U.S. patent application number 16/283115 was filed with the patent office on 2019-09-26 for system and method for estimating and optimizing transaction costs.
This patent application is currently assigned to ITG Software Solutions, Inc.. The applicant listed for this patent is ITG Software Solutions, Inc.. Invention is credited to Artem Asriev, Ananth Madhavan.
Application Number | 20190295167 16/283115 |
Document ID | / |
Family ID | 29732138 |
Filed Date | 2019-09-26 |
United States Patent
Application |
20190295167 |
Kind Code |
A1 |
Madhavan; Ananth ; et
al. |
September 26, 2019 |
SYSTEM AND METHOD FOR ESTIMATING AND OPTIMIZING TRANSACTION
COSTS
Abstract
A method and system for forecasting the transaction cost of a
portfolio trade execution that may be applied to any given trade
strategy or an optimal trade strategy that minimizes transaction
costs. In preferred embodiments, a server comprises one or more
computers that act as an automated forecaster whereby it accepts
user-defined input variables from customers and generates a
transaction cost estimation report based on those variables. The
server is programmed with specific transaction cost estimation and
optimization algorithms that model the transaction costs of a
specific trade execution based on the user's trading profile and
market variables.
Inventors: |
Madhavan; Ananth; (New York,
NY) ; Asriev; Artem; (Winchester, MA) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
ITG Software Solutions, Inc. |
Culver City |
CA |
US |
|
|
Assignee: |
ITG Software Solutions,
Inc.
Culver City
CA
|
Family ID: |
29732138 |
Appl. No.: |
16/283115 |
Filed: |
February 22, 2019 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
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13840862 |
Mar 15, 2013 |
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16283115 |
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13459859 |
Apr 30, 2012 |
8412621 |
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13840862 |
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13170626 |
Jun 28, 2011 |
8190510 |
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13459859 |
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10166719 |
Jun 12, 2002 |
7974906 |
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13170626 |
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Current U.S.
Class: |
1/1 |
Current CPC
Class: |
G06Q 10/04 20130101;
G06Q 40/00 20130101; G06Q 40/04 20130101 |
International
Class: |
G06Q 40/04 20060101
G06Q040/04; G06Q 10/04 20060101 G06Q010/04; G06Q 40/00 20060101
G06Q040/00 |
Claims
1-14. (canceled)
15. A method for estimating transaction costs of a security trade
execution according to a trading strategy selected by a user, the
method performed by a transaction cost optimization server coupled
to one or more electronic markets and one or more client devices
via an electronic communication network, said method comprising the
steps of: receiving, at said transaction cost optimization server
from a client device over said electronic communication network,
data defining parameters of a proposed trade execution from a user,
and data specifying a user-selected trading strategy that is
selected from among a plurality of predefined trading styles
displayed in a user interface on the client device, or is
specifically defined by said user using the user interface;
estimating, by said transaction cost optimization server, the
transaction costs of the received proposed trade execution based on
the user-selected trading strategy and market data; optimizing, by
said transaction cost optimization server using real-time market
conditions, said estimated transaction costs under said
user-selected trading strategy; and providing, by said transaction
cost optimization server over said electronic communication network
to a device associated with said user, at least one recommended
action based on said optimizing step, wherein said at least one
recommended action is displayed in the user interface in real-time
based on the market conditions, wherein said user minimizes
transaction costs by said at least one recommended action in
executing said trade.
16. The method of claim 15, wherein the method further comprises
providing, by the transaction cost optimization server, an
estimation report to the customer over the network.
17. The method of claim 15, wherein an adjustment factor adjusts
for trade difficulty and the real-time market conditions to allow
for an accurate comparison of trades performed under different
circumstances and trading conditions.
18. The method of claim 17, wherein said adjustment factor provides
an expected trading cost for each security for each day based on a
statistical analysis of measures of trade difficulty.
19. The method of claim 15, wherein a plurality of servers are
connected to a plurality of customers over said electronic
communication network, and customers enter their risk aversion
profile and hypothetical trade order characteristics through the
communication network to the server associated with transaction
cost optimization.
20. The method of claim 15, wherein the user interface allows a
user to identify relevant data and trends in a dataset, and to
locate factors that affect transaction performance.
21. The method of claim 20, wherein a user is able to change a
subset of the dataset under consideration and perform real-time
analytic calculations without additional pre-processing.
22. The method of claim 20, wherein a user may add new user
aggregates, without additional pre-processing.
23. The method of claim 15, wherein the server is adapted to
provide a direct interface to a securities price database to enable
the display of transaction cost analysis results in real-time.
24. The method of claim 15, wherein the server is programmed with a
specific strategy transaction cost algorithm that allows for
intra-day calculation of price-based benchmarks for optimizing said
estimated transaction costs.
25. The method of claim 19, wherein each server accepts proposed
orders and other customer input data directly over the
communication network from customers wishing to estimate the
transaction costs of one or more securities to be traded according
to the particular trading strategy set by the customer, and all
servers have access to multiple trading destinations, access to
real-time and historical market data, and real-time analytic data,
and each server has access to other servers on the communication
network such that market and historical data, or compilations of
data, can be exchanged between the servers, and the servers can
interoperate more efficiently.
26. The method according to claim 15, wherein said transaction cost
estimation takes into account temporary price impact, permanent
price impact, and price improvement factors.
27. The method according to claim 15, wherein said transaction cost
estimation recommends specific share quantity trade executions for
each of a number of time duration bins according to the trading
strategy selected by the user, to optimize transaction costs under
said selected trading strategy.
