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Athula Alwis, Vladimir Kremerman, Junning ShiWillis Analytics

©Copyright 2005 Willis Limited all rights reserved.

D&O Reinsurance PricingA Financial Market Approach

March 10, 2005

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Contents

• Securities Class Action Landscape

• Purpose of the Approach

• Proposed Methodology

• Data and Assumptions

• Modeling Losses

• Risk Transfer – Reinsurance and Capital Markets

• Conclusion

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Securities Class Action Landscape

Largest settlements to date

Rank Corporation Settlement Amount1 Cendant Corporation $3,527 million2 Citi Bank (WorldCom) $2,650 million3 Lucent $517 million4 Bank of America $490 million5 Waste Management $457 million6 Rite Aid $320 million7 Daimler/Chrysler $300 million *8 Oxford Health $300 million

*Two other ongoing class action suits pending

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Securities Class Action Landscape

The settlement amounts for the top 7 law firms as of 2003

Rank Law Firm Settlement Amount

1 Milberg Weiss Bershad Hynes & Lerach $2.1 billion2 Bernstein Litowitz Berger & Grossman $950 million3 Grant & Eisenhofer $611 million4 Goodkind Labaton Rudoff & Sucharow $551 million5 Barrack Rodos & Bacine $390 million6 Entwistle & Cappucci $311 million7 Chitwood & Harley $303 million

Source: Securities Class Action Services (SCAS)

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Securities Class Action Landscape

Types of Allegations in 2004

• Misrepresentations in financial documents: 79%• False forward looking statements: 67%• GAAP violations: 48%• Insider Trading 39%

Note: 87% of the claims were Section 10b-5 claims

Source: Cornerstone Research – 2004: A Year in Review

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Purpose of the Approach

• Objective reinsurance pricing methodology based on financial market theory to quantify the risk of writing a public D&O reinsurance portfolio

• Risk transfer mechanisms using reinsurance and capital markets

• Return on capital indication based on the proposed

pricing methodology

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Proposed Methodology

ƒ(L) = ƒ(M, D, L, C), where

• ƒ(L) – Distribution of D&O losses

• M - Market Capitalization of the company• D – Frequency of law suits as a function of default rates, credit

spreads, volatility of the stock price and/or credit spreads, regulatory investigations, prior M&A or IPO activity, number of shareholders owning 5.0% or more of the outstanding stock

• L – Loss as a function of the market cap• C – Correlation within and between sectors

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Data and Assumptions

Market Capitalization

• Independent exposure base that is publicly available and easily verifiable

• Objective exposure base not dependant on company management

• Reasonable and consistent relationship between market cap and corresponding losses

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Data and Assumptions

Frequency of Law Suits

The base number of law suits is generated using publicly

available credit ratings from Moody’s and S&P to represent

industry defaults.

The fundamental assumption is that each default corresponds to a

potential D&O law suit.

The base number will be increased using various parameters to

reflect additional law suits that are likely to be filed beyond the

number of defaults.

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Data and Assumptions

Adjustments to the Frequency Parameter

• Credit ratings are adjusted to reflect outlook of each security, and minimum of adjusted ratings is selected.

• Credit spreads indicate a credit rating for each company. Each company’s credit rating is further down graded if the spread implied credit rating is lower than the rating adjusted for the outlook.

• The volatility of the financial performance is measured using two parameters:

– volatility of the credit spreads – volatility of the stock price.

• Based on the volatility index, a downgrade of adjusted credit rating is recommended.

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Data and Assumptions

Adjustments to the Frequency Parameter

Stock Price MovementStock Price Volatility31/1/052002200320040102030405060708090100110S&P 500 COMPOSITE - PRICE INDEXMICROSOFTINTL.BUS.MACH.LUCENT TECHNOLOGIESSource: DATASTREAM

Example: Comparison of stock price movement of IBM, LU, MSFT against S&P 500 (all rebased to 100)

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Data and Assumptions

Example: Comparison of the stock price movement of IBM, LU, MSFT against S&P 500 (all rebased to 100)

10 Year Stock Price Volatility9/2/051995199619971998199920002001200220032004020040060080010001200LUCENT TECHNOLOGIESMICROSOFTINTL.BUS.MACH.S&P 500 COMPOSITE - PRICE INDEXSource: DATASTREAM

Adjustments to the Frequency Parameter

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Data and Assumptions

Adjustments to the Frequency Parameter

Volatility of SpreadsVolatility of Spreads31/1/0520002001200220032004050100150200250300350400450LUCENT TECHNOLGIES 1998 6 1/2% 15/01/28 S - SPREAD OVR T-BONDFORD MOTOR COMPANY 1992 8 7/8% 15/01/22 S - SPREAD OVR T-BONDJOHNSON & JOHNSON 1993 6.73% 15/11/23 S - SPREAD OVR T-BONDSSource: DATASTREAM

Example: Comparison of spreads for Ford, LU, J&J (all rebased to 100)

Source: Datastream

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Data and Assumptions

Adjustments to the Frequency Parameter

• If the company is under a regulatory investigation the credit rating has to be adjusted downward to reflect the increased likelihood of a law suit.

• A downgrade of the credit rating is applied if there are institutional investors owning more than 5.0% of the outstanding stock.

• A downgrade of the credit rating is applied if there has been any M&A activity or an Initial Public Offering during the past three years by the company

As the adjusted credit rating decreases the corresponding default rate increases

(reflecting a higher probability of default, thus a higher number of law suits)

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Data and Assumptions

Loss as a function of Market Cap

Willis Analytics

Settlement Amount as a Percentage of Market Cap (in millions)

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

50 150 250 350

500 800 1,500 3,500 152,500

Market Cap (in millions)

Settlement Amt. as a % of Market Cap

Source: Stanford Law School data

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Data and Assumptions

Correlation within and between sectors

• Projection of material correlation within industry sectors and a nominal amount of correlation between sectors.

