U.S. patent application number 14/051042 was filed with the patent office on 2014-07-10 for system and method for providing systemic casualty reserve protection.
This patent application is currently assigned to Guy Carpenter & Company, LLC. The applicant listed for this patent is Guy Carpenter & Company, LLC. Invention is credited to Jose R. Couret, Michelle HARNICK, Priyantha L. Perera.
Application Number | 20140195273 14/051042 |
Document ID | / |
Family ID | 49487963 |
Filed Date | 2014-07-10 |
United States Patent
Application |
20140195273 |
Kind Code |
A1 |
HARNICK; Michelle ; et
al. |
July 10, 2014 |
System And Method For Providing Systemic Casualty Reserve
Protection
Abstract
A system, method and computer readable storage medium for
calculating a first industry index amount at an index year based on
selected loss values for the index year for a plurality of
companies in a defined line of business and a predetermined number
of years preceding the index year for the plurality of companies
and loss estimates for a number of years subsequent to the index
year corresponding to a predetermined term of a systemic risk
product for the plurality of companies, calculating a second
industry index amount based on selected loss values for the index
year for the plurality of companies, a predetermined number of
years preceding the index year for the plurality of companies and
at least one year subsequent to the index year and calculating an
industry index value based on the first and second industry index
amount.
Inventors: |
HARNICK; Michelle; (New
York, NY) ; Couret; Jose R.; (New York, NY) ;
Perera; Priyantha L.; (New York, NY) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Guy Carpenter & Company, LLC |
New York |
NY |
US |
|
|
Assignee: |
Guy Carpenter & Company,
LLC
New York
NY
|
Family ID: |
49487963 |
Appl. No.: |
14/051042 |
Filed: |
October 10, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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13611965 |
Sep 12, 2012 |
8577786 |
|
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14051042 |
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Current U.S.
Class: |
705/4 |
Current CPC
Class: |
G06Q 40/08 20130101;
G06Q 40/00 20130101 |
Class at
Publication: |
705/4 |
International
Class: |
G06Q 40/08 20120101
G06Q040/08 |
Claims
1-24. (canceled)
25. A method, comprising: calculating, by a processor, a first
industry index amount at an index year based on (i) selected actual
loss values for the index year for a plurality of companies in a
defined line of business, (ii) selected actual loss values for a
predetermined number of years preceding the index year for the
plurality of companies in the defined line of business, and (iii)
loss estimates for a number of years subsequent to the index year
corresponding to a predetermined term of a systemic risk product
for the plurality of companies in the defined line of business;
calculating, by the processor, a second industry index amount based
on (i) the selected actual loss values for the index year for the
plurality of companies in the defined line of business, (ii) the
selected actual loss values for the predetermined number of years
preceding the index year for the plurality of companies in the
defined line of business, and (iii) selected actual loss values for
at least one year subsequent to the index year for the plurality of
companies in the defined line of business, wherein the at least one
year subsequent to the index year is equal to the predetermined
term of the systemic risk product; calculating, by the processor,
an industry index value based on the first and second industry
index amounts; and calculating a settlement amount based on the
industry index value, an index trigger and an index limit.
26. The method of claim 25, wherein the defined line of business is
based on a Schedule P defined line of business, wherein the
Schedule P is a National Association of Insurance Commissioners
(NAIC), Annual Statement schedule, wherein the Schedule P includes
defined lines of business.
27. The method of claim 25, wherein the selected actual loss values
for the index year are one of actual paid loss values and case
reserved loss values from Schedule P filings for the plurality of
companies, wherein the Schedule P filings are a National
Association of Insurance Commissioners (NAIC), Annual Statement
schedule, wherein each Schedule P includes ten years worth of paid
loss data.
28. The method of claim 25, wherein the predetermined term is any
of one year to nine years.
29. The method of claim 25, wherein the selected actual loss values
for the index year and the loss estimates are one of gross losses
or net losses.
30. The method of claim 25, further comprising: determining a
portion of the selected actual loss values for the predetermined
number of years preceding the index year for adjustment based on a
consistency check; and adjusting, prior to calculating the first
and second industry indices, the portion of the selected actual
loss values for the predetermined number of years preceding the
index year.
31. The method of claim 25, wherein calculating the second industry
index comprises: calculating an interim industry index amount based
on the selected actual loss values for the index year for the
plurality of companies, the predetermined number of years preceding
the index year for the plurality of companies and at least one year
subsequent to the index year; and calculating a final industry
index amount based on the selected actual loss values for the index
year for the plurality of companies, the predetermined number of
years preceding the index year for the plurality of companies and
the number of years subsequent to the index year corresponding to
the predetermined term of the systemic risk product, wherein the
industry index value is calculated based on the first, interim and
final industry index amounts.
32. A system, comprising: a memory storing a set of instructions;
and a processor executing the set of instructions to perform
operations comprising: calculating a first industry index amount at
an index year based on (i) selected actual loss values for the
index year for a plurality of companies in a defined line of
business, (ii) selected actual loss values for a predetermined
number of years preceding the index year for the plurality of
companies in the defined line of business, and (iii) loss estimates
for a number of years subsequent to the index year corresponding to
a predetermined term of a systemic risk product for the plurality
of companies in the defined line of business; calculating a second
industry index amount based on (i) the selected actual loss values
for the index year for the plurality of companies in the defined
line of business, (ii) the selected actual loss values for the
predetermined number of years preceding the index year for the
plurality of companies in the defined line of business, and (iii)
selected actual loss values for at least one year subsequent to the
index year for the plurality of companies in the defined line of
business, wherein the at least one year subsequent to the index
year is equal to the predetermined term of the systemic risk
product; calculating an industry index value based on the first and
second industry index amounts; and calculating a settlement amount
based on the industry index value, an index trigger and an index
limit.
33. The system of claim 32, wherein the defined line of business is
based on a Schedule P defined line of business, wherein the
Schedule P is a National Association of Insurance Commissioners
(NAIC), Annual Statement schedule, wherein the Schedule P includes
defined lines of business.
34. The system of claim 32, wherein the selected actual loss values
for the index year are one of actual paid loss values and case
reserved loss values from Schedule P filings for the plurality of
companies, wherein the Schedule P filings are a National
Association of Insurance Commissioners (NAIC), Annual Statement
schedule, wherein each Schedule P includes ten years worth of paid
loss data.
35. The system of claim 32, wherein the predetermined term is any
of one year to nine years.
36. The system of claim 32, wherein the selected loss actual values
for the index year and the loss estimates are one of gross losses
or net losses.
37. The system of claim 32, wherein the operations further
comprise: determining a portion of the selected actual loss values
for the predetermined number of years preceding the index year for
adjustment based on a consistency check; and adjusting, prior to
calculating the first and second industry indices, the portion of
the selected actual loss values for the predetermined number of
years preceding the index year.
