U.S. patent application number 14/109843 was filed with the patent office on 2014-04-17 for transformation weighted indexes offering concentrated multi-risk factor exposure.
This patent application is currently assigned to LUCAS MENDOZA INTELLECTUAL PROPERTY, INC.. The applicant listed for this patent is LUCAS MENDOZA INTELLECTUAL PROPERTY, INC.. Invention is credited to Ian LUCAS, Christopher MENDOZA.
Application Number | 20140108299 14/109843 |
Document ID | / |
Family ID | 50001788 |
Filed Date | 2014-04-17 |
United States Patent
Application |
20140108299 |
Kind Code |
A1 |
LUCAS; Ian ; et al. |
April 17, 2014 |
TRANSFORMATION WEIGHTED INDEXES OFFERING CONCENTRATED MULTI-RISK
FACTOR EXPOSURE
Abstract
Computer-based systems, software, and computer-implemented
methods for creating an index of securities based upon various data
transformations of risk factor metrics regarding entities or
securities associated with the entities and weighting each index
member in proportion to its combined transformed weighting
value.
Inventors: |
LUCAS; Ian; (La Jolla,
CA) ; MENDOZA; Christopher; (San Diego, CA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
LUCAS MENDOZA INTELLECTUAL PROPERTY, INC. |
La Jolla |
CA |
US |
|
|
Assignee: |
LUCAS MENDOZA INTELLECTUAL
PROPERTY, INC.
La Jolla
CA
|
Family ID: |
50001788 |
Appl. No.: |
14/109843 |
Filed: |
December 17, 2013 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13757197 |
Feb 1, 2013 |
8645256 |
|
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14109843 |
|
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61695919 |
Aug 31, 2012 |
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Current U.S.
Class: |
705/36R |
Current CPC
Class: |
G06Q 40/06 20130101 |
Class at
Publication: |
705/36.R |
International
Class: |
G06Q 40/06 20120101
G06Q040/06 |
Claims
1. Non-transitory computer-readable storage media encoded with a
computer program including instructions executable by a processor
to create an application comprising: a. a software module
configured to select a universe of securities or receive input
indicating a universe of securities; b. a software module
configured to select one or more security risk factor metrics or
receive input indicating one or more security risk factor metrics;
c. a software module configured to create an index, the index
comprising a plurality of member securities selected from the
universe of securities, each member security having a weight in the
index; provided that selection of member securities and the weight
in the index of each member security is determined by applying one
or more data transformations to the one or more security risk
factor metrics for each security in the universe of securities
according to the following formula: w.sub.i=[f(m).sub.1*f(n).sub.2
. . . f(m).sub.q].sub.i/.SIGMA.[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.n wherein i is a given security, wherein w is the
weight of a security in the index, wherein m is a security risk
factor metric, wherein n is the number of member securities in an
index, wherein f(m).sub.1 is a transformed weighting value of a
first security risk factor metric, wherein f(m).sub.2 is a
transformed weighting value of a second security risk factor
metric, wherein f(m).sub.q is a transformed weighting value of an
ultimate security risk factor metric, and wherein * is a
mathematical operation to be performed on transformed security risk
factor metrics.
2. The storage media of claim 1, wherein the one or more security
risk factor metrics include a non-numeric datum for which a value
or score has been substituted.
3. The storage media of claim 1, wherein the one or more data
transformations are selected from: a binary transformation, inverse
transformation, linear transformation, log transformation,
percentile transformation, power transformation, rank
transformation, root transformation, or variance-stabilization
transformation.
4. The storage media of claim 1, wherein the weight of a security
in the index is determined by applying one or more subsequent data
transformations to one or more of the transformed weighting
values.
5. The storage media of claim 1, wherein the mathematical operation
to be performed on transformed security risk factor metrics is
selected from: multiplication, division, addition, subtraction, an
average, weighted average, or a median.
6. The storage media of claim 1, wherein the application further
comprises a software module configured to update the values of the
one or more security risk factor metrics for each security in the
universe of securities.
7. The storage media of claim 6, wherein the application further
comprises a software module configured to add or remove securities
from the index by re-applying the one or more data transformations
to the updated one or more security risk factor metrics for each
security in the universe of securities.
8. The storage media of claim 6, wherein the application further
comprises a software module configured to update the weight of
securities in the index by re-applying the one or more data
transformations to the updated one or more security risk factor
metrics for each security in the universe of securities.
9. A computer-implemented method comprising the steps of: a.
creating an index of securities, by a processor, by selecting
securities from a universe of securities to be index members based
upon one or more data transformations of one or more security risk
factor metrics regarding entities or securities associated with the
entities; and b. weighting each index member, by a processor, based
upon dividing said one or more data transformations by the sum of
said one or more data transformation for all said index
members.
10. The method of claim 9, wherein the one or more security risk
factor metrics are for the most recent period, an average over any
time period, a change over any time period, or the variance over
any time period.
11. The method of claim 9, wherein the one or more data
transformations comprise: conversion of a set of numerical or
non-numerical data into a transformed data set by the application
of a binary transformation, inverse transformation, a linear
transformation, a log transformation, a percentile transformation,
a power transformation, a rank transformation, a root
transformation, or a variance-stabilization transformation.
12. The method of claim 9, wherein selecting securities as index
members comprises: a. calculating, by a processor, for each entity
associated with a security in the universe of securities, a first
transformed weighting value based upon a security risk factor
metric; b. calculating, by a processor, one or more additional
transformed weighting values based upon one or more security risk
factor metrics; c. calculating, by a processor, a combined
transformed weighting value specific to each entity associated with
a security by applying a mathematical relationship to all said one
or more transformed weighting values; and d. selecting, by a
processor, a subset of securities from the universe of securities
to be index members based upon said combined transformed weighting
value.
13. The method of claim 9, wherein weighting each index member
comprises: a. calculating, by a processor, a first transformed
weighting value based upon a security risk factor metric for each
index member; b. calculating, by a processor, one or more
additional transformed weighting values based upon one or more
security risk factor metrics for each index member; c. calculating,
by a processor, a combined transformed weighting value specific to
each entity associated with a security by applying a mathematical
relationship to all said one or more transformed weighting values;
d. calculating, by a processor, a weighting percentage by dividing
said combined transformed weighting value by the sum of said
combined transformed weighting values of all index members; and e.
weighting, by a processor, each index member in proportion to said
weighting percentage.
14. The method of claim 9, further comprising the step of
maintaining the index at periodic time intervals, by a processor,
wherein maintaining comprises: adding and removing securities index
members based upon one or more data transformations of one or more
security risk factor metrics regarding entities or securities
associated with the entities.
15. The method of claim 9, further comprising the step of
maintaining the index at periodic time intervals, by a processor,
wherein maintaining comprises: adjusting weightings of index
members based upon dividing said one or more data transformations
by the sum of said one or more data transformation for all said
index members.
16. A computer-implemented system comprising: a. a digital
processing device comprising an operating system configured to
perform executable instructions and a memory device; b. a computer
program including instructions executable by the digital processing
device to create an application comprising: i. a software module
configured to create an index of securities by selecting securities
from a universe of securities to be index members based upon one or
more data transformations of one or more security risk factor
metrics regarding entities or securities associated with the
entities; and ii. a software module configured to weight each index
member based upon dividing said one or more data transformations by
the sum of said one or more data transformations for all said index
members.
17. The system of claim 16, wherein the one or more data
transformations comprise: conversion of a set of numerical or
non-numerical data into a transformed data set by the application
of a binary transformation, inverse transformation, a linear
transformation, a log transformation, a percentile transformation,
a power transformation, a rank transformation, a root
transformation, or a variance-stabilization transformation.
18. The system of claim 16, wherein selecting securities as index
members comprises: a. calculating for each entity associated with a
security in the universe of securities, a first transformed
weighting value based upon a security risk factor metric; b.
calculating one or more additional transformed weighting values
based upon one or more security risk factor metrics; c. calculating
a combined transformed weighting value specific to each entity
associated with a security by applying a mathematical relationship
to all said one or more transformed weighting values; and d.
selecting a subset of securities from the universe of securities to
be index members based upon said combined transformed weighting
value.
19. The system of claim 16, wherein weighting the index members
comprises: a. calculating a first transformed weighting value based
upon a security risk factor metric for each index member; b.
calculating one or more additional transformed weighting values
based upon one or more security risk factor metrics for each index
member; c. calculating a combined transformed weighting value
specific to each entity associated with a security by applying a
mathematical relationship to all said one or more transformed
weighting values; d. calculating a weighting percentage by said
combined transformed weighting value by the sum of said combined
transformed weighting values of all index members; and e. weighting
each index member in proportion to said weighting percentage.
20. The system of claim 16, wherein the application further
comprises a software module configured to maintain the index at
periodic time intervals, wherein maintaining comprises: adding and
removing securities index members based upon one or more data
transformations of one or more security risk factor metrics
regarding entities or securities associated with the entities.
21. The system of claim 16, wherein the application further
comprises a software module configured to maintain the index at
periodic time intervals, wherein maintaining comprises: adjusting
weightings of index members based upon dividing said one or more
data transformations by the sum of said one or more data
transformations for all said index members.
22. Non-transitory computer-readable storage media encoded with an
index, the index comprising a plurality of member securities
selected from a universe of securities, each member security having
a weight in the index; provided that selection of the member
securities and the weight in the index of each member security is
determined by applying one or more data transformations to the one
or more security risk factor metrics for each security in the
universe of securities according to the following formula:
w.sub.i=[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.i/.SIGMA.[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.n wherein i is a given security, wherein w is the
weight of a security in the index, wherein m is a security risk
factor metric, wherein n is the number of member securities in an
index, wherein f(m).sub.1 is a transformed weighting value of a
first security risk factor metric, wherein f(m).sub.2 is a
transformed weighting value of a second security risk factor
metric, wherein f(m).sub.q is a transformed weighting value of an
ultimate security risk factor metric, and wherein * is a
mathematical operation to be performed on transformed security risk
factor metrics.
23. The storage media of claim 22, wherein the one or more security
risk factor metrics include a non-numeric datum for which a value
or score has been substituted.
24. The storage media of claim 22, wherein the one or more data
transformations are selected from: a binary transformation, inverse
transformation, linear transformation, log transformation,
percentile transformation, power transformation, rank
transformation, root transformation, or variance-stabilization
transformation.
25. The storage media of claim 22, wherein the weight of a security
in the index is determined by applying one or more subsequent data
transformations to one or more of the transformed weighting
values.
26. The storage media of claim 22, wherein the mathematical
operation to be performed on transformed security risk factor
metrics is selected from: multiplication, division, addition,
subtraction, an average, weighted average, or a median.
Description
CROSS-REFERENCE TO RELATED APPLICATIONS
[0001] This application claims the benefit of U.S. Application Ser.
No. 61/695,919, filed Aug. 31, 2012, and is a continuation of U.S.
application Ser. No. 13/757,197, filed Feb. 1, 2013, each of which
is hereby incorporated by reference in its entirety.
BACKGROUND OF THE INVENTION
[0002] In finance, an index is a statistical aggregate that usually
refers to a measure of economic performance or market performance.
