JP2010529553A - System, method, and program for agency cost estimation - Google Patents

Abstract

  A method, system, and computer program product for predicting the transaction cost of portfolio execution that can be applied to any given trading strategy, or an optimal trading strategy that minimizes transaction costs. The system accepts user-defined input variables from the customer and generates a transaction cost estimate report based on these variables. Two models are used: discretionary and non-discretionary. Specific transaction cost estimation and optimization is performed that models the transaction cost of a specific trade execution based on the user's trading profile and market variables.

Description

Reference to Related Applications In accordance with 35 U.S.C. 119 (e), this application is a US Provisional Patent Application No. 60 / 924,904 filed on June 5, 2007, the entire contents of each of which are incorporated herein by reference. And claims priority to US Provisional Patent Application No. 60 / 929,929, filed July 18, 2007. This application is a continuation-in-part of pending US patent application Ser. No. 10 / 166,719, filed Jun. 12, 2002, the entire contents of which are incorporated herein by reference. Claim priority.

  The present invention relates to a system, method, and computer program product for managing execution costs. More particularly, the present invention provides mathematical / econometrics that provides a pre-trade estimate of the price impact cost of a given order that trades some shares of one or more tradeable assets such as securities. The present invention relates to systems, methods, and computer program products for creating and implementing genetic models, and optimization techniques that utilize cost estimates.

  Investment performance reflects both the investment strategy of the portfolio manager and the execution costs incurred while fulfilling the investment strategy objectives. Execution costs can be large, especially when compared to total revenue, and can thus have a significant impact on performance. Management of execution costs can determine the success or failure of a particular investment strategy. For institutional traders who trade large volumes, the implicit cost, first and foremost, the price impact of the transaction usually represents a significant portion of the total execution cost. For example, see Domowitz, Glen, and Madhavan (2002) for various definitions of cost, as well as discussion and analysis.

  Due to fragmented liquidity, algorithmic trading, direct market access, and structural and regulatory changes such as decimalization (implemented in 2001) and regulation NMS (implemented in 2007) in today's equity market, The importance of accurately measuring execution costs has increased. In addition, the recent demand of some legislators and funder advocates seeking better disclosure of brokerage fees and other execution costs has further increased their importance (see, for example, Teitelbaum (2003)). As a result, management of execution costs becomes an important issue for institutional investors whose transactions are large relative to the average daily volume.

US Provisional Patent Application No. 60 / 924,904 US Provisional Patent Application No. 60 / 929,929 U.S. Patent Application No. 10 / 166,719

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  Accordingly, there is a continuing need for new and improved systems and methods for estimating transaction costs.

  The present invention provides systems, methods, and computer program products for predicting price impact costs of trade execution that can be applied to any given trading strategy.

  In accordance with aspects of the present invention, an Agency Cost Estimator (ACE®) system, method, and computer program product are provided, which are priced for any pre-designated strategy. A first part that includes a computer-based model that allows a user to obtain an impact cost estimate and that is executed by a computer that generates an optimal trading strategy subject to some assumptions about the user's ultimate goal And a second part including a mathematical model.

  In accordance with aspects of the present invention, the model is based on a discretionary model based on all transactions, including opportunistic transactions, and non-discretionary based on non-opportunistic transactions only (i.e., not based on data related to opportunistic transactions). Including models. As a result, users of the system can use modeling that more accurately reflects their trading strategy.

  According to aspects of the invention, systems, methods, and computer program products are provided for building and complementing discretionary and non-discretionary models.

  The present invention will become more fully understood from the following detailed description of the preferred embodiments, read in conjunction with the accompanying drawings. Both the detailed description and the drawings are provided by way of example only and are not intended to limit the invention.

1 is a block diagram of a system for predicting transaction costs for proposed transaction execution according to a particular transaction strategy and a preferred embodiment of the present invention. FIG. 4 is a flow diagram of an exemplary system for estimating and optimizing transaction costs for trade execution performed in accordance with a particular trading strategy in accordance with the present invention. It is a graph which shows a price impact model. 2 is a graph showing the intraday trading volume of a security and its liquidity group. It is a graph which shows the intraday bid-a-side spread of Atlantic Telenetwork and its liquidity group. It is a graph which shows various trading strategies for buying 300,000 stocks of Boeing. FIG. 6 is a graph showing various volume-weighted average price trading strategies for buying 300,000 securities. 6 is a graph showing various distributions of transaction cost estimates. It is a graph which shows the effective frontier of transaction cost. It is a graph which shows the various optimal trading strategies for buying 300,000 stocks of securities. Figure 6 is a graph showing various neutral optimal trading strategies for various buy order sizes of securities. It is a table | surface which shows the estimated transaction cost with respect to various risk avoidance values, the standard deviation of transaction cost, and the transaction range. 3 is a graph showing empirical and theoretical permanent price impact functions. 3 is a graph showing empirical and theoretical permanent price impact functions. 3 is a graph showing empirical and theoretical permanent price impact functions. 3 is a graph showing empirical and theoretical permanent price impact functions. It is a graph which shows a daytime price impact comparison. It is a graph which shows a daytime price impact comparison. Table reporting the countries covered by the ACE model. It is a graph which shows an average empirical cost. It is a graph which shows an average empirical cost. It is a graph which shows an estimated transaction cost. It is a graph which shows an estimated transaction cost. It is a graph which shows a relative price improvement. It is a graph which shows a relative price improvement. It is a graph which shows generalized t distribution. Figure 6 is a graph showing various calibrated distributions. It is a graph which shows the comparison with estimated cost and discretionary cost. It is a graph which shows the comparison with estimated cost and discretionary cost. It is a graph which shows the comparison with estimated cost and non-discretionary cost. It is a graph which shows the comparison with estimated cost and non-discretionary cost. It is a graph which shows the comparison with estimated cost and non-discretionary cost. It is a graph which shows the comparison with estimated cost and non-discretionary cost. FIG. 5 is a table reporting descriptive statistics for ACE® calibration / test data. FIG.