38. The system of claim 32, wherein the operations further
comprise: calculating an interim industry index amount based on the
selected actual loss values for the index year for the plurality of
companies, the predetermined number of years preceding the index
year for the plurality of companies and at least one year
subsequent to the index year; and calculating a final industry
index amount based on the selected actual loss values for the index
year for the plurality of companies, the predetermined number of
years preceding the index year for the plurality of companies and
the number of years subsequent to the index year corresponding to
the predetermined term of the systemic risk product, wherein the
industry index value is calculated based on the first, interim and
final industry index amounts.
39. A non-transitory computer readable storage medium with an
executable program stored thereon, wherein the program instructs a
processor to perform the following steps: calculating a first
industry index amount at an index year based on (i) selected actual
loss values for the index year for a plurality of companies in a
defined line of business, (ii) selected actual loss values for a
predetermined number of years preceding the index year for the
plurality of companies in the defined line of business, and (iii)
loss estimates for a number of years subsequent to the index year
corresponding to a predetermined term of a systemic risk product
for the plurality of companies in the defined line of business;
calculating a second industry index amount based on (i) the
selected actual loss values for the index year for the plurality of
companies in the defined line of business, (ii) the selected actual
loss values for the predetermined number of years preceding the
index year for the plurality of companies in the defined line of
business, and (iii) selected actual loss values for at least one
year subsequent to the index year for the plurality of companies in
the defined line of business, wherein the at least one year
subsequent to the index year is equal to the predetermined term of
the systemic risk product; calculating an industry index value
based on the first and second industry index amounts, and
calculating a settlement amount based on the industry index value,
an index trigger and an index limit.
40. The non-transitory computer readable storage medium of claim
39, wherein the steps further comprises: determining a portion of
the selected actual loss values for the predetermined number of
years preceding the index year for adjustment based on a
consistency check; and adjusting, prior to calculating the first
and second industry indices, the portion of the selected actual
loss values for the predetermined number of years preceding the
index year.
41. The non-transitory computer readable storage medium of claim
39, wherein the steps further comprise: calculating an interim
industry index amount based on the selected actual loss values for
the index year for the plurality of companies, the predetermined
number of years preceding the index year for the plurality of
companies and at least one year subsequent to the index year; and
calculating a final industry index amount based on the selected
actual loss values for the index year for the plurality of
companies, the predetermined number of years preceding the index
year for the plurality of companies and the number of years
subsequent to the index year corresponding to the predetermined
term of the systemic risk product, wherein the industry index value
is calculated based on the first, interim and final industry index
amounts.
Description
BACKGROUND INFORMATION
[0001] A customer of an insurance company or a reinsurance company
pays the (re)insurance company a premium to bind a (re)insurance
policy for the customer. The (re)insurance policy allows the
customer to make a claim against the (re)insurance company for a
covered amount when the customer suffers a loss covered by the
(re)insurance policy. The (re)insurance company is generally
required by law or insurance regulation to keep a certain amount of
the premium payment available to pay anticipated losses. These
funds that are set aside to pay later losses are referred to as
loss reserves.
[0002] (Re)insurance companies may also hedge their risk on a
(re)insurance policy by using other financial instruments related
to the entire (re)insurance industry, such as CAT bonds or industry
loss warranties ("ILWs"). These industry-based or index-based
securities generally use industry losses as a trigger mechanism for
payout of a specified amount of money to a (re)insurance company or
other insured entity. It is noted that throughout this description
when the term "security" or "securities" is used it refers to the
reinsurance or ILW instruments, which may or may not be a security
as that term is defined by law. An ILW contract is a manner through
which one party will purchase protection based on the total loss
arising from an event or series of events to the entire
(re)insurance industry rather than its individual loss. The maximum
amount of protection offered by the contract is referred to as the
"limit." The industry loss threshold whose exceedance results in a
payment under the contract for as much as the limit is referred to
as the "trigger." To provide a specific example, an insurance
company may purchase a contract having a limit of $200 million that
is payable upon an industry loss event of $25 billion (the
trigger). That is, if an event occurs (e.g., an earthquake) where
the total industry loss exceeds $25 billion, the insurance company
will receive a payment up to a limit of $200 million, regardless of
actual losses suffered by the insurance company during the
event.
[0003] However, there are no effective instruments that are offered
to hedge an insurance company's risk for casualty lines of business
based on systemic risks, e.g., those risks that are of, relating
to, or common to the entire system and experienced across and
entire line of business or the entire industry. An example of
systemic risk is aggregation risk, which is an exposure
concentration affecting similar types of risks or a particular
coverage involving multiple accident years arising out of a
particular product, substance or some common causative factor such
as a design, business activity, error or omission. Other examples
of systemic risk include a new legal theory, a new coverage
interpretation, liability arising out of a relatively new or
existing product or technology, changes in the macroeconomic
conditions (e.g., medical inflation driven by a costly new
technology or unforeseen cost shifts associated with universal
health insurance), changes in the regulatory environment or other
unforeseen causes that affect the entire industry.
[0004] There are several reasons that these security products do
not exist to deal with systemic risk, including moral hazard (e.g.,
the hazard associated with the individual company's ability to
manipulate reserves), high capital charges associated with the long
tailed (slow to settle) lines of business (make it uneconomic for
reinsurers to write), and significant underwriting expense and due
diligence and market reservations to write casualty due to external
factors including social, economic and political influences.
SUMMARY OF THE EXEMPLARY EMBODIMENTS
[0005] A first exemplary embodiment is directed to a method for
calculating a first industry index amount at an index year based on
selected loss values for the index year for a plurality of
companies in a defined line of business and a predetermined number
of years preceding the index year for the plurality of companies
and loss estimates for a number of years subsequent to the index
year corresponding to a predetermined term of a systemic risk
product for the plurality of companies; calculating a second
industry index amount based on selected loss values for the index
year for the plurality of companies, a predetermined number of
years preceding the index year for the plurality of companies and
at least one year subsequent to the index year and calculating an
industry index value based on the first and second industry index
amount.
[0006] A second exemplary embodiment is directed to a system having
a memory storing a set of instructions and a processor executing
the set of instructions to perform a method. The method including
calculating a first industry index amount at an index year based on
selected loss values for the index year for a plurality of
companies in a defined line of business and a predetermined number
of years preceding the index year for the plurality of companies
and loss estimates for a number of years subsequent to the index
year corresponding to a predetermined term of a systemic risk
product for the plurality of companies, calculating a second
industry index amount based on selected loss values for the index
year for the plurality of companies, a predetermined number of
years preceding the index year for the plurality of companies and
at least one year subsequent to the index year and calculating an
industry index value based on the first and second industry index
amount.
