Note: Descriptions are shown in the official language in which they were submitted.
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
TITLE OF THE INVENTION
SYSTEM, METHOD AND PROGRAM FOR AGENCY COST ESTIMATION
REFERENCE TO RELATED APPLICATION
[0001] Pursuant to 35 U.S.C. 119(e), this application claims priority to
U.S.
Provisional Patent Application Serial No. 60/924,904 filed on June 5, 2007,
and U.S.
Provisional Patent Application Serial No. 60/929,929 filed on July 18, 2007,
the entire
contents of each application is incorporated herein by reference. This
application is a
continuation in part of and claims priority to pending U.S. Patent Application
Serial No.
10/166,719 filed on June 12, 2002, the entire contents of which is
incorporated herein
by reference.
BACKGROUND OF THE INVENTION
Field of the Invention
[0002] This invention relates to systems, methods and computer program
products managing executions costs. More particularly, the invention relates
to
systems, methods and computer program products for creating and implementing
mathematical/econometric models that provide pre-trade estimates of the price
impact
costs of a given order to trade a number of shares of one or more tradable
assets, such
as securities, as well as optimization techniques utilizing the cost
estimates.
Background of the Related Art
[0003] Investment performance reflects both the investment strategy of the
portfolio manager and the execution costs incurred while implementing the
objectives of
the investment strategy. Execution costs can be large, especially when
compared to
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
gross returns, and thus can affect performance significantly. Managing
execution costs
can make or break the success of a particular investment strategy. For
institutional
traders who trade large volumes, implicit costs, most importantly the price
impact of
trading, typically represent a significant portion of total execution costs.
See, for
example, Domowitz, Glen, and Madhavan (2002) for various definitions of costs
along
with discussions and analyses.
[0004] The importance of accurately measuring execution costs has grown in
recent years due to fragmented liquidity in today's equity markets,
algorithmic trading,
direct market access, and structural and regulatory changes such as
decimalization
(implemented in 2001) and Reg NMS (implemented in 2007). Moreover, the recent
demand of some legislators and fund share holder advocates for better
disclosure of
commissions and other execution costs increases their importance even further
(see,
for example, Teitelbaum (2003)). This makes the management of execution costs
an
important issue for institutional investors whose trades are large relative to
average
daily volume.
[0005] Thus, there is a continued need for new and improved systems and
methods for estimating transaction costs.
SUMMARY OF THE INVENTION
[0006] The present invention provides systems, methods and computer program
products for forecasting the price impact costs of a trade execution that may
be applied
to any given trading strategy.
2
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[00071 According to aspects of the present invention, an Agency Cost Estimator
("ACE ") system, method and computer program product is provided that
includes: 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.
[0008] According to aspects of the present invention, the models include a
discretionary model that is based on all trades, including opportunistic
trades, and a
non-discretionary model that is based only on non-opportunistic trades (i.e.,
is not
based on data relating to opportunistic trades). As a result, a user of the
system can
utilize modeling that more accurately reflects one's own trading strategy.
[0009] According to aspects of the invention, systems, methods and computer
program products are provided for building and complementing the discretionary
and
non-discretionary models.
[0010] 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
[0011] 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;
3
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[0012] 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;
[0013] FIG. 3 is a graph illustrating a price impact model.
[0014] FIG. 4 is a graph illustrating intraday volume for a security and for
its
liquidity group.
[0015] FIG. 5 is a graph illustrating intraday bid-ask spread for Atlanta Tele-
Network Inc. and for its liquidity group.
[0016] FIG. 6 is a graph illustrating different trading strategies for buying
300,000
shares of Boeing Co.
[0017] FIG. 7 is a graph illustrating different volume-weighted average price
trading strategies for buying 300,000 shares of a security
[0018] FIG. 8 is a graph illustrating different distributions of transaction
cost
estimates.
[0019] FIG. 9 is a graph illustrating an efficient frontier of transaction
costs.
[0020] FIG. 10 is a graph illustrating different optimal trading strategies
for buying
300,000 shares of a security.
[0021] FIG. 11 is a graph illustrating different neutral optimal trading
strategies for
different buy order sizes of a security.
[0022] FIG. 12 is a table illustrating the expected treading costs, standard
deviation of trading costs, and trading horizons for different values of risk
aversion.
[0023] FIG. 13 is a graph illustrating empirical and theoretical permanent
price
impact functions.
4
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[0024] FIG. 14 is a graph illustrating empirical and theoretical permanent
price
impact functions.
[0025] FIG. 15 is a graph illustrating empirical and theoretical permanent
price
impact functions.
[0026] FIG. 16 is a graph illustrating empirical and theoretical permanent
price
impact functions.
[0027] FIG. 17 is a graph illustrating intraday price impact comparisons.
[0028] FIG. 18 is a graph illustrating intraday price impact comparisons.
[0029] FIG. 19 is a table reporting countries covered by ACE models.
[0030] FIG. 2Q is a graph illustrating average empirical costs.
[0031] FIG. 21 is a graph illustrating average empirical costs.
[0032] FIG. 22 is a graph illustrating estimated transaction costs.
[0033] FIG. 23 is a graph illustrating estimated transaction costs.
[0034] FIG. 24 is a graph illustrating relative price improvement.
[0035] FIG. 25 is a graph illustrating relative price improvement.
[0036] FIG. 26 is a graph illustrating generalized t-distributions.
[0037] FIG. 27 is a graph illustrating different calibrated distributions.
[0038] FIG. 28 is a graph illustrating a comparison of estimated versus
discretionary costs.
[0039] FIG. 29 is a graph illustrating a comparison of estimated versus
discretionary costs.
[0040] FIG. 30 is a graph illustrating a comparison of estimated versus non-
discretionary costs.
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[0041] FIG. 31 is a graph illustrating a comparison of estimated versus non-
discretionary costs.
[0042] FIG. 32 is a graph illustrating a comparison of estimated versus non-
discretionary costs.
[0043] FIG. 33 is a graph illustrating a comparison of estimated versus non-
discretionary costs.
[0044] FIG. 34 is a table reporting descriptive statistics of the data for the
calibration/testing of the ACEO model.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0045] ITG INC., the assignee of the present invention, provides a variety of
tools
that help investors minimize their execution costs, and hence maximize their
realized
returns. The present invention is directed to features and aspects of ITG's
ACEO
(Agency Cost Estimator), which is a product that applies a
mathematical/econometric
model that provides a pre-trade estimate of the price impact costs of a given
order.
ACEO can measure execution costs using the implementation shortfall approach
introduced by Perold (1988), which defines execution costs as the
appropriately signed
difference between the average execution price and the prevailing price at the
start of
the order execution. This measure includes both the bid-ask spread as well as
the price
impact costs of the order - the two most important cost components. Explicit
cost
components, such as commissions, can easily be added to the ACEO estimate to
obtain
total costs of trading. Components and features of ACEO, including the
original ACEO
model, upon which certain aspects of the present invention are based, are
disclosed in
6
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
U.S. Patent Application Serial No. 10/166,719 filed on June 12, 2002, the
entire
contents of which have already been incorporated herein by reference above.
[0046] The present invention can be used in conjunction with other pre-trade
analytic tools in many ways, including:
= to provide accurate cost estimates (e.g., expected execution costs and
standard
deviation of execution costs of an order),
= to estimate statistical characteristics of the distribution of execution
costs,
including distribution percentiles and confidence intervals,
= to form pre-trade cost benchmarks to evaluate the execution performance of
traders and brokers for a variety of common pre-specified strategies (in
particular,
Volume Weighted Average Price (VWAP)-strategy - constant fraction of average
daily
volume, uniform strategy, ACE Optimal Strategy) or any arbitrary user-
specified
strategy,
= to analyze how the costs of trading depend on the trading strategy,
= to fine-tune a trading strategy in terms of trading horizon, aggressiveness,
and
other parameters, and
= to recommend an optimal trading strategy that balances execution costs
against
the uncertainty in the realized costs of trading (opportunity costs).
[0047] In addition, ACE can be used as post-trade cost benchmark for trading
performance.
[0048] Unlike many other conventional products, ACE includes a dynamic
model that recognizes that a trader or automated system will typically need to
break up
7
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
a large order into several smaller trades to minimize price impact costs.
There are three
critical features of ACEO that merit special attention:
1. ACEO recognizes that traders incur price impact costs because a trade moves
the price adversely in the market when it is executed. It is the cost of
demanding
liquidity. Price impact has both a permanent and a temporary component. The
permanent component is information-based: it captures the persistent price
change as a
result of the information the occurrence of a trade conveys to the market. The
temporary
price impact is transitory in nature: it is the additional price concession
necessary to get
the liquidity provider to take the other side of the order. The permanent
price impact
implies 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 sequence of trades spread over time.
2. ACEO recognizes that there is no such thing as "the" cost estimate of a
trade. In
reality, trading costs are a function of the trader's strategy or execution
approach. The
more aggressive the trading strategy, the higher the costs are. Trading
aggressiveness
can be measured in terms of how rapidly the trader wants to execute the trade
given the
trade's size relative to normal volume. Thus, the ACEO estimate is based on a
particular
trading strategy.
3. ACEO can also be used to find an "optimal strategy" that balances price
impact
costs against opportunity costs. Such an ACEO optimal strategy represents a
solution
of a very general optimization problem (with time-varying parameters) for both
the single
name and the portfolio case. Opportunity costs are largely due to price
volatility, which
creates uncertainty in the realized costs of trading as it does for the
realized returns of
8
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
investing. When executing an agency order, the balance between price impact
and
opportunity costs is chosen on the basis of the motivation for the order,
which is
ultimately given by the investment manager. Passive managers are mainly
concerned
about price impact while growth or momentum managers are more worried about
opportunity costs. Reference is made to the investment manager's sensitivity
to
opportunity costs as weight on risk, or risk aversion, just as is done for an
investment
manager's sensitivity to investment risk. ACEO estimates the expected costs
and the
standard deviation of the costs of the agency trading strategy that optimally
balances
the trade-off between paying price impact costs and incurring opportunity
costs for a
given level of risk aversion and trading horizon. The trading horizon can
either be
chosen by the user or ACEO can determine an optimal time horizon for a given
order.
