11

Casualty Loss Reserve Seminar September 14, 1999

Presented by: Susan E. Witcraft

Milliman & Robertson, Inc.

DYNAMIC FINANCIAL ANALYSISWhat Does It Look Like?

22

WHAT IS DFA?

Management tool

Regulatory tool

33

USES FOR DFA

Estimate probability of attaining certain results

Identify risks to company

Capital allocation

Evaluation of alternate strategies

44

OVERVIEW OF PROCESS

Input

Scenarios

Output

SelectStrategy

FinancialCalculator

55

OVERVIEW OF PROCESS

Input

Scenarios

Output

SelectStrategy

FinancialCalculator

66

INPUT

PREMIUM

Amount

Earning pattern

Collection pattern

77

INPUT

LOSSES AND LAE Loss ratio on small claims

Frequency of large claims

Severity of large claims

Catastrophes

Reserve adjustments

Payment patterns

88

INPUT

EXPENSES

Fixed

Variable

99

INPUT MODELS

Premium volume

Losses and LAE

Reserve development

Payment patterns

Expenses

Assets

1010

LOSS RATIO MODEL

where i is the year

l/r is the undiscounted loss ratio

int is the short-term yield

inf is the inflation rate

a, b, c, and d are constants

e is a random error term

l/ri = a(l/ri-1 ) + b(inti-1 - int) + c (infi - inf) + d + ei

1111

EXPENSE MODEL

Fixed expensesi = Fixed expensesi-1 x (1 + infi) + ei

where i is the years

inf is the inflation rate

e is a random error term

1212

OVERVIEW OF PROCESS

Input

Scenarios

Output

SelectStrategy

FinancialCalculator

1313

STRATEGIES

Investment

Reinsurance

Business mix

Pricing

1414

STRATEGIES

Asset Type CurrentMore

CorporatesStocks &

CorporatesMore Non-Taxables

DurationMatch

Government Bonds 40% 10% 0% 5% 40%

Non-taxable Bonds 25% 25% 14% 60% 25%

Corporate Bonds 20% 50% 50% 20% 20%

Common Stocks 4% 4% 25% 4% 4%

Cash 11% 11% 11% 11% 11%

Bond Maturity 10 yrs. 10 yrs. 10 yrs. 10 yrs. 5 yrs.

Distribution of New Investments Among Types

1515

PORTFOLIO OPTIMIZER

Entire business (both assets and liabilities) viewed as a single portfolio

Considers risk from the perspective of the entire organization

1616

PORTFOLIO OPTIMIZER

Calculates line of business and asset mix that maximizes expected return for any

given level of standard deviation

- OR -

Calculates mix that provides lowest risk for a given level of return

1717

PORTFOLIO OPTIMIZER

Inputs Reserve to premium ratios for each line of business Expected underwriting and asset returns and standard

deviations Correlation matrix between underwriting returns, asset

returns, and between underwriting and asset returns

Constraints Constraints on line of business mix and percentages of

asset portfolio invested in various asset classes Reserve to surplus ratio (alternatively, premium to

surplus ratio)

1818

OPTIMAL ASSET MIX

Asset Type 7% 8% 9% 10% 11%

Government Bonds 44% 39% 33% 26% 20%

Non-taxable Bonds 0% 1% 8% 15% 21%

Corporate Bonds 48% 48% 42% 36% 30%

Common Stocks 6% 12% 17% 23% 29%

Cash 2% 0% 0% 0% 0%

Standard Deviation 21% 22% 24% 26% 29%

TARGET RETURNSTARGET RETURNS

1919

OVERVIEW OF PROCESS

Input

Scenarios

Output

SelectStrategy

FinancialCalculator

2020

SCENARIOS

Economy

Underwriting cycle

Catastrophes

Large claims

Failure of reinsurer

Mass torts

2121

ECONOMIC SCENARIOS

GDP growth Inflation Interest rates

Short-term Long-term

Stock returns Bond default rates

Produce simulated projections of:

2222

ECONOMIC VARIABLES

-4%

-2%

0%

2%

4%

6%

8%

10%

1998 1999 2000 2001 2002 2003 2004 2005 2006

-40%

-20%

0%

20%

40%

60%

80%

100%

Short Term Yields Inflation Dividend Yields Stock Appreciation

Note: Stock Appreciation is plotted against the axis on the right of the graph.

2323

ECONOMIC SCENARIOS

Output used as inputs for income and balance sheet variables

Each scenario provides consistent set of assumptions for projection of future financial results

2424

OVERVIEW OF PROCESS

Input

Scenarios

Output

SelectStrategy

FinancialCalculator

2525

FINANCIAL CALCULATOR-UNDERWRITING

Project net premium, losses and expenses

Income statement basis

Cash basis

Tax basis

2626

FINANCIAL CALCULATOR-ASSET MODEL

Calculate investment income Add cash from operations, asset

maturities and asset sales Produce total funds available for investment each

projection period

Invest total funds available for investment Strategy specified by user

State end-of-year balance sheet Carried forward to next projection period

2727

OVERVIEW OF PROCESS

Input

Scenarios

Output

SelectStrategy

FinancialCalculator

2828

CHANGE IN SURPLUS

-150%

-100%

-50%

0%

50%

100%

150%

200%

250%

1998 1999 2000 2001 2002 2003 2004 2005 2006

2929

FINDINGS

Strategy

Average AnnualSurplus Growth

to 2006

Probability ThatSurplus Growth Is

Less than 10%

Current 7.7% 69.9%

More Corporates 7.8% 69.1%

Stocks & Corporates 10.0% 73.3%

More Non-Taxables 7.5% 70.1%

Duration Match 7.1% 72.9%

3030

RISK/REWARD ILLUSTRATION

A

B

CD E

Risk

Rew

ard X

+ +

+

+

+

++

+

+

++

+

++

++

+

+

+

+

+

+

++ + +

++

+

+

+

+

+

+

+

+

++

+

+

++ ++ +

+

+

+

+

+ ++

++

+ +

3131

RISK/REWARD SUMMARY

4%

6%

8%

10%

12%

68% 69% 70% 71% 72% 73% 74%Ave

rag

e A

nn

ual

Su

rplu

s I

ncr

ease

Probability Net Income/Surplus < 10%

21 4 5

3

1. Current 2. More Corporates 3. Stocks & Corporates 4. More Non-Taxables 5. Duration Match

3232

RISK/REWARD SUMMARY

4%

6%

8%

10%

12%

20% 22% 24% 26% 28% 30%

Ave

rag

e A

nn

ual

Su

rplu

s I

ncr

ease

Standard Deviation of Surplus Increase

5

42

1

3

1. Current 2. More Corporates 3. Stocks & Corporates 4. More Non-Taxables 5. Duration Match

3333

Casualty Loss Reserve Seminar September 14, 1999

Presented by: Susan E. Witcraft

Milliman & Robertson, Inc.

DYNAMIC FINANCIAL ANALYSISWhat Does It Look Like?