[0007] A further exemplary embodiment is directed to a
non-transitory computer readable storage medium comprising a set of
instructions that are executable by a processor to perform a
method. The method including calculating a first industry index
amount at an index year based on selected loss values for the index
year for a plurality of companies in a defined line of business and
a predetermined number of years preceding the index year for the
plurality of companies and loss estimates for a number of years
subsequent to the index year corresponding to a predetermined term
of a systemic risk product for the plurality of companies,
calculating a second industry index amount based on selected loss
values for the index year for the plurality of companies, a
predetermined number of years preceding the index year for the
plurality of companies and at least one year subsequent to the
index year and calculating an industry index value based on the
first and second industry index amount.
BRIEF DESCRIPTION OF THE DRAWINGS
[0008] FIG. 1 shows an exemplary derivation of a cumulative payment
pattern (labeled % Paid) and incremental payment pattern (labeled
.DELTA.% Paid) using a 2-year weighted average paid chain ladder
method. The estimate corresponds to index year 2000. The payment
patterns and the loss amounts used in their derivation serve as
inputs into the calculation of the index.
[0009] FIG. 2 shows an exemplary initial index based on projected
payments over the next five calendar years using the data from FIG.
1 for the index year 2000.
[0010] FIG. 3 shows an exemplary updated index one year forward
based on updated actual payments for the next calendar year and
projected initial payments for the next four calendar years
following the next year using the data from FIG. 1 for the index
year 2000. Other interim values of the index would be based on the
same procedure but would include more years of actual payments. For
example, the index two years forward would be based on two calendar
years of actual payments and three years of projected payments (as
originally calculated).
[0011] FIG. 4 shows an exemplary final value of the index based on
updated actual payments after five years for the index year
2000.
[0012] FIG. 5 illustrates an exemplary method for implementing the
exemplary systemic risk product.
[0013] FIG. 6 shows a gross paid loss table that has gross paid
loss values from various annual reports and an incremental paid
loss table that is calculated from the gross paid loss table.
[0014] FIG. 7 illustrates a table showing gross premiums that
correspond to the same time periods as the gross loss paid values
in the gross paid loss table of FIG. 6.
[0015] FIG. 8 shows a first table illustrating unadjusted
age-to-age factors based on the gross paid loss table values of
FIG. 6 and a second table illustrating adjusted age-to-age factors
based on an adjustment calculation.
[0016] FIG. 9 shows an adjusted gross paid loss table based on the
gross paid loss table of FIG. 6 and the adjusted age-to-age factors
of FIG. 8.
[0017] FIG. 10 shows an adjusted incremental paid loss table based
on the adjusted gross paid loss table of FIG. 9.
[0018] FIG. 11A shows a first portion of exemplary calculated
default factors for use when observed factors fail consistency
checks.
[0019] FIG. 11B shows a second portion of the exemplary calculated
default factors for use when observed factors fail consistency
checks, as illustrated in FIG. 11A.
DETAILED DESCRIPTION
[0020] The exemplary embodiments may be further understood with
reference to the following description of the exemplary embodiments
and the related appended drawings, wherein like elements are
provided with the same reference numerals. The exemplary
embodiments are related to systems and methods for providing
systemic casualty reserve protection. Specifically, the exemplary
embodiments provide a product based on an industry index to hedge
against systemic risk (hereinafter referred to as the "systemic
risk product"). The following will provide a description of the
systemic risk product, a manner of calculating the proprietary
industry index, and a manner of calculating the payoff if the
trigger is satisfied subject to the other terms and conditions of
the systemic risk product.
[0021] Throughout this description it will be described that an
insurance company will be the purchaser of the systemic risk
product to hedge its risk against systemic risk. However, those
skilled in the art will recognize that other entities may also be
the purchaser of the systemic risk product. For example, as
described above, reinsurers may have the same issues as insurance
companies, thus, a reinsurer may be the purchaser of the systemic
risk product. In another example, a company may self insure against
certain risks. This company may be the purchaser of the exemplary
systemic risk product. Thus, it should be understood that the term
"insurance company" is not limited to the traditional definition of
that term. As will be noted below, the exemplary systemic risk
product may be in the form of a reinsurance product or an ILW
product. Thus, throughout this description, where the term
"reinsurer" is used, it is meant to refer to any entity that is the
seller of the exemplary systemic risk product, not only entities
that engage in the reinsurance business as that business is
understood by those skilled in the art.
[0022] Insurance companies use various actuarial techniques to
estimate their paid losses for upcoming calendar years. These
techniques may include, for example, chain ladder models,
generalized linear models (GLM's), etc. Based on these techniques,
the insurance companies estimate and set aside the proper loss
reserves to eventually pay out for any actual losses suffered by
the insured parties. Empirical data indicates that calendar year
trends for actual paid losses tend to be cyclical and that all
insurance companies in a particular line of business tend to move
in tandem. While there is always the possibility of outliers, e.g.,
a particular insurance company has written policies that suffer
losses based on a particular event while another insurance company
does not have exposure to a particular event, etc., the data
supports the proposition of the general rule that losses in
individual lines of business tend to move in the same direction for
all companies writing policies in that line of business. This leads
to a conclusion that systemic losses that are spread throughout the
entire industry will impact an individual company. These systemic
losses cannot be accounted for by the actuarial techniques because
the data relating to such systemic losses is not typically observed
in the historical data because the data does not capture unforeseen
and/or extremely rare events. Some examples of systemic risk or
causes of systemic losses were provided above. The particular
reason for a systemic loss is not important, because in most cases,
it is not foreseeable and therefore cannot be built accurately into
the models. Most insurance companies know or intuitively know that
the systemic risk exists and desire to hedge their exposure to the
risk. However, as described above, there is no well-designed
synthetic product available for such a hedge.
[0023] The exemplary systemic risk product described herein
provides a mechanism for an effective hedge against adverse
developments in unpaid losses driven by systemic shocks to the
system or the industry as a whole. Thus, the purpose of the
systemic risk product is to protect the insurance company against
systemic events, not firm specific risk. For this reason, the
systemic risk product is based on an industry index, e.g., a
plurality of companies that represent the industry. The industry
index may be generally described as a ratio of actual paid losses
against projected paid losses, although other data points may be
used. An exemplary calculation of an index is provided below.
[0024] It has been found that the industry development trends have
better predictability than an individual insurance company's
development trends. Further, the industry index based on paid loss
data eliminates the moral hazard associated with any individual
company's reserving practices, e.g., the carried reserves of any
individual company do not influence the systemic risk product.
[0025] Each insurance company is required to file a Schedule P for
its line of businesses that includes paid loss data. Thus, the
index that is used for the exemplary systemic risk product
described herein is based on publicly available paid loss data for
each of the insurance companies in the index. Since all the
underlying data for the calculation is publicly available data, the
calculation is verifiable, transparent and there is little or no
due diligence required on individual companies, thereby expediting
the process.