In ACEO, the user can define the weight. on risk. To allow for this, ACEO
formulates the
trading problem as a multi-period stochastic control problem. The solution to
this
stochastic control problem is the optimal strategy that minimizes the weighted
sum of
price impact and opportunity costs. ACEO provides the expected costs and
standard
deviation of the costs for the'resulting optimal strategy. This strategy is
recommended
for traders who want to weigh the opportunity costs associated with trading
over a long
interval of time consistent with their weight on risk.
[0049] The ACEO model is not a purely econometric model calibrated based on
transaction cost data. Rather, it is a structural model that uses parameters
estimated
econometrically. In particular, ACEO relies on stock-specific econometric
models of
volatility, price impact, and price improvement, as well as a risk model. In
addition, a
purely econometric model based on empirical data would not allow one to
provide cost
9
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
estimates for large orders, since there simply are not many observations for
large
orders (diBartolomeo (2006)). By employing a structural model, ACEO does
mitigate
this problem.
[0050] The ACEO framework of the present invention builds on the system and
methods introduced in U.S. Patent Application Serial No. 10/166,719 filed on
June 12,
2002.
[0051] Referring to Figure 1, one or more transaction cost optimization
servers 11
can be provided on a communication network 10. The network 10 may be a public
network or a private dedicated network. A server 11 can be programmed with
transaction cost estimation and optimization computer program products, and
has
access to various trading mechanisms or exchanges through the network 10, such
as
the New York Stock Exchange (NYSE) 18, the POSITO 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.
[0052] According to preferred embodiments of the present invention, the server
11 is configured to be 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.
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[0053] 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.
[0054] 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
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.
11
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[0055] Figure 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 and models. Customers wishing to execute the ACEO
transaction cost estimation and optimization for proposed portfolio trades
input requests
for analyses and transmit them directly to the ACEO server. The ACEO server
performs
one or more transaction cost analyses (TCA).
[0056] 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,
which is
preferably 0.3. At step 203, the customer specifies the optimal trading 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,
estimations are
calculated 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 (expected cost and standard deviation)
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,
optimal
12
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
trade strategies are calculated and displayed for a customer's inputted
parameters, from
which the customer may choose the strategy that best fits the customer's
particular
situation.
[0057] As can be seen from Figure 2, the ACEO method and system can include
a computer-executed set of statistical models that forecasts the transaction
costs of a
trade execution. In ACEO, costs are measured as the difference between the
average
execution price and the prevailing price at the start of order execution.
[0058] An important aspect of ACEO is that it can be used to recommend a
particular trading strategy for a user. ACEO balances two considerations:
expected
cost and standard deviation. The ACEO model can estimate the expected cost
("E(C)")
and the standard deviation ("SD(C)") of the cost of the agency trading
strategy that
optimally balances the trade-off 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.
[0059] 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. ACEO can estimate the expected cost of the
agency
trading strategy as follows:
[0060] In an exemplary method, the trading horizon is first divided into a
number
of bins, or time periods of equal duration. For example, in the U.S. market,
ACEO
preferably considers thirteen bins of 30 minute duration per trading day.
However, any
13
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
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.
[0061] 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.
[0062] 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
costs 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.
[0063] The total realized transaction costs C can be defined as:
14
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
T
C = E[Ci(ni) + (a + E;a + Tini)xil (1)
i=1
where ni = total number of shares traded on day i
ci = cost on day I for trading ni shares
a = expected daily price change
E:i = random price disturbance for day i
Q= standard deviation of daily price change
Ti = linear coefficient for price impact persistence after trade on day i
xi = residual at the end of day i.
[0064] 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
T
EC = E[EC;(n;) + (ax; + T;n;x;)], (2)
i=1
where
EC;(n;) = I[ci n?j +(ai +yjn;j)z;~~+(ao +J)n;, (3)
;=I
cj = linear coefficient for temporary price impact for bin j
aj = standard deviation of price change in bin j
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
aO = standard deviation of price change between closing and opening
yj = linear coefficient for price impact persistence after trade in bin j
ni,j = shares traded in bin j of day i
J = half bid-ask spread
xi,j = residual for the day after bin j of day i
N= number of bins in trading horizon.
[0065] In the first use, 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}, the
expected price in each bin is computed using e.g., (3) and then sum across
bins
(weighting by ni) using e.g., (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.
[0066] In the second use of ACEO, the optimal trading strategy, denoted by
{n*},
is computed by solving a particular optimization problem that balances
expected cost
against variance of cost. The optimization problem of ACEO is then given as:
PD = min {(1- \ )EC + A*Var C),
where,\ 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),
16
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
whereas high values correspond to aggressive trading styles (e.g., a trader
who is
concerned about adverse price movements) where trading is accomplished
rapidly.
[0067] According to the present invention, ACEO can reliably forecast
transaction
costs and estimate their statistical characteristics for any scenario selected
by a user.
ACEO estimates depend on the user's strategy and the underlying price impact
model
parameters. The user's strategy is reflected in trading style and
aggressiveness. The
price impact model parameters can be calibrated using proprietary ITG PEER
GROUP
data in order to be in line with "typical" costs of large institutions. The
trading style can
be characterized by the aggressiveness (participation rate) and the level of
opportunistic
trading.
[0068] Further examples and details regarding aspects of the base ACEO
system, method and computer program product are disclosed in U.S. Patent
Application
Serial No. 10/166,719 filed on June 12, 2002.
[0069] The inventors have discovered that realized costs for opportunistic
traders
do not match with the realized costs of traders that have to execute most of
the times
(i.e., non-opportunistic or non-discretionary traders). In order to better
account for this
discrepancy, the present invention improves upon the original ACEO invention
by
providing two cost estimates: one called ACEO Discretionary and another one
called
ACEO Non-Discretionary.
[0070] As the names indicate, for ACEO Discretionary, all executions are used
for
the building (also called calibration) of the ACEO model, i.e., even orders
for which the
traders can postpone or abandon trading to take advantage of market
conditions. For
ACEO Non-Discretionary, opportunistic executions are excluded from the
building of the
17
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
model and only execution data are included for orders that traders do not have
much
discretion and must execute regardless of whether market conditions are
favorable.
[0071] ACEO can be implemented for equities or for non-equity asset classes.
[0072] The ACEO model can be estimated for each exchange of each country
separately. This approach is necessary since transaction costs vary
significantly
between different countries and exchanges (see, for example, Munck (2006)).
[0073] ACEO can distinguished between the market price, defined as a stock
mid-quote price, and the average execution price, at which a given bin's
shares are
executed. The average execution price differs from the market price since it
includes
temporary price impact costs and average price improvement. For small orders
this
difference is typically only half of the prevailing bid-ask spread, net of any
price
improvement. Price improvement is defined as receiving a price better than the
prevailing prices (bid for a sell or ask for a buy) at the time the order was
placed. For
larger orders that exceed the bid/ask size, the execution price reflects both
permanent
and temporary price impacts. Permanent price impact captures the information
content
of the order, while the temporary price impact is the cost of demanding
liquidity. Trade
execution affects not only the trade price, but the market price as well.
Large size
trades move the market price not only within the execution period, but have a
persistent
effect on the market price to the end of the trading day. Such an effect is
usually called
a permanent price impact. The market price is also affected by other factors
that are
captured in a stochastic disturbance term. Of course, both the temporary price
impact
and the permanent price impact increase with the number of shares traded
within a bin.
18
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[0074] Execution costs can be considered the appropriately signed difference
between the market price of the stock at the beginning of the trading horizon
and the
average execution price for the order. Since there are both deterministic and
random
factors involved in the dynamic analysis, execution costs are stochastic in
nature and
should be analyzed by statistical methods. Further, given the multi-period
nature of the
optimization control problem, the analysis also requires the use of stochastic
dynamic
programming.
[0075] FIG. 3 provides an illustration to the above-described concepts and
terms.
The temporary and permanent price impact applies to both single and multiple
executions. FIG. 3 illustrates the concept behind the ACEO price impact model
for a sell
trade. The execution price of the stock is lower than the pre-trade price as
the law of
supply and demand suggests. The larger the size of the trade, the more likely
the sale
price will be lower. The difference between pre-trade market price and
execution price
consists of two parts - permanent and temporary price impact. While the
temporary
price impact only affects the price of the trade itself, the permanent price
impact has a
persistent effect on the market price.
[0076] Providing reliable estimates of the model's parameters presents a
special
challenge, and indeed is the most difficult aspect of creating and maintaining
the ACEO
model. Stock market dynamics are complex and are subject to a variety of
institutional
features. For example, price impact is extremely difficult to measure given
the low
signal-to-noise ratio induced by intraday price volatility, and very
comprehensive
statistical techniques to extract the "useful" signal are needed. In short,
the econometric
implementation of ACEO is the most critical element of the model development.
19
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[0077] All ACEO implementations preferably use stock-specific parameters
estimated from the most recent market data, including security master
information
(ticker, cusip/sedol, exchange), the previous trading day's closing price, and
estimates
for volatility, average trading volume, and bid-ask spread of each security.
[0078] The volatility is preferably the historical 60-day price volatility
where the
daily returns are adjusted by the VIX level. VIX is the ticker symbol for the
Chicago
Board Options Exchange Volatility Index, which is a measure of the implied
volatility of
S&P 500 index options. It represents one measure of the market's expectation
of
volatility over the next 30-day period. Average trading volume is estimated as
the
median daily dollar volume for the 21 most recent trading days. The bid-ask
spread is
computed as the 5-day time-weighted average daily bid-ask spread. The
estimation
methodologies for average trading volume and bid-ask spread are selected to
balance
the latest trends in stock behavior against fluctuations generated by market
news,
earnings announcements, and other temporary factors. It is worthwhile noting
that any
other estimation approaches can be used as well, if so desired.
[0079] The ACEO framework is preferably built in such a way that the market
price behavior of a stock may depend on its expected intraday stock returns.
By default,
these returns are set to zero, but client-specific "alpha" models may be
included in the
ACEO analysis.
[0080] Besides estimating transaction costs for single name trades, ACEO may
also be used efficiently for pre- and post-trade analysis of portfolios. In
all ACEO
implementations, correlations between stock returns are preferably estimated
using ITG
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
Risk Models. Depending on the stock universe in the trade list, the
corresponding
country, region, or global ITG Risk Model is used.
