SYSTEME ET PROCEDE PERMETTANT D'OPTIMISER LA QUANTITE DE TITRES ACHETES OU VENDUS SUR UNE BASE PERIODIQUE

SYSTEM AND METHOD FOR OPTIMIZING QUANTITY OF SECURITY PURCHASED OR SOLD ON A PERIODIC BASIS

Abrégé français

L'invention concerne un système et un procédé permettant de calculer un certain nombre d'unités d'un titre ou d'un autre instrument d'investissement destiné à être négocié périodiquement dans un marché fluctuant, d'une manière qui optimise la valeur en dollar par unité de la transaction correspondante. Ce système et ce procédé comprennent chacun des équations destinées à calculer le nombre d'unités à acheter (SACIN) ou à vendre (SACOUT) pendant plusieurs périodes de transaction sur la base (1) d'une quantité cible d'argent destinée à acheter le titre pendant chaque période de transaction, ou devant être reçue de la vente du titre pendant chaque période de transaction, (2) un prix unitaire de base non nul (Pb) et (3) un prix unitaire courant (P) pendant la période de transaction correspondante. Dans un mode de réalisation, chaque équation comporte en outre un commande de gains qui, lorsque toutes les autres variables sont fixées, permet à un investisseur d'ajuster le nombre d'unités négociées afin qu'elles cadrent avec ses projets d'investissement et/ou qu'elles cadrent avec les conditions du marché.

Abrégé anglais

A system and method for calculating a number of units of a security or other
investment instrument to be traded periodically in a fluctuating market in a
manner that optimizes the per-unit dollarvalue of the corresponding
transaction. The system and method each comprise equations for calculating the
number of units to be purchased (SACIN) or sold (SACOUT) during each of a
plurality of transaction periods based upon (1) a target amount of money for
purchasing, or to be received from the sale of, the security duringeach
transaction period, (2) a non-zero baseline unit price (Pb) and (3) a current
per unit price (P) during the corresponding transaction period. In one
embodiment, each equation further includesa gain control that, when all other
variables are fixed, allowsaninvestor to adjust the number of units traded to
suit his or her investment goals and/or to suit market conditions.

Revendications

What is claimed is:
1. A method of calculating a number N of units of a security to be traded at a
unit price P in
each of a series of consecutive periods based upon a desired monetary amount A
for each
of the consecutive periods, the method comprising the steps of:
a) establishing a baseline unit price P b not equal to zero;
b) selecting a mathematical equation having the number N of units as an
unknown term,
said mathematical equation comprising a function of the desired monetary
amount A,
the unit price P and said baseline unit price P b; and
c) solving said mathematical equation for N.
2. A method according to claim 1, wherein said baseline unit price P b is an
historical
average.
3. A method according to claim 1, wherein said baseline unit price P b is
equal to the unit
price P at the first of the series of consecutive periods.
4. A method according to claim 1, wherein said baseline unit price P b varies
with time.
5. A method according to claim 1, wherein N is the number of units to be
purchased and
said equation automatically increases N as the unit price P falls and
decreases N as the
unit price P rises.
6. A method according to claim 5, wherein said mathematical equation further
includes a
gain constant K that adjusts the gain of said mathematical equation to control
the
magnitude of the change in units N resulting from the difference between the
baseline
unit price P b and the unit price P.
23

7. A method according to claim 6, wherein said mathematical equation is:
<IMG>
8. A method according to claim 6, wherein each of said baseline unit price P b
and said gain
constant K varies with time.
9. A method according to claim 1, wherein N is the number of units to be sold
and said
mathematical equation automatically increases N as the unit price P rises and
decreases N
as the unit price P falls.
10. A method according to claim 9, wherein said mathematical equation further
includes a
gain constant K that adjusts the gain of said mathematical equation to control
the
magnitude of the change in units N resulting from the difference between the
baseline
unit price P b and the unit price P.
11. A method according to claim 10, wherein said mathematical equation is:
<IMG>
12. A method according to claim 10, wherein each of said baseline unit price P
b and said gain
constant K varies with time.
13. A method according to claim 1, further comprising the step of trading said
N units, as
determined in said step c, of a security.
14. A computer readable storage medium containing a computer program
implementing a
method of calculating a number N of units of a security to be traded at a unit
price P in
each of a series of consecutive periods based upon a desired monetary amount A
for each
of the consecutive periods, the security having a baseline unit price P b, the
method
comprising the steps of:
24

a) obtaining a non-zero value for the baseline unit price P b;
b) solving a mathematical equation having the number N of units as an unknown
term,
said mathematical equation comprising a function of the desired monetary
amount A,
the unit price P and the baseline unit price P b; and
c) outputting the number N of units to at least one of a user display, a
storage device and
another computer.
15. A computer readable storage medium according to claim 14, wherein step c)
is performed
by receiving the baseline unit price P b from a user.
16. A computer readable storage medium according to claim 14, wherein step c)
is performed
by receiving the baseline unit price P b from a computer database.
17. A computer readable storage medium according to claim 14, wherein said
baseline unit
price P b is an historical average.
18. A computer readable storage medium according to claim 14, wherein said
baseline unit
price P b is equal to the unit price P at the first of the series of
consecutive periods.
19. A computer readable storage medium according to claim 14, wherein said
baseline unit
price P b varies with time.
20. A computer readable storage medium according to claim 14, wherein N is the
number of
units to be purchased and said equation automatically increases N as the unit
price P falls
and decreases N as the unit price P rises.
21. A computer readable storage medium according to claim 20, wherein said
mathematical
equation further includes a gain constant K that adjusts the gain of said
mathematical
25