For example, a stock market index is a method of measuring the
value of a section of the stock market. Investors sometimes use
stock indexes to describe market conditions, to benchmark
investment results, or to construct portfolios. Index construction
methodologies generally determine the relative contribution of each
member to the overall index using equal weighting or some measure
of market or fundamental data. Portfolios based on such indexes
suffer from numerous disadvantages. For instance, in indexes
weighted by market capitalization or a measure of fundamental size,
a small number of constituents tend to have disproportionately
large weight, thus introducing a degree of idiosyncratic risk. On
the other extreme, equal weight indexes have horizontal weighting
curves and give no extra weight to securities that may possess
desirable characteristics as determined through various techniques
of security analysis. Further, in market or fundamentals-based
indexes, the difference in weights between constituents is uneven,
leading to a lack of standardization between indexes or even in the
same index over time. These conventional indexes are rigid, lacking
any mechanism to alter their weighting percentage curves to resolve
these structural limitations. Moreover, modern finance recognizes
various risk factors, sometimes referred to as anomalies, which
account for investment performance, such as the size, value,
momentum, and low volatility effects. Existing indexes offer only
incidental, narrow, and/or exclusionary access to these risk
factors. Therefore, a distinct disadvantage is that these indexes
fail to take advantage of a synergistic effect of holdings that are
rich in multiple risk factors. Finally, portfolios based on these
indexes require many separate funds to gain broad risk factor
exposure, increasing complexity and costs associated with portfolio
management. Existing methods cannot provide consistent,
customizable, direct, and diversified exposure to the many
investment risk factors in a single index.
SUMMARY OF THE INVENTION
[0003] Various embodiments disclose systems, computer programs, and
methods for securities index construction. While prior indexing
methodologies utilize raw data values, the systems, software, and
methods described herein transform the variables into new,
standardized, and versatile forms that produce remarkably different
indexes and are optionally further combined to yield entirely novel
composite indexes. The systems, software, and methods described
herein provide a number of advantages. First is the ability to use
both fundamental and market data, simultaneously, to produce a
weighting. Second, the ability to incorporate both numeric and
non-numeric data into constituent weightings. Third, the employment
of novel data transformations such as binary, inverse, linear, log,
percentile, power, rank, root, and variance-stabilization
transformations. Fourth, various transformation applications
provide the ability to shape weighting percentage curves. Fifth,
mitigation of overexposure to poor securities and underexposure to
excellent securities, as compared with conventional indexes. Sixth,
direct access all known investment risk factors for entities or
securities associated with entities. Seventh, any degree of
emphasis or de-emphasis on concentrations of a given risk factor in
a single index. Eighth, simplification of portfolio management
because a single index will be able to provide comprehensive,
diversified risk factor exposure, thereby negating the need to
purchase and rebalance multiple index funds from various
distributors.
[0004] In some embodiments, advantages of the systems, software,
and methods described herein include utilization of percentile
transformations, which offer many beneficial features. Percentiles
are indifferent toward negative data or unit type, they mitigate
outliers, and separate densely clustered raw data values. Relative
to equal weighting, indexes weighted by percentiles enable a
steeper weighting percentage curve without excessive exposure to
the most prominent members. In other words, the weighting
percentage curve is gradually and consistently sloped rather than
horizontal, which current methods are unable to replicate. Thus, a
percentile transformation of a single risk factor metric works to
reduce overexposure to the most prominent index members while
permitting substantial differentials in weighting concentrations on
extreme ends of the index. Moreover, one may combine percentiles
for two or more metrics to produce uniquely tilted curves. For
example, an average of multiple percentiles will result in a
weighting percentage curve that is convex and concave at different
points. Alternatively, if one instead multiplies those same
percentiles, a convex curve that produces higher factor
concentration results. Optionally, one can perform a subsequent
percentile transformation of the percentile average or product in
preparation for additional transformations.
[0005] In some embodiments, advantages of the systems, software,
and methods described herein include utilization of power
transformations. Powers provide the ability to bend the weighting
percentage curve to produce a larger or smaller differential in the
highest/lowest-weighted members. Power transformations are suitable
to create "large cap" and "small cap" indexes (or "large company"
or "small company" or any other orientation, depending on the
nature of the index) without the need to exclude hundreds or
thousands of securities, by bending the weighting percentage curve
more or less steeply.
[0006] In some embodiments, the systems, methods, and computer
programs disclosed herein use risk factor metrics (i.e.,
entity-specific indicators of investment merit) to create indexes
of securities. In some embodiments, a Transformation Weighted Index
(TWI) is suitable to serve as a model for an investment portfolio
that reduces concentrations in securities with undesirable
characteristics while offering advantageous features such as broad
diversification and practical implementation.
[0007] Disclosed herein, in various embodiments, are
computer-implemented methods for design and maintenance of a first
TWI, wherein members may be weighted based on one or more data
transformations of one or more risk factor metrics regarding
entities associated with securities and/or securities associated
with the entities.
[0008] In other embodiments are computer-implemented methods for
design and maintenance of a second TWI, wherein member weights may
be computed by one or more data transformations of one or more
fundamental size metrics regarding entities associated with
securities.
[0009] In further embodiments, two TWIs combine to form a composite
TWI. Optionally, in such embodiments, a composite TWI may satisfy
additional investment objectives. By way of non-limiting example,
in a composite TWI, member weightings may combine high investment
capacity with high multi-risk factor exposure.
[0010] In some embodiments, the systems, methods, and computer
programs disclosed herein further include: maintaining a TWI by
reestablishing member weightings based upon changes in securities
that are members of said TWI or after new data for an entity or its
associated security is available.
[0011] In another aspect, disclosed herein are computer-implemented
methods comprising the steps of: creating an index of securities,
by a processor, by selecting securities from a universe of
securities to be index members based upon security type or
investment capacity, the investment capacity comprising: thresholds
of liquidity or market capitalization; and performing, by a
processor, one or more data transformations of one or more risk
factor metrics regarding index members; and weighting the index
members, by a processor, based upon dividing said one or more data
transformations by the sum of said data transformations of all
index members.
[0012] In one aspect, disclosed herein are computer-readable
storage media encoded with a computer program including
instructions executable by a processor to create an application
comprising: a software module configured to select a universe of
securities or receive input indicating a universe of securities; a
software module configured to select one or more risk factor
metrics or receive input indicating one or more risk factor
metrics; a software module configured to create an index, the index
comprising a plurality of member securities selected from the
universe of securities, each member security having a weight in the
index; provided that selection of member securities and the weight
in the index of each member security is determined by applying one
or more transformations to the one or more risk factor metrics for
each security in the universe of securities according to the
following formula:
w.sub.i=[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.i/.SIGMA.[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.n
wherein i is a given security, wherein w is the weight of a
security in the index, wherein m is a risk factor metric, wherein n
is the number of member securities in an index, wherein f(m).sub.1
is a data transformation weighting value of a first risk factor
metric, wherein f(m).sub.2 is a data transformation weighting value
of a second risk factor metric, wherein f(m).sub.q is a data
transformation weighting value of an ultimate risk factor metric,
and wherein * is a mathematical operation to be performed on
transformed risk factor metrics.
[0013] In some embodiments, the one or more risk factor metrics
include a non-numeric datum for which a value or score has been
substituted. In some embodiments, the one or more data
transformations are selected from: a binary transformation, inverse
transformation, linear transformation, log transformation,
percentile transformation, power transformation, rank
transformation, root transformation, or variance-stabilization
transformation. In some embodiments, the weight of a security in
the index is determined by applying one or more subsequent data
transformations to one or more of the previously calculated data
transformation weighting values. In some embodiments, the
mathematical operation to be performed on transformed risk factor
metrics is selected from: multiplication, division, addition,
subtraction, an average, weighted average, or a median. In some
embodiments, the first, second, and subsequent risk factor metrics
are the same metric. In other embodiments, the first, second, and
subsequent risk factor metrics are different metrics. In some
embodiments, the application further comprises a software module
configured to update the values of the one or more risk factor
metrics for each security in the universe of securities. In further
embodiments, the application further comprises a software module
configured to add or remove securities from the index by
re-applying the one or more data transformations to the updated one
or more risk factor metrics for each security in the universe of
securities. In further embodiments, the application further
comprises a software module configured to update the weight of
securities in the index by re-applying the one or more data
transformations to the updated one or more risk factor metrics for
each security in the universe of securities.
[0014] In another aspect, disclosed herein are computer-implemented
methods comprising the steps of: creating an index of securities,
by a processor, by selecting securities from a universe of
securities to be index members based upon one or more data
transformations of one or more risk factor metrics regarding
entities or securities associated with the entities; and weighting
each index member, by a processor, based upon dividing said one or
more data transformations by the sum of said one or more data
transformations for all said index members. In some embodiments,
the securities comprise a whole or fractional unit of interest in
one or more of a: note; stock; treasury stock; bond; debenture;
certificate of interest or participation in a profit-sharing
agreement or in an oil, gas, or mineral royalty or lease;
collateral trust certificate; pre-organization certificate or
subscription; transferable share; investment contract; voting-trust
certificate; certificate of deposit, for a security, put, call,
straddle, option, or privilege on a security, certificate of
deposit, or group or index of securities; put, call, straddle,
option, or privilege entered into on a national securities exchange
relating to foreign currency; certificate of interest or
participation in, temporary or interim certificate for, receipt
for, or warrant or right to subscribe to or purchase, any of the
foregoing; currency or any note, draft, bill of exchange, or
banker's acceptance which has a maturity at the time of issuance of
not exceeding nine months, exclusive of days of grace, or any
renewal thereof the maturity of which is likewise limited; a
physical resource; inventory; finished good; and intellectual
property. In some embodiments, the one or more risk factor metrics
are for the most recent period, an average over any time period, a
change over any time period, or the variance over any time period.
In some embodiments, the one or more data transformations comprise:
conversion of a set of numerical or non-numerical data into a
transformed data set by the application of a deterministic
mathematical function. In further embodiments, the deterministic
mathematical function is selected from: a binary transformation, an
inverse transformation, a linear transformation, a log
transformation, a percentile transformation, a power
transformation, a rank transformation, a root transformation, and a
variance-stabilization transformation. In some embodiments,
selecting securities as index members comprises: calculating, by a
processor, for each entity associated with a security in the
universe of securities, a first data transformation weighting value
based upon a risk factor metric; calculating, by a processor, one
or more additional data transformation weighting values based upon
one or more risk factor metrics; calculating, by a processor, a
combined data transformation weighting value specific to each
entity associated with a security by applying a mathematical
relationship for each data transformation weighting value; and
selecting, by a processor, a subset of securities from the universe
of securities to be index members based upon said combined data
transformation weighting values. In some embodiments, weighting
each index member comprises: calculating, by a processor, a first
data transformation weighting value based upon a risk factor metric
for each index member; calculating, by a processor, one or more
additional data transformation weighting values based upon one or
more risk factor metrics for each index member; calculating, by a
processor, a combined data transformation weighting value specific
to each entity associated with a security by applying a
mathematical relationship for each data transformation weighting
value; calculating, by a processor, a weighting percentage by
dividing said combined data transformation weighting value by the
sum of said combined data transformation weighting values of all
index members; and weighting, by a processor, each index member in
proportion to said weighting percentage. In some embodiments, the
method further comprises the step of maintaining the index at
periodic time intervals, by a processor, wherein maintaining
comprises: adding and removing index members based upon one or more
data transformations of one or more risk factor metrics regarding
entities or securities associated with the entities as said one or
more risk factor metrics change over time. In some embodiments, the
method further comprises the step of maintaining the index at
periodic time intervals, by a processor, wherein maintaining
comprises: adjusting weightings of index members based upon
dividing said combined data transformation weighting value by the
sum of said combined data transformation weighting values of all
index members.