[0026] In general, the industry index that is used for the
exemplary systemic risk product described herein does not require a
calculation to be performed for each insurance company. Once the
index has been calculated and verified, the same index may be used
for any insurance company wishing to purchase a cover for the line
of business for which the index was calculated. It should be noted
that the industry index is flexible and may be modified to improve
the hedge for individual insurance companies or groups of insurance
companies. In one example, the paid loss data used to calculate the
index may be gross paid loss data, whereas in another example the
paid loss data may be net paid loss data. In a further example, a
specific insurance company may have certain overweight geographical
exposures (e.g., California, Illinois and Florida), the industry
index may be modified to more closely match this geographical
overweight exposure of the insurance company to improve the hedging
effect of the systemic risk product.
[0027] Those skilled in the art will understand that the Schedule P
filing has ten (10) years worth of paid loss data. Thus, the
exemplary calculation provided below shows the calculation based on
the most current ten (10) years of publicly available paid loss
data based on the Schedule P filings. However, historical years may
be retained such that more than ten (10) years of data may be used
in the calculation. Another point of flexibility of the systemic
risk product is that it may have any term from 1-9 years. The
exemplary calculation provided below will assume a term of five (5)
years, but the term could also be 2 years, 3 years, 7 years,
etc.
[0028] The exemplary systemic risk product that is based on the
index calculation may be a reinsurance product and/or an ILW
product. The exemplary calculation provided below will be for a
reinsurance product, but characteristics of an exemplary ILW
product will also be provided. A general description of the
systemic risk product is a synthetic adverse development cover that
includes an accelerated formulaic mandatory commutation feature
allowing for commutation after a defined term of 1-9 years. As
described above, the systemic risk product is based on an industry
index calculated from Schedule P paid loss data and is designed to
cover the systemic contribution to company adverse development.
[0029] The exemplary methods of calculating the industry index and
the corresponding payoffs for the systemic risk product that are
described below may be advantageously implemented using one or more
computer programs executed on a computer system having a processor
or central processing unit, such as, for example, a computer using
an Intel-based CPU, such as a Pentium or Centrino, running an
operating system such as the WINDOWS or LINUX operating systems,
having non-transitory storage mediums, such as, a hard drive, RAM,
ROM, a compact disc, magneto-optical storage device, and/or fixed
or removable media, and having a one or more user interface
devices, such as, for example, computer terminals, personal
computers, laptop computers, and/or handheld devices, with an input
means, such as, for example, a keyboard, mouse, pointing device,
and/or microphone. The methods may also be implemented via a server
executing a computer program and having users remotely access the
results generated by the server for display on their personal
devices, e.g., over the Internet, a company intranet, cloud
computing devices and/or services, etc.
[0030] The following provides an exemplary index calculation and
reinsurance systemic risk product based on a worker's compensation
line of business. In this example, ABC insurance company has a
$500M portfolio of workers compensation reserves and the company's
management wants coverage for a systemic shock on these reserves.
Thus, a reinsurer will develop a systemic risk product for the
workers compensation line of business by calculating an industry
index and negotiating and/or offering several other terms to ABC
insurance company, which will be described below. The ABC insurance
company may then elect to purchase the systemic risk product for
the workers compensation line of business.
[0031] In this example, the exemplary index provided below is based
on thirty-six (36) large workers compensation insurance writers
that made up 60% of the industry based on premium volume in 2009.
From this example, it can be seen that the index is based on a
substantial number (but not all) of companies in the industry.
There is no specific threshold of a required number of companies or
premium volume within the index, but it should be clear that the
higher the number and/or volume within the index, the more accurate
the index will be for the purpose of hedging against systemic risk.
Also, while the example used throughout this description is based
on the workers compensation line of business, the exemplary
embodiments may be applied to any Schedule P defined line of
business, e.g., homeowners insurance, private passenger auto,
medical malpractice, other liability occurrence, etc.
[0032] The commutation amount of the systemic risk product is
calculated based upon the final value of the industry index and the
paid losses of ABC insurance company. In this example, it is
considered that the parties have negotiated a limit of $200M and a
retention of $600M. In the scenario of the reinsurance systemic
risk product, the parties have also negotiated a dual trigger and
corresponding values to activate the cover. In this example, ABC
insurance company reserves must develop by $50M (10% of the $500M
reserve described above) and the index value at year 5 expressed as
a ratio to the initial index value must exceed an index trigger of
1.10. The index trigger and an exemplary manner of calculating the
index trigger value are described below.
[0033] In this example, the estimation of the outstanding losses
for payment at commutation (e.g., end of the defined 5 year term)
is based on the index year 2000. The selection of the year 2000 is
merely for illustrative purposes and any index year may be
selected. The formula for outstanding loss or commutation amount
(CA) in the layer based on the above-described parameters is
calculated as follows:
CA=Min(Max(I(5)-1.1, 0), 0.1).times.$2B
[0034] where, [0035] I(5) is the index value at year 5 expressed as
a ratio to the initial index value (as described above, the
exemplary systemic risk product has a selected term of 5 years in
this example), the value 1.1 is based on the negotiated index
trigger point of 1.1, [0036] the value 0.1 is the negotiated index
limit, and the $2B value is a scalar that is negotiated to convert
the index value to a monetary value.
[0037] Exemplary calculations using this formulas will be provided
below. Those skilled in the art will understand that the values and
parameters used above are only exemplary and that different sellers
and/or buyers of a systemic risk product may use and/or negotiate
different values and parameters.
[0038] FIG. 1 shows an exemplary 2-year weighted average paid chain
ladder estimate triangle 100 for the index year 2000 as described
above. This exemplary data will be used to show an exemplary
calculation of the industry index on which the systemic risk
product is to be based. Again, it is noted that using a 2-year
weighted average is only exemplary and other time frames and method
may also be used, e.g., 3-year weighted average, 5-year straight
average, etc. Initially, the column 105 shows the accident years
from 1989-2000 and the row 110 shows the development years from
year 1-10. The values in the triangle 100 represent the actual
cumulative paid loss values for the business line as of December
31, 2000, e.g., workers compensation. For example, for accident
year 1998, after development year 1 (December 31, 1998), a
cumulative total 173 of $2,986,866 has been paid, after development
year 2 (December 31, 1999), a cumulative total 171 of $6,606,706
has been paid and after development year 3 (December 31, 2000) a
cumulative total 179 of $8,825,324 has been paid. In another
example, for accident year 1993, after development year 6 (December
31, 1998), a cumulative total 191 of $13,487,296 has been paid,
after development year 7 (December 31, 1999), a cumulative total
192 of $13,923,433 has been paid and after development year 8
(December 31, 2000), a cumulative total 193 of $14,253,401 has been
paid. As described above, the values in this upper left portion 115
of the triangle 100 are actual cumulative paid loss values that
have been extracted from Schedule P filings for a number of
insurance companies in the workers compensation line of business.