[0081] The present invention takes into account that trading volume, price
volatility, and bid-ask spreads
= vary significantly within the same trading day,
= change over the course of time,
= are stock-specific,
= are relatively stable for very liquid securities, and
= are not stable for illiquid securities.
[0082] The intraday variations in volume, volatility, and spreads can be
measured
statistically and incorporated within ACE's cost estimation. Ideally, if one
intends to
estimate costs for a stock, the intraday volume, volatility, and spread
distributions for the
particular stock should be used. The research, however, demonstrates that such
distributions are unstable for less liquid stocks due to both market and stock-
specific
fluctuations. FIGs. 4 and 5 show intraday volume and spread distributions for
Atlantic
Tele-Network Inc. (ATNI) during several time periods. Atlantic Tele-Network
Inc. has
been selected for illustrative purposes at random. The stock belongs to the
category of
relatively illiquid stocks, its market capitalization is $394.2 million and
the median daily
share volume is 50,000 shares as of May 1, 2007.
[0083] FIG. 4 shows the intraday volume pattern for Atlanta Tele-Network Inc.
(ATNI) for the months January, February, and March of 2007. The stock is a
relatively
illiquid stock, its market capitalization is $394.2 million, and the median
daily share volume
is about 50,000 shares as of May 1, 2007. The distributions show some
fluctuations,
21
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
especially at the beginning and at the end of the trading day. The bold line
represents the
smoothed average intraday volume distributions for all stocks which belong to
the same
market and liquidity group as ATNI. The average was taken over the three-month
period
from January to March, 2007.
[0084] FIG. 5 shows the intraday bid-ask spread pattern for Atlanta Tele-
Network
Inc. (ATNI) for the months January, February, and March of 2007. The stock is
a
relatively illiquid stocks, its market capitalization is $394.2 million and
the median daily
share volume is about 50,000 shares as of May 1, 2007. The distributions show
some
fluctuations, especially at the beginning and at the end of the trading day.
The bold line
represents the smoothed average intraday bid-ask spread distribution for all
stocks
which belong to the same market and liquidity group as ATNI. The average was
taken
over the three-month period from January to March, 2007.
[0085] Note, in the remainder of this document, if not specified otherwise,
all
ACEO numbers presented in tables and figures are based on the ACEO Non-
Discretionary embodiment. Clearly, with such variation, for example, in the
intraday
volume or spread pattern for ATNI, one cannot be certain that using the latest
available
distribution calculated from, e.g., March data will be a good estimate for
April. A
possible alternative for less liquid stocks is to use aggregated distributions
based on a
significant number of stocks, for example, all stocks included in similar
markets
(NYSE/AMEX, Nasdaq) and liquidity groups. These distributions are much more
stable
as demonstrated by the bold lines in FIGs. 4 and 5, and they provide more
robust
forecasts. IT is assumed that distributions of trading volume, volatility, and
spreads are,
respectively, averages of trading volume, volatility, and spread distributions
across
22
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
individual stocks on an equally-weighted basis. All stocks included in this
distribution are
of equal importance. This makes sense, since the main purpose of the
aggregation is to
get meaningful and stable estimates for illiquid stocks. The same approach is
applicable
to international markets. Volume, volatility and spread distributions are
updated
monthly, based on the most recent available trade and quote data. Both stock-
specific
and aggregated distributions are smoothed to control for market noise.
[0086] In general, trading strategies can be subdivided into two categories:
structured and opportunistic trading strategies.
[0087] Opportunistic trading strategies do not strictly follow a pre-specified
trading schedule. Instead, these strategies are continuously searching for
liquidity and
opportunities for favorable execution based on real-time information. The
success of
such algorithms requires reliable quantitative forecasts of price movements
and liquidity
patterns, as well as intelligently combined use of trading venues and
alternative order
types (such as discretionary limit orders, Immediate-Or-Cancel (IOC) orders,
or pegged
orders). Opportunistic trading strategies work well for orders that do not
have to be
completed. However, they are not suitable for orders that need to be executed
in full
within a certain time horizon.
[0088] In contrast, structured, or more precisely scheduled, strategies are
generally linked to a certain benchmark, for instance Volume Weighted Average
Price
(VWAP) or implementation shortfall, and are mostly based on historical data
and their
underlying analytics like the historical intra-day volume, volatility, and
spread patterns.
At the macro-level, these algorithmic trading strategies suggest how to
optimally slice a
large order in different time intervals within a specified horizon, but
additional intelligent
23
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
rules have to be used to execute each part of the original order, taking
specifically into
account
= how close one should follow the suggested trading schedule (order timing,
deviation rule),
= order type selection (limit orders, market orders, discretionary orders, and
IOC
orders, etc.),
= trading venue selection (smart order routing to execute at the best
available price
and to discover undisclosed liquidity).
[0089] Most of the rules require the input of real-time information and depend
on
models/algorithms that can be used to search for the best price with the
fewest time
constraints. For more information about strategy classifications and
selections given the
specific objectives and scenarios, see for example, Domowitz and Yegerman
(2005) or
Yang and Jiu (2006).
[0090] ACEO uses trading strategies that belong to the class of structured
strategies. In ACEO, a strategy is defined as a sequence of number of shares
that
should be executed within an execution period according to a bin scheme. A bin
is a
30-minute period during a trading day. For example, in the U.S., 9:30-10:00
a.m. is bin 1
of day 1, 10:00-10:30 a.m. is bin 2 of day 1, ... , 3:30-4:00 p.m. is bin 13
of day 1; for
multi-day strategies, 9:30-10:00 a.m. is bin 1 of day 2, etc.
[0091] There are several standard strategies that can be expressed by the bin
scheme of ACE:
24
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
= The Instant Strategy trades all shares in the starting bin. This strategy
can
be invoked in ACEO by setting any of the other strategies supported by ACEO to
start
and end in the same bin.
= The Uniform Strategy assumes the same number of shares to be
executed for each bin within the trading horizon. For example, if the order
size is
300,000 shares and the trade should be completed between 10:00 a.m. and 1:00
p.m.,
the uniform strategy suggests executing 50,000 shares within each bin (bins 2
to 7).
Bertsimas and Lo (1998) propose uniform strategies to minimize expected costs
of
trading fixed number of-shares.
= The VWAP Strategy by Horizon. For each order input, ACEO generates a
prediction of the stock's volume pattern over the desired time horizon,
whether partial-
day, full day, or multi-day. For each order, the VWAP Strategy by Horizon is a
trading
strategy that matches the volume pattern of the underlying stock over the
desired time
horizon, participating more heavily during the periods when volume is expected
to be
heaviest. This helps to minimize the impact of trading during thin volume
periods and
allows the order to benefit from the most liquid conditions. FIG. 6 presents
the VWAP
Strategy by Horizon for a trade of 300,000 shares of stock Boeing Co. (BA)
that
executes between 10:00 a.m. and 1:00 p.m. Boeing Co. has been selected for
illustrative purposes at random. The stock is a relatively liquid stock; its
market
capitalization is $73.7 billion and the median daily share volume is 3.5
million shares as
of May 1, 2007.
[0092] FIG. 6 shows different types of trading strategies for buying 300,000
shares (approximately 8.5% of ADV) of Boeing Co. (BA) between 10:00 a.m. and 1
p.m.
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
The stock belongs to the category of relatively liquid stocks, its market
capitalization is
$73.7 billion and the median daily share volume is 3.5 million shares as of
May 1, 2007.
The instant strategy places all the shares in the first trading bin (bin 2,
i.e. 10:00 a.m. -
10:30 a.m.). The uniform strategy assumes the same number of shares to be
executed
for each bin within the trading period. The VWAP strategies by horizon and by
30%
participation rate match the intraday volume pattern of the stock. As the
intraday volume
suggests, more shares are executed in the early morning.
[0093] ADV is the median daily dollar volume for the 21 most recent trading
days.
The VWAP Strategy by Horizon is compared to the Instant Strategy, Uniform
Strategy,
and VWAP Strategy by Participation Rate with 30% participation rate. 300,000
shares of
Boeing Co. represent approximately 8.5% of average daily volume (ADV) as of
May 1,
2007.
[0094] FIG. 7 shows VWAP trading strategies with varying participation rates
(5%, 10%, 20%, and 30%) for buying 300,000 shares (approximately 8.5% of ADV)
of
Boeing Co. (BA). The stock belongs to the category of relatively liquid
stocks, its market
capitalization is $73.7 billion and the median daily share volume is 3.5
million shares as
of May 1, 2007. In contrast to a VWAP trading strategy by horizon, the trade
horizon is
not fixed but rather depends on the participation rate. The lower the
participation rate,
the longer it takes to fill the order.
= The VWAP Strategy by Participation Rate is defined similarly to the VWAP
Strategy by Horizon. For each order, the trading strategy is formed using the
volume
pattern of the underlying stock by participating proportionately with the
specified
participation rate in the estimated day's volume. If the fraction of order
size relative to
26
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
the average daily trading volume is larger than the participation rate, a
multi-day
strategy with the same intraday stock-specific volume pattern for each day is
employed.
FIG. 7 displays four VWAP Strategies by Participation Rate with different
participation
rates (5%, 10%, 20% and 30%) for buying 300,000 shares of BA. The trading
always
begins at 10:00 a.m. (i.e., in bin 2). The plot shows that the higher the
participation rate
is, the shorter the time horizon and thus the more aggressive the strategy.
= The ACE Optimal Strategy represents a solution of a very general
optimization problem (with time-varying parameters). The ACE model estimates
the
expected costs and the standard deviation of the costs of the agency trading
strategy
that optimally balances the trade-off between paying price impact costs and
incurring
opportunity costs (for a given level of risk aversion and trading horizon.)
[0095] The crucial question facing traders is how to define and quantify
trading
objectives in order to implement them in an appropriate strategy. This
question is non-
trivial since common trading objectives often compete with each other and
cannot be
completely satisfied simultaneously. For example, a cost-minimizing strategy
is not
necessarily the ideal solution. A trader who minimizes costs by breaking up a
trade over
a very long time horizon faces risk from significant market movements. But
conversely,
trading aggressively to control risk implies "front-loading" the order and
typically raises
costs. Therefore, an optimal strategy should balance both costs and risk. From
this
perspective, the ACE Optimal Strategy is a valuable trading tool because it
provides a
mathematically derived optimal solution given certain model assumptions. These
assumptions are discussed in detail below.