[0015] In another aspect, disclosed herein are computer-implemented
systems comprising: a digital processing device comprising an
operating system configured to perform executable instructions and
a memory device; a computer program including instructions
executable by the digital processing device to create an
application comprising: a software module configured to create an
index of securities by selecting securities from a universe of
securities to be index members based upon one or more data
transformations of one or more risk factor metrics regarding
entities or securities associated with the entities; and a software
module configured to weight each index member based upon dividing
said one or more data transformations by the sum of said data
transformations of all index members. In some embodiments, the
securities comprise a whole or fractional unit of interest in one
or more of a: note; stock; treasury stock; bond; debenture;
certificate of interest or participation in a profit-sharing
agreement or in an oil, gas, or mineral royalty or lease;
collateral trust certificate; pre-organization certificate or
subscription; transferable share; investment contract; voting-trust
certificate; certificate of deposit, for a security, put, call,
straddle, option, or privilege on a security, certificate of
deposit, or group or index of securities; put, call, straddle,
option, or privilege entered into on a national securities exchange
relating to foreign currency; certificate of interest or
participation in, temporary or interim certificate for, receipt
for, or warrant or right to subscribe to or purchase, any of the
foregoing; currency or any note, draft, bill of exchange, or
banker's acceptance which has a maturity at the time of issuance of
not exceeding nine months, exclusive of days of grace, or any
renewal thereof the maturity of which is likewise limited; a
physical resource; inventory; finished good; and intellectual
property. In some embodiments, the one or more data transformations
comprise: conversion of a set of numerical or non-numerical data
into a transformed data set by the application of a deterministic
mathematical function. In further embodiments, the deterministic
mathematical function is selected from: a binary transformation, an
inverse transformation, a linear transformation, a log
transformation, a percentile transformation, a power
transformation, a rank transformation, a root transformation, and a
variance-stabilization transformation. In some embodiments,
selecting securities as index members comprises: calculating for
each entity associated with a security in the universe of
securities, a first data transformation weighting value based upon
a risk factor metric; calculating one or more additional data
transformation weighting values based upon one or more risk factor
metrics; calculating a combined data transformation weighting value
specific to each entity associated with a security by applying a
mathematical relationship for each data transformation weighting
value; and selecting a subset of securities from the universe of
securities to be index members based upon said combined data
transformation weighting values. In some embodiments, weighting the
index members comprises: calculating a first data transformation
weighting value based upon a risk factor metric for each index
member; calculating one or more additional data transformation
weighting values based upon one or more risk factor metrics for
each index member; calculating a combined data transformation
weighting value specific to each entity associated with a security
by applying a mathematical relationship to each data transformation
weighting value; calculating a weighting percentage by dividing
said combined data transformation weighting value by the sum of
said combined data transformation weighting values of all index
members; and weighting each index member in proportion to said
weighting percentage. In some embodiments, the application further
comprises a software module configured to maintain the index at
periodic time intervals, wherein maintaining comprises: adding and
removing index members based upon one or more data transformations
of one or more risk factor metrics regarding entities or securities
associated with the entities as said one or more risk factor
metrics change over time. In some embodiments, the application
further comprises a software module configured to maintain the
index at periodic time intervals, wherein maintaining comprises:
adjusting weightings of index members based upon dividing said
combined data transformation weighting value by the sum of said
combined data transformation weighting values of all index
members.
[0016] In another aspect, disclosed herein are computer-readable
storage media encoded with an index, the index comprising a
plurality of member securities selected from a universe of
securities, each member security having a weight in the index;
provided that selection of the member securities and the weight in
the index of each member security is determined by applying one or
more data transformations to the one or more risk factor metrics
for each security in the universe of securities according to the
following formula:
w.sub.i=[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.i/.SIGMA.[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.n
wherein i is a given security, wherein w is the weight of a
security in the index, wherein m is a risk factor metric, wherein n
is the number of member securities in an index, wherein f(m).sub.1
is a data transformation weighting value of a first risk factor
metric, wherein f(m).sub.2 is a data transformation weighting value
of a second risk factor metric, wherein f(m).sub.q is a data
transformation weighting value of an ultimate risk factor metric,
and wherein * is a mathematical operation to be performed on
transformed risk factor metrics.
[0017] Unless otherwise defined, all technical terms used herein
have the same meaning as commonly understood by one of ordinary
skill in the art to which this invention belongs. As used in this
specification and the appended claims, the singular forms "a,"
"an," and "the" include plural references unless the context
clearly dictates otherwise. Any reference to "or" herein is
intended to encompass "and/or" unless otherwise stated.
BRIEF DESCRIPTION OF THE DRAWINGS
[0018] FIG. 1 shows a non-limiting, exemplary flowchart of a method
for selecting a security for inclusion in a Transformation Weighted
Index (TWI).
[0019] FIG. 2 shows a non-limiting, exemplary block diagram of
three TWIs.
[0020] FIG. 3 shows non-limiting, exemplary weighting percentage
curves of the percentile and equal weighted indexes of Example
1.
[0021] FIG. 4 shows non-limiting, exemplary weighting percentage
curves from power transforming percentiles as discussed in Example
1.
[0022] FIG. 5 shows non-limiting, exemplary weighting percentage
curves from various methods of combining percentiles of multiple
risk factor metrics as discussed in Example 1.
[0023] FIG. 6 shows non-limiting, exemplary comparison of the
weighting percentage curves of TW-1 and an equal weight index as
discussed in Example 2.
[0024] FIG. 7 shows non-limiting, exemplary comparison of the
weighting percentage curves of TW-2, a fundamentally weighted
index, and a capitalization weighted index as discussed in Example
2.
[0025] FIG. 8 shows non-limiting, exemplary comparison of
constituent-by-constituent weight differentials for TW-2 and a
non-transformed fundamentally weighted index as discussed in
Example 2.
[0026] FIG. 9 shows non-limiting, exemplary comparison of the
weighting percentage curves of TW-1, TW-2, and TW-3 as discussed in
Example 2.
DETAILED DESCRIPTION OF THE INVENTION
[0027] Conventional index weighting methodologies fail to provide
comprehensive, concentrated exposure to desirable investment risk
factors in a single index. In these indexes, risk factor exposure
tends to be either incidental or, if targeted explicitly, very
narrow and exclusionary. All such indexes fail to capture the
synergistic benefit from concentrating weights on those securities
that exhibit multiple risk factors simultaneously, as indicated by
various metrics used to assess the presence of a risk factor.
Further, investors who seek risk factor exposure must purchase
multiple index-based products to achieve complete exposure, which
can add needless cost and complexity. Accordingly, described
herein, in certain embodiments, are computer-readable storage media
encoded with a computer program including instructions executable
by a processor to create an application comprising: a software
module configured to select a universe of securities or receive
input indicating a universe of securities; a software module
configured to select a risk factor metric or receive input
indicating a risk factor metric; a software module configured to
create an index, the index comprising a plurality of member
securities selected from the universe of securities, each member
security having a weight in the index; provided that selection of
member securities and the weight in the index of each member
security is determined by applying a data transformation to the
risk factor metric for each security in the universe of securities
according to the following formula:
w.sub.i=[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.i/.SIGMA.[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.n
wherein i is a given security, wherein w is the weight of a
security in the index, wherein m is a risk factor metric, wherein n
is the number of member securities in an index, wherein f(m).sub.1
is a data transformation weighting value of a first risk factor
metric, wherein f(m).sub.2 is a data transformation weighting value
of a second risk factor metric, wherein f(m).sub.q is a data
transformation weighting value of an ultimate risk factor metric,
and wherein * is a mathematical operation to be performed on
transformed risk factor metrics.
[0028] Also described herein, in certain embodiments, are
computer-implemented methods comprising the steps of: creating an
index of securities, by a processor, by selecting securities from a
universe of securities to be index members based upon one or more
data transformations of one or more risk factor metrics regarding
entities or securities associated with the entities; and weighting
each index member, by a processor, based upon dividing said one or
more data transformation weighting value by the sum of said data
transformation weighting values of all index members said one or
more data transformations.
[0029] Also described herein, in certain embodiments, are
computer-implemented methods comprising the steps of: creating an
index of securities, by a processor, by selecting securities from a
universe of securities to be index members based upon security-type
or investment capacity, the investment capacity comprising:
thresholds of liquidity or market capitalization; and performing,
by a processor, one or more data transformations of one or more
risk factor metrics regarding index members; and weighting the
index members, by a processor, based upon dividing said one or more
data transformation weighting value by the sum of said data
transformation weighting values of all index members said one or
more data transformations.
[0030] Also described herein, in certain embodiments, are
computer-implemented systems comprising: a digital processing
device comprising an operating system configured to perform
executable instructions and a memory device; a computer program
including instructions executable by the digital processing device
to create an application comprising: a software module configured
to create an index of securities by selecting securities from a
universe of securities to be index members based upon one or more
data transformations of one or more risk factor metrics regarding
entities or securities associated with the entities; and a software
module configured to weight each index member based upon dividing
said one or more data transformation weighting value by the sum of
said data transformation weighting values of all index members said
one or more data transformations.
[0031] Also described herein, in certain embodiments, are
computer-readable storage media encoded with an index, the index
comprising a plurality of member securities selected from a
universe of securities, each member security having a weight in the
index; provided that selection of the member securities and the
weight in the index of each member security is determined by
applying one or more data transformations to the one or more risk
factor metrics for each security in the universe of securities
according to the following formula:
w.sub.i=[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.i/.SIGMA.[f(m).sub.1*f(m).sub.2 . . .
f(m).sub.q].sub.n
wherein i is a given security, wherein w is the weight of a
security in the index, wherein m is a risk factor metric, wherein n
is the number of member securities in an index, wherein f(m).sub.1
is a data transformation weighting value of a first risk factor
metric, wherein f(m).sub.2 is a data transformation weighting value
of a second risk factor metric, wherein f(m).sub.q is a data
transformation weighting value of an ultimate risk factor metric,
and wherein * is a mathematical operation to be performed on
transformed risk factor metrics.
Transformation Weighted Indexes
[0032] Generally, an embodiment of the present invention takes the
form of a Transformation Weighted Index (TWI) comprising at least
two securities. In further embodiments, the securities are weighted
by data transformations of risk factor metrics regarding entities
and/or securities associated with the entities.
[0033] In some embodiments, "securities" generally refers to any
whole or fractional unit of interest in any investable asset.
[0034] In some embodiments, "weighting percentage" generally refers
to the determination of the degree to which a security will be
represented in an index based on the relative presence of a given
factor relating to the security or the entity affiliated with the
security. For example, in a capitalization-weighted index of
equities, each included equity affects the index in proportion to
the number of shares of the equity outstanding multiplied by the
equity's price.
[0035] In some embodiments, a "data transformation" generally
refers to conversion of a set of numerical or non-numerical data
into a transformed data set by the application of a deterministic
mathematical function. In further embodiments, each data point m is
replaced with the transformed value y.sub.i=f(m), where f is a
function. In various embodiments, data transformations include, but
are not limited to, inverse transformations, linear
transformations, log transformations, percentile transformations,
power transformations, rank transformations, binary digit
assignments, root transformations, or variance-stabilization
transformations. In some embodiments, data transformations are
specific to the field of statistics and are wholly distinct from
the concept of data manipulation (in other words the two concepts
do not have overlapping definitions and are not synonymous). In
cases where data are non-numerical, such as when an entity uses
First In First Out (FIFO) or Last In First Out (LIFO) accounting, a
number will be assigned to each datum, and this number may be
further transformed.