As described previously, in this example, the values are based on
thirty-six (36) workers compensation insurance writers that made up
60% of the industry based on premium volume in 2009.
[0039] As shown in FIG. 1, the bottom right portion 117 is the
forecast period for which there are no actual paid values at this
time (assuming it is December 31, 2000). The calculation of these
forecast values that will be filled in the bottom right portion 117
will be discussed in greater detail below.
[0040] FIG. 1 also includes a table 120 that shows an age-to-age
(ATA) factor 130, an age-to-ultimate (ATU) factor 140, a cumulative
percentage paid factor 150 and an incremental percentage paid
factor 160 for each of the corresponding development years. Each of
these factors and the calculation of their corresponding values
130-160 will be described. The ATA factor 130 is the change in
payments made on a defined set of claims between successive points
in time. In this example, this change is measured based on a
two-year weighted average of successive accident years and
successive development years. For example, the first ATA factor
value 131 of 2.27063 is calculated by adding the values for the
second year of development of accident year 1998 (value 171 of
6,606,706) and accident year 1999 (value 172 of 7,061,371) to give
a total of 13,668,077. Then, the values for the previous (first)
year of development of accident year 1998 (value 173 of 2,986,866)
and accident year 1999 (value 174 of 3,032,646) are added resulting
in the summed value of 6,019,512. The first summed value is then
divided by the second summed value to calculate the ATA factor
value 131 (13,668,077/6,019,512=2.27063). A second exemplary
calculation of the ATA factor value 132 will be performed to
provide a further example. In this example, the values for the
sixth year of development of accident year 1994 (value 175 of
11,793,143) and accident year 1995 (value 176 of 10,498,280) are
summed to give a total of 22,291,423. Then, the values for the
previous (fifth) year of development of accident year 1994 (value
177 of 11,260,574) and accident year 1995 (value 178 of 10,017,405)
are added resulting in the summed value of 21,277,979. The first
summed value is then divided by the second summed value to
calculate the ATA factor value 132 (22,291,423/21,277,979=1.04763).
The remaining ATA factors 130 may be calculated in the same
manner.
[0041] The ATU factor 140 is the cumulated ATA factors 130. In this
example, it is considered that the ultimate payment amount occurs
at year 10 of development, e.g., there is no paid development after
year 10. Thus, the ATU factor value corresponding to development
year 10 is unity as shown by the ATU factor value 141. The
remaining ATU factor 140 values for any development year may be
calculated by multiplying the ATA factor 130 value of the
development year of interest by the ATU factor 140 value of the
next development year. Thus, to calculate the ATU factor value 142
of 1.01339 for development year 9, the ATA factor value 133 of
1.01339 of the same development year is multiplied by the ATU
factor value 141 of 1.00000 of the next development year 10,
resulting in the ATU factor value 142 of 1.01339. To provide a
further example, the ATU factor value 143 of 1.41203 for
development year 3 is calculated by multiplying the ATA factor
value 134 of 1.14676 of development year 3 by the ATU factor value
144 of 1.23132 of development year 4. Again, the remaining ATU
factors may be calculated in the same manner.
[0042] The cumulative percentage paid factor 150 is the cumulative
percentage of the amount paid in the development year against the
projected ultimate cumulative amount paid. Thus, the amounts paid
in development year 1 are projected to be approximately 23.5%
(0.23503) of the ultimate cumulative paid amount. The cumulative
amounts paid through development year 2 are projected to be
approximately 53% (0.53366) of the ultimate cumulative paid amount.
The cumulative paid factor at each report is the reciprocal of the
ATU Factor; that is, it is calculated by dividing one by the ATU
factor.
[0043] The incremental percentage paid factor 160 is the difference
from development year to development year in the cumulative
percentage paid factor 150. Thus, as described above, the
percentage paid factor values for development years 2 and 1 are
0.53366 and 0.23503, respectively. Subtracting the value of
development year 2 from the value of development year 1 results in
(0.53366-0.23503=0.29863) which is the value for development year 2
for the incremental percentage paid factor 160. Again, the
remaining incremental percentage paid factor 160 values may be
calculated in the same manner.
[0044] The meaning of the exemplary data presented by the triangle
100 and table 120 will be described. In an example, accident year
1995 is selected. Through the sixth development year, a cumulative
total of $10,498,280M has been paid as shown by value 176. This
cumulative paid value 176 represents approximately 92.07% of the
cumulative paid loss projected through development year 10 as shown
by the value 182. In development year 6, approximately 4.186% of
the ultimate cumulative paid loss will be paid as shown by the
value 184.
[0045] FIG. 2 shows an exemplary initial index based on projected
payments over the next five calendar years using the data from FIG.
1 for the index year 2000. Initially, it can be seen that the data
presented in table 200 is incremental paid loss data rather than
cumulative paid loss data as shown in FIG. 1. The actual
incremental paid loss data is shown as data 210 and may be
calculated using the cumulative paid loss data presented in FIG. 1.
The calculation is performed, for each accident year, by
subtracting the cumulative paid loss in previous development year
from the current development year thereby resulting in the
incremental paid loss for the current development year. To provide
an example, to calculate the incremental paid loss value 212 of
4,028,725 for accident year 1999, development year 2, the
cumulative paid loss value 174 for accident year 1999, development
year 1, is subtracted from the cumulative paid loss value 172 for
accident year 1999, development year 2
(7,061,371-3,032,646=4,028,725). The remaining incremental values
210 may be calculated in the same manner.
[0046] The table 200 also includes the projected incremental paid
loss data 220 over the next five years. For example, the actual
paid loss data for accident year 2000 only includes development
year 1. However, projected incremental paid loss data for
development years 2-6 is also included. As noted above, the
projected incremental values may be calculated for any number of
years from 1-9 for the purposes of the index, but in this example,
the number of years has been selected to be five to match the term
of the contract in this example. This projected paid loss data is
calculated based on the data from FIG. 1 and illustrated in table
250 of FIG. 2. For example, as shown in table 250, for accident
year 2000 (column 251), the cumulative paid loss from the latest
report (development year 1, column 252) is 3,135,073 (column 253).