28. A system for estimating and optimizing transaction costs of
proposed execution trades of securities according to a risk value
selected by a user, the system comprising: a plurality of
transaction cost optimization servers connected to a plurality of
client devices over an electronic communication network with one or
more electronic markets, each transaction cost optimization server
configured to: receive, from a client device over said electronic
communication network, said user-selected risk value and data
specifying parameters of a proposed trade order that are selected
from a user interface on the client device, estimate the
transaction costs of the received proposed trade execution based on
the user-selected risk value and market data, optimize, using
real-time market conditions, said estimated transaction costs under
said user-selected risk value and market data; and provide, to a
client device associated with said user over said electronic
communication network, at least one recommended action based on
said optimization, wherein said at least one recommended action is
displayed in the trading interface in real-time based on the market
conditions, and wherein a user minimizes transaction costs by
performing said at least one recommended action in executing said
trade.
Description
FIELD OF THE INVENTION
[0001] This invention relates generally to securities markets, and
more particularly relates to a system and method for estimating the
transaction costs of a trade execution and developing an optimized
trading strategy for securities in advance of trading.
BACKGROUND OF THE INVENTION
[0002] Securities portfolio transactions typically incur
transaction costs arising not only from commissions and bid-offer
spreads, but also from price movements (market impact) associated
with execution. Execution costs can be large, especially when
compared against gross returns, and might substantially reduce or
even eliminate the notional returns to a particular investment
strategy..sup.1 A large body of research (Keim and Madhavan (1998)
provide a survey) shows that market or price impact is a major
component of total trading cost. Consequently, minimization of
transaction costs has been a long-standing aim, especially for
traders handling portfolio transactions; e.g., transactions that
rebalance securities positions in a portfolio over a specified
period of time. A related goal is to develop optimal trading
strategies to minimize trading costs or some other objective
criterion. .sup.1For an equally weighted global portfolio of
stocks, turned over twice a year, such costs alone account for 23
percent of returns over recent history. See Domowitz, Glen, and
Madhavan, "Liquidity, Volatility, and Equity Trading Costs Across
Countries and Over Time," working paper, Pennsylvania State
University, January, (2001) for discussion, analysis, and precise
definitions of cost.
[0003] To this end, statistical and mathematical models have been
developed in an attempt to forecast the transaction costs of a
proposed portfolio trade execution. These models typically build on
some known empirical facts about trading costs. For example,
empirical studies have established that costs increase in trade
difficulty, a factor systematically related to order size (relative
to average trading volumes), venue (e.g., Exchange Listed Trades
vs. Over The Counter ("OTC")), trade direction (Buys vs. Sells),
firm size (Market Capitalization), Risk (e.g., the volatility of
security returns), and price level. In addition, costs are also
systematically related to trading style, as reported by Keim and
Madhavan (1998). Traders who trade passively (using limit orders
and spreading their trades over a long period of time) incur lower
costs, on average, than traders who trade more aggressively using
market orders to demand immediacy. Two otherwise identical orders
might have very different trading costs depending on how a trader
presents them to the market. See Madhavan (2000) for details.
[0004] Of the many statistical and mathematical forecasting models
developed, most suffer from the inability to perform comprehensive
analyses of transaction costs because the level of trade difficulty
and the impact of trading style (e.g., horizon over which trading
takes place) is not analyzed or not accurately analyzed. Therefore,
there is a need in the field to include in a forecasting model an
adjustment factor that accurately accounts for trade difficulty and
market conditions, allowing for a valid comparison of trades
executed in different circumstances and trading conditions. It is
important that this system accommodate parameters for trading
style. Since the trader's style is closely related to their
ultimate objectives (e.g., a value trader might trade passively
over several days to minimize price impact costs, tolerating the
risk of adverse price movements in the interim), this creates a
need for a model that ties strategy to a trader's subjective
assessment of risk. In particular, there is a need in the field to
provide a model that would recommend an optimal trading strategy to
a trader based on the trader's risk tolerance and other
considerations such as the horizon over which the trade is to be
completed. In order to meet these needs and to overcome
deficiencies in the field, the present invention enables portfolio
traders to forecast the transaction costs of a proposed trade
execution based on a user-selected trading style and inputs
pertaining to order characteristics and trade difficulty. The
invention also provides an optimized trading strategy to satisfy
user-defined constraints.
SUMMARY OF THE INVENTION
[0005] The present invention provides a system for forecasting the
price impact costs of a trade execution that may be applied to any
given trade strategy.
[0006] The present invention provides an Agency Cost Estimator
("ACE") method and system comprising two parts: a first part that
comprises computer-based models that allow a user to obtain price
impact cost estimates for any pre-specified strategy, and a second
part that comprises computer-executed mathematical models that
generate an optimal trading strategy subject to certain assumptions
about the user's ultimate objectives.
[0007] In another aspect of the present invention, a server
comprises one or more computers that act as an automated forecaster
whereby a computer accepts a user-specified trade strategy and
input variables from a customer and generates a transaction cost
analysis or estimation based on those variables and market data.
The server is programmed with specific transaction cost analysis
and optimization algorithms that model the transaction costs of a
proposed trade execution based on the user's risk aversion profile,
characteristics of the proposed trade execution, and market
variables. The servers may be connected to a plurality of customers
over a communication network, such as the Internet, and customers
enter their strategy profile and hypothetical trade order
characteristics through the communication network to the server
associated with transaction cost optimization. In yet another
aspect of the present invention, the transaction cost analysis web
site allows a user to perform inquires and calculations in
real-time. According to another aspect of the present invention,
the transaction cost analysis process is adapted to provide a
direct interface to a securities price database to enable the
display of transaction cost analysis results in "real-time."
