Note: Descriptions are shown in the official language in which they were submitted.
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AUTOMATED FINANCIAL SCENARIO MODELING AND ANALYSIS TOOL
HAVING AN INTELLIGENT GRAPHICAL USER INTERFACE
BACKGROUND AND SUMMARY OF THE INVENTION
The present invention relates to an automated tool for modeling the cash
flows of financial scenarios, which typically involve use of at least one
financial
instrument, between various parties to a financial transaction by providing
analysts with the ability to graphically represent the parties to the
transaction,
and their complex interrelationships in a manner that simplifies analysis of
various options for completing the deal. In particular, the instant invention
is
directed to a modeling tool that analyzes various aspects of a proposed
financial
arrangement between parties to the transaction on the basis of information
provided through a high level graphical user interface, and prepares,
competitive
financial proposals, structures the proposals in an optimal manner, and which
may further be used to manage and administer the final transaction to ensure
compliance and delivery of the financial benefits determined by the tool.
The computer has become a critical tool for financial analysts whose job it
is to analyze extremely complex financial transactions such as leveraged
leases.
The computer allows the numerous variables in such transactions to be
manipulated and
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analyzed in a fraction of the time required for these calculations to be
performed by
hand. Of course, in order to allow a computer to perform useful functions,
whether
the area is financial analysis or virtually any other subject, software
designed for the
particular application is needed. Such software is often referred to as a
"tool."
Certain software tools for financial analysis of complex transactions have
been
developed; however, they have inherent limitations and are very difficult to
use for a
number of reasons, including, for example, their inflexibility in altering
existing models,
their requirement of complex commands and codes for building and modifying a
proposed model, and their inability to manipulate a financial structure at the
higher
level of an overview. The invention described herein was designed to overcome
the
problems with these earlier tools and represents a major advance in the field
of
financial engineering and analysis. The invention incorporates extremely
sophisticated aspects of computer aided design (CAD) resulting in a graphical
user
interface unique to financial analysis. As a result, an analyst using the
invention is
able to quickly and easily analyze many different potential scenarios and to
determine
optimal terms for the particular transaction under consideration. For example,
this
novel approach gives the analyst the ability to see partial results when
building a
model, provides the financial analyst with dynamic overviews (pictures) of the
financial
structure that can be directly manipulated to alter the financial structure,
and provides
an object-oriented distinction between high level structure and financial
details which
allow the user to defer details until they become available or relevant.
As described in greater detail below, an important part of the invention is a
computer software engine which has been designed to automatically obtain and
generate information relating to a particular financial transaction or
scenario in
response to inputs from the user. The software engine and the CAD-like
graphical
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user interface have been designed to work cooperatively together in order to
create a
graphical representation of the particular transaction or scenario on the
screen of the
analyst's computer. The system is designed to allow the analyst to cause this
graphical representation to be manipulated, modified or revised so that
information
useful to many different aspects of the transaction or scenario can be quickly
and
easily obtained. The end result is a system that is easy to use, extremely
flexible and
far more efficient than prior financial analysis tools.
There are many automated financial engineering and analysis tools currently
available for use by analysts to determine various components of a financial
transaction and to optimize the transaction based on the particular data
associated
with the parties to the transaction. One such well-known tool is provided by
Warren
and Selbert, Inc., of Santa Barbara, California. and is referred to as "ABC".
ABC has
been used by analysts to generate various alternatives within the constraints
of a
particular financial instrument and optimize the results so that analysts can
generate a
deal that is acceptable to all parties to the transaction. One such commonly
used
financial instrument is referred to as a multiparty leveraged lease. There are
various
other proprietary systems that provide such automated financial analysis.
However, all of these known systems suffer from numerous disadvantages. For
example, the ABC program, and others like it, require the use of complex
commands
and codes for building and altering a proposed model. Moreover, the models
typically
must be built prior to having the ability to view any intermediate results.
This, in
combination with the complex programming-like language that is required,
results in a
very long learning curve for analysts who use the tool. Furthermore, the
model, once
built and run, does not typically enable the analyst to easily change
variables or to
easily view the resulting change in the transaction.
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A primary source of these problems is the complex and inflexible user
interface
typically associated with these known tools. Another problem with such prior
art tools
is that they do not enable a user to model the financial deal visually and
mathematically and in a manner which enables interfunctionality and dependency
between the visual model and the mathematical model. As a result, the tools
currently in use provide limited ability to deal with higher levels of
complexity and the
ever expanding universe of evolving financial products in use today, and which
will be
used in the future. Additionally, the inflexible interface makes it very
difficult for
different analysts to be able to discern the exact relationships and variables
of a
model that another analyst may have been manipulating when the model was being
built and later modified.
To overcome the above and other shortcomings with prior art financial
modeling tools, the present invention provides a much more user friendly,
flexible tool
incorporating easy to understand graphics and interfaces to enable more
efficient and
practical application of the tool. To that end, the invention provides a
financial
modeling tool that addresses model complexity with a graphical CAD-like
approach to
financial and/or mathematical modeling, which facilitates, among other things:
the
ability to see partial results while building a model; a short learning curve;
the ability to
make changes when the user views the results of the analysis; flexible "point
and
click" interfacing; easy handling of indexed data; integrated and automatic
handling of
certain variables, e.g., taxes and accrual; menu of building blocks, e.g.,
loans, rents,
fees, purchases, etc.; menu of built in reports; and an interactive and
intelligent
graphical representation of the model.
In accordance with an important aspect of the instant tool, a software engine,
hereinafter referred to as "engine", is provided in the tool and is programmed
to
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automatically obtain and generate information on a financial scenario in
response to
the user creating a graphical representation of the scenario with the CAD-like
user
interface. In other words, the manipulation of the graphical user interface to
generate
a visual representation of the scenario automatically results in the
generation of
5 information, such as formulas, objects, templates, timelines, calculations,
constraints,
parameters, optimizable parameters, cash flows, reports, or any other suitable
information that is helpful in modeling the scenario represented by the visual
representation created by the user using the CAD-like interface. The
information
generated preferably at least partially model at least a portion of the
scenario. After
drawing a scenario, such as a proposed financial deal, using the interface,
the
interface enables the user to enter data and formulas, edit the information
automatically generated by the engine in response thereto, and to further
define the
scenario in a manner which enables the engine to fully model and analyze the
scenario. Once the scenario is fully modeled, the tool gives the user the
ability to
instruct the engine to attempt to optimize the scenario, either directly or by
creating
formulations to be optimized and passing the formulations to a separate
optimizing
program. Once the deal is optimized, the results can be viewed by the user
using the
interface. The scenario can also be modified by the user and new results based
on
the modification can be viewed. When the visual representation of the scenario
is
modified, the engine automatically modifies the information previously
generated in a
manner which corresponds to the modification to the visual representation.
In accordance with a main aspect of the instant invention, a financial
transaction modeling and analysis tool is provided which includes: a graphical
user
interface which enables a user of the tool to create a graphical model of a
financial
scenario, generally including at least one financial transaction, on a display
screen;
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and an engine operable, in response to creation of the graphical model, to
generate
information which at least partially models at least a part of-the financial
scenario
using information collected by the engine during creation of the graphical
model.
The graphical user interface preferably enables the user to create party
graphics respectively representing parties to the financial scenario, and to
generate
financial instrument graphics representing financial instruments, wherein each
financial instrument graphic connects two of the party graphics. The party
graphics
and the financial instrument graphics define the graphical model of the
financial
scenario. Preferably, the financial instrument graphics indicate a direction
of flow,
relative to the financial instrument represented thereby, between the parties
connected by the financial instrument graphic.
In accordance with an important aspect of the instant invention, the engine
generates, in response to the creation of a graphical model, an instrument
information, such as an instrument object or template, for each of the
instruments in
the graphical model. Once an instrument is defined, the graphical user
interface
enables the user to interact with the instrument information, such as adding
scenario
specific instrument data to each of the instrument objects generated by the
engine.
The instrument data entered in connection with the instrument object
constitutes
either a fixed part of the financial scenario or a variable part of the
financial scenario.
The graphical user interface also enables the user to enter and define date
information relating to the financial transaction for use by the engine.
Preferably, the
graphical user interface is operable to display the date information in
graphical form
on the display screen. The tool preferably enables the date information to be
entered
using a natural date language, wherein the engine is operable to process the
date
information from the natural date language.
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In accordance with another aspect of the invention, the graphical user
interface
enables the user to modify the graphical model of the financial scenario, and
the
engine is operable, in response to the modification of the graphical model, to
modify
the information previously generated in accordance with the modification of
the
graphical model.
In accordance with another aspect of the invention, the engine is operable, in
response to the creation of the financial instrument graphic, to define roles
for parties
represented by the party graphics connected by the financial instrument
graphic,
wherein the roles are used by said engine to define the parties interaction
with the
financial instrument represented by the financial instrument graphic when
modeling
the financial scenario.
The engine is preferably operable to determine and display an optimal solution
or result for the financial scenario relative to at least one of the parties
thereto, and to
calculate optimal values for each of the variables defined by the instrument
data
based on the optimal solution.
The financial transaction modeling and analysis tool of the instant invention
preferably includes an extensible library of predefined financial instruments,
and the
graphical user interface enables the user to select and use one or more of the
predefined instruments during creation of the graphical model of the financial
scenario. In other words, numerous common and canned financial instruments are
provided to the user to facilitate easy modeling of common transactions that
may be
used in financial scenarios.
In accordance with another aspect of the invention, the engine is operable, in
response to creation of each of the party graphics to generate a party-
specific
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information on the party, and the graphical user interface enables the user to
retrieve
and modify the information in the party-specific information.
In accordance with another aspect of the invention, the graphical user
interface
includes a worksheet section, also referred to herein as "smart paper," which
enables
the user to input scenario information which is independent of or
supplementary to the
date and instrument information relating to the financial scenario, and the
engine is
operable to use the scenario information when modeling the financial scenario.
Preferably, the instant tool includes a formula language for use in creating
the
scenario information, wherein the formula language includes a library of
predefined
functions and keywords which can be used by the user when creating the
scenario
information.
The worksheet section is preferably a non-cell based, outline based interface
for inputting data and formulas in an outline format. More particularly, the
worksheet,
also called "smart paper" herein, is a non-cell based calculation interface
wherein
references are based on a hierarchical outline rather than a position
reference. In a
preferred embodiment of smart paper, the interface enables one formula per row
to
be defined in an outline-type format.
The engine is preferably operable upon entry of scenario information, such as
deal formulas, in the worksheet section to establish links between related
scenario
information and between scenario information and date information, thereby
establishing a dependence therebetween, and further wherein the engine is
operable
to use the links when modeling the financial scenario. Preferably, the tool
includes a
library of predefined worksheets for use in the worksheet section, and the
graphical
user interface enables the user to select predefined worksheets from the
library for
use in the worksheet section.
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The instant tool also enables a plurality of possible outcomes to be modeled
based on different information provided by the user.
In accordance with yet another aspect of the invention, the graphical user
interface is presented on the display screen in a book-like configuration in
which a
plurality of different sections of the graphical user interface are
represented by
different chapters in the book-like configuration, each of the chapters having
a tab
graphic associated therewith, wherein upon selection of the tab graphic by the
user,
the user interface is operable to display the chapter associated therewith.
Preferably,
the tab graphics are located along a side of the display screen, and each
chapter may
include a plurality of pages, the pages having page tab graphics which are
also
displayed to the user when a chapter having the pages is selected by the user.
Preferably, the graphical user interface enables the user to view two of the
chapters simultaneously in a split-screen format on the display. The engine is
preferably operable to update information in each chapter in response to
changes
made by the user in a chapter.
In a preferred embodiment of the graphical user interface, the chapters
include
a diagram chapter for creating the graphical model, a parties chapter for
providing
data relating to the parties, a time chapter for viewing and editing dates
associated
with the financial deal, an instruments chapter for viewing and editing
instrument data,
a worksheet chapter for enabling the user to define scenario information or
formulas
relating to the financial scenario, an optimization chapter for use in
optimizing the
financial scenario, a payment chapter for viewing payment flows in the
financial
scenario, and a reports chapter for enabling reports to be generated relating
to the
financial scenario.
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BRIEF DESCRIPTION OF THE DRAWINGS
These and other objects, features, aspects and advantages of the instant
invention will become apparent to one skilled in the art upon review of the
detailed
5 description of the invention provided herein when read in conjunction with
the
appended drawings, in which:
FIG. 1 is a block diagram showing the major components in the modeling and
analysis tool of the instant invention;
FIG. 2 is a flow chart showing the main functions and steps involved in using
10 the modeling and analysis tool of the instant invention to model and
analyze a
financial scenario;
FIG. 3 is a flow chart showing the main steps used to create a graphical model
of a financial scenario, in accordance with the instant invention;
FIG. 4 is a flow chart showing the main steps used to create a worksheet, also
referred to as "smart paper", for use in connection with modeling of the
financial
scenario, in accordance with the instant invention;
FIGS. 5-12 show, in a split screen format, exemplary information that is
automatically generated by the engine in various chapters of the instant tool
in
response to creation of the exemplary graphical representation of a financial
scenario
shown in the Payment Diagram chapter.
FIG. 13 shows a graphical diagram of an exemplary financial deal created in
accordance with the instant invention;
FIG. 14 shows a party graphic being made in the parties chapter as a first
step
in modeling the deal of Fig. 13, in accordance with the instant invention;
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FIG. 15 shows a further step in creating a graphical modeling the deal of Fig.
13, wherein two parties and a financial instrument are shown, in accordance
with the
instant invention.
FIG. 16. shows date information related to the exemplary deal of Fig. 13 being
displayed in the time organizer chapter of the graphical user interface of the
instant
invention.
FIG. 17 shows another view of the time organizer of Fig. 16, where an early
buy-out option is displayed;
FIG. 18 shows a view of the instruments chapter containing data relating to
the
exemplary deal of Fig. 13;
FIG. 19. shows an enlarged, partial view of the display screen of Fig. 18,
wherein the interest rate is being modified;
FIG. 20 shows a view of the smart paper chapter of the instant invention
containing information from the exemplary deal of Fig. 13;
FIG. 21. shows the constraints sub-chapter of the optimization chapter of the
instant invention, containing information from the exemplary deal of Fig. 13;
FIG. 22. shows an exemplary report produced in the reports chapter of the
instant invention based on the exemplary deal of Fig. 13; and
FIG. 23. shows the payment organizer chapter of the instant invention
containing information on the exemplary deal of Fig. 13.
FIGS. 24-29 show example uses of the smart paper feature of the instant
invention.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
Referring now to the drawings, Fig. 1 shows an overview of the main elements
which comprise a preferred embodiment of the financial scenario modeling and
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analysis tool of the present invention. More particularly, as shown in Fig. 1,
the tool
includes a user interface 12 which preferably enables both builder users 16
and
end users 18 to interact therewith, a software engine 14, an optimizer system
20,
which is preferably a software package known as CPLEX Optimization (version
6.0)
5 offered by CPLEX, ILOG CPLEX Division, but any other suitable optimization
software
may be used, file I/O and support functions 22, output device(s) 26 such as a
printer,
and a hard disk 24 or other storage device for use in storing information and
data
provided with the tool 10 and input by the users thereof. The engine 14
performs all
calculations when modeling a deal using the tool, including parsing of the
formula
10 inputs. The engine 14 also reduces the data representing the deal into an
abstract
form for submission to the optimizer 20 in order to perform optimization
functions for
the deal. The user interface 12 and the engine 14 are the main elements of the
present invention and will be described in greater detail below.
In order to enable a better understanding of the instant invention, the
following
glossary of definitions are provided for terms commonly used herein to
describe the
instant invention:
Smart Paper - is one of the chapters in the user interface of the tool. Smart
Paper is a non-cell based calculation interface wherein references are based
on a
hierarchical outline as opposed to a positional reference. Smart Paper is also
referred to herein as a "worksheet."
Party - represents a potential (or actual) participant in a financial
transaction
or scenario, and as such its meaning is close to that of colloquial English.
Parties
connect to the roles of instruments to define the financial interactions among
the
parties.
Instrument - is a tool object that encapsulates an atomic financial
transaction
among a pair of parties, including the tax consequences and classification of
the
transaction (e.g. rental payments).
Role - is a party connection point of an instrument that defines how the party
interacts with the instrument.
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Key Date - is a globally available date defined by the user in the Time
Organizer.
Date Stream - is a chronological pattern of dates that defines both discrete
dates and their relationship to time periods.
Timeline - is a globally available Date Stream defined in the Time Organizer
that can be used for synchronizing payments and data throughout a user's
model.
Decision - represents a "yes or no" option at some point in time that is
available within the transaction being modeled with the tool, wherein the tool
then
tracks both the "yes" and "no" results.
Outcome - is the result of some specific set of assumptions regarding
Decisions, i.e. a specific assumption as regards the "yes" or "no" of each
Decision
(see also ACOE below)
Alternative Courses of events (ACOE) - is the full set of possible Outcomes
in a model, all of which are active within the model. For example, a deal or
scenario
may include the leasing of an airplane over 20 years where the lessee has the
option
to buy the plane after 10 years. One outcome of the case is the 20 year lease,
the
other would be the 10 year buy out option.
Decision Handler - is the mechanism within Instruments that defines the
action for a "yes" Decision.
Parameter - is a piece of information within a case which has a name, a
mathematical formula, and a value. The value can be a number, date stream,
formula or other item.
Case - A case is a single file created with the tool which has all the
different
elements of a single deal or scenario.
Referring now to Fig. 2, there is shown a general overview of the main steps,
according to a preferred embodiment of the present invention, which are
followed
when using the tool 10 to model and analyze a financial scenario, deal or
transaction.
As will be described in greater detail below, the tool 10 provides a graphical
CAD-like
interface which is used to model the flow of financial instruments and data
between
various parties to a financial scenario, including individual, corporations,
institutions
and/or the like. In accordance with the instant invention, the tool enables
users to
visually define the parties involved in the scenario and, for example, the
flows of
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money and assets in the form of a graphical model of the scenario. Parties are
preferably represented by boxes which display the name-of the party. Arrows
are
preferably used to represent the flows of instruments. Once the model is
defined in
the tool in graphical form, the specifics of each party and the flows are
further defined
in various interfaces until the model is fully defined.
If the model as defined satisfies the requirements of all parties involved,
the
tool provides an interface which enables the user to create various reports
relating to
the model generated for the scenario. These reports include, for example, the
flow of
instruments and assets over various time periods. On the other hand, if
variables
exist in the scenario based on requirements of the parties, the tool enables
the
scenario to be optimized. For example, the deal may require that a party
obtain a
return on investment of at least 5%. The party may desire an even greater
return
provided all other aspects of the model of the scenario are satisfied. Such
requirements are known as constraints of the model. The process of
optimization
involves creating the best model which satisfies all such constraints and
determines
the best possible model based on the requirements and goals of the parties.
The
instant tool enables optimization against a number of constraints that may
exist in the
scenario.
The tool operates in two basic modes: build mode and end user mode. In build
mode, the user creates the definition of certain aspects of the tool, such as
creating
instruments which model real world financial instruments. These instruments
are then
stored in the tool for use by end users when modeling a scenario using the
tool. In
other words, the builder user provides a library of "canned" instruments which
can be
used by the user to more easily and efficiently model the scenario with the
tool. The
instruments involve a set of inputs and calculations based on those inputs.
The end
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user incorporates the built instruments into a model and supplies the real
inputs
corresponding to the actual deal that is being modeled. The build user mode
also
enables the builder user to create calculation templates to be used by the end
user in
conjunction with various instruments.
5 Fig. 2 illustrates the steps performed by the end user when using the tool
to
model a scenario. More particularly, when a deal opportunity 28 is presented
to a
user of the tool, the first step 30 is for the user to draw a graphical
diagram of the
scenario using the CAD- like user interface section of the tool. Once the
diagram is
drawn, the next step 32 is to define and modify dates relating to the
scenario. Once
10 the dates are defined, the next step 34 is for the user to modify data and
numbers in a
worksheet section, also referred to herein as "smart paper", in order to
provide all of
the information necessary to model the deal. If the deal is determined to be
acceptable in step 36, the user can generate reports (step 40) using a reports
section
or chapter of the tool, and then the scenario or deal can be presented (step
46) to the
15 client or the person contemplating participating in the deal. If the deal
is not
accepted in step 36, but optimization is not desired or possible based on the
particular
deal, the user can review all of the input (step 44) and edits or modify the
deal as
needed to make the deal acceptable. If optimization is desired, the user can
run the
optimizer (step 42) and then review the optimized deal. If the optimized deal
is then
acceptable, the user can run reports and present the deal to the client (steps
40 &
46).
