## Mortgage abstract
A system for creating and managing securities that evaluates the
cash flows of mortgage securities that are to be restructured into
new securities. The securities to be restructured can be either
mortgage securities that qualify as collateral for a CMO/REMIC or
securities that were issued by an existing CMO/REMIC. Based upon
the original mortgage securities, the system may create four new
securities: two each that have principal-only cash flows and two
each that have interest-only cash flows.
## Mortgage claims
What is claimed:
1. An apparatus for creating new securities from underlying securities
collateralized by mortgage obligations, comprising:
means for creating a plurality of first securities collateralized
by the underlying securities and having total principal payments
equal to an allocated amount of the principal payments from the
underlying securities based upon a preselected interest rate and
total interest payments equal to total payments of a first interest-only
security;
means for creating a plurality of second securities collateralized
by the underlying securities and having total principal payments
equal to a remainder of the principal payments from the underlying
securities and total interest payments equal to the interest payments
on a second interest-only security;
means for creating said first interest-only security collateralized
by said plurality of first securities and having payments equal
to the total interest payments from said plurality of first securities;
means for creating said second interest-only security collateralized
by said plurality of second securities and having payments equal
to the total interest payments from said plurality of second securities;
and
means for printing at least one securities document for the new
securities;
wherein an interest rate on each of said first and second securities
varies linearly subject to a minimum and a maximum.
2. An apparatus according to claim 1, further comprising means
for creating at least one principal-only security collateralized
by said plurality of first securities and said plurality of second
securities and having total payments equal to the total principal
payments from said plurality of first securities and said plurality
of second securities.
3. An apparatus according to claim 1, wherein principal payments
from the underlying securities are allocated equally among said
first and second securities.
4. An apparatus according to claim 1, wherein principal payments
from the underlying securities are allocated unequally among said
first and second securities.
5. An apparatus according to claim 3 or 4, wherein principal payments
from the underlying securities are distributed to each of said first
and second securities in proportion to a stated principal amount.
6. An apparatus according to claim 1, wherein each of said first
and second securities is a single segment variable rate security.
7. An apparatus according to claim 1, wherein said first and second
interest-only securities are monotonic variable rate securities.
8. An apparatus according to claim 2, further comprising means
for combining at least two of said first and second interest-only
securities and said first and second principal-only securities into
a combination security.
9. An apparatus according to claim 8, wherein said combination
security increases in value as interest rates decline.
10. An apparatus according to claim 8, wherein said combination
security increases in value as interest rates rise.
11. An apparatus for creating new securities from underlying securities
collateralized by mortgage obligations, comprising:
means for creating a plurality of first securities collateralized
by the underlying securities and having total principal payments
equal to an allocated amount of the principal payments from the
underlying securities based upon a preselected interest rate and
total interest payments equal to total payments of a first interest-only
security;
means for creating a plurality of second securities collateralized
by the underlying securities and having total principal payments
equal to a remainder of the principal payments from the underlying
securities and total interest payments equal to the interest payments
on a second interest-only security;
means for creating a third security collateralized by said plurality
of first securities and having principal payments equal to an allocated
amount of the principal payments from the underlying securities
and interest payments equal to the total interest payments from
said plurality of first securities;
means for creating a fourth security collateralized by said plurality
of second securities and principal payments equal to a remainder
of the principal payments from the underlying securities and interest
payments equal to the total interest payments from said plurality
of second securities; and
means for creating said first interest-only security collateralized
by said third security and having payments equal to the interest
payments from said third security;
means for creating said second interest-only security collateralized
by said fourth security and having payments equal to the interest
payments from said fourth security;
means for printing at least one securities document for the new
securities;
wherein an interest rate on each of said first and second securities
varies linearly subject to a minimum and a maximum.
12. An apparatus according to claim 11, further comprising means
for creating at least one principal-only security collateralized
by said third and fourth securities and having total payments equal
to the total principal payments from said third and fourth securities.
13. An apparatus according to claim 11, wherein principal payments
from the underlying securities are allocated equally among said
first and second securities.
14. An apparatus according to claim 11, wherein principal payments
from the underlying securities are allocated unequally among said
first and second securities.
15. An apparatus according to claim 13 or 14, wherein principal
payments from the underlying securities are distributed to each
of said first and second securities in proportion to a stated principal
amount.
16. An apparatus according to claim 11, wherein each of said first
and second securities is a single segment variable rate security.
17. An apparatus according to claim 11, wherein said first and
second interest-only securities are monotonic variable rate securities.
18. An apparatus according to claim 12, further comprising means
for combining at least two of said first and second interest-only
securities and said first and second principal-only securities into
a combination security.
19. An apparatus according to claim 18, wherein said combination
security increases in value as interest rates decline.
20. An apparatus according to claim 18, wherein said combination
security increases in value as interest rates rise.
21. A method for creating new securities from underlying securities
collateralized by mortgage obligations, comprising the steps of:
creating a plurality of first securities collateralized by the
underlying securities and having total principal payments equal
to an allocated amount of the principal payments from the underlying
securities based upon a preselected interest rate and total interest
payments equal to total payments of a first interest-only security;
creating a plurality of second securities collateralized by the
underlying securities and having total principal payments equal
to a remainder of the principal payments from the underlying securities
and total interest payments equal to the interest payments on a
second interest-only security;
setting an interest rate on each of said first and second securities
to vary linearly subject to a minimum and a maximum;
creating said first interest-only security collateralized by said
plurality of first securities and having payments equal to the total
interest payments from said plurality of first securities;
creating said second interest-only security collateralized by said
plurality of second securities and having payments equal to the
total interest payments from said plurality of second securities;
and
printing at least one securities document for the new securities.
22. A method according to claim 21, further comprising the step
of creating at least one principal-only security collateralized
by said plurality of first securities and said plurality of second
securities and having total payments equal to the total principal
payments from said plurality of first securities and said plurality
of second securities.
23. A method according to claim 21, further comprising the step
of allocating principal payments from the underlying securities
equally among said first and second securities.
24. A method according to claim 21, further comprising the step
of allocating principal payments from the underlying securities
unequally among said first and second securities.
25. A method according to claim 23 or 24, further comprising the
step of distributing principal payments from the underlying securities
to each of said first and second securities in proportion to a stated
principal amount.
26. A method according to claim 21, further comprising the step
of combining at least two of said first and second interest-only
securities and said first and second principal-only securities into
a combination security.
27. A method according to claim 26, further comprising the step
of designing said combination security to increase in value as interest
rates decline.
28. A method according to claim 26, further comprising the step
of designing said combination security to increase in value as interest
rates rise.
29. An apparatus for creating new securities from underlying securities
collateralized by mortgage obligations, comprising:
a memory for recallably storing information;
a keyboard for entering information to be stored in said memory
describing the underlying securities and the new securities to be
created;
a processing unit utilizing the information stored in said memory
for:
(i) defining a plurality of first securities collateralized by
the underlying securities and having total principal payments equal
to an allocated amount of the principal payments from the underlying
securities based upon a preselected interest rate and total interest
payments equal to total payments of a first interest-only security,
wherein an interest rate on each of said first securities varies
linearly subject to a minimum and a maximum;
(ii) defining a plurality of second securities collateralized by
the underlying securities and having total principal payments equal
to a remainder of the principal payments from the underlying securities
and total interest payments equal to the interest payments on a
second interest-only security, wherein an interest rate on each
of said second securities varies; linearly subject to a minimum
and a maximum;
(iii) defining said first interest-only security collateralized
by said plurality of first securities and having payments equal
to the total interest payments from said plurality of first securities;
and
(iv) defining said second interest-only security collateralized
by said plurality of second securities and having payments equal
to the total interest payments from said plurality of second securities;
a display for displaying information on each of the securities
defined by said processor; and
a printer for printing at least one securities document for the
new securities.
30. An apparatus according to claim 29, wherein said processor
utilizes the information stored in said memory for defining at least
one principal-only security collateralized by said plurality of
first securities and said plurality of second securities and having
total payments equal to the total principal payments from said plurality
of first securities and said
plurality of second securities.
31. An apparatus according to claim 29, further comprising means
associated with said keyboard to allow interactive access to the
apparatus by a user.
32. An apparatus according to claim 31, further comprising means
associated with said keyboard for allowing the user to alter information
on either the underlying securities or the new securities.
33. An apparatus according to claim 29, further comprising a printer
for printing reports on securities defined by said processor.
34. An apparatus according to claim 29, further comprising a printer
for printing drafts of securities to be issued.
35. An apparatus according to claim 29, further comprising a printer
for printing payment checks to holders of issued securities.
36. An apparatus according to claim 29, further comprising means
associated with said display for displaying structure and financial
performance of the new securities.
37. An apparatus according to claim 29, further comprising means
associated with said display for displaying a distibution of cash
flows to the new securities.
38. An apparatus according to claim 29, further comprising means
associated with said display for displaying timing on cash flows
to security holders under a plurality of interest rate and prepayment
conditions.
## Mortgage description
BACKGROUND OF THE INVENTION
This invention relates to systems for creating and managing securities.
More particularly, this invention relates to systems for creating
and managing securities that are collateralized by mortgage obligations.
The mortgage securities industry is the largest financial business
in the United States and consists primarily of products related
to mortgage loans on residential and commercial properties. The
great majority of residential mortgage loans are extended to individuals
for the purpose of financing their primary or secondary place of
residence. Mortgages are loans with a principal amount that is usually
scheduled to be gradually paid-off over an extended period of time,
such as 15 or 30 years. The mortgage loan carries an interest rate
that is periodically (usually monthly) applied to the remaining
principal balance of the loan. The "scheduled" periodic
payment usually consists of the interest owed on the outstanding
balance for the previous period plus some amount of principal which
reduces the outstanding balance of the loan.
A characteristic of the current mortgage industry is that most
of the money for residential mortgages is ultimately provided by
institutional investors--not by the banks or mortgage bankers who
usually arrange the mortgages for homeowners. Once a group of mortgages
with similar terms has been arranged, they will often be packaged
into a single unit called a mortgage pool and sold to institutional
investors. Most residential mortgage loans issued in recent years
have ended up as components in large mortgage pools that were ultimately
resold to institutional investors or to investment bankers that
repackage them into other forms of mortgage-backed securities.