[0036] In some embodiments, "weighting values" generally refers to
output values of data transformations. In various embodiments,
exemplary weighting values include, but are not limited to,
percentile and power transformations of revenue, share price
momentum, share price volatility, and so forth.
[0037] In some embodiments, a "risk factor metric" generally refers
to an entity-specific measure (or signal or indicator) of
investment merit, as would concern a financial economist tasked
with allocating capital across security markets under conditions of
uncertainty. In a particular non-limiting embodiment, risk factors
include market capitalization, valuation, price momentum, and price
volatility. Risk factor metrics used to signal these risk factors
include conventional as-reported and manipulated data such as Total
Revenue, 4-quarter Price Change, and 5-quarter Price Standard
Deviation, respectively.
[0038] In some embodiments, "accounting or non-accounting data"
generally refers to information that relates to an entity or an
entity's associated securities. In further embodiments, such
information is contained in said entity's financial statements or
in other reports or data feeds produced by or about an entity or an
entity's securities.
[0039] In some embodiments, "as-reported" generally refers to an
original datum that has not been manipulated whereas "manipulated"
generally refers to an original datum that has been combined with
or related to one or more other data values (which may include the
same datum from other periods). In further embodiments, both
as-reported and manipulated data may be transformed by a function
into a new value for the purposes of determining weighting within a
TWI. Non-limiting examples of as-reported data include Operating
Revenue, Total Assets, Net Income, Operating Cash Flow, and Share
Price for a given period or point in time. Non-limiting examples of
manipulated data include Asset Turnover (which may be defined as
Revenue divided by Assets), Accruals (which may be defined as Net
Income subtracted from Operating Cash Flow) or Price Volatility
(which may be measured by standard deviation of a share price) for
a given period.
[0040] In some embodiments, "security" or "securities" comprise any
of a whole or fractional unit of interest in one or more of a:
note; stock; treasury stock; bond; debenture; certificate of
interest or participation in a profit-sharing agreement or in an
oil, gas, or mineral royalty or lease; collateral trust
certificate; pre-organization certificate or subscription;
transferable share; investment contract; voting-trust certificate;
certificate of deposit, for a security, put, call, straddle,
option, or privilege on a security, certificate of deposit, or
group or index of securities; put, call, straddle, option, or
privilege entered into on a national securities exchange relating
to foreign currency; certificate of interest or participation in,
temporary or interim certificate for, receipt for, or warrant or
right to subscribe to or purchase, any of the foregoing; currency
or any note, draft, bill of exchange, or banker's acceptance which
has a maturity at the time of issuance of not exceeding nine
months, exclusive of days of grace, or any renewal thereof the
maturity of which is likewise limited; a physical resource;
inventory; finished good; and intellectual property.
[0041] In various embodiments, suitable risk factor metrics
include, by way of non-limiting examples, as-reported and
manipulated accounting or non-accounting data regarding entities
and/or securities associated with the entities. In further
embodiments, the as-reported and manipulated accounting or
non-accounting data include, by way of non-limiting examples, all
variations of Accounts Payable, Accounts Receivable, Accrued
Expenses, Accrued Interest, Accrued Interest Payables, Accrued
Investment Income, Accrued Liabilities, Accrued Taxes, Accumulated
Depreciation & Depletion, Additional Paid In Capital, Allowance
for Loans and Lease Losses, Bankers Acceptance Outstanding,
Building & Improvements, Capital Lease Obligations, Cash and
Due from Banks, Cash and Equivalents, Claims and Claim Expense,
Common Par, Common Stock Equity, Construction in Progress, Cost in
Excess, Cumulative Translation Adjustment, Current Deferred Income
Taxes, Deferred Acquisition Cost, Deferred Income Taxes, Deferred
Revenues, Due from Customers Acceptance, Federal Funds
Purchased/Securities Sold, Federal Funds Sold/Securities Purchased,
Finished Goods, Foreign Currency Adjustments, Future Policy
Benefits, Gross Fixed Assets (Property, Plant, and Equipment),
Intangibles, Interest Bearing Deposits, Inventories, Inventories
Adjustments & Allowances, Inventory Valuation
computer-implemented method, Investment Securities, Net, Land &
Improvements, Loans Receivable, Long Term Debt, Machinery,
Furniture & Equipment, Marketable Securities, Minority
Interest, Net Fixed Assets (Net Property, Plant, and Equipment),
Net Loans, Net Other Unearned Losses/Gains, Net Unrealized
Loss/Gain on Foreign Currencies, Net Unrealized Loss/Gain on
Investments, Non-Current Deferred Income Taxes, Non-Interest
Bearing Deposits, Notes Payable, Other Assets, Other Current
Assets, Other Current Liabilities, Other Equity Adjustments, Other
Fixed Assets, Other Inventories, Other Liabilities, Other
Non-Current Assets, Other Non-Current Liabilities, Other Payables,
Other Receivables, Participating Policyholder Equity, Policy Holder
Funds, Preferred Equity Outside Stock Equity, Preferred Securities
of Subsidiary Trust, Preferred Stock Equity, Preferred Stock
Equity, Premises and Equipment, Prepaid Expenses, Purchased
Components, Raw Materials, Receivables, Restricted Cash, Retained
Earnings, Separate Accounts Business, Shares Outstanding, Short
Term Debt, Time Deposits Placed, Total Assets, Total
Capitalization, Total Current Assets, Total Current Liabilities,
Total Equity, Total Fixed Assets, Total Liabilities, Total
Liabilities & Stock Equity, Non-Current Assets, Total
Non-Current Liabilities, Trading Account Securities, Treasury
Stock, Unearned Premiums, or Work in Progress, Adjustments to
Revenue, Advertising, Amortization Deferred, Policy Acquisition
Costs, Amortization, Amortization of Intangibles, Capitalized Lease
Obligations, Commercial and Industrial Template, Cost of Sales,
Current and Future Benefits, Deposits, Depreciation, Depreciation
Unreconciled, Domestic Sales, Earnings from Equity Interest, Excise
Taxes, Extraordinary Income/Losses, Federal Funds
Purchased/Securities Sold, Federal Funds Sold/Purchased, Foreign
Sales, Gross Operating Profit, Income before Income Taxes, Income
from Cumulative Effect of Accounting Change, Income from Tax Loss
Carry-forward, Income Taxes, Income Year-to-Date from Total
Operations, Income, Acquired in Process Research and Development,
Income, Restructuring and Merger and Acquisitions, Interest Bearing
Deposits, Interest Expense, Interest Income, Investment Banking
Profit, Investment Securities, Latest Quarter Indicator, Lease
Financing Income, Loans, Loans Held for Resale, Minority Interest,
Net Income Available for Common, Net Income from Continuing
Operations, Net Income from Discontinued Operations, Net Income
from Total Operations, Net Interest Income/Expense, Net Occupancy
Expense, Net Realized Capital Gains, Normalized Income, Operating
Income, Operating Income After Depreciation, Operating Income
before Depreciation (EBITDA), Operating Revenue (Revenue/Sales),
Other Gains (Losses), Other Income, Net Other Interest Expense,
Other Interest Income, Other Money Market Investments, Other
Non-Interest Expense, Other Non-Interest Income, Other Service
Charges, Other Special Charges, Policy Acquisition Costs, Pre-tax
Income (EBT), Preferred Dividends, Preferred Securities of
Subsidiary Trust, Premium Tax/Credit, Premiums Earned, Promotions
and Advertising, Property-Liability Insurance Claims, Provision for
Loan Loss, Research & Development Expense, Revenues
Year-to-Date, Salaries and, Employee Benefits, Security
Transactions, Selling, General and Administrative Expense, Service
Charge on Deposit Accounts, Short Term Debt, Special
Income/Charges, Time Deposits Placed, Total Income Avail for
Interest Expense (EBIT), Total Interest Expense, Total Interest
Income, Total Money Market, Investments, Total Net Income, Total
Non-Interest Expense, Total Non-Interest Income, Total Revenues,
Trading Account Securities, Trust Fees by Commissions,
Acquisitions, Amortization, Amortization of Intangibles, Cash at
Beginning of Period, Cash at End of Period, Cash Dividends Paid,
Cash Flow, Cash from Disc. Financing Activities, Cash from Disc.
Investing Activities, Change in Assets (Receivables), Change in
Income Taxes, Change in Liabilities (Payables), Change of Short
Term Debt, Deferred Income Taxes, Depreciation, Depreciation and
Amortization, Effect of Exchange Rate Changes, Extraordinary
(Gains) Losses, Free Cash Flow, (Increase) Decrease in Inventories,
(Increase) Decrease in Other Current Liabilities, (Increase)
Decrease in Other Current Assets, (Increase) Decrease in Other
Working Capital, (Increase) Decrease in Payables, (Increase)
Decrease in Prepaid Expenses, (Increase) Decrease in Receivables,
Invested Capital, Investment Securities Gain, Issuance of Capital
Stock, Issuance of Common Stock, Issuance of Debt, Issuance of Long
Term Debt, Issuance of Preferred Stock, Net Cash from Continuing
Operations, Net Cash from Discontinued Operations, Net Cash from
Financing Activities, Net Cash from Investing Activities, Net Cash
from Operating Activities, Net Change in Cash & Cash
Equivalents, Net Change in Deposits, Net Income (Loss), Net
Increase Federal Funds Sold, Net Policy Acquisition Costs, Net
Premiums Receivables, Operating (Gains) Losses, Other Financing
Activities, Other Financing Charges, Net, Other Investing Changes
Net, Other Non-Cash Items, Payment of Cash Dividends, Provision for
Loan Losses, Purchase of Investment Securities, Purchase of Long
Term Investments, Purchase of Property, Plant, Equipment, Purchase
of Short Term Investments, Purchase of Treasury Stock, Realized
Investment Gains, Repayment of Debt, Repayment of Long Term Debt,
Repurchase of Capital Stock, Sale of Long Term Investments, Sale of
Property, Plant, Equipment, or Sale of Short Term Investments,
Discontinued Operations, Restructurings, Divestures/Spin-offs,
Mergers, Acquisitions, Ownership, Insider Trading, Officer
Turnover, Chairman/CEO Separation, Related Party Transactions,
Board Performance, Board Composition, Material Restatements, Late
Filings, Amended Filings, Auditor Opinions, Auditor Changes, Audit
Fees, Salaries, Supply, Demand, Stocks, Interest Rates, Security
Pricing, Accruals, Capital Intensity, Asset Turnover, Inventory
Turnover, Payables Turnover, Receivables Turnover, Sales Per
Employee, Times Interest Earned, Total Coverage, Long-term Debt to
Equity, Total Debt to Equity, Acid Ratio, Cash Conversion Cycle,
Cash Ratio, Current Ratio, Book to Market, Dividend Yield, Earnings
Yield, Free Cash Flow Yield, Price to Sales, Profit Margin, Return
on Assets, Return on Capital, or Return on Equity for the most
recent period, the change in any individual and combined accounting
or non-accounting data regarding entities and/or securities
associated with the entities over time, the average of any
individual and combined accounting or non-accounting data regarding
entities and/or securities associated with the entities over time,
and the variance of any individual and combined accounting or
non-accounting data regarding entities and/or securities associated
with the entities over time.