This represents a cumulative percentage paid 150 value of 23.503%
of the total projected paid loss through development year 10
(column 254). Dividing the cumulative percentage paid 150 by the
latest reported cumulative paid loss results in the cumulative
projected paid loss through the tenth development year (column
255). In this example, the calculation is
3,135,073/0.23503=13,339,181. The cumulative projected paid loss
value through the tenth report may then be multiplied by the
incremental percentage paid factor 160 value for any development
year to result in the projected incremental paid loss value for
that development year. Continuing with the example of accident year
2000, the cumulative projected paid loss of 13,339,181 may be
multiplied by the incremental percentage paid factor 160 value of
0.298633 for development year 2 to result in
(13,339,181.times.0.298633=3,983,514) which is the incremental paid
loss value 222 for accident year 2000, development year 2. The
remaining projected incremental paid loss values 220 for other
accident and development years may be calculated in the same manner
as shown in table 250.
[0047] It is noted that table 200 also includes the incremental
projected losses 230 for further years. These values were provided
to complete the table, but are not necessary because, as stated
above, it has been selected in this example to use the term of five
years for the cover. It is also noted that the above calculations
and further calculations presented below may include some rounding
errors if it is attempted to reproduce these calculations from the
values presented in FIGS. 1 and 2. These rounding errors add an
insignificant amount of error to the calculations and do not affect
the general intent of the index.
[0048] The table 250 also includes the base forecast 260 for the
index. The base forecast 260 is the total projected payments over
the next five calendar years for the most recent nine accident
years. This value is calculated by summing the projected
incremental paid losses 220 for each accident year through five
calendar years as shown in column 257 and then summing all these
values. For example, for accident year 1993, there are two
development years of projected incremental losses shown as values
224 (228,510) and 226 (193,924), the sum of which is 422,434 as
shown in column 257 of table 250. The summation of each of the
calendar years results in the base forecast 260 value of
23,475,906. The index can be expressed as a ratio to the base
forecast. Thus, the index is initially unity by construction. The
base forecast 260 is considered to be the index value I(0)=1. The
purpose of this index value will be described in greater detail
below.
[0049] FIG. 3 shows an exemplary updated index based on updated
actual payments and projected payments over the next four calendar
years using the data from FIG. 1 for the index year 2000. Thus, in
this example, it is time 1 year or the end of 2001 (December 31,
2001). At this time, the actual paid losses 310 for calendar year
2001 have been added to the table 300. The remaining projected paid
losses 320 are the same as the projected paid losses 220 from table
200.
[0050] The actual paid losses 310 from calendar year 2001 are
different from the projected paid losses that were shown in table
200. Therefore, the summation of the actual paid losses for
calendar year 2001 and the projected paid losses for the next four
calendar years can be re-performed as shown in table 350. As shown,
the summation for this updated forecast is the value 360 of
23,996,090, which is greater than the original base forecast 260 of
23,475,906. This updated forecast expressed as a ratio to the base
forecast is the index value at year 1 I(1).
I(1)=23,996,090/23,475,906=1.022. As each successive calendar year
passes, a new index value may be calculated in a similar manner as
a ratio to the base forecast 260.
[0051] FIG. 4 shows an exemplary updated index based on updated
actual payments after five years for the index year 2000. The table
400 is for time 5 years or the end of 2005 December 31, 2005). At
this time, the actual paid losses 410 that correspond to the
original projected paid losses 220 have occurred such that the
actual values 410 are shown in table 400. Therefore, the summation
of the actual paid losses for the 5 years may be performed as shown
in table 450 resulting in the updated forecast 460 value of
27,130,311. Thus, since the exemplary product has a time horizon of
five years, a Settlement Value of the index may be determined. The
Settlement Value is the index value at year 5 expressed as a ratio
to the base forecast, I(5), calculated in the same manner as
described above, i.e., I(5)=27,130,311/23,475,906=1.156.
[0052] Now that the exemplary five years have expired, an exemplary
commutation can be provided. It will be assumed that the conditions
of the reinsurance contract have been met, e.g., the ABC insurance
company reserves developed adversely from $500M to $700M, thus
meeting the condition of a mimimum $50M or 10% adverse development.
In addition, as calculated above, the index value at year 5, I(5),
exceeds the condition of being greater than an trigger point value
of 1.1. As should be clear, if either or both of these conditions
have not been satisfied, no commutation or payoff will be due ABC
insurance company. However, this example has been provided to show
how a commutation may be paid to ABC insurance company based on the
purchased systemic risk product. It will also be assumed that the
ABC insurance company has paid zero in the layer $200M excess of
$600M. Otherwise, the Commutation Amount would be reduced for any
loss recoveries that have already been made. The Commutation Amount
(CA) may then be calculated using the formula provided above as
follows:
CA=Min(Max(I(5)-1.1, 0), 0.1).times.$2B
where, in this example,
[0053] I(5)=1.156
[0054] Index Trigger=1.1
[0055] Max (1.156-1.1,0)=0.056
[0056] Min (0.056, 0.1)=0.056
[0057] Company Paid in Layer=0
[0058] CA=0.056.times.$2B=$112M
[0059] Therefore, in this exemplary embodiment, if ABC insurance
company had purchased the systemic risk product based on the index
as described above, and the losses developed in the exemplary
manner described above, ABC insurance company would be entitled to
a payoff of $112M after year 5.
[0060] As described above, the provided example is based on a
reinsurance product. A similar ILW product may also be provided and
calculated in the same manner described above for the reinsurance
product. The normal difference between the reinsurance product and
the ILW product is that the ILW product would typically not include
the attachment limit (e.g., $200/$600) or the condition of adverse
development on the purchaser of the cover and commutation amount
will be based on:
CA=Min(Max(I(5)-1.1, 0), 0.1).times.$2B
[0061] Those skilled in the art will understand that the
above-described exemplary embodiments may be implemented in any
suitable software or hardware configuration or combination thereof.
An exemplary hardware platform for implementing the exemplary
embodiments may include, for example, an Intel x86 based platform
with compatible operating system, a Mac platform and MAC OS, etc.
In a further example, the exemplary embodiments of the systems and
methods for comparing company losses to industry indices may be a
program containing lines of code stored on a non-transitory
computer readable storage medium that, when compiled, may be
executed on a processor.
[0062] FIG. 5 illustrates an exemplary method 500 for implementing
the exemplary systemic risk product. In step 510, an exemplary
industry index for a selected index year is calculated based on the
actual paid loss data from the Schedule P filings of the insurance
companies that are included in the industry index. However, it is
noted that the index is not limited to being calculated based on
the actual paid loss, but may also be calculated based on other
data reported in the Schedule P filings, e.g., case incurred loss,
etc. The calculations of the industry index for exemplary index
year 2000 were described above with reference to FIGS. 1 and 2. The
industry index is based on the actual paid values and the paid
estimates for the term of the systemic risk product. As described
above, the base factor 260 that corresponds to an index value
I(0)=1 is calculated.
[0063] In step 520, the index value at the latest reported year is
calculated. In the example above, FIG. 3 and the related
description describe calculating the index value I(1) for the
latest reported year using the actual paid values for the latest
reported year and the original projected values for the remainder
of the term.