For example, a mortgage lender may collect several million dollars
of 30-year mortgage loans that it originates and place them into
one package. Whereas the individual mortgages may carry interest
rates of 8.85% to 9.30%, the interest rate on the package will usually
be a single fixed rate such as 8.50%. The difference between the
interest paid on underlying loans (the "gross coupon rates")
and the interest rate paid on the package (the "pool rate"
or the "net coupon rate") is usually retained by the original
mortgage lender as a fee for arranging the mortgage and for continuing
to service it (i.e., collect payments, perform bookkeeping, etc.).
Currently, the great majority of mortgage loans and mortgage pools
are repackaged and restructured before they are ultimately sold
to investors. The most common device for this is the collateralized
mortgage obligation ("CMO"). The procedure for creating
a CMO is as follows:
(1) An issuer/underwriter purchases a large amount of mortgages
or mortgage pools--usually $250 to $500 million in value. This is
the collateral for the CMO.
(2) The collateral is deposited with a trustee who will thereafter
receive the payments generated by the collateral and who will arrange
payments to be made on new securities to be. issued.
(3) The issuer/underwriter issues securities whose payments of
principal and/or interest are collateralized by the payments of
principal and interest that will be generated by the collateral.
These securities are structured so that there will always be sufficient
cash flow from the collateral (i.e., the mortgages) to fulfill the
stated obligations of the newly issued CMO securities. The new securities
are called CMO tranches, CMO bonds, or CMO classes.
Most CMOs are subject to real estate mortgage investment conduit
("REMIC") legislation designed to apply to various mortgage-related
securities. Such CMOs are often simply referred to as REMICs. REMIC
legislation and regulations provide for various tax, structural
and other regulatory rules and regulations that govern the origination
and structure of CMO/REMICs.
The regulations govern what securities qualify as collateral for
a CMO/REMIC as well as what securities may be issued by the REMIC.
The conventional securities that may be issued by a REMIC subject
to the various REMIC restrictions are called "regular interests."
It is these securities that are of greatest interest to the vast
majority of investors. An important property of a regular interest
is that any regular interest issued by a REMIC qualifies to be utilized
as collateral for another REMIC. Each REMIC may issue any number
of regular interests. In addition, each REMIC must issue one "residual
interest" which receives whatever cash flow remains after the
regular interests are paid.
At times the issuance of a desired regular interest security may
be achievable only by utilizing several REMICS. In such a procedure
the initial collateral from which the desired security is to be
derived is placed into a REMIC which issues one or more regular
interests. Some of these regular interests then serve as the collateral
for another REMIC which issues other regular interests. This may
be done several times until the desired regular interest security
can be issued. When the creation of these several REMICS is done
simultaneously, the procedure is referred to as a multistage REMIC.
At times, the REMIC regulations limit the ability to design and
structure securities that would otherwise be attractive to certain
investors. These restrictions are most restrictive in governing
the amount and formulas for interest that may be paid on REMIC securities.
These restrictions often prevent the creation of securities whose
performance characteristics would make them most suitable as hedging
vehicles for clients that own assets that could be significantly
impacted by large or sudden movements in interest rates or mortgage
prepayments.
In particular, the current and proposed REMIC regulations regulate
what type of interest rates may be paid by a regular REMIC interest.
For example, a regular interest may pay interest at a rate equal
to: 1) a fixed rate of interest--e.g., 7.0%, 2) a recognized interest
rate index or a multiple thereof plus or minus a fixed rate of interest--(e.g.,
2 times the T-bill rate+1.50%), or 3) interest equal a fixed portion
of the total interest on the collateral. An interest formula that
is not directly provided for under the REMIC regulations is the
payment of a variable percentage of the total interest on the collateral
(e.g., the interest paid equals 25% of the total interest paid on
the collateral if the T-bill rate is 5.0% or below, and equals 75%
if the T-bill rate is above 5.0%).
Three popular securities that are often created within a CMO/REMIC
are 1) principal-only ("PO") bonds which pay no interest
and are therefore sold at a discount to their par amount (i.e.,
at less than the principal amount), 2) interest only ("IO")
and similar bonds that pay little or no principal amount but are
expected to pay a substantial amount of interest (relative to the
principal amount if any), and 3) variable rate bonds that have an
interest rate that varies with changes in some interest rate index.
In general, the performance of these types of securities can be
very volatile and the returns to investors in these securities may
vary substantially depending on future interest rate levels and
the rate at which the underlying mortgage loans are paid off by
their homeowners. Nevertheless, these securities are attractive
and useful to a variety of investors that utilize them to hedge
their assets against interest rate risks or to achieve other performance
objectives.
There are several drawbacks to these securities, however. Two of
the drawbacks are that 1) the performance of these securities can
be significantly affected in unanticipated fashion if the underlying
mortgage loans are prepaid at either a faster or slower rate than
expected, and 2) many potential institutional investors are prohibited
from purchasing IO-type securities that have relatively little or
no principal amount, because the investor is not promised even the
return of the original investment.
Accordingly, there exists a need for a system to provide an investment
vehicle whose performance is more predictable and controllable than
conventional principal-only and interest-only securities. Further,
there exists a need to meet investor objectives within current REMIC
regulations.
SUMMARY OF THE INVENTION
With the foregoing in mind, it is an objective of the invention
to provide a system to create securities that provide the performance
of Principal-Only and Interest-Only type securities but which avoid
some of the major problems associated with these securities.
It is a further object of the invention to provide a system to
create investments that can be tailored to achieve investor objectives
with greater precision than is currently possible.
It is a further objective of the invention to provide a system
to create securities that achieve a wider range of performance than
was previously available.
These and other objectives of the invention are met by providing
a system for creating and managing securities that evaluates the
cash flows of underlying securities collateralized by mortgage obligations
(the "collateral") that are to be restructured into new
securities. The underlying securities to be restructured can be
either mortgage securities that qualify ad collateral for a CMO/REMIC
or securities that were issued by an existing CMO/REMIC. The system
determines the cash flows based on the Original Term of the underlying
securities, as well as the Remaining Term and Loan Age, Gross Coupon,
Net Coupon, Settlement Date, Issue Date, Payment Dates, Present
Value, and various other mortgage loan characteristics.
When a particular bond of a CMO is to be considered, the pertinent
parameters that describe how the bond is derived from the underlying
securities and that determine the timing and amount of its cash
flows are analyzed. The system then determines the timing and amount
of both principal and interest payments that would be produced under
a variety of potential prepayment and interest rate scenarios input
to the system. The system determines the market value of the principal
payment cash flows and the interest payment cash flows and compares
their sum to the cost of the combined cash flows.
The system may then create four new securities: two each that have
Principal Only cash flows ("PROs") and two that have Interest
Only cash flows ("IOs"). The system utilizes user-provided
input to determine how the principal payments generated by the underlying
securities will be allocated between the PRO securities and how
the interest payments will be divided between the IO securities.
The system projects the cash flows for each of these four securities
under a variety of interest rate and mortgage prepayment scenarios.
These cash flows may be analyzed and a market value placed on each
and their total market value compared to the cost of the underlying
securities. The system repeats this procedure in automated fashion
or under user control by altering the proposed method for allocating
principal and interest between the PROs and IOs. The adjusted cash
flows and market values of the PROs and IOs are determined and compared
to the previous values. This iterative procedure may be repeated
until a cash flow allocation procedure that results in the most
marketable PRO and IO securities is determined.
The system may also analyze the properties and market value of
combinations of the PROs and IOs. The system accepts any user-defined
combination of the PROs and IOs and creates the cash flows of the
proposed combination security. The system then projects the cash
flows under any set of interest rate and prepayment rate scenarios,
and analyzes its performance if the component prices are given.
Alternatively, the system may determine the market value of the
combination security if its performance levels are specified.
After the characteristics of the PROs and IOs to be issued have
been determined, the system creates a multistage CMO/REMIC, with
a "Lower REMIC" and an "Upper REMIC." The underlying
securities to be restructured into the PROs and IOs are placed into
the Lower REMIC where they generate the principal and interest cash
flows that collateralize the new securities to be issued. The system
then creates two variable rate bonds ("LA" and "LB"
bonds) in the Lower REMIC.
The LA and LB bonds are then placed into the Upper REMIC as the
collateral that generates the principal and interest cash flows
that collateralize the new securities to be issued by the Upper
REMIC. The Upper REMIC may issue four securities:
a) an interest-only security that receives 100% of the interest
paid on the LA bond,
b) an interest-only security that receives 100% of the interest
paid on the LB bond, and
c) two principal-only securities that have respective principal
amounts and payment priorities equal to the above-described PRO
securities.
BRIEF DESCRIPTION OF THE DRAWINGS
The accompanying drawings, referred to herein and constituting
a part hereof, illustrate preferred embodiments of the invention,
and, together with the description, serve to explain the principles
of the invention, wherein:
FIG. 1 is a data processing system implementing the mortgage-backed
securities system according to the invention;
FIG. 2 is a conceptal overview of the mortgage-backed securities
system according to the invention;
FIG. 3 is a flow chart illustrating the operation of the system
wherein underlying securities are restructured and new securities
are defined;
FIG. 4 is a flow chart illustrating the operation of the system
wherein proposed new securities are evaluated;
FIG. 5 is a flow chart illustrating the operation of the system
wherein a multistage REMIC is created and securities are defined
in first stage of the Lower REMIC;
FIG. 6 is a flow chart illustrating the operation of the system
wherein new multisegment variable rate securities are created in
the second stage of the Lower REMIC;
FIG. 7 is a flow chart illustrating the operation of the system
wherein new unidirectional multisegment variable rate securities
are created in the second stage of the Lower REMIC;
FIG. 8 is a flow chart illustrating the operation of the system
wherein new principal-only and interest-only securities are created
in the Upper REMIC;
FIG. 9 is a graphical illustration of the coupon formula for a
multisegment variable rate security; and
FIG. 10 is a graphical illustration of the coupon formula for a
unidirectional multisegment variable rate security.
DETAILED DESCRIPTION OF THE INVENTION
As shown in FIG. 1, the mortgage-backed securities system according
to the invention preferably includes a data processing system 110
comprising (i) means for entering 112 (e.g., an alphanumeric keyboard)
the financial data concerning the underlying mortgage securities
that are to be analyzed and restructured, (ii) a processing unit
114 (e.g., an IBM AT series personal computer) with associated data
storage memory and I/O capability to perform analysis on underlying
securities and to structure and analyze new securities, (iii) means
for providing system output 116, 118 (e.g., a graphics quality CRT,
a hardcopy printer or both) that describes the structure and the
financial performance characteristics of newly created securities,
and (iv) means to structure and describe financial parameters so
that regulatory requirements are satisfied.