[0008] In another aspect of the present invention, the transaction
cost analysis allows for intra-day calculation of price-based
benchmarks.
[0009] According to another aspect, the invention provides a method
for estimating and/or optimizing transaction costs for a proposed
trade order for a security. The method comprises the steps of
providing a server connected to a communication network, the server
being programmed with a specific transaction cost optimization
and/or estimation algorithm; receiving at the server over the
network a proposed trade order from a customer; calculating the
estimated transaction costs for the proposed order according to the
specific trading strategy of the customer and the transaction cost
estimation algorithm; and providing an estimation report to the
customer over the network.
[0010] In preferred embodiments of the present invention, multiple
servers may be deployed where each server accepts proposed orders
and other customer input data directly over the communication
network from customers wishing to estimate the transaction costs of
one or more securities to be traded according to the particular
trading strategy set by the customer. All servers have access to
multiple trading destinations, access to real-time and historical
market data, and real-time analytic data. Furthermore, each server
has access to other servers on the communication network such that
market and historical data, or compilations of data, can be
exchanged between the servers, and the servers can interoperate
more efficiently. The user can edit or modify the proposed trading
strategy received from the cost estimator, then send the resulting
trade list to a trading venue or to an automated trading system
such as ITG Inc's VWAP Smart Server.
[0011] The present invention will become more fully understood from
the forthcoming detailed description of preferred embodiments read
in conjunction with the accompanying drawings. Both the detailed
description and the drawings are given by way of illustration only,
and are not limitative of the present invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] FIG. 1 is a block diagram of a system for forecasting
transaction costs for a proposed trade execution according to a
specific trading strategy and according to a preferred embodiment
of the invention; and
[0013] FIG. 2 is a flow diagram of an exemplary system for
estimating and optimizing the transaction costs of a trade
execution carried out under a specific trading strategy according
to the invention.
DETAILED DESCRIPTION OF THE INVENTION
[0014] The present invention embodies a transaction cost estimation
method and system comprising a first part having computer-based
price impact and volatility models that allow a user to obtain
transaction cost estimates for any given strategy, and a second
part comprising computer-executed mathematical models that generate
an optimal strategy based on certain assumptions and the results of
the first part.
[0015] Referring to FIG. 1, one or more transaction cost
optimization servers 11 is provided on a communication network 10.
The network 10 may be a public network or a private dedicated
network. A server 11 is programmed with transaction cost estimation
and optimization algorithms, and has access to various trading
mechanisms or exchanges through the network 10, such as the New
York Stock Exchange (NYSE) 18, the POSIT.RTM. intra-day equity
matching system 20, the over-the-counter (OTC) market 22
(including, but not limited to, the NASDAQ stock market), or an
electronic communications network (ECN) 24.
[0016] According to preferred embodiments of the present invention,
the server 11 is electronically accessible directly by customers
through the network 10. This access can be either through a
personal computer (PC) 12 or a dedicated client terminal 16 which
is electronically connected to the network 10 such as via the
Internet or a dedicated line. Alternatively, clients could interact
with the network via a trading desk 14 through which a customer can
perform a transaction cost analysis. Particularly, the trading desk
is a user interface that provides comprehensive agency trading
services utilizing multiple liquidity sources.
[0017] According to preferred embodiments of the present invention,
a number of different servers 11 may be provided on the network,
with each server 11 running a transaction cost analysis program and
having access to various appropriate trading forums and various
electronic communication networks. A customer may submit a proposed
portfolio trade execution for analysis with any specific one of the
servers 11. A server 11 receives the proposed portfolio trade
execution from the customer over the network 10 and processes and
analyzes the execution according to the user-selected preset
trading strategy algorithm being run by the server 11. The server
11 then executes the transaction cost analysis and optimization and
preferably transmits the execution results to the customer in real
time.
[0018] By providing such servers, a significant advantage over the
prior art system (where analyses are executed manually by human
traders or by computer using outdated information) is achieved. The
server 11 can handle much more complex trades including trades
involving large volumes and many more different equities.
Additionally, the server 11 can provide expert results for a very
large number of equities, unlike a trader who may be able to
concentrate on or follow only a relatively small number of equities
at once. A server according to the present invention has a further
advantage over a human trader in that it can be electronically
connected via the network 10 to a real time market information
provider 15 as well as sources providing historical and derived
market data such that it can receive and process multiple
indicators on a continuous basis. Further, multiple requests for
transaction cost analysis having different desired trading
strategies (e.g., levels of risk aversion) can be simultaneously
executed by routing proposed portfolio trade orders to the
appropriate server 11.
[0019] FIG. 2 illustrates one example of a system for estimating
and optimizing the transaction costs of a trade execution according
to the invention, wherein transaction costs are estimated according
to a transaction cost estimation and optimization algorithms. The
ACE algorithms are programmed into a server 11, and customers
wishing to execute the ACE transaction cost estimation and
optimization for proposed portfolio trades input requests for
analyses and transmit them directly to the ACE server. The ACE
server performs one or more transaction cost analyses (TCA).
[0020] According to this method, at step 201 the customer's order
specifications are retrieved. For example, a customer may wish to
sell 1 million shares of security XYZ. At step 202, the customer
specifies (and inputs) a value for the risk aversion parameter
(RAP). If no value is retrieved, the program sets the default value
to 0.4. At step 203, the customer specifies the optimal trade time
horizon, e.g., selling 1 million shares of XYZ security over 7
days. At step 204, the program retrieves market parameters, e.g.,
security master information (i.e., ticker symbol, cusip, exchange)
closing price, volatility, and trading volume. At step 205, the
program calculates estimations for the customer's set of parameters
and system inputs based on the most recent market data. At step
206, the results are displayed to the customer as a table of
expected costs and standard deviation of costs for different RAP
values. At step 207, the customer selects a pair of values (EC and
SD) from the table that are most appropriate in the particular
case, and a value of RAP corresponding to the chosen pair of
values. At step 208, the customer inputs the new RAP value (while
maintaining the other parameters) to see a new set of expected cost
and cost standard deviation. This establishes a range of cost
estimates. At step 209, the program calculates (and displays) the
optimal trade strategies based on the customer's inputted
parameters, from which the customer may choose the strategy that
best fits the customer's particular situation.