  ITG INC., The assignee of the present invention, provides various tools to help investors minimize their execution costs and thus maximize their realized revenue. The present invention is directed to the features and aspects of ITG's ACE® (Agency Cost Estimator), which is a mathematical that provides a pre-trade estimate of the price impact cost of a given order. / Products that apply econometric models. ACE® can measure execution costs using the implementation shortfall technique introduced by Perold (1988), which uses average execution price and order execution start Define execution costs as the appropriately signed difference between the prevailing price of the time. This measure includes both the two most important cost components, the bid-ask spread and the price impact cost of the order. Explicit cost components such as brokerage fees can easily be added to the ACE® estimate to get the total cost of the transaction. The components and features of ACE®, including the original ACE® model, on which some aspects of the invention are based are described in US patent application Ser. No. 166,719, the entire contents of which are already incorporated herein by reference above.

The present invention can be used in conjunction with other pre-trade analysis tools in a number of ways, including:
Provide an accurate cost estimate (eg, order's expected execution cost and standard deviation of execution cost).
-Estimate the statistical characteristics of the distribution of execution costs, including the percentile and confidence interval of the distribution.
-Various pre-designated strategies (particularly volume-weighted average price (VWAP) strategy-a percentage of daily average volume, uniform strategy, ACE (R) optimized strategy), forming a pre-trade cost benchmark Evaluate trader and broker execution performance for, or any, user-specified strategies.
-Analyze how trading costs depend on trading strategies.
-Fine-tune trading strategy in terms of trading scope, aggressiveness, and other parameters.
-Recommend an optimal trading strategy that balances execution costs against uncertainty (opportunity costs) in realization costs.

  In addition, ACE® can also be used as a post-trade cost benchmark for trade performance.

Unlike many other traditional products, ACE® says that a trader or automation system typically needs to break up large orders into some small transactions to minimize price impact costs. Recognizing that includes a dynamic model. ACE® has three critical features that deserve special attention:
1. ACE® recognizes that a trader incurs a price impact cost because the transaction moves the price adversely in the market when the transaction is executed. This is the cost of requiring liquidity. Price impact has both permanent and temporary components. The permanent component is information-based. That is, it captures persistent price changes as a result of the information that the occurrence of the transaction conveys to the market. The temporary price impact is transient in nature. That is, the additional price concessions necessary to have the liquidity provider turn around the other side of the order. A permanent price impact implies that the first trade of a multi-trade order will affect the price of all subsequent sub-blocks sent to the market. Modeling this dynamic link is an important factor in calculating the price impact of a series of transactions over a period of time.
2. ACE® recognizes that there is no such thing as a “best” cost estimate for a transaction. In reality, transaction costs are a function of a trader's strategy or enforcement approach. The more aggressive the trading strategy, the higher the cost. Trading aggressiveness can be measured in terms of how quickly a trader wants to execute a trade given the size of the trader relative to normal volume. Therefore, ACE® estimates are based on a specific trading strategy.
3. ACE® can also be used to find “optimal strategies” that balance price impact costs against opportunity costs. Such an ACE® optimization strategy represents a solution to a very general optimization problem (with parameters that vary over time) for both single stock and portfolio cases. Opportunity costs are primarily due to price volatility, which creates uncertainty in the realized cost of a transaction as well as creates uncertainty about the realized return on investment. When executing an agency order, the balance between price impact and opportunity cost is selected based on the motivation for the order, which is ultimately given by the investment manager. Passive managers primarily care about price impacts, but growth or momentum managers are more concerned about opportunity costs. The investment manager's sensitivity to opportunity costs is referred to as a weight for risk, or risk aversion, as it is referred to for an investment manager's sensitivity to investment risk. ACE® is the expected cost of an agency trading strategy that optimizes the trade-off between paying price impact costs and incurring opportunity costs at a given risk avoidance level and trading scope. And estimate the standard deviation of costs. The trading range can be selected by the user, or ACE® can determine the optimal time range for a given order. In ACE®, the user can define weights for risk. To make this possible, ACE® formulates the trading problem as a multi-period stochastic control problem. The solution to this probability control problem is the optimal strategy that minimizes the weighted sum of price impact and opportunity cost. ACE® provides the expected cost and standard deviation of costs for the resulting optimal strategy. This strategy is recommended for traders who want to weight the opportunity costs associated with trading over a long time interval that matches their weight for risk.

  The ACE® model is not a purely econometric model that is calibrated based on transaction cost data. Rather, it is a structural model that uses econometrically estimated parameters. In particular, ACE® relies on stock-specific econometric models of volatility, price impact, and price improvement, and relies on risk models. In addition, a purely econometric model based on empirical data cannot provide a cost estimate for large orders (simply there are not many observations about large orders (diBartolomeo (2006)). By utilizing a structural model, ACE® alleviates this problem.

  The ACE® framework of the present invention is based on the system and method introduced in US patent application Ser. No. 10 / 166,719 filed Jun. 12, 2002.

  With reference to FIG. 1, one or more transaction cost optimization servers 11 may be provided on a communication network 10. The network 10 may be a public network or a private private network. The server 11 can be programmed with a transaction cost estimation / optimization computer program product, via the network 10, via the New York Stock Exchange (NYSE) 18, POSIT (registered trademark) intraday equity matching system 20, over-the-counter transactions ( OTC) market 22 (including but not limited to NASDAQ stock market), or electronic communications network (ECN) 24, and access to various trading institutions or exchanges.