equation to control the magnitude of the change in units N resulting from the
difference
between the baseline unit price P b and the unit price P.
22. A computer readable storage medium according to claim 21, wherein said
mathematical
equation is:
<IMG>
23. A computer readable storage medium according to claim 21, wherein each of
said
baseline unit price P b and said gain constant K varies with time.
24. A computer readable storage medium according to claim 14, wherein N is the
number of
units to be sold and said mathematical equation automatically increases N as
the unit
price P rises and decreases N as the unit price P falls.
25. A computer readable storage medium according to claim 24, wherein said
mathematical
equation further includes a gain constant K that adjusts the gain of said
mathematical
equation to control the magnitude of the change in units N resulting from the
difference
between the baseline unit price P b and the unit price P.
26. A computer readable storage medium according to claim 25, wherein said
mathematical
equation is:
<IMG>
27. A computer readable storage medium according to claim 24, wherein each of
said
baseline unit price P b and said gain constant K varies with time.
28. A system for optimizing a number N of units of a security to be traded in
each of a series
of periods at a unit price P based upon a desired monetary amount A, the
system
comprising:
26

a) a central processing unit;
b) an application program for controlling said central processing unit, said
application
program containing a mathematical equation comprising a function of the
desired
monetary amount A, the unit price P and a baseline unit price P b not equal to
zero;
and
c) a memory connected to said central processing unit and storing said
application
program.
29. A system according to claim 28, further comprising an I/O section
connected to said
central processing unit, said I/O section connected to at least one output
device.
30. A system according to claim 29, wherein said at least one output device is
a display.
31. A system according to claim 28, wherein said system further comprises a
service
computer attachable to a network, said service computer containing said
central
processing unit, said application program and said memory.
32. A system according to claim 28, wherein said baseline unit price P b is an
historical
average.
33. A system according to claim 28, wherein the series of periods has a first
period and said
baseline unit price P b is equal to the unit price P at said first period.
34. A system according to claim 28, wherein said baseline unit price P b
varies with time.
35. A system according to claim 28, wherein N is the number of units to be
purchased and
said equation automatically increases N as the unit price P falls and
decreases N as the
unit price P rises.
27

36. A system according to claim 35, wherein said mathematical equation further
includes a
gain constant K that adjusts the gain of said mathematical equation to control
the
magnitude of the change in units N resulting from the difference between the
baseline
unit price P b and the unit price P.
37. A system according to claim 36, wherein said mathematical equation is:
<IMG>
38. A system according to claim 36, wherein each of said baseline unit price P
b and said gain
constant K varies with time.
39. A system according to claim 28, wherein N is the number of units to be
sold and said
mathematical equation automatically increases N as the unit price P rises and
decreases N
as the unit price P falls.
40. A system according to claim 39, wherein said mathematical equation further
includes a
gain constant K that adjusts the gain of said mathematical equation to control
the
magnitude of the change in units resulting from the difference between the
baseline unit
price P b and the unit price P.
41. A system according to claim 40, wherein said mathematical equation is:
<IMG>
42. A system according to claim 40, wherein each of said baseline unit price P
b and said gain
constant K varies with time.
43. A system according to claim 28, wherein said central processing unit is
operative with
said application program to determine a number N of units of securities to be
traded using
said mathematical equation.
28

44. A method of determining a number N of units of a security to be traded in
each of a series
of periods, the method comprising the steps of:
a) establishing a baseline price P b, a current unit price P and a desired
monetary amount
A for each period; and
b) determining the number N as a function of said baseline price P b, said
current unit
price P, said desired monetary amount A and a gain constant K, wherein:
i) when selling the security, said function automatically increases N when P
is
greater than P b and automatically decreases N when P is less than P b; and
ii) when purchasing the security, said function automatically decreases N when
P is
greater than P b and automatically increases N when P is less than P b.
45. A computer readable storage medium containing a computer program for
implementing a
method of determining a number N of units of a security to be traded in each
of a series of
periods, the method comprising the steps of:
a) establishing a baseline price P b, a current unit price P and a desired
monetary amount
A for each period; and
b) determining the number N as a function of said baseline price P b, said
current unit
price P, said desired monetary amount A and a gain constant K, wherein:
i) when selling the security, said function automatically increases N when P
is
greater than P b and automatically decreases N when P is less than P b; and
ii) when purchasing the security, said function automatically decreases N when
P is
greater than P b and automatically increases N when P is less than P b.
29

Description

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SYSTEM AND METHOD FOR OPTIMIZING QUANTITY OF SECURITY PURCHASED
OR SOLD ON A PERIODIC BASIS
FIELD OF INVENTION
The present invention relates generally to the field of securities and other
investment
instruments. More particularly, the present invention is directed to a system
and method for
optimizing the number of units of a security or other investment instrument
purchased or sold
on a periodic basis.
BACKGROUND OF THE INVENTION
A number of methods exist for optimizing investments in securities such as
stocks, bonds,
mutual funds, futures and options, among others. At least one known method for
optimizing
investments in a fluctuating market is dollar cost averaging (DCA). DCA is a
method for
periodically purchasing units, or units, of a security in a manner such that
the average per-
unit cost over a plurality of periodic purchases will be less than the average
price of the units
over the entire period during which an investor makes the periodic purchases.
DCA always
results in an average per-unit cost lower than the average price, regardless
of whether the
long-term trend of the market is increasing or declining, as long as the
purchase price
fluctuates among the periodic purchases. DCA is an alternative to buying a
fixed number of
units periodically or buying a number of units at only one time with a lump
sum of money
and hoping that the price of the security increases between the time the units
are purchased
and the time they are sold.
DCA involves investing a fixed amount of money at regular intervals over an
extended period
of time. TABLE 1 illustrates the impact of DCA versus purchasing a fixed
number of units
over twelve periodic purchases.

