D&O Reinsurance Pricing
A Financial Market Approach
Athula Alwis, Vladimir Kremerman, Junning Shi
Willis Analytics
March 10, 2005
©Copyright 2005 Willis Limited all rights reserved.
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Contents
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•
•
•
•
•
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2
Securities Class Action Landscape
Purpose of the Approach
Proposed Methodology
Data and Assumptions
Modeling Losses
Risk Transfer – Reinsurance and Capital Markets
Conclusion
Securities Class Action Landscape
Largest settlements to date
Rank Corporation
1
Cendant Corporation
2
Citi Bank (WorldCom)
3
Lucent
4
Bank of America
5
Waste Management
6
Rite Aid
7
Daimler/Chrysler
8
Oxford Health
*Two other ongoing class action suits pending
3
Settlement Amount
$3,527 million
$2,650 million
$517 million
$490 million
$457 million
$320 million
$300 million *
$300 million
Securities Class Action Landscape
The settlement amounts for the top 7 law firms as of 2003
Rank
1
2
3
4
5
6
7
Law Firm
Settlement Amount
Milberg Weiss Bershad Hynes & Lerach
$2.1 billion
Bernstein Litowitz Berger & Grossman
$950 million
Grant & Eisenhofer
$611 million
Goodkind Labaton Rudoff & Sucharow
$551 million
Barrack Rodos & Bacine
$390 million
Entwistle & Cappucci
$311 million
Chitwood & Harley
$303 million
Source: Securities Class Action Services (SCAS)
4
Securities Class Action Landscape
Types of Allegations in 2004
•
•
•
•
Misrepresentations in financial documents:
False forward looking statements:
GAAP violations:
Insider Trading
Note: 87% of the claims were Section 10b-5 claims
Source: Cornerstone Research – 2004: A Year in Review
5
79%
67%
48%
39%
Purpose of the Approach
6
•
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
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
•
•
7
Data and Assumptions
Market Capitalization
8
•
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
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.
9
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:
–
–
•
10
volatility of the credit spreads
volatility of the stock price.
Based on the volatility index, a downgrade of adjusted credit
rating is recommended.
Data and Assumptions
Adjustments to the Frequency Parameter
Example: Comparison of stock price movement of IBM, LU, MSFT
against S&P 500 (all rebased to 100)
Stock Price Movement
S to c k
P r ic e
V o l a ti l i ty
3 1 /1 /0 5
1 1 0
1 0 0
9 0
8 0
7 0
6 0
5 0
4 0
3 0
2 0
1 0
0
2 0 0 2
5 0 0 C O M P O S IT E
S & P
M IC R O S O F T
IN T L .B U S .M A C H .
11
- P R IC E
2 0 0 3
IN D E X
L U C E N T
2 0 0 4
T E C H N O L O G IE S
S o u rc e : D A T A S T R E A M
Data and Assumptions
Adjustments to the Frequency Parameter
Example: Comparison of the stock price movement of IBM, LU,
MSFT against S&P 500 (all rebased to 100)
10 Year Stock Price Volatility
9 /2 /0 5
1 2 0 0
1 0 0 0
8 0 0
6 0 0
4 0 0
2 0 0
0
1 9 9 5
1 9 9 6
1 9 9 7
1 9 9 8
L U C E N T
T E C H N O L O G IE S
M IC R O S O F T
IN T L .B U S .M A C H .
12
1 9 9 9
2 0 0 0
S & P
2 0 0 1
2 0 0 2
2 0 0 3
2 0 0 4
5 0 0 C O M P O S IT E
- P R IC E
IN D E X
S o u rc e : D A T A S T R E A M
Data and Assumptions
Adjustments to the Frequency Parameter
Example: Comparison of spreads for Ford, LU, J&J (all rebased to 100)
Volatility of Spreads
V o l a ti l i ty
o f
S p r e a d s
3 1 /1 /0 5
4 5 0
4 0 0
3 5 0
3 0 0
2 5 0
2 0 0
1 5 0
1 0 0
5 0
0
2 0 0 0
2 0 0 1
2 0 0 2
L U C E N T
T E C H N O L G IE S
1 9 9 8 6 1 /2 %
1 5 /0 1 /2 8
F O R D
M O T O R
C O M P A N Y
1 9 9 2 8 7 /8 %
1 5 /0 1 /2 2
J O H N S O N
&
J O H N S O N
1 9 9 3 6 .7 3 %
1 5 /1 1 /2 3 S
13
2 0 0 3
S
- S P R E A
S
- S P R E A
- S P R E A DS