  According to a preferred embodiment of the present invention, the server 11 is configured to allow electronic access directly from the customer via the network 10. This access can be through a personal computer (PC) 12 or a dedicated client terminal 16 that is electronically connected to the network 10 via the Internet, a dedicated line, or the like. Alternatively, the client can interact with the network via a trading desk 14 where the customer can perform transaction cost analysis. In particular, a trading desk is a user interface that provides a comprehensive agency trading service that utilizes multiple liquidity sources.

  According to a preferred embodiment of the present invention, a number of different servers 11 can be provided on the network, each server 11 executing a transaction cost analysis program, various suitable trading forums and various electronic communications. Have access to the network. The customer can submit a proposed portfolio trade execution for analysis by any particular one of the servers 11. Server 11 receives proposed portfolio trade executions from customers via network 10 and processes and analyzes the executions according to a user-selected pre-configured trading strategy algorithm being executed by server 11. The server 11 then performs transaction cost analysis and optimization, preferably sending the execution results to the customer in real time.

  By providing such a server, significant advantages are achieved over prior art systems (analysis is performed manually or by a computer with a human trader using old information). Server 11 can handle much more complex transactions, including transactions with large volumes and much more different equity. In addition, the server 11 can provide professional results for a very large number of equity, unlike traders that may focus or track only a relatively small number of equity at a time. The server according to the invention can be electronically connected via the network 10 to the real-time market information provider 15 and to sources providing historical and derivative market data, so that multiple indicators can be continuously received and received. It has yet another advantage over human traders in that it can be processed. Further, by routing proposed portfolio trading orders to the appropriate server 11, multiple transaction cost analysis requests with different desired trading strategies (eg, risk avoidance levels) can be executed simultaneously.

  FIG. 2 shows an example of a system for estimating and optimizing transaction costs for trade execution according to the present invention, where the transaction costs are estimated according to a transaction cost estimation / optimization algorithm and model. A customer who wants to perform ACE® transaction cost estimation and optimization for a proposed portfolio transaction inputs requests for analysis and sends these requests directly to the ACE® server. The ACE® server performs one or more transaction cost analysis (TCA).

  According to this method, at step 201, the customer's order specifications are retrieved. For example, a customer may want to sell 1 million shares of securities XYZ. In step 202, the customer specifies (and inputs) a value for a risk avoidance parameter (RAP). If no value is retrieved, the program sets a default value, which is preferably 0.3. In step 203, the customer specifies an optimal trading time range, for example, selling 1 million shares of XYZ securities over 7 days. At step 204, the program retrieves market parameters such as securities master information (ie, ticker symbol, CUSIP, exchange), closing price, volatility, and trading volume. At step 205, estimates are calculated for a set of customer 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 deviations of costs for various RAP values. At step 207, the customer selects from the table a pair of values (expected cost and standard deviation) that is most appropriate for a particular case, and selects a value for the RAP corresponding to the selected pair of values. At step 208, the customer enters this new RAP value (while maintaining other parameters) and sees a new set of expected costs and cost standard deviations. This establishes a range of cost estimates. In step 209, an optimal trading strategy is calculated and displayed for the parameters entered by the customer. From these, the customer can select the strategy that best fits the customer's particular situation.

  As can be seen from FIG. 2, the ACE® method and system can include a set of computer-implemented statistical models that predict the transaction costs of trade execution. In ACE®, cost is measured as the difference between the average execution price and the prevailing price at the start of order execution.

  One important aspect of ACE® is that it can be used to recommend specific trading strategies for users. ACE® balances two considerations: expected cost and standard deviation. The ACE model optimally balances the trade-off between price impact costs (considering liquidity demand) and incurred opportunity costs for user-specified weights for costs and risks, and trading scope The expected cost (E (C)) and standard deviation of costs (SD (C)) of the agency trading strategy can be estimated. This is done by expressing the transaction problem as a multi-period probability control problem. Then, the expected cost and standard deviation of the cost of the obtained optimal strategy are calculated.

  Execution costs are signed (ie, positive or negative) differences between the values of securities or securities portfolios at the beginning and end of a specified trading range. ACE® can estimate the expected cost of an agency trading strategy as follows.

  In one exemplary method, the trading range is first divided into partial bins or time periods of equal duration. Preferably, for example in the US market, ACE® considers 13 bins with a duration of 30 minutes per trading day. However, any number of bins of any duration can be used as long as the bin parameters are appropriately configured for the selected duration. A trading range may consist of multiple trading days, with an arbitrary starting bin on the first day and an ending bin on the last day. A trading order is defined by its trading range, trading side (buy or sell), size, and trading strategy (a sequence of stock quantities per bin over a given trading range). All share volume transactions specified in each bin shall be completed within each bin.

  The price improvement is a better received price than the prevailing price (ie, bid to sell order, or ask to buy order). In general, all orders initiated by buyers / sellers are expected to execute at prevailing ask / bid quotes. However, due to sudden and unforeseen market trends, buyers / sellers often receive better execution prices than the prevailing ask / bid quotes when the order is placed. These better receiving prices are defined as price improvements.

  For any given security, volume and price volatility varies significantly from bin to bin within the same trading day. Volume and volatility distributions per bin are determined statistically and taken into account when estimating transaction costs and generating optimal strategies. When estimating the transaction cost of a particular stock, ideally the volume and volatility distribution for that stock should be used, but research has shown that such a distribution can be marketed even for highly liquid stocks. It has been demonstrated that it may be unstable due to noise. Thus, as an alternative, an aggregate bin distribution of a larger number of stocks can be used. Such an aggregate distribution has been shown to be much more stable.

  The total realized transaction cost C can be defined as follows:

Where ni = total number of shares traded on day i,
the cost on day i to trade ci = ni shares,
α = Expected daily price change,
εi = random price disturbance on day i,
σ = 1 standard deviation of price change per day,
Ti = linear coefficient for price impact persistence after trading on day i,
xi = residue at the end of day i.