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TABLE 1
Security Fixed Number DCA
Price of Units
Performance
Units Units
Period Price Cost PurchasedCost (A) Purchased
(N)
I 10 100 10 100 10
2 11 110 10 100 9.09
3 9 90 10 100 11.1 I
4 10 100 10 100 10
1 I I 10 10 100 9.09
6 9 90 10 100 1 I.I 1
7 10 100 10 100 I.0
8 11 110 10 100 9.09
9 9 90 10 100 11.11
10 100 10 100 10
1 I 1 I 110 10 I 00 9.09
12 9 90 10 100 11.11
Total $1,200 $1,200
Cost
Total 120 120.8
Units
Av . $10 $9.93
Per-Unit
Cost
5 As seen in TABLE 1, the fixed-dollar purchasing scheme of DCA results in
fewer units being
purchased when the per-unit price is high and more units being purchased when
the per-unit
price is low. In DCA, the number of units purchased each period can be
expressed as:
N - A ~I~
p-pb
where N is the number of units purchased, A is the dollar amount of the
purchase, P is the
current unit price at which the purchase is made and Pb is a baseline unit
price equal to zero.
The equation for N is a simple hyperbolic function asymptotic to the N-axis as
P approaches
zero and asymptotic to the P-axis as P approaches infinity. DCA will always
yield an
average per-unit cost lower than the average price of the units over the
entire period because
DCA yields a weighted average, whereas purchasing a fixed number of units will
result
simply in the average per-unit cost being equal to the average price, which is
an un-weighted
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average. DCA may be considered a weighted averaging because the number of
units
purchased with the fixed dollar amount varies inversely with the current per-
unit price of the
security at the time of purchase. That is, when the per-unit price is high,
the fixed dollar
amount purchases a smaller number of units than when the per-unit price is
low. Thus,
whenever the unit price of the security varies over a number of purchase
periods, the total
number of units purchased using DCA will always be greater than the total
number of units
purchased by purchasing a fixed number of units each period.
A drawback of DCA is that, while the number of units N purchased varies
inversely with the
price P, an investor is limited to the purchasing only the number of units
given by the simple
equation, N = A/P. In addition, DCA lacks a gain control that would allow an
investor to
optimize the DCA method.
The DCA method may also be used for selling units of a security periodically
over an
I S extended period. In this scenario, rather than a fixed dollar amount being
used to purchase
units of a security, a fixed dollar amount of the security is sold each
period. However, DCA
is not a desirable method for selling securities since the per-unit yield of
the units sold would
be less than the average price of the units over the extended period.
Obviously, it is more
desirable that the per-unit yield be greater than the average price.
In view of the foregoing, it is an object of the present invention to provide
a method for
automatically determining the number of units of a security to be purchased
that yields a
lower per-unit cost than DCA. It is also an object of the present invention to
provide a
method that allows an investor to adjust the number of units purchased based
upon personal
investment goals and/or market conditions. It is another object of the present
invention to
provide a method that allows an investor to determine the number of units of a
security to be
sold in each of a number of periods such that the per-unit yield of the units
sold is higher than
the average price of the security over the number of periods. It is yet
another object of the of

CA 02385114 2002-03-18
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the present invention to provide a method that allows an investor to adjust
the number of
units sold based upon personal investment goals and/or market conditions.
SUMMARY OF THE INVENTION
In one aspect, the present invention is directed to a method of calculating a
number N of units
of a security to be traded at a unit price P in each of a series of
consecutive periods based
upon a desired monetary amount A for each of the consecutive periods. The
method
comprises establishing a baseline unit price Pb not equal to zero and
selecting a mathematical
equation having the number N of units as an unknown term and comprising a
function of the
desired monetary amount A, the unit price P and the baseline unit price Pb.
Then, the
mathematical equation is solved for N.
In another aspect, the present invention is directed to a computer readable
storage medium
containing a computer program implementing a method of calculating a number N
of units of
a security to be traded at a unit price P in each of a series of consecutive
periods based upon a
desired monetary amount A for each of the consecutive periods, wherein the
security has a
baseline unit price Pb. First, a non-zero value is obtained for the baseline
unit price Pb. A
mathematical equation is then solved. The mathematical equation has the number
N of units
as an unknown term and comprises a function of the desired monetary amount A,
the unit
price P and the baseline unit price Pb. The number N of units is then
outputted to at least one
of a user display, a storage device and another computer.
In yet another aspect, the present invention is directed to a system for
optimizing a number N
of units of a security to be traded in each of a series of periods at a unit
price P based upon a
desired monetary amount A. The system includes a central processing unit and
an
application program for controlling said central processing unit. The
application program
contains a mathematical equation comprising a function of the desired monetary
amount A,
the unit price P and a baseline unit price Pb not equal to zero. A memory is
connected to the
central processing unit and stores the application program.
4

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In still another aspect, the present invention is directed to a method of
determining a
number N of units of a security to be traded in each of a series of periods.
The method
comprises establishing a baseline price Pb, a current unit price P and a
desired monetary
amount A for each period and determining the number N as a function of the
baseline
price Pb, the current unit price P, the desired monetary amount A and a gain
constant K.
When selling the security, the function automatically increases N when P is
greater than Pb
and automatically decreases N when P is less than Pb. When purchasing the
security, the
function automatically decreases N when P is greater than Pb and automatically
increases N
when P is less than Pb.
In a further aspect, the present invention is directed to a computer readable
storage medium
containing a computer program for implementing a method of determining a
number N of
units of a security to be traded in each of a series of periods. The method
comprises
establishing a baseline price Pb, a current unit price P and a desired
monetary amount A for
each period and determining the number N as a function of the baseline price
Pb, the current
unit price P, the desired monetary amount A and a gain constant K. When
selling the
security, the function automatically increases N when P is greater than Pb and
automatically
decreases N when P is less than Pb. When purchasing the security, the function
automatically
decreases N when P is greater than Pb and automatically increases N when P is
less than Pb,
BRIEF DESCRIPTION OF THE DRAWINGS
For the purpose of illustrating the invention, the drawings show a form of the
invention that is
presently preferred. However, it should be understood that this invention is
not limited to the
precise arrangements and instrumentalities shown in the drawings.
FIG. I is a graph of Per-Unit Price of a Security versus Time for one
embodiment of the
SACIN and SACOUT aspects of the present invention.