As indicated above, one step involved in modeling a deal using the tool of the
instant invention involves creating a party diagram (step 30) or graphical
model of the
deal. Fig. 3 shows flow chart of the steps involved in creating this graphical
model.
Similarly, Fig. 4 shows the preferred steps involved in creating smart paper
or a
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worksheet in step 34 of Fig. 2. It is noted that the flow charts of Figs. 2
and 3 are self-
explanatory. Thus, no further explanation of the particular steps in the flow
charts of
Figs. 3 and 4 are provided at this time. However, further details regarding
model
creation and smart paper use are provided below.
THE GRAPHICAL USER INTERFACE (GUI)
The following is a description of the functionality of the present invention
in
terms of the graphical user interface (also referred to herein as "GUI"). It
is noted
that, in accordance with the instant invention, the GUI may be implemented
using
Windows 98, Windows NT, MAC, or it may be Web-based. In other words the
instant
system may be implemented on any suitable standalone, networked or web-based
platform. In a preferred embodiment, the tool can be implemented using the
following
hardware, however any suitable hardware may be used in accordance with the
invention:
- A Pentium compatible machine running Windows NT 4 with service pack 3
- 64 Megabytes Ram
- 45 Megabytes hard disk space
- Cplex Optimization software version 6.0
- Actuate reporting modules including all DLL's and OCX's (Actuate is a
commercially available reporting technology)
- Version v4.72.2106.4 or later of ComCtr132.dII
The instant invention preferably uses a book-like display as a viewing device.
More particularly, the invention displays its data as pages in a familiar-
looking tabbed
notebook configuration on the display screen. Each tab of the notebook
represents a
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"Chapter", corresponding to one part of system's functionality. Users can work
with
one copy of the book visible (see Figs. 14-18 and 20-23), or with two copies
visible at
once (see Figs. 5-12). Viewing two copies of the book lets the user see
related
"pages" in both chapters simultaneously. When two book copies are visible, the
books can turn each other's pages, so the user can click on a model component
in
one book to see more detail about that component in the other book.
Preferably, the
user should never be more than a couple of clicks away from seeing any part of
the
model or system. The GUI is designed so that the user never feels lost inside
the
program.
The first chapter in the GUI is the Payment Diagram (see Figs. 14 and 15),
which
provides a graphic boxes and arrows overview of the relationship among parties
and
instruments, as well as the payments the parties make to one another. This is
valuable because ideas for financial structures are often presented as boxes
and
arrows drawn on paper. The payment diagram provides an analogous
representation.
However, as explained herein the payment diagram represents much more than
simply a graphic diagram. The user can control or create the program's model
by
modifying the picture or graphical representation of the deal shown in the
payment
diagram. An advantage of this approach is that there are no separate languages
to
learn and no complicated controls to master. The GUI provides for
instantiation and
deletion of parties. The user can drag-and-drop a box onto the diagram to
create a
new model participant, and can delete a box to remove a model participant. The
GUI
provides for instantiation and deletion of arrows representing financial
instruments
which, in turn, represent payments made by one participant to another, and/or
represent the tax effects of those payments. The user can rearrange who pays
what
to whom by moving the instrument arrows from one box to another. The GUI also
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enables selection of an overview by possible outcome. In other words, in
transactions
with several contingencies, it is often helpful to show only those payments
contingent
on a particular decision path. The user can rearrange the participant boxes on
the
diagram using a drag-and-drop method. The connected instrument arrows follow
automatically in response to the drag-and-drop operation. The GIJI provides a
list of
pre-defined instrument types immediately upon creating the instrument. Double-
clicking on an instrument and party tells the system to show detailed
information
about that instrument or party. Clicking the second mouse button offers a list
of
actions appropriate for the instrument or party clicked. The GUI also provides
navigation to the Payment Organizer (preset for specified party) via the
second-
mouse-button menu
The next chapter is the Parties chapter. The program simulates "parties,"
which are entities that participate in a financial transaction. It provides
automatic
creation and deletion of party-specific information. This party-specific
information
includes items, such as tax rates, fiscal-year-ending months, or yield
requirements.
The GUI provides support to the Payment Diagram for party detail information.
The
GUI also provides the user with a standardized and extensible location for
party data.
Each party can have individual tax attributes, paying different kinds of taxes
to
different governments (U.S. states or foreign countries).
The next chapter is the Time and Decision Organizer, which is also called
"Time Organizer" in the program for short (see Fig. 16). In this chapter, the
GUI
provides users with control of globally available (case-wide) key dates,
timelines and
outcomes (from decisions). This is important because: (a) transactions often
require
numerous payments to be synchronized; (b) payments are often contingent; (c)
contingencies can interact or cancel each other out; and (d) having all these
in one
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place, and graphically editable, can make a transaction much easier to explain
and
understand. In addition, the GUI provides the ability to create, delete, and
edit Key
dates, timelines and decisions. This is important because: (a) assumed closing
dates
usually have to change; (b) there are constraints on when important deal
events are
allowed to occur; and (c) deal economics can be enhanced or harmed by proper
choice of such dates. The GUI also provides a graphic overview of key dates.
Also
provided is a graphic overview of instrument payment date streams, aggregated
by
timelines. This lets the user see quickly whether the model's payments are
properly
synchronized. The system also provides graphic control of decision interaction
to
create and delete mutually exclusive outcomes. The user can thus see whether
decisions occur in the proper order, and that they are also properly
contingent on
each other. The GUI also provides the user with control over the global
default for
"Calendar" (conventions used for counting the number of days in an interval).
This
makes it easy to modify a model's calendar convention for use in Europe, Asia,
or the
U.S., in addition to following the particulars of any model. The GUI also
provides a
"default" timeline to synchronize newly created Instruments' activities
automatically.
The next chapter is the Instruments Chapter (see Fig. 18). Instruments are the
containers for the systems built-in financial expertise. They handle a lot of
the routine
bookkeeping that financial models demand, leaving the user free to concentrate
on
the nonroutine business aspects of the transaction. The GUI of this chapter
provides
controls for creation and definition of payment streams between parties, and
the tax
effects of such payments on the paying or receiving party. An expandable
library of
instruments keeps the system up-to-date. Instruments have clearly separated
and
protected "input" and "output" sections, so all users can rely on their
integrity. The
system connects parties (badges) to payment streams via role definitions and
allows
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the user to switch parties. This is how the model knows which parties pay or
receive
the payments the instrument defines. This chapter also connects payment
streams to
payment organizer classifications (cash and income badges) via role
definitions and
allows users to change the classification. This is how the model puts labels
on each
5 payment, so that it can show up in an informative place on summary reports.
The system allows paying and receiving parties to have distinct
interpretations of
the instrument payments, tax effects, and classification. This is an important
feature,
because tax law often makes these distinctions. Instruments contain pre-built
and
pre-tested Smart Paper computation sections, making the system more reliable
and
10 freeing the user from having to do repetitive programming. The system
automatically
activates and deactivates instrument Smart Paper computation sections
according to
the user's selection of role information for the parties. Thus, sections not
in use
remain visible and available and do not distract the user. Glyphs are used to
highlight
the relationship between role specifications and the calculations. Specific
items
15 representing payment or receipt of funds, or of taxable income or
deductions, are
identified with symbols that make those items easy to find. The system also
allows
the user to change the name of the instance of the instrument. These name
changes
show up on the party diagram and the payment organizer, making both of these a
lot
easier to read and understand. In addition, model pieces can be named with the
20 names that other transaction negotiators are using, making communication a
lot
easier. The system also automatically generates the parallel payment streams
for
different outcomes using handlers for each possible decision. Each instrument
can
thus generate different specific payments depending on the state of various
contingencies. This is important because exercise or non-exercise of certain
options
can mandate different behavior on the part of the same instrument. The system
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allows the user to modify the handlers' termination behavior. Thus, special
cases do
not require modifications to the system. In addition, the system uses Smart
Paper
"protection" modes to preclude user corruption of instrument functionality,
but
otherwise allows users the ability to modify instrument Smart Paper. Thus,
users can
be confident that canned (and therefore tested and reliable) model parts are
being
used, instead of model parts which may not be correct given an unforeseen
peculiarity
of a particular model.
Users can supply their own formulas. Such formulas are clearly marked, so that
other users know they have to validate the formulas before using the model.
The
system also provides canned calculations for specific types of financial
elements (e.g.
rent, loans, etc.). These canned calculations cover a very large fraction of
the
payments users would run into when modeling a financial scenario. Thus, users
will
spend little time having to invent new payment mechanisms. In addition, this
set of
canned calculations is contained in an expandable library, so as the industry
changes,
additions can be added to the library to keep it up to date. The system
provides the
user the ability to customize the calculations, making use of the invention a
lot easier.
Pre-defined reports of the instrument results are also provided. As a result,
explanations of what an instrument is doing are only a click away. The system
also
allows the user to specify that an instrument only exists when a certain
decision is
assumed. Contingent instruments can be put into the model and will thus
automatically be properly handled. The system also supports automatic decision
and
outcome creation for termination values and other make-whole payments. These
contingency dates are too numerous to include as separate instruments or
outcomes,
and so including them here provides a compact way of computing them as a
class.
In addition to general financial instruments, the system may also include
instruments
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for advanced corporate finance operations, such as mergers, acquisitions and
the
like.
The next chapter is the Smart Paper chapter (see Figs. 20 & 25-29). Smart
paper
is a powerful non-cell based calculation interface wherein references are
based on a
hierarchical outline as opposed to a positional reference. Unlike spreadsheet
programs, smart paper is non-cell based and does not rely on a positional
reference
for use in calculations. Smart paper is the bridge between the ease-of-use
that
spreadsheet users depend on, and the power of financial and optimization
packages.
It makes computations visible, understandable, and accessible. Users do not
need to
be computer programmers or learn to work as programmers in order use the
system
effectively and efficiently. The system has enhanced data capabilities, which
automatically perform a lot of rote date-related manipulation that makes
spreadsheets
hard to create and even harder to modify. Thus, the system provides
capabilities
normally found in relational database packages. The smart paper chapter is the
component where the user specifies the computations he wants the system to
perform. Users can define values directly, or they can provide a formula which
will tell
the system how to compute the desired values. Smart paper provides user
control
over outline-like (i.e. tree-like) format of parameters and several nested
layers of
headings. This makes Smart Paper work much more readable, and provides a
mechanism for the system to resolve (or ask the user to resolve) formula
ambiguities.
Smart paper allows the user to create one or more sheets of smart paper.
Related
computations can be kept together, and unrelated ones can be segregated. Tabs
are
provided for moving among sheets of smart paper. As a result, users do not
feel lost
in the program and are able to find quickly what they are looking for using
the GUI.
The GUI provides controls for viewing "formulas" versus "results" or both.
Thus, users
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can get immediate feedback as to whether they have properly specified a
formula.
The GUI provides editing capabilities for headings and parameter names, as
well as
provides access to the template library and instantiation of templates. Smart
paper
defines parameter name scope and parameter index scope automatically via
outline
format. This resolves many "name clashes," which would be otherwise inevitable
in a
model of any size. It also provides a view of dependency relationships among
parameters. Users can thus identify information relationships among their
parameters. Also provided is general support goal-directed "search" for
setting
parameter values. The system automates some of the trial-and-error involved in
changing parameters' values in order to produce the desired answer. It also
allows
the user to specify formulas that define (dynamically) activation/deactivation
of sub-
trees. This gives models the ability to be "context-sensitive," responding
sensibly to
particular values of input data. It also provides capability for import/export
of data and
formulas from/to Microsoft EXCEL or the like. Models can be created using the
system and the system will automatically reconstruct the model in Microsoft
EXCEL.
The GUI also provides a date stream bar that always displays the index of the
uppermost indexed stream. The important pairing between dates and date-indexed
data is therefore always visible on the screen. This eliminates a lot of
meaningless
clicking back and forth to keep the index visible, and eliminates the need for
a lot of
"split-screen" display. The GUI supports multiple data-entry modes: simple-
edit, full-
edit and rapid-entry. These modes make constructing models easier and faster.
Also, smart paper items (e.g. headings, templates, formulas, indexes) can be
changed into each other. Tool bar and menus provide editing to morph, promote,
demote, insert, and delete operations. This eliminates the need for learning a
lot of
jargon. Instead, all the alternatives are displayed, and the user can choose
the most
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logical one. The system also provides graphic feedback as to the type of
indexed
data represented by parameters. Moreover, in accordance with the invention
formulas for dates resemble "English-language" instruction. Formulas can be
printed,
providing human-readable documentation for a model. This differs significantly
from
spreadsheets, wherein formulas consist largely of a list of data locations
instead of
identities, resulting in a nearly useless documentation tool for a human. The
system
creates templates as white-box functions which allow the user internal access.
Thus,
there is no need to refer to external, written documentation to figure out
what a
template/function is doing, because all the code is right there, visible.
In addition, smart paper has an extremely powerful formula language (with
input/edit wizards). This formula language automates many tasks which are
routine in
finance but which are now cumbersome for spreadsheet users. The formula
language, which is described in greater detail below, has the following
exemplary
features:
= Uses Prefixes attached to formulas to define special types of parameters
for -
= Accrue: Automated accrual over time periods
= Table/Interpolate: Data Tables (regular and interpolated)
= Advance: Advance payments
= Arrears: Arrears payments
= StartDates: Date streams that represent the start of time periods
= EndDates: Date streams that represent the end of time periods
= List: Named members of an ordered set.
= ActsLike: Ties one parameter's type to the type of another parameter.
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= Uses Prefixes attached to formulas to define goal-oriented setting of
parameter values
= Optimize: To have values set by the Linear Programming optimizer.
= Search: To have the system set a parameter value based on a defined
5 target result.
= Single formula defines entire array of data.
= Array data is keyed by index parameter. Thus, there is provided what
amounts to a relational database structure, without making users learn a
bunch of relational database jargon.
10 = Intelligent translation of data from one index to another based on the
dates
and the prefix type.
= Relational database capability without making users use a separate
program or even learn relational database jargon.
= Automatic maintenance of minimal name expansion for parameter
15 references. Names are thus presented as short as possible, keeping the
mental burden down and reducing the possibility for confusion.
= Intuitive, English-like and flexible syntax (and wizards) for creating date
streams. These date streams can thus be easily changed and maintained,
unlike spreadsheets, which are very rigid in their handling of this
20 information.
= Parameter labels define the parameter name for formula references. This
is different from spreadsheets, in that, in spreadsheets, values are
identified
generally by where they are, not by their names (despite a cumbersome
facility spreadsheets offer for naming cells).
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= Notes can be added to any heading or parameter, and the identify of the
user making the note is recorded. This helps with auditing and
documentation of models.
= Assertions can be added to any parameter. Assertions let a "product
manager" create models and guide future users in the model's use.
= Optimization constraints can be added to any parameter.
= Optimization constraints can be "OR'd" together to make a single constraint
that is satisfied by any one. Users do not need to deal with linear
programming jargon, which is often unfamiliar to them. This makes it easy
to specify commonly desired constraints that are difficult to implement with
binary variables in a strict "linear program" setup.
= An activation formula can be attached to a constraint that makes the
constraint inactive when the formula evaluates false. Thus, constraints can
be "data-driven." This lets model builders build models for less-
sophisticated users, who can operate complicated models by providing
values for variables.
= An activation formula can be attached to a heading to make the sub-tree
(for which it is a root) inactive when the formula evaluates false.
= Glyphs reflect the existence of notes and assertions including the pass/fail
state of assertions. Thus, the user doesn't need to open a parameter in
order to tell whether a note or assertion is inside it.
= Glyphs indicate the protected state (if any) of the parameters.
= Allows for partial null data in an array.
= The "Collect...()" functions let models be defined concretely ("add this to
that") or abstract/symbolically ("add everything labeled principal to
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everything labeled interesf'). The abstract/symbolic capability means that
product managers can write models that stand up to use in many different
contexts.
= An extensive range of mathematical functions for use in formulas(see
below).
= Intelligent/selective recalculation helps program performance.
The next chapter is the Optimization chapter (see Fig. 21). In this chapter
the
system is able to solve mathematical linear programs and other "search for
best
answer" problems. It also provides extensive tools for managing and seeing the
effect
of model constraints. This feature is very important as models get complex,
and the
number of constraints grows to, for example, several dozen. A deterministic,
formula
based model can be used as the basis for an optimizable model: starting with a
deterministic model, the user can simply identify the objective and add
constraints. In
accordance with the invention, there is no need to write a separate,
optimization-
ready version of a model. The optimization chapter provides an overview of all
optimization constraints and parameters in a case and defines the objective
function
for optimization. The system analyzes the optimization instructions and data
contained in a model. It provides diagnostic status indicators for :
= the mathematical type of optimization problem (e.g. linear, integer, non-
linear, etc.);
= the state of the constraints (satisfied or not satisfied). Thus, a
hypothetically
optimal solution can be hard-coded and compared against constraints,
identifying those parts of the hypothetical solution that do not meet the
constraints; and
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= the state of optimization (e.g. optimal, not optimal, infeasible,
unbounded);
In addition, the system gathers all model constraints for viewing on one page.
This is important because constraints are often of definitive concern in tax-
motivated
transactions. The system also sorts constraints by failing, binding, non-
binding, and
inactive. This helps negotiators identify the critical points in their deals,
or helps a
user figure out why his model might fail to provide an answer he would expect.
It also
provides detail results of the values, slack, shadow prices or failure margin
of
constraints. This information helps the user explain anomalous results, or
suggest
ways that financial objectives may be attained at less cost. Also provided is
a simple
algebraic list of all constraints, making it easier to make sure that no
constraints have
been mistakenly taken out or left in. This list can be printed, and becomes an
important "output" for deal participants to examine and approve. The system
also
gathers all optimizable parameters, search parameters, and non-linear
parameters for
display separately on their own pages, helping make sure that the linear
program
model has been set up properly. It also automatically determines whether there
are
any parameters causing non-linearity and thus precluding being solved by the
built-in
linear optimizer The user can then more easily decide how to change the model
to be
solvable by the available optimizer. The system automatically traces the non-
linear
parameters to corresponding optimizable parameters and displays them with the
non-
linear parameter. This helps modelers find linear models that are approximate
solutions to otherwise unsolvable nonlinear problems. The system also allows
users
to specify facets of optimization in a way that is intuitive and easy to
understand.
Constraints are expressed in terms of comparisons and not just formulas. Prior
art
systems treat formulas with constraints as one and the same making it
difficult to
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discern between a formula that is incorrect and a formula which is correct but
not
satisfied in the model. Constraints are entered and evaluated separately from
the
associated formulas making it easy to see where the true problem lies. Results
from
the optimization software (e.g. CPLEX) are likewise translated back into these
terms
producing a result that users can easily interpret. It also provides button
access to
the optimizer. The system automatically converts the model to "optimizable"
form for
the optimizer, and then re-converts the optimizer's solution to code; thus,
optimization
is a transparent process to the user.
The GUI presents user with detailed progress screen and saves the results
back to the user's file. The system also re-evaluates constraints in the
context of the
user's model to provide more useful feedback from optimization. This is
important
because the specific analytical assignment is often to reverse-engineer the
set of
constraints that produced a particular answer. The system also automatically
invokes
Successive Linear Programming (SLP) when needed to solve for a search
parameter.
This saves the user the labor of having to determine that the problem at hand
is SLP
and then perform the SLP by successively invoking the optimizer. It also
automatically
combines point-by-point searching and mathematical optimization, saving the
user the
labor of searching over various valid values of nonlinear data.
The next chapter is the Payment Organizer (see Fig. 23). The Payment
Organizer shows all the payments a given party receives, or taxable income
effects a
party might recognize (contingent on the exercise or non-exercise of a
particular set of
decisions, if there are any). In short, this is the party-specific "bottom-
line." It also
provides user top-level control over payment stream classifications and
summary
report of all payments. The system calculates and summarizes the cash flows
and
taxable income effects of all instruments automatically. It also provides
ability to add,
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delete, rename and reorganize (tree-like) all payment stream classifications.
The
system also provides the capability to filter payment streams according to
party,
outcome, or cash versus taxable income. It also provides capability to view
payment
stream summary according to any ad-hoc date stream specified by the user. Data
5 can be summarized annually, monthly, daily, or even in combination (daily
for the first
couple years, annually thereafter). This is enormously difficult to do in a
spreadsheet.