  The average or expected cost EC can simply be thought of as the average value of the total cost when the execution can be repeated many times (the total execution cost C is not a deterministic value or number, but a random variable or Because it is a random variable). This is due to the fact that the total execution cost depends on a number of unknown factors, including uncertain behavior of other market participants and market trends related to macroeconomic factors or stock-specific factors. This is because of the above. EC can be defined as follows:

  Where

cj = linear coefficient for the temporary price impact of bin j,
αj = standard deviation of price change in bin j,
α0 = standard deviation of price change between close and close,
γj = linear coefficient for price impact persistence after trading in bin j,
ni, j = shares traded in bin j on day i,
J = half of the bid spread spread,
~
xi, j = the remainder of the day after bin j on day i,
N = number of bins in trading range.

  In the first usage, i.e. the calculation of the cost of the pre-designated trading strategy, the predicted cost is generated using equations (2) and (3). Specifically, given a pre-specified distribution of shares over the bin trading range given by {n}, the expected price in each bin is calculated using, for example, (3) and then multiple bins The sum over (weighted by ni) is calculated using, for example, (2) to obtain the total cost. Proprietary daily risk models are used to obtain future cost variance estimates and take into account the possibility of price movements across bins.

In the second usage of ACE®, the optimal trading strategy denoted by {n *} is calculated by solving a specific optimization problem that balances the expected cost against the cost variance . In this case, the optimization problem of ACE (registered trademark) is given as follows.
PD = min {(1-λ) EC + λ * Var C}
Where λ is a non-negative parameter called risk avoidance parameter (or weight to opportunity cost) and Var C is the variance or square of the standard deviation of cost C. The weight for the opportunity cost is usually entered by the user and is a number between 0 and 1. Very low weights correspond to trading styles where opportunity costs are not a significant consideration (e.g. value traders without information), high values correspond to aggressive trading styles where trading is achieved quickly (e.g. disadvantageous) Traders who plan price movements).

  According to the present invention, ACE (registered trademark) can reliably predict a transaction cost and estimate statistical characteristics of a transaction cost for any scenario selected by a user. The ACE® estimate depends on the user's strategy and the underlying price impact model parameters. User strategy is reflected in trading style and aggressiveness. Price impact model parameters can be calibrated using owned ITG PEER GROUP data to meet the “typical” cost of large institutions. Trading style can be characterized by aggressiveness (participation rate) and level of opportunistic trading.

  Still other examples and details regarding aspects of the underlying ACE® system, method, and computer program product are disclosed in US patent application Ser. No. 10 / 166,719, filed Jun. 12, 2002. .

  The inventors have discovered that the realization cost of opportunistic traders does not match the realization cost of traders that must be executed at most times (ie non-opportunistic or non-discretionary traders). In order to better consider this discrepancy, the present invention improves upon the original ACE® invention by providing two cost estimates. One of the cost estimates is called ACE® discretion, and the other is called ACE® non-discretion.

  As the name implies, in the case of ACE® discretion, all enforcement is used to build the ACE® model (also called calibration). That is, even orders that allow traders to postpone or abandon transactions to take advantage of market conditions are used. In the case of ACE® non-discretionary, opportunistic execution is excluded from model building and execution data on orders that traders must execute regardless of whether the market conditions are favorable without having a lot of discretion Only included.

  ACE® can be implemented for equity or non-equity asset classes.

  The ACE® model can be estimated separately for each exchange in each country. This approach is necessary because transaction costs vary greatly between different countries and exchanges (see, eg, Munck (2006)).

  ACE® can distinguish between the market price, defined as the stock market price, and the average execution price at which a given bin's stock is executed. The average execution price differs from the market price because it includes temporary price impact costs and average price improvement. For small orders, this difference is typically only half of the net bid-ask spread that is the net of any price improvement. Price improvement is defined as receiving a price that is better than the prevailing price (bid for sell or ask for buy) when the order is 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 an order, and temporary price impact is the cost of requiring liquidity. Trade execution affects market prices as well as transaction prices. Large size transactions not only move the market price within the execution period, but also have a lasting effect on the market price until the end of the trading day. Such an effect is usually called a permanent price impact. Market prices are also affected by other factors that are captured in terms of stochastic disturbances. Of course, both temporary and permanent price impacts increase with the number of shares traded in the bin.

  Execution costs can be considered as a properly signed difference between the stock market price at the beginning of the trading range and the average execution price of the order. Because there are both deterministic and random factors associated with dynamic analysis, execution costs are probabilistic in nature and should be analyzed by statistical methods. Furthermore, because the optimization control problem is multi-periodic in nature, analysis also requires the use of stochastic dynamic programming.

  FIG. 3 provides an illustration of the aforementioned concepts and terms. Temporary and permanent price impact applies to both single and multiple executions. FIG. 3 shows the concept behind the ACE® price impact model for sell transactions. As suggested by the supply and demand laws, the stock execution price is lower than the pre-trade price. The larger the transaction size, the more likely the selling price will be lower. The difference between pre-trade market prices and execution prices consists of two parts: permanent and temporary price impact. A temporary price impact only affects the price of the transaction itself, but a permanent price impact has a lasting effect on the market price.

  Providing reliable estimates of model parameters presents special challenges and is in fact the most difficult aspect of creating and maintaining ACE models. Stock market dynamics are complex and subject to various institutional characteristics. For example, price impact is extremely difficult to measure when the signal-to-noise ratio induced by daytime price volatility is low, requiring complex statistical techniques to extract “useful” signals. In short, ACE® econometric implementation is the most critical element of model development.