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FIG. 2 is a graph of Per-Unit Price of a Security versus Time illustrating the
use of the
embodiment of FIG. 1 where the general trend of the price of the security is
upward.
FIG. 3 is a graph of Per-Unit Price of a Security versus Time illustrating an
alternative
embodiment of the SACIN and SACOUT optimization methods of the present
invention.
FIG. 4 is a block diagram illustrating a computer network containing a service
computer
implementing the SACIN and SACOUT optimization methods of the present
invention.
I O FIG. 5 is a flow diagram for implementing the embodiment of FIG. 1 in the
application
program of FIG. 4.
FIGS. 6A and 6B show, respectively, one embodiment each of a SACIN worksheet
and a
SACOUT worksheet that may be used with the flow diagram illustrated in FIG. 5.
DETAILED DESCRIPTION OF THE INVENTION
As an overview, the present invention is directed to a method for periodically
trading units of
a security or other investment instrument, such as stocks, bonds, mutual funds
shares,
options, futures and the like, in a fluctuating market in a manner that
optimizes the per-unit
dollar value of the corresponding transaction. In general, the method adjusts
the number of
units purchased or sold based upon the difference between a current unit price
and a baseline
unit price, such as an historical average price.
The method comprises equations for calculating the number of units to be
traded in a given
transaction period in accordance with certain rules for each of the purchasing
and selling
scenarios. In a purchasing scenario, the method reduces the number of units
purchased when
the current unit price is higher than the baseline unit price. Conversely,
when the current unit
price is lower than the baseline unit price, the method increases the number
of units
6

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purchased. Using these rules, the per-unit price over a number of transaction
periods is lower
than the average unit price over the same transaction periods.
In a selling scenario, the method increases the number of units sold when the
current unit
price is above the baseline unit price. If the current unit price is below the
baseline unit price,
the method reduces the number of units sold. Accordingly, the per-unit price
of the units sold
over a number of transaction periods is higher than the average sale price
over the same
transaction periods.
Preferably, each equation selected for determining the number of units of a
security to be
purchased, or sold, during each of a plurality of transaction periods as a
function of ( 1 ) a
target amount of money for purchasing, or to be received from the sale of, the
security during
each transaction period, (2) a baseline unit price and (3) the current unit
price during the
corresponding transaction period. In a presently preferred embodiment, each
equation further
includes a gain control that, when all other variables are fixed, allows an
investor to adjust the
variation in the number of units traded caused by changes in the current unit
price to suit his
or her investment goals and/or to suit market conditions.
To illustrate the foregoing concepts, in a purchasing scenario a presently
preferred
embodiment, denoted SACIN (security average cost in), of periodically
purchasing units of a
security is to purchase a number N of units such that:
N = Nb ~2i
P-Ki(Pb)
where P is the current per-unit price of the security, Pb is a baseline price
of the security,
Nb is the number of units that could be purchased with a target nominal dollar
amount A
when the current price P equals the baseline price Pb, and Ki is a gain
constant where
7

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0 < K~ < 1. Since target dollar amount A and gain constant K; are determined
by an investor
and Nb cannot be determined without A. Nb can be written as a function of A
and K; by
setting P = Pb and:
A = (N)pb = pb K~ (Pb ) Pb { 3 }
The result is that Nb = A(1-Ki). Substituting A(1-Ki) for Nb in equation {2}
yields:
N= A(1_Ki) {4}
P-(Kipb)
wherein the only unknown at the time of purchase is the number N of units to
be purchased.
It is worth noting that when K; = 0, Equation {4} reduces to N = P/A, which is
equivalent to
the equation of the DCA method.
As mentioned above, baseline price Pb may be an historical average, but it may
be another
value such as the unit price of the security at the first purchase. The price
of the security at
the first purchase may be more conveniently obtained than an historical
average.
TABLE 2 shows examples using the SACIN method to purchase units of a security
monthly
over a twelve-month period with three different values for K;. The results
shown in
TABLE 2 may be compared to the results of the DCA example of TABLE 1. which
uses the
same period and current price information.
TABLE 2
Security SACIN
Price for A
Performance = $100/mo.
and Pb
= $10/unit
K;=.2 K;=.5 K;=.8
Mo. P 80 Cost = 50 Cost 20 Cost
N=P_2 (P)x(N) N=P_5 = N=P_8 =
(P)x(N) (P)x(N)
1 $10 10 $100.00 I 0 $100.00 10 $100.00
2 11 8.89 97.79 8.33 91.63 6.67 73.37
8

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3 9 11.43 102.87 12.5 112.50 20.00 180.00
4 10 10 100.00 10 100.00 10 I 00.00
11 8.89 97.79 8.33 91.63 6.67 73.37
6 9 11.43 102.87 12.5 112.50 20.00 180.00
7 10 10 100.00 I 0 100.00 10 100.00
8 11 8.89 97.79 8.33 91.63 6.67 73.37
9 9 11.43 102.87 12.5 112.50 20.00 180.00
10 10 100.00 10 100.00 10 100.00
11 11 8.89 97.79 8.33 91.63 6.67 73.37
12 9 11.43 102.87 12.5 112.50 20.00 180.00
Total Cost 1,202.64 1,216.52 1,413.48
Total 121.28 123.32 146.68
Units
Avg. $9.92 $9.86 $9.64
Per-Unit
Cost
TABLE 2 shows that the average per-unit cost beneficially decreases as gain
constant Ki is
increased. In addition, it is seen that the total purchase cost also increases
as gain constant Ki
is increased, and for Ki greater than zero the total purchase cost may be
different from target
5 amount A multiplied by the number of purchase periods. Thus, for an investor
to optimize
the SACIN embodiment for his or her own investment plan, the investor must
weigh the
ability to absorb the variability of actual purchase cost against the benefit
of a low per-unit
cost.
10 In a selling scenario a presently preferred embodiment for periodically
selling units of a
security, denoted SACOUT (security average cost out), is to sell a number N of
units such
that:
K Pb-P ~5~
o b
where P is the current per-unit price of the security, Pb is a baseline price
of the security,
Nb is the number of units that could be sold to yield a nominal dollar amount
A when the
current price P is equal to the baseline price Pb, and Ko is a gain constant
greater than one.
Since target dollar amount A and gain constant Ko are determined by an
investor and Nb
9