The data processing system also includes a means for determining
and providing visual output on (v) how available cash flows will
be distributed among newly created securities, (vi) the timing and
cash flow amounts that are projected to be paid to security holders
under a variety of interest rate and prepayment scenarios, and (vii)
the yield, duration, average life and other financial performance
measures that describe the newly created securities.
The means for entering 112 also provides the user with constant
interactive access to the system that enables the user to alter
the structure of the newly created securities and evaluate the financial
effect of such changes on the performance characteristics, marketability
and value of the securities. The system also constantly monitors
the profit or loss the user would realize if the new securities
were to be created as described. The means for providing system
output also provides the user with the facility to print reports
120 on the analysis of any proposed securities, drafts of any new
securities to be issued and checks to holders of issued securities
when payments are due.
The mortgage-backed securities system according to the invention
is particularly adapted to restructure underlying securities and
to create new securities with bullish and bearish characteristics
in accordance with investor preferences. A bullish security is considered
to be a security whose value increases as interest rates decline
and a bearish security is considered to be a security whose value
increases as interest rates rise. A conceptual overview of the mortgage-backed
securities system is shown in FIG. 2. The preferred method and apparatus
for implementing the system are detailed hereinafter.
Flowcharts illustrating the operation of the data processing system
according to the invention is shown in FIGS. 3 through 8. Referring
to FIG. 3, data that describes the securities to be restructured
(the "underlying securities" or the "collateral")
is entered at block 302. The underlying securities may be residential
mortgage loans, pools of such loans, or other securities derived
from mortgage loans or securities that were issued as regular interest
in another REMIC. The underlying securities must qualify as collateral
in a CMO/REMIC under REMIT regulations.
The underlying securities may have a variety of maturity dates,
amortization schedules, issue dates, fixed or floating coupon rates,
payment delays, interest payment dates, prices, and anticipated
prepayment rates. This and any other information necessary to determine
the projected principal and interest payments under proposed scenarios
is entered at block 302. The principal amount of the collateral
that is outstanding for any period is denoted by PRN.sub.c and its
coupon rate (i.e., Interest Rate) is denoted by CPN.sub.c.
Based on this data, the system creates a data array in memory at
block 304. This data file includes the remaining principal balance,
the amount of principal paid and the amount of interest paid on
each of the underlying securities. These data items are calculated
at each principal and/or interest payment period (usually monthly)
and for each requested interest rate and prepayment scenario that
might affect the timing or amount of any of the payments. The data
items are then aggregated into a single array in memory that contains
the projected remaining balance, principal payment and interest
payment that would occur at each payment period under each interest
rate and prepayment rate scenario for the aggregate of the underlying
securities.
At block 306, the system separates the cash flows produced at block
304 into two separate arrays in memory; one file that contains only
the principal payments on the aggregate underlying securities and
one file that contains only the interest payments. The system allocates
the aggregate cost entered at block 302 between the principal and
the interest based on market yields or input prices.
At block 308, the parameters are input that define how the principal
and interest cash flows generated by the underlying securities are
to be allocated among new securities to be issued. At each period
that a cash flow occurs, the allocation depends on the value of
an "Index Rate" applicable to that period. The choice
of the Index Rate is specified at block 308 and should be a recognized
objective interest rate (e.g., the 30 day Treasury Bill rate) or
some other rate provided for by REMIC regulations. An Allocation
Formula/Table is then specified at block 308 and is stored in memory.
This Allocation Formula/Table file determines how the cash flows
are to be allocated for any given value of the Index Rate
and includes:
a) a series of specified values for the Index Rate, R.sub.1, R.sub.2,
. . . , R.sub.N, R.sub.N+1 (where N is a positive integer) in ascending
or descending order (e.g., 3%, 5%, 7%, 10%);
b) a corresponding series of Interest Allocation Percentages, IPCTA.sub.1,
IPCTA.sub.2, . . . , IPCTA.sub.N, IPCTNA.sub.N+1 with values between
0% and 100% (e.g., 15%, 35%, 65%, 90%); and
c) a corresponding series of Principal Allocation Percentages,
PPCTA.sub.1, PPCTA.sub.2, . . . , PPCTA.sub.N, PPCTA.sub.N+1 with
values between 0% and 100%.
TABLE 1 __________________________________________________________________________
Allocation Formula/Table Index Rate R.sub.1 = 3.0% R.sub.2 = 5.0%
R.sub.3 = 7.0% R.sub.4 = 10.0% __________________________________________________________________________
Principal PPCTA.sub.1 = 24% PPCTA.sub.2 = 44% PPCTA.sub.3 = 80%
PPCTA.sub.4 = 100% Allocation Percentage Interest IPCTA.sub.1 =
15% IPCTA.sub.2 = 35% IPCTA.sub.3 = 65% IPCTA.sub.4 = 90% Allocation
Percentage __________________________________________________________________________
The Allocation Formula/Table is designed to function as follows.
At each payment period, the applicable value "r" of the
Index Rate is determined (usually by consulting one or more publications
or news services) and the value of IPCT.sub.A (r) is determined
where IPCT.sub.A (r) represents the percentage of total interest
to be allocated by the proposed security IO.sub.A. IPCT.sub.A (r)
is the general formula for the Interest Allocation Percentage and
is defined as follows:
a) IPCT.sub.A (r)=IPCTA.sub.1 if r.ltoreq.R.sub.1, i.e., IPCT.sub.A
(r) equals the allocation value corresponding to the lowest listed
Index Rate in the Allocation Formula/Table if the applicable Index
Rate is less than the lowest listed Index Rate;
b) IPCT.sub.A (r)=IPCTA.sub.N+1 if r.gtoreq.R.sub.N+1, i.e., IPCT.sub.A
(r) equals the allocation value corresponding to the highest listed
Index Rate in the Allocation Formula/Table if the applicable Index
Rate is greater than the highest listed Index Rate;
c) IPCT.sub.A (r) is derived by linear interpolation from the Allocation
Formula/Table for all other values of the applicable Index Rate
r (i.e., if R.sub.1 <r.ltoreq.R.sub.N+1).
Using the standard form of a linear function, the allocation percentage
can be expressed in terms of the applicable Index Rate as follows:
a) INTP.sub.A (r)=IPCTA.sub.1 if r.ltoreq.R.sub.1
b) INTP.sub.A (r)=IPCTA.sub.N+1 if r>R.sub.N+1
c) INTP.sub.A (r)=m.sub.k .times.r+b.sub.k if R.sub.k <r.ltoreq.R.sub.k+1
for k=1, . . . , N
where ##EQU1##
IPCT.sub.B (r) is de fined to equal 100% minus the Interest Allocation
Percentage, IPCT.sub.A (r), and IPCT.sub.B (r) represents the percentage
of total interest to be allocated to the IO.sub.B security. Then
a) IPCT.sub.B (r)=100%-IPCT.sub.A (r)=100%-IPCTA.sub.1 if r.ltoreq.R.sub.1
b) IPCT.sub.B (r)=100%-IPCT.sub.A (r)=100%-IPCTA.sub.N+1 if r>R.sub.N+1
c) IPCT.sub.B (r)=100%-IPCT.sub.A (r)=n.sub.k .times.r+d.sub.k
if R.sub.k <r.ltoreq.R.sub.k+1 where n.sub.k =-m.sub.k and d.sub.k
=100%-b.sub.k. Similarly, PPCT.sub.A (r) and PPCT.sub.B (r) are
determined where PPCT.sub.B (r)=100%-PPCT.sub.A.
At block 310, the principal and interest payments derived from
the underlying securities will be distributed among four proposed
securities; two securities IO.sub.A and IO.sub.B that will receive
only interest payments and two securities PRO.sub.A and PRO.sub.B
that will receive only principal payments. IO.sub.A will receive
the total interest amount generated by the underlying securities
at each period multiplied by the Interest Allocation Percentage
IPCT.sub.A (r) calculated in block 308; IO.sub.B will receive the
remainder of the interest.
Since the interest paid on the underlying securities equals PRN.sub.C
.times.CPN.sub.C where PRN.sub.C is the principal balance and CPN.sub.C
is the interest or coupon rate for the period,
a) the interest paid to IO.sub.A =PRN.sub.C .times.CPN.sub.C .times.IPCT.sub.A
(r)
b) the interest paid to IO.sub.B =PRN.sub.C .times.CPN.sub.C .times.IPCT.sub.B
(r)
where r is the applicable value of the Index Rate. It may be appreciated
that since the total amount of interest paid on a mortgage may vary
depending on when the mortgage is paid off, the total cashflow of
IO.sub.A and IO.sub.B may also vary.
The allocation of principal payments to the principal-only securities
differs from that for the interest-only securities in that each
of PRO.sub.A and PRO.sub.B is assigned a stated principal amount
which is specified at block 310 and which in total cannot exceed
PRN.sub.C. The total amount of principal that each of these securities
may receive is limited to its stated principal amount. The principal
payments generated by the underlying securities at each period are
distributed to PRO.sub.A and PRO.sub.B in accordance with the Principal
Allocation Formulas PPCT.sub.A (r) and PPCT.sub.B (r) as derived
from the Allocation Formula/Table. However, once one of the two
principal-only securities has received principal payments equal
to its initial stated principal, it may receive no more principal.
At that point, all future principal payments are allocated to the
other principal-only security until it receives all of its stated
principal. It may be appreciated that since the principal amounts
of PRO.sub.A and PRO.sub.B are specified, only the timing as to
when they receive their respective cash flows may vary--their total
amounts cannot vary.
At block 310, the data processing system creates four new arrays
as files in memory which represent four proposed securities. The
IO.sub.A and IO.sub.B (Interest Only A and B) arrays represent the
proposed securities that will receive payments of a portion of the
interest only that is generated by the underlying securities; the
PRO.sub.A and PRO.sub.B (PRincipal Only A and B) arrays will receive
only principal payments. The first element in each array represents
the price to be paid for the security on the settlement date. Each
array also has additional elements corresponding to each payment
date of the underlying securities. For each payment period, the
principal payment cash flows that were projected at block 304 are
divided between PRO.sub.A and PRO.sub.B ; PRO.sub.A is allocated
the portion specified by the Principal Allocation Percentage from
the Allocation Formula/Table and PRO.sub.B is allocated the remainder
of the projected principal payment. Similarly, the projected interest
payments generated by the underlying securities are divided between
the proposed IO.sub.A and IO.sub.B securities in accordance with
the Interest Allocation Percentage from the Allocation Formula/Table.
