C D

LOB

"First-in"

"Last-in"

Shapley


Z54

Shapley Value Comparison to Marginal Results

WCWC

ALAL

PropProp

GLGL

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Marginal Shapley

Assets

WCWC

ALAL

PropProp

GLGL

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

Marginal Shapley

Assets

Excluding Assets Including Assets

Z55

DFA is a useful tool when allocating capital

Incorporation of new business and existing reserves makes a difference

Including Assets in the analysis is important

Selection of the Risk Metric is important

Work still needs to be done:

Conclusions

Allocation of the asset-related capital back to line Examining whether the asset mix needs to vary by LOB

Z Swiss Re Investors, Inc. Z Using DFA to Allocate Capital: Extending the Traditional Approach Dan...

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