Also, categories can be collapsed to show less detail, or expanded to show
more
detail. Categories can also be expanded to show individual payments contained
in
the category for auditing purposes. Subtotals can be shown on top of items
totaled or
10 below them, with a button-click. This makes reading the reports easier. The
editor for
the symbols is useable in symbolic-definition formulas (i.e.,
"CollectWhatever").
Additionally, the system provides standard financial statements (income,
balance
sheet, funds flow).
The next chapter is Reports (see Fig. 22). The Reports chapter provides the
15 user with the ability to create, edit, view and print model data in reports
that are
useable as explanatory documents. Users do not have to load data into some
other
program for cosmetic improvements. A report can consist of several sections
(each
of which could otherwise be a freestanding report of its own, all arranged on
a single
report's page. The system provides the ability to create report "sections"
(report
20 parts), and provides the ability to drag and drop report sections on a
layout editor to
organize above/below and left/right arrangements of report sections. It also
provides
for push-button pivoting of individual sections of a report so that dates
and/or labels
can be shown vertically or horizontally. The system automatically creates
headings
for data rows/columns based on parameter names. The user can change these
25 names. It also supports user-driven and automatic creation of nested super-
headings
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(i.e., headings running across several columns). This makes reports more
readable
because it groups data into fewer, more easily understandable chunks, and
helps the
report reader find a particular column of interest more quickly. It also
provides titles,
headings, footnotes and control over data format. Reports can thus be
"customer-
ready" without having to be imported for clean-up into commercial word-
processing or
spreadsheet software. The system also supports the creation of sets of many
reports
to be printed or viewed. This is important because the "story" of a financial
product
often requires several related reports. It may optionally bind reports to user
models
(so that they are stored with the model), or to instrument definitions (so
that they are
stored with the instrument definition and thus available in every model in
which such
an instrument is used). Reports are language-independent: thus output can be
in a
language other than the system user's working language. The user does not have
to
speak the output language.
The next chapter is Template Builder. A "template" is a white-box piece of pre-
built and pre-tested Smart Paper. A library of such templates provides a large
part of
the built-in financial knowledge that users can draw on. This makes it
worthwhile for
an organization to invest in well-constructed Smart Paper pieces that can be
reliably
shared. The GUI provides the ability to create Template definitions to be used
for
instantiation. Generally, only specially trained "builder/users" would invoke
the
Template Builder. It provides user access to protection controls over
read/write
specifications of parameters. It also allows the builder of templates to work
in the
same manner as in regular Smart Paper. Thus, they are familiar in appearance
and
do not require users to learn how separate components look and work. The
system
provides linkage to the currently active model so as to provide useful
feedback to the
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builder. It also allows the builder to create, edit and delete template
definitions, and to
make these definitions available to the larger user community.
The next chapter is Instrument Builder. This chapter provides a special
"build"
mode for instrument builders to create the definitions of instruments.
Instruments can
be designed to, for example, calculate tax effects for numerous governments
(U.S.
states, foreign countries) simultaneously. Tax instruments can be designed to,
for
example, handle complex multinational tax interactions (foreign tax credits
and the
implications of various international tax treaties).
The next chapter or feature contains Main Menu Items. These items include
an extensive, full-featured on-line "help" system which provides documentation
for
system features and behavior, and also provides financial examples which can
serve
as a tutorial; options for adjusting the program's appearance (horiz/vert
tabs); and a
program that follows the Windows NT "Control Panel" settings for cosmetics
(dates,
mouse clicks).
In addition to the above, there are some general features found in several of
the chapters or components of the system described above. For example, print
previews are provided for enabling the user see output before committing it to
paper,
thereby saving time, paper, and aggravation. In addition, general cosmetic
formatting
capability is provided which is similar to that found in commercially
available word
processing or spreadsheet programs.
Another chapter or feature of the invention provides the ability to manage
multiple cases. A financial analyst may spend as much time managing and
summarizing the cases he produces as he would spend producing the cases in the
first place. The GUI also provides tree, containment, or list views of the
files. It also
provides an overlapping grouping capability, so files can be treated as a
group in
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addition to individually. The system also provides a mechanism for extracting
key
results for several files and presenting them in a tabular report. It also
provides file
search capabilities based on the contents of the file in addition to the
file's name, as
well as filtering and sorting capability (e.g. show only my files). A "recent
files" section
and "all-files" section is provided. This is important because a great
majority of the
time users work on a single project continuously, and, with this feature, they
don't
have to look through hundreds of files to find one they were recently working
on. The
system intelligently identifies differences between two or more selected
files, making it
easier to explain their differences. It also provides capability to reorganize
files (i.e.
the tree), and the capability to read and add notes to files. Thus, a file's
owner can
protect the file from changes, while letting colleagues look at, and then
attach notes to
the file. In addition, the system provides detail records of file (e.g.
ancestry). This is
important because the great majority of files will probably not be created
anew, but
rather will be modified versions of existing files. The ability to track the
changes that
produced a file is a very advantageous and time-saving feature.
It is noted that not all of the "chapters" discussed above necessarily have a
"Tab" always visible on the GUI. In other words, some of the chapters or
features, i.e.
Template Builder, are accessed through menu items or other suitable means for
enabling the selection thereof.
Referring now more particularly to Figs. 5-12, there is shown an example of
the
Payment Diagram chapter 50, having a graphical representation 52 of a simple
financial scenario involving a two parties (54 and 56) and a "loan" instrument
arrow 58
connected therebetween. In Figs. 5-12 the two book view is used in order to
more
clearly explain the functionality of the invention. It is noted that, in Figs.
5-12, the
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Payment Diagram chapter 50 has a reduced size so that greater information can
be
seen in the other chapters on the right side of the display.
In accordance with an important aspect of the invention, the Engine is
operable, in response to creating of a graphical model, to automatically
create useful
information in certain of the other chapters. More particularly, in response
to drawing
an instrument in the Payment Diagram chapter, such as "loan" as shown in Fig.
5, the
engine automatically generates time lines 62 in the Time Organizer chapter 60.
This
functionality is illustrated in the split screen view of Fig. 5, wherein the
Payment
Diagram 50 is shown on the left side of the display, while the Time Organizer
60 is
shown on the right side of the display. The badged parameter in the instrument
marks the most important cash flow which is displayed graphically in the Time
Organizer. It is noted that the engine uses default data for generating the
time lines
of Fig. 5, and that the user can then edit the information, if necessary, to
comply with
the particular scenario being modeled.
Similarly, Fig. 6 shows an instrument calculation that is automatically
generated
in the instruments chapter 68 in response to drawing of the "Loan" instrument
58 in
the Payment Diagram chapter 50 . Default settings are also used for this
canned loan
instrument, but after it has been created, the user can modify the data in the
instrument chapter as required to correspond with the particular scenario
being
modeled. Thus, by adding an instrument in the payment diagram 50 the engine
automatically generates the instrument definition including related
calculation in the
instrument chapter 68. Fig. 7 shows the badged parameters in the instrument of
Fig.
6. The box to arrow graphic on the left side of the instruments chapter, as
shown in
Fig. 7, indicates the important cash stream which shows up in the cash link in
the
payment organizer and in the time organizer link. The triangles and squares
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combined with the plus and minus signs (also on the left side of the
instruments
chapter) show the tax effect which shows up as the income in the payment
organizer.
Fig. 8 shows the information automatically created in the constraints page of
the optimization chapter 70 in response to drawing of the instrument shown in
the
5 instrument chapter 50. Fig. 9 shows another page, i.e. the optimizable
parameter
page 70a, of the optimization chapter 70 and the related information
automatically
generated by the engine in response to drawing of the "Loan" instrument.
Fig. 10 shows the information (cash) that is automatically generated by the
engine in the payment organizer chapter 72 in response to drawing of the
"loan"
10 instrument in the payment organizer chapter 50. Similarly, Fig. 11 shows
the (Income
- tax effects) payment organizer view which is also automatically generated by
the
engine. The user can switch between the view in Fig. 10 and Fig, 11 by
modifying the
"Payment Type" in the pull-down menu at the top of the Payment Organizer
chapter
72.
15 Finally, Fig. 12 shows the information that is automatically generated in
the
Reports chapter 74 in response to creation of the graphical party diagram in
the
payment diagram chapter 50 shown therein.
Of course, all of the information shown in Figs. 5-12 is only exemplary, and
is
only based on the exemplary graphical representation shown in the payment
diagram
20 50 which has the exemplary loan instrument. This information will, of
course, vary
depending on the particular instruments used with the tool and the particular
application in which the invention is utilized.
EXAMPLE CASE
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The following description provides an example of case or financial scenario
modeled using the tool of the instant invention.
This exemplary case is called a QTE or Qualified Telecommunications
Equipment case. A graphical representation of this exemplary financial
scenario is
shown in Fig. 13. The party LessorNameHere is the client or main focus of the
deal
and is called the lessor. The lessor wants the tax effects associated with
owning QTE
equipment. The party LesseeNameHere, called the lessee, currently owns the
equipment and thus has the tax effects. The lessor proposes a deal to buy the
asset
and lease it back to the lessee thus acquiring the tax effects. The lessee
still gets to
use the equipment. To get the lessee to agree to the deal, a portion of the
money
used to buy the asset goes to the lessee as well. The tool is used, in this
example, to
model the deal from the perspective of the lessor. The company, FeeRecipients,
known as the advisor, has been hired by the lessor to arrange the deal and
thus the
fee is paid to it. Likewise, only the lessor is shown to pay taxes because the
deal is
from their perspective. FIG. 7 provides a graphic representation of this
exemplary
financial scenario or deal. The diagram was created in using the tool of the
present
invention.
The following steps present a high level description of what is happening in
this
deal:
1) The lessor borrows money from the lender (LenderNameHere in the diagram) to
buy the assets.
2) The lessor buys the assets from the lessee as indicated by the HardAsset
and
SoftAsset lines (the direction of the arrow indicates which way the money
flows,
not the asset).
3) The lessee pays rent to use the assets.
4) The lessor pays taxes during the deal.
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5) The lessor pays a fee to the advisor for arranging the deal.
6) At the end of the lease, the lessor sells the assets to another party
(Generic in the
diagram). This is indicated by the residual line.
7) At some point in the middle of the deal, the lessee can buy the assets back
and
terminate the deal. This is illustrated by the PurchaseOp(EBO) line.
Step 1- Draw the diagram as shown in Fig. 13 in the Payment Diagram chapter.
The first step in creating a case involves drawing the diagram shown in Fig.
13
using the Payment Diagram chapter 50 of the user interface. The basic steps
for this
involve adding the various parties to the diagram, as represented by boxes,
and
drawing financial instruments, as represented by directional arrows connecting
the
boxes. Fig. 14 shows the Payment Diagram interface used to create the diagram,
and also shows the result of the first step executed in this example, wherein
a first
party 78 named "LenderNameHere" has been drawn in the Payment Diagram chapter
50 The white area of Fig. 14 is the drawing area where the diagram of the deal
is
created. The tools above the drawing area are used to create and view the
diagram.
For example, the magnifying glasses allow the user to zoom in and out.
This image also shows the general interface for the product. It is noted that
not
all figures herein show the full interface of the full chapter. In other
words, some of
the figures only show an enlarged partial view of the interface or chapter.
The tabs 76
on the left side of the screen are used to navigate around the program to the
different
interfaces or "chapters" of the user interface. Each major step in creating a
deal is
represented by a chapter. The icons under the menu bar are general purpose
tools
used , for example, to save a case to a hard disk or load a new case.
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To do this first step, the user clicks the party tool (the round box with a
plus
sign) and then clicks in the drawing area where he wishes to locate the party.
He can
then select from a list of predefined parties or enter his own.
When the user adds a new box to the party diagram, such as party 78, there is
no specific action in the engine, except for the possible generation of a
party object in
the Parties Chapter. If this is a party that does not appear anywhere else in
the
payment diagram, then the engine adds a new section to the Parties chapter
with two
parameters which the user can then edit and augment. The two parameters
represent, for example, the first month of that party's fiscal year, and the
name of his
tax counsel. This data is reflected in engine parameters to provide
persistence to the
data, and to make the data available to instruments which will be connected to
this
party.
Referring now to Fig. 15, after adding a two or more parties 78, the user can
then begin to add financial instruments 80. The user does this by clicking on
the first
party( the one who will be making payments), and dragging a line to the second
party
(the one who will be receiving the payments). The arrow indicates the
direction the
payments flow. Figure 15 shows this next step with two parties and a single
loan
instrument. When considering the arrows of an instrument line, the loan is a
misnomer because payments or money flows in two directions. The borrower
receives the loan and then makes payments back. However, the convention used
by
this embodiment of the program is to show only the direction in which the loan
is paid
back.
When the user draws an instrument 80 on the Payment Diagram, the
application creates a representative object in the engine to calculate and
generate the
calculations and cash flows for that instrument. More specifically, the client
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application tells the engine General Registry to create a new instrument
object, which
initially is an empty shell. The client application reads in from a data file
the
representation of the instrument that has been saved by the instrument
designer, and
splits this up into graphic and engine data and passes the engine part to the
new
Instrument object. The engine then reconstructs the instrument from this data;
this
includes a hierarchy of parameters and parameter lists, a couple of instrument
party
objects, and a default instrument handler. Each instrument party contains the
role
information needed to create the cash and tax implications for the party at
one end of
the instrument arrow. The default instrument handler contains the information
needed on whether and how to truncate the flows in non-base outcomes. Each
parameter's formula is parsed into its expression objects, and named
references are
registered with the general registry's name reference manager, which, if
possible,
resolves them, so that the parameter's values can be calculated when needed.
As
these references are resolved, links are made between the parameters'
dependency
managers so that changes are correctly propagated through the entire system.
For
each decision that the user has created in the time organizer, the engine
creates an
instrument,handler containing the information on whether and how to truncate
the
flows for outcomes containing that decision. Each handler starts as a simple
copy of
the default handler, but can be changed by the user. The client tells the
engine
instrument object the names of the parties at each end of the arrow. The
engine then
looks in the parties data to find a section of data for that party, which it
then uses to
complete the instrument party role information (e.g. date of fiscal year end).
The
engine instrument synchronizer object then springs into action, generating the
actual
flow parameters for each party and outcome. The instrument party information
is
used to determine which parameters contain the cash and tax flows for that
party.
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For non-base outcomes, the synchronizer searches for the first decision that
terminates the flow, according to the instrument handlers. It then generates a
truncating parameter (if necessary), and a final parameter which it identifies
to the
internal database by attaching badges indicating the party, cash or income
5 classification, outcome, instrument name, other party and tax authority (for
income
flows). The engine internal database recognizes these new badged parameters
and
changes any collected data in (for example) yield calculation templates to
update their
values. This process also enables the payment organizer to update its display
to
show the new instrument.
10 The user continues to add parties and instruments until the deal is modeled
fully as shown in Fig. 13.
Step 2 - Define the dates
Dates and timelines are defined in the Time Organizer as depicted in Fig. 16.
15 In the top portion 82 of this chapter, the user defines single case dates
known as Key
Dates. The user clicks the add date tool (the calendar with a plus sign) and
then
enters a name for the date as well as the actual date. Similar to parties, the
dates are
stored in the engine and can be referenced by other parts of the case. The
other
tools next to the add date tool are used to modify the dates including
changing or
20 deleting a date.
In the bottom section 84 of the interface, the user defines the overall deal
dates called the EventDates. This sets the basic start and end of a deal and
also the
periodicity (annual, quarterly). The user changes the EventDates by right
clicking on
the line and selecting "Edit timeline" from the menu. The other lines are for
visual
25 purposes only. All key dates defined in the deal are shown. Each primary
cash flow
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41
for an instrument is represented by a line in the time organizer. Badging
information
stored within the engine for each instrument defines which is the primary cash
flow for
that instrument.
For this exemplary deal, the following changes are defined in the Time
Organizer:
- Closing: Dec 30, 1998 - the date the deal closes and all the transactions
begin
(every deal has a closing date)
- EBO: Jan 2, 2011 - the date the lessee can option to purchase the assets
back
(EBO stands for early buy out)
- Residual: Dec 30, 2014 - the date the lease ends
- EventDates: from the Closing to the Residual - the main deal time line
starts at
the closing and continues annually until the residual date
Once the EBO date is defined, it is turned into a "decision" by the engine,
which means the deal splits in to two possible courses or "outcomes". The
normal
case, or BaseOutcome, means the deal comes to term and the assets are just
sold to
the market place. The EBO outcome occurs when the lessee purchases the assets
prior to the end of the deal. For the purpose of financial analysis, all
outcomes can be
fully modeled to get the deal approved by the client. The outcome tool, the
triangle
with a plus sign (currently disabled in Fig. 16), is used to define an
outcome.
When the user adds an outcome to the time organizer chapter, the engine
performs numerous functions. More particularly, the engine creates a new
outcome
object to house data specific to this outcome, with links to the decision
objects which
comprise the outcome. For each tax-like instrument (for which the instrument
designer has specified a "fresh copy for each outcome"), a complete copy of
its
parameter, party and classification data is generated. For each instrument,
the
instrument synchronizer generates new terminating parameters as necessary.
These
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parameters terminate the flows generated by this instrument at the first
decision
contained in the new outcome that has been designated by the user as a
terminating
decision in the instrument's decision handlers. For each instrument, the
instrument
synchronizer generates new badged parameters to identify the flows to the
internal
database. These parameters take their value from the terminating parameters
defined in the previous section (or the original parameters if not
terminated), with
possibly a sign change. They are given badges based on the data in the party
and
classification sections of the instrument; the categories are Party, Outcome,
Cash or
Income Classification, Other Party, Instrument Name and (for income
classifications)
Tax Authority. When the internal database receives the information about the
new
badged parameters, it signals all effected collector parameters that a change
has
occurred. These are parameters which have been designated as extraction
parameters, or as formula parameters using one of the special "collect"
functions.
The next time that their values are requested, they will re-establish all
links with
badged parameters so that the new ones are included. The collector parameters
signal a value change via their dependency managers to tell all other
parameters
whose value depends on theirs that a change has occurred. In this way the
flows
generated by the new outcome spread their effect throughout the model.
Fig. 17 graphically shows the decisions and outcomes which result from the
early buy-out (EBO) option in this example.
Step 3 - Entering instrument data
Once the diagram is created and the dates are defined, the user next fills in
all
the data and calculations necessary to complete the deal. The first part of
this is
filling in instrument data. Instrument data is entered in the Instruments
chapter as
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seen in Fig. 18. Fig. 18 shows the Calculations section of an instrument where
data,
such as the rate of a loan or cost of an asset, and calculations, such as the
amortization of a loan or depreciation of an asset, are entered.
The first two tabs near the top of the figure and next to the "Calculations"
tab
are used to enter role information for each party associated with an
instrument (as
defined by the payment diagram explained earlier). In Fig. 18, the Borrower
tab can
be seen where information about the party borrowing the money for the loan is
modified such as how the loan interest is deducted. Lender information is
modified by
selecting the next tab. The Event handlers tab contains the settings for how
the
instrument is processed if a different outcome is used. For example, loans are
generally paid off if a deal ends early. The Reports tab lists the reports
specific to the
instrument, such as the loan payments.
Starting with the loan instrument, the only item which needs to change is the
loan rate. The other default or initial values for the instrument are
sufficient for how
the loan should be setup in this deal. Money is borrowed at a fixed rate of
5.0625%.
The steps are as follows: 1) Double click on the current value for the loan
rate (this is
the Rate parameter in the Calculations section of the Loan instrument); and 2)
Change the value from the default value to 5.0625%. (See Fig. 19). It is noted
that
the formula includes additional syntax that indicates how the Rate parameter
is to be
used throughout the model.
When the user changes the Rate formula in the user interface, the engine will
record the new formula for that parameter, parse it into its expression
objects, and
transmit a value-changed message through the network of dependency managers
for
parameters whose values depend on this parameter. Each of these parameters
will
then know to recalculate its value when it is next requested.
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To complete the instrument changes, data will need to be entered for several
other instruments. Instrument data generally falls into two categories. It is
either a
fixed part of a deal such as the cost of an asset or the interest rate of a
loan. Or it is
an optimized value that gets calculated when the optimal solution is found.
The
instruments in this case are set up in the following way:
Fixed data:
HardAsset - $700,00. The cost of the asset which is generally a given in the
deal
SoftAsset - $300,00. The cost of the asset which is generally a given in the
deal
Fee - This is 1% of the assets purchased and is negotiated with the client or
lessor.