[0042] In certain embodiments, any or all of the calculations,
methodologies, strategies, operations, processes, and/or functions
discussed herein (whether relating to selection or weighting) may
be performed by the systems, software, or methods described herein,
a third party, or a user. For example, any such calculations,
methodologies, strategies, operations, processes, and/or functions
discussed herein may be implemented in a hardware or software
implementation, and may take the form of computer-readable
instructions on a computer-readable storage medium. Accordingly,
such calculations, methodologies, strategies, operations,
processes, functions and so forth should be considered to be within
the scope of the present invention.
Exemplary Selection Criteria
[0043] Many different types of securities are suitable to be
represented in a TWI. Further, within the different security types,
some securities may be more desirable (or otherwise preferred) for
inclusion and/or relative representation in a TWI. For example,
while equities are one example of a security, an investor may
prefer to hold a higher concentration in equities inferred, through
various techniques of security analysis, to have greater investment
merit based on their exposure to risk factors and anomalies
including, but not limited to, size, value, momentum, volatility,
accruals, profitability, earnings surprises, share issuance,
financial distress, exchange rate, and governance. Such is the
focus of the present invention. Other considerations are optionally
employed as selection criteria to choose particular securities for
inclusion within a TWI. Exemplary selection criteria include, but
are not limited to, security type (i.e., equity, bond, put, call,
option, future, and so forth), trading forum of security (i.e.,
NASDAQ, NYSE, Chicago Futures Exchange, and so forth), geographic
location of issuing entity or headquarters thereof, date of
security maturation, costs associated with transacting or owning
the security (i.e., commissions, management fees, taxes, bid-ask
spreads, and so forth), investment capacity (i.e., liquidity,
market capitalization, and so forth), presence in another index
(such as the Dow Jones Industrial Average, Russell 1000, S&P
1500, and so forth), and/or any other information regarding
entities and/or securities associated with the entities.
[0044] It should be noted that, in various embodiments, selection
criteria are satisfied in a number of ways, depending on the
criteria. By way of non-limiting example, a primary TWI (from which
composite TWIs are optionally created) optionally use a minimum
data transformation weighting value (or output, e.g., a percentile)
of a risk factor metric (e.g., Return on Assets) for affiliated
entities as a selection criterion. Similarly, in another
embodiment, a primary or composite TWI may be based on a minimum
value resulting from a combination or relationship of two or more
data transformation weighting values (e.g., a percentile of a first
risk factor metric multiplied by a power transformation of a second
risk factor metric, or a power transformation of a percentile based
on a first risk factor metric). For such indexes, the minimum
selection criterion represents a lower bound. Accordingly, in a
particular embodiment, only securities having a product of a Book
to Market percentile and a Return on Equity percentile equal to or
greater than the selection criterion will be included in the TWI.
Alternative embodiments, however, may optionally use a maximum
product of a Book to Market percentile and a Return on Equity
percentile as a selection criterion. In such a TWI, the selection
criterion is an upper bound, and only securities having data
transformation weighting values less than the criterion are
included in the TWI. Thus, selection criteria optionally operate as
an upper or lower bound, an exact value, or define a range.
[0045] Multiple selection criteria are suitable to be combined to
yield a smaller universe of securities for inclusion in a TWI.
Essentially, any combination or variation of selection criteria is
suitable to determine securities eligible for weighting or
inclusion in the makeup of a TWI. It should be understood that any
selection criterion discussed herein is exemplary only and that
variations and alternatives may be used.
Weighting Values and Weighting Percentages
[0046] In some embodiments, once securities matching certain
selection criteria (or a single selection criterion) are
determined, the securities are weighted. In further embodiments, a
variety of different data transformations are optionally used to
produce output values (weighting values) in order to weight
securities in a TWI.
[0047] In some embodiments, component securities are weighted in a
TWI by dividing the chosen weighting value by the sum of all
weighting values for every security in the TWI, to arrive at a
security weighting percentage. In such cases, the security in
question then comprises a portion of the TWI equal to the security
weighting percentage.
[0048] Expressed mathematically, the weighting formula for a TWI,
in some embodiments, is as follows:
w.sub.i=[f(m).sub.1].sub.i/.SIGMA.[f(m).sub.1].sub.n
wherein i is a given security, wherein w is the weight of a
security in the index, wherein m is a risk factor metric, wherein n
is the number of member securities in the index, and wherein
f(m).sub.1 is a data transformation weighting value of a risk
factor metric,
[0049] As a non-limiting example, presume a TWI is an Accrual-based
percentile-weighted equity TWI of 1000 companies. Also presume the
sum of Accrual percentiles (weighting values) of all 1000 companies
to be represented in the TWI is 50000%. Presuming the entity
associated with equity #1 has an Accrual percentile of 50% within
the chosen timeframe, equity #1's total weight in the exemplary TWI
is: 50%/50000%=0.001, or 0.10%. Thus, in this example, equity #1
would compose 0.10% of the exemplary TWI. In the present
embodiment, the weighting value is an Accrual percentile, although
other weighting values may be used.
[0050] In another embodiment of the weighting methodology, the
weighting percentage for a given security equals the product of two
weighting values for the security divided by the sum of the product
of every TWI member's two weighting values. Mathematically, this is
expressed as:
w.sub.i=[f(m).sub.1*f(m).sub.2]/.SIGMA.[f(m.sub.n).sub.1*f(m.sub.n).sub.-
2]
wherein i is a given security, wherein w is the weight of a
security in the index, wherein m is a risk factor metric, wherein n
is the number of member securities in an index, wherein f(m).sub.1
is a data transformation weighting value of a first risk factor
metric, wherein f(m).sub.2 is a data transformation weighting value
of a second risk factor metric, and wherein * is a multiplicative
product.
[0051] The above mathematical expressions suitably accommodate any
number of weighting values. Alternatively, in various embodiments,
rather than multiplication, weighting values for each security can
be combined through adding, subtracting, dividing, averaging, or
determining a median.
[0052] As a non-limiting example of weighting employing the
foregoing methodology, a TWI comprising 1000 companies based on
Market Capitalization-to-Total Revenue and Price Momentum is
indicated to have an aggregate Market Capitalization-to-Total
Revenue and Price Momentum percentile product of approximately
25000% based on summed Total Revenue for the trailing four quarters
and change in split-adjusted Share Price for the trailing four
quarters. The weighting percentage for equity #1 in the TWI having
an indicated Market Capitalization-to-Total Revenue and Price
Momentum percentile of 75% and 100%, respectively, would be:
[75%*100%]/[25000%]=75%/25000%=0.003, or 0.30%. In this example,
the weighting value of 75% is calculated by first multiplying the
Market Capitalization-to-Total Revenue percentile by the Price
Momentum percentile for the company associated with equity #1. This
same weighting value would then be calculated for every equity in
the TWI and summed, the summation of which is the indicated
aggregate Market Capitalization-to-Total Revenue and Price Momentum
percentile product for all the companies included within the TWI
(indicated, in this example, to be 25000%).
[0053] Additionally, as previously mentioned, weighting values are
suitably time-based. By way of non-limiting example, the weighting
value optionally takes the most recent quarter into account.
However, the weighting value is suitably based on any measurable
period of time, such as, by way of non-limiting examples, the past
quarter, the past two or three quarters, the past year, the past
ten years, and so forth.
[0054] Further, in some embodiments TWIs are re-weighted or
otherwise rebalanced periodically. By way of non-limiting example,
preferred stocks tracked by a TWI are re-selected every quarter or
at various time intervals. By way of further non-limiting example,
in a preferred-stock index securities are added to or dropped from
a TWI as new entities issuing preferred stocks meet selection
criteria or old entities fail to meet the same criteria. Similarly,
indexes are optionally re-weighted at certain intervals, based on
the weighting values of each included security at the time of the
re-weighting interval.
TWI Creation
[0055] FIG. 1 is a non-limiting, exemplary flowchart depicting a
method for creating a TWI having weighted securities, through
operations of a computer. The operations described with respect to
FIG. 1 and FIG. 2 are suitably carried out on any suitable
computing device, including, but not limited to, personal
computers, mainframe computers, minicomputers, personal data
assistants ("PDAs"), mobile phones, Internet-enabled telephones,
laptop computers, computer workstations, Web tablets, wireless
devices, network servers, and any other currently available or to
be available device(s) capable of executing the below-referenced
operations, as set forth by the various embodiments of the systems,
software, and methods described herein. The operations are suitably
carried out at a single location or by a single computing device,
or may be carried out by multiple computing devices connected to
one another, distributed across, or otherwise capable of
transmitting data across a network. Exemplary networks include, but
are not limited to, packet switched networks (such as the Internet,
intranets, extranets, Ethernets, local area networks (LANs), wide
area networks (WANs), and the like), circuit switched networks
(such as the "plain old telephone service" (POTS) and some cellular
systems), combinations of packet and circuit switched networks, and
any other communications topologies configured to facilitate the
transmission of data.
[0056] Referring to FIG. 1, in a particular embodiment, the process
begins at operation 100, in which one or more selection criteria
(risk factor metrics) are determined. As discussed in more detail
above and below, the selection criteria are chosen by an operator
to determine which specific securities of a universe are to be
represented in the TWI. Exemplary selection criteria are also given
above and below.
[0057] Continuing to refer to FIG. 1, in operation 105, a database
containing entries corresponding to various securities may be
accessed. Typically, each database entry includes as-reported
accounting and non-accounting data of the affiliated entity such
as: a security trading symbol, name, or other identifier; a
security price; a state or region in which an entity issuing,
securing, or otherwise affiliated with the security has its
corporate headquarters or location of business incorporation; an
average daily U.S. dollar trading volume for the security; a
trading exchange for the security; the number of common shares
outstanding or free float shares outstanding for a security; and so
forth. The database record may include additional information such
as any of the selection criteria discussed herein, or may omit any
or all of the information listed. Further, any one or more of the
listed data may be transformed and used individually or in
combination either as selection criteria or weighting values. The
database may be provided by any of a variety of data purveyors. For
example, the present embodiment employs a customized database
provided through FACTSET RESEARCH SYSTEMS. Alternate embodiments
may use a database supplied by REUTERS, S&P COMPUTSTAT, THOMSON
FINANCIAL, VALUE LINE, and/or AAII. Additionally, an affiliated
entity's 10-Q or 10-K filings with the Securities and Exchange
Commission may supplement database information. Accordingly, these
filings are also considered "databases" for purposes of this
document.
[0058] Continuing to refer to FIG. 1, in operation 110, securities
meeting or exceeding a first selection criterion are selected from
the database. These securities form a security universe. Presuming
only a single selection criterion exists, all securities in the
security universe for which requisite data comprising the selection
criterion will be represented in the TWI.
[0059] Continuing to refer to FIG. 1, in operation 115, the
embodiment determines whether all selection criteria have been
considered and compared against the securities in the security
universe. If so, the embodiment proceeds to operation 130.
Otherwise, the embodiment executes operation 120.
[0060] Continuing to refer to FIG. 1, in operation 120, the next
selection criterion is implemented. Many times, securities may be
subjected to analysis against multiple selection criteria, with
only those securities meeting all criteria represented or included
in the TWI.
[0061] Continuing to refer to FIG. 1, in operation 125, securities
from the security universe established in operation 110 are
compared against the selection criterion implemented in operation
120. Those securities matching this additional selection criterion
remain in the security universe, while securities not meeting the
selection criterion are discarded. Effectively, the security
universe is winnowed to include only those securities matching
every selection criterion implemented during operation of the
selection process. After operation 125, operation 115 is again
executed.