[0021] As can be seen from FIG. 2, The agency cost estimator (ACE)
method and system is a computer-executed set of statistical models
that forecasts the transaction costs of a trade execution. In ACE,
cost is measured as the difference between the average execution
price and the prevailing price at the start of order execution.
[0022] ACE can be used to: [0023] Provide estimates of the price
impact cost for any specified trading strategy [0024] Form
pre-trade cost benchmarks to evaluate the execution performance of
traders and brokers, calibrated to a variety of common
pre-specified strategies (constant fraction of average daily
volume, VWAP-strategy) or any arbitrary user-defined strategy
[0025] Evaluate the costs of trading as a function of the desired
trading strategy of a trader [0026] Fine tune a trading strategy in
terms of trading horizon and aggressiveness [0027] Recommend an
optimal trading strategy that balances execution costs against the
uncertainty in the realized cost of trading [0028] Generate a
confidence interval which contains the realized cost Unlike many
other conventional products, ACE is a dynamic model that recognizes
that a trader will typically break an order into several trades to
minimize execution costs. Three significant features of ACE are as
follows:
[0029] ACE recognizes that agency traders incur price impact
because a trade moves the prevailing price when he/she executes a
trade. It is the cost of demanding liquidity. Price impact has both
permanent and temporary components. The permanent component is
information based; it captures the persistent price change as a
result of the information conveyed to the market that the trade
occurred. The temporary price impact is transitory in nature; it is
the additional liquidity concession to get the liquidity provider
to take the order into inventory. The permanent impact means that
the first trade of a multi-trade order will affect the prices of
all subsequent sub-blocks sent to the market. Modeling this dynamic
link is a key element of computing the price impact for a program
of trades spread over time.
[0030] ACE also recognizes that there is no such thing as "the"
cost estimate for a trade. In reality, cost is a function of the
trader's strategy. The more aggressive the trading strategy, the
higher the cost. Aggressiveness can be measured in terms of how
rapidly the trader wants to execute the trade given the trade's
size relative to normal liquidity. Thus, the ACE estimate is
predicated on a particular trading strategy. ACE 2.0 recognizes
several benchmark strategies and also allows the user to specify
any arbitrary trading strategy. These include VWAP (a participation
strategy that mimics the volume pattern in the security based on
historical data), uniform (a flat or linear strategy), the optimal
ACE strategy (described below), or any user-specified custom
strategy. ACE can also be used to develop an "optimal strategy"
that balances price impact costs against opportunity costs.
Opportunity costs are largely due to price volatility and create
uncertainty in the realized cost of trading as they do for the
realized return of investing. When executing an agency order the
balance between price impact and opportunity cost is chosen on the
basis of the motivation for the order, which ultimately comes from
the investment manager. Passive managers are mainly concerned about
price impact. Growth or momentum managers are more worried about
opportunity costs. We refer to the investment manager's sensitivity
to opportunity costs as his/her risk aversion, just as is done for
an investment manager's sensitivity to investment risk. The ACE
model estimates the expected cost and the standard deviation of the
cost of the agency trading strategy that optimally balances the
tradeoff between paying price impact and incurring opportunity
costs for a given level of risk aversion and trading horizon. The
user can either define the weight on risk directly or by telling
ACE the fraction of the order to be completed by mid-horizon. It
does so by expressing the trading problem as a multi-period
stochastic control problem. It then calculates the expected cost
and the standard deviation of the cost for the resulting optimal
strategy. This strategy is recommended for traders who want to
weight the opportunity cost associated with trading over a long
interval of time.
[0031] The ACE model is not a purely econometric model. Rather, it
is a structural model that uses parameters estimated from
econometric models of agency trade execution. In particular, ACE
relies on stock specific econometric models of volatility and price
impact. ACE uses market parameters as an input, including security
master information (ticker, cusip, exchange), closing price,
volatility, trading volume, bid/ask spread, distribution of trading
volume and volatility by 30 minute intraday bin (based on latest
available market data for several months). We estimate volatility
as the standard deviation of returns for the most recent 60 trading
days, volume as the 21-day median dollar volume, and bid/ask spread
as the 5-day average time and size weighted bid/ask spread. These
approaches allows us to take into account the latest trends in
stock price behavior and at the same time to filter out
fluctuations, which often are generated by market news, earnings
announcements and other factors.
[0032] ACE model is a tool to reliably forecast transaction cost
and statistical characteristics of this forecast for a scenario
selected by a user. The ACE estimate depends on the user's strategy
and trading aggressiveness. Further, the model is a dynamic one
that assumes trading through market orders. It is not intended to
be a model of upstairs trading costs or block pricing. The agency
cost estimator and optimizer of the present invention is unique in
that it allows the user to specify a particular trading style as
the basis for estimation of costs.
[0033] An important aspect of the ACE model and system is that it
can be used to recommend a particular trading strategy for a user.