It may be appreciated that the number of elements of each array
for each cash flow period corresponds to the number of Index Rate
and prepayment scenarios specified at block 302.
As an example, if the Index Rate at the specific payment date is
7.0% and the Principal Allocation Percentage is 80% and the Interest
Allocation Percentage is 65% as illustrated in TABLE 1, PRO.sub.A
would receive 80% of all principal paid on that date and PRO.sub.B
would receive the remaining 20% of principal whereas IO.sub.A would
receive 65% of the interest paid on that date and IO.sub.B would
receive 35% of the interest. It may also be appreciated that while
the amount of principal and interest available for distribution
will depend on the prepayment rate as well as other factors, the
percentages of the principal and interest that each of the proposed
securities receive depends only on the Index Rate applicable to
the cash flow period and the specified allocation.
At block 312 combination securities from the PRO.sub.A, PRO.sub.B,
IO.sub.A and IO.sub.B securities may be created. In particular,
the data processing system may automatically analyze two specific
combinations which have significant market appeal: 1) a bullish
combination security that consists of the PRO and IO securities
that would be expected to perform best when interest rates are low,
and 2) a bearish combination security that would be expected to
perform best when interest rates are high. These combination securities
will often possess overall performance characteristics that are
similar to conventional Principal-Only (PO) and Interest-Only (IO)
securities that pay only a fixed percentage of the principal-only
or the interest-only payments generated by the collateral, respectively.
The performance of the securities created by utilizing this invention,
however, can be predicted and controlled more accurately than conventional
PO and IO securities because the allocation percentages may be variable.
In addition, the performance of the new securities is far less subject
to influence by factors other than changes in the Index Rate. In
addition, each of the new combination securities has a stated principal
amount (equal to the principal of its PO component) that must be
repaid and may therefore be a permissible investment for many institutional
clients that are precluded from purchasing conventional IO-type
securities which do not guarantee the return of any principal.
Referring to FIG. 4, at block 402 an estimate of the market price
for each of the proposed securities is entered. Alternatively, an
estimate of the market yield at which the securities would be salable
may be input (together with an Index Rate and prepayment scenario
under which the market yield would apply). If a yield was entered
at block 402, which is decided at block 404, the corresponding price
that would result in that yield under the specified interest rate
and prepayment scenario must be calculated.
At block 406, the system calculates a price if a yield was entered
at block 402 by discounting the projected cash flows for the given
scenario at the specified yield. If a price was entered at block
402, the system proceeds to block 408.
The data processing system now has available to it an estimate
of the price/market value for each of the new securities and may
now prepare a detailed analysis of the proposed securities. Using
the input or calculated price, the data processing system calculates
the yield, the duration, the average life (for the PROs) and the
start and end dates of the cash flows for each of the proposed securities.
These calculations are performed at block 408 from the cash flow
arrays created at block 310. The calculations are performed for
each Index Rate and prepayment rate scenario that was input in block
302. The results calculated at block 408 may provide an overall
analysis of how each of the proposed securities would perform under
the potential market scenarios specified in blocks 302 and 308.
The results obtained by the data processing system may either be
displayed on a CRT or printed.
Upon examining the results of block 408, a decision may be made
as to whether the proposed securities are fairly priced at the estimated
prices/yields input at block 402. If the proposed securities are
fairly priced, the data processing system may be instructed at block
410 to continue to block 412. If not, the system returns to block
402 where the previous set of price/yield estimates nay be replaced
by another set of estimates. This iterative loop from block 402
to block 410 is repeated until a best estimate of prices/yields
for the proposed securities is determined.
At block 412, the estimate of the prices at which the proposed
securities can be sold, that was determined in block 109, may then
be compared to the cost of issuing these securities which includes
the cost of the underlying securities plus any underwriting and
other issuance costs such as rating agency fees, legal and accounting
fees, trustee fees, etc. The cost is compared to the sum of the
market values of the securities. Based upon the comparison a determination
may be made as to whether to proceed with the issuance. Even if
the estimated value of the proposed securities exceeds their cost,
the difference may not be large enough to warrant their issuance.
Furthermore, even if issuance is warranted on cost basis, other
potential structures may be examined in an attempt to improve the
potential profit and/or marketability of the securities. At block
414 a decision is made as to whether the creation of the proposed
securities is desired. If so, the system continues to FIG. 5, otherwise
the system proceeds to block 416.
At block 416, the structure of any one or all of the proposed securities
may be altered by changing a) the stated principal amounts of PRO.sub.A
and PRO.sub.B or b) the Allocation Formula/Table specified at blocks
308, 310. An increase of the Interest Allocation Percentage at any
specific Index Rate value insures that IO.sub.A (IO.sub.B) will
receive a greater (lesser) proportion of the available interest
cash flow at all periods for which that value is the applicable
value of the Index Rate. A change in the Principal Allocation Percentage
has a similar effect on PRO.sub.A and PRO.sub.B.
Although the PRO and IO securities or combinations thereof as previously
described would be readily marketable to many clients, their direct
issuance as regular interests in a CMO/REMIC may not be provided
for under current REMIC regulations. Advantageously, however, this
invention provides a system for creating these securities in a manner
that is permissible and consistent with REMIC regulations. The invention
utilizes a multistage REMIC process with a Lower REMIC stage and
Upper REMIC stage. The underlying securities serve as the collateral
for the Lower REMIC (which itself may constitute a multistage REMIC)
which issues a new set of securities LA and LB that have fixed principal
amounts and variable interest rates. These securities serve as the
collateral for the Upper REMIC, which issues IO.sub.A, IO.sub.B,
PRO.sub.A and PRO.sub.B.
FIGS. 5, 7 and 8 illustrates the operation of the data processing
system that creates securities IO.sub.A, IO.sub.B, PRO.sub.A and
PRO.sub.B with the properties described in blocks 308 and 310 of
FIG. 3 using a multistage CMO/REMIC procedure.
In general, the data processing system according to the invention
accomplishes the creation of the proposed securities in the following
manner. In the Lower REMIC, two bonds (LA and LB) with the following
characteristics are issued,
a) LA and LB each have a stated principal amount and a interest
rate formula that qualify them as regular REMIC interests,
b) the principal cash flows generated by the underlying securities
are passed through simultaneously to LA and LB in proportion to
their stated principal amounts,
c) the interest paid each period on LA equals the interest to be
paid each period on the proposed IO.sub.A security, and
d) the interest paid each period on LB equals the interest to be
paid each period on the proposed IO.sub.B security.
The LA and LB bonds are then placed into another REMIT (i.e., the
Upper REMIC) where they serve as the collateral for the issuance
of the proposed new securities as follows,
a) an interest only security (IO.sub.A) that receives 100% of the
interest paid on the LA bond, IO.sub.A receives no principal payments;
b) an interest only security (IO.sub.B) that receives 100% of the
interest paid on the LB bond, IO.sub.B receives no principal payments;
and
c) two principal only securities (PRO.sub.A and PRO.sub.B) that
have respective principal amounts and payment priorities equal to
the above-described principal only securities.
It may be appreciated that, since IO.sub.A is an interest-only
strip of LA, it qualifies as a regular REMIC security under REMIC
regulations. Similarly, IO.sub.B is a 100% interest-only strip of
LB which also qualifies it as a REMIC regular interest.
Although the cash flows of the IO.sub.A and IO.sub.B securities
in effect equal a variable portion (that may change periodically)
of the interest amount on the underlying securities, their creation
by the means of this invention, however, is consistent with current
REMIC regulations because the invention creates the IO.sub.A and
IO.sub.B securities by combining fixed portion (i.e., 100%) of the
interest amount on a group of other regular REMIC securities; (i.e.,
the LA and LB bonds).
The procedure for accomplishing this is as follows. At block 502,
a two stage CMO/REMIC with an Upper and Lower stage is created.
The underlying securities are placed into the Lower stage of this
CMO/REMIC as the collateral that generates the cash flows to be
restructured. The principal amount is denoted by PRN.sub.C, the
coupon rate (i.e., interest rate) is denoted by CPN.sub.C.
At block 504, two variable rate bonds, LA and LB, are defined such
that a) the sum of their principal amounts, PRN.sub.A and PRN.sub.B,
equals the total principal, PRN.sub.C, of the underlying securities,
and b) principal payments as they occur will be distributed simultaneously
to the LA and LB bonds in proportion to their principal amounts.
At block 506, the coupon formula (i.e., interest rate formula)
for LA is defined such that the interest that would be paid (i.e.,
principal times coupon rate) on LA each period equals the amount
to be paid to proposed security IO.sub.A as calculated at block
310. The mathematical formula for this is:
It may be appreciated that since the interest paid on bond LA is
determined by multiplying its coupon rate CPN.sub.A (r) by its outstanding
principal PRN.sub.A, this equals
which is the amount of interest to be paid to IO.sub.A as determined
at block 310.
The coupon formula for LB is defined similarly as,
The total interest paid each period on bond LB is
which equals the cash flow amount of IO.sub.B as determined at
block 310.
It may be appreciated from the above formulas that whereas the
coupon formulas for LA and LB depend on the principal amounts (PRN.sub.A
and PRN.sub.B) of LA and LB, the amount of interest paid on LA and
LB do not depend on PRN.sub.A and PRN.sub.B. Therefore, PRN.sub.A
may be increased and PRN.sub.B decreased, or vice versa, without
altering their interest payments which are designed to equal the
cash flow amounts of IO.sub.A and IO.sub.B. The choice of PRN.sub.A
and PRN.sub.B may therefore be optional and the simplest choice
is PRN.sub.A =PRN.sub.B =PRN.sub.C /2. At times a different choice
may be necessary to ensure that LA and LB qualify as regular REMIC
interests.
To illustrate, REMIC regulations may require that the total market
value of certain regular interests do not exceed 125% of the principal
amount of the security. Thus, if the anticipated market value of
the LA bond (value of principal plus value of interest payments)
is judged to exceed 125% of its principal amount, PRN.sub.A, an
increase in principal amount may bring the bond back into compliance.