[0062] Continuing to refer to FIG. 1, if the embodiment determines
in operation 115 that all selection criteria have been considered
(and, correspondingly, that all securities remaining in the
security universe satisfy all selection criteria), then operation
130 is executed. In operation 130, the weighting percentage for
each security is determined. The process for determining a
security's weighting percentage is discussed in more detail above,
in the section entitled "Weighting values and Weighting
Percentages."
[0063] Continuing to refer to FIG. 1, finally, in operation 135,
the security is added to the TWI in the amount dictated by the
weighting percentage determined in operation 130. The amount of the
security may be measured in either dollar value or shares,
depending on the nature of the TWI.
[0064] The above-described process (or portions thereof) may be
implemented at any time, and in some embodiments occurs at
regularly timed intervals. For example, a TWI may be subjected to
the above process, or portions of the above process, once per year
(as a further example, component companies may be selected as of
the close of the last trading day in November for reconstitution on
a set date in December) to determine which equities or securities
will be included in the TWI. Generally speaking, this process is
referred to as an "initial selection" the first time a TWI is
created and a "reconstitution" when an already-existing Index is
again subject to some portion of the process. More specifically,
reconstituting refers to the application of the selection criteria
to determine which securities remain in, and/or are to be included
in, the TWI. "Reweighting," as used herein, refers to the process
of determining each security's weighting percentage within the TWI
and may occur quarterly, semi-annually, annually, or at any other
reconstitution date. Similarly, "rebalancing" refers to adjustments
made to a TWI, often at set intervals such as a quarterly basis, to
reflect certain corporate actions, including the issuance or
repurchase of common shares outstanding. The exact dates and/or
times of any operations described herein, including reestablishment
of weighting percentages, reconstitution, or rebalancing of a TWI
may vary in alternative embodiments.
[0065] Alternate embodiments may implement the processes described
herein, or portions thereof, for a TWI annually, semi-annually,
quarterly, weekly, monthly, daily, and so forth. As another
example, a TWI may be reconstituted periodically, for example every
January, April, July, and October, to determine which equities
initially selected for inclusion in the TWI no longer meet the
selection criteria and are therefore removed from the TWI. This
reconstitution may operate only on the equities initially selected
to comprise the TWI, and so may constitute a narrowing or reduction
in the number of securities in the TWI. In such a case, certain
operations may be omitted, such as accessing a database in
operation 105 and the formation of a security universe in operation
110, since the TWI already comprises the security universe in
question.
[0066] Alternately, the reconstitution may operate to review all
securities in a database, and thus may act to add securities that
meet the selection criteria as of the rebalancing date.
Additionally, some embodiments may vary the reconstitution period
depending on the nature of the TWI.
[0067] Similar to reconstitution, reestablishment of weighting
percentages for the TWI according to the above-referenced process
occurs, in various embodiments, at any time, or at regular
predetermined intervals, such as weekly, monthly, quarterly,
annually, and so on. Further, reestablishment of weighting
percentages occurs, in some embodiments, each time a reconstitution
of the TWI is performed. In alternative embodiments,
reestablishment of weighting percentages occurs more often than
reconstitution. By way of non-limiting example, a TWI is optionally
reconstituted annually, such as in December, and reweighted every
six months, such as in June and at the next reconstitution in
December. In another implementation, the TWI may be reconstituted
and reweighted simultaneously and annually, such as in June.
[0068] In some embodiments, the above-referenced process, or
portions thereof, is implemented substantially continuously as
market and security data is received. By way of non-limiting
example, a TWI value is optionally calculated during specific time
intervals, such as every fifteen seconds, hour, day, month, second,
and so forth, as desired. In further embodiments, as the TWI value
changes, reflecting changes in the underlying market prices of the
companies that comprise the TWI (presuming that market prices are
included in any of the risk factor metrics transformed into
weighting values), the weightings for each security typically vary
from the weightings that were initially established using the
weighting methodologies described herein. These variances generally
continue to be affected by changes in risk factor metrics of the
component companies until the next reestablishment of weighting
percentages and/or reconstitution, at which time weightings are
reestablished using the weighting methodologies described
herein.
[0069] Although the above process has been described as a set of
computer-implemented operations, it should be understood that the
process may be carried out manually in order to identify securities
for inclusion and weighting in a TWI. Accordingly, the present
invention embraces both computer-implemented and
non-computer-implemented processes for identifying and weighting
securities in a TWI. It should also be understood that operations
of the above-described process may be implemented or executed in an
order other than that described without departing from the spirit
or scope of the present invention. As one example, the database may
be accessed prior to determining all selection criteria.
Exemplary TWI Creation
[0070] Implementation of various selection criteria for use with
embodiments of the invention is now discussed. In an embodiment
employing multiple selection criteria, a set of securities included
in a TWI may be chosen to satisfy several different selection
criteria. For example, criteria may include a business being
incorporated in, or being headquartered in, a particular country,
such as the United States, or particular countries within specific
continents, such as Europe. Additional selection criteria may
require a security to have outstanding common equity trading on a
particular equity exchange, such as the NYSE, AMEX or NASDAQ
National Market. In alternative embodiments, one, more or fewer
selection criteria may be employed, depending on the goals assigned
to the particular TWI involved.
[0071] Once a particular set of securities has been selected via
one or more selection criteria, the same set of securities may be
further apportioned to yield composite indexes composed solely of
those included in the first, or "primary," TWI. Such a composite
TWI may be formed by employing one or more additional selection
criteria, which must be satisfied by each security of the primary
TWI, for employment in the composite TWI. Further, the basis for
the apportionment of the primary TWI may be a ranking of the
securities of the primary TWI according to one of the original
selection criteria (or a completely separate selection criterion).
A specified percentage or number of securities chosen from some
reference point within the ranked list of securities also may be
used to constitute the composite TWI.
[0072] FIG. 2 provides a non-limiting example of two primary
Transformation Weighted Indexes, TW-1 and TW-2, and a composite
TW-3. All three indexes may contain identical securities. For
example, TW-1, consisting of n equities, selected by way of one or
more selection criteria, may be weighted according to a particular
first weighting value, such as percentiles of Price Momentum. In
the embodiment of FIG. 2, the primary TW-1 consists of all domestic
equities associated with companies for which Price Momentum based
on the trailing four quarters can be calculated. Securities
selected for TW-1 must also have trailing four quarters of Total
Revenue in order to subsequently be combined in TW-3. In the
present example, TW-1 may be regarded as having a small entity and
small market capitalization orientation in that no consideration to
size was given in the weighting process, which is a preferred
embodiment.
[0073] Referring to FIG. 2, a second primary Transformation
Weighted Index, TW-2, may be created, as follows. TW-2, consisting
of the same n equities as TW-1, may be weighted according to a
particular two-step weighting value, such as percentiles of Total
Revenue raised to a power. In the present example, TW-2 may be
regarded as being oriented toward high investment capacity because
the metric on which it is based is highly correlated with market
capitalization, which is a preferred embodiment.
[0074] Continuing to refer to FIG. 2, once both TW-1 and TW-2 are
formed, composite TW-3 can be formed. In the present non-limiting
example, security weights in TW-3 are calculated by averaging the
respective weighting values used as the basis for the weighting
percentages in TW-1 and TW-2. Composite TW-3 may be thought of as
having both a high factor exposure (depending on the one or more
risk factor metrics used to create TW-1) and relatively high
investment capacity.
Exemplary Transformation Weighted Indexes
[0075] Three exemplary TWIs (representing primary TW-1, primary
TW-2, and composite TW-3) are presented herein. These TWIs are
provided by way of illustration and not limitation; alternate
embodiments may employ indexes based on different risk factors,
using different metrics for the same risk factors, or including a
different universe of securities. Tables summarizing each exemplary
TWI are provided below.
TABLE-US-00001 TABLE 1 Notional TW-1 metrics, transformations, and
weights for top 10 of 1000 stocks sorted by TW-1 Weighting
Percentage in descending order Percentile of Percentile Value
Momentum Volatility Percentile of Average TW-1 Valuation Momentum
Volatility Metric Metric Metric Percentile Percentile Raised to a
Weighting Security Metric Metric Metric Percentile Percentile
Percentile Average Average Power of 2 Percentage A 2.93 0.11 0.04
0.93 0.12 0.93 0.66 1.00 1.00 0.30% B 3.76 -0.04 0.03 0.96 0.02
0.98 0.65 1.00 1.00 0.30% C 2.22 0.05 0.02 0.88 0.07 1.00 0.65 1.00
0.99 0.30% D 4.95 0.06 0.05 0.97 0.07 0.87 0.64 1.00 0.99 0.30% E
2.67 0.05 0.04 0.92 0.07 0.94 0.64 1.00 0.99 0.30% F 6.15 0.13 0.06
0.98 0.15 0.78 0.64 0.99 0.99 0.30% G 2.04 0.05 0.03 0.86 0.07 0.98
0.63 0.99 0.99 0.30% H 2.69 0.10 0.05 0.92 0.12 0.86 0.63 0.99 0.98
0.30% I 7.33 0.19 0.07 0.99 0.24 0.64 0.62 0.99 0.98 0.30% J 4.31
0.74 0.21 0.96 0.87 0.02 0.62 0.99 0.98 0.29%
[0076] The above table illustrates a TW-1, comprising 1000
hypothetical stocks as of a particular date, wherein the security
weights are determined by calculating a percentile for three risk
factor metrics, averaging these percentiles, calculating a
percentile of this average, and raising the percentile of the
average percentile to a power of two to compute a weighting
percentage for each stock. For example, stock A's ("A")
non-transformed Valuation metric value is 2.93, its non-transformed
Momentum metric is 0.11, and its non-transformed Volatility metric
is 0.04. The respective percentile values for these three metrics
are 0.93, 0.12, and 0.93. Stock A's average percentile based on
these three metrics is 0.66. Its percentile of this percentile
average is 1.00, which remains at 1.00 when raised to an exponent
of two. Thus, A's weight in the exemplary TWI shown in Table 1
would be its percentile of its percentile average raised to a power
of two divided by the sum of that weighting value for all companies
in the TWI, or: 1.00/331.83=0.30%.
[0077] Table 2 depicts a second exemplary TW-2. This TWI includes
the same companies as TW-1, but uses a different weighting value
based on a notional fundamental Size metric.
TABLE-US-00002 TABLE 2 Notional TW-2 based on a percentile
transformation of a fundamental size metric raised to a power of
10, compared with TW-1 weights for the same stocks, shown in
descending order of TW-1 weight Percentile of Fundamental
Percentile of Size Metric TW-2 TW-1 Secu- Fundamental Fundamental
Raised to a Weighting Weighting rity Size Metric Size Metric Power
of 10 Percentage Percentage A 30,771 0.89 0.29 0.33% 0.30% B 27,878
0.88 0.28 0.30% 0.30% C 37,913 0.92 0.42 0.46% 0.30% D 40,940 0.92
0.44 0.49% 0.30% E 33,910 0.91 0.37 0.41% 0.30% F 109,899 0.98 0.84
0.93% 0.30% G 6,040 0.58 0.00 0.01% 0.30% H 18,189 0.84 0.16 0.18%
0.30% I 98,160 0.98 0.80 0.89% 0.30% J 103,831 0.98 0.82 0.90%
0.29%
[0078] As shown, the weighting percentages in Table 2 differ from
the weighting percentages shown in Table 1. As an example, consider
stock H ("H"). Stock H's indicated fundamental size metric is
$18,189 million; its percentile of this size metric is 0.84, which
declines to 0.16 when raised to a power of 10 (the sum of this
weighting value for all 1000 stocks is 90.41). Accordingly, H's
weighting percentage based on fundamental size is 0.18% of TW-2:
0.16/90.41=0.18%.