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cannot be determined without A, unknown Nb can be written as a function of A
and Ko by
setting P=Pb and:
(N)Pb Ko ( h ) - Pb Pb
The result is that Nb = A(Ko - 1 ). Substituting A(Ko - 1 ) for Nb in equation
{ 5 } yields:
N- A(Ko -I) ~7}
(KoPb)-P
wherein the only unknown at the time of purchase is number N of units to be
purchased.
TABLE 3 shows examples using the SACOUT method to sell units of a security
monthly
over a twelve-month period with three different values for Ko.
TABLE 3
Security SACOUT
Price for A
Performance = $100/mo.
and Pb=
$10/unit
Ko=2.0 Ko=1.5 Ko=1.2
Mo. P _ 100 Yield _ 50 Yield _ 20 Yield
N 20 - = N 15 - = N 12 - =
P (P) x P (P) x P (P) x
(N) (N) (N)
1 $10 10 $100.00 10 $100.00 10 $ I 00.00
2 11 11.11 122.21 12.5 137.50 20 220.00
3 9 9.09 81.81 8.33 74.97 6.67 60.03
4 10 10 100.00 10 100.00 10 100.00
5 11 11.11 122.21 12.5 137.50 20 220.00
6 9 9.09 81.81 8.33 74.97 6.67 60.03
7 10 10 I 00.00 10 100.00 I 0 100.00
8 11 11.11 122.21 12.5 137.50 20 220.00
9 9 9.09 81.81 8.33 74.97 6.67 60.03
10 10 10 100.00 10 100.00 I 0 100.00
11 11 11.11 122.21 12.5 137.50 20 220.00
12 9 9.09 81.81 8.33 74.97 6.67 60.03
Total $1,216.08 $1,249.88 $1.520.12
Yield
Total 120.8 123.32 146.68
Units
Avg. $10.07 $10.14 $10.36
Per-Unit
Yield

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TABLE 3 shows that the average per-unit yield beneficially increases as gain
constant Ko is
decreased. In addition, it is seen that the total number of units sold and the
total yield
increase as gain constant Ko is decreased. Thus, for an investor to optimize
the SACOUT for
his or her own investment plan, the investor must weigh the fact that the
larger the gain
constant Ko is, the more the rate of depletion of the units owned may vary
against the benefit
of a high per-unit yield.
Referring now to the drawings, there is shown in FIG. 1 a graph 100
illustrating the SACIN
and SACOUT embodiments, which are based upon, respectively, Equations {4} and
{7}.
Graph 100 visually illustrates a number of important relationships among gain
constants Ki
and Ko, the actual transaction price P and number N of units traded during a
particular
transaction period. In the buying scenario, the product Ki(Pb) should always
be lower than
the lowest actual price over a period of time. For example, Ki(Pb) should be
less than the
lowest price at Pmin. In addition, the closer actual transaction price P is to
Ki(Pb) or Ko(Pb),
the larger the number of units traded will be. This is so because the closer
actual transaction
price P is to Ki(Pb), the closer the denominator of Equation {4} is to zero.
To avoid the
problem of buying too many units, which will result in an inordinately high
total purchase
cost, Ki should be a value less than the minimum price Pmin divided by
baseline price Pb.
Similarly, in a selling scenario, to avoid an inordinate number of units being
sold, Ko should
be a value greater than maximum price Pmax divided by baseline price Pb.
FIG. 2 shows a graph 200 of the SACIN and SACOUT embodiments for a security
have an
upward long-term trend. In this situation, it may be desirable to periodically
adjust Ki, Ko
and/or Pb to avoid purchasing or selling an inordinate number of units of the
security. For
example during Period 1, it may be desirable to use Kjl and h'01 withPgl , and
during
Period 2, it may be desirable to use h';2 and li~~ with Pv~ . The lengths of
Periods 1
and 2 and the magnitudes of Kr 1, K~ 2 , h'o 1 and Ko 2 will depend on
variables such as the
slope of the long-term trend and the magnitudes of short-teen fluctuations.
Accordingly, and

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unlike DCA, the SACIN and SACOUT embodiments may be modified to optimize their
performance to suit a particular investment goal and/or to suit particular
market conditions.
In another embodiment, gain constants Ki and Ko and baseline price Pb need not
be a fixed
values but may vary with time. For example, as shown in graph 250 of FIG. 3,
gain constants
Klt and Kot and baseline price Pbt may take the slope of the long term trend
of the unit
price of the security.
Although the invention has been described in connection with particular
equations for the
SACIN and SACOUT methods, it is to be appreciated that the invention is not
limited to only
these equations. Rather, the invention encompasses other equations that define
a number of
units of a security that should be purchased or sold during a series of
periodic transaction
periods so as to optimize the per-unit purchase or sales price, as the case
may be. A guideline
in selecting other formulas is that such formulas identify the number of units
of a security that
should be purchased or sold with respect to a non-zero baseline price and/or
using a gain
control by, respectively, automatically (a) increasing the number of units
purchased when the
current per-unit price is lower than the baseline price and decreasing the
number of units
purchased when the current per-unit price is higher than the baseline price,
for SACIN, and
(b) decreasing the number of units sold when the current per-unit price is
lower than the
baseline price and increasing the number of units sold when the current per-
unit price is
higher than the baseline price, for SACOUT.
For example, in Equation {4} of the SACIN method as described above, Ki must
be less than
one so that K;Pb is less than Pb (see FIG. 1). However, an equation different
from
Equation 4 may be selected such that Ki is greater than one and Ki Pb is
greater than Pb. An
example of such an equation is:
N= A(K'pb p) {g}
Pb2(Ki -I)
12

