D&O Reinsurance Pricing
A Financial Market Approach
Athula Alwis and Junning Shi
Willis Analytics, Willis Re Inc.
©Copyright 2005 Willis Limited all rights reserved.
W
Contents
•
•
•
•
•
•
•
•
2
Securities Class Action Landscape
Purpose of the Approach
Proposed Methodology
Data and Assumptions
Modeling Losses
Risk Transfer
Conclusion
Q&A
Securities Class Action Landscape
Largest settlements to date
Rank Corporation
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
10.
10.
3
Settlement Amount
Cendant Corporation
McKesson
Adelphia
Lucent
Bank of America
Dynergy
Raytheon
Waste Management
Rite Aid
Daimler/Chrysler
Oxford Health
Bristol-Myers Squibb
*Two other ongoing class action suits pending
$3.5 billion
$960 million
$765 million
$517 million
$490 million
$473 million
$460 million
$457 million
$320 million
$300 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
The settlement amounts for the top 7 law firms as of 2004
Rank
1
2
3
4
5
6
7
Law Firm
Bernstein Litowitz Berger & Grossman
Barrack Rodos & Bacine
Milberg Weiss Bershad & Schulman
Chitwood & Harley
Berman DeValerio Pease ….
Grant & Eisenhofer
Stull Stull & Brody
Source: Securities Class Action Services (SCAS)
5
Settlement Amount
$3.5 billion
$2.9 billion
$900 million
$583 million
$579 million
$569 million
$536 million
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
6
79%
67%
48%
39%
Securities Class Action Landscape
Types of Law Suits
Type of Law Suit
2001
2002
2003
2004
Mutual Fund
Analyst
IPO Allocation
Classic
0
5
312
175
0
41
1
229
19
18
0
184
21
1
0
214
Sub-total
492
271
221
236
Source: Stanford Law School: Securities Class Action Clearing House in cooperation with Cornerstone
Research
7
Purpose of the Approach
8
•
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
•
•
9
Data and Assumptions
Market Capitalization
10
•
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.
11
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:
–
–
•
12
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 .
13
- 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 .
14
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
15
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)
16
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
17
800
1,500
3,500
152,500
Data and Assumptions
Loss as a function of Market Cap
Future Development
18
•
Separate curves for side A vs. side B (?)
•
Incorporate the effect of SOX (easier said than done)
Data and Assumptions
Correlation within and between sectors
19
•
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 
20
N ( 2) ( N 1 (ui ), N 1 (u j ),  ijM )  ui u j
ui (1  ui )u j (1  u j )
Data and Assumptions
Correlation within and between sectors
Rebonato and Jackel Adjustment
•
To make the correlation matrix positive definite
Improvements
•
21
Generalized form of Archemedian Copula to attain better tail
dependency and to incorporate the time of default
Modeling Losses
22
•
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
21
22
23
24
25
23
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
Company 21
Company 22
Company 23
Company 24
Company 25
1
1
200
6
10,000
4
Market Cap
150,000,000,000
140,000,000,000
120,000,000,000
110,000,000,000
110,000,000,000
110,000,000,000
110,000,000,000
100,000,000,000
100,000,000,000
100,000,000,000
90,000,000,000
90,000,000,000
80,000,000,000
80,000,000,000
80,000,000,000
80,000,000,000
80,000,000,000
70,000,000,000
70,000,000,000
70,000,000,000
70,000,000,000
70,000,000,000
60,000,000,000
60,000,000,000
60,000,000,000
Sector
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
6
Original Adjusted
Rating
Rating
Aa3
A2
Aa3
A1
Baa2
Ba2
Ba1
Ba2
A2
Baa1
Aa1
Aa3
Aa3
A3
Aa3
A2
Aa3
A2
A3
Baa1
Aa3
A1
Aa2
A1
Ba1
Ba3
Aa3
A1
A1
A2
Ba1
B1
A1
A1
Aaa
Aa2
A1
A2
Aa3
A3
A3
Baa1
A3
Baa3
A1
A2
Aa3
A3
A3
Baa3
Loss as %
of Mkt Cap
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
0.73%
Stressed
Std. Dev. Default Rate
2.23%
0.03%
2.23%
0.01%
2.23%
1.50%
2.23%
1.50%
2.23%
0.20%
2.23%
0.00%
2.23%
0.08%
2.23%
0.03%
2.23%
0.03%
2.23%
0.20%
2.23%
0.01%
2.23%
0.01%
2.23%
2.38%
2.23%
0.01%
2.23%
0.03%
2.23%
3.33%
2.23%
0.01%
2.23%
0.00%
2.23%
0.03%
2.23%
0.08%
2.23%
0.20%
2.23%
0.50%
2.23%
0.03%
2.23%
0.08%
2.23%
0.50%
IG Flag
1
1
0
0
1
1
1
1
1
1
1
1
0
1
1
0
1
1
1
1
1
1
1
1
1
Modeling Losses
Willis Analytics
Directors & Officers Reinsurance Model
Reinsurance Terms
Per Risk Limit
Per Risk Attachment
Aggregate Limit
Aggregate Deductible
Gross
999,999,999,999
999,999,999,999,999
-
XOL 1
10,000,000
50,000,000
5,000,000,000
-
XOL 2
10,000,000
60,000,000
5,000,000,000
-
XOL 3
5,000,000
70,000,000
5,000,000,000
-
Losses
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%
80.0%
90.0%
95.0%
96.0%
97.0%
98.0%
99.0%
99.5%
24
Gross
267,217,216
728,973,973
273%
25,649,508
0
5,129,298,104
254
243,748
2,711,322
25,649,508
59,526,921
132,303,792
286,465,545
561,757,063
1,232,527,645
1,259,346,346
1,369,173,327
1,564,548,151
4,500,631,555
4,814,964,829
XOL 1
7,375,730
13,021,415
177%
0
0
74,806,776
4,137,753
10,000,000
10,000,000
20,000,000
30,000,000
30,001,864
30,355,262
40,928,633
70,048,068
72,427,422
Counts
XOL 2
6,777,288
12,190,323
180%
0
0
70,000,000
10,000,000
10,000,000
20,000,000
30,000,000
30,000,000
30,300,000
40,404,292
60,312,448
65,156,224
XOL 3
3,324,719
6,051,508
182%
0
0
35,000,000
5,000,000
5,000,000
10,000,000
15,000,000
15,000,000
15,150,000
20,200,000
30,050,000
32,525,000
Gross
4.32
6.56
152%
2
0
54
1
1
2
2
3
4
6
9
14
15
18
18
20
37
XOL 1
0.79
1.39
176%
0
0
8
1
1
1
2
3
3
4
5
7
8
XOL 2
0.70
1.28
182%
0
0
7
1
1
2
3
3
3
4
7
7
XOL 3
0.67
1.21
181%
0
0
7
1
1
2
3
3
3
4
6
7
Risk Transfer
•
•
25
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 risk-return profile of the
primary company 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
26
Questions
?
Athula Alwis
Senior Vice President
Global Credit Analytics
Willis Re Inc
27
Junning Shi
Senior Vice President
and Senior Actuary
Willis Re Inc