[0079] It should be noted that the weightings for other companies
change more/less dramatically in a TWI based on fundamental size
(TW-2) as compared to risk factor metrics (TW-1). For example,
Company G's ("G") weighting may decrease and Company J's ("J")
weighting increase substantially. This can be seen by comparing the
relative weighting percentages of E and J in Table 1 versus the
relative percentages for the same stocks in Table 2. Using the
methodology described herein, TW-2 gives investors an opportunity
to own a "high investment capacity" TWI.
[0080] Table 3 depicts a third exemplary TWI. Here, TW-3 is a
composite of TW-1 and TW-2. It uses a different weighting value
comprising: a multiplicative product of the weighting values used
to set the weighting percentages of TW-1 and TW-2.
TABLE-US-00003 TABLE 3 Notional composite TW-3 based on multiplying
the weighting values of TW-1 and TW-2, compared with weights for
TW-1 and TW-2 as well as non-transformed fundamental size-based
index, market capitalization weighting, and equal weighting;
weights for the same stocks, shown in descending order of TW-1
weight Percentile of Percentile of Product of Non- Percentile
Fundamental TW-1 and Transformed Market Average Size Metric TW-2
TW-3 TW-2 TW-1 Fundamental Capitalization Equal Raised to a Raised
to a Weighting Weighting Weighting Weighting Weighting Weghting
Weighting Security Power of 2 Power of 10 Values Percentage
Percentage Percentage Percentage Percentage Percentage A 1.00 0.29
0.29 0.67% 0.33% 0.30% 0.22% 0.06% 0.10% B 1.00 0.28 0.27 0.62%
0.30% 0.30% 0.20% 0.04% 0.10% C 0.99 0.42 0.41 0.94% 0.46% 0.30%
0.28% 0.09% 0.10% D 0.99 0.44 0.44 0.99% 0.49% 0.30% 0.30% 0.04%
0.10% E 0.99 0.37 0.36 0.83% 0.41% 0.30% 0.25% 0.07% 0.10% F 0.99
0.84 0.83 1.89% 0.93% 0.30% 0.80% 0.09% 0.10% G 0.99 0.00 0.00
0.01% 0.01% 0.30% 0.04% 0.02% 0.10% H 0.98 0.16 0.16 0.37% 0.18%
0.30% 0.13% 0.04% 0.10% I 0.98 0.80 0.79 1.78% 0.89% 0.30% 0.72%
0.07% 0.10% J 0.98 0.82 0.80 1.82% 0.90% 0.29% 0.76% 0.13%
0.10%
[0081] It should be noted that the member securities of TW-3 are
the same as TW-1 and TW-2, but their weights are very different.
This selection criterion, using the methodology described herein,
may give investors an opportunity to own a high capacity TWI that
is also highly concentrated on multiple risk factors.
[0082] It should generally be noted with respect to the various
indexes and/or weighting methodologies discussed herein that
rounding weights and/or positions might prove useful. In the
present example, positions in the exemplary indexes are rounded to
the nearest tenth of a percent. Alternate embodiments optionally
round to the nearest hundredth of a percent or whole percentage
point, or any other convenient point.
Digital Processing Device
[0083] In some embodiments, the systems, software, and methods
described herein include a digital processing device, or use of the
same. In further embodiments, the digital processing device
includes one or more hardware central processing units (CPU) that
carry out the device's functions. In still further embodiments, the
digital processing device further comprises an operating system
configured to perform executable instructions. In some embodiments,
the digital processing device is optionally connected a computer
network. In further embodiments, the digital processing device is
optionally connected to the Internet such that it accesses the
World Wide Web. In still further embodiments, the digital
processing device is optionally connected to a cloud computing
infrastructure. In other embodiments, the digital processing device
is optionally connected to an intranet. In other embodiments, the
digital processing device is optionally connected to a data storage
device.
[0084] In accordance with the description herein, suitable digital
processing devices include, by way of non-limiting examples, server
computers, desktop computers, laptop computers, notebook computers,
sub-notebook computers, netbook computers, netpad computers,
set-top computers, handheld computers, Internet appliances, mobile
smartphones, tablet computers, personal digital assistants, video
game consoles, and vehicles. Those of skill in the art will
recognize that many smartphones are suitable for use in the system
described herein. Those of skill in the art will also recognize
that select televisions, video players, and digital music players
with optional computer network connectivity are suitable for use in
the system described herein. Suitable tablet computers include
those with booklet, slate, and convertible configurations, known to
those of skill in the art.
[0085] In some embodiments, the digital processing device includes
an operating system configured to perform executable instructions.
The operating system is, for example, software, including programs
and data, which manages the device's hardware and provides services
for execution of applications. Those of skill in the art will
recognize that suitable server operating systems include, by way of
non-limiting examples, FreeBSD, OpenBSD, NetBSD.RTM., Linux,
Apple.RTM. Mac OS X Server.RTM., Oracle.RTM. Solaris.RTM., Windows
Server.RTM., and Novell.RTM. NetWare.RTM.. Those of skill in the
art will recognize that suitable personal computer operating
systems include, by way of non-limiting examples, Microsoft.RTM.
Windows.RTM., Apple.RTM. Mac OS X.RTM., UNIX.RTM., and UNIX-like
operating systems such as GNU/Linux.RTM.. In some embodiments, the
operating system is provided by cloud computing. Those of skill in
the art will also recognize that suitable mobile smart phone
operating systems include, by way of non-limiting examples,
Nokia.RTM. Symbian.RTM. OS, Apple.RTM. iOS.RTM., Research In
Motion.RTM. BlackBerry OS.RTM., Google.RTM. Android.RTM.,
Microsoft.RTM. Windows Phone.RTM. OS, Microsoft.RTM. Windows
Mobile.RTM. OS, Linux.RTM., and Palm.RTM. WebOS.RTM..
[0086] In some embodiments, the device includes a storage and/or
memory device. The storage and/or memory device is one or more
physical apparatuses used to store data or programs on a temporary
or permanent basis. In some embodiments, the device is volatile
memory and requires power to maintain stored information. In some
embodiments, the device is non-volatile memory and retains stored
information when the digital processing device is not powered. In
further embodiments, the non-volatile memory comprises flash
memory. In some embodiments, the non-volatile memory comprises
dynamic random-access memory (DRAM). In some embodiments, the
non-volatile memory comprises ferroelectric random access memory
(FRAM). In some embodiments, the non-volatile memory comprises
phase-change random access memory (PRAM). In other embodiments, the
device is a storage device including, by way of non-limiting
examples, CD-ROMs, DVDs, flash memory devices, magnetic disk
drives, magnetic tapes drives, optical disk drives, and cloud
computing based storage. In further embodiments, the storage and/or
memory device is a combination of devices such as those disclosed
herein.
[0087] In some embodiments, the digital processing device includes
a display to send visual information to a user. In some
embodiments, the display is a cathode ray tube (CRT). In some
embodiments, the display is a liquid crystal display (LCD). In
further embodiments, the display is a thin film transistor liquid
crystal display (TFT-LCD). In some embodiments, the display is an
organic light emitting diode (OLED) display. In various further
embodiments, on OLED display is a passive-matrix OLED (PMOLED) or
active-matrix OLED (AMOLED) display. In some embodiments, the
display is a plasma display. In other embodiments, the display is a
video projector. In still further embodiments, the display is a
combination of devices such as those disclosed herein.
[0088] In some embodiments, the digital processing device includes
an input device to receive information from a user. In some
embodiments, the input device is a keyboard. In some embodiments,
the input device is a pointing device including, by way of
non-limiting examples, a mouse, trackball, track pad, joystick,
game controller, or stylus. In some embodiments, the input device
is a touch screen or a multi-touch screen. In other embodiments,
the input device is a microphone to capture voice or other sound
input. In other embodiments, the input device is a video camera to
capture motion or visual input. In still further embodiments, the
input device is a combination of devices such as those disclosed
herein.
Non-Transitory Computer Readable Storage Medium
[0089] In some embodiments, the systems, software, and methods
disclosed herein include one or more non-transitory computer
readable storage media encoded with a program including
instructions executable by the operating system of an optionally
networked digital processing device. In further embodiments, a
computer readable storage medium is a tangible component of a
digital processing device. In still further embodiments, a computer
readable storage medium is optionally removable from a digital
processing device. In some embodiments, a computer readable storage
medium includes, by way of non-limiting examples, CD-ROMs, DVDs,
flash memory devices, solid state memory, magnetic disk drives,
magnetic tape drives, optical disk drives, cloud computing systems
and services, and the like. In some cases, the program and
instructions are permanently, substantially permanently,
semi-permanently, or non-transitorily encoded on the media.
Computer Program
[0090] In some embodiments, the systems, software, and methods
disclosed herein include at least one computer program, or use of
the same. A computer program includes a sequence of instructions,
executable in the digital processing device's CPU, written to
perform a specified task. In light of the disclosure provided
herein, those of skill in the art will recognize that a computer
program may be written in various versions of various languages. In
some embodiments, a computer program comprises one sequence of
instructions. In some embodiments, a computer program comprises a
plurality of sequences of instructions. In some embodiments, a
computer program is provided from one location. In other
embodiments, a computer program is provided from a plurality of
locations. In various embodiments, a computer program includes one
or more software modules. In various embodiments, a computer
program includes, in part or in whole, one or more web
applications, one or more mobile applications, one or more
standalone applications, one or more web browser plug-ins,
extensions, add-ins, or add-ons, or combinations thereof.
Web Application
[0091] In some embodiments, a computer program includes a web
application. In light of the disclosure provided herein, those of
skill in the art will recognize that a web application, in various
embodiments, utilizes one or more software frameworks and one or
more database systems. In some embodiments, a web application is
created upon a software framework such as Microsoft.RTM. .NET or
Ruby on Rails (RoR). In some embodiments, a web application
utilizes one or more database systems including, by way of
non-limiting examples, relational, non-relational, object oriented,
associative, and XML database systems. In further embodiments,
suitable relational database systems include, by way of
non-limiting examples, Microsoft.RTM. SQL Server, mySQL.TM., and
Oracle.RTM.. Those of skill in the art will also recognize that a
web application, in various embodiments, is written in one or more
versions of one or more languages. A web application may be written
in one or more markup languages, presentation definition languages,
client-side scripting languages, server-side coding languages,
database query languages, or combinations thereof. In some
embodiments, a web application is written to some extent in a
markup language such as Hypertext Markup Language (HTML),
Extensible Hypertext Markup Language (XHTML), or eXtensible Markup
Language (XML). In some embodiments, a web application is written
to some extent in a presentation definition language such as
Cascading Style Sheets (CSS). In some embodiments, a web
application is written to some extent in a client-side scripting
language such as Asynchronous Javascript and XML (AJAX), Flash.RTM.