Residual - For this example, the residual is actually fixed at 20% of the cost
of the
assets.
Variable or optimized data:
Loan -The loan payments or debt service are optimized to satisfy the deal (see
the
optimization step).
Rents - The rent payments are likewise optimized to satisfy the deal.
PurchaseOp(EBO) - The purchase option payments which are used when the EBO is
exercised are optimized as part of the deal.
No changes are needed in the Taxes instrument since this is based on the
standard federal tax rate.
Step 4 - Building Smart Paper
Any data or calculation not specified as date or in the instruments is entered
in
Smart Paper. Smart Paper is a calculation based feature very similar to a
enhanced
spreadsheet (more details on Smart Paper are provided below) . However, while
a
spreadsheet is based on individual cells linked together strictly by formulas,
Smart
Paper formulas know about each other and about links to dates. More
particularly, as
explained above, Smart Paper is a non-cell based calculation interface where
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references are based on a hierarchical outline as opposed to a positional
reference.
The linking information is stored in the engine. For example, one formula may
contain
a set of values linked to the first date of every year for 20 years. A second
formula
may only need the value from a specific date, such as the fifth date, within
the first
5 formula. The second formula need only specify the specific date and the
engine will
search out the most appropriate value.
The Smart Paper in this deal is built up in two ways. First, the user has a
variety of templates he can add that perform pre-defined calculations. Second,
the
user can create custom calculations or enter custom data into Smart Paper.
Figure
10 20 shows the interface for creating Smart Paper. The main screen with all
the data
and calculations is where the user creates his outline of data and
calculations. The
tools along the top are used to change the view of Smart Paper and to operate
on
specific entries in the outline.
Each tab is a different sheet of Smart Paper where the user can create his
15 outline and enter his data and calculations. When the user adds a piece of
Smart
Paper, the engine creates a worksheet in the General Registry. As the user
creates
Headings and Parameters in the piece of Smart Paper, the engine creates
mirroring
Parameter Lists and Parameters. When a Parameter is created and named, the
engine registers it with the name reference manager. This will attempt to
resolve any
20 outstanding references to this name by formulas in other parameters. It
will also see
if references to other parameters of the same name need to be more fully
qualified to
prevent ambiguities. When a reference to this parameter is resolved, the
referencing
parameter sets up a link between its dependency manager and that of the new
parameters, so that any changes in value of this parameter will be signaled to
the
25 referencing parameter.
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When the user specifies the formula for the new parameter, the engine parses
it into its basic expression nodes. Any references to other parameters are
registered
with the name reference manager which will attempt to resolve it immediately.
If it
cannot be resolved immediately, then the name reference manager keeps the
request
as pending, in case it can be later resolved. Any resolved reference causes
links to
be set up between the dependency managers as described above.
As the user enters parameters into Smart Paper, the values of these
parameters are immediately displayed. It does this by asking the engine to
calculate
the parameter's value, which triggers an evaluation of the parsed expression
nodes.
These nodes do the basic arithmetic operations, references to other parameters
and
evaluation of functions. The value returned can be either a scalar or some
sort of
array. Scalars are single quantities like numbers, dates, frequencies, elapsed
times,
character strings. Arrays are lists of these scalars.
In Fig. 20, we see that the user has set up five sheets of Smart Paper. The
first one contains all the IRS related calculations which become important
when
optimizing the deal. A fully optimized deal has certain legal requirements it
must meet.
The next one calculates the present value benefit of the deal for the lessee.
In fact,
the entire purpose of this deal is to maximize the present value benefit. The
next two
sheets calculate the lessor's MISF yield for the EBO and BaseOutcomes. And the
last sheet just has a general collection of data used throughout the deal. All
parts of
Smart Paper except the general section are created using pre-defined
templates.
Step 5 - Optimizing the deal
Optimization is the process of imposing constraints or requirements on a case
and the varying values and other parts of the case until the best result is
found. By a
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constraint, it is meant, for example, that some cases fall under certain
restrictions
from, for example, tax laws relating to leasing and rents which must be
satisfied if the
case involves a lease or rents. The elements of a case that can be varied are
called
optimizable parameters.
In this deal, we are maximizing the present value benefit to the lessee. The
following constraints exist on this deal and must be satisfied when optimizing
to the
best result:
- IRS tests for profit, EBO compulsion, minimum investments and uneven rents
- Rent payments must be greater than 0
- Loan payments and the loan balance must always be greater than 0
- Loan payments must be less than rents received
- EBO payments must be less than the taxes paid by the lessor
- The loan amount must be less than or equal to 80% of the asset cost
- Standard constraints on the calculation of a MISF yield for both the
BaseOutcome
and the EBO outcome
The following parameters are then varied to reach the optimal deal:
- The loan payments
- The rent payments
- The purchase option payments
- MISF minimum investment balance
The optimization screen is divided into several pages by the tab across the
top
of the screen, as shown in Fig. 21. The "Constraints" tab which is selected
and
shown in Fig. 21 shows those aspects of the deal which can't change or must be
satisfied. These constraints are added to parameters spread throughout the
instruments and sheets of Smart Paper. The engine collects these and displays
them
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in a precise form for the user to view and evaluate. The Optimizable
Parameters tab
lists those items which can change. The other tabs provide other relevant
information
to help the user evaluate his model. The Objective Function shows what is
being
optimized and whether a maximum or minimum value is sought. The user simply
clicks the Optimize button near the top of the screen to start an
optimization.
When the user hits the optimize button, the engine analyzes all the parameter
definitions and constraints that the user has entered, and tries to set up a
linear (or
mixed integer) programming representation of these suitable to be sent to the
CPLEX
linear optimizer. Assuming that this can be done, it sends the model to CPLEX,
gets
the results back and puts the resulting values for optimizable parameters back
into
their formulas.
Step 6 - Viewing output
The final step is viewing the data either in the reports chapter or in the
payment
organizer. A report from the reports chapter is displayed in Fig. 22. The
tools are
provided to allow the user to view different aspects of the report including
zooming in
and out or printing the report.
The data for a report is collected directly from Smart Paper and instruments.
The only function the reports chapter performs is formatting the data for
professional
output. Likewise, the Payment Organizer chapter, allows the user to view the
data
and cash flows according to a specific party, outcome and time frame within
the deal.
This again is only a viewing interface which collects data directly from the
data and
calculations entered in other parts of the model. The Payment Organizer
interface is
displayed in Fig. 23. Fig. 23 shows the annual cash flows for the lessor party
from the
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base outcome of the deal. The user changes the view by manipulating the
various
controls provided at the top of the screen.
As can be seen from the example case above, the user can model a financial
scenario easily and quickly using the tool of the present invention.
SMART PAPER EXAMPLES
The following are examples demonstrating the functionality of the worksheet
section or Smart Paper feature of the instant invention.
Smart Paper is a non-cell based calculation interface where references are
based on a hierarchical outline as opposed to a positional reference. Figs. 24
and 25
show a simple, example piece of Smart Paper created in accordance with the
instant
invention, and demonstrates some of the benefits of the non-cell based
formulas
used therein.
The smart paper example of Figs. 24 and 25 show a portfolio of airplane rents.
Under the heading Aircraft, we see rents for Planel and Plane2. The rents for
each
aircraft are paid on different dates and for different amounts. The Totals
section
sums all the dates that the rents are paid on and shows the rents paid on each
date.
In a sense, this acts as a summary table. The AnnualTotals section refers
directly to
the Totals section but uses an annual date stream as opposed to the dates each
rent
is paid. This effectively shows the viewer how much rent is paid each year
regardless
of the specific day that rent is paid.
Fig. 24 shows the values or results of the formulas created in Smart Paper,
while Fig. 25 shows the corresponding (or hidden) formulas used to obtain the
values
in Fig. 24. It is noted that the actual rents are just dummy values used for
illustration
purposes. The two functions used in this example are Subtotal and Union (see
description of Formula Language below). Union collects a bunch of date streams
and
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combines them into one. Subtotal searches all the parameters underneath a
heading
and collects values from all the parameters with the same name as specified
for the
function.
From this example, we see some of the benefits of the non-cell based
5 worksheet of the instant invention. For example, if another plane is added
under the
heading Aircraft, and the rent stream is called Rents, then the TotalRents
parameter
will always show the total of all rents, because the Subtotal function finds
all
parameters named Rents under the Aircraft heading. Likewise, if a rent payment
is
added to any of the existing Rents parameters, TotalRents is automatically
updated.
10 In a conventional spreadsheet, solving these two problems would ultimately
involve
inserting cells or rows or columns and updating formulas that sum the data.
The
hierarchical nature of the outline, made possible by Smart Paper, lets the
same name
be used more than once in the manner indicated above. As a result, a very
convenient, flexible and powerful calculation interface is provided by the
Smart Paper
15 chapter of the instant invention.
This example also demonstrates the advantage of the dynamic non-cell based
formulas used in Smart Paper. For example, the AnnualTotals collects all the
rents
paid for each year. In a spreadsheet, the user would have to examine each rent
stream and individually select which rent payments fall in each year. If the
Annual
20 table then needed to be changed to quarterly, the user would have to go
back and re-
do the entire process from scratch. However, with the non-cell based worksheet
of
the instant invention, formulas know how to link values to dates so that the
final
formula can interpret the input values based on the actual date rather than
the
position the date falls in a spreadsheet, which relies on positional
references rather
25 than the hierarchical references of the instant invention.
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Similar to the AnnualTotals, the TotalDates parameter benefits from non-cell
based references if a new date is entered for any rent stream. The TotalDates
will
always collect all rent dates regardless of how many or few there are.
A second smart paper example is shown in Figs. 26 and 27. This example
relates to a simple loan structure in which calculations of the loan amount
and its
amortization is based on a present value (PV) factor and a fixed debit
service. Fig. 26
shows the actual values in this smart paper example, while Fig. 27 shows the
underlying formulas used to calculate the values. The following table explains
the
particular headings, parameters and formulas used in the example of Figs. 26
and 27.
Simple Loan Example
Headin /Parameter Details
In uts.Scalars
Cost Amount on which loan will be based (i.e., the cost of an
asset)
Calendar Calendar day-counting method to use in the calculations
that follow.
Refers to Time Or anizer default calendar settin .
In uts.RateSchedule
RateDates Dates that interest rates are set and the periods to
which those rates apply.
First and Last links the first and last dates of the
current schedule with those of another schedule, which
in this instance is the PaymentDates index in the
In uts.Pa ments section.
Rate Interest rates indexed to RateDates
Table means a given value applies to every day in its
period.
For uses a repetition value to map the same value to
a certain number of periods.
The semicolon (;) symbol stops the current
sequence of values.
Thereafter maps the last given value to remaining
index dates.
In uts.Pa ments
PaymentDates Dates of payment and the periods to which those
payments a I .
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StartDates: recognizes the dates that follow as first
days of periods.
InputAmounts Debt service paid, based on asset cost and number of
periods.
COUNT determines the number of elements in an
array. Therefore, Cost/COUNT (PaymentDates) is
1,000,000 divided by 11.
Thereafter maps the given value to each remaining
period.
Amortization
AmortDates Dates of debt service calculations and the periods to
which those numbers apply.
ActsLike ensures that any change in the
PaymentDates prefix or dates is automatically passed
on to the current parameter.
Principal Applied to balance after interest is paid.
Interest Interest due for each period, paid in arrears.
Arrears applies each amount to the period that
precedes the index date.
Previous defines an array in which each value refers
(relative to its position on the index) to the value of the
argued parameter in the preceding period.
For example, Interest 30,036.66 on 01 Jul 2000
refers to Balance 730,064.69 on 01 Jan 2000.
Periodlnterval returns the length in years of a period
on the current date index. The length is .5 due to the
semiannual dates of the AmortDates index.
The offset of -1 instructs the application to use
the previous period for its calculation, since interest is
paid in arrears.
DebtService Direct reference.
Balance Remainder after payment of principal.
Previous defines an array in which each value refers
(relative to its position on the index) to the value of the
argued parameter in the preceding period.
The second argument for the Previous function
tells the application to return the value of the
LoanAmount parameter to the first period. Thereafter,
each new balance is reduced by principal paid during
the current period.
PVFactor Constructs a PV curve.
For Previous, refer to Balance parameter detail.
For Periodinterval, refer to Interest parameter detail.
Result
LoanAmount Loan amount based on the PV of the total Debt Service
payments.
SUM returns the total of all its arguments; i.e., the
sum of the products of all debt service payments and
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the corresponding PV factors.
A third smart paper example is shown in Figs. 28 and 29. This third example
illustrates ways in which smart paper can be used to determine the nominal
daily
present value (PV) and investor rate of return (IRR) for all pre-tax and after-
tax cash
flows with respect to an investment. Again, Fig. 28 shows the actual values,
while
Fig. 29 shows the underlying formulas used to calculate the values. The
following
table explains the particular headings, parameters and formulas used in the
example
of Figs. 28 and 29.
Present Value and IRR Example
Headin /Parameter Details
Inputs
Investor Name of party whose investment is to be analyzed.
Selected list member from category "Party".
Calendar Day-counting method to use in calculations on this
sheet of Smart Paper.
Selected list member from cate or "Calendar".
CashFlow Summary
Project_Dates Dates returns the dates of flows found by the
CollectPayments function.
CollectPayments identifies all payment flows
classified as AfterTaxCash for the Investor
parameter.
Investor_PTCF Identifies payment flows classified as PreTaxCash
for the Investor party.
Investor_Taxes Identifies payment flows classified as Taxes for the
Investor party.
Investor_ATCF Identifies payment flows classified as
AfterTaxCash for the Investor party.
IRR_Calculation
FirstlRRDate MonthEndOf returns the last calendar day of a
month defined by the First, Dates, and
CollectPayments functions. One month is
subtracted from the result.
First(Dates(CollectPayments...)) finds the first
date among the dates of all payment flows
classified as AfterTaxCash for the Investor party.
LastIRRDate As above, except the month for the MonthEndOf
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function is defined as the Last of all dates for
payment flows classified as AfterTaxCash for the
Investor party.
IRRDates Starting and Ending refer to the dates defined
above to specify the First and Last dates for date
stream.
Monthly specifies that dates continue monthly
from the first date in the stream.
InvestmentBalance Cumulative returns the accumulation of all
Investor_ATCF values up to each period. The
cumulative Earnings values are added to the
result.
Earnings Arrears recognizes that each value occurs in
arrears. For example, the value on 31 Mar 1999
applies to the period that began 28 Feb 1999.
Previous defines an array in which each value
refers to the product of InvestmentBalance in the
preceding period multiplied by 13.6156%
(NominallRR_UsingSearch) times the
Periodlnterval for the previous period.
Periodinterval returns the length in years of a
period. With monthly dates and a US_30_360
calendar, the length is 0.083....
PV Calculation
PVRate_Effective Noindex: recognizes the value that follows as a
scalar, i.e., a single value that is independent of
the current date index.
PVRate_Nominal As above. The formula that follows converts an
annual rate into a nominal rate.
PV_Dates Starting and Ending refer to names of key dates
in Time Organizer to define the respective first and
last dates in the date stream, with monthly dates in
between.
PVFactor Semicolon(;) stops the current stream. In the
subsequent stream:
For its first value, Previous divides 1 (the value
of the preceding period) by the sum of 1+9.5690%
times the period interval value.
See Periodinterval in
IRR_Calculation.Earnings above.
Thereafter, Previous uses the result of the
preceding period in the calculation for the current
period.
BasePTCF Simple reference.
Discounted_PTCF Simple arithmetic.
Base_ATCF Simple reference.
Discounted_ATCF Simple arithmetic.
PV Summar
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PVofPTCF_UsingFunction Daily_Present_Value uses the value of
PVRate_Nominal to calculate the daily present
value of Base_PTCF (the base pre-tax cash flow)
as of the Closing date.
Closing is not defined on this sheet; it refers to
a key date in Time Organizer.
The function uses the Inputs.Calendar setting
for the da -countin metrics.
PVofPTCF_UsingSP Sum returns the sum of all values in the
Discounted_ATCF parameter. The result is the
same as the result of the Daily_Present_Value
function as argued above.
PVofATCF_Usin Function See PVofPTCF_Usin Function above.
PvofATCF_Usin SP See PVofPTCF_Usin SP.
Summary
NominallRR_UsingSearch Search performs iterative calculations until it finds
a nominal IRR rate between 10% and 200% that
makes the last investment balance equal to the
target value of 0.
The search increment accuracy is le 8.
NominallRRUsingFunction Monthly_IRR calculates the nominal monthly
investor rate of return using the dates and values
of the Investor_ATCF parameter. The result is the
same as the search iteration method as argued
above.
EffectivelRR Simple arithmetic to convert the nominal IRR to an
annual IRR.
As can be seen from the examples above, the Smart Paper feature of the
instant invention provides a very useful calculation interface and tool. It is
noted that
5 the Smart Paper tool can, in accordance with the instant invention, be used
independently from the modeling and analysis tool of the instant invention as
an
improvement to spreadsheet applications.
THE ENGINE
10 As explained above, the graphical user interface and the engine provide an
intelligent interface which enables data to be generated which models the deal
in
response to graphical modeling of the deal by the user. Thus, the graphical
model
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not only provides a visual representation of the deal, but it also causes the
engine to
generate useful information which at least partially model the deal based on
the
information the engine is able to obtain from actions performed by the user
during
creation of the graphical model of the deal.
In the preferred embodiment of the instant invention, the engine operates in
accordance with the description below. More particularly, the engine is a
computational server designed to support client applications wanting
spreadsheet-like
formula evaluation, manipulation of indexed streams of quantities and linear
and
mixed integer programming optimization. The engine has the following main
features:
The engine is designed as a COM server which can be initiated either in-
process or out-of-process. In the latter case, it can be either local or
remote, and can
handle multiple clients.
The engine has a hierarchical organization of data; at the topmost level the
predefined general registry can contain multiple worksheets and instruments;
these
can contain an arbitrarily deeply nested hierarchy of parameter lists, each
containing
parameters and other parameter lists.
The engine has interfaces which stream in or out all of the data that has been
specified by the client in the form of an indexed bit stream. This enables the
client to
save and restore cases in files. The index can be used by the client to view
the
structure of the data and compare files; it is used by the engine to recover
as best it
can from a corrupted bit stream. Copies of each index entry are included in
the bit
stream so that a client may attempt to recover from a corrupted index.
Parameter lists may be independently streamed in and out. This enables the
client to maintain a library of templates, which are sets of parameters which
can be
instantiated into any case. Instruments may also be independently streamed in
and
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out. This enables the client to maintain a library of instruments which can be
instantiated into any case.
Each parameter is a fundamental calculation unit. It has a name by which it
can be referred to by other parameters, a value, and possibly a means of
calculating
that value. Parameters can have badges identifying them to the internal
database.
Each badge is a list of "category = member" specifications, where the list of
possible
categories is defined by the client, though there are specific categories
assumed by
instruments. The tool uses categories like "cash classification", "party" and
"outcome"
to model the flows of a financial model. Parameters can be designated as
defining
results. Each result is attached to a specific name, party and outcome. The
result
parameters can then be collated by the client into capsule summary reports,
for
example. The values manipulated by the parameters can have many types. Some
are single quantities (scalars) representing numbers, logical values (true and
false),
dates, time intervals, frequencies (annual, monthly, etc.), character strings
and
enumerated types. Other values are arrays, plain, sorted or indexed. There are
also
some values which are neither scalars nor arrays, but become indexed arrays
when
referred to from a keyed parameter. These are used to represent income that
will
automatically be accrued, for example. There are special values to represent
null,
which is like an empty cell in a spreadsheet, and the results of calculation
errors (e.g.
divide-by-zero).
There are some built-in enumerated types (e.g. "calendar"), which enumerates
the different ways of calculating the length of time between two dates, and
the client
can create its own using special list-definition parameters.
A plain array is a set of values indexed by the natural numbers (1, 2, 3,
...).
Normally there is only a finite number of elements in the array, but limited
support is
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provided for infinite arrays which are regular beyond a certain point. A
sorted array is
always in ascending order of its elements, with no duplicates; it is.used for
streams of
dates representing events in a financial model. An indexed array, or stream,
is an
array which is attached to a sorted array for indexing purposes. This is used
to
represent streams of cash flows in a financial deal, where each flow is
attached to a
date. The elements of arrays can be other arrays, thus providing support for
multi-
dimensional arrays.
A keyed parameter is a parameter that has been connected to another
parameter for the purposes of providing a key (or index) for its array value.