[0064] In step 530, it is determined whether the latest reported
year was the term year. If the latest reported year was not the
term year, the method loops back to step 520 to calculate the index
value for the next reported year when that data becomes available.
If the latest reported year was the term year, for example, the
index value I(5) for a term of 5 years as calculated above with
reference to FIG. 4, the method continues on to step 540.
[0065] In step 540, the commutation amount (CA) is calculated using
the formula provided above. As described above, the values provided
in the formula are based on the industry index and some values are
based on values that are negotiated between the reinsurer and the
insurance company purchasing the systemic risk product. As also
described above, the commutation amount assumes that all other
terms of the systemic risk product have been met (e.g., the dual
triggers of the exemplary reinsurance product have been met).
[0066] An exemplary system may perform the steps of method 500. The
exemplary system may comprise a receiving arrangement having
hardware, software or a combination thereof that may, for example,
receive the data necessary for performing the calculations of steps
510-540. The same system may also comprise a calculating
arrangement having hardware, software or a combination thereof that
may, for example, perform the calculations described with reference
to steps 510-540. It is noted that the above-described arrangements
are only exemplary and that the various arrangements may have its
functionalities combined into a single component or distributed to
multiple components. For example, the receiving arrangement and
calculating arrangement may be implemented via the same computer
code being executed on the same processor.
[0067] Throughout this description, it has been described that
values from Schedule P for multiple insurance companies are used in
the various calculations. However, since the values that are used
in the calculations are spread out over multiple years of the
reports, there may be inconsistencies between various years. The
inconsistencies may be the result of, for example, mergers,
acquisitions, rehabilitation, liquidation, distortions due to
inter-company pooling or the insurance company's data clearly
appears to be seriously distorted for reasons that are not readily
apparent. Thus, the exemplary embodiments provide a series of rules
for adjusting the inconsistencies.
[0068] FIGS. 6-10 illustrate a first example of an inconsistency
correction. Initially, FIG. 6 shows a gross paid loss table 600
that has gross paid loss values from various annual reports. These
values are used to calculate an incremental paid loss table 610. To
provide a specific example, a gross loss value 602 (521) that is
from a first annual report is subtracted from a gross loss value
604 (3,435) that is from a different annual report to result in the
calculated incremental loss value 612 (2,914). Thus, for the
calculation to be meaningful, the values taken from various annual
statements should be consistent.
[0069] In one example, inconsistencies among annual statements may
be determined based on gross premiums. For example, FIG. 7
illustrates a table 700 showing gross premiums on December 31, 2004
that correspond to the same time periods as the gross loss values
in table 600. As shown by this table 700, there is a slight
inconsistency between 2003 and 2004 Annual Statements for accident
year 2002. Specifically, the value 705 is 7,140 while the value 710
is 6,962. A factor can be calculated by dividing the value 710 by
the value 705 resulting in (6,962/7,140=0.975). In this example, it
has been determined that premium factors that fall within a
tolerance level of 0.95 to 1.05 are considered minor
inconsistencies that can be mechanically adjusted as described
below. The range will be subject to negotiation.
[0070] An exemplary rule of applying a paid loss ratio development
value is applied if the premium change is within the tolerance
range (e.g., +/-5%). In this example, referring to table 600, the
calculated 2nd to 3rd factor for accident year 2002 gross paid loss
is the value 604 divided by the value 602 or 3,435/521=6.593.
However, based on the rule described above, the paid loss ratio
age-to-age factor is used as a proxy for the paid loss age-to-age
factor. In this example, this value is calculated as: (gross paid
loss value 604/premium value 710)/(gross paid loss value
602/premium value 705) or (3,435/6,962)/(521/7,140)=6.762.
Equivalently, the original development factor of 6.593 may be
adjusted by dividing it by the premium adjustment of 0.975
(6.593/.975=6.762), yielding an adjusted development factor of
6.762.
[0071] FIG. 8 shows a table 800 that includes the age-to-age
factors before adjustments, including the unadjusted age-to-age
factor 805 (6.593) as calculated above. FIG. 8 also shows a table
810 that includes the age-to-age factors after adjustments,
including the adjusted age-to-age factor 815 (6.762) as calculated
above.
[0072] FIG. 9 shows the adjusted gross paid loss table 900
including the adjusted gross loss value 910 (3,523). As can be seen
from the figures, the table 900 is identical to the table 600,
except for the adjusted gross loss value 910. This value 910 is
calculated by multiplying the previous year gross loss value 905 by
the adjusted age-to-age factor 815 calculated above or
521.times.6.762=3,523.
[0073] FIG. 10 shows an adjusted incremental paid loss table 1000
including an adjusted incremental paid loss value 1010 (3,002). As
can be seen from the figures, the table 1000 is identical to the
table 610, except for the adjusted incremental loss value 1010.
This value 1010 is calculated based on the adjusted gross loss
value 910 minus the gross loss value 905 or 3,523-521=3,002. Thus,
the above calculation shows one example of a rule for dealing with
inconsistencies in annual reports.
[0074] The above example provided a rule if the inconsistency was
within the tolerance range (e.g., +/-5%). The following example
provides a rule for correcting an inconsistency that is greater
than the tolerance range. Most of the companies or "combos" in the
index are actually groups of affiliated companies. For example,
combo 70 is the Travelers Group of Companies for which a
consolidated annual statement is filed. Whenever possible, we make
use of the consolidated group annual statements. In this example,
for simplicity of explanation, it is considered that the group of
companies filing a consolidated annual statement only consists of
two companies, Company A and Company B. Those of skill in the art
will understand that the principles of correcting for the
inconsistencies described below may be extended to groups that are
larger than two companies. In this example, the group accident year
2011 premium on annual statements 2011 is $500M and the group
accident year 2011 premium on annual statements 2012 is $530M.
Thus, this 6% discrepancy exceeds the example tolerance of +/-5%.
Since the premium consistency check for the consolidated (group)
annual statements fails, the same consistency check is applied to
each individual company in the group. A weight is assigned to each
company in the group based on the percentage of loss relative to
that of all companies in the group. This results in a rule that if
the combined weight of the matching companies in the group totals
less than 90% of the "sum of the pieces", the age-to-age factor is
flagged for later adjustment. An example of this process is
provided below.
[0075] Again, in this example, there are only two companies in the
group. Company A accident year 2011 premium on annual statement
2011 is $460M and accident year 2011 premium on annual statement
2012 is $450M. Company A passes the premium consistency check since
the discrepancy is less than the exemplary 5%. Company A is a
"matching" company. Company A accident year 2011 Paid Loss on
annual statement 2011 is $46M and accident year 2011 Paid Loss on
annual statement 2012 is $85.5M. Thus, the Company A development
factor is (85.5/450)/(46/460)-1.9000.