For example, assume PRN.sub.A =$50 million and its value is $40
million (i.e., each dollar of principal is valued at eight cents)
and assume the value of the interest payments on LA is $25 million.
Then the total value of LA is $65 million which is 130% of its principal
amount of $50 million. However, if PRN.sub.A is increased to $60
million (and PRN.sub.B decreased to $40 million) then the value
of the principal is $48 million (80% of $40 million) and the total
value of LA is $73 million (since value of interest is fixed at
$30 million) which is 121.667% of the principal amount of $60 million.
It is an advantage of this invention that an arbitrary choice may
be made initially for PRN.sub.A and PRN.sub.B and a final choice
may be made at the time of final issuance of the securities without
compromising the validity of the results.
If the formulas for IPCT.sub.A (r) and IPCT.sub.B (r) as determined
at block 310 are substituted into CPN.sub.A (r) and CPN.sub.B (r)
then,
a) CPN.sub.A (r)=(PRN.sub.C /PRN.sub.A).times.CPN.sub.C .times.IPCTA.sub.1
if r<R.sub.1
b) CPN.sub.A (r)=(PRN.sub.C /PRN.sub.A).times.CPN.sub.C .times.IPCTA.sub.N+1
if r.gtoreq.R.sub.N+1
c) CPN.sub.A (r)=(PRN.sub.C /PRN.sub.A).times.CPN.sub.C .times.{m.sub.k
.times.r+b.sub.k } if R.sub.k <r.ltoreq.R.sub.k+1 =mA.sub.k .times.r+bA.sub.k
where m.sub.k and b.sub.k were determined at block 104 for k=1,
. . . , N, and mA.sub.k =(PRN.sub.C /PRN.sub.A).times.CPN.sub.C
.times.m.sub.k and bA.sub.k =(PRN.sub.C /PRN.sub.A).times.CPN.sub.C
.times.b.sub.k For bond LB,
a) CPN.sub.B (r)=(PRN.sub.C /PRN.sub.B).times.CPN.sub.C .times.(1-IPCTA.sub.1)
if r<R.sub.1
b) CPN.sub.B (r)=(PRN.sub.C /PRN.sub.B).times.CPN.sub.C .times.(1-IPCTA.sub.N+1)
if r.gtoreq.R.sub.N+1
c) CPN.sub.B (r)=(PRN.sub.C /PRN.sub.B).times.CPN.sub.C .times.{n.sub.k
.times.r+d.sub.k } if R.sub.k <r.ltoreq.R.sub.k+1 =nB.sub.k .times.r+dB.sub.k
where n.sub.k and d.sub.k are as described at block 310 for k=1,
. . . , N; and
nB.sub.k =(PRN.sub.C /PRN.sub.B).times.CPN.sub.C .times.n.sub.k
and dB.sub.k =(PRN.sub.C /PRN.sub.B).times.CPN.sub.C .times.d.sub.k
This type of bond is called a multisegment variable rate bond because
when the Index Rate r falls within each specified range [R.sub.k,
R.sub.k+1 ] of the Index Rate its coupon formula is determined by
a linear function of the Index Rate. The issuance of such bonds
however as regular REMIC interests is not directly provided for
by current REMIC regulations. Utilization of the data processing
system according to this invention, however, enables their issuance
as qualifying regular interests in a REMIC within the provisions
of current regulations. The detailed procedure for issuance of a
regular REMIC interest that is equivalent to such a multisegment
variable rate bond is described in more detail below with respect
to FIG. 6 and FIG. 7.
The data processing system according to the invention particularly
enables the issuance of a regular REMIC security equivalent to a
multisegment variable rate bond. A multisegment variable rate bond
has:
a) a stated principal amount and a coupon formula that depends
on a specified Index Rate such that,
b) the coupon formula may be expressed as a linear function of
the Index Rate within each of several predefined ranges of the Index
Rate.
Notationally, the coupon formula can be written as,
a) CPN(r)=m.sub.1 .times.R.sub.1 +B.sub.1 if r.ltoreq.R.sub.1
b) CPN(r)=m.sub.k .times.r+B.sub.k if R.sub.k <r.ltoreq.R.sub.k+1
for k=1, 2, . . . , N
c) CPN(r)=m.sub.N .times.R.sub.N+1 +B.sub.N if r>R.sub.N+1
and is graphically illustrated in FIG. 9.
It may be appreciated that the LA and LB bonds as defined at blocks
504 and 506 are multisegment variable rate bonds since their coupon
formulas CPN.sub.A (r) and CPN.sub.B (r) are of the form described
here. It may also be appreciated that the creation of single segment
variable rate bond that has a coupon formula consisting of,
a) a multiplier times an Index Rate, plus (or minus) a fixed percentage
of interest, and
b) is subject to a minimum and a maximum interest rate is directly
provided for by REMIC regulations. Thus, the coupon rate formula
above would qualify as the coupon formula for a REMIC bond if the
formula had only one multiplier m.sub.1 and one offset b.sub.1,
i.e., if it were only a single segment rate bond.
Two important special cases of a multisegment bond are where
a) CPN(r) may only increases as r increases (i.e., CPN(r.sub.1).ltoreq.CPN(r.sub.2)
if r.sub.1 .ltoreq.r.sub.2); and
b) CPN(r) decreases as r increases (i.e., CPN(r.sub.1).gtoreq.CPN(r.sub.2)
if r.sub.1 .ltoreq.r.sub.2).
These are called monotonic multisegment variable rate bonds.
The data processing system according to the invention includes
a general procedure for creating a bond that qualifies as regular
interest in a REMIC and is equivalent to any specified multisegment
variable rate bond. In addition, this invention also includes an
additional procedure for creating a regular REMIC security that
is functionally equivalent to a specified monotonic multisegment
variable rate bond.
At block 508 the coupon formulas CPN.sub.A (r), CPN.sub.B (r) of
LA and LB are examined. If they are monotonic, the system branches
to FIG. 7 to create bonds LA and LB. Otherwise, the system procedes
to FIG. 6.
FIG. 6 is a schematic representation of how the system according
to the invention may be utilized to create a bond that qualifies
as a regular interest under REMIC regulations and is equivalent
to a specified multisegment variable rate bond. FIG. 7 is the schematic
representation of the procedure for the monotonic case.
At FIG. 6, block 602, two series of bonds LA.sub.1, . . . , LA.sub.N
and LB.sub.1, . . . , LB.sub.N with corresponding principal amounts
PRNA.sub.1, . . . , PRNA.sub.N and PRNB.sub.1, . . . , PRNB.sub.N
are issued such that PRNA.sub.1 + . . . + PRNA.sub.N =PRN.sub.A
and PRNB.sub.1, . . . , PRNB.sub.N =PRN.sub.B where PRN.sub.A and
PRN.sub.B are the principal amounts of bonds LA and LB as defined
in block 506. Principal is paid simultaneously to all of these bonds
in proportion to their principal amounts.
For simplicity it may be assumed that PRNA.sub.1 =. . .=PRNA.sub.N
=PRN.sub.A /N and PRNB.sub.1 =. . .=PRNB.sub.N =PRN.sub.B /N. However,
the IA.sub.k and LB.sub.k series bonds need not have equal principal
amounts. As was discussed earlier, a different choice for PRNA.sub.1,
. . . , PRNA.sub.N may be necessary to satisfy other REMIC requirements.
Since the issuance of both the LA and LB bonds defined at block
506 occurs simultaneously for both bonds, the remainder of the procedure
will be described here in detail for the LA bond only. The procedure
is the same for bond LB.
At block 604 the coupon formulas for LA.sub.1, . . . , LA.sub.N
are defined as,
a) CPNA.sub.k (r)=mA.sub.k .times.r+bA.sub.k for R.sub.k <r.ltoreq.R.sub.k+1
b) CPNA.sub.k (r)=V.sub.k =CPNA.sub.k (R.sub.k) if r.ltoreq.R.sub.k
c) CPNA.sub.k (r)=V.sub.k+1 =CPNA.sub.k (R.sub.k+1) if r.gtoreq.R.sub.k+1
It may be appreciated that for values of the Index Rate, r, within
the range [R.sub.k, R.sub.k+1 ], CPNA.sub.k (r)=CPN.sub.A (r). For
values outside of the range [R.sub.k, R.sub.k+1 ], CPNA.sub.k (r)
equals its value at the end points R.sub.k, R.sub.k+1 of the range.
It may be appreciated that each individual series LA.sub.k (r)
bond is a single segment variable rate bond because its coupon may
be expressed as a single linear function of the Index Rate subject
to a minimum and maximum rate. Therefore, each of the individual
LA.sub.k bonds qualifies as a regular REMIC interest.
At block 606, the second stage of the Lower REMIC is created. Bonds
LA.sub.1, . . . , LA.sub.N are placed into this REMIC as its collateral
upon which bond LA will be issued.
At block 608, bond LA is created in the second stage of the Lower
REMIC. It receives all the principal payments paid to LA.sub.1,
. . . , LA.sub.N so its principal amount is PRNA.sub.1 +. . .+PRNA.sub.N
=PRN.sub.A.
At block 610, the coupon rate formula for bond LA at any value
r of the Index Rate is defined to be,
where V.sub.k is the value of CPN.sub.A (r) at Index Rate point
R.sub.k.
It may be appreciated that with this formulation the value of CPN.sub.A
(r) is as specified in block 506 for any value r of the Index Rate.
This may be shown by evaluating CPNA.sub.1 (r), . . . , CPNA.sub.N
(r). Assuming R.sub.k <r.ltoreq.R.sub.k+1 for some k=2, . . .
, N.
CPNA.sub.1 (r)=CPNA.sub.1 (R.sub.2)=V.sub.2 since R.sub.2 <r
. . .
CPNA.sub.k-1 (r)=CPNA.sub.k-1 (R.sub.k)=V.sub.k since R.sub.k <r
CPNA.sub.k (r)=mA.sub.k .times.r+bA.sub.k since R.sub.k <r.ltoreq.R.sub.k+1
CPNA.sub.k+1 (r)=CPNA.sub.k+1 (R.sub.k+1)=V.sub.k+1 since r.ltoreq.R.sub.k+1
. . .