Normally,
the key parameter has a date stream (i.e. a sorted array of dates) as its
value, and
these represent the dates of the flows defined in the keyed parameter. When a
keyed
parameter refers to another parameter in a formula, it triggers special
calculations to
convert the keys. This is normally an "accumulate to date" algorithm, but can
be
changed to effect accrual, table lookup, interpolation and extrapolation by
using
formula prefixes.
The normal rules of arithmetic have been extended to handle all the different
types of values, wherever possible. Thus a date and a time interval can be
added to
produce another date. A scalar can be added to an array (it is added to each
element
of the array). Two arrays can be added by adding corresponding elements. If
these
are indexed arrays, then the corresponding elements are found by matching the
indexes (i.e. two streams of payments are added by adding the payments on the
same dates).
Parameter values can be specified in several ways. The client could simply
specify a value, or it could specify a way of calculating the value. A formula
parameter has a formula specified, which is an algebraic combination of
constants,
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references to other parameters, and functions. A copied parameter simply
duplicates
the value of another parameter. An extracted parameter-is designed to extract
data
from the internal database. In that case, the client specifies a list of
"category =
member" specifications and the value is calculated by matching these
requirements
with the badges of all parameters, and adding up those which match. This
enables
the client to request, for example, all of a certain party's rental income,
without
knowing the details of the instruments in the model.
The formula language includes an extensive set of functions to provide
spreadsheet capabilities for manipulating data. Also included are functions
for
manipulating dates and arrays. The formula language also includes a set of
prefixes
specified at the beginning of the formula. These prefixes affect the way that
the
parameter is handled in references by other parameters, and can trigger
automatic
accrual, table lookup, interpolation and extrapolation. The prefixes are also
used to
specify variability during optimization and to trigger search and repetitive
calculations.
In addition to the built-in functions, the client can define custom functions.
These are named objects created in a worksheet which can then be referred to
from
any worksheet in the same way that a parameter could be, except that the
reference
is followed by a list of arguments. The definition of the custom function
specifies how
the result of the function is to be calculated from its arguments. Arguments
can be
specified as mandatory or optional, with a default value.
There is a special formula syntax used to specify date streams and arrays of
values. This uses keywords like "starting", "ending", "then", "also" to make
the
specification of these types of values easier and more understandable. The
engine
can provide the client with detailed parsing information about formulas. This
can be
used to write formula wizards. The engine parses each formula into a tree of
basic
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expression nodes. Each expression node handles a specific job like addition,
multiplication, references to other parameters, function evaluation, etc.
Parameters
can refer to themselves in expressions with array values, provided that they
use either
the "previous" or "next" function to avoid a logical circularity. In this
case, the engine
5 duplicates the expression tree for each element in the array (normally for
each date),
so that the expression nodes can be evaluated without encountering circular
reasoning. More generally, a set of parameters can form a self-referential
group,
triggering duplication for each parameter in the group.
Each expression node keeps its calculated value until it is invalidated by a
10 client change. This "intelligent recalculation" minimizes unnecessary
repetition of
calculations. When a formula refers to another parameter, it does so by
specifying
the other parameter's name, possible qualified by the names of its worksheet
or
instrument and levels of the parameter list hierarchy. Qualifiers are other
names
preceding the parameter name, separated by periods. Many levels of
qualification are
15 possible, e.g. "Loanl.Calculations.Amortization.Interest". Internally, the
general
registry has a name reference manager which maintains all these references. As
parameters or parameter lists are created, destroyed and renamed by the
client, the
references get automatically updated. Unnecessary qualifiers are removed.
Qualifiers are added if the original reference becomes ambiguous, thus
maintaining
20 the intended parameter linkages.
Each parameter has a dependency manager which handles the invalidation of
expression nodes when the client changes a parameter. When the name reference
manager resolves a reference, the target parameter sets up a link between the
source's and target's dependency managers. If the source value changes, an
event
25 is triggered in its dependency manager which is transmitted via the link to
the target;
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in turn this is passed on to the target's dependents. The dependency managers
can
also provide the client with lists of dependents and precedents for any
parameter.
Dependency managers are also created for parameter lists, worksheets,
instruments, and indeed the general registry. Changes are propagated up the
parent
chain so that each level knows when there has been some change inside them.
This
information can be tapped by clients to provide an intelligent refreshing
mechanism;
i.e. don't bother to redraw interfaces for objects which have not changed. The
client
requests a modification server for any level from parameter up to general
registry.
This modification server can be polled to determine whether there has been any
change since the last poll.
Search parameters are formula parameters with a search prefix. There are
three kinds: the optimization search, the targeting search and the
maximization
search. The optimization search only uses the first three arguments (low, high
and
accuracy) to the search prefix; it has no effect on calculations outside of
the optimizer.
The other types of search specify a target formula as the fourth argument. The
targeting search specifies a value to target in the fifth argument, while the
maximization search uses one of the keywords "maximum" or "minimum" as the
fifth
argument. Whenever a non-optimizing search parameter's value is requested, it
iterates guesses for its value until the target formula is equal to the target
value, or
maximized, or minimized, depending on the fifth argument. Its value is saved
until the
dependency managers invalidate it, to avoid pointless recalculation.
The targeting search preferably uses third-party software which is designed to
find the zeroes of functions. This software does a good job if the function is
monotonic. However, it can get confused by non-monotonic functions which may
have several solutions. The maximization search uses a custom algorithm which
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uses quadratic interpolation to refine the guesses. It depends on the function
being
fairly well-behaved as well. However, any suitable application can be used to
perform
this function.
The engine has a facility for collating multiple parameters into a single date-
indexed table. It is called a parameter date table, and there is one in every
worksheet
(more are available on request). The client specifies which parameters it
wants in the
table, and the engine collates their dates and outputs a combined list of
dates and a
matrix of values. If the client wants to collate the data in regular intervals
(e.g.
annually), it can specify any number of date buckets; these override the
table's
normal "daily" rule.
The engine maintains a set of client-specified numeric formatting rules. These
can be specified at any level of the data tree, from parameter up to general
registry.
The client can then request the effective formatting for any parameter, and
use it to
format numeric values using special engine calls. The facilities include comma
insertion, fixed number of decimal places, prefixes and suffixes, percentages
and
scaling.
The internal database uses a bill-of-materials structure to enable parameters
to
collate data which has been identified via badges on parameters. Inside each
category there are members which can be connected in a directed a cyclic graph
structure, with numeric coefficients applied to each link. Thus a category
representing
the parties in a deal can establish ownership links between the parties, e.g.
A owns
50% of B. When a parameter which has a badge specifying party B is extracted
by a
parameter requesting flows for party A, its values will automatically be
multiplied by
the 50% factor. The links are also used to establish rules on the cash
classifications,
like "after-tax cash" equals "pre-tax cash" plus "taxes". The categories and
members
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are completely arbitrary, and maintained by the client. An interface is
provided to
stream the entire table in or out, so that the client can save a default table
in a file.
Parameters can extract data from the internal database either by designating
them as extraction parameters, or by designating them as formula parameters
and
using one of the "collect" functions. Either way, the parameter specifies a
list of
category-member pairs and receives back from the database a list of parameters
matching those specifications, with corresponding coefficients, and it then
combines
their values to get a value.
Parameter lists can be given an activation formula by the client. This is a
formula that should evaluate to true or false. When the formula evaluates to
false,
the parameter list and all of its contents are labeled as inactive. Inactive
parameters
do not have values. If an active parameter tries to reference an inactive one,
it will get
an error value. Clients can use this facility to de-emphasize blocks of the
model that
are not currently being used, and prevent useless calculations from slowing
down the
program. There are several restrictions on the formula that can be used - for
example, it must not refer to a parameter inside its own parameter list.
Invalid
formulas will always make the parameter list inactive. The engine can supply
the
reason why a parameter list is inactive.
The general registry contains a predefined worksheet called the timeline. This
is designed to hold basic date and date stream definitions for the rest of the
model,
and has special interfaces to enable the client to manage them. The timeline
acts as
a preferred source of parameters to the name reference manager. If a reference
cannot be resolved within the parameter's own worksheet or instrument, then
the
timeline is searched before going to any other worksheet or instrument. This
gives a
"global" nature to the timeline parameters.
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The engine maintains lists of decisions and outcomes. Decisions are named
objects attached to date-valued parameters. They are designed to represent
points in
a financial model from which the deal could proceed in different directions;
e.g.
depending on whether an option is exercised. Outcomes are named objects that
are
the result of saying whether each decision has been taken or not. The outcome
in
which no decisions have been taken always exists and is called the base
outcome.
Other outcomes can be created by the client by adding a decision to an already
existing outcome. For example, if the client has created three decisions. then
there
are seven possible outcomes in addition to the base outcome obtained from the
seven different ways of saying which combination of the three decisions has
been
exercised. These extra outcomes are not created automatically because the
decisions may not correspond to independent decisions in real life - only
certain
combinations of decisions may be realistic.
Instruments are objects created by the client in the general registry. They
are
like worksheets in that they have an arbitrarily complex parameter list, but
they also
have data geared toward modeling financial instruments like loans, rent
agreements,
etc. They simplify designing badges for parameters.
Each instrument can have one or more parties specified. (The tool always
uses precisely two parties for each instrument, corresponding to the two ends
of the
arrows in the party diagram.) The client can specify a role for each party.
For
example in an instrument modeling a loan, the two parties could be designated
"lender" and "borrower". In the parameters, the client may refer to the roles
in
formulas; they are automatically defined to take the value of the name of the
party
filling that role. For example, if there is a party called "MyBank" with a
role of "lender",
then a formula may use the identifier "lender" with the same effect as
specifying the
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character string "MyBank". This allows instrument builders to write parameters
which
automatically follow party substitutions.
The general registry has a special worksheet called the parties worksheet. It
corresponds with the parties chapter in the tool. It is completely maintained
by the
5 client. However, if an instrument party finds a section in the parties
worksheet that
has the same name as itself, then it generates role parameters echoing the
data
inside that section. For example, if the parties worksheet has a section
called
"MyBank" with a parameter called "FirstFiscalMonth", then an instrument
parameter
could refer to its value as "Lender.FirstFiscalMonth". (Assuming that the
instrument
10 contains a party with name "MyBank" and role "Lender".)
Each instrument party can have one or more cash classifications, and each
cash classification can have one or more income classifications. Each cash
classification generates cash flows for that party by specifying the name of a
parameter defined in the instrument, the section of the topmost parameter list
in which
15 to find the parameter, whether there is a sign change (for paying parties),
and the
name of the category member to be used to generate badges. Each income
classification functions similarly with the extra information of which tax
authority to
badge it for.
Each instrument has a default decision handler which specifies how the flow-
20 generating parameters are treated in outcomes involving a decision. The
client can
override this behavior for any actual decision that has been created. There
are only
two possibilities: either the decision is ignored, i.e. has no effect on cash
flows, or the
flows are truncated at the decision date. If they are truncated, the client
can specify a
formula for an extra amount to be assessed on the decision date. To generate
the
25 flows for a particular outcome, the earliest truncating decision is found
which is in that
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outcome, and that controls the flow for that outcome. If there is no
truncating decision
for that parameter in that outcome, the flows are the same as the base outcome
flows.
The client may specify for each instrument that it only generates flows for
outcomes containing a certain required decision. This is designed to model
purchase
options which are only present if the corresponding decision is taken.
The client may instruct an instrument to generate its own decision and outcome
for the purposes of calculating parameters and generating flows. This is
designed to
model termination values where a set of cash values needs to be calculated to
terminate the deal at any of a fixed set of dates. The instrument contains a
date-
valued parameter which becomes the decision date; the client can vary this
date to
get a table of termination values, or have the engine vary it automatically by
specifying formula parameters with the TerminateByDate prefix.
The object responsible for generating flows from instruments is the instrument
synchronizer. Whenever the client changes some data, the synchronizer
regenerates
(as necessary) parameters defining the flows and identifies them to the
internal
database with badges. Within each classification within each party within each
instrument, the synchronizer identifies the instrument parameter representing
that flow
according to the client inputs. For each outcome, it generates an auxiliary
parameter
which may change the sign of the flow and/or truncate it at the appropriate
decision
date. It badges the auxiliary parameters using the categories "party", "other
party",
"cash or income classification", "outcome", "instrument name" and "tax
authority" for
income classifications.
The client may designate that certain instruments are to be cloned for each
outcome. This is designed to model tax payment instruments where the basic
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parameters have to take different values for each outcome. In this case, the
instrument synchronizer clones the parameter lists and party sections for each
non-
base outcome before generating the auxiliary parameters. It sets up default
collection
parameters for each clone to ensure that parameters extracting data from the
internal
database pick the right outcome in each clone.
The general registry may also contain specialists. These are named objects
designed to act like building blocks. Each specialist contains its own version
of the
general registry which can have worksheets and instruments and other
specialists.
Since they are in their own registry, there is no contact between them and the
world
outside; no danger of references being erroneously resolved. They are safer
versions
of the "template" concept. Special parameters are designated as inputs to and
outputs from the specialist, and they do have interactions with the world
outside the
specialist.
An action is a named object representing a calculation that is too complicated
for simple formulas to accomplish. There are predefined actions for building
the
optimization model, and executing the optimizer. The client can create new
actions
inside worksheets to do things like targeting and repetitive (sensitivity)
calculations.
Also the client can create action sequences, which are sequential series of
actions, to
create a primitive macro language.
Actions can be executed synchronously or asynchronously. In the latter case,
the client starts off the action, and sits in a loop requesting action
progress, until the
progress report indicates that the action is complete. This enables the client
to
provide visual feedback to the user during actions which could take some time.
For
example, the client could display messages sent back from Cplex during
optimization.
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Internally, actions are executed in a sub-thread to free the main thread to
respond to
progress requests.
The engine preferably has an interface with the Cplex optimizer. This is a
solver, provided by a third-party, of linear (LP) and mixed integer (MIP)
programming
problems. It is encapsulated as an out-of-process COM server which can be run
locally or remotely, with multiple users. The server can be started by the
client or by
the engine with the client specifying on which machine to initiate it. The set
of
instructions for the Cplex optimizer is generated by an optimizer model. This
is a
named object containing the data needed for the optimization. There can be
more
than one optimizer model in each case, if desired. An optimizer needs three
kinds of
information to operate. It must know which parameters the optimizer can vary,
what
constraints have to be satisfied, and what the objective function is. For each
parameter with some information pertinent to an optimization model, there is a
model
parameter which houses this information. The client can request a model
parameter
from an optimization model for any given parameter in the system.
To specify that a parameter is variable in a given optimizer model, it is made
an
input parameter and the corresponding model parameter is given certain
properties
defining the variability, count (for array parameters), continuity
(continuous, binary,
integer), and any special ordering instructions for arrays (increasing,
decreasing,
SOS1, SOS2). Alternatively, the parameter can be made a formula parameter and
the formula given an "optimize" prefix; this only works for the main optimizer
model.
To specify constraints, the client requests constraint parameters from a model
parameter. Constraints are parameters with some extra properties. The value of
a
constraint parameter represents the right-hand-side of a constraint, and could
be a
formula involving variable parameters. The left-hand-side of the constraint is
the
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owning parameter, and the relation is specified by the client: greater-than,
equals or
less-than. The client can specify that adjacent constraints be combined in an
OR-
relation rather than the default AND-relation. Constraints have their own
activation
formulas; this enables the client to activate and de-activate constraints
automatically.
Constraints can be turned into assertions by setting their test-only switch.
Assertions
do not affect the optimization, but they can be queried by the client as to
passing or
failing just like constraints.
To specify the objective function to an optimizer model, the client requests a
model parameter for each component of the objective function and sets its
"objective
function coefficient" property to the appropriate number; a positive number
implies
maximization, negative minimization. If there is more than one parameter with
a
coefficient, the optimizer will optimize the sum of the values multiplied by
their
respective coefficients.
The solving of an optimization model is done in phases. During the first
phase, the formulas involved in constraints (and the objective function) are
visited to
determine the set of parameters that contribute (directly or indirectly) to
constraints or
the objective function. During the second phase, the definitions of all these
parameters are visited to determine which are variable. The next few
optimization
phases are designed to determine array sizes and array element variabilities
for those
parameters with array values. This is done by generating an auxiliary set of
parameters whose formulas are cloned from the original. The auxiliary
parameters
corresponding to parameters that the client has specified as variable are
given special
place-holder values which have a trivial pass-through arithmetic. When the
other
auxiliary parameters are evaluated, the result is normally a place-holder
value, or an
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array of such. Wherever a place-holder value is encountered, that represents a
variable (column) to be created in the optimization model. -
Next, objects representing the basic variables (columns) of the model are
created, and the coefficients, or rows, of the matrix are generated. Some rows
5 correspond to the definitions of parameters, others to the constraints as
supplied by
the client. To generate the coefficients, a special type of value is used
which is
basically a linear combination of variables. Once an arithmetic of these
values has
been programmed, then they can be passed through the normal expression
evaluator, and the rows created from the results. A second set of auxiliary
10 parameters with cloned formulas is used to do this. Only client constraints
that
cannot be interpreted as bounds on the variables generate rows.
During coefficient generation, OR-groups of constraints, and some non-linear
functions are linearized by creating extra binary variables to "take the
decisions".
Functions that cannot be linearized generate non-linear errors.
15 After the model has been generated this far, a lot of information is
available to
the client such as linearity of the model, lists of constraints and
optimizable
parameters. The model is finalized by removing any egregious scaling problems
(for
example caused by the client defining some parameters in dollars and some in
percents), and replacing some symbolic large and small constants (introduced
with
20 the extra binary variables) with real numbers estimated from other
constants in the
matrix.
The arrays that Cplex expects as inputs are created and the model transmitted
to the Cplex server. The engine waits until that server has completed,
forwarding any
progress messages back to the client. The results are obtained from the Cplex
25 server, and put back into the file wherever the client has specified that
parameters are
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variable. Binding information and shadow prices are obtained from Cplex and
stored
in the corresponding constraints. To assist users in tracking down
infeasibilities, only
the values that the user has specified as optimizable are put back into the
model; any
dependent parameters and constraints are then recalculated from their
formulas, and
lists of failing constraints are available the client (user) to display.
If there are any optimization search parameters, then the model building and
solving steps are repeated using different guesses for the search parameters
until the
best objective value is found. Optimization search parameters are formula
parameters with a search prefix in which only the first three arguments have
been
specified (low, high, accuracy). This kind of search prefix has no effect
outside of
optimization. It is used by the client to solve for variable parameters which
cannot be
specified as variable to the optimization model without sending the model non-
linear.
The algorithm for choosing the guesses is a custom quadratic-fit algorithm for
finding
the maximum of a function.
For the purposes of generating the optimization model, any non-optimization
search parameters are frozen at their current values. If one of these has a
new value
as a result of the optimization in such a way as to invalidate the
optimization, then a
message about this is generated and sent to the client, and a special status
condition
set.
There are two optimization actions provided for the client to execute. The
,
"optimize" action will perform all of the above steps. The "build model"
action
performs only the first few steps, enough to get the client data on linearity,
constraints, etc. This last action is performed by the Advantage optimization
chapter
to provide visual feedback while the data to display the chapter is being
prepared.
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The engine can export its model to Microsoft's EXCEL software, creating as far
as possible a working spreadsheet model of all the parameter formulas. The
exported model is limited in that it cannot handle date changes or changes in
frequency or term that require re-dimensioning of arrays. It does a good job
of
formatting the resulting sheets to reflect the data hierarchy of the model.
The client
has control over the sheets and what is included in them.
The client can create other types of actions in worksheets. A marksman is a
targeting action which works similarly to the search prefix. Being an action,
however,
it can be executed asynchronously with the client displaying progress. Each
time
round the loop, the variable parameter is guessed, and a specified list of
actions
performed, which could include optimization and other marksmen. This is
repeated
until a target variable reaches a specified value, or is maximized or
minimized. A
matrix is a repetitive action designed to vary a parameter over a range of
values,
perform a list of actions which could include optimization and marksmen at
each
iteration, and store a set of results. These results are collated into a two-
dimensional
matrix of values assigned to a result parameter. An action sequence is a set
of
actions which is executed serially; this could be used to implement a
primitive macro
language.
The engine preferably has a background thread which steals idle cycles to
perform tasks in advance of the client requesting them. For example,
evaluation of
parameters, including searches, and generation of the optimization model. This
can
markedly improve interaction speed as the client may well find that whatever
it needs
to create a display has already been prepared by the engine. For example, the
engine may submit background optimizations to Cplex so that should the user
decide
to press the optimize button, he would get an instantaneous result.