ACE balances two considerations: expected cost and standard
deviation. The ACE model estimates the expected cost ("EC") and the
standard deviation ("SD") of the cost of the agency trading
strategy that optimally balances the tradeoff between paying price
impact (in consideration for liquidity demand) and incurring
opportunity costs for a user-specified weights on cost and risk and
trading horizon. It does so by expressing the trading problem as a
multi-period stochastic control problem. It then calculates the
expected cost and the standard deviation of the cost for the
resulting optimal strategy.
[0034] The execution cost is a signed (i.e., positive or negative)
difference between the value of a security or portfolio of
securities at the beginning and the end of the specified trading
horizon. The ACE model estimates the expected cost of the agency
trading strategy as follows:
[0035] The trading horizon is first divided into a number of bins,
or time periods of equal duration. For example, in the U.S. market,
ACE considers thirteen bins of 30 minute duration per trading day.
However, any number of bins of any duration may be used so long as
the bin parameters are appropriately configured for the chosen
duration. The trading horizon may consist of several trading days,
with an arbitrary starting bin in the first day and ending bin in
the last day. The trade order is defined by its trading horizon,
trade side (buy or sell), size and trading strategy (sequence of
share quantities per bin for a given trading horizon). Trading of
all share quantities specified for each bin is assumed to be
completed within the respective bin.
[0036] The ACE model distinguishes between market price, defined as
a security mid-quote price or average of bid and ask quote prices,
and an average execution price for which a given bin share quantity
was executed. The average execution price includes temporary price
impact and average price improvement. A temporary price impact
represents a liquidity concession made to induce the taking of an
order into inventory, typically half the prevailing bid-ask spread
(net of any price improvement). A permanent price impact is the
effect on market price (as contrasted with trade price) caused by
the execution of the trade. Large size trades affect market price
not only within the execution period, but have a persistent effect
to the end of the trading day.
[0037] Price improvement is a price received that is better than
the prevailing prices (i.e., bid for a sell order or ask for a buy
order). Generally, all buyer/seller initiated orders are expected
to execute at the prevailing ask/bid quote price. However, a
buyer/seller often may receive a better execution price than the
prevailing ask/bid quote price at the time the order was placed,
due to sudden and unpredictable market moves. Such better received
price is defined as a price improvement.
[0038] For any given security, volume and price volatility vary
significantly by bin within the same trading day. The volume and
volatility distributions by bin are determined statistically and
taken into account when estimating transaction cost and generating
an optimal strategy. While volume and volatility distributions for
a particular stock ideally should be used when estimating
transactions costs for that stock, research has demonstrated that
such distributions may be unstable, even for very liquid stocks,
because of market noise. Consequently, as an alternative aggregated
bin distributions of a larger number of stocks may be used. Such
aggregated distributions have been shown to be much more
stable.
[0039] The total realized transaction cost C can be defined as
C = i = 1 T [ C i ( n i ) + ( .alpha. + .di-elect cons. i .sigma. +
T i n i ) x i ] ( 1 ) ##EQU00001##
where n.sub.i=total number of shares traded on day i [0040]
.alpha.=expected daily price change [0041] =random price
disturbance for day i [0042] .sigma.=standard deviation of daily
price change [0043] T.sub.i=linear coefficient for price impact
persistence after trade on day i [0044] x.sub.i=residual at the end
of day i
[0045] The mean or expected cost EC may be considered as simply an
average value of total cost if the execution could be repeated many
times, since the total execution cost C is a stochastic or random
variable rather than a deterministic value or number. This is so
because total execution cost is subject to a large number of
unknown factors, including uncertain behavior of other market
participants, market movements related to macroeconomic or
stock-specific factors, etc. EC may be defined as
EC = i = 1 T [ EC i ( n i ) + ( .alpha. x i + T i n i x i ) ] ,
where ( 2 ) EC i ( n i ) = j = 1 N [ C i ( n i , j ) 2 + ( .alpha.
j + .gamma. j n i , j ) x ~ i , j ] + ( .alpha. 0 + J ) n i , ( 3 )
##EQU00002## [0046] .alpha..sub.j=standard deviation of price
change in bin j [0047] .alpha..sub.0=standard deviation of price
change between closing and opening [0048] .gamma..sub.j=linear
coefficient for price impact persistence after trade in bin j
[0049] n.sub.ij=shares traded in bin j of day i [0050] J=half
bid-ask spread [0051] {tilde over (x)}.sub.i,j=residual for the day
after bin j of day i [0052] N=number of bins in trading horizon
[0053] In the first use of ACE, computing a cost of a pre-specified
trading strategy, equations (2) and (3) are used to generate a
predicted cost. Specifically, given a pre-specified distribution of
shares across the trading horizon, by bin, given by {n}, we compute
the expected price in each bin using (3) and then sum across bins
(weighting by ni) using (2) to get total cost. A proprietary daily
risk model is used to get a forward looking estimate of the
variance of cost, allowing for the possibility of price movements
across bins.
[0054] In the second use of ACE, the optimal trading strategy,
denoted by {n*}, is computed by solving a particular optimization
problem that balances expected cost against variance. The
optimization problem of ACE is then given as:
PD=min{(1-.lamda.)EC+*Var C},
where .lamda. is a non-negative parameter called the risk aversion
parameter (or weight on opportunity cost), and Var C is the
variance or square of the standard deviation of cost C. The weight
on opportunity cost is typically input by the user and is a number
between 0 and 1; very low weights correspond to styles of trading
where opportunity costs are not a significant consideration (e.g.,
a value trader without information), whereas high values correspond
to aggressive trading styles (e.g., a trader who is concerned about
adverse price movements) where trading is accomplished rapidly.