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Similarly, for SACOUT an equation other than Equation {7} may be selected such
that a Ko
less than one and a KoPb less than Pb may be used. For example, such an
equation may be:
N= A(P-Kol'b) {9}
Pb2(1-Ko)
In addition, equations other than Equations {4} and {7}-{9} may be used to
determine the
number of units to be transacted. Such equations include power functions,
conical functions
and trigonometric functions, among others. For example, a suitable power
function for
SACIN may be:
N-P ~ PbJn {10}
b
where n is greater than zero and Ki is zero, since there is no Ki term in the
equation. It is
noted that when n = 0, Equation { 10} reduces to N = A/Pb, which results in
buying the same
number of units each period and when n = 1, Equation { 10} reduces to N = A/P,
which is
equivalent to DCA. One skilled in the art will recognize that Equations {4}
and {7}-{ 10}are
illustrative and are not intended to limit the scope of the invention defined
by the claims
appended hereto.
FIG. 4 shows a computer system 300 that includes a network 301 and a service
computer 302
connected to the network for performing the SACIN and/SACOUT optimization
methods of
the present invention over the network, which allows one or more users to use
these methods.
Network 301 may be the Internet, an Intranet, a local or wide area network
(LAN or WAN)
or a dial-in network. Network 301 may be wireless, linked by cable or optical
fiber, or a
combination thereof. Service computer 302 has a central processing unit (CPU)
304,
typically one or more microprocessors, embedded controllers, ASICs or other
logic devices,
memory 306, typically fast access, low capacity memory such as RAM, and slower
access,
high capacity memory, such as optical and magnetic disk drives and an
input/output (I/O)
section 308, typically including various communication adapters for
communicating with
13

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user computers 310 over network 301 and various device drivers for
communicating with
I/O devices such as a display, a keyboard, a printer and a mouse, among
others. Service
computer 302 will typically be a conventional server computer of the type used
in client-
server networks. Although described as a single computer, service computer 302
may
comprise several linked computers, in a single or multiple locations.
Service computer 302 also includes an application program 312 stored in memory
306. As
described in detail below and as shown in FIG. 5, application program 312
contains
computing steps for implementing the above-described SACIN and SACOUT
optimization
methods of the present invention. These steps are executed as logical
operations by CPU 304
in combination with memory 306 and I/O section 308.
User computer 310 may be one of a wide variety of computing systems such as
personal
computers, set-top boxes, mobile telephones, personal digital assistants, so-
called ''network
appliances," interactive TV and other electronic devices and venues. Each user
computer 310
includes a display (not shown) or other output device for displaying text
and/or graphics.
While only four user computers 310 are illustrated in FIG. 4, it is to be
appreciated that
network 301 may contain millions, and some day even billions, of user
computers, which
could be located in offices, homes, cars, kiosks or be completely mobile.
Each user computer 310 includes a communications program (not shown) for
communicating
with service computer 302 over network 301. The communication program allows
the
service computer to prompt a user for particular input, receive such input,
and display to the
user via user computer 310 information, e.g., the tabular information
presented in FIGS. 6A
and 6B and described below in more detail. For example, if network 301 is the
Internet, the
communications program may be a conventional browser, such as that available
from
Microsoft Corporation, Redmond, Washington, under the trademark EXPLORER, and
from
Netscape Communications Corporation, Mountain View, California, under the
trademark
14

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NAVIGATOR. Such communications programs are known in the art and, therefore,
are not
described in detail herein.
In addition to being implemented over a network, the SACIN and SACOUT
optimization
methods of the present invention may be implemented on a stand-alone computing
device
(not shown) such as a non-networked personal computers, hand-held calculator,
personal
digital assistant and the like. In this case, the stand-alone computing device
would generally
have the same features as service computer 302. That is, the stand-alone
computing device
would include a CPU 304, memory 306, application program 312 and I/O section
308. The
stand-alone computing device would also include a display (not shown) for
presenting text
and/or graphics to a user and an input device that allows the user to input
the data requested
by application program 312.
FIGS. SA-SB illustrate a flow diagram, denoted generally by the numeral 400,
for one
embodiment of application program 312. In particular, flow diagram 400
incorporates
Equations {4} and {7} for the SACIN and SACOUT optimization methods,
respectively.
However, as mentioned above, the SACIN and SACOUT methods are not limited to
these
particular equations. In addition, the SACIN and SACOUT optimization methods
may be
implemented independent of one another in separate programs.
At step 402, application program 312 starts and prompts a user to select
either the SACIN or
SACOUT method, depending on whether the user is interested in purchasing or
selling units
of a security. If the user selects the SACIN method, at step 404 application
program 312
prompts the user to select one of three functions, New Security, Recommend
Periodic
Purchase or Update Last Period with Actual Purchase Data. Although three
functions are
described, more or fewer functions may be provided. For example, a fourth
function, Change
Previous Period, may be provided for correcting errors or working through a
number of
purchasing scenarios. The Change Previous Period function could also include
an option for
allowing the user to save or discard any changes made during the session.
IS