  Preferably, all ACE® implementations include the securities master information (ticker, CUSIP / SEDOL, exchange), the closing price of the previous trading day, the volatility of each security, the average trading volume, and the bid-ask spread. Use stock specific parameters estimated from the most recent market data, including estimates.

  Preferably, the volatility is historical 60-day price volatility and daily revenue is adjusted at the VIX level. VIX is the ticker symbol for the Chicago Options Exchange Volatility Index, a measure of the implied volatility of S & P 500 index options. This represents a measure of volatility market expectations over the next 30 day period. Average turnover is estimated as the mid-day dollar turnover of the most recent 21 trading days. The bidask spread is calculated as an average daily bidask spread of 5 days weighted by time. Average volume and bid-ask spread estimation methods are selected to balance the latest trends in stock behavior against fluctuations generated by market news, revenue announcements, and other temporary factors. It is worth mentioning that any other estimation technique may be used if desired.

  Preferably, the ACE® framework is constructed such that the market price behavior of a stock can depend on its expected intraday stock earnings. By default, these revenues are set to 0, but a client-specific “alpha” model can be included in the ACE® analysis.

  In addition to estimating transaction costs for single name trades, ACE® can also be used efficiently for pre-trade and post-trade analysis of portfolios. Preferably, in all ACE® implementations, the correlation between stock returns is estimated using an ITG risk model. Depending on the stock universe in the trade list, the corresponding country, territory, or global ITG risk model is used.

In the present invention, transaction volume, price volatility, and bida spread are
-Large fluctuations within the same trading day,
-Change over time,
-Stock-specific,
-Relatively stable for very liquid securities, and
-Take into account that illiquid securities are not stable.

  Volume, volatility, and spread intraday fluctuations can be statistically measured and incorporated into ACE® cost estimates. Ideally, if you are trying to estimate the cost of a stock, you should use intraday volume, volatility, and spread distributions for that particular stock. However, studies have demonstrated that such distributions are unstable for less liquid stocks, due to both market fluctuations and share-specific fluctuations. Figures 4 and 5 show the distribution of Atlantic Tele-Network Inc. (ATNI) daytime volume and spread during some time periods. Atlantic Telenetwork Corporation randomly selected for illustrative purposes. The shares belong to the category of relatively illiquid stocks with a market capitalization of $ 394,200,000, with a central daily share volume of 50,000 shares as of May 1, 2007.

  Figure 4 shows the daytime volume patterns of Atlantic TeleNetwork (ATNI) for January, February, and March 2007. The shares are relatively illiquid stocks with a market capitalization of $ 394,200,000, and the median daily trading volume is approximately 50,000 shares as of May 1, 2007. The distribution shows some variation, especially at the beginning and end of the trading day. The thick line represents the smoothed average daytime volume distribution for all stocks belonging to the same market and liquidity group as ATNI. The average was taken over a three-month period from January to March 2007.

  Figure 5 shows the Atlantic Japan Telecom Network (ATNI) daytime bid-ask spread pattern for January, February, and March 2007. The shares are relatively illiquid stocks with a market capitalization of $ 394,200,000, and the median daily trading volume is approximately 50,000 shares as of May 1, 2007. The distribution shows some variation, especially at the beginning and end of the trading day. The bold line represents the smoothed average intraday bida spread spread for all stocks that belong to the same market and liquidity group as ATNI. The average was taken over a three-month period from January to March 2007.

  Note that in the remainder of this document, unless otherwise specified, all ACE® numbers presented in the tables and figures are based on ACE® non-discretionary embodiments. Obviously, such fluctuations in, for example, ATNI's daytime volume or spread pattern, so using the latest available distribution calculated, for example, from March data would be a good estimate for April. I can't be sure. Possible alternatives for less liquid stocks use aggregate distributions based on a significant number of stocks, for example similar stocks (NYSE / AMEX, Nasdaq) and all stocks in the liquidity group That is. These distributions are much more stable as demonstrated by the thick lines in FIGS. 4 and 5 and provide a more robust prediction. The volume, volatility, and spread distributions shall each be the average of the volume, volatility, and spread distribution across the equally weighted individual stocks. All stocks included in this distribution are equally important. This makes sense (since the main purpose of aggregation is to obtain a meaningful and stable estimate of illiquid stocks). The same approach can be applied 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 aggregate distributions are smoothed and controlled against market noise.

  In general, trading strategies can be subdivided into two categories: structured trading strategies and opportunistic trading strategies.

  Opportunistic trading strategies do not strictly follow a pre-specified trading schedule. Instead, these strategies are continually searching for liquidity and opportunities for advantageous enforcement based on real-time information. The success of such algorithms requires reliable quantitative predictions of price movements and liquidity patterns, as well as trading venues and alternative order types (discretionary limit orders, IOC (Immediate-Or-Cancel) orders, or fixed) (pegged)) in an intelligent combination. Opportunistic trading strategies work well for orders that do not need to be completed. However, it is not suitable for orders that need to be fully executed within a certain time range.

In contrast, structured or more accurately scheduled strategies are typically linked to certain benchmarks, such as volume-weighted average prices (VWAP) or implementation shortfalls, and historical daytime volume, volatility , And based on historical data and analytics underlying the strategy, such as spread patterns. At the macro level, these algorithmic trading strategies suggest how to optimally slice large orders at different time intervals within a specified range, but using additional intelligent rules, each part of the original order This is done with special consideration of the following:
-How strictly should you follow the proposed trading schedule (order timing, deviation rules)?
-Order type selection (such as limit orders, market orders, discretionary orders, and IOC orders).
-Selection of trading venues (sensible order routing to execute at the best available price and to discover undisclosed liquidity).

  Most of the rules require real-time information input and rely on models / algorithms that can be used to find the best price with minimal time constraints. See, for example, Domowitz and Yegerman (2005) or Yang and Jiu (2006) for more information on strategy classification and selection given specific goals and scenarios.