27
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[0096] Execution costs are subject to a large number of unknown factors. These
include, for example, the uncertainty caused by the behavior of other market
participants and market movements related to macroeconomic or stock-specific
factors.
It is impossible to model all these factors. Therefore, we consider execution
costs as a
random variable rather than as a deterministic value or number. In other
words, the
same strategy may provide different results if it is executed repeatedly under
the same
circumstances. Generally, a probability distribution is characterized by a
number of
parameters. In particular, the mean and standard deviation are widely used in
statistics
as such parameters. Note that these parameters, in general, do not define a
distribution
uniquely, but if one assumes certain distributions, it is sufficient to
consider only these
two parameters to identify the distribution. The normal distribution is one
widely used
example of such distributions. The mean of the distribution of costs may be
interpreted
simply as the average value of costs if the execution could be repeated many
times.
The standard deviation of costs characterizes how much the value of costs may
deviate
from the expected costs. Therefore, selecting a strategy best suited for given
trading
objectives is equivalent to selecting the best suited distribution of costs.
[0097] Clearly, every trader prefers both lower expected costs and lower risk
(standard deviation of costs). Hence, both of these parameters enter the
optimization
objective function. To find the optimal trading strategy, we need to balance
the trade-off
between expected costs and the variance of costs. This yields the ACEO
optimization
problem
[0098] (1- A) = E(C) + A = Var(C) -> min, (4)
28
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[0099] where C is the total execution costs of the trade, E(C) is the expected
value of C, and Var(C) is the variance of C. A is the risk aversion parameter
in the
interval [0,1]. A can also be considered as "weight on risk." The optimal
solution is the
trading strategy, among all strategies for a given set of trade side, trade
size, and
trading horizon that minimizes the objective function in (4).
[00100] The ACE Optimal Strategy is the solution of the optimization problem
in
(4). It is very important to realize that the solution depends on the trade
characteristics
and the selected risk aversion parameter. Different trade characteristics and
different
values of risk aversion produce different ACE Optimal Strategies. Therefore,
it is
crucial to understand how to select the inputs into the optimization problem
according to
each particular situation.
[00101] The side and size of a trade are usually given, but a user may select
the
trade horizon and the risk aversion parameter. In order to select them more
effectively,
it is useful to be reminded that more aggressive trading strategies have
higher expected
costs, but a lower standard deviation of costs. Both, a shorter trading
horizon and a
higher value of risk aversion correspond to a more aggressive trading
strategy. FIG. 8
shows several probability distributions of execution costs for different risk
aversions with
a fixed one-day horizon for an order to buy 300,000 shares of Boeing Co. (BA).
The plot
reveals that a higher risk aversion provides lower expected costs but higher
standard
deviation and thus, greater uncertainty. Therefore, a user should make a
selection
based on appropriate values of both expected costs and standard deviation of
costs.
[00102] FIG. 8 illustrates the distributions of Non-Discretionary transaction
cost
estimates based on different values of risk aversion (0, 0.3, 0.6, 0.9, and 1)
for an order
29
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
to buy 300,000 shares (approximately 8.5% of average daily volume (ADV)) of
Boeing
Co. (BA). The distributions are based on ACE Optimal Strategies with a one-
day
trading horizon. The plot suggests that the choice of a greater risk aversion
provides
higher expected costs, but lower standard deviation of costs and, thus,
potentially less
opportunity costs.
[00103] The following example demonstrates how to make such a selection:
Suppose we need to buy again 300,000 shares of the stock Boeing Co. (BA) in
one day.
We could trade the order using a variety of strategies - some more passive and
some
more aggressive. Each of these strategies has a corresponding risk aversion
parameter. FIG. 9 shows the possible expected cost/risk outcomes for various
risk
aversions. For most traders, a risk aversion of zero is too passive: while the
expected
costs are low the risk is very high. The high risk due to the long trading
horizon implies
the possibility of executing at inferior prices - potentially destroying any
alpha that a
particular investment was anticipated to capture. However, if volatility in
transaction
costs is of no concern, then this strategy is the best since it will, over
many orders,
average to the lowest costs. Conversely, a risk aversion of one produces a
very low-risk
trading strategy, but with exceptionally high costs - yet another way to
destroy alpha.
The solution to avoiding these two extreme outcomes is to choose a risk
aversion that
balances costs and risk somewhere between the extremes.
[00104] FIG. 9 graphically displays ACE Optimal Strategies for different risk
aversions for an order to buy 300,000 shares (approximately 8.5% of ADV) of
Boeing
Co. (BA) using Non-Discretionary. The 300,000 share order corresponds to about
8.5%
of ADV. Obviously, there are many choices of optimal strategies between the
two
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
extremes of minimizing expected transaction costs (Point B) and minimizing the
standard deviation of transaction costs (Point A). Each point on the efficient
frontier
corresponds to a specific risk aversion. The graph highlights selected risk
aversion
values. From left to right, one can see that one can incrementally reduce the
expected
transaction costs of a trading strategy (relative to the most expensive) by
assuming
more risk. Somewhere along this "efficient frontier" of transaction costs is a
strategy
that, beyond which, begins to accumulate more risk than the reduction in
expected
transaction costs is worth. This would be a desirable choice of risk aversion.
For
comparison, trading strategies other than ACEO Optimal Strategies are also
included.
As expected, theses alternative trading strategies do not lie on the efficient
frontier as
they are not optimal: There are trading strategies with lower expected
transaction costs
with the same standard deviation of transaction costs, or there are trading
strategies
with the same expected transaction costs, but lower standard deviation of
transaction
costs. Note, for all strategies the trading horizon was restricted to one
trading day (with
potential start in the first bin). For the VWAP By Participation Strategies,
the order size
is sufficiently small to ensure that the trading horizon is less than one
trading day.
[00105] As FIG. 9 demonstrates, trading strategies based on high risk aversion
have low opportunity costs (opportunity costs are measured as the standard
deviation of
the transaction cost distribution). This lower standard deviation is achieved
by trading
more shares earlier in the trading horizon - which is closer to the decision
price. The
decision price is the prevailing price at the time the decision to place the
order is made.
This "front-loading" tends to move the stock price more rapidly in the
unfavorable
direction than an order executed more patiently. In the ACEO framework, this
31
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
movement in the stock price is market impact. Therefore, if you desire low
opportunity
costs (low uncertainty in the transaction costs or low standard deviation)
then you must
be prepared to pay more market impact costs. If you are willing to keep open
the
chance of having large realized opportunity costs, you can slow the order
execution
down and avoid high market impact costs.
[00106] FIG. 10 shows the ACE Optimal Strategies of ACE/2 Non-Discretionary
for buying 300,000 shares (approximately 8.5% of ADV) of Boeing Co. (BA)
obtained
using values of risk aversion of 0, 0.3, 0.6, 0.9, 0.95 and 1, and a one-day
trading
horizon. Also shown is a VWAP Strategy by Horizon with a one-day trading
horizon.
The ACE Optimal Strategy for larger risk aversion parameters always suggests
to
trade more aggressively at the beginning of the trading horizon to minimize
opportunity
costs.
[00107] FIG. 11 illustrates different ACE Optimal Strategy trading
distributions for
risk aversion 0.3 (ACE/2 Non-Discretionary Neutral) and fixed one-day horizon
for
Boeing Co. (BA) and different order sizes (15, 20%, 100%, and 1000% of ADV).
FIG. 9
also shows the trading distribution for a one-day VWAP trading strategy. The
chart
shows that risk aversion 0.3 yields ACE Optimal Strategies that are close to
a VWAP
trading strategy. Moreover, the ACE Optimal Strategy becomes more and more
back-
loaded with increasing order size due to market impact costs.
[00108] Such a selection becomes more complicated if the trading horizon needs
to be selected in addition to the risk aversion parameter, but the approach
remains the
same. As an alternative, ACE can be configured to determine an "optimal"
trading
32
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
horizon for an order, thereby leaving the selection of risk aversion as the
only user-
specified input parameter.
[00109] The selection of the trading horizon for an order is another parameter
users need to choose. ACEO can provide an optimal trading horizon. The
solution of
finding such an optimal trading horizon may vary in practical situations.
After
considering client's feedback and analyzing several different approaches, the
following
method proved to be the best suited for ACEO implementations. ACEO continues
to
increment the number of days by one until the expected transaction costs in
equation
(1) of the optimization problem decreases by less than a threshold value. In
other
words, the method suggests that there is no need to extend the trading horizon
for one
more day if the benefit of extending the horizon is not significant. This
significance is
determined by an algorithm that accounts for order size, costs, and
volatility. The order-
dependent threshold adjusts so that very large orders have a low cost to share
value
ratio as threshold, whereas smaller orders have a higher cost to share ratio
as
threshold. Additionally, more volatile names have a higher threshold since
adding an
additional trading day will increase the variance term significantly. In
general, thresholds
are around 3-5 bps but can be lower for very large order sizes.
[00110] FIG. 12 illustrates the expected treading costs, standard deviation of
trading
costs, and trading horizons for different values of risk aversion for ACEO
Discretionary and
ACEO Non-Discretionary, respectively. The underlying order is to buy a)
300,000 shares
(approximately 8.5% of ADV) or b) 1,500,000 shares (approximately 42.5% of
ADV) of
stock BA (Boeing Co.). The cost estimates are based on ACEO Optimal
Strategies. Panel
33
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
A reports values in cents and Panel B in basis points. ACEO is computed based
on
information as of May 1, 2007.
[00111] According to aspects of the present invention, client-specific "alpha"
models may be included into the ACEO analysis through input of intra-day
expected
returns. However, using non-zero expected returns to generate ACEO Optimal
Strategies has one potential complication. ACEO may suggest optimal strategies
which
include orders of opposite direction to that of the overall order. For
example, consider a
sell order and assume constant positive expected intraday returns. As the
stock price is
expected to be higher at the end of the day, a profitable strategy for a
trader is to buy
shares at the beginning of the day and then sell the entire position at the
end of the day
at a higher price. Such a strategy is an optimal solution of the ACEO
optimization
problem, but users view it as undesirable since the strategy would try to
benefit from
short-term price movement predictions, which is not what ACEO is built for.