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FORMULA LANGUAGE
As explained above, the instant invention includes a powerful formula language
which can be used in the worksheet, as well as in other chapters of the
invention, to
provide scenario information. This formula language includes a library of
predefined
functions and keywords which can be used by the user when using the tool. An
exemplary set of these functions and keywords which comprise the formula
language,
together with an associated syntax, is provided below.
ABS function
ABS (Number)
Returns the absolute value of an argument.
Number is any numeric value or expression that is a real number.
Accrue prefix
Accrue(Calendar):source_values
Tells the application to recognize values as amounts to be allocated uniformly
to each
day in their time periods.
= Source values come from one or more previously defined numbers streams.
= If Calendar is omitted, the application applies its own calendar selection
method.
= To calculate accrual amounts, the application looks at three factors:
1. Overlap between source periods and accrual periods.
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2. Given or selected calendar method.
3. Daily rate of source value (source value divided by days in source period).
Accruelnterval function
Accruelnterval (Offset, Calendar)
Accrues Advance or Arrears payments into a set of user-defined intervals.
This function differs from its cousin Periodinterval in that it takes into
account
the Advance or Arrears nature of the payment stream in which it occurs. It
combines this information with the StartDates or EndDates prefix of the
payment stream date index to determine which interval is relevant to the
current payment.
= Offset is an integer that defines the periods in which to accrue values.
= Offset 0 (or blank) accrues to each interval containing a value.
= Offset +1 accrues to the interval of the next period of value, offset +2
includes
the next two periods of value, and so on.
= Offset -1 accrues to the interval of the previous period of value, offset -2
includes
the previous two intervals, and so on.
= Calendar is a calendar method such as Actual_360, European_30_360, and so
on.
= If Calendar is omitted, the application applies its own calendar selection
method.
AccumulateByPeriod function
AccumulateByPeriod (Stream, Period)
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Accumulates values from an indexed array into the overlapping periods under a
different index.
= Stream is the name of an indexed numbers stream.
= Period is the name of the date index of periods to serve as points of
5 accumulation.
= Activation Switches
An activation switch is a formula that evaluates to True or False (e.g. x=y)
in regard to
10 a heading or a constraint.
= An activation switch on a Smart Paper heading is symbolized by a blue
rectangle.
= Headings in instruments and templates are activated through payment
classifications rather than activation switches, so there are no activation
symbols
in those forms.
15 = If a heading activation switch evaluates to False, the entire section
(heading,
subordinates and constraints) is deactivated, and the section is dimmed.
= The activation switch for a constraint is not symbolized or visible until
you display
the constraint in full edit mode. If the switch evaluates to False, the
constraint is
inactive and gets ignored during optimization.
20 Adding an Activation Switch
1. Click the heading or the constrained parameter you want to modify and press
Ctrl+Enter to enter full edit mode.
= Enter a heading activation formula in the formula edit field, or....
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= Click a constraint name to select it, then right-click for a shortcut menu
of options.
Choose Add Activation Formula and enter the formula in the field provided.
Rules for activation switches
= An activation formula must not depend on anything optimizable. If it does,
it will
always deactivate its section, even if the formula appears to evaluate to
True.
= An activation formula with an error, or one which evaluates to something
other
than True or False, will always deactivate its section.
Functions and Activation Switches
An attempt to reference an inactive parameter returns an error unless:
= You use the WhenActive or FindValue functions to return an argued value when
an inactive parameter is found.
= You use the Subtotal function, which automatically excludes inactive
parameters.
ActsLike prefix
ActsLike(reference):additional_formula
Makes a parameter mimic the behavior defined by the formula for another
parameter.
= Reference is name of parameter to mimic.
= The formula that follows the colon (:) can be the reference parameter name
(to
use its values) and/or other formula definition.
Actual 360 function
This is one of four calendar methods you can choose to evaluate intervals
between
dates for the purposes of calculation.
= Actual_360 divides the actual number of days in a given month into a year of
360
days.
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Actual 365 function
This is one of four calendar methods you can choose to evaluate intervals
between
dates for the purposes of calculation.
= Actual_365 divides the actual number of days in a given month into a year of
365
days.
AddYears function
AddYears (Dates, Years, Calendar)
AddYears returns a date based on the calculated interval between a given date
and
given number of years, using the day-counting metrics of the current calendar.
= The interval is internally calculated using the Interval function, where its
Datel
and Calendar arguments use the Date and Calendar argued in the AddYears
function.
= The interval is the sum of a whole number of years and a fractional part.
Only the
fractional part is affected by the calendar argument.
= Date is any date expression.
= Years is a whole or decimal number to express the number of years.
= Calendar is a calendar method such as Actual_360, European_30_360, and so
on.
= If Calendar is omitted, the application applies its own calendar selection
method.
Advance prefix
Advance: values
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Defines a payment stream in which each payment applies to the period following
the
date on which the payment occurs.
= In Smart Paper, the ~ symbol identifies Advance payments.
After keyword
After date
Defines the first value in a date stream or maps the first value in a sorted
numbers
stream.
= In a date stream, use After to begin the stream on the first anniversary of
the
After date. The interval to the anniversary is determined by a frequency
keyword
such as Annual.
= In a numbers stream, use After to key the first value in the stream to the
index
date that follows the given date.
Align keywords
Alignment keywords anchor the anniversaries in continuing dates to a month/day
or
the same day each month at a given frequency. There are two ways to express
alignment:
Align frequency mm/dd
In this expression, you anchor continuing dates (at the given frequency) to
the relative
date mm/dd rather than the first date defined in the formula.
Align Monthly On dd
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In this expression, you anchor monthly continuing dates to a day of the month
other
than the starting date.
Also keyword
Also date
Use the Also keyword at the end of a date stream formula to insert a date that
will not
otherwise occur according to the preceding formula.
Anchor Date
An anchor date is the point of departure in the calculation of an anniversary
or other
fixed date.
= The anchor date is expressed as a relative date modified by the keyword
expressions Align frequency or Align Monthly On.
AND function
AND (conditionl, condition2, ...)
AND returns a logical value that asserts if a set of conditions are true or
false.
= Returns True if all of the arguments are true.
= Returns False if any one or more of the arguments is false.
= Conditionl, condition2, and so on are the conditions you want to test for
being
true or false.
Anniversary (definition)
An anniversary is a date that occurs on the basis of a given anchor date and
frequency.
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= If the anchor date is March 1 and the frequency is Monthly, the first
anniversary
of the anchor date is April 1, the second anniversary is-May 1, and so on.
There is also an Anniversary function that lets you calculate the occurrence
of an
anniversary based on a set of arguments.
5 Anniversary function
Anniversary (AnchorDates, Dates, Frequency)
Returns the last anniversary of an anchor date up to (and including) a cutoff
date.
Anniversaries occur at the specified frequency beginning on the anchor date.
= AnchorDate is the date from which the anniversary countdown begins.
10 = Date is any date expression for the cutoff date.
= Frequency is Monthly, Quarterly, Semiannual, or Annual.
Annual keyword
Annual (or Annually) is a frequency keyword used to define the interval
between
15 continuing dates in a date stream.
ArrayBylndex function
ArrayByl ndex(Array, I ndex)
Returns the values in a source array that correspond to a given index
position.
= Array is the name of the indexed array that contains the value to be
returned.
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= Index is an integer (or array of integers) that refers to the key location
of an index
array value against its index. The reference for the value in the first
position is 1,
the second position is 2, and so on.
Array parameters (definition)
An array is a type of parameter that contains a series of one or more values.
The
values are arranged according to a formula. There are three types of arrays:
Sorted array Stream of values in ascending order, with no
duplicates.
= A typical sorted array is an index parameter, as
seen in the underlined set of dates used to
coordinate a set of cash flows.
= Since each position on an index parameter may
be a key to a value in another array, an index is
also referred to as a key parameter.
Indexed array Stream of values in the scope of an index (sorted
array).
= A typical indexed array is a set of cash flows in a
deal, where each flow is keyed (attached) to a
position on a date index.
Plain array Stream of values indexed by the natural numbers (1, 2,
3, ...).
= May also be referred to as an unsorted array, as
its elements occur in whatever order they are
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entered in the formula.
ArraySum function
ArraySum(Array)
ArraySum returns the total of all the values in an array.
= Array is the name of any array parameter.
Arrears prefix
Arrears: values
The Arrears prefix means that each payment applies to the period that precedes
the
date on which the payment is incurred.
= In Smart Paper, the a symbol identifies Arrears payments.
Badge (definition)
A badge is an internal ID that associates certain data to a list member within
a
category ("category=list member"). For example:
= The category "Instrument" includes the list members "Rent", "Asset", "Loan",
and
so on.
= The category "IncomeClassification" includes the list members
"RentReceived",
"SourcesOf Funds", and so on.
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Before keyword
Before date
Defines the last date in a date stream or defines the date on which the last
value in a
numbers stream occurs.
= In a date stream, use Before to make the stream end on the latest possible
anniversary (in a continuing dates sequence) that occurs prior to the given
date.
= In a numbers stream, use Before to assign the last value in the numbers
stream
to the index date that most immediately precedes the given date.
Bookend date (definition)
A bookend date is a date index element that does not represent the beginning
or end
of a period. The period prefix used in the date index determines the bookend
date.
= When the StartDates prefix applies, the bookend date is the last date on the
index.
= When the EndDates prefix applies, the bookend date is the first date on the
index.
Calendar Functions
The tool relies on a user-specified calendar method to evaluate intervals
between
dates for the purposes of calculations such as:
= interest on a loan
= accrual of payments that cover periods across fiscal years (for tax
purposes)
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= present value and yield calculations
The active calendar method in a calculation affects payment values because
there
are more or fewer days in a given interval based on the calendar.
Multiple Calendars in the Same Case
= Every case has a global default calendar set in Time Organizer. You can
change
this default and you can also use different calendars at local levels (i.e.
for an
instrument or a sheet of Smart Paper).
= In the event of multiple calendars, the application has a process to
determine
which one is in effect for a given calculation. See Calendar Selection Method.
Calendar selection method (definition)
You can specify different calendar methods for different requirements in the
same
case. If a case has more than one calendar method, the application uses a
decision
tree to determine the method that applies to a particular calculation.
Decision Tree for Calendar Selection
When a case contains multiple calendar methods, the application applies the
closest
method it can find based on this order:
1) Does the formula contain a calendar?
= Some prefixes (Accrue, for example) prompt you to select a calendar method.
= You can also add or insert a calendar as a function.
= For example, the list of functions available through Formula Assistant to
add/insert a function includes each of the four methods: Actual_360,
Actual_365, and so on.
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2) Failing that, does the current sheet of Smart Paper contain a parameter
named
Calendar?
3) Failing that, the application applies the default calendar method setting
in Time
Organizer.
5 Cash prefix
Cash: values
Cash is the default prefix for a payment stream when neither the Advance
prefix nor
the Arrears prefix is given. Use the Cash prefix (or omit a prefix) to specify
that each
payment applies to the date on which it is incurred.
10 Categories and List Member Reference
A badge is an internal ID that that comprises a category and one of the list
members
within that category. Certain functions use the list member portion of a badge
as an
argument to collect or extract data.
15 CEILING function
CEILING(Number,Significance)
Returns a number rounded up to the nearest multiple you specify.
= For example, to round up the value 575.29 to the nearest multiple of 0.5,
you use
the formula CEILING(575.29, 0.5). The application returns 575.50.
20 = Number is any numeric expression that you want to round up.
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= Significance is the multiple to which you want to round Number. The
application
rounds the number up away from zero.
= Number and Significance cannot have different signs.
CHAR function
CHAR(Code)
Returns a character value from the ANSI code you specify.
= Code is a number between 1 and 255 that specifies a character on your
computer.
CHOOSE function
CHOOSE(Index,Valuel,Value2, ...)
Returns a value from a list of arguments based on an index number.
= Index specifies which value(s) to select from the list of arguments. Index
can be
any scalar or array value, including numbers or parameter references. For
example, if the value of Index is 2, the application returns the second
argument.
If Index has a fractional value, the application truncates the fraction and
uses the
resulting integer to select an argument.
= Valuel, Value2 and so on are the list of arguments from which the
application
selects based on the value of Index. The arguments can be any number or
expression, including scalar or arrays.
Classifications (definition)
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A classification is a financial label. It tells the application how to
retrieve values given
a context such as instrument, outcome, party/role, and so on.
Guidelines for Working with Classifications
1) Keep other arguments in context when given a classification argument.
= For example, when the Rent instrument is instated for the base outcome, the
following two classifications are active:
= RentPaid by the lessee, and
= RentReceived by the lessor.
= If you write a Collect function to look for RentPaid but add filters such as
Party=Lessor or Instrument=Asset, the RentPaid classification is meaningless
and the function cannot find the rent paid values.
2) Classifications are spelling-sensitive.
= For example, the application recognizes SourcesOfFunds and Sourcesoffunds,
but not SourceOfFunds or SourcesOf Funding.
=
Identifying Classification List Members
There are three ways to see a list of payment (income/cash) classification
members.
In Smart Paper
a) In SmartPaper, add a parameter.
b) Change the parameter to a List Member parameter.
In Payment Organizer
a) Change Payment Organizer Data.
In Instrument Chapter
a) Modify Payment Classification Settings for Instrument
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CODE function
CODE(String)
Returns an ANSI code that specifies the first character in a text string.
= String is a series of text characters or a reference to a parameter that
contains
text characters.
= Enclose String in quote marks.
CollectData function
CollectData (CategoryMemberList)
Collects data from parameters that match up to one or more badges.
= CategoryMemberList is an expression of one or more badges, with one set of
quote marks to encase the entire string. See Categories and List Member
Reference.
= Use the word and to separate multiple badges.
= To reference a party by its role rather than the party name, use the syntax
"+Rolename+" as seen in the Example2 parameter.
Collectincome function
Collectincome (Party, Classification, Outcome, Instrument, OtherParty,
TaxAuthority)
Collects income from parameters that match a set of one or more badges. Each
argument position represents a category and takes a user-specified list member
name.
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= See Category and List Member Reference for help on names for parties,
classifications, and so on.
= Party identifies the entity whose income flows you want to collect. You can
use
either a party name or a role name for the argument.
= Party versus role: you must encase a party name in quote marks, whereas a
role
name does not require quote marks.
= Classification is the Income classification name (in quote marks) for the
flows to
be collected.
= Outcome is the name of the outcome (encased in quote marks) under which
income is to be collected. The function assumes "BaseOutcome" if no outcome
is specified.
= Instrument is the name of the instrument (in quote marks) for which income
is to
be collected. The function considers all instruments if no instrument is
specified.
= OtherParty identifies the other party for flows from two-party instruments.
= You can use a party name in quote marks or a role name (no quote marks)
= Tax Authority identifies the tax collector for the income to be collected.
= You can use a party name in quote marks ("IRS") or the role name
TaxCollector
without quote marks.
CollectPayments function
CollectPayments (Party, Classification, Outcome, Instrument, OtherParty)
Collects payments from parameters that match a set of one or more badges. Each
argument represents a category and takes a user-specified list member name.
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= See Category and List Member Reference for help on names for parties,
classifications, and so on.
= Party identifies the entity whose payments you want to collect. You can use
either a party name or a role name for the argument.
5 = Party versus role: you must encase a party name in quote marks, whereas a
role
name does not require quote marks.
= Classification is the Payment classification name (in quote marks) for the
flows to
be collected.
= Outcome is the name of the outcome (encased in quote marks) under which
10 payments are to be collected. The function assumes "BaseOutcome" if no
outcome is specified.
= Instrument is the name of the instrument (in quote marks) for which payments
are to be collected. The function considers all instruments if no instrument
is
specified.
15 = OtherParty identifies the other party for flows from two-party
instruments.
= You can use a party name in quote marks or a role name (no quote marks)
CONCATENATE function
CONCATENATE(Stringl, String2, ...)
Links multiple text strings into one string.
20 = Stringl, String2, and so on are a series of text characters or a
reference to a
parameter that contains text characters. Enclose each text string in quote
marks.
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Constraint/Assertion (definition)
A constraint/assertion is a formula you can add to a parameter along with the
formula
that generates the parameter values.
= The constraint /assertion formula defines the degree to which values can be
re-
calculated during optimization.
= You can only add a constraint /assertion to a parameter in full edit mode
(Ctrl+Enter).
= The constraint /assertion can be binding or non-binding.
= Binding. Optimization fails if constraint or assertion cannot be honored.
= Non-Binding. Inability to meet the constraint or assertion is noted, but
does not
cause Optimization to fail.
Context function
Context(Reference)
Returns the full pathname (i.e. SheetName.Heading.SubHeading.Parameter) to the
given reference.
= This is useful when you have multiple parameters with the same name and need
to distinguish between them.
= For example, if you instate the MISFYieIdByMonth template twice in one case,
you end up with two parameters named lnput.MinYield.
= If you insert a Context parameter in the Inputs section of each template,
you can
then use the FindValue or GetResults function to locate the value under
Headingl.Input.MinYield versus Heading2.lnput.MinYield.
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= Reference is an instrument name, a Smart Paper sheet name, or any heading or
parameter name.
COUNT function
COUNT(Array)
Counts the number of values in an array.
= Array is a series of values separated by semicolons, or the name of any
array
parameter such as a numbers stream or date index.
= Empty or blank elements in the array are included in the count.
Cumulative function
Cumulative(Array)
Returns an array in which each value is the accumulated value of all preceding
values
in the argued array.
= Array is the name of an array parameter, or it can be a series of values
defined
by numbers stream keywords.
The opposite function is Difference (returns difference between each
successive element in an array or series of values).
A related function is SumToDate (returns a single number for the sum value of
an array or series of values as of a given date).
Daily Present Value function
Daily_Present_Value (Flows, PVRate, PVDate, Calendar)
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Returns the daily present value of a set of cash flows.
= Flows is the parameter name for a set of cash flows. -
= PVRate is a percentage for the nominal monthly discount rate.
= PVDate is any single date expression to which the cash flows are discounted
or
accreted.
= Calendar is a calendar method such as Actual_360, European_30_360, and so
on.
= If Calendar is omitted, the application applies its own calendar selection
method.
DATE function
DATE(Year, Month, Day)
Returns a date value from numeric values that represent a year, month, and
day.
To create a date you can use to produce a date stream consisting of last days
of months, use MonthEndOf.
= Year is a number from 1900 to 9999.
= Month is a number that represents the month of Year.
= If Month is greater than 12, the value is added to January of Year. See
Example
vi.
= If Month is less than 1, the value is subtracted from December of Year. See
Example V2.
= Day is a number that represents day of Month.
= If Day is greater than the days in Month, the value is added to day 1 of
Month.
See Example V3.
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= If Day is less than 1, the value is subtracted from day 1 of Month. See
Example
V4.
DateAsEntered function
DateAsEntered (Date)
Returns a date value in format "dd mon, yyyy" (including the quotation marks).
= Date can include a day number between 1 and 31 irrespective of the month.
Date Expression (definition)
A date expression is a date included in a formula. The date can be given in
any of the
following formats (refer to example):
1) Calendar date, as in 01 Jan 2000.
2) Parameter reference, as in ClosingDate (where ClosingDate is previously
defined).
3) Date location by keyword reference, as in First datestream or Last
datestream.
4) Elapsed time before or after a date, as in date +3y.
5) Inserted function that defines a date.
Date Index (definition)
A date index is an array parameter that contains an ascending series of dates.
The
dates are used to coordinate series of values according to when they occur
over time.
0 Each element on the index is a key (a point of coordination for sorting
values).
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= Parameters below the index are indexed arrays of values that are keyed to
the
index positions.
Dates function
Dates (First, Second...)
5 Returns a date stream consisting of dates used to key the argued numbers
stream(s)
without regard to the StartDates or EndDates prefix designation of the source.
= If you want true end dates of periods as a result, you must specify the
EndDates
prefix with the Dates function.
= Otherwise, the returned dates automatically default to the StartDates prefix
and
10 therefore represent the beginnings of periods.
= First (and so on) is the parameter name of a payment or income stream, or a
table of values.
DATEVALUE function
DATEVALUE(Date)
15 Converts a text string representation of a date to a date value.
= Date is any name reference or text string that represents a date.
DAY function
DAY(Date)
Returns an integer value (between 1 and 31) for the day of the month in a date
value.
20 = Date is any name reference or text string that represents a date.
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DAYS360 function
DAYS360(Starting Date, Ending Date, Method)
Returns the number of days between two dates on 360-day calendar (twelve 30-
day
months).