  ACE® uses trading strategies that belong to the class of structured strategies. In ACE®, a strategy is defined as a series of numbers of shares that are to be executed within an execution period according to a bin method. One bin is a 30 minute period between trading days. For example, in the United States, 9: 30-10: 00 am is bin 1 of the first day, 10: 00: 00: 30 am is bin 2 of the first day, ..., 3: 30-4: 00 am In the case of bin 13 on the first day, and a multi-day strategy, 9:30 am to 10:00 am is bin 1 on the second day, and so on.

There are some standard strategies that can be expressed in the ACE bin format.
-Instant strategy trades all stocks in the opening bin. This strategy can be invoked in ACE® by setting any of the other strategies supported by ACE® to start and end in the same bin.
-The uniform strategy shall execute the same number of shares for each bin within the trading scope. For example, if the order size is 300,000 shares and the trade should be completed between 10:00 am and 1:00 pm, the uniform strategy will increase 50,000 shares in each bin (bins 2-7). Suggest to execute. Bertsimas and Lo (1998) propose a uniform strategy to minimize the expected cost of trading a fixed number of stocks.
-Scope-based VWAP strategy. For each order entry, ACE® generates a forecast of the stock volume pattern over the desired time range (partial, full day, or multiple days). . For each order, the range-based VWAP strategy is a trading strategy that matches the underlying stock volume pattern over the desired time range and participates more actively during the period when the volume is expected to be the highest. This helps to minimize the impact of trading during periods of inactivity, and allows orders to benefit from the most liquid conditions. Figure 6 presents a range-based VWAP strategy for the trade of 300,000 shares of Boeing Co. (BA) executed between 10:00 am and 1:00 pm. Boeing selected at random for illustrative purposes. The stock is a relatively liquid stock with a market capitalization of $ 73.7 billion and a central daily share volume of 3.5 million shares as of May 1, 2007.

  Figure 6 shows various types of trading strategies for buying 300,000 Boeing (BA) shares (approximately 8.5% of ADV) between 10:00 am and 1:00 pm. The shares belong to the relatively liquid stock category, with a market capitalization of $ 73.7 billion and a central daily share volume of 3.5 million shares as of May 1, 2007. The instant strategy places all stocks in the first trading bin (bin 2, ie, 10:00 am to 10:30 am). The uniform strategy shall execute the same number of shares for each bin during the trading period. The range-based VWAP strategy and the 30% participation-based VWAP strategy match the stock's intraday volume pattern. More stocks are executed early in the morning, as daytime volume suggests.

  ADV is the central daily dollar volume for the most recent 21-day trading day. Scope-based VWAP strategies are compared to instant strategies, uniform strategies, and 30% participation-based VWAP strategies. Boeing's 300,000 shares represent approximately 8.5% of the average daily volume (ADV) as of 1 May 2007.

Figure 7 shows VWAP trading strategies with various participation rates (5%, 10%, 20%, and 30%) to buy 300,000 Boeing (BA) shares (approximately 8.5% of ADV) . The shares belong to the relatively liquid stock category, with a market capitalization of $ 73.7 billion and a central daily share volume of 3.5 million shares as of May 1, 2007. Unlike the scope-based VWAP trading strategy, the trading scope is not fixed and depends on the participation rate. The lower the participation rate, the longer it takes to fill the order.
-Participation-based VWAP strategies are defined in the same way as scope-based VWAP strategies. For each order, a trading strategy is formed by participating in proportion to the specified participation rate at the estimated daily trading volume using the underlying equity trading volume pattern. If the ratio of the order size to the average daily trading volume is greater than the participation rate, a multi-day strategy with the same intraday stock specific volume pattern is used each day. FIG. 7 presents four participation-based VWAP strategies with various participation rates (5%, 10%, 20%, and 30%) to buy 30,000 shares of BA. Trading always starts at 10:00 am (ie Bin 2). This plot shows that the higher the participation rate, the shorter the time range and thus the more aggressive the strategy.
The -ACE® optimization strategy represents a solution to a very general optimization problem (with parameters that vary over time). The ACE® model is an agency trading strategy that optimizes the trade-off balance between paying price impact costs and incurring opportunity costs (with a given level of risk avoidance and trading scope). Estimate the expected cost and standard deviation of the cost.

  The decisive problem that emerges before traders is how to define and quantify trading goals in order to achieve trading goals in an appropriate strategy. The problem is not trivial (in many cases, general trading objectives compete with each other and cannot be fully met at the same time). For example, a strategy that minimizes costs is not always the ideal solution. Traders that minimize costs by splitting transactions over a very long time range face risks from large market trends. But conversely, trading aggressively and controlling the risk implies that the order is “ahead” and usually increases costs. The optimal strategy should therefore balance both cost and risk. From this point of view, the ACE® optimal strategy is a valuable trading tool (since it provides a mathematically derived optimal solution given some model assumptions). These assumptions are discussed in detail below.

  Execution costs are susceptible to many unknown factors. These include, for example, uncertainties caused by the behavior of other market participants, and market trends related to macroeconomic factors or stock-specific factors. It is impossible to model all these factors. We therefore consider execution costs as random variables, not deterministic values or numbers. In other words, if the same strategy is repeatedly executed under the same circumstances, the same strategy may yield different results. In general, the probability distribution is characterized by some parameters. In particular, mean deviation and standard deviation are widely used in statistics as such parameters. Note that these parameters generally do not uniquely define a distribution, but given some distributions, it is sufficient to consider these two parameters to identify the distribution. A normal distribution is an example of such a widely used distribution. The average of the cost distribution can be simply interpreted as the average value of costs when the execution can be repeated many times. The standard deviation of the cost characterizes how much the cost value may deviate from the expected cost. Thus, selecting a strategy that best fits a given trading goal is equivalent to selecting a cost distribution that best fits.