[0076] Company B accident year 2011 premium on annual statement
2011 is $50M and accident year 2011 premium on annual statement
2012 is $85M. Company B accident year 2011 Paid Loss on annual
statement 2011 is $5M and accident year 2011 Paid Loss on annual
statement 2012 is $17M. Note that Company B premium changes by 70%,
which exceeds the exemplary 5% tolerance. Since Company B fails the
premium consistency check, we do not need to calculate the
development factor. Company B is not a matching company.
[0077] The weight for Company A is determined based on dividing the
Company A 2011 Paid Loss on annual statement 2011 by the sum of
Company A and B 2011 Paid Loss on annual statement 2011 or
$46/($46+$5)=90.2%. Since the combined weight of the matching
companies in the group totals at least 90% (threshold subject to
negotiation) of the "sum of the pieces", the age-to-age factor is
not flagged for later adjustment. A default 1st-to-2nd factor for
this group is calculated to be 2.02495. The calculation of this
factor is explained in more detail below. The deemed 1st-to-2nd
factor is then calculated by multiplying the Company A weight by
the Company Development factor and then adding the product of
(1--the Company A weight) times the default 1st-to-2nd factor or
90.2%.times.1.900+(1-90.2%).times.2.02495=1.912.
[0078] Again in this example, suppose that 1.sup.st report paid
loss for the group as reported on the 2011 annual statement is $52
million. Applying the 1.912 factor derived above to $52 million
1.sup.st report loss yields $99.424 million--which we deem to be
the actual accident year 2011 paid loss at a 2.sup.nd report. This
figure may not equal the amount actually reported on the 2012
annual statement.
[0079] In another example, the observed consolidated factor fails
consistency check and the combined weight of the matching companies
in the group totals less than 90% of the "sum of the pieces" In
this case, the age-to-age factor cannot be calculated accurately
and the deemed development factor will be based on a default
factor. This example will be described with reference to FIGS. 11A
and 11B that show a table 1100 incorporating the described
calculations. For each accident year and age a weighted average
age-to-age factor is calculated across all companies in the basket
using only the un-flagged factors. A default age-to-age factor for
each company at each age is then calculated by applying the
negotiated adjustment factors (from a table) to the base weighted
average factor. The table lists report adjustment factors for the
companies in the index. Although the factors are subject to
negotiation, they are intended to capture idiosyncratic development
for each combo relative to industry development. Column (5) 1125
lists the negotiated adjustment factors for the entities (combos of
column (1) 1105).
[0080] For example, Combo 70 (as shown in row 1150) has a first
report Adjustment Factor of 0.81 (column (5) 1125). This means that
it is expected that the 1.sup.st-to-2.sup.nd development factor for
Combo 70 to be about 81% of the industry factor; that is,
historically, Combo 70's first report factor has been approximately
81% of the industry factor. Suppose the accident year 2011 weighted
average 1st-to-2nd factor turns out to be 2.5000. As described
above, only groups of companies that are not flagged for
inconsistencies are included in the average. As shown in this
example, a weighted average of the non-flagged development factors
in column (4) 1120 yields the average factor of 2.500 (value 1155);
that is, the average factor, 2.500, equals the sum of column (3)
1115 (value 1160--9,103,455) divided by the sum of column (2) 1110
(value 1165--3,641,378). Then the default 1st-to-2nd factor for
Combo 70, would be 0.81.times.2.5000=2.025 as shown in column (6)
1130. Thus, if the actual data needed to calculate a
1.sup.st-to-2.sup.nd factor for this Combo becomes unusable due to
a reporting inconsistency between the successive annual statements,
the default value of 2.025 may be used as a proxy for the unusable
factor.
[0081] For each entity in column (1) 1105, a default factor is
calculated as the product of the adjustment factor in column (5)
1125 and the average factor of 2.5 (value 1155). Each of the
default factors are listed in column (6) 1130.
[0082] Continuing with the example of Combo 70 started above, it
may be considered that the actual accident year 2011 1st-to-2nd
factor for Combo 70 turns out to be 2.00000, so that the percent
difference between actual and default is a deviation of
12.3%=(2.000000-2.025)/2.025. As described above, a default factor
is estimated for each of the companies that have not been flagged
and compared to the actual age-to-age factors. The two observations
with the largest deviations and the two with the lowest are
flagged. If an observation has been flagged, the age-to-age factor
is set to the company default factor for that age (e.g., 2.6523 for
Combo 914 in row 1170). The intent is to reduce the sensitivity of
the index to extreme data points. Otherwise, the age-to-age factor
is set to the observed factor (2.00 for Combo 70). Note that the
default factor is sensitive to systemic risk since it is based on
the average factor for a group of companies.
[0083] In another example, two companies may merge or one company
may acquire another company. If the companies being merged are both
in the reference portfolio, age-to-age factors can be calculated
based on the combined entity. This entails constructing an as-if
combined Schedule P Part I for the calendar year prior to the
merger. For example, Company A merges with Company B during 2010. A
combined Annual Statement in 2010 is filed. For accident year 2009
the first annual statement in 2009 shows a paid loss of $2M of
Company A and $3M for company B. For accident year 2009, the second
annual report in 2010 shows a paid loss of $6M for the combined
Company A+B. The 1st-to-2nd factor is thus $6M/5M=1.20. Thus, the
deemed incremental paid for accident year 2009--calendar year 2010
is calculated as cumulative deemed paid through 12/31/2009 times
(1.20-1) which is $400K for A; $600K for B.
[0084] If one of the companies being merged is not in the reference
portfolio but files annual statements, age-to-age factors can be
calculated based on the combined entity. This entails constructing
an as-if combined Schedule P Part I for the calendar year preceding
the merger. In some cases, companies may file both a post-merger
consolidated annual statement and individual company annual
statements, making it possible to calculate age-to-age factors for
the companies originally in the portfolio. The principle is to use
the figures that best match the original entity. If the company
being acquired is relatively small, the resulting distortion may be
within the negotiated (e.g. 5%) tolerance level, resulting in a
mechanical adjustment as described above.
[0085] If a company in the index stops reporting reliable annual
statements due to rehabilitation or liquidation, the calculation
agent will select a similar company or basket of companies of
comparable volume to serve as a proxy in the calculation of
age-to-age factors. Previously calculated age-to-age factors remain
unchanged.
[0086] If the calculation yields a negative incremental paid, the
age-to-age factor is flagged and deemed to be an error. The default
age-to-age factors for all company-age combinations are subject to
a minimum of unity.
[0087] It will be apparent to those skilled in the art that various
modifications may be made in the present invention, without
departing from the spirit or the scope of the invention. Thus, it
is intended that the present invention cover modifications and
variations of this invention provided they come within the scope of
the appended claims and their equivalents.
* * * * *