= Starting Date and Ending Date are the two date values you want to calculate
the
number of days between. If Ending Date occurs before Starting Date, a negative
number is returned.
= Method is False to specify the U.S. method of calculation or True to specify
the
European method.
Days365 function
Days365 (StartDate, EndDate)
Returns the number of days between two dates based on a 365-day year.
= StartDate is the first date to include in the count.
= EndDate is a bookend date that is not included in the count of days.
= For example, to obtain a count of days in the period Jan 1 to Jan 31 that
includes
the 31 St , the End Date is Feb 1.
= Days365 returns a negative number if StartDate is later than EndDate,
DayslnPeriod function
DaysinPeriod (Period, Calendar)
Returns the number of days in period according to specified calendar.
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= Period is two dates from a date index expressed mm/dd/yy to mm/dd/yy (or
using
other valid date syntax; see example).
= Calendar is a calendar method such as Actual_360, European_30_360, and so
on.
= If Calendar is omitted, the application uses the decision tree for multiple
calendars to choose a method.
DayslnYear function
DayslnYear (Calendar)
Returns the number of days in a calendar year.
= Calendar is a calendar method such as Actual_360, European_30_360, and so
on.
= If Calendar is omitted, the application uses the decision tree for multiple
calendars to choose a method.
Destination Parameter (definition)
A destination parameter is one in which the formula refers to another
parameter in
order to use the referenced parameter as a source of data.
Difference function
Difference (Array)
Returns the difference between each successive value in an array or series of
values.
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= Array is the name of an array parameter or a series of values defined by
numbers stream keywords.
Also see Cumulative (returns accumulated value of all preceding values in an
array or series of values).
ElapsedTime function
ElapsedTime (Years, Months, Days)
Returns an elapsed time value in whole numbers for years, months, and days.
= Use this function when other parameters in the case depend on an elapsed
time
value.
= Each argument uses any whole number.
= Insert commas as placeholders for omitted arguments.
EndDates prefix
Indicates that each date on the index (except the first date) represents the
LAST day
of a period.
= Each period begins the day after the index date and ends on the next index
date.
= The first date in the index is a bookend. It does not represent the end of a
period.
= The f- symbol indicates the EndDates prefix.
EndDatesOf function
EndDatesOf (First, Second, ...)
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Returns the combined dates used to organize a set of number streams, first
converting them to end dates if necessary.
= This lets you create an index comprising the date values of various indexed
parameters without having to remember anything about the indexes themselves.
= If an argued numbers stream is keyed to an EndDates: date index, the
function
returns the dates as they appear on that index.
= If an argued numbers stream is keyed to a StartDates: date index, the
function
first subtracts one day from each date to return it as an end date.
= To make the resulting dates represent true end dates, you must supply the
EndDates: prefix as well as the function. See example.
= First (and so on) are the parameter names of numbers streams (tables, cash
and
income streams).
The similar EndDatesOf Periods function slows down optimization performance,
but it is more flexible in the types of arguments it accepts.
EndDatesOfPeriods function
EndDatesOf Periods (First, Second, ...)
Derives period start dates from one or more numbers streams and/or date
indexes,
then creates a date index of dates that reflect the end dates of the
underlying periods.
Also incorporates dates or date streams given as arguments.
= To calculate dates for the result, the function subtracts one day each from
the
start dates.
= To make the resulting dates represent true end dates, you must supply the
EndDates prefix as well as the function.
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= First (and so on) can be any one or more of the following:
= Parameter name of a date index with the StartDates prefix (StartDates is the
default if no prefix is present).
= Parameter name of a numbers stream (i.e. income or payment flow, table) that
is
keyed to a StartDates date index.
= Single date expression or date stream expression.
Ending keyword
Ending date
Defines the last date in a date stream.
European 30 360 function
This is one of four calendar methods you can choose to evaluate intervals
between
dates for the purposes of calculation
= Consists of twelve 30-day months (each month is one 12th of the year).
= February is given two extra days.
= If a period starts or ends on the 31St, the day counts as the 30th of the
same
month.
= For example, the interval of 1 st to 31 st is 29 days.
EVEN function
EVEN(Number)
Returns a number rounded away from zero to the next even integer.
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= Number is the value to round.
Except keyword
;Except value On date
or
;Except On date
Allows for a break in a sequence of values being mapped to an index.
= The Except term always begins with a ; (semicolon) separator to halt the
previous
formula sequence.
= It is optional to include an exception value with the Except keyword. If you
do not
provide an exception value, there is no value shown for the Except date (see
NumberStream2 in example).
= Except can only be used at the end of the numbers stream formula.
EXP function
EXP(number)
Returns the natural logarithm base e(2.71828182845904) raised to the power you
specify.
= Number is the power to which you want the application to raise e.
FALSE function
FALSE
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Returns the logical value False.
FIND function
FIND(FindText,WithinText,StartNum)
Finds and returns the starting position of a text string within another text
string.
= FindText and WithinText are series of text characters (or references to a
parameter that contains text characters) encased in quote marks.
= FindText is the text string you want to find (no wildcard characters).
= WithinText is the text string that contains FindText.
= StartNum is the character position where you want the application to start
the
search. For example, to start with the third character in WithinText, use a
StartNum of 3. If you omit StartNum, the application uses 1.
= If FindText is not contained in WithinText, the application returns an
error.
= If StartNum is zero or less, or if StartNum is greater than the length of
WithinText, the application returns an error.
FindValue function
FindValue (Context, Parameter, InactiveNull)
Locates a value given its context within the case.
= Context can be any of the following:
= the name of a Smart Paper sheet, heading, or instrument encased in quote
marks
= the name of a parameter defined with the Context function (no quote marks)
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= the name of a parameter that defines an array of sheet names, heading names,
or instrument names
= Parameter is the name of the parameter that contains the value you want to
find.
= InactiveNull lets you specify a value to return in lieu of the error
Inactive Parameter if the context/parameter specification points to an
inactive
parameter.
First function
First (Array)
Refers to the first value in a given array.
= Array can be a numbers stream or date stream.
First keyword
First datestream
Refer to the first date in a date stream in order to use the date itself in
another date
stream.
FLOOR function
FLOOR(Number,Significance)
Returns a number rounded down to the nearest multiple you specify.
= Number is any numeric expression that you want to round down.
= Significance is the multiple to which you want to round Number. The
application
rounds the number down toward zero.
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= Number and Significance cannot have different signs.
For keyword
For n
Use the For keyword to repeat a numbers stream value or extend a date stream
sequence.
= In a date stream, use For to specify the number of anniversaries to continue
the
date stream at its current frequency.
= For n ends the stream after n periods at the given frequency unless the For
stream is further defined following a separator keyword such as ; (semicolon)
or
Then.
= In a numbers stream, use For to specify the number of increments to repeat a
value.
Forever keyword
Forever
Use the Forever keyword in date stream in lieu of an ending date phrase if you
want
to specify that the stream never ends.
GetResult function
GetResult (Result, Party, Outcome, Context, SubsidiaryParameter)
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Locates a SetResult parameter flagged with a matching set of arguments and
returns
the parameter value. Or, if optional arguments are included, the function can
return a
subsidiary parameter value.
= Result, Party, and Outcome must exactly match the arguments provided for a
previously established SetResult parameter, including quote marks.
= Context is the name of a parameter that uses the Context function to
pinpoint its
location.
= If Context is argued without the SubsidiaryParameter argument, the GetResult
function returns the value of the Context parameter.
= SubsidiaryParameter (which can only be argued in conjunction with Context)
is
the name of any parameter located under the same subheading as the given
Context parameter .
IF function
IF(LogicalTest,ValuelfTrue,ValuelfFalse)
Returns one of two values depending on the results of a logical test for a
true or false
condition.
= LogicalTest is any expression that the application can evaluate to be true
or
false.
= ValuelfTrue is any value or expression you want the application to return if
LogicalTest is true. If you omit ValuelfTrue and the LogicalTest evaluates to
True, the application returns the value True.
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= ValuelfFalse is any value or expression you want the application to return
if
LogicalTest is false. If you omit ValuelfFalse and the LogicalTest evaluates
to
False, the application returns the value False.
The application can return text if it is encased in quote marks.
Index (definition)
An index is a type of parameter used to coordinate values.
= Elements on an index look like an underlined series of column headings in a
table.
= In rows of values beneath the index, each value is keyed to an element on
the
index.
= You can create a date index to sort values over time, as shown here.
INDEX function
INDEX(Array,Firstlndex,Secondlndex,...)
Returns a value from any type of array based on the relative position of the
value
within the array.
= Array is the name of any array or date index parameter.
= Firstlndex (and so on) is a whole number representing the index key position
for
the value you seek.
INT
INT(number)
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Returns a number rounded down to the next integer of lesser value.
= Number is any real number you want to round down to-the next lowest integer.
Interpolate prefix
Interpolate (Calendar):
Tells the application to interpret each of its values as a lookup value that
is linearly
applied across its time period, creating a stepped value for each day in the
time
period
= You can then reference the Interpolate table (by parameter name) in the
formula
to calculate values for a destination parameter.
= If Calendar is omitted, the application applies its own calendar selection
method.
= If the destination date falls outside the date range of the Interpolate
parameter,
the application uses the two Interpolate dates that are closest to the
destination
date to figure the stepped value.
= In Smart Paper, the ,l symbol identifies a parameter with Interpolate table
values.
Interval (definition)
An interval is the length of a date index period calculated as a portion of a
year.
= For example, the first interval on a StartDates index is .5 if the index is
semiannual, .25 if the index is quarterly, and so on.
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= On a StartDates index, the first interval begins on the first date and ends
on the
day before the next index date. The last date on the index is a zero-length
interval (starts and ends on same date).
= On an EndDates index, the first date on the index is a zero-length interval
(starts
and ends on same date). The second interval begins the day after the first
date
and extends through the next date on the index.
Interval function
Interval (Date1, Date2, Calendar)
Calculates the numbers of years between two dates based on the day-counting
metrics of the given calendar.
= The function is calculated as the sum of a whole number of years and a
fractional
part. Only the fractional part is affected by the calendar designation.
= For example, the Interval between Feb 15, 2000 and Mar 15, 2001 using the
calendar Actual_360 is 1+28/360, not 394/360.
= For the most accurate results, format the row to permit multiple decimal
places.
= Datel and Date2 are any two single date expressions.
= Calendar is a calendar method such as Actual_360, European_30_360, and so
on.
= If Calendar is omitted, the application uses the decision tree for multiple
calendars to choose a method.
If you know Date1 and want to add an interval to obtain Date2, see AddYears.
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Key, Keyed (definition)
A key is a point of coordination on an index that is used to sort values.
= Keys can be defined as dates, integers, or alphanumeric strings encased in
quote marks.
= Each value in a array below the index is "keyed" to one position (element)
on the
index.
Keys function
Keys(Stream)
Returns the index used to coordinate the values in a numbers stream.
= A returned date index assumes the StartDates prefix (whereby dates represent
the beginnings of periods), even if the source index uses the EndDates prefix.
= You can also use the Dates function to return a date index or a combination
of
date indexes.
= Stream is the parameter name of a payment or income stream.
Last function
Last (Array)
Refers to the last value in a given array.
0 Array can be any numbers stream or date stream.
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Last keyword
Last stream
Refer to the last date in a date stream in order to use the date itself in
another date
stream.
LEFT function
LEFT(String,NumChars)
Returns one or more of the leftmost characters of a text string.
= String is a series of text characters or a reference to a parameter that
contains
text characters.
= Enclose String in quote marks.
= NumChars is the number of characters you want returned starting with the
first
character. NumChars must be greater than or equal to zero.
= If NumChars is greater than the length of String, the application returns
all of
String.
= If you omit NumChars, the application returns the single left-most
character.
LEN function
LEN(String)
Counts the number of characters in a text string, including spaces.
= String is a series of text characters or a reference to a parameter that
contains
text characters.
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= Enclose the text string in quote marks.
LN function
LN(Number)
Returns the natural logarithm of the number you specify.
= Number must be a positive real number. The application returns the natural
logarithm of Number.
LOG function
LOG(number,base)
Returns the logarithm of a number to a specified base.
= Number must be a positive real number. The application returns the logarithm
of
the number.
= Base is the base of the logarithm. If you omit Base, the application assumes
it is
10.
LOG10 function
LOG10(number)
Returns the logarithm of a number to base 10.
= Number must be a positive real number. The application returns the logarithm
of
the number to base 10.
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Lookup function
Lookup(OutputList, InputList, LookupValue, Action, NotFoundValue, Calendar)
Returns the occurrence of values shared between two parameters keyed to
different
indexes.
= OutputList is a parameter that contains the values to return where there is
a
match between InputList and LookupValue.
= Can be an indexed array (i.e. numbers stream) or a date index.
= If not specified, OutputList is assumed to be the natural numbers
(1;2;3....).
= InputList is a parameter that contains or organizes the LookupValue.
= Can be an indexed array (i.e. numbers stream), an index, or an unsorted (non-
indexed) array.
= If InputList is omitted and OutputList is an indexed array, then InputList
is
assumed to be the index of OutputList. Otherwise, it is assumed to be the
natural numbers (1;2;3....).
= If InputList is an unsorted array, then only exact value matches are
possible
(Action must be 0).
= LookupValue is a parameter that contains the values the function should
search
for within the InputList.
= Action specifies a code number for the type of result to return when an
exact
match is not found.
= NotFoundValue specifies the result to be returned if LookupValue is not
found in
InputList according to the preceding arguments.
= Calendar is a calendar method such as Actual_360, European_30_360, and so
on.
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= If Calendar is omitted, the application applies its own calendar selection
method.
LOWER function
LOWER(String)
Converts a text string to lower case.
= String is a series of text characters or a reference to a parameter that
contains
text characters. Enclose the text string in quote marks.
Max function
Max (argumenti, argument2,...)
Returns a scalar value or array of values, depending on the number of
arguments
given and if the Max parameter is indexed.
= Argumentn (and so on) is any number or parameter name.
MaxBylndex function
MaxBylndex (argumentl, argument2,...)
Returns array in which each position holds the maximum value found at the
corresponding position within a set of arguments.
= Argumentn (and so on) is any number or parameter name.
MaxOfAll function
MaxOfAll (argumentl, argument2,...)
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Returns the single maximum value found in a set of arguments.
= Equivalent to MAX in Microsoft Excel.
= Argument is any number or parameter name.
MID function
MID(String,StartNum,NumChars)
Extracts one or more characters from within a string.
= String is a series of text characters or a reference to a parameter that
contains
text characters. String contains the characters you want to extract.
= Enclose String in quote marks.
= StartNum is the position of the first character you want to extract.
= If StartNum is greater than the length of String or less than 1, the
application
returns an error.
= NumChars is the number of characters you want to extract, starting with the
character in the StartNum position.
= If StartNum plus NumChars is greater than the length of String, the
application
returns the characters up to the end of String.
Min function
Min (argumenti, argument2,...)
Returns a scalar value or array of values, depending on the number of
arguments
given and if the Min parameter is indexed.
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= Argumentn (and so on) is any number or parameter name.
MinByindex function
MinBylndex (argumentl, argument2,...)
Returns array in which each position is the minimum value found at the
corresponding
position within a set of arguments.
= Argumentn (and so on) is any number or parameter name.
MinOfAll function
MinOfAll (argumentl, argument2,...)
Returns the single minimum value found in a set of arguments.
= Equivalent to MIN in Microsoft Excel.
= Argumentn (and so on) is any number or parameter name.
MOD function
MOD (number, divisor)
Returns the remainder of a number after a division.
= Number is any numeric value for which you want to find a remainder.
= Divisor is any numeric value by which you want to divide the number. If the
divisor is zero, the application returns an error.
Month function
Month(Date)
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Returns an integer between 1 and 12 that represents the month in a date value.
= Date is any single date expression.
MonthEndOf function
MonthEndOf (Date)
Returns the last calendar day of the month for a given date scalar or stream.
= This function is typically used to produce a date stream consisting of the
last
days of months, the equivalent of writing the date constant 31 MON YEAR.
= Date streams based on the MonthEndOf date display the last calendar day of
each month, but each date behaves as the 31 S' when used in formulas.
= Date is any single date expression.
Monthly keyword
Monthly is a frequency keyword used to define the interval between continuing
dates
in a date stream.
Monthly MISF Yield function
Monthly_MISF_Yield (Flows, SinkingFundRate)
Returns the nominal monthly MISF yield of a given array of cash flows.
= This function uses a built-in search (invisible to you) to determine the
rate of
return to apply to a set of cash flows in order to end up with a net
investment
balance of 0 on the last yield date.
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= Use this function in place of the MISFYieIdByMonth template when you do not
need to assert or constrain the result.
= Flows is the parameter name for a set of cash flows keyed to a monthly date
index.
= If you argue a payment stream that is keyed to a different frequency, the
result
will be incorrect.
= SinkingFundRate is a percentage. The default is 0%.
Next function
Next(Array,LastValue)
Returns an array in which, relative to the current position, each value refers
to the
next sequential value in a source array.
= Array is the name of the current parameter or the name of a source array
from
which you want to retrieve the next values.
= This function and the Previous function can be used to create self-
referential
formulas.
= LastValue is a value used to calculate the final value of the array.
Nolndex prefix
Noindex: remainder of formula
Lets you specify that a parameter is not keyed to an index, even if the
parameter
appears to be within the scope of an index.
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= Typically, you use the Nolndex prefix to identify a scalar value that
happens to be
placed in the scope of a date index.
NOT function
NOT(Condition)
Reverses the logical truth or falseness of the argument.
= Condition is an expression that the application can evaluate to be true or
false. If
Condition is true, the application returns False. Otherwise, the application
returns True.
Null function
Null
= Returns a null (blank) value as opposed to the number zero.
ODD function
ODD(Number)
Returns a number rounded up to the next odd integer away from zero.
= Number is the numeric value you want to round up. If Number is an odd
integer,
the application does not round it up.
On keyword
On date
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Assigns a given value to the given date, or (with the Except keyword) lets you
exclude
a value on the given date.
= The value can precede the keyword or follow the date.
= If the given date does not a match a date in the index, the value is
ignored.
Optimize prefix
Optimize (Count/Date, Variability, Scale, Restriction):
Tells the application to calculate values to meet the objective function of a
case. An
example of an Objective Function is the total cash of a transaction.
= If you have entered a constraint on the parameter, the application
calculates an
optimized value that meets the requirements defined by the constraint.
= After you perform an optimization in the Optimization chapter, the
application
replaces the entire formula in each parameter that has the Optimize prefix
with
the calculated value(s).
= If you want to retain a portion of a parameter formula, split the formula
between
two parameters.
= In one parameter, use the Optimize prefix and enter the portion of the
formula
that can be replaced with values.
= In the other parameter, do not use the Optimize prefix. Enter the portion of
the
formula you want to retain, and refer to the parameter that contains the
Optimize
prefix.
= You can combine the Optimize prefix with other prefixes in a formula. For
example:
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Advance Optimize(argl, arg2, arg3, arg4):
= Count/Date is the number of, or last date of, the elements in the parameter
to be
set. If you omit a value for this argument, the application returns a value
for each
position in the parameter index.
= For Count/Date, you can also enter the number of periods (such as 30 years),
or
the end date (such as 12/31/2010), or the number of elements in the parameter
you want to set.
= Variability is one of the following functions:
= Variable. Allows any value to be returned.
= IntegerVariable. Allows integer values only to be returned.
= BinaryVariable. Allows one or zero only to be returned.
= Constant. Does not allow the current value(s) to change. Use this option to
freeze a value from a previous optimization.
= You can also enter a formula for any of the Variability options. Enter the
formula
in place of the Variability option, or refer to a parameter that has the
formula.
= Scale. If Variability is set to Integer or BinaryVariable, enter the scale
you want
to use.
= Restriction can be one of the following functions:
= None. There are not any restrictions on the values returned.
= Increasing. The values returned must be in ascending order (xl <=x2<=x3...).
= Decreasing. The values returned must be in descending order (xl
>=x2>=x3...).
= OnlyOne. Only one of the values returned can be non-zero.
= OnlyTwo. Only two of the values returned can be non-zero, and they must be
adjacent.
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= You can also enter a formula for any of the Restriction options. Enter the
formula
in place of the Restriction option, or refer to a parameter that has the
formula.
OR function
OR(condition 1,condition2,...)
Returns the logical value True if any of the arguments are true. If all of the
arguments
are false, returns False.
= Condition 1, condition2, and so on are the conditions you want to test for
being
true or false.