CPNA.sub.N (r)=CPNA.sub.N (R.sub.N)=V.sub.N since r.ltoreq.R.sub.N
So,
CPNA.sub.1 (r)+. . .+CPN.sub.N (r)=(V.sub.2 +. . .+V.sub.k-1)+mA.sub.k
.times.r+bA.sub.k +(V.sub.k +. . .+V.sub.N) =(V.sub.2 +. . .+V.sub.N)+mA.sub.k
.times.r+bA.sub.2
Therefore, CPN.sub.A (r) as defined
CPN.sub.A (r)=[CPNA.sub.1 (r)+. . .+CPNA.sub.N (r)]-(V.sub.2 +.
. .+V.sub.N) =(V.sub.2 +. . .+V.sub.N)+mA.sub.k .times.r+bA.sub.k
-(V.sub.2 +. . .+V.sub.N) =mA.sub.k .times.r+bA.sub.k which is the
desired coupon formula of bond LA as defined at block 506.
It may be appreciated that CPN.sub.A (r) as defined here is the
weighted average of the coupon rates on the LA.sub.1, . . . , LA.sub.N,
bonds minus a fixed percentage. Since the LA.sub.1, . . . , LA.sub.N
series bonds serve as the collateral for the Upper REMIC, the weighted
average of their coupon rates minus a fixed percentage qualifies
bond LA as defined in block 608 as a regular REMIC interest.
Thus, the use of the data processing system according to the invention
permits the creation of a qualifying regular REMIC interest equivalent
to almost any multisegment variable rate bond.
Simultaneously with the issuance of bond LA with coupon formula
CPN.sub.A (r) in block 604 through block 610, the data processing
system also issues bond LB. The procedure is the same and the resultant
coupon formula CPN.sub.B (r) for bond LB will have a value for any
Index Rate r that is equal to that defined at block 506.
Having issued bonds LA and LB as defined at block 506, the system
continues to FIG. 8 to create bonds IO.sub.A and IO.sub.B.
A particular class of multisegment variable rate bonds; that holds
particular appeal to many investors are those whose coupon rates
cannot decrease as the Index Rate increases and those whose coupon
rates cannot increase as the Index Rate increases.
Although such bonds can be created in a manner that qualifies as
a regular interest under REMIC regulations by utilizing the procedure
described above with respect to FIG. 6, an alternate procedure that
is more efficient at times may be utilized in this special case.
If bonds LA and LB as described at blocks 504 and 506 are unidirectional,
this procedure may be utilized. The procedure as described below
with respect to FIG. 7 is for bond LA which is assumed to have a
non-decreasing coupon formula as graphically illustrated in FIG.
10. It will be appreciated that a variable rate bond with a non-increasing
coupon rate may be treated similarly. It may also be appreciated
that, as defined at block 506, bond LB will be non-increasing if
LA is non-decreasing (and vice versa).
At block 702 two series of bonds LA.sub.1, . . . , LA.sub.N and
LB.sub.1, . . . , LB.sub.N with corresponding principal amounts
PRNA.sub.1, . . . , PRNA.sub.N and PRNB.sub.1, . . . , PRNB.sub.N
are created by the Lower REMIC such that PRNA.sub.1 +. . .+PRNA.sub.N
=PRN.sub.A and PRNB.sub.1, . . . , PRNB.sub.N =PRN.sub.B. Principal
is paid simultaneously to each of
these bonds in proportion to their principal amounts. Currently,
it may be assumed that PRNA.sub.k =PRN.sub.A /N and PRNB.sub.k =PRN.sub.B
/N (for k=1, . . . , N) but at times it may be necessary to apportion
the principal among the lower REMIC bonds differently in order to
satisfy various other REMIC requirements as discussed earlier.
As before, the value of CPN.sub.A (r) at the Index Rate points
R.sub.1, R.sub.2, . . . , R.sub.N+1 is denoted by V.sub.1, . . .
, V.sub.N+1. Thus V.sub.1 =CPN.sub.A (R.sub.1), . . . , V.sub.N+1
=CPN.sub.A (R.sub.N+1). Since LA is non-decreasing this implies
that V.sub.1 .ltoreq.V.sub.2 .ltoreq.. . .<V.sub.N .ltoreq.V.sub.N+1.
At block 704 CPNA.sub.1 (r) is defined as,
a) CPNA.sub.1 (r)=(PRN.sub.A /PRNA.sub.1).times.V.sub.1 if r<R.sub.1
b) CPNA.sub.1 (r)=(PRN.sub.A /PRNA.sub.1).times.{mA.sub.1 .times.r+bA.sub.1
} if R.sub.1 <r.ltoreq.R.sub.2
c) CPNA.sub.1 (r)=(PRN.sub.A /PRNA.sub.1).times.{mA.sub.1 .times.R.sub.2
+b.sub.1 }=(PRN.sub.A /PRNA.sub.1).times.V.sub.2 if r.gtoreq.R.sub.2
For k=2, . . . N, CPNA.sub.k (r) is defined as,
a) CPNA.sub.k (r)=0 if r<R.sub.k
b) CPNA.sub.k (r)=(PRN.sub.A /PRNA.sub.k).times.([mA.sub.k .times.r+b.sub.k
]-V.sub.k) if R.sub.k <r.ltoreq.R.sub.k+1
c) CPNA.sub.k (r)=(PRN.sub.A /PRNA.sub.k).times.(V.sub.k+1 -V.sub.k)
if r.gtoreq.R.sub.k+1
where mA.sub.k and b.sub.k are as defined at block 506.
It may be noted that each of LA.sub.1, . . . , LA.sub.N are defined
as single segment variable rate bonds subject to a minimum and maximum
and therefore qualify as regular interests in a REMIC. Further,
the amount of interest paid on bond LA.sub.1 each period equals
its coupon rate multiplied by its principal which equals
a) PRNA.sub.1 .times.CPNA.sub.1 (r)=PRNA.sub.1 .times.(PRN.sub.A
/PRNA.sub.1).times.{mA.sub.1 .times.r+bA.sub.1 }=PRN.sub.A .times.{mA.sub.1
.times.r+bA.sub.1 }, which equals the interest paid on the multisegment
bond LA defined at block 506 if R.sub.1 <r.ltoreq.R.sub.2
b)=PRN.sub.A .times.V.sub.1 if r.ltoreq.R.sub.1
c)=PRN.sub.A .times.V.sub.2 if r>R.sub.2
The amount of interest paid on bonds LA.sub.k for k=2, . . . ,
N equals
a) PRNA.sub.k .times.CPNA.sub.k (r)=PRNA.sub.k .times.(PRN.sub.A
/PRNA.sub.k).times.(mA.sub.k .times.r+bA.sub.k -V.sub.k) if R.sub.k
<r.ltoreq.R.sub.k+1
b)=0 if r<R.sub.k
c)=PRN.sub.A .times.V.sub.k+1 -PRN.sub.A .times.V.sub.k if r>R.sub.k+1
Furthermore, for any value of the Index Rate r such that R.sub.k
<r.ltoreq.R.sub.k+1 the sum total of all the interest paid on
all the LA.sub.1, . . . , LA.sub.N bonds equals
INTEREST on LA.sub.1 =PRN.sub.A .times.V.sub.2
+INTEREST on LA.sub.2 =PRN.sub.A .times.V.sub.3 -PRN.sub.A .times.V.sub.2
. . .
+INTEREST on LA.sub.k-1 =PRN.sub.A .times.V.sub.k -PRN.sub.A .times.V.sub.k-1
+INTEREST on LA.sub.k =PRN.sub.A .times.{mA.sub.k .times.r+bA.sub.k
}-PRN.sub.A .times.V.sub.k
+INTEREST on LA.sub.k+1 =0 . . .
+INTEREST on LA.sub.N =0
TOTAL INTEREST=PRN.sub.A .times.(mA.sub.k .times.r+bA.sub.k)
which is the amount of interest to be paid on bond LA as defined
at block 506 of FIG. 5.
At block 706 the LA.sub.1, . . . , LA.sub.N bonds are placed into
the second stage of the Lower REMIC as its collateral.
At block 708 bonds LA and LB are issued by the second stage of
the Lower REMIC such that LA receives all the principal and all
the interest on each of LA.sub.1, . . . , LA.sub.N. Then by the
above calculation the interest paid on bond LA equals,
which equals the cashflow on IO.sub.A as determined at block 105.
It may be appreciated that the interest paid on bond LA is not
derived by multiplying a principal amount by a coupon rate. In fact,
LA does not have a coupon formula in the conventional sense. Rather
it is defined as the sum of the interest portions on the LA.sub.1,
. . . , LA.sub.N bonds. This qualifies it as a regular interest
in a REMIC. Thus, although bond LA as ultimately created by the
system does not have a conventional coupon formula, the amount of
interest paid on LA is precisely equal the amount that would be
derived by utilizing the formula defined at block 506.
In a similar manner the coupon formulas for bonds LB.sub.1, . .
. , LB.sub.N are defined at block 704 such that the sum of the amounts
of interest paid on LB.sub.1, . . . , LB.sub.N equals the amount
specified for LB in block 506. Bond LB is created as a regular REMIC
interest,
The formulas for CPNB.sub.k (r) when k=1, . . . , N-1 are,
a) CPNB.sub.k (r)=(PRN.sub.B /PRNB.sub.k).times.([nB.sub.k .times.r+dBk]-W.sub.k+1)
if R.sub.k <r.ltoreq.R.sub.k+1
b) CPNB.sub.k (r)=0 if r.gtoreq.R.sub.k+1
c) CPNB.sub.k (r)=(PRN.sub.B /PRNB.sub.k).times.(W.sub.k -W.sub.K+1)
if r<R.sub.k
where nB.sub.k, dB.sub.k were defined at block 506 and W.sub.k
=CPN.sub.B (R.sub.k).
For CPNB.sub.N (r) the formula is
a) CPNB.sub.N (r)=(PRN.sub.B /PRNB.sub.N).times.W.sub.N if r.ltoreq.R.sub.N
b) CPNB.sub.N (r)=(PRN.sub.B /PRNB.sub.N).times.(nB.sub.N .times.r+dB.sub.N)
if R.sub.N <r.ltoreq.R.sub.N+1
c) CPNB.sub.N (r)=W.sub.N+1 if r>R.sub.N+1
At block 708 bond LB is issued such that it receives all principal
and interest paid on bonds LB.sub.1, . . . , LB.sub.N. Thus LB receives
interest equal to the amount to be paid to IO.sub.B as provided
at block 310. The system then proceeds to FIG. 8.