[0055] The ACE optimal strategy is a solution of the optimization
problem. Note that ACE requires the user to select a value of risk
aversion parameter that reflects the user's risk tolerance level,
in addition to trading horizon for the specific transaction to be
executed. The risk aversion parameter does not have an absolute
value, i.e., a value which represents a user's risk aversion level
for one particular scenario does not necessarily represent the same
level for another one. Rather, RAP identifies a scenario within the
same order. Because RAP doesn't have an absolute value, two
parameters must be taken into account for each scenario under
consideration: the expected cost (EC) and the standard deviation
(SD) of a trading strategy. For an aggressive strategy, expected
cost is relatively higher, but standard deviation is lower.
Therefore, on average, expected cost is slightly higher than for
less aggressive strategies, but the level of uncertainty is lower,
that is, the range of possible values of cost around expected cost
is somewhat narrow.
[0056] The ACE model and system does not suggest aggressive or
passive strategies. Rather, ACE provides optimal strategies and
corresponding parameter forecasts for all different scenarios and
allows a user to select a scenario which best fits the trader's
particular situation. For example, if it is more important for a
trader not to exceed a certain reasonable level of transaction cost
rather than minimize the average cost (e.g., if a trader is
penalized for under-performance and not credited for
over-performance), it is suggested to use more aggressive
strategies. For each value of risk aversion, ACE will calculate
expected cost and standard deviation of expected cost, and will
generate an optimal trade execution strategy for the selected
trading horizon.
[0057] In contrast to the prior art, the ACE model is not a purely
econometric model, but rather a structural model that uses
parameters estimated from econometric models of agency trade
execution. In particular, the ACE model relies on stock-specific
econometric models of volatility and price impact. ACE uses market
parameters as an input, including security master information
(ticker, cusip, exchange), closing price, volatility, trading
volume, bid/ask spread, distribution of trading volume and
volatility by 30 minute intraday bin.
[0058] The ACE model also accounts for market volatility. The ACE
model estimates volatility as the standard deviation of price
returns for the most recent 60 trading days, volume as the 21-day
median dollar volume, and bid/ask spread as the 5-day average time
and size weighted bid/ask spread. These approaches take into
account the latest trends in stock price behavior, and at the same
time filter out fluctuations, which often are generated by market
news, earnings announcements and other factors.
[0059] The ACE model and system considers specific effects from
calendar milestones, such as the end of a month, quarter or year,
or the effect of a holiday or Monday, when volatility is usually
higher as a result of news disseminated from a company announcement
or from over the weekend.
[0060] A unique aspect of the present invention is the model's
consideration of single stocks as a single name case. Particularly,
the single name case considers a trade for a single stock, in
isolation from any other orders the user may be executing at the
same time. The inputs for the single name case may include, inter
cilia, ticker symbol (or cusip), side (buy or sell), number of
shares to trade, trading horizon, risk aversion parameter, and
starting bin.
[0061] The ACE model also considers the trading horizon in
analyzing a proposed portfolio trade execution. If there is no
requirement on selection of trading horizon for an order, it may be
selected as an optimal one. An optimal trading horizon is defined
as:
min{k=1,2, . . . :p66.sub.k/p66.sub.k+1<1.05}
where p66.sub.k --66%-percentile of cost for k-day trading
horizon.
[0062] For example, if a trader trades 1 million shares of security
XYZ and the ACE system sets the optimal horizon to be equal to 6,
it means that for a 7 day trading horizon the 66%-percentile of
transaction cost drops less than 5% of its value, compared against
the 6-day horizon. For fewer than 6 days, it drops more than 5%, if
comparing 66%-percentile of transaction cost for any two
consecutive days. This definition, however, does not restrict users
who would prefer another optimal trading horizon. They may run the
ACE program for several consecutive numbers of days and apply their
own definition.
Example 1
Executing a Single Name Case.
[0063] In this example, the system and method considers a trade for
a single stock, in isolation from any other orders the user may be
executing at the same time. The user (trader) may access the
computer program through a user interface (UI), and the program
executes according to the following steps:
[0064] 1. The user selects all parameters according to the trader's
order specifications and any reasonable value of RAP. By default,
0.4 is used as the value for RAP. In most cases, this particular
value suggests a moderately aggressive strategy, which is typically
appropriate for an initial run. The user then selects the
"Calculate" command, e.g., by clicking on a "calculate" button on
the user interface. The software program will display ACE estimates
for the user's set of parameters and system inputs based on the
most recent (e.g., real time) market data.
[0065] 2. The user accesses the Risk Frontier screen. A table is
presented with values of EC and SD for different values of RAP. The
user selects a pair of values (EC, SD) from the table that are the
most appropriate in the particular case, and a value of RAP
corresponding to the chosen pair of values. The user may change the
values for Lower and Upper Limits and Step. The user may select the
Draw Chart option (e.g., a button or icon) to select an appropriate
chart to graphically represent the range of values.
[0066] 3. After selecting the most appropriate pair (EC, SD) and
corresponding RAP value, the user may return to the Cost Estimates
screen. The user inputs the selected RAP value and then selects the
"Calculate" button.
[0067] 4. The user may go to the Trade Strategy screen to view the
optimal trade strategy. The user may select the chart button to
view a distribution by interval within a selected day or by trading
day, if the trading horizon consists of more than one trading day.
The user may go to the Shares Frontier screen to change the size of
the order to study how it will affect the ACE cost estimation
estimates. The user may change the values for Lower and Upper
Limits and a Step, and then select the Draw Chart button to choose
an appropriate range of share values.
Example 2
Executing a List Case.
[0068] In this example, the system and method considers a trade for
a list of stocks in a portfolio. The list case is designed for
portfolio trading. In the list case, the ACE method and system
includes a risk model, which takes into account correlation between
price movements for all stocks in a portfolio. The list case has
the same inputs as the single name case, except it uses a portfolio
list instead of a security symbol. As with the single name case,
the user (trader) may access the computer program through a user
interface, and the program executes according to the steps outlined
in Example 1.