ACEO can
be constrained to require that all bin executions of the ACEO Optimal Strategy
are on
the same side of the market. Moreover, additional bin volume constraints can
be added
to the optimization problem such as trading at least 1% and at most 20% of
historic
average bin share volume in each bin.
[00112] The modeling of both temporary and permanent price impact is the most
complex and crucial part of ACE. Various ways of specifying a price-impact
function can
be found in the academic literature. The simplest method is to assume a linear
relationship between the (absolute or relative) price change caused by a trade
and the
trade's size. Typically, trade size is the number of shares executed, either
in absolute
34
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
terms or relative to the average (or median) total number of shares traded
throughout
the trade's duration.
[00113] Examples of articles that assume a linear price-order flow relation
are Kyle
(1985), Bertsimas and Lo (1998), Breen, Hodrick and Korajczyk (2002), and
Farmer, J.
D. (2002). Kyle presents one of the seminal market microstructure models that
derives
equilibrium security prices when traders have asymmetric information. In
Bertsimas and
Lo, the authors introduce a price impact model and apply stochastic dynamic
programming to derive trading strategies that minimize the expected costs of
executing
a portfolio of securities over a fixed time period. Breen, Hodrick and
Korajczyk develop
a measure of liquidity and quantify the change in a stock price by the
observed net
trading volume. Farmer studies the internal dynamics of markets - for example,
volatility clustering - proposing a non-equilibrium price formation rule.
[00114] Although initial models of price impact were linear with respect to
trading
volume, empirical evidence shows existence of non-linearities. Hasbrouck
(1991a),
(1991b) investigates non-linearities in the impact of trades on midquotes and
reports an
increasing, concave relation between price impact and order flow for several
stocks
traded on the NYSE. De Jong, Nijman and Roell (1995) use data on French stocks
traded on the Paris Bourse and SEAQ International and show that the assumption
of a
linear impact of orders on prices is incorrect. Kempf and Korn (1999) use
intraday data
on German index futures to come to the same conclusion. Zhang (1999) offers a
heuristic derivation of a non-linear market impact rule. For more discussions
of
empirical evidence concerning non-linearity of market impact, see, e.g.,
Hausman, Lo
and McKinlay (1992) or Chan and Lakonishok (1993). Nonlinear price impact
models
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
can be found, for instance, in Seppi (1990), Barclay and Warner (1993), Keim
and
Madhavan (1996), and Chen, Stanzl and Watanabe (2002). While Seppi, and Keim
and
Madhavan focus on the different impacts of block trades and market trades on
prices,
Barclay and Warner justify the non-linearity in the price-order flow relation
by the
"stealth-trading" hypothesis. This hypothesis claims that privately informed
traders
concentrate their trades in the medium size range. Since medium-size trades
are
associated with informed trading, larger trades add relatively little
additional information.
This results in a concave price-order flow relation.
[00115] ACEO supports two different price impact models, serving both the U.S.
and international markets - ACE/1 and ACE/2. Both methodologies belong to the
non-
linear class of models discussed above. ACEO allows for non-linear temporary
and
permanent price impact functions.
[00116] ACE/1 uses an enhanced version of the original ACEO price impact
model. The original model assumed that price impact is a linear function of
trade size,
with coefficients based on stock-specific volume and volatility estimates.
While this
original version was only applicable for relatively small orders not higher
than 30% of
the stock's ADV, the enhanced ACE/1 methodology provides meaningful
transaction
cost estimates beyond a 30% of ADV order size.
[00117] The ACE/2 price impact model is a sophisticated
mathematical/econometric model that is in line with recent academic empirical
findings.
It uses an econometric technique to estimate price impact functions based on
market
tick data. This technique is at the core of ACE/2 and depends on several stock-
specific
parameters that are estimated daily and monthly using market data for every
stock in
36
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
the ACEO universe. Methods developed by the ITG Financial Engineering group
provide accurate estimates for different segments of the universe (exchange-
specific
and by liquidity group). This task is most challenging for illiquid stocks and
varying
methodologies are applied for segments of stocks with different liquidity
characteristics.
Permanent price impact coefficients are estimated based on one year's of tick
data
similar to the method in Hasbrouck and Seppi (2001). In particular, we
aggregate
trading for each stock over 30-minute intervals and measure price changes
using the
quote mid-points at the beginning and end of each interval. The observed price
changes
(normalized by the historical volatility for the bin) are regressed against
the
corresponding trade imbalances and approximated by a concave, bin-specific
function.
Assuming market equilibrium in the ACEO framework, the resulting functions can
be
used to forecast the accumulated price impact within a 30-minute interval
caused by
partial fills of the order.
[00118] Figs. 13 through 16 show the empirical and theoretical ACEO permanent
price impact functions for bin 1 for four different stock segments: the most
liquid U.S.
Listed stocks, all Listed stocks, the most liquid OTC stocks, and all OTC
stocks. The
graphs show that the empirical functions become noisier when one restricts the
stock
universe. Nevertheless, all smoothed theoretical functions exhibit the same
behavior
and they can be characterized by three parameters: the slope s, the value x
that
represents the order size at which concavity starts and the concavity
parameter alpha.
Empirical evidence suggests that this behavior holds for all liquidity groups
and all time
intervals of the day.
37
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[00119] FIG. 13 shows the empirical permanent price impact function in bin
1(9:30
a.m. - 10:00 a.m.) for the most liquid, U.S. Listed stocks (solid line). The
empirical
permanent price impact function is obtained by segmenting the observations in
trade
imbalance groups and then taking averages in each group. The empirical
permanent
price impact is linear until some point when it becomes concave. This behavior
is the
same for all time intervals, liquidity groups, and markets and can be observed
for both
permanent and temporary price impacts. Consequently, all theoretical price
impact
functions in ACEO are characterized by three parameters: the slope s, the
value x that
represents the order size at which concavity starts, and the concavity
parameter alpha.
The dashed line shows the fitted theoretical permanent price impact function.
[00120] FIG. 14 shows the empirical permanent price impact function in bin 1
(9:30
a.m. - 10:00 a.m.) for the all U.S. Listed stocks (solid line).The empirical
permanent
price impact function is obtained by segmenting the observations in trade
imbalance
groups and then taking averages in each group. The empirical permanent price
impact
is linear until some point when it becomes concave. This behavior is the same
for all
time intervals, liquidity groups, and markets and can be observed for both
permanent
and temporary price impacts. Consequently, all theoretical price impact
functions in
ACEO are characterized by three parameters: the slope s, the value x that
represents
the order size at which concavity starts, and the concavity parameter alpha.
The dashed
line shows the fitted theoretical permanent price impact function. Compared to
FIG. 13,
the empirical permanent price impact function is much smoother due to the
aggregation
over all U.S. Listed stocks.
38
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[00121] FIG. 15 shows the empirical permanent price impact function in bin 1
(9:30
a.m. - 10:00 a.m.) for the most liquid, U.S. OTC stocks (solid line). The
empirical
permanent price impact function is obtained by segmenting the observations in
trade
imbalance groups and then taking averages in each group. The empirical
permanent
price impact is linear until some point when it becomes concave. This behavior
is the
same for all time intervals, liquidity groups, and markets and can be observed
for both
permanent and temporary price impacts. Consequently, all theoretical price
impact
functions in ACE are characterized by three parameters: the slope s, the
value x that
represents the order size at which concavity starts, and the concavity
parameter alpha.
The dashed line shows the fitted theoretical permanent price impact function.
[00122] FIG. 16 shows the empirical permanent price impact function in bin 1
(9:30
a.m. - 10:00 a.m.) for the all U.S. OTC stocks (solid line). The empirical
permanent price
impact function is obtained by segmenting the observations in trade imbalance
groups
and then taking averages in each group. The empirical permanent price impact
is linear
until some point when it becomes concave. This behavior is the same for all
time
intervals, liquidity groups, and markets and can be observed for both
permanent and
temporary price impacts. Consequently, all theoretical price impact functions
in ACE
are characterized by three parameters: the slope s, the value x that
represents the order
size at which concavity starts, and the concavity parameter alpha. The dashed
line
shows the fitted theoretical permanent price impact function. Compared to FIG.
13, the
empirical permanent price impact function is much smoother due to the
aggregation
over all U.S. OTC stocks.
39
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[00123] FIG. 17 illustrates the intraday pattern of the slopes of the
permanent price
impact functions for U.S. Listed stocks. The stocks are segmented into 10
different
liquidity groups. Stocks in all liquidity groups show the same intraday
pattern. The price
impact is the largest in the morning and is relatively low around noon and at
the dose.
[00124] FIG. 18 illustrates the intraday pattern of the slopes of the
permanent price
impact functions for Euronext stocks. Euronext is the combined market of
France,
Belgium, Netherlands and Portugal. The stocks are segmented into six different
liquidity
groups. Stocks in all liquidity groups show the same intraday pattern. The
price impact
is small in the morning, around noon, and at the close.
[00125] Extensive research and testing with U.S. and international execution
data
have demonstrated the accuracy of the approach for orders up to 100% ADV. The
price
impact methodology is available for the U.S. market and the most liquid
international
markets (21 countries in total). FIG. 19 lists the countries currently covered
by different
ACE modules, ACE/1 and ACE/2.
[00126] In ACE/2, the magnitude of price impact for each security and order
size is
defined by a quarterly calibration to ITG's Peer Group Database. As such, the
price
impact functions are sensitive to the orders contained in the database. Since
the
database is extremely large and comprehensive, it contains executions
representing not
only a wide spectrum of sizes, brokers, execution venues, and stock
characteristics, but
a broad range of trading behavior stemming from investment management styles,
market conditions, trade motivations, and news events. This richness of the
dataset
allows the unique opportunity to provide transaction cost estimates that
reflect more
than a "market average" trading behavior.
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[00127] For those seeking cost estimates that reflect what market participants
in
aggregate pay, a dataset including all orders is appropriate. The suitability
of each of
these estimates is guided by the nature of the orders to be benchmarked, and
will vary
by institution and within an institution, by manager or investment style.