2 0 0 4
D
O V R
T -B O N D
D
O V R
T -B O N D
O
B A
O T
N A
D S
S T R E A M
o V
u rR
c eT: - D
Source: Datastream
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)
14
Data and Assumptions
Loss as a function of Market Cap
Willis Analytics
Settlement Amount as a Percentage of Market Cap (in millions)
Settlement Amt. as a % of Market Cap
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
0.00%
50
150
250
350
500
Market Cap (in millions)
Source: Stanford Law School data
15
800
1,500
3,500
152,500
Data and Assumptions
Correlation within and between sectors
16
•
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
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)
ij 
17
N ( 2) ( N 1 (ui ), N 1 (u j ),  ijM )  ui u j
ui (1  ui )u j (1  u j )
Modeling Losses
18
•
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
Modeling Losses
Willis Analytics
Directors & Officers Reinsurance Model
Average Life
Default Stress Factor
Number of Accounts
Number of Sectors
Number of Simulations
layers
Index
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
19
Account Name
Company 1
Company 2
Company 3
Company 4
Company 5
Company 6
Company 7
Company 8
Company 9
Company 10
Company 11
Company 12
Company 13
Company 14
Company 15
Company 16
Company 17
Company 18
Company 19
Company 20
1
1.25
20
13
20,000
4
Market Cap
5,615,101,390
1,247,762,880
221,642,688
210,080,000
196,820,000
166,790,000
162,630,000
161,460,000
156,520,000
149,890,000
148,200,000
144,560,000
136,890,000
126,620,000
112,710,000
108,550,000
104,910,000
98,930,000
95,680,000
93,340,000
Sector
6
3
4
1
7
4
8
9
10
11
2
5
1
5
12
13
3
1
4
3
Original Adjusted
Rating
Rating
A2
Baa1
Baa2
Baa3
B1
B3
Ba3
B1
A3
Baa1
Ba2
B2
Aaa
Aa1
Baa1
Baa2
A3
Baa1
A3
Baa2
B1
B2
B1
B2
Caa1
Caa3
Baa3
Ba1
Baa1
Baa2
Aaa
Aa1
Ba1
B3
Ba2
Ba3
Ba3
B1
A1
A3
Loss as %
of Mkt Cap
0.73%
1.59%
2.73%
2.73%
3.64%
3.64%
3.64%
3.64%
3.64%
3.64%
3.64%
3.64%
3.64%
3.64%
3.64%
3.64%
3.64%
5.91%
5.91%
5.91%
Stressed
Std. Dev. Default Rate
5.00%
0.25%
10.00%
0.63%
10.00%
14.96%
10.00%
4.16%
10.00%
0.25%
10.00%
8.93%
7.00%
0.00%
9.00%
0.38%
10.00%
0.25%
15.00%
0.38%
15.00%
8.93%
15.00%
8.93%
15.00%
30.00%
15.00%
0.94%
15.00%
0.38%
15.00%
0.00%
15.00%
14.96%
15.00%
2.98%
15.00%
4.16%
15.00%
0.10%
IG Flag
1
1
0
0
1
0
1
1
1
1
0
0
0
0
1
1
0
0
0
1
Modeling Losses
Reinsurance Terms
Per Risk Limit
Per Risk Attachment
Aggregate Limit
Aggregate Deductible
Percentiles of Ceded
Losses
Mean
Std Dev
C.V.
Median
Min
Max
10.0%
20.0%
30.0%
40.0%
50.0%
60.0%
70.0%
75.0%
80.0%
85.0%
90.0%
95.0%
96.0%
97.0%
98.0%
99.0%
99.5%
20
LAYER 1
999,999,999,999
999,999,999,999,999
-
LAYER 1
5,588,660
30,526,281
546%
0
0
2,574,045,522
LAYER 2
30,000,000
5,000,000,000
-
LAYER 2
2,667,336
8,514,460
319%
0
0
92,365,559
-
0
0
9
1,255
38,005
638,283
5,445,602
36,999,599
49,955,485
68,325,409
90,472,637
122,027,858
137,245,013
0
0
9
1,255
38,005
638,283
5,445,602
30,000,000
30,000,000
30,000,000
30,026,587
33,546,726
47,542,359
LAYER 3
30,000,000
30,000,000
60,000,000
-
LAYER 4
40,000,000
60,000,000
80,000,000
-
LAYER 3
1,320,448
6,073,512
460%
0
0
60,000,000
LAYER 4
940,980
5,802,938
617%
0
0
80,000,000
5,044,157
17,816,625
30,000,000
30,000,000
30,000,000
30,000,000
3,966,949
26,045,716
40,000,000
40,000,000
LAYER 1 counts LAYER 2 counts LAYER 3 counts LAYER 4 counts
1.01
1.01
0.06
0.03
1.34
1.34
0.24
0.18
132%
132%
425%
553%
1
1
0
0
0
0
0
0
16
16
3
2
1
1
1
1
1
1
2
2
2
2
2
2
3
3
4
4
1
4
4
1
4
4
1
1
5
5
1
1
6
6
1
1
7
7
1
1
Risk Transfer
•
•
21
Reinsurance
–
Quota Share
–
XOL
Capital Markets
–
CDO type structures
–
Call Options
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
22
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.
23
Q&A
24