[0069] The user may obtain estimates for a default set of
parameters and may consider different values of RAP from the Risk
Aversion Frontier screen in the same fashion as was performed in
the single name case. The user may select the appropriate set of
values for a particular case value. Trade horizon also can be
adjusted as desired.
[0070] The ACE model and system generates a pre-trade report as
part of a preliminary analysis of a proposed portfolio trade. The
pretrade report is designed to run a list of trades as a set of
separate "stand-alone" trades. The pre-trade report includes a list
of single name cases. Entering a list of trades is performed in the
same manner as the list case in Example 2. As with the other cases,
in the pre-trade report case, a user may select an appropriate
value of RAP, which should be the same for all trades in the
list.
Portfolio Characteristics Report
[0071] The ACE model also can generate a portfolio characteristics
report that describes the risk characteristics of the portfolio.
The model uses a propreitary daily risk model to construct
forecasts of the return volatility of the portfolio (the standard
deviation of the return of the portfolio on a daily basis, relative
to a user-selected benchmark portfolio such as the S&P 400,
etc.) and risk characteristics. In particular, the report shows the
percentage of the portfolio's value by sector (e.g., raw materials,
etc.) as well as select statistics. See attached screen shot.
Optimization of Transaction Cost
[0072] In addition to portfolio transaction cost estimation, the
ACE method and system comprises an algorithm that calculates an
optimal trade strategy that minimizes transaction costs. As
described above, the invention generally comprises two parts: A
first part based on price impact and volatility models that allows
a user to obtain transaction cost estimates for any given strategy,
and a second part comprising an algorithm that builds an optimal
strategy based on the results of the first part.
[0073] After randomly simulating millions of strategies and for
each strategy calculating the value of the criteria based on the
expected cost and the standard deviation of the cost for a
strategy, an optimal strategy with the lowest value of the criteria
was selected. That is, by performing a significant number of
simulations, a very close approximation of the optimal strategy
provided by ACE was discovered. Such a simulation was performed,
and it demonstrated that ACE method and system provides an optimal
trading strategy. In fact, after millions of repetitions, no
strategy was obtained that provided a lower value of the criteria
than the ACE strategy provided.
[0074] An optimal strategy is a subject of model definitions and
assumptions. The ACE optimal strategy is "optimal" only for a
user's specific criteria, e.g., level of risk aversion, and under
the assumption that expected cost and standard deviation are
estimated correctly. The correctness of the assumptions was tested
and verified using historical order execution data.
[0075] The validity of the ACE model was proven by testing how well
the model estimated the expected cost and the standard deviation of
the cost for a set of orders traded consistently using a fixed
strategy. The test validated the estimated daily volatility as well
as the estimated coefficients for the price impact functions. For
the order execution history, data was collected from ITG Inc.'s
VWAP (Volume Weighted Average Price) SmartServer because the orders
are completed in a systematic way by always trading a given
fraction of the target in every half-hour bin of the day. The data
comprised a set of all orders executed through the VWAP server
during a period of 10 months. For each order, the number of shares
traded during each half-hour bin and the average execution price
was obtained. Certain orders were excluded, e.g., orders that
constituted less than 1% of the 21-day median volume, orders that
had short sales, or for which there was a separate, simultaneous
order in the same security. The sample size comprised 11,852
orders. The data set covered 1,304 exchange-listed securities and
49 NASDAQ securities.
[0076] The transaction cost per share was defined as the difference
between the average execution price and the price available at the
beginning of the trading period (the benchmark price). The sign
(positive or negative) of the difference was used so that a
positive value represented a bad outcome. For each order t in the
data set, the realized transaction cost x.sub.t is computed. Also
calculated, using the parameters of the ACE model, is the estimated
expected transaction cost m.sub.t and the estimated standard
deviation of the cost s.sub.t. The variable
z.sub.t=(x.sub.t-m.sub.t)/s.sub.t is referred to as the normalized
excess cost. The random variable z.sub.t is expected to have the
mean of 0 and the standard deviation of 1. A t-test is performed
for the hypothesis that the mean of z.sub.t is 0 assuming that
standard deviation is unknown, and a chi-square test for the
hypothesis that the standard deviation of z.sub.t is 1 assuming
that the mean is unknown.
[0077] In general, statistical tests are used under the same
assumptions that samples they are run on have been built. ACE
assumes that the expected daily return, called a for all stocks, is
0. Standard deviation is higher for months when the market was very
volatile (see Table 1). However, for a relatively stable market,
positive and negative effects will compensate each other, and it is
appropriate to use the sample to test at least the mean of the
normalized excess cost. From this perspective, the test is
considered a benchmark of the model's applicability. Tests were
performed for the entire order data set and several subsets of the
data. The data was divided into subsets, e.g., by month, trade
share volume relative to 21-day median volume, 21-day median
volume, 5-day average spread, 5-day average spread relative to
price, volatility (60-day standard deviation) of daily percentage
price returns and share price.
[0078] The results are provided in the tables below. The "Mean" and
"StandDev" in the tables represent the mean and standard deviation
of the normalized excess cost, respectively.