[00128] To accommodate the need for two benchmarks for identical orders
(besides the amount of discretion), starting with ACE/2.3, ACE/2 has the
ability to
provide two different cost estimates - one based on orders that have been
fully
executed no matter how the market conditions were and another based on all
executed
orders. From a pre-trade perspective, the ACEO Non-Discretionary estimate is
highly
suitable for vetting trading strategies and determining the feasibility of
executing an
order in its entirety. The more general ACEO Discretionary cost estimate
provides a
number that is suitable for comparing incurred transaction costs with what
other
participants experience. Systematically under- (or over-) performing compared
to this
number might suggest a trend in an institution's competitiveness. From a post-
trade
perspective, the choice of price impact models should be guided by the
prevailing
nature of the order. For example, orders that require immediate and continuous
trading
until completion should be compared against a cost estimate derived from a
price
impact model that reflects determined, non-opportunistic trading (ACEO Non-
Discretionary). However, an exception to this might be if the impetus for
order creation
frequently results from an observation of favorable market conditions or if
orders are
often not fully executed.
[00129] The associated price impact coefficients for ACEO Non-Discretionary
and
ACEO Discretionary are derived from different subsets of the same peer group
41
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
database. For the ACE Discretionary model, the entire database of orders
minus
those eliminated by outlier filtering is included in the calibration process.
For the ACE
Non-Discretionary model, a sophisticated set of heuristics is used to
eliminate database
participants that exhibit opportunistic trading. These methods focus on
identifying
participants whose orders do not meet minimum transaction cost requirements
with
respect to increasing order size. More precisely, all orders of clients who
have
unusually low average transaction costs for a given exchange, liquidity group,
and order
size segment are filtered out. Liquidity groups are defined based on the
deciles of the
average daily dollar volume distribution from all stocks. Order size segments
are
defined as 0-1 %, 1-5%, 5-10%, 10-25%, 25-50% and >50% of average daily share
volume. The grouping is justified by the fact that different accounts or
portfolio
managers can trade very differently within the same firm. Actual average costs
of a
client are considered to be abnormally low (signaling opportunistic trading)
if they are
lower than a cutoff for the specific segment. The cutoff is determined by two
thresholds:
a) based on a certain cutoff that equals the average half spread for all
orders multiplied by a certain factor for the given segment (e.g. the factor
is 1 for order
sizes around 15% of ADV),
b) based on the average realized costs of all market participants.
[00130] If the average trading costs of a client is less than both of the two
thresholds determined by a) and b) above, the client's trading styie for this
segment is
classified as opportunistic and is filtered out for ACE Non-Discretionary.
[00131] FIG. 20 and FIG. 21 plot the average realized costs curves that are
associated with ACE Discretionary and ACE Non-Discretionary along with the
42
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
average realized cost curve for opportunistic orders for Listed and OTC
stocks,
respectively. In both charts it is apparent that opportunistic orders are very
different,
they have very low costs, often close to zero and costs do not increase with
order size.
The cost curve associated with ACEO Non-Discretionary is above the cost curve
associated to ACEO Discretionary, as expected. Excluding the opportunistic
orders
pushes the cost curve up. As discussed above, the difference in the curves is
bigger the
larger the order size is. It is likely that the larger an order is, the more
care is applied
and the more discretion is given to the trader.
[00132] The underlying execution data is the ITG PEER GROUP Database during
the period from January 2005 to December 2006.
[00133] FIG. 22 and FIG. 23 show the difference in cost estimates for Atlantic
Tele-Network Inc. (ATNI) and Boeing Co. (BA) using ACEO Non-Discretionary and
ACEO Discretionary for various order sizes. In FIG. 22, the cost estimates are
based on
a VWAP by Horizon Strategy with a one-day trading horizon. As expected,
transaction
costs for orders that need to be completed are higher than those that reflect
a market
average amount of opportunistic trading. In FIG. 23, the cost estimates are
based on a
VWAP By Participation Strategy with 10% participation rate. As a result,
orders can
span multiple days. Compared to FIG. 22, the cost estimates are higher for
very small
orders, but lower for larger orders. The one-day horizon in FIG. 22 forces the
execution
of an order into one day even if for larger sizes. This explains the higher
costs in FIG.
22 for larger orders compared to FIG. 23. For very small orders, the logic
works the
other way around. Whereas the one-day horizon in FIG. 22 allows for the order
to be
spread over the entire day, the 10% participation rate in FIG. 23 forces the
execution in
43
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
the early half-hour intervals of the trading day. This leads to higher cost
estimates for
two reasons. First, the trading is concentrated in the early bins and at 10%
participation
rate may be much higher than the one-day horizon trading rate in FIG. 22.
Second,
spread costs are highest early in the morning (see FIG. 3), and thus the 10%
participation strategy incurs those higher spread costs early in the morning.
There is
one more observation in FIG. 23 that needs explanation. For ATNI, the ACEO Non-
Discretionary cost estimates are higher declining in order size for he very
smallest order
sizes. The explanation, again, is due to the fact, that for small orders, the
10%
participation rate will imply full execution of the order in the early
morning, thereby
incurring the spread costs that are highest in the early morning. By
increasing the order
incrementally, cost estimates actually go down since the costs due to spread
costs are
declining as the order is spread more and more into the day outweighing any
price
impact costs that arise with larger order size. This effect subsides and the
effect of
larger price impact for larger orders takes over at a certain order size
resulting in the
usual increasing cost function. For ACEO Discretionary, this pattern is not
observed
since opportunistic traders may use limit orders and time their trading such
that the
spread costs do not have an impact on their costs and the lower costs of the
opportunistic traders outweighs the effect from the non-opportunistic traders.
[00134] Generally, all buyer- (seller-) initiated orders are expected to be
executed
at the prevailing ask (bid) price. However, a trader may often achieve a
better execution
price and, therefore, realize a price improvement. Price improvement may
appear
simply because the market moved favorably during the time it took to route the
order to
the exchange, resulting in a lucky saving. But there are also other more
sophisticated
44
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
market microstructure theories why price improvement occurs. An excellent
overview
can be found in Rhodes-Kropf (2002). The discussion there is focused mostly on
price
improvement in dealership markets. Petersen and Fialkowski (1994) and Ready
(1999)
explain the existence of price improvement in auction type markets like the
NYSE
through hidden limit orders or stopped orders. For details about hidden limit
orders and
how to predict the volume executed against hidden limit orders for different
market
conditions, see e.g., Bongiovanni, Borkovec and Sinclair (2006).
[00135] The ACE Price Improvement model allows users to quantify the price
improvement of small size orders for different exchanges and values of order
side, size,
and liquidity. The model is based on ITG proprietary execution data for U.S.
and the ITG
PEER GROUP Database for international orders, respectively. These sources
provide
the necessary information to obtain market prices and to measure price
improvement at
any particular moment of trade execution. Not surprisingly, the results
indicate that price
improvement can be very different for quote- and order-driven stock markets.
[00136] Calculation of relative price improvement for different exchanges,
trade
sides, trade sizes, and groups of liquidity can be made the equation:
(PQ - P)
R=8=
(pask pbid ) (5)
[00137] where p is the trade price, pbid and pask are the prevailing bid and
ask
quotes, respectively, pQ = pask and b= 1 for buys, pQ = pbid and 6 =-1 for
sells. Such
a parameter has a very clear interpretation. For relatively small trades the
value of R
usually lies between 0 and 0.5. If a buy (sell) trade was executed at the ask
(bid) price,
R is equal to 0; i.e. there was no price improvement.
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[00138] FIG. 24 demonstrates that the average empirical relative price
improvement for stocks traded on the NYSE depends on trade size and trade
side. The
graph is based ITG proprietary execution data for June 2006. Highest average
relative
price improvement occurs for the smallest trades and decreases as trade size
increases.
[00139] FIG. 24 reports the average empirical relative price improvement for
stocks traded on the NYSE depending on trade size and trade side. Relative
price
improvement is defined in Equation (5) of this document. It lies between 0 and
1, with 0
indicating no price improvement and 1 indicating an execution at the other
side of the
spread. The graph is based on ITG proprietary execution data for June, 2006.
The
highest average relative price improvement can be observed for orders in size
of less
than 100 shares. The larger the order size, the less average relative price
improvement
can be observed. On average, sell trades get more price improvement than buy
trades.
[00140] FIG. 25 compares average empirical relative price improvement for
stocks
traded on the NYSE that belong to different liquidity groups. The plot shows
that there is
almost a linear relation between average relative price improvement and
liquidity.
Relative price improvement is the highest for the most liquid stocks and the
lowest for
the most illiquid stocks. However, note that price improvement in absolute
terms can be
still highest for illiquid stocks due to the generally much larger spread.
Sell trades, on
average, obtain more price improvement than buy trades.
[00141] As discussed in the previous sections, the execution of orders can be
thought of as a trade-off between the risk of delayed execution and the cost
of
immediacy (see also, Hasbrouk and Schwartz (1988)). Much research has focused
on
46
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
the optimal execution of orders under various assumptions. Various forms of
market
impact models have been considered by practitioners, using theoretical or
empirical
methods to develop a set of market impact functions, both temporary and
permanent
(e.g., ACE/1, ACE/2, Kissell and Glantz (2003), or Almgren et al. (2003)). A
common
feature of these approaches is the assumption that the uncertainty in
transaction costs
can be represented entirely by the volatility of the security's return. The
implication of
this assumption is that there is no interplay between trading activity and a
security's
return volatility. This requires that the market in the security is near
equilibrium during
trading, that is, the security's return volatility remains constant while the
return itself is
affected by the market impact due to the trading. The assumption of
independence of
the moments of the return distribution and trading seems unrealistic. Almgren
(2003)
makes some important advances in the study of the interaction between trading
activity
and observed volatility. He derives optimal execution strategies for cases
where
volatility increases linearly with trading rate. ACEO takes a different
approach, rather
than modeling a security's return volatility conditional on trading, ACEO
models the
uncertainty in transaction costs directly as discussed in what follows.