At block 802, the Upper REMIC is created and the bonds LA and LB
issued by the Lower REMIC utilizing the procedure described in FIG.
6 or FIG. 7 are placed into the Upper REMIC as the collateral for
the Upper REMIC.
At block 804, two securities are issued, IO.sub.A and IO.sub.B
; IO.sub.A will receive 100% of all the interest generated by LA
and IO.sub.B will receive 100% of all the interest generated by
LB. These securities will have interest only cash flows which equal
the amounts specified by the Allocation Formula/Table at block 310.
At block 806, two other securities are created, PRO.sub.A and PRO.sub.B.
The same procedure is not applied to the creation of the PRO.sub.A
and PRO.sub.B securities as for the IO.sub.A and IO.sub.B securities.
The principal of the LA and LB bonds is not allocated between them
in a manner that reflects the proposed PRO.sub.A and PRO.sub.B bonds.
However, once the LA and LB bonds are placed into the Upper REMIC
and their interest portions are stripped to create IO.sub.A and
IO.sub.B, their principal cash flows can be restructured and reallocated
into the PRO.sub.A and PRO.sub.B securities (or into other securities)
without resorting to a multistage REMIC. This is because REMIC regulations
are less restrictive of how principal payments on the underlying
securities may be distributed than of how interest payments on the
underlying securities may be distributed. The total principal cash
flows from LA and LB, which equals the total principal of the initial
underlying securities is allocated to PRO.sub.A and PRO.sub.B as
indicated in block 310 of FIG. 3.
At block 808 securities that are combinations of PRO.sub.A, PRO.sub.B,
IO.sub.A and IO.sub.B may be created.
The securities certificates created in accordance with the invention
and offered by an issuer/underwriter may be issued e.g., in minimum
denominations of $1,000 and integral multiples of $1 in excess thereof
in fully registered, certificated form. The securities certificates
may also be maintained on the book-entry system of the Federal Reserve
Banks in a manner that permits separate trading and ownership. Each
class of securities certificates may be assigned a CUSIP number
and may be tradable separately under such CUSIP number.
The securities certificates may be issued and guaranteed by the
Federal National Mortgage Association ("Fannie Mae").
Fannie Mae's fiscal agent for the securities certificates may be,
e.g., the Federal Reserve Bank of New York. The Federal Reserve
Banks may issue the securities certificates in book-entry form and
maintain book-entry accounts with respect to the securities certificates
and make payment distributions on the securities certificates on
behalf of Fannie Mae on the applicable distribution dates by crediting
securities holder's accounts at the Federal Reserve Banks.
It may be appreciated that under such an arrangement the securities
certificates may be held of record only by entities eligible to
maintain book-entry accounts with the Federal Reserve Banks. Further,
a securities holder may not necessarily be the beneficial owner
of a securities certificate. Beneficial owners thus will ordinarily
hold the securities certificates through one or more financial intermediates,
such as banks, brokerage firms and securities clearing organizations.
A securities holder that is not the beneficial owner of a securities
certificate, and each other financial intermediary in the chain
to the beneficial owner, will have the responsibility of establishing
and maintaining accounts for their respective customers. The rights
of the beneficial owner of a securities certificate with respect
to Fannie Mae and the Federal Reserve Banks are therefore exercised
only through the securities holder of such securities certificate.
EXAMPLE
An underwriter purchases $200 million of mortgage pools paying
9.0% interest for $210 million and can sell $100 million of the
principal for $80 million. The underwriter wants to issue new securities
to be collateralized by the future cashflows of the remaining $100
million of principal plus the interest payments at 9.0% on the $200
million of principal.
The detailed operation of the invention as it applies to this example
may be understood by reference to FIGS. 3, 4, 5, 7 and 8.
At block 302 the parameters describing the underlying securities
(the collateral) are input into the system. These include:
a) the principal amount of the underlying securities PRN.sub.C
=$200,000,000;
b) the coupon rate of the underlying securities CPN.sub.C =9%/year,
payable monthly;
c) the remaining average maturity of the mortgages of 330 months;
and
d) anticipated mortgage prepayment scenarios of 12%, 24% and 36%
annually (i.e., scenarios under which 12%, 24% and 36% of the remaining
mortgage balance would be prepaid each year).
Throughout this example all calculation and formulas are presented
on an annualized basis which is common industry practice. Thus the
coupon rate is quoted as CPN.sub.C =9%, but the actual interest
payments occur monthly and equal the principal balance at the start
of the month multiplied by one-twelfth the annual coupon rate.
At block 304 the system creates an array of cash flows that describe
the behavior of the underlying securities under several prepayment
scenarios.
At block 306 the system separates the cash flows produced at block
304 into two arrays; one that contains only the anticipated future
principal payments on the underlying securities and one that contains
only the anticipated interest payments on the underlying securities
for each of the specified prepayment scenarios. Based on the initial
cost, the principal-only portion is assigned a cost of $160 million
(i.e., 80% of par value for $200 million principal) and the interest
only portion is assigned a cost of $50 million (i.e., $50 million
for 9% annual interest on $300 million of mortgage pools).
Some of the cash flow characteristics of the principal-only and
interest-only portions of the underlying securities under the anticipated
scenarios are shown in TABLE 2.
TABLE 2 __________________________________________________________________________
Cash Flow Characteristics Prepayment Scenario: 6% 15% 30% 45% __________________________________________________________________________
Average Life 10.75 yrs 5.61 yrs 2.75 yrs. 1.83 yrs. of Principal
Total Amount $261,160,000 $168,300,000 $116,800,000 $100,260,000
of Interest __________________________________________________________________________
Although $100 million of principal will ultimately be sold without
being reallocated, the system proceeds as if all the principal is
subject to allocation.
At block 308 the Allocation Formula/Table that determines how the
cash flows will be allocated among the proposed new securities is
specified. For this example,
a) The Index Rate selected is the one-month Libor rate and is denoted
by r;
b) Three values of the Index Rate are specified; R.sub.1 =0.375%,
R.sub.2 =3.375% R.sub.3 =6.375%; and
c) The Principal Allocation Percentages and Interest Allocation
Percentages for the given Index Rate points are specified in TABLE
3.
TABLE 3 __________________________________________________________________________
Principal And Interest Allocation Percentages If Libor equals: R.sub.1
= 0.375% R.sub.2 = 3.375% R.sub.2 = 6.375% Principal Allocation
Percentage PPCTA.sub.1 = 0.0% PPCTA.sub.2 = 66.667% PPCTA.sub.3
= 100% Interest Allocation Percentage IPCTA.sub.1 = 0.0% IPCTA.sub.2
= 57% IPCTA.sub.3 = 100% __________________________________________________________________________
The values of the Principal Allocation Percentage and Interest
Allocation Percentage for any given Index Rate value r are denoted
by PPCT.sub.A (r) and IPCT.sub.A (r), respectively. The general
formulations for PPCT.sub.A (r) and IPCT.sub.A (r) as derived from
TABLE 3 by linear interpolation are shown in TABLE 4 where IPCT.sub.B
(r) is defined to be IPCT.sub.B (r)=1-IPCT.sub.A (r).
TABLE 4 ______________________________________ Interest Allocation
Formulas Index Rate Value IPCTA.sub.A (r) IPCT.sub.B (r) = 1-IPCT.sub.A
(r) ______________________________________ r < 0.375% 0 1.0 0.375%
< r < 3.375% m.sub.1 .times. r + b.sub.1 or n.sub.1 .times.
r + d.sub.1 or 19 .times. r - 0.07125 1.07125 - 19 .times. r
3.375% < r < 6.375% m.sub.2 .times. r + b.sub.2 or n.sub.2
.times. r + d.sub.2 or 14.333 .times. r + 0.08625 0.91375 - 14.333
.times. r r > 6.375% 1.0 0.0 ______________________________________
At block 310 four arrays are created, one each for PRO.sub.A, PRO.sub.B,
IO.sub.A, and IO.sub.B. Each month the principal payments generated
by the underlying securities are allocated to PRO.sub.A amd PRO.sub.B
only, and the interest payments are allocated to IO.sub.A and IO.sub.B.
The principal amounts of PRO.sub.A and PRO.sub.B are $66 million
and $134 million respectively. Each month the total principal payment
generated by the underlying securities is allocated to PRO.sub.A
and PRO.sub.B in proportion to their principal allocation percentages
PPCT.sub.A (r) and PPCT.sub.B (r), respectively, where r is the
value of the Index Rate applicable to that month. Neither PRO.sub.A
nor PRO.sub.B may receive more than its stated amount of principal.
Each month the total interest amount generated by the underlying
securities is allocated to IO.sub.A and IO.sub.B in proportion to
their Principal Allocation Percentages IPCT.sub.A (r) and IPCT.sub.B
(r), respectively, where r is the value of the Index Rate applicable
to that month.
The total annual interest paid on the underlying securities equals
the coupon rate (CPN.sub.C =9% or CPN.sub.C =0.09 in decimal form)
multiplied by the principal balance of the underlying securities.
Therefore, the amount of interest to be paid to IO.sub.A and IO.sub.B
on an annual basis equals, IO.sub.A interest=PRN.sub.C .times.CPN.sub.C
.times.IPCT.sub.A (r)=PRN.sub.C .times.0.09.times.IPCT.sub.A (r)
IO.sub.B interest=PRN.sub.C .times.CPN.sub.C .times.IPCT.sub.B (r)=PRN.sub.C
.times.0.09.times.IPCT.sub.B (r) where r is the applicable value
of the Index Rate.
The amounts that would be paid IO.sub.A and IO.sub.B for selected
values of the Index Rate are calculated and shown in TABLE 5. In
each case PRN.sub.C represents the remaining principal balance of
the underlying securities for the applicable period. The amounts
shown are on an annual basis.
TABLE 5 ______________________________________ Interest Payments
for IO.sub.A And IO.sub.B Interest on IO.sub.A = Interest on IO.sub.B
= Index Rate Value PRN.sub.C .times. 0.09 .times. IPCT.sub.A (r)
PRN.sub.c .times. 0.09 .times. IPCT.sub.B ______________________________________
(r) r = 0.0% 0 0.09 .times. PRN.sub.c r = 2% 0.027875 .times. PRN.sub.c
0.0622125 .times. PRN.sub.c r = 5% 0.0722625 .times. PRN.sub.c 0.0177375
.times. PRN.sub.c r = 7% 0.09 .times. PRN.sub.c 0.0 ______________________________________
At block 312 two combination securities are created. One is a "bullish"
security designed to perform well if the index rate remains low
and consists of half the cash flows of PRO.sub.A plus all of the
cash flows of IO.sub.A. The other combination security consists
of half the cash flows (i.e., $67 million of principal) of PRO.sub.B
and all of the cash flows of IO.sub.B. (The remaining halves of
PRO.sub.A and PRO.sub.B will be combined and sold in original form
as $100 million of principal-only securities as noted above.)