• Recognition of the potential for correlated loss events when generating aggregate D&O losses.

• Development of a correlation matrix available for simulation

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Data and Assumptions

Correlation within and between sectors

Creation of a Correlated Multi-Variate distribution• A Normal Copula Function

• Formula based on Merton (Pugachevsky 2002)

)1()1(

)),(),(( 11)2(

jjii

jiMijji

ijuuuu

uuuNuNN

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Modeling Losses

• Apply the proposed methodology to a portfolio of risks simultaneously in a simulation environment

• Create a correlated multi-variate default distribution to model a distribution of D&O losses

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Modeling Losses

Willis AnalyticsDirectors & Officers Reinsurance Model

Average Life 1Default Stress Factor 1.25Number of Accounts 20Number of Sectors 13Number of Simulations 20,000 layers 4

Original Adjusted Loss as % StressedIndex Account Name Market Cap Sector Rating Rating of Mkt Cap Std. Dev. Default Rate IG Flag

1 Company 1 5,615,101,390 6 A2 Baa1 0.73% 5.00% 0.25% 12 Company 2 1,247,762,880 3 Baa2 Baa3 1.59% 10.00% 0.63% 13 Company 3 221,642,688 4 B1 B3 2.73% 10.00% 14.96% 04 Company 4 210,080,000 1 Ba3 B1 2.73% 10.00% 4.16% 05 Company 5 196,820,000 7 A3 Baa1 3.64% 10.00% 0.25% 16 Company 6 166,790,000 4 Ba2 B2 3.64% 10.00% 8.93% 07 Company 7 162,630,000 8 Aaa Aa1 3.64% 7.00% 0.00% 18 Company 8 161,460,000 9 Baa1 Baa2 3.64% 9.00% 0.38% 19 Company 9 156,520,000 10 A3 Baa1 3.64% 10.00% 0.25% 110 Company 10 149,890,000 11 A3 Baa2 3.64% 15.00% 0.38% 111 Company 11 148,200,000 2 B1 B2 3.64% 15.00% 8.93% 012 Company 12 144,560,000 5 B1 B2 3.64% 15.00% 8.93% 013 Company 13 136,890,000 1 Caa1 Caa3 3.64% 15.00% 30.00% 014 Company 14 126,620,000 5 Baa3 Ba1 3.64% 15.00% 0.94% 015 Company 15 112,710,000 12 Baa1 Baa2 3.64% 15.00% 0.38% 116 Company 16 108,550,000 13 Aaa Aa1 3.64% 15.00% 0.00% 117 Company 17 104,910,000 3 Ba1 B3 3.64% 15.00% 14.96% 018 Company 18 98,930,000 1 Ba2 Ba3 5.91% 15.00% 2.98% 019 Company 19 95,680,000 4 Ba3 B1 5.91% 15.00% 4.16% 020 Company 20 93,340,000 3 A1 A3 5.91% 15.00% 0.10% 1

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Modeling Losses

Reinsurance Terms LAYER 1 LAYER 2 LAYER 3 LAYER 4Per Risk Limit 999,999,999,999 30,000,000 30,000,000 40,000,000 Per Risk Attachment - - 30,000,000 60,000,000 Aggregate Limit 999,999,999,999,999 5,000,000,000 60,000,000 80,000,000 Aggregate Deductible - - - -

Percentiles of Ceded Losses LAYER 1 LAYER 2 LAYER 3 LAYER 4 LAYER 1 counts LAYER 2 counts LAYER 3 counts LAYER 4 counts

Mean 5,588,660 2,667,336 1,320,448 940,980 1.01 1.01 0.06 0.03 Std Dev 30,526,281 8,514,460 6,073,512 5,802,938 1.34 1.34 0.24 0.18

C.V. 546% 319% 460% 617% 132% 132% 425% 553%Median 0 0 0 0 1 1 0 0

Min 0 0 0 0 0 0 0 0Max 2,574,045,522 92,365,559 60,000,000 80,000,000 16 16 3 2

10.0% - - - - - - - - 20.0% - - - - - - - - 30.0% - - - - - - - - 40.0% - - - - - - - - 50.0% 0 0 - - 1 1 - - 60.0% 0 0 - - 1 1 - - 70.0% 9 9 - - 1 1 - - 75.0% 1,255 1,255 - - 2 2 - - 80.0% 38,005 38,005 - - 2 2 - - 85.0% 638,283 638,283 - - 2 2 - - 90.0% 5,445,602 5,445,602 - - 3 3 - - 95.0% 36,999,599 30,000,000 5,044,157 - 4 4 1 - 96.0% 49,955,485 30,000,000 17,816,625 - 4 4 1 - 97.0% 68,325,409 30,000,000 30,000,000 3,966,949 4 4 1 1 98.0% 90,472,637 30,026,587 30,000,000 26,045,716 5 5 1 1 99.0% 122,027,858 33,546,726 30,000,000 40,000,000 6 6 1 1 99.5% 137,245,013 47,542,359 30,000,000 40,000,000 7 7 1 1

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Risk Transfer

• Reinsurance– Quota Share

– XOL

• Capital Markets– CDO type structures

– Call Options

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Conclusion

This financial market approach has the ability to

• Use an objective model to test the portfolio periodically

throughout the year

• Evaluate current and prospective reinsurance strategies

• Test assumptions during the year and change strategies

• Allocate capital in an objective and reasonable manner

• Test internal loss reserve indications

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This presentation is based on the research paper “D&O

Pricing – A Financial Market Approach,” written by

Athula Alwis, Junning Shi, and Vladimir Kremerman, published

in the Casualty Actuarial Society ‘s Forum.

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Q & A