[00142] Typically, a portfolio manager will construct a portfolio on the basis
of net
returns (i.e., gross alpha less transaction costs). Such a model provides not
only
expected transaction costs, but also an uncertainty measure associated with
it. Often, a
moderately volatile stock will exhibit uncertainty of equal or even much
greater
magnitude than the expected costs, so a good measure of the uncertainty in
transaction
costs resulting from the security's return volatility under liquidity pressure
is crucial to an
accurate transaction cost model. When analyzing ex-post trading performance,
this
47
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
same uncertainty about transaction cost estimates is used to determine the
quality of
execution. A trading desk manager may ask: "Did 67% of trading costs fall
within one
standard deviation of the expected trading costs?" Basing the answer to this
question
on a security's return volatility estimates, rather than the actual expected
distribution of
transaction costs will be misleading due to the described dependence between
return
volatility and trading.
[00143] A second concern is that most previous work on optimal trade execution
has assumed constant, normal distributions of security returns during trading.
We have
shown that a large cross-section of actual executions' exhibit fat tails and
skewness not
accurately described by a normal distribution. Instead, we find that the
distribution of
transaction costs can be accurately modeled with an asymmetric generalized t-
distribution. The generalized t-distribution was introduced by McDonald and
Newey
(1988) and the skewed extension of it was proposed by Theodossiou (1998). The
family
of asymmetric generalized t-distributions is very flexible and includes five
parameters:
two parameters p and q define the general shape of the distribution (FIG. 49
illustrates
some examples of generalized t-distributions with different choices of p and
q), one
parameter a defines the asymmetry of the distribution and the final two
parameters are
location and scale parameters that determine the mean and variance of the
distribution.
The generalized asymmetric t-distribution contains many families of
distributions,
amongst them are the normal distributions (p=2 and q-> oo) and the Student's t-
distributions (p=2 and q = 2,6, where 8 denotes the degree of freedom of the
Student t-
distribution).
From ITG's Peer Group Database.
48
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[00144] FIG. 26 illustrates different generalized t-distributions given the
choice of
the parameters p and q. It is well-known that one can obtain the regular
Student's t-
distribution by setting p=2. As a consequence, p=2 and q-> oo yield the normal
distribution.
[00145] The ACEO transaction cost distributions are generalized asymmetric t-
distributions with fixed, order-independent coefficients p, q, and a while the
location and
scale parameters reflect the expected cost of the order and the security's
return
standard deviation over the trading horizon adjusted by the order size
relative to the
security's ADV. The adjustment is in line with Almgren (2003) and empirical
evidence
that predicted standard deviations of transaction costs solely based on the
security's
return are lower than the empirical standard deviations. The adjustment of the
standard
deviation and the shape and asymmetry coefficients are derived from ITG PEER
GROUP data similarly as described in Arellano-Valle et al. (2004).
[00146] FIG. 27 presents the fit of the empirical distribution of the z-scores
of all
actual costs with the ACEO z-score distribution (determined by the three
parameters p,
q and a). For illustration purpose we have added some other calibrated
theoretical
distributions. Clearly, the generalized t-distribution outperforms all other
distributions.
Statistical techniques such as the Kolmogorov-Smirnoff test confirm this fact.
[00147] FIG. 27 compares the aggregated distribution of the z-scores of actual
peer group database costs with four different calibrated distributions: the
normal
distribution, the asymmetric t-distribution, the symmetric generalized t-
distribution and
the asymmetric generalized t-distribution. Both the normal and the asymmetric
t-
distribution do not fit the empirical distribution well. The asymmetric
generalize t-
49
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
distribution captures all the observed properties. It is heavy-tailed,
leptokurtic and
asymmetric (the median is smaller than the mean).
[00148] In summary, the ACEO cost distributions are characterized by three
fixed
parameters, the expected transaction costs and the standard deviation of the
transaction costs. However, since the cost distributions are not normal
distributions, one
needs to use care when constructing confidence intervals based on mean and
standard
deviation. The usual interpretation that mean +/- one standard deviation
contains two
thirds of the observation no longer applies. Consequently, it is beneficial to
also look at
percentiles of the distribution. The percentiles of the cost distribution for
a given
scenario are part of the output of ACEO.
[00149] As for any model, the key question for ACEO is how well the model
actually performs. The accuracy of the model is controlled and validated
through a
process of calibration and statistical testing. The goal of calibration is to
tune the price
impact coefficients derived from market tick-data to achieve an alignment with
realized
transaction costs from a large database of known orders. Statistical testing
is used to
ensure that the model is returning unbiased results (i.e., costs that are not
systematically over- or underestimated.)
[00150] Each quarter, ACEO is calibrated to ITG's Peer Group Database. A
moving two-year span of data is used, comprised of (as of December 2007)
approximately seven trillion U.S. dollars in trades from over 140 large
investment
management firms. For more information about the underlying data see FIG. 53
for the
most important countries of the ACEO universe.
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
[00151] FIG. 28 reports descriptive statistics of the data for the
calibration/testing
of the ACEO model for some of the markets in the ACEO universe. The statistics
are
based on the time period from January 2004 to December 2006. Reported are the
number of executions, the number of clusters (or order decisions), the volume
of the
executions in local currency, the number of stocks executions are recorded
for, and the
number of clients in ITG's Peer Group Database. The countries are sorted by
decreasing number of executions.
[00152] Establishing a suitable data set for calibration and testing is a
difficult
endeavor for several reasons. Firstly, execution data often do not contain as
much
detailed information as desirable. For example, execution and decision times
might be
missing or there is no clear declaration if the underlying order was a market
or a limit
order. Secondly, transaction costs depend on execution strategies and these
strategies
are, in most cases, not formalized by traders and certainly not recorded. Due
to
numerous factors (e.g., market conditions, work load, explicit instructions
from portfolio
managers) it is very likely that traders execute similar trades very
differently over the
course of a year.
[00153] Finally, an additional challenge exists in finding an approach to
discount
significant market and/or stock-specific movements, allowing for the
measurement of
the pure unperturbed magnitude of transaction costs. To this end, ITG
carefully
establishes a methodology that reflects the needs of the calibration and
testing
processes, while being sensitive to challenges presented by the data.
[00154] Since investment managers' orders are often broken into smaller orders
or
trades, an aggregation must be performed before arriving at a basic order unit
suitable
51
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
for analyzing trading activity, its effect on prices and, thus, comparison
with ACE
average cost estimates. To perform this aggregation, trade packages (ex-ante
orders)
are created that correspond to groups of trades where the same investment
manager is
in the market for a stock (buying or selling) over a sustained period of time.
[00155] The clusterization concept is in line with academic literature (see
e.g.,
Chan and Lakonishok (1995)) as well as industry practice. The entire sequence
of
trades (ex-ante order) is treated as the basic unit of analysis in order to
determine price
impact and execution costs of institutional trading. In particular, a "buy ex-
ante order" is
defined to include the manager's successive purchases of the stock. The order
ends
when
(a) the manager stays out of the market for at least one day,
(b) the manager does not execute more than 2% of ADV,
(c) there are no other trades that have been placed as an order within the
execution
horizon of the package.
[00156] "Sell ex ante orders" are defined analogously. For each ex-ante order,
the
trading aggressiveness (participation rate) and the average execution price is
determined. Since execution time stamps are generally not reported, it is
assumed that
each ex-ante order has been executed according to a VWAP strategy with the
empirically estimated participation rate. In most cases, this assumption is
reasonable
since large institutions are often measured against the VWAP benchmark.
[00157] The transaction costs per share are defined as the difference between
the
average execution price and the opening price of the order placement date (the
benchmark price). The sign (positive or negative) of the difference is used so
that a
52
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
positive value represented a bad outcome. For each ex-ante order in the data
set, the
realized transaction costs are computed. Also calculated, using the parameters
of the
ACEO model and the actual trading strategy for each order, are the estimated
expected
transaction costs. This enables a one-to-one comparison between actual and
estimated
transaction costs.
[00158] For model calibration and testing, average actual costs and ACEO
estimates are computed for the data set, segmented by size relative to ADV, by
exchange, and by liquidity group. More specifically, for a given exchange and
liquidity
group, orders are subdivided into the following different size categories: 0-
1%, 1-2%, 2-
3%,... , 98-99%, 99-100%.
[00159] A two-step regression approach can be applied to ensure that average
actual costs and ACEO cost estimates coincide. Loosely speaking, the
calibration
procedure adjusts the price impact coefficients in such a way that the average
ACEO
cost estimates fit to the actual average costs. The adjustment is applied
uniformly
across all bins in order to avoid destroying the intra-day relationship of the
price impact
coefficients. As a consequence, low actual average costs will imply low price
impact
coefficients and therefore low ACEO cost estimates. FIGs. 29 to 34 serve as
examples
for the goodness-of-fit of empirical cost curves from the ITG PEER GROUP
Database
and the calibrated ACEO model.
[00160] FIGs. 29 and 30 show equally- and dollar-weighted average empirical
costs and ACE/2 Discretionary cost estimates for different order sizes for all
U.S. trades
in the ITG PEER GROUP Database from January 2005 to December 2006. The charts
53
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
demonstrate a very good fit for the ACE/2 Discretionary model. Similar fits
can be
observed for all other ACE/2 countries and are available upon request.
[00161] FIGs. 31 FIG. 32 show equally- and dollar-weighted average empirical
costs and ACE/2 Non-Discretionary cost estimates for different order sizes for
all U.S.
trades in the ITG PEER GROUP Database from January 2005 to December 2006. The
charts demonstrate a very good fit for the ACE/2 Non-Discretionary model.
Similar fits
can be observed for all other ACE/2 countries and are available upon request.
REFERENCES
[00162] The following publications were referenced throughout the document
above. The content of these publications are incorporated herein by reference
for the
purpose as used.
Almgren, R. (2003) Optimal execution with nonlinear impact functions and
trading-enhanced
risk, Applied Mathematical Finance, 10, 1-18.
Almgren, R. and Chriss, N. (2000) Optimal execution of portfolio transactions,
Journal of Risk,
3, Winter 2000/2001, 5-39.
Almgren, R., Thum, Ch., Hauptmann, E. And Li, H. (2003) Direct estimation of
equity market
impact, http://www.courant.nyu.edu/ almgren/papers/costestim.pdf.
Arellano-Valle, R. and G6mez, H. and Quintana, F. (2004). A New Class of Skew-
Normal
Distributions, Communications in Statistics, Series A, 33, 1465-1480.