Parameter (definition)
A parameter is data that represents a calculation and can be used in other
calculations.
= The components of a parameter include its name, its formula, and the
value(s)
computed as a result of the formula.
= The formula for one parameter can refer to other parameters.
= You create and view parameters on sheets of Smart Paper.
PeriodEdge function
PeriodEdge (Date, Periods, First/Last, Containing/Following)
Returns the first or last day in a period. You can specify whether you want
the day to
be in the period, or before or after the period.
0 Date is any single date expression.
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= Periods is the parameter name of the date index that contains the period of
interest.
= First/Last requires the logical value True or False.
= Enter True to get the last date.
= Enter False to get the first date.
= Containing/Following requires the logical value True or False.
= Enter True to get a date within the defined period.
= Enter False to get a date within the period that follows the defined period.
PeriodEnd function
PeriodEnd(Period)
Returns the end date of a period defined by a set of bookend dates.
= Period is expressed mm/dd/yy to mm/dd/yy (you cannot use a parameter
reference for either date).
Periodlntersection function
Periodlntersection (PeriodStreaml, PeriodStream2)
Returns a period stream based on the intersecting dates of two other period
streams.
= PeriodStreaml is the parameter name of a date stream.
= PeriodStream2 is the parameter name of a date stream.
Periodinterval function
Periodlnterval (Offset, Calendar)
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Maps a numbers stream into a set of user-defined intervals.
If you need to use the period interval for a parameter with an Advance or
Arrears prefix, use Accruelnterval.
= Offset is an integer that defines the periods in which to return interval
values.
= A blank or 0 offset assumes an interval of each period containing a value.
= A +1 offset assumes the interval of the next period of value, +2 includes
the next
two periods of value, and so on.
= A -1 offset assumes the interval of the previous period of value, -2
includes the
previous two intervals, and so on.
= Calendar is a calendar method such as Actual_360, European_30_360, and so
on.
= If Calendar is omitted, the application applies its own calendar selection
method.
PeriodLength function
PeriodLength (Period, Calendar)
Returns the portion in years of a period according to specified calendar.
= Period is a pair of dates expressed as mm/dd/yy to mm/dd/yy (do not use a
parameter reference).
= Calendar is a calendar method such as Actual_360, European_30_360, and so
on.
= If Calendar is omitted, the application applies its own calendar selection
method.
Periods function
Periods (IncomeStream)
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Returns a stream of periods to which values in the given numbers stream are
keyed.
= IncomeStream is the parameter name of a payment or income stream.
PeriodStart function
PeriodStart (Period)
Returns the start date of a period defined by a set of bookend dates.
= Period is expressed mm/dd/yy to mm/dd/yy (you cannot use a parameter
reference for either date).
PeriodStream function
PeriodStream (StartDate, DateStream, EndDate)
Creates a period stream from a pair of bookend dates and an existing date
stream.
= StartDate is the first date of the first period in the stream to be created.
= DateStream is the parameter name of the date stream that contains the
periods
to be used in the period stream following the given StartDate.
= EndDate is the end date of the last period in the period stream to be
created.
POWER function
POWER(number,power)
Returns a number raised to the power you specify.
= Number is any real number you want to raise to a power.
= Power is the exponent to which you want to raise the number.
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Prefix (definition)
A prefix is a keyword you use at the beginning of a formula. The prefix
applies to all
the values in the formula and determines how the values apply to time periods.
Previous function
Previous (Array, FirstValue)
Returns an array in which, relative to the current position, each value refers
to the
preceding value in a source array.
= Array is the name of the current parameter or the name of a source array
from
which you want to retrieve the previous values.
= The design of this function permits it to be self-referential without
returning a
circular reference error. See example.
= FirstValue defines a value to assume for the first position in the resulting
array.
= The inverse of this function is the Next function.
Quarterly keyword
Quarterly is a frequency keyword to define the interval between continuing
dates in a
date stream.
RegularAscendingArray function
RegularAscendingArray (Start, Step, Number)
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Creates an ascending array of in which each value increases by a specified
increment.
= Start is the first value of the array.
= Step is the amount you want to add to the starting value and each resulting
value
to create the next value in the array.
= Number is an optional number of values you want in the resulting array.
RegularDateStream function
RegularDateStream (StartDate, Frequency, Number, SecondDate, LastDate, Term)
Creates a date stream or date index.
= You can obtain the same results with natural stream language or the date
stream
composer.
= All arguments are optional, but not all combinations of arguments are
compatible.
= For example, if you provide StartDate, Frequency, and Number, the SecondDate
and Term arguments will either repeat or contradict what is already defined.
= Use any single date expression to express StartDate, SecondDate, and
LastDate.
= StartDate is the first date in the stream.
= Frequency is Monthly, Quarterly, Annual or Semiannual.
= Number is the number of dates to be included in the stream.
= SecondDate is the second date in the stream.
= LastDate is the last date in the stream. Omit LastDate to create an
unterminated
stream.
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= Term is the elapsed time between StartDate and LastDate. It can be given as
an
elapsed time expression or in the form of the ElapsedTime function.
REPLACE function
REPLACE(OldString,StartNum,NumChars,NewString)
Replaces a portion of a text string with another string.
= OldString is the text string you want to replace. It can be given as a
series of text
characters or as a reference to a parameter that contains text characters.
= Enclose OldString in quote marks.
= StartNum is the position of the first character in OldString that you want
to
replace.
= NumChars is the number of characters you want to replace starting with the
character in the StartNum position.
= NewString is the string you want to insert as a replacement for OldString.
REPT function
REPT(String,NumberTimes)
Repeats a text string the number of times you specify.
= String is a series of text characters or a reference to a parameter that
contains
text characters. String is the text string you want to repeat.
= Enclose String in quote marks.
= NumberTimes is the number of times you want to repeat String. If NumberTimes
is zero, the application returns an empty text string.
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RIGHT function
RIGHT(String,NumChars)
Returns one or more rightmost characters of a text string.
= String is a series of text characters or a reference to a parameter that
contains
text characters
= Enclose String in quote marks.
= NumChars is the number of characters you want to extract starting with the
last
character. NumChars must be greater than or equal to zero.
= If NumChars is greater than the length of String, the application returns
all of
String.
= If you omit NumChars, the application uses 1.
Role (definition)
A role is the name for the set of properties that defines Party interaction
with an
Instrument.
= Roles are defined by the flow of connective endpoints of instruments.
= For example, when a Rent instrument is drawn between two parties, the
connector begins with the Lessee and terminates with the Lessor to reflect the
direction of payments.
ROUND function
ROUND(number,num_digits)
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Returns a number rounded to the number of digits you specify.
= Number is any number you want the application to round up or down.
= Num_digits is the number of digits you want in the resulting number.
= If Num_digits is greater than zero, then the application rounds Number to
the
number of decimal places you specify.
= If Num_digits is zero, then the application rounds Number to the nearest
integer.
= If Num_digits is less than zero, then the application rounds Number to the
left of
the decimal point.
ROUNDDOWN function
ROUNDDOWN(number,num_digits)
Returns a number rounded down to the number of digits you specify.
= Number is any number you want the application to round down.
= Num_digits is the number of digits you want in the resulting number.
= If Num_digits is greater than zero, then the application rounds Number down
to
the number of decimal places you specify.
= If Num_digits is zero, then the application rounds the Number down to the
nearest integer.
= If Num_digits is less than zero, then the application rounds Number down to
the
left of the decimal point.
ROUNDUP function
ROUNDU P(number, num_digits)
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Returns a number rounded up (away from zero) to the number of digits you
specify.
= Number is any number you want the application to round up.
= Num_digits is the number of digits you want in the resulting number.
= If Num_digits is greater than zero, then the application rounds Number up to
the
number of decimal places you specify.
= If Num_digits is 0, then the application rounds Number up to the nearest
integer.
= If Num_digits is less than 0, then the application rounds Number up to the
left of
the decimal point.
Scalar parameter (definition)
A scalar parameter defines a single quantity that does not change over time or
other
direction. A scalar parameter is not attached to a key position (such as a
date) on an
index, even if the scalar parameter happens to be located in the scope of an
index.
To create a scalar parameter under an index, use the Nolndex prefix.
Search prefix
The Search prefix tells the application to perform search and repetitive
calculations to
determine the value of a scalar parameter.
There are three ways to use the Search prefix:
1) Optimization search (also known as a multistep or 3-step search)
2) Targeted search (also known as a 5-step search)
3) Maximization search
Optimization Search
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Search (LowerBound, UpperBound, SearchAccuracy):
In an optimization search, you set up the Search parameter formula, then you
perform
an optimization with an objective function.
= Also known as a multistep search or a three-argument search.
= Successive optimizations are performed until the best objective function is
found.
For example, "Find the best EBO date to meet the Present Value objective where
PV objective is itself an optimized value."
= LowerBound is the minimum value in the range of values you want to optimize
within. For example, if you are looking for a percentage no smaller than 2%,
enter 2%.
= UpperBound is the maximum value in the range of values you want to optimize
within. For example, if you are looking for a percentage no higher than 25%,
enter 25%.
= SearchAccuracy is the degree of accuracy your search requires.
= For example, enter .1 to search for values within 10% of the target.
Targeted Search
Search (LowerBound, UpperBound, SearchAccuracy, TargetExpression, TargetValue,
TargetAccuracy, InitialGuess):
Searches for a value for which the target expression equals the target value.
For
example:
= "Find me an interest rate that will give me 200$ TV over this term of
investment."
= Interest rate = search prefix
0 200$ TV = target value
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= term of investment = target expression
= In this example, the search stops whenever a value is found for which the
difference is less than the target accuracy.
= LowerBound is the minimum value in the range of values you want to optimize
within. For example, if you are looking for a percentage no smaller than 2%,
enter 2%.
= UpperBound is the maximum value in the range of values you want to optimize
within. For example, if you are looking for a percentage no higher than 25%,
enter 25%.
= SearchAccuracy is the degree of accuracy your search requires.
= For example, enter .1 to search for values within 10% of the target.
= TargetExpression is the name of the parameter that will contain the target
value.
= TargetValue is the name of the parameter that defines objective of the
search.
= TargetAccuracy is the extent to which the search should continue, i.e. you
can
enter a value like ? to truncate the search (speed it up).
= If not supplied, the search continues until the variable is known to be
within the
SearchAccuracy value.
= InitialGuess is another way to accelerate the search by indicating a
starting point
- i.e. if you are expecting a value between 10% and 15%, set InitialGuess to
10%.
= If InitialGuess is omitted, the search starts at the current value.
Semiannual keyword
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Semiannual (or Semiannually) is a frequency keyword used to define the
interval
between continuing dates in a date stream.
Semicolon (;) keyword
The semicolon symbol (;)stops the current sequence of dates or values in a
stream.
The stream then continues or ends according what follows the semicolon in the
formula.
= In a date stream, use a semicolon to interrupt the stream of anniversaries
at one
frequency and continue them at a different frequency.
= In a numbers stream, use multiple semicolons to omit values under key
positions
in an index.
= If value; is the first portion of the formula, value is assumed to coincide
with the
first key position on the index.
SetResult prefix
SetResult (Result, Party, Outcome):
The SetResult prefix lets you define a three-argument identity of sorts to
bookmark a
value. You can then retrieve the value, when needed, with the Get Result
function.
= The values you provide for Result, Party, and Outcome can be arbitrary,
provided
you follow rules for using quote marks as given below.
= For example, the arguments("Amo","Amas","Amat") work just as well as
("MyResult", Lessor,"BaseOutcome").
= Result is any alphanumeric text encased in quote marks.
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= Party is any alphanumeric text encased in quote marks, or it can be the name
of
a role (without quote marks) within the case. For example, you can use Lessor
when a Rent instrument is present.
= Outcome is any alphanumeric text encased in quote marks.
SIGN function
SIGN(number)
Returns the sign of a number. If the number is positive, the application
returns 1; if the
number is 0, the application returns 0; if the number is negative, the
application
returns -1.
= Number is any real number.
Source Parameter (definition)
A source parameter is one that contains data you want to use in another
parameter.
= For example, in writing a formula to show accrued rent, you would refer to
the
parameter that contains actual rent levels as the source of data.
= The formula that shows the accrued rent is the destination parameter.
SORT function
SQRT(number)
Returns the positive square root of a number.
= Number is any numeric value.
= If the number is negative, the application returns an error.
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StartDates prefix
Indicates that each date on the index (except the last date) represents the
FIRST day
of a period.
= Each period begins as of the index date and ends on the day before the next
index date.
= The last date in the index is a bookend. It does not represent the start of
a new
period.
= StartDates is the default when the date stream formula does not specify a
period
prefix.
= The -} symbol indicates the StartDates prefix.
StartDatesOf function
StartDatesOf (First, Second, ...)
Returns the combined dates used to organize a set of number streams, first
converting them to start dates if necessary.
= This lets you create an index comprising the date values of various indexed
parameters without having to remember anything about the indexes themselves.
= If an argued numbers stream is keyed to an StartDates: date index, the
function
returns the dates as they appear on that index.
= If an argued numbers stream is keyed to an EndDates date index, the function
first adds one day to each date to return it as a start date.
= First (and so on) are the parameter names of numbers streams (tables, cash
and
income streams).
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The similar StartDatesOf Periods function slows down optimization
performance, but it is more flexible in the types of arguments it accepts.
StartDatesOf Periods function
StartDatesOf Periods (First, Second...)
Derives period end dates for one or more numbers streams and/or date indexes,
then
creates a date index of dates that reflect the start dates of the underlying
periods.
Also incorporates dates or date streams given as arguments.
= To calculate dates for the result, the function adds one day each to the
collected
end dates.
= First (and so on) can be any one or more of the following:
= parameter name of an EndDates date index.
= parameter name of a numbers stream (i.e. income or payment flow, table) that
is
keyed to a EndDates date index.
= single date expression or date stream expression
Starting keyword
Starting date
Defines the first date in a date stream or assigns the first value in a
numbers stream
to the given date.
SubArray function
SubArray (Array, Start,Count)
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Returns a portion of an existing array as of a specified key position.
= Array is the name of any array parameter: a numbers stream, a date index,
and
so on.
= Start specifies the key position in the source array that contains the first
element
you want to retrieve.
= Count specifies the number of elements you want to retrieve from the source
array.
SUBSTITUTE function
SUBSTITUTE (String, OldString, NewString, InstanceNum)
Substitutes any number of instances of a text string with another text string.
= String is the text string in which you want to substitute characters.
= OldString is the text string you want to replace.
= NewString is the text string you want to insert in place of OldString.
= InstanceNum specifies the instance of OldString you want to replace. If you
omit
InstanceNum, the application changes every occurrence of OldString to
NewString.
Subtotal function
Subtotal (Heading, Index, Parameter)
Returns the total of all values in one or more indexed parameters of the same
name
under a given heading.
0 Heading is closest heading above the parameter.
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= Index is the name of the date index (or other index) to which the parameter
is
linked.
= Parameter is the parameter name.
SUM function
SUM(argumentl,argument 2, ...)
Returns the sum of all values in all of the arguments.
= Argumentl, argument2, can be numbers, logical values (such as True), or
arrays
that you want the application to add.
SumToDate function
SumToDate (Value, Date)
Returns a single number that is the sum of an array up to, but not including,
the
specified date.
= This function is useful in defining a truncation point for an accrued
payment or
income stream.
= Value is the name of a numbers stream.
= If Value is a non-accrued numbers stream, the function returns the sum of
values
on dates that precede the given date. See Result_1 in example.
= If Value is an accrued numbers stream, the function returns the total
accrual from
the beginning of time up to (not including) the given date. See Result_2 in
example.
= Date is any single date expression.
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= Date is optional in the SumToDate function when it is nested inside the
Truncate
function (SumToDate defaults to the Truncate date).
Table prefix
Table: values
The Table prefix tells the application to interpret each value in the
parameter as a
simple lookup value along a date index.
When you reference the Table parameter in the formula to calculate values for
a
destination parameter, the application applies the table value in effect as of
the Table
parameter period that contains the destination parameter date.
= If a date for the destination parameter falls outside the date range of the
Table
parameter, the application applies the Table value that occurs closest to the
destination date.
= In Smart Paper, the symbol identifies a parameter with Table values.
TableValue function
TableValue (Table, Value)
Extracts a value or values from a table.
= Table is the name of any parameter with a Table or Interpolate prefix.
= Value is any expression of a single value or array of values that is
compatible
with the index to which Table is keyed (usually dates).
Then keyword
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Stops the current sequence of continuing dates in a date stream. The stream re-
continues or ends according what follows in the formula.
= Use Then to create a date stream with different frequencies for different
portions
of the stream.
Thereafter keyword
Assigns the given value to each remaining period on the current index
according to
the payment prefix, unless:
= the Except keyword is added, or
= the formula also contains the Advance prefix, so that there is no value
applicable
to the last date of the index.
TimeSlice function
TimeSlice (Timeline, StartDate, EndDate)
Returns a date stream using given dates and dates from another date stream.
= Timeline is the name of a date stream parameter or a Time Organizer
timeline.
= The referenced Timeline must contain at least one date that falls between
the
argued StartDate and EndDate.
= StartDate is any valid date expression.
= EndDate is any valid date expression later than StartDate.
Today function
Today
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= Returns the current date.
TRIM function
TRIM(String)
Changes multiple blank spaces between words to a single space.
= String is a series of text characters or a reference to a parameter that
contains
text characters. String is the text in which you want the application to
delete
spaces.
= Enclose String in quote marks.
TRUE function
TRUE
Returns the logical value True.
TRUNC function
TRUNC(number)
Converts a number to an integer by removing the fractional part of the number.
The
application rounds the number down to the next integer toward zero.
= Number is any numeric value.
Truncate function
Truncate (Value, TruncationDate, TruncationValue)
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Returns a numbers stream stops as of the index date that precedes the given
truncation date.
= Value is the name of a numbers stream.
= TruncationDate is any single date expression.
= TruncationValue is an extra amount to add in on the actual TruncationDate.
Union function
Union(Argumentl,Argument2,...)
Combines all values found within the given arguments and returns an ascending
array
with duplicates removed.
= Typically used to combine multiple date indexes into a single date index.
= Argumentl, argument2, and so on are names of parameters or indexes. The
arguments can be any scalar or array value, including constants or parameter
references.
Until keyword
Until date
Assigns the last value in a sorted numbers stream to the key position that
contains
the given date.
Unsorted Array (Definition)
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An unsorted array is a type of array parameter that comprises a series of
independent
values. That is, the values are not keyed to an index (even if the unsorted
array
appears below an index).
= You use the List: prefix to create an unsorted array.
= You can give an unsorted array the appearance of an index, but it will not
behave
as an index.
= For example, you cannot key values to unsorted array elements, and the
application cannot calculate or measure the "value" of unsorted array
elements.
UPPER function
UPPER(String)
Converts a text string to upper case.
= String is a series of text characters or a reference to a parameter that
contains
text characters.
= Enclose String in quote marks.
US 30 360 function
This is one of four calendar methods you can choose to evaluate intervals
between
dates for the purposes of calculation
= Consists of twelve 30-day months (each month is one 12 th of the year).
= February is given two extra days.
= The status of the 31 St depends on how dates relate to periods.
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WhenActive function
WhenActive(Parameter, Default)
If the first argument is active, the function returns the value of the first
argument. If
first argument is inactive, the function returns the second argument.
= Parameter is any parameter name.
= Default is a number or parameter name for the value(s) you want the function
to
return if the status of the first argument is inactive.
YEAR function
YEAR(Date)
Determines the year for a given date.
= Date is any single date expression.
As is readily apparent from the description of the invention above, the
instant
financial modeling and analysis tool provides a user friendly, effective and
efficient
tool for modeling financial or other mathematical scenarios of almost any
kind. The
graphical user interface combined with the powerful engine provide a greatly
improved modeling tool as compared to the prior art.
It is noted that the invention is not limited to modeling financial scenarios
or
deals, but, instead, can be used to model any scenario involving mathematical
values
over time.
The implementations described above illustrate the characteristics, features
and advantages of the present invention. These implementations, of course, are
not
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exhaustive, and other implementations within the scope and spirit of the
present
invention will be apparent to those skilled in the art. In other words, while
the
invention has been described in connection with what is presently considered
to be
the most practical and preferred embodiments, it is to be understood that the
invention is not to be limited to the disclosed embodiments, but on the
contrary, is
intended to cover various modifications and equivalent arrangements which fall
within
the true spirit and scope of the appended claims.