Actionscript, Javascript, or Silverlight.RTM.. In some embodiments,
a web application is written to some extent in a server-side coding
language such as Active Server Pages (ASP), ColdFusion.RTM., Perl,
Java.TM., JavaServer Pages (JSP), Hypertext Preprocessor (PHP),
Python.TM., Ruby, Tcl, Smalltalk, WebDNA.RTM., or Groovy. In some
embodiments, a web application is written to some extent in a
database query language such as Structured Query Language (SQL). In
some embodiments, a web application integrates enterprise server
products such as IBM.RTM. Lotus Domino.RTM.. In some embodiments, a
web application includes a media player element. In various further
embodiments, a media player element utilizes one or more of many
suitable multimedia technologies including, by way of non-limiting
examples, Adobe.RTM. Flash.RTM., HTML 5, Apple.RTM. QuickTime.RTM.,
Microsoft.RTM. Silverlight.RTM., Java.TM., and Unity.RTM..
Mobile Application
[0092] In some embodiments, a computer program includes a mobile
application provided to a mobile digital processing device. In some
embodiments, the mobile application is provided to a mobile digital
processing device at the time it is manufactured. In other
embodiments, the mobile application is provided to a mobile digital
processing device via the computer network described herein.
[0093] In view of the disclosure provided herein, a mobile
application is created by techniques known to those of skill in the
art using hardware, languages, and development environments known
to the art. Those of skill in the art will recognize that mobile
applications are written in several languages. Suitable programming
languages include, by way of non-limiting examples, C, C++, C#,
Objective-C, Java.TM., Javascript, Pascal, Object Pascal,
Python.TM., Ruby, VB.NET, WML, and XHTML/HTML with or without CSS,
or combinations thereof.
[0094] Suitable mobile application development environments are
available from several sources. Commercially available development
environments include, by way of non-limiting examples, AirplaySDK,
alcheMo, Appcelerator.RTM., Celsius, Bedrock, Flash Lite, .NET
Compact Framework, Rhomobile, and WorkLight Mobile Platform. Other
development environments are available without cost including, by
way of non-limiting examples, Lazarus, MobiFlex, MoSync, and
Phonegap. Also, mobile device manufacturers distribute software
developer kits including, by way of non-limiting examples, iPhone
and iPad (iOS) SDK, Android.TM. SDK, BlackBerry.RTM. SDK, BREW SDK,
Palm.RTM. OS SDK, Symbian SDK, webOS SDK, and Windows.RTM. Mobile
SDK.
[0095] Those of skill in the art will recognize that several
commercial forums are available for distribution of mobile
applications including, by way of non-limiting examples, Apple.RTM.
App Store, Android.TM. Market, BlackBerry.RTM. App World, App Store
for Palm devices, App Catalog for webOS, Windows.RTM. Marketplace
for Mobile, Ovi Store for Nokia.RTM. devices, Samsung.RTM. Apps,
and Nintendo.RTM. DSi Shop.
Standalone Application
[0096] In some embodiments, a computer program includes a
standalone application, which is a program that is run as an
independent computer process, not an add-on to an existing process,
e.g., not a plug-in. Those of skill in the art will recognize that
standalone applications are often compiled. A compiler is a
computer program(s) that transforms source code written in a
programming language into binary object code such as assembly
language or machine code. Suitable compiled programming languages
include, by way of non-limiting examples, C, C++, Objective-C,
COBOL, Delphi, Eiffel, Java.TM., Lisp, Python.TM., Visual Basic,
and VB .NET, or combinations thereof. Compilation is often
performed, at least in part, to create an executable program. In
some embodiments, a computer program includes one or more
executable complied applications.
Software Modules
[0097] The systems, software, and methods disclosed herein include,
in various embodiments, software, server, and database modules, or
use of the same. In view of the disclosure provided herein,
software modules are created by techniques known to those of skill
in the art using machines, software, and languages known to the
art. The software modules disclosed herein are implemented in a
multitude of ways. In various embodiments, a software module
comprises a file, a section of code, a programming object, a
programming structure, or combinations thereof. In further various
embodiments, a software module comprises a plurality of files, a
plurality of sections of code, a plurality of programming objects,
a plurality of programming structures, or combinations thereof. In
various embodiments, the one or more software modules comprise, by
way of non-limiting examples, a web application, a mobile
application, and a standalone application. In some embodiments,
software modules are in one computer program or application. In
other embodiments, software modules are in more than one computer
program or application. In some embodiments, software modules are
hosted on one machine. In other embodiments, software modules are
hosted on more than one machine. In further embodiments, software
modules are hosted on cloud computing platforms. In some
embodiments, software modules are hosted on one or more machines in
one location. In other embodiments, software modules are hosted on
one or more machines in more than one location.
EXAMPLES
[0098] The following illustrative examples are representative of
embodiments of the methods, devices, and systems for
transformation-based index construction described herein and are
not meant to be limiting in any way.
Example 1
TWI Characteristics
[0099] A percentile transformation is applied to a notional risk
factor metric for a set of 1000 securities.
[0100] Table 4 shows a sampling of percentiles at either end of the
1000-member index with weighting percentages calculated by dividing
a given percentile by the sum of the percentiles for each index
constituent with respect to a notional metric.
TABLE-US-00004 TABLE 4 Percentiles of a 1000 member index of
marketable securities; weighting percentage determined by dividing
percentile by aggregate of all index member percentiles Weighting
Weighting Percentiles, Percentage, Percentiles, Percentage, Top 10
Top 10 Bottom 10 Bottom 10 1.0000 0.2003% 0.0090 0.0018% 0.9980
0.1999% 0.0080 0.0016% 0.9970 0.1997% 0.0070 0.0014% 0.9960 0.1995%
0.0060 0.0012% 0.9950 0.1993% 0.0050 0.0010% 0.9940 0.1991% 0.0040
0.0008% 0.9930 0.1989% 0.0030 0.0006% 0.9920 0.1987% 0.0020 0.0004%
0.9910 0.1985% 0.0010 0.0002% 0.9900 0.1983% 0.0000 0.0000%
[0101] FIG. 3 depicts the graphical appearance of a
percentile-based weighting percentage curve compared with a
weighting percentage curve of an equal weight index of 1000
constituents. In the transformed index, weighting percentages vary
between 0.20% to 0.00%. The equal weight index allocates 0.10% to
all constituents. This suggests how a Transformation Weighted index
may accentuate one or more factors on which it is based.
[0102] To a percentile, one may optionally administer an additional
transformation, such as a power, to change the shape of the
weighting percentage curve and as well as the relative
concentration of one or more risk factors on which it is based.
Table 5 uses decile analysis of a 1000-member index to show how the
process of transforming percentiles with powers affects the
distribution of index member weighting percentages. Powers greater
than one result in higher weighting percentage concentrations. This
suggests how a Transformation Weighted index may further accentuate
one or more factors on which it is based.
TABLE-US-00005 TABLE 5 Decile concentrations resulting from the
application of various exponents to a percentile for a notional
1000-member index. Expo- Expo- Expo- Expo- Expo- nent of 2 nent of
4 nent of 6 nent of 8 nent of 10 Applied to Applied to Applied to
Applied to Applied to Decile Percentiles Percentiles Percentiles
Percentiles Percentiles One 27.1267% 40.9961% 52.2298% 61.3276%
68.6950% Two 21.7081% 26.2772% 26.8376% 25.2834% 22.7411% Three
16.9048% 15.9564% 12.7242% 9.3713% 6.5974% Four 12.6955% 9.0171%
5.4211% 3.0156% 1.6062% Five 9.0942% 4.6411% 2.0107% 0.8082%
0.3119% Six 6.0927% 2.0943% 0.6142% 0.1679% 0.0442% Seven 3.6919%
0.7770% 0.1408% 0.0240% 0.0040% Eight 1.8926% 0.2092% 0.0203%
0.0019% 0.0002% Nine 0.6952% 0.0306% 0.0012% 0.0000% 0.0000% Ten
0.0984% 0.0010% 0.0000% 0.0000% 0.0000%
[0103] FIG. 4 displays weighting percentage curves that result from
the application of different powers to the percentiles, suggesting
how a Transformation Weighted index may be used to customize the
emphasis of one or more risk factors on which it may be based.
[0104] Subsequent to the preceding two-step transformations for
multiple risk factors of a security, one optionally combines the
transformed values into a single index. Two ways to do so are
averaging and multiplying. In this non-limiting example, the output
values may again undergo a percentile transformation before being
transformed further with an exponent. A decision to average, to
multiply, or to perform subsequent transformations has a
significant impact on the weighting percentage curve that results,
as shown in FIG. 5 (here, the straight-line weighting percentage
curve results from a percentile applied to the average, similar to
FIG. 3, but in this case is based on several factors, demonstrating
the ability to combine different data types into a standardized
format).
[0105] Whereas conventional indexes are structurally rigid,
transformations make weighting percentage curves malleable and make
it possible to bend them to suit different objectives. The choice
of transformations and their combinations is without limit.
Example 2
TWI Construction
[0106] In this example, three TWIs are derived from a 1000-stock
universe selected by highest market capitalization.
[0107] A first Transformation Weighted Index, TW-1, may directly
access three risk factors: low volatility, value, and momentum.
TW-1 may also provide inherent exposure to the size and market
factors. For each stock, percentiles of the following metrics may
be multiplied: Shareholder Equity for the most recent quarter (a
value risk factor), four-quarter Share Price Change (a momentum
risk factor), and a twelve-month exponentially weighted average
Beta (a volatility risk factor; here the percentile may be
subtracted from 1.00 to emphasize low volatility stocks). To this
product, a subsequent percentile-power transformation may be
applied, using an exponent of two, to produce a weighting value. An
investor may consider most relevant benchmark to be an equal
weighted index because of TW-1's relatively similar investment
capacity and constituent weighting percentages.
[0108] FIG. 6 shows weighting percentage curves for TW-1 and an
equal weighted index.
[0109] A second Transformation Weighted Index, TW-2, may be based
on economic size. TW-2's construction may follow the same
percentile-power process previously described. First, a percentile
transformation of trailing four-quarter Total Revenue may be
performed. Then, the percentile of each stock may be raised by a
power of 10 to create an index with features that resemble a
non-transformed fundamentally weighted index based on the same risk
factor metric and a capitalization weighted index, which may be
considered benchmarks for TW-2.
[0110] FIG. 7 provides a weighting percentage curve comparison of
TW-2 and the two benchmarks mentioned previously. The comparison is
limited to the top 250 holdings to highlight how TW-2 underweights
about one dozen of its largest holdings, relative to its
benchmarks, while weighting the remainder of the top two deciles
more heavily.
[0111] FIG. 8 shows another feature of TW-2: the gradual grade of
its weighting percentage curve, which may be described as the
difference in weighting percentages between adjacent index
members.
[0112] A third Transformation Weighted Index, TW-3, may be a
composite of TW-1 and TW-2 created by multiplying the weighting
values used to set the weighting percentages of TW-1 and TW-2. This
product may be used as the weighting value for TW-3. When produced
through this process, TW-3 may be regarded as high investment
capacity and exposure to multiple investment risk factors.
[0113] FIG. 9 compares the weighting percentage curves of TW-1,
TW-2, and TW-3.
[0114] While preferred embodiments of the present invention have
been shown and described herein, it will be obvious to those
skilled in the art that such embodiments are provided by way of
example only. Numerous variations, changes, and substitutions will
now occur to those skilled in the art without departing from the
invention. It should be understood that various alternatives to the
embodiments of the invention described herein may be employed in
practicing the invention.
* * * * *