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Ifthe user selects the New Security function, at step 406 application program
312 displays to
the user a brief explanation of the SACIN method. For example, application
program 312
may display the following message: ''When used for periodic purchases, SACIN
automatically produces a per-unit cost lower that the average unit cost per
period and dollar
cost averaging (DCA) by investing more dollars when the price is low and fewer
dollars
when the price is high."
Next, at step 408 application program 312 prompts the user to change the
default name of the
worksheet from "New Investment" to any name the user desires. Preferably, the
user should
select the name of the security, such as ''XYZ Company Common Stock," ''ABC
Growth
Fund" or the like. If the user does not change the default name, application
program 312 will
use the default name. At step 410, application program 312 prompts the user to
input the
desired values for A, Pb and Ki of Equation {4}. If the user requests
application program 312
for help, at step 412 application program 312 may display to the user
explanations of
A, Pb and Ki. For example, for A, application program 312 may display the
following: "A is
the nominal dollar amount you wish to invest each period. You should monitor
SACIN's
total amount invested and adjust A, Pb and/or Ki to stay on track toward your
long-term
goals." For Pb, application program 312 may display the following: "Pb is not
very critical,
it is simplest to use the current unit price. You can also use a recent
historical price to
estimate an average price during the SACIN period." For Ki, application
program 312 may
display the following: "Ki is a gain control. The larger Ki is, the more the
periodic
investment will change with price and the lower your per-unit cost will be. Ki
= 0 provides a
constant dollar investment as in dollar cost averaging (DCA). Above Ki = 0.5,
a falling
current price will result in larger investments." Application program 312 may
be configured
to display the explanations all at once or one at a time, depending on the
user's request.
After the user inputs values for A, Pb and Ki, at step 414 application program
312 displays to
the user a worksheet 500, see FIG. 6A. having a first period numbered and
dated with the
16

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current date. Alternatively, application program 312 may prompt the user to
input a date to
be associated with the first period. Next, at step 416 application program 312
obtains the
current price P of a unit of the security. Application program 312 may obtain
the price by
querying the user or linking to a database, e.g., a database maintained by a
brokerage house
or an online provider of such information. After application program 312
obtains the current
price P, at step 418 application program 312 displays a caution based upon
current price P
relative to baseline price Pb. For example, if current price P is less than
baseline price Pb,
application program 312 may display the following: "If P lowers and approaches
(Ki) x (Pa),
large purchases will result." However, if current price P is greater than
baseline price Pb,
application program 312 may display the following: "Large increases in P
reduce the gain."
At step 420, application program 312 queries the user as to whether or not he
or she is
satisfied with the selected values of A, Pb and Ki. If the user is not
satisfied, at step 422
application program 312 prompts the user to change any or all of the
previously selected
values of A, Pb and Ki. The user may seek help from application program 312,
at which
point application program 312 displays the explanations of the variable at
step 412, which is
described above. If the user is satisfied with the selected values of A, Pb
and Ki, at
step 424 application program 312 calculates the remaining information
presented on
worksheet 500, i.e., units purchased, amount invested, total units purchased,
total amount
invested, average unit price per period and average purchase price per-unit,
to be displayed in
worksheet 500. At step 426, worksheet 500 is updated and the information for
the entire
period is displayed. At step 428, application program 312 queries the user as
to whether or
not his or her investing objectives are being met. If the user answers in the
negative,
application program 312 returns to step 422 and prompts the user to change one
or more of
A, Pb and Ki, after which application program 312 executes the subsequent
steps until
step 428 is again reached. If the user answers in the affirmative, at step 430
worksheet 500 is
saved and application program 312 is ended. Alternatively, application program
312 may
return to step 402 to allow the user to change from SACIN to SACOUT, add a new
period,
enter a new security or the like.
17

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If the user selects Recommend Periodic Purchase at step 404, application
program 312
proceeds to step 432 where the program displays worksheet 500 with a new
period
consecutively numbered and dated with the current date. The new period is
preferably
displayed with the column headings 502 as many previous periods as will fit on
the output
device, typically a screen of a computer monitor. Application program 312 also
copies from
the immediately preceding period the values for A, Pb and Ki and displays them
in
worksheet 500. After step 432, application program 312 proceeds to steps 416-
430 as
described above with respect to the New Security Function.
If the user selects Update Last Period with Actual Purchase Data at step 404,
application
program 312 proceeds to step 434 where the program obtains the current price P
in a manner
similar to step 416. At step 436, application program 312 then prompts the
user to input the
actual number of units purchased and/or the actual amount invested. If the
user provides only
one of the requested values, at step 438 application program 312 calculates
the other and then
proceeds to step 440. If the user provides both of the requested values,
application
program 312 proceeds immediately from step 436 to 440.
At step 440, application program 312 calculates the total units purchased,
total amount
invested, average unit price per period and average purchase price per-unit.
Then, at
step 442 application program 312 updates the current period and displays the
current period
in worksheet 500. After program displays updated worksheet 500, application
program 312
proceeds to step 430 in which worksheet 500 is saved and the program is ended.
Alternatively, application program 312 may return to step 402 to allow the
user to change
from SACIN to SACOUT, add a new period, enter a new security or the like.
In an alternative embodiment of the SACIN method of application program 312,
if the user
answers the query of step 428 in the affirmative, application program 312 may
provide an
option that would link the SACIN aspect of application program 312 to a
trading program
18

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that would allow the user to purchase the recommended number of units. The
trading
program could then transmit the actual purchase data, i.e., the current price
P, number of units
purchased and/or the amount invested, to the Update Last Period with Actual
Purchase Data
function at steps 434 and 436 to automatically update the latest investment
period.
If the user selects SACOUT at step 402, application program 312 proceeds to
step 450 and
prompts the user to select one of three functions, New Security, Recommend
Periodic Sale or
Update Last Period with Actual Sale Data. Although three functions are
described, more or
fewer function may be provided. For example, a fourth function, Change
Previous Period,
may be provided for correcting errors or working through a number of selling
scenarios. The
Change Previous Period function could also include an option for allowing the
user to save or
discard any changes made during the session.
If the user selects the New Security function, at step 452 application program
312 displays to
the user a brief explanation of the SACOUT method. For example, application
program 312
may display the following message: "When used for periodic sales, SACOUT
automatically
produces a per-unit cost of units sold higher than the average unit cost per
period by selling
more units when the price is high and fewer when the price is low."
Next, at step 454 application program 312 prompts the user to change the
default name of the
worksheet from "New Sale" to any name the user desires. Preferably, the user
should select
the name of the security, such as "XYZ Company Common Stock," "ABC Growth
Fund" or
the like. If the user does not change the default name, application program
312 will use the
default name. At step 456, application program 312 prompts the user to input
the desired
values for A, Pb and Ko of Equation {7}. If the user requests application
program 312 for
help, at step 458 the program may display to the user explanations of A, Pb
and Ko. For
example, for A, application program 312 may display the following: "A is the
nominal dollar
amount you wish to sell each period. You should monitor SACOUT's total amount
sold and
total units sold and adjust A, Pb and/or Ko to stay on track toward your long-
term goals." For
19