Obviously, every trader prefers both lower expected costs and lower risks (standard deviation of costs). Thus, both these parameters fall into the optimization objective function. Finding the best trading strategy requires a trade-off between expected cost and cost variance. This results in the following ACE® optimization problem.
(1-λ) ・ E (C) + λ ・ Var (C) → min (4)
Where C is the total execution cost of the transaction, E (C) is the expected value of C, and Var (C) is the variance of C. λ is a risk avoidance parameter in the interval [0,1]. λ can also be considered a “weight for risk”. The optimal solution is the trading strategy that minimizes the objective function in (4) out of all strategies for a given set of trading side, trading size, trading range.

  The ACE® optimization strategy is a solution to the optimization problem in (4). It is very important to recognize that the solution depends on the transaction characteristics and the selected risk avoidance parameters. Different trading characteristics and different risk avoidance values produce different ACE® optimal strategies. It is therefore crucial to understand how to select the input to the optimization problem according to each particular situation.

  Trading side and size are usually given, but the trading scope and risk avoidance parameters can be selected by the user. To select these more effectively, it is useful to recall that a more aggressive trading strategy has a higher expected cost but lower cost standard deviation. Both shorter trading scope and higher risk aversion values correspond to more aggressive trading strategies. Figure 8 shows the probability distribution of a portion of execution costs for various risk avoidances within a fixed day range for an order to buy 300,000 shares of Boeing (BA). This plot reveals that higher risk avoidance results in lower expected costs, but results in higher standard deviation and thus greater uncertainty. Thus, the user should make a selection based on appropriate values of both the expected cost and the standard deviation of the cost.

  Figure 8 shows the various risk avoidance values (0, 0.3, 0.6, 0.9, and) for an order to buy 300,000 Boeing (BA) shares (approximately 8.5% of the average daily volume (ADV)). The distribution of non-discretionary transaction cost estimates based on 1) is shown. Distribution is based on ACE® optimal strategy with daily trading scope. This plot suggests that a larger risk avoidance choice results in a higher expected cost, but lowers the standard deviation of costs, and thus potentially lower opportunity costs.

  The following example demonstrates how to make such a selection. Again, suppose you need to buy 300,000 Boeing (BA) shares a day. Various strategies can be used to trade this order, some strategies are more passive and some strategies are more aggressive. Each of these strategies has a corresponding risk avoidance parameter. Figure 9 shows possible expected cost / risk results for various risk aversions. For most traders, risk aversion 0 is too passive. The expected cost is low, but the risk is very high. The high risk due to the long trading scope implies the possibility of executing inferior prices, which can destroy any alpha that a particular investment is expected to capture. However, if you don't care about transaction cost volatility, this strategy is best (because it averages the lowest cost across many orders). Conversely, risk avoidance1 produces a very low risk trading strategy, but the cost is extraordinarily high, which is yet another way to destroy alpha. The solution to avoid these two extreme results is to choose a risk avoidance that balances cost and risk between the two poles.

  Figure 9 is a graph of ACE® optimal strategies for avoiding various risks when ordering 300,000 Boeing (BA) shares (approximately 8.5% of ADV) using non-discretionary discretion. Is displayed. An order of 300,000 shares corresponds to about 8.5% of ADV. Obviously, there are many optimal strategy choices between the two extremes that minimize the expected transaction cost (point B) and minimize the transaction cost standard deviation (point A). Each point on the effective frontier corresponds to a specific risk avoidance. The graph highlights the selected risk avoidance value. From left to right, it can be seen that by assuming more risk, the expected transaction cost of the trading strategy (relative to the most expensive cost) can be reduced incrementally. Somewhere along the “effective frontier” of transaction costs is a strategy just before the beginning of accumulating risk that exceeds the value of expected transaction cost reduction. This is a desirable choice for risk avoidance. For comparison, trading strategies other than the ACE (registered trademark) optimal strategy are also included. As expected, these alternative trading strategies are not optimal and therefore do not lie on the effective frontier. There is a trading strategy with a lower expected transaction cost with the same transaction cost standard deviation, or a trading strategy with the same expected transaction cost but lower transaction cost standard deviation. Note that for all strategies, the trading scope was limited to one trading day (which may have started in the first bin). For participatory VWAP strategies, the order size is small enough to ensure that the trading scope is less than one trading day.

  As FIG. 9 demonstrates, trading strategies based on high risk avoidance 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 stocks earlier in the trading range (closer to the decision price). The decision price is the prevailing price at the time when the decision to place an order is made. This “advance” tends to move the stock price in an unfavorable direction more quickly than orders that are executed more swiftly. In the ACE® framework, this trend in stock prices is a market impact. Therefore, if you want low opportunity costs (low uncertainty in transaction costs, or low standard deviation), you must be prepared to pay more market impact costs. If there is a willingness to keep an opportunity with a large realization opportunity cost, the order execution can be slowed to avoid high market impact costs.

  Figure 10 shows 300,000 Boeing (BA) shares (approximately 8.5% of ADV) obtained using risk avoidance values of 0, 0.3, 0.6, 0.9, 0.95, 1, and daily trading range. Shows the ACE / 2 non-discretionary ACE (R) optimal strategy when buying. It also shows a range-based VWAP strategy with daily trading scope. The ACE® optimal strategy for larger risk aversion parameters always suggests more aggressive trading at the beginning of the trading scope to minimize opportunity costs.

  Figure 11 shows risk avoidance 0.3 (ACE / 2 non-discretionary neutral) and fixed daily range for Boeing (BA) and various order sizes (1%, 20%, 100%, and 1000% of ADV) The distribution of various ACE (registered trademark) optimal strategy transactions is shown. Figure 11 also shows the trading distribution of the daily VWAP trading strategy. This chart shows that risk avoidance 0.3 yields an ACE® optimal strategy that is close to the VWAP trading strategy. In addition, ACE® optimization strategies become increasingly stretched as order sizes increase due to market impact costs.