Barclay, M. J. and Warner, J. B. (1993) Stealth trading and volatility,
Journal ofFinancial
Economics, 34, 281-305.
Berkowitz, S., Logue, D. and Noser E. (1988) The total cost of transactions on
the NYSE,
Journal ofFinance, 41, 97-112.
Bertsimas, D. and Lo, A. W. (1998) Optimal control of execution costs, Journal
of Financial
Markets, 1, 1-50.
Bongiovanni, S., Borkovec, M. and Sinclair, R. (2006) Let's play hide-and-
seek: the location and
size of undisclosed limit order volume, Journal of Trading, Summer 2006, 34-
46.
54
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
Borkovec, M. and Heidle, H. (2007) The magic of hindsight: creating a post-
trade transaction
cost estimate based on realized market conditions, ITG Inc. Research Report.
Breen, W.J., Hodrick, L.S. and Korajczyk, R.A. (2002) Predicting equity
liquidity, Management
Science, INFORMS, 48, 470-483.
Burghart, G., Hanweck, J. and Lei, L. (2006) Measuring Market Impact and
Liquidity, Journal of
Trading, Fall 2006, 70-84.
Chakravarty, S., Panchapagesan, V. and Wood R.A. (2002) Did decimalization
hurt institutional
investors? Journal of Financial Markets, 4, 400-420.
Chan, L.K.C. and Lakonishok, J. (1993) Institutional trades and intraday stock
price behavior,
Journal ofFinancial Economics, 33, 173-199.
Chan, L.K.C. and Lakonishok, J. (1995) The behavior of stock prices around
institutional trades,
Journal ofFinance, 50, 1147-1174.
Chan, K., Christie, W. and Schultz, P. (1995a) Market structure and the
intraday pattern of bid-
ask spreads for Nasdaq securities, Journal of Business, 68, 35-60.
Chan, K., Chung, P. and Johnson, H. (1995b) The intraday behavior of bid-ask
spreads for
NYSE stocks and CBOE options, Journal of Financial and Quantitative Analysis,
30, 329-346.
Chen, Z., Stanzl, W. and Watanabe, M. (2002) Price impact costs and the limit
of arbitrage,
http://students.som.yale.edu/Phd/mw239/research/Price Impact.pdf
Chung, K. H. and Van Ness, R. A. (2001) Order handling rules, tick size, and
the intraday
pattern of bid-ask spreads for Nasdaq stocks, Journal ofFinancial Markets, 4,
143-161.
De Jong, F., Nijman, T. E. and Roell, A. (1995) A comparison of the cost of
trading French
shares on the Paris Bourse and on SEAQ International, European Economic
Review, 39, 1277-
1301.
diBartolomeo, D. (2006) Building a better bear trap - new concepts in cost and
impact modeling,
Journal ofAutomated and Algorithmic Trading, July 2006, 18-21
Domowitz, I., Glen, J. and Madhavan, A. (2002) Liquidity, volatility and
equity trading costs
across countries and over time, International Finance, 4, 221-256.
Domowitz, I. and Yegerman, H. (2005) Measuring and interpreting the
performance of broker
algorithms, ITG Inc. Research Report.
Farmer, J. D. (2002) Market force, ecology, and evolution, Industrial and
Corporate Change, 11,
895-953.
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
Foster, F. D. and Viswanathan, S. (1993) The effect of public information and
competition on
trading volume and price volatility, Review ofFinancial Studies, 6, 23-56.
Harris, L. (1986) How to profit from intradaily stock returns, Journal
ofPortfolio Management,
2, 61-65.
Hasbrouck, J. and Schwartz, R. A. (1988) Liquidity and execution costs in
equity markets,
Journal ofPortfolio Management, 14, 10-17.
Hasbrouck, J. (1991 a) Measuring the information content of stock trades,
Journal of Finance, 66,
179-207.
Hasbrouck, J. (1991b) The summary informativeness of stock trades: an
econometric analysis,
Review ofFinancial Studies, 4, 571-595.
Hasbrouck, J. and Seppi, D. J. (2001) Common Factors in Prices, Order Flows
and Liquidity,
Journal ofFinancial Economics, 59, 383-411.
Hausman, J. A., Lo, A. W. and McKinlay, A. C. (1992) An ordered probit
analysis of transaction
stock prices, Journal of Financial Economics, 31, 319-379.
Huberman, G. and Stanzl, W. (2005) Optimal liquidity trading, Review of
Finance, 9, No. 2, 165-
200.
ITG Inc. (2007) Intraday parameter distributions for world equity markets, ITG
Financial
Engineering, Technical Report.
ITG Inc. (2007) ITG Risk Models - Version 3, ITG Inc. White Paper.
Jain, P. and Joh, G.-H. (1988) The dependence between hourly prices and daily
volume, Journal
of Financial and Quantitative Analysis, 23, 269-284.
Karpoff, J. M. (1988) Costly short sales and the correlation of returns with
volume, Journal of
Financial Research, 11, 173-188.
Keim, D.B. and Madhavan, A. (1996) The upstairs market for large-block
transactions: analysis
and measurement of price effects, Review of Financial Studies, 9, 1-36.
Kempf, A. and Korn, O. (1999) Market depth and order size, Journal of
Financial Markets, 2,
29-48.
Kissell, R. and Glantz, M. (2003) Optimal trading strategies: quantitative
approaches for
managing market impact and trading risk, American Management Association.
Kyle, A. S. (1985) Continuous auctions and insider trading, Econometrica, 53,
1315-1336.
56
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
Lee, C., Mucklow, B. and Ready, M. (1993) Spreads, depths and the impact of
earnings
information: an intraday analysis, Review ofFinancial Studies, 6, 345-374.
Lert, P. (2001) Methods of Measuring Transaction Costs, Investment Guides,
Spring 2001.
Lo, A. and MacKinlay (1988) Stock market prices do not follow random walks:
evidence from a
simple specification test, Review of Financial Studies, 1, 203-238.
Madhavan, A. and Smidt, S. (1991) A Bayesian model of inraday specialist
pricing, Journal of
Financial Economics, 30, 99-134.
Madhavan, A. (2002) VWAP Strategies, Investment Guides, Spring 2002.
McDonald, J. B. and Newey, W. K. (1988) Partially adaptive estimation of
regression models via
the generalized t distribution, Econometric Theory, 4, 428-457.
Mclnish, T. and Wood, R. (1992) An analysis of intraday patterns in bid/ask
spreads for NYSE
stocks, Journal of Finance, 47, 753-764.
Munck, N. H. (2006) When Transactions Went High-Tech: A Cross-Sectional Study
of Equity
Trading Costs in Light of More Sophisticated Trading Systems, Journal of
Trading, Fall 2006,
90-103.
Perold, A. (1988) The Implementation Shortfall: Paper versus Reality, Journal
ofPortfolio
Management, 14, 4-9.
Petersen, M. and Fialkowski, D. (1994) Posted versus effective spreads: good
prices or bad
quotes, Journal of Financial Economics, 35, 269-292.
Ready, M. J. (1999) The specialist's discretion: stopped orders and price
improvement, Review of
Financial Studies, 12, 1075-1112.
Rhodes-Kropf, M. (2005) Price improvement in dealership markets, Journal of
Business, 78,
1137-1172.
Schwartz, R.A. and Steil, B. (2002) Controlling institutional trading costs:
we have met the
enemy and it is us, Journal of Portfolio Management, 28, 39-49.
Seppi, D. J. (1990) Equilibrium block trading and asymmetric information,
Journal ofFinance,
45, 73-94.
Spierdijk, L., Nijman, T. E., van Soest, A. H. O. (2004) Price dynamics and
trading volume: a
semiparametric approach, http://papers.ssrn.com/sol3/papers.cfm?abstract
id=512342.
Teitelbaum, R. (2003) Know a Fund's' Cost? Look Deeper, The New York Times
Company,
February 9, 2003.
57
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
Theodossiou, P. (1998) Financial Data and the Skewed Generalized T
Distribution, Management
Science, 44, 1650-1661.
"Transaction Costs - A Cutting-Edge Guide to Best Execution" (2001) Investment
Guides,
Spring 2001, edited by Brian R. Bruce, Institutional Investor Inc.
"Transaction Performance - The Changing Face of Trading" (2002) Investment
Guides, Spring
2002, edited by Brian R. Bruce, Institutional Investor Inc.
Yang, J. and Jiu, B. (2006) Algorithm selection: a quantitative approach,
Algorithmic Trading II,
edited by Brian R. Bruce, Institutional Investor Inc.
Zhang, Y. (1999) Toward a theory of marginally efficient markets, Physica A,
269, 30-44.
[00163] Systems, processes, and components described in this document may be
implemented using one or more general purpose computers, microprocessors, or
the
like programmed according to the teachings of the present specification, as
will be
appreciated by those skilled in the relevant art(s). Appropriate software may
be
available that may be customized or used off-the-shelf to perform one or more
aspects
of the present invention. Further, aspects of the present invention can be
implemented
with one or more computer program modules developed by skilled programmers in
readily available computer languages such as C++, PHP, HTML, XML, etc., based
on
the teachings of the present disclosure, as will be apparent to those skilled
in the
relevant art(s).
[00164] Similarly, one skilled in the art will understand that the present
invention
may be embodied in numerous configurations, including different computer
architectures, such as centralized or distributed architectures.
[00165] One or more aspects of the present invention may includes a computer-
based product, which may be hosted on a storage medium and include executable
code
58
CA 02689491 2009-12-02
WO 2008/153909 PCT/US2008/007083
for performing one or more steps of the invention. Such storage mediums can
include,
but are not limited to, computer disks including floppy or optical disks or
diskettes,
CDROMs, magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, flash memory,
magnetic or optical cards, or any type of media suitable for storing
electronic
instructions, either locally or remotely.
[00166] While this invention has been described in conjunction with specific
embodiments thereof, many alternatives, modifications and variations will be
apparent
to those skilled in the art. Accordingly, the preferred embodiments of the
invention as
set forth herein, are intended to be illustrative, not limiting. Various
changes may be
made without departing from the true spirit and full scope of the invention as
set forth
herein.
59