From block 312 the system proceeds to FIG. 4 where various prices
for the new securities are analyzed at blocks 402 thru 416 until
it is determined that the bullish combination security can be sold
for approximately $32 million and the bearish security for $101
million. Since the remaining $100 of principal-only securities can
be sold for $80 million, total proceeds would be approximately $213
million and the deal is viable with the cost of the collateral at
$210 million before expenses.
TABLES 6 and 7 below show the a) yield, b) average life of principal
and c) total cash flow for the combination securities for several
Index Rate and prepayment scenarios.
TABLE 6 ______________________________________ Bullish Combination
At $32,233,000 Prepayment Scenarios (%/Yr.) Index Rate 6% 15% 30%
42% ______________________________________ 2.375% 45% 53% 63% 69%
5.3 yrs. 2.3 yrs. 1.2 yrs. 0.8 yrs. $153.1 mm $95.5 mm $63.6 mm
$53.3 mm 3.375% 27% 28% 30% 31% 10.6 yrs. 5.4 yrs. 2.6 yrs. 1.7
yrs. $116.5 mm $76.6 mm $54.4 mm $47.3 mm 5.375% 6% 5.6% 6.0% 6.8%
18.0 yrs. 10.5 yrs. 5.2 yrs. 3.4 yrs. $61.3 mm $47.9 mm $40.6 mm
$38.2 mm ______________________________________
TABLE 7 ______________________________________ Bearish Combination
At $101,227,000 Prepayment Scenarios (%/Yr.) Index Rate 6% 15% 30%
42% ______________________________________ 2.375% 3.4% 0.6% -4.6%
-9.5% 13.4 yrs. 7.2 yrs. 3.5 yrs. 2.4 yrs. $141,1 mm $105.8 mm $86.2
mm $79.9 mm 3.375% 7.5% 4.5% -2.1% -7.9% 10.85 yrs. 5.7 yrs. 2.8
yrs. 1.9 yrs. $177.7 mm $124.7 mm $95.4 mm $86.0 mm 5.375% 14.4%
11.8% 4.0% -47% 7.2 yrs. 3.2 yrs. 1.5 yrs. 1.0 yrs. $232.9 mm $153.4
mm $109.2 mm $95.1 mm ______________________________________
It may be appreciated that since the total cash received by the
bullish combination always exceeds its cost of $32,233,000, its
yield is always postive. The cash flow of the bearish combination,
however, may be less than its $101 million cost under some scenarios
and, therefore, may have a negative return. The negative return,
however, is limited because its cash flow must be at least equal
to its $67 million principal amount. Traditional bearish instruments
such as interest-only bonds may have much greater risk because they
have no principal amount and, therefore, are guaranteed no minimum
cash flow.
Having determined that proposed securities warrant issuance, the
system proceeds to FIG. 5 for the actual issuance process.
In FIG. 5 the system proceeds to issue two bonds, LA and LB, such
that the interest paid on them equals the intended cashflows of
IO.sub.A and IO.sub.B, respectively.
At block 502 a REMIC with a Lower and Upper stage is created; the
Lower REMIC itself also has first and second stages. The underlying
securities are placed into the first stage of the Lower REMIC as
its collateral; PRN.sub.C =$200 million and CPN.sub.C =9%., Bond
LA is issued with principal PRN.sub.A =%100 million and coupon formula,
Bond LB is issued with principal PRN.sub.B =$100 million and coupon
formula,
where r is the applicable value of the Index Rate.
Using the formulas for IPCT.sub.B (r) and IPCT.sub.B (r) as shown
in TABLE 5, the formulas for CPN.sub.A (r) and CPN.sub.B (r) are
calculated as shown in TABLE 8.
The values of CPN.sub.A (r) and CPN.sub.B (r) at the points R.sub.1
=0.375%, R.sub.2 =3.375%, R.sub.3 =6.375% are denoted by V.sub.1,
V.sub.2, V.sub.3, W.sub.1, W.sub.2 and W.sub.3 and are also calculated
and shown TABLE 8.
TABLE 8 ______________________________________ Coupon Formulas
For LA and LB Index Rate CPN.sub.A (r) = 0.18 .times. CPN.sub.B
(r) = 0.18 .times. Value = IPCT.sub.A (r) IPCT.sub.B (r) ______________________________________
r < r.sub.1 = 0.375 V.sub.1 = 0.0 W.sub.1 = 0.36 0.375% <
r .ltoreq. 3.375% mA.sub.1 .times. r + bA.sub.1 nB.sub.1 .times.
r + dB.sub.1 3.42 .times. 4 - .012825 -3.42 .times. r + 0.192825
r = R.sub.2 = 3.375% V.sub.2 = 0.1026 W.sub.2 = 0.0774 3.375% <
r .ltoreq. 6.375% mA.sub.2 .times. r + bA.sub.2 nB.sub.2 .times.
r + dB.sub.2 2.58 .times. r + 0.015525 -2.58 .times. r + 0.164475
r > R.sub.3 = 6.375% V.sub.3 = 0.18 W.sub.3 = 0.0 ______________________________________
At block 508 CPN.sub.A (r) and CPN.sub.B (r) are examined. It is
determined that CPN.sub.A (r) can only increase and CPN.sub.B (r)
can only decrease as the value of the Index Rate r increases. Therefore,
LA and LB are unidirectional multisegment variable rate bonds and
the data processing system proceeds to FIG. 7.
At block 702, bonds LA.sub.1, LA.sub.2, LB.sub.1, and LB.sub.2
are issued in the first stage of the lower REMIC such that,
The principal generated by the underlying securities is paid simultaneously
to LA.sub.1, LA.sub.2, LB.sub.1, and LB.sub.2, in proportion to
their principal amounts.
At block 704 CPNA.sub.1 (r), CPNA.sub.2 (r), CPNB.sub.1 (r) and
CPNB.sub.B (r) are defined as,
where mA.sub.1, mA.sub.2, bA.sub.1, bA.sub.2, nB.sub.1, nB.sub.2,
dB.sub.1, dB.sub.2, V.sub.1, V.sub.2, W.sub.1, W.sub.2 are as calculated
above at block 506.
TABLE 9 ______________________________________ Coupon Formula For
LA.sub.1, LA.sub.2, LB.sub.1 And LB.sub.2 Index Rate Value CPNA.sub.1
(r) CPNA.sub.2 (r) CPNB.sub.1 (r) CPNB.sub.2 (r) ______________________________________
r < R.sub.1 = 0.0 0.0 0.2052 0.1548 0.375% 0.375% < r .ltoreq.
6.84 .times. r - 0.0 6.34 .times. r + 0.1548 3.375% 0.02525 0.23085
r = R.sub.2 = 0.2052 0.0 0.0 0.1548 3.375% 3.375% < r .ltoreq.
0.2052 5.16 .times. r - 0.0 -5.16 .times. r + 6.375% 0.17415 0.32895
r .gtoreq. R.sub.2 = 6.375% 0.2052 0.1548 0.0 0.0 ______________________________________
The interest paid on LA.sub.1, LA.sub.2, LB.sub.1 and LB.sub.2
is calculated for several values of the Index Rate as shown in TABLE
10.
TABLE 10 __________________________________________________________________________
Interest Paid on LA.sub.1, LA.sub.2, LB.sub.1 And LB.sub.2. Index
Rate Value INTA.sub.1 (r) INTA.sub.2 (r) INTB.sub.1 (r) INTB.sub.2
(r) __________________________________________________________________________
r = 0% 0.0 0.0 0.0573 0.03875 .times. PRN.sub.c r = 2% 0.027875
.times. PRN.sub.c 0.0 0.0235125 .times. PRN.sub.c 0.03875 .times.
PRN.sub.c r = 5% 0.0513 .times. PRN.sub.c
0.0209625 .times. PRN.sub.c 0.0 0.0177375 .times. PRN.sub.c r =
7% 0.0513 .times. PRN.sub.c 0.0387 .times. PRN.sub.c 0.0 0.0 __________________________________________________________________________
At block 706 bonds LA.sub.1, LA.sub.2, LB.sub.1 and LB.sub.2 are
placed into the second stage of the Lower REMIC to serve as its
collateral.
At block 708 bonds LA and LB are issued by the second stage of
the Lower REMIC. LA will receive all the principal and all the interest
paid on LA.sub.1 and LA.sub.2. LB will receive all of the principal
and all of the interest paid on LB.sub.1 and LB.sub.2.
Upon examination of TABLE 10, it may be seen that the total interest
paid on LA.sub.1 and LA.sub.2 equals the interest payments for IO.sub.A
derived at block 310 and shown in TABLE 5 and the total interest
paid on LB.sub.1 and LB.sub.2 equals the interest payments for IO.sub.B.
The system proceeds to FIG. 8 where LA and LB are placed into the
upper REMIC at block 802. At block 804 and 806, PRO.sub.A, PRO.sub.B,
IO.sub.A and IO.sub.B are issued as specified at block 310. At block
808, IO.sub.A is combined with half of PRO.sub.A to form the bullish
combination security and IO.sub.B is combined with half of PRO.sub.B
to form the bearish combination security. The remaining halves of
PRO.sub.A and PRO.sub.B are combined and sold as the original principal-only
bond.
It may be appreciated that ultimately the upper REMIC issues only
three regular REMIC securities. Namely a) the $100 million principal-only
bond, b) the bullish security with $33 million principal and c)
the bearish security with $67 million principal. If the PRO.sub.A,
PRO.sub.B, IO.sub.A and IO.sub.B will not be sold separately, the
combination securities may be issued directly without first issuing
and then combining the PRO.sub.A, PRO.sub.B, IO.sub.A and IO.sub.B
securities.
While the invention has been described in its preferred embodiments,
it is to be understood that the words which have been used are words
of description, rather than limitation, and that changes may be
made within the purview of the appended claims without departing
from the true scope and spirit of the invention in its broader aspects. |