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Pb, application pro~~ram 312 may display the following: ''Pb is not very
critical, its simplest
to use the current unit price. You can also use a recent historical price to
estimate an average
price during the SACOUT period." For Ko, application program 312 may display
the
following: "Ko is a gain control. The smaller Ko is, the more the periodic
sale will change
with price and the higher your per-unit sale price will be. A large number for
Ko approaches
selling a fixed number of units per period, which results in your average per-
unit sale price
equaling the average per-unit sale price per period. This is better than
selling a fixed dollar
amount per period, which is dollar cost averaging (DCA) for the buyer. When Ko
is close
to l, a rising price will result in larger sales." Application program 312 may
be configured to
display the explanations all at once or one at a time, depending on the user's
request.
After the user inputs values for A, Pb and Ki, at step 460 application program
312 displays to
the user a worksheet 510, see FIG. 6B, having a first period numbered and
dated with the
current date. Alternatively, application program 312 may prompt the user to
input a date to
be associated with the first period. Next, at step 462 application program 312
obtains the
current price P of a unit of the security. Application program 312 may obtain
the price by
querying the user or linking to a database, e.g., a database maintained by a
brokerage house
or an online provider of such information. After application program 312
obtains the current
price P, at step 464 the program displays a caution based upon current price P
relative to
baseline price Pb. For example, if current price P is greater than baseline
price Pb,
application program 312 may display the following: "If P increases and
approaches
(Ko) x (Pa), large sales will result." However, if current price P is less
than baseline price Pb,
application program 312 may display the following: "Large decreases in P
reduce the gain."
At step 466, application program 312 queries the user as to whether or not he
or she is
satisfied with the selected values of A, Pb and Ko. If the user is not
satisfied, at step 468
application program 312 prompts the user to change any or all of the
previously selected
values of A, Pb and Ko. The user may seek help from application program 312,
at which
point the program displays the explanations of the variable at step 458, which
is described

CA 02385114 2002-03-18
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above. If the user is satisfied with the selected values of A, Pb and Ko, at
step 470 application program 312 calculates the remaining information
presented on
worksheet 510, i.e., units sold, dollar amount sold, total units sold, total
dollar amount sold,
average unit sale price per period and average sale price per-unit, to be
displayed in
worksheet 500. At step 472, worksheet 5 I 0 is updated and the information for
the entire
period is displayed. At step 474 application program 312 queries the user as
to whether or
not his or her investing objectives are being met. If the user answers in the
negative,
application program 312 returns to step 468 and prompts the user to change one
or more of
A, Pb and Ko, after which application program 312 executed the subsequent
steps until
step 474 is again reached. If the user answers in the affirmative, at step 476
worksheet 510 is
saved and application program 312 is ended. Alternatively, application program
312 may
return to step 402 to allow the user to change from SACOUT to SACIN, add a new
period,
enter a new security or the like.
If the user selects Recommend Periodic Sale at step 450, application program
312 proceeds to
step 478 where the program displays worksheet 510 with a new period
consecutively
numbered and dated with the current date. The new period is preferably
displayed with the
column headings 512 as many previous periods as will fit on the output device,
typically a
screen of a computer monitor. Application program 312 also copies from the
immediately
preceding period the values for A, Pb and Ko and displays them in worksheet
510. After
step 478, application program 312 proceeds to steps 462-476 as described above
with respect
to the New Security Function.
If the user selects Update Last Period with Actual Sale Data at step 450,
application
program 312 proceeds to step 480 where the program obtains the current price P
in a manner
similar to step 462. At step 482, application program 312 then prompts the
user to input the
actual number of units sold and/or the actual dollar amount sold. If the user
provides only
one of the requested values, at step 484 application program 3 I 2 calculates
the other and then
21

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proceeds to step 486. If the user provides both of the requested values,
application program
312 proceeds immediately from step 482 to 486.
At step 486, application program 312 calculates the total units sold, total
dollar amount sold,
average unit sale price per period and average sale price per-unit. Then, at
step 488
application program 312 updates the current period and displays the current
period in
worksheet 510. After program displays updated worksheet 510, application
program 312
proceeds to step 476 in which worksheet 510 is saved and the program is ended.
Alternatively, application program 312 may return to step 402 to allow the
user to change
from SACOUT to SACIN, add a new period, enter a new security or the like.
In an alternative embodiment of the SACOUT method of application program 312,
if the user
answers the query of step 474 in the affirmative, application program 312 may
provide an
option that would link the SACOUT aspect of application program 312 to a
trading program
that would allow the user to sell the recommended number of units. The trading
program
could then transmit the actual sale data, i.e., the current price P, number of
units sold and/or
the dollar amount sold, to the Update Last Period with Actual Sales Data
function at
steps 480 and 482 to automatically update the latest investment period.
While the present invention has been described in connection with preferred
embodiments of
its various aspects, it will be understood that it is not so limited. On the
contrary, it is
intended to cover all alternatives, modifications and equivalents as may be
included within
the spirit and scope of the invention as defined in the appended claims.
22

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