TABLE-US-00001 TABLE 1 T-Test Results by Month month December 1998
January 1999 February 1999 March 1999 July 1999 August 1999 Number
of orders 1,150 884 1,611 1,834 975 1,020 Mean 0.001 -0.016 0.007
-0.003 -0.006 -0.029 p-value 0.979 0.602 0.811 0.906 0.862 0.330
StandDev 0.773 0.888 1.120 1.020 0.992 0.943 month September 1999
October 1999 November 1999 December 1999 all number of orders 942
900 1,146 1,390 11,852 Mean 0.010 0.011 -0.018 -0.003 -0.004
p-value 0.831 0.818 0.596 0.906 0.680 StandDev 1.393 1.432 1.168
1.127 1,093
[0079] Overall, the mean of normalized excess cost is very close to
the desired value of zero. Thus, on average the ACE model
accurately forecasted trading costs for the sample. Moreover, the
relatively high p-values mean that one cannot distinguish, in a
statistical sense, the small values from zero.
TABLE-US-00002 [0079] TABLE 2 T-test Results by Percentage of
21-day Median Daily Share Volume % 1-4% 5-9% 10-14% 15-19% 20%+ all
5%+ Number of orders 8,857 2,434 422 112 27 11,852 2,995 Mean
-0.006 -0.002 0.011 0.031 -0.069 -0.004 0.0007 p-value 0.62 0.94
0.84 0.76 0.79 0.68 0.97 StandDev 1.088 1.117 1.078 1,093 1.281
1.093 1.111
[0080] Even though the mean actual cost increases with trade size
(as a multiple of the 21-day median trading volume), the mean
normalized excess cost stays close to 0. This indicates that the
model is forecasting the correct magnitude of the cost across
orders of widely varying liquidity. The p-value for orders of 1-4%
of the 21-day median daily share volume is the lowest among all
subgroups. It stays inline with the fact that the influence of
other factors for price movement compared to the influence of the
order execution is relatively weaker for small trades than for
relatively large trades. For example, considering only samples for
orders of the magnitude higher than 4% of the 21-day median trading
volume (see last column of the Table 4), the estimated mean equals
0.0007 and the p-value is 0.97. Tables 3-7 present the results of
T-tests for other subsets of data.
TABLE-US-00003 [0080] TABLE 3 T-test Results by 21-Day Median of
Daily Share Volume volume (in thousands) <50 50-100 100-250
25-500 500-1,000 >1,000 all number of orders 1,095 1,319 3,237
2,913 1,798 1,490 11,852 Mean -0.422 0.018 0.006 0.005 0.010 0.005
-0.004 p-value 0.19 0.60 0.76 0.80 0.71 0.87 0.68 StandDev 1.055
1.260 1.048 1.083 1.098 1.074 1.093
TABLE-US-00004 TABLE 4 Table 4: T-test Results by Absolute Value of
Spread spread (in cents) Lower Between Between Between Between
higher than 10 10 and 13 14 and 16 17 and 20 21 and 30 than 30 all
Number of orders 1,448 3,617 3,610 2,264 840 73 11,852 Mean 0.007
0.000 -0.006 0.000 -0.345 -0.135 -0.004 p-value 0.80 1.00 0.76 0.98
0.33 0.30 0.680 StandDev 1.102 1.084 1.162 1.010 1.030 1.093
1.093
TABLE-US-00005 TABLE 5 T-test Results by Spread Relative to Price
Spread to price % p <0.2% 0.2%-0.3% 0.3%-0.4% 0.4%-0.5%
0.5%-0.7% 0.7%-1% >1% all Number of orders 636 2,269 2,597 2,036
2,465 1,174 675 11,852 Mean 0.052 0.005 -0.018 -0.000 -0.009 -0.009
-0.022 -0.004 p-value 0.21 0.80 0.40 1.00 0.68 0.83 0.60 0.680
StandDev 1.043 1.013 1,089 1.041 1.089 1,342 1.110 1.093
TABLE-US-00006 TABLE 6 T-test Results by Volatility Relative to
Price Volatility to price percentage <1% 1-2% 2-3% 3-4% 4-5%
>5% all Number of orders 270 5,436 4,527 1,314 240 65 11,852
Mean -0.016 -0.005 0.004 -0.021 -0.010 -0.086 -0.004 p-value 0.82
0.75 0.80 0.46 0.86 0.34 0.680 StandDev 1.177 1.166 1.037 1.005
0.877 0.709 1.093 Volatility to price <50 50-100 100-250 25-500
500-1,000 >1,000 all Number of orders 1,095 1,319 3,237 2,913
1,798 1,490 11,852 Mean -0.422 0.018 0.006 0.005 0.010 0.005 -0.004
p-value 0.19 0.60 0.76 0.80 0.71 0.87 0.68 StandDev 1.055 1.260
1.048 1.083 1.098 1.074 1.093
TABLE-US-00007 TABLE 7 T-test Results by Price Price (in dollars)
5-15 15-30 30-50 50-100 >100 all Number of orders 1,124 4,134
3,938 2,467 189 11,852 Mean -0.010 -0.004 -0.009 -0.002 0.093
-0.004 p-value 0.78 0.84 0.59 0.93 0.17 0.680 Standllev 1.170 1.142
1.064 1.032 0.923 1.093
[0081] The results strongly validate the parameters behind the ACE
model. The p-value is relatively low only for the most illiquid
stocks, in terms of extreme values of price, median volume or
volatility. However, it is never low enough to reject the null
hypothesis that the normalized excess cost is different from 0.
[0082] As can be readily seen by an person of ordinary skill in the
art, in alternative embodiments of the present invention proposed
trade executions can be automatically transferred within the
network from one server operating according to a first trade
strategy algorithm to another server having a second different
trade strategy algorithm.
[0083] The invention being thus described, it will be apparent to
those skilled in the art that the same may be varied in many ways
without departing from the spirit and scope of the invention. Any
and all such modifications are intended to be included within the
scope of the following claims.
* * * * *