  Such a selection is more complicated if the trading scope needs to be selected in addition to the risk avoidance parameters, but the approach remains the same. Alternatively, ACE® can be configured to determine the “optimal” trading scope for an order, thereby leaving the risk avoidance choice as the only user-specified input parameter.

  The selection of the trading scope for an order is another parameter that the user needs to select. ACE® can provide an optimal trading range. The solution to finding such an optimal trading range may vary in actual situations. After considering client feedback and analyzing some different approaches, the following method proved to be the best fit for the ACE implementation. ACE® continues to increment the number of days by one until the expected transaction cost in equation (1) of the optimization problem decreases below the threshold. In other words, this method suggests that you do not need to extend the trading scope for another day if the benefits of extending the trading scope are not important. This importance is determined by an algorithm that considers order size, cost, and volatility. Order-dependent thresholds adjusted so that very large orders have a low cost-to-stock ratio as a threshold, whereas smaller orders have a higher cost-to-stock ratio as a threshold Is done. In addition, more volatile stocks have a higher threshold (because adding an additional trading day increases the variance period significantly). Generally the threshold is around 3-5 bp, but may be lower if the order size is very large.

  FIG. 12 shows the expected transaction costs, standard deviation of transaction costs, and transaction ranges for various risk avoidance values for ACE (registered trademark) discretionary and ACE (registered trademark) non-discretionary discretion, respectively. The underlying order is to buy BA (Boeing) shares a) 300,000 shares (approximately 8.5% of ADV) or b) 1.5 million shares (approximately 42.5% of ADV). The cost estimate is based on the ACE® optimal strategy. Panel A reports values in cents and Panel B reports in basis points. ACE® is calculated based on information as of May 1, 2007.

  In accordance with an aspect of the present invention, a client-specific “alpha” model can be included in the ACE® analysis via the input of expected daily revenue. However, generating an ACE® optimal strategy using a non-zero expected return has one potential complication. ACE® may propose an optimal strategy that includes orders in the opposite direction to the overall order direction. For example, consider a sell order and assume a certain positive expected intraday revenue. Since stock prices are expected to be higher at the end of the day, a profitable strategy for traders is to buy stocks at the beginning of the day and then sell all positions at higher prices at the end of the day. Such a strategy is an optimal solution to the ACE® optimization problem, but the user sees it as undesirable (this strategy will try to profit from short-term price movement predictions and ACE ( (Registered trademark) is not built for such prediction). ACE® can be constrained to require that all bin executions of the ACE® optimal strategy be on the same side of the market. In addition, additional bin volume constraints can be added to the optimization problem, such as trading at least 1% and at most 20% of the historical average bin volume in each bin.

  Modeling both temporary and permanent price impact is the most complex and critical part of ACE. Various methods for specifying the price impact function can be found in the academic literature. The simplest method is to assume a linear relationship between the price change (absolute or relative) caused by the transaction and the size of the transaction. Typically, the trade size is the number of shares executed, expressed in absolute terms or relative to the average (or median) total number of shares traded over the duration of the trade.

  Examples of papers that assume a linear price-order flow relationship are Kyle (1985), Bertsimas and Lo (1998), Breen, Hodrick, and Korajczyk (2002), and Farmer, J.D. (2002). Kyle presents one of the original market microstructure models that derives the equilibrium security price when a trader has asymmetric information. In Bertsimas and Lo, the authors introduce a price impact model and apply probabilistic dynamic programming to derive a trading strategy that minimizes the expected cost of portfolio execution of a security over a fixed time period. Breen, Hodrick, and Korajczyk develop liquidity measures and quantify changes in stock prices by observed net trading volume. Farmer studies the internal dynamics of the market, such as volatility clustering, and proposes nonequilibrium pricing rules.

  Although the initial model of price impact was linear with transaction volume, empirical evidence indicates the existence of non-linearities. Hasbrouck (1991a), (1991b) investigates non-linearities in the impact of trading on the central market and reports an increasing concave relationship between price impact and order flow for some stocks traded in NYSE. To do. De Jong, Nijman, and Roell (1995) use data on French stocks traded on the Paris Stock Exchange and SEAQ International and show that the assumption of the linear impact of orders on prices is incorrect. Kempf and Korn (1999) arrive at the same conclusion using intraday data on German index futures. Zhang (1999) provides a heuristic derivation of nonlinear market impact rules. See, for example, Hausman, Lo, and McKinlay (1992), or Chan and Lakonishok (1993) for more discussion on empirical evidence regarding market impact nonlinearities. Nonlinear price impact models can be found, for example, in Seppi (1990), Barclay and Warner (1993), Keim and Madhavan (1996), and Chen, Stanzl, and Watanabe (2002). Seppi, and Keim and Madhavan focus on the various impacts of block and market trading on prices, and Barclay and Warner justify non-linearities in the price-order flow relationship with the "stealth trading" hypothesis. This hypothesis argues that a secretly informed trader concentrates his transactions in an intermediate size range. Larger transactions add relatively little additional information because intermediate size transactions are related to informed transactions. As a result, the price-order flow relationship is concave.

  ACE® supports two different price impact models, ACE / 1 and ACE / 2, that serve both the US and international markets. Both of these methods belong to the non-linear class model discussed above. ACE® enables non-linear temporary and permanent price impact functions.

  ACE / 1 uses an enhanced version of the original ACE® price impact model. The original model assumed that price impact was a linear function of transaction size, and that the coefficients were based on stock-specific volume and volatility estimates. This original version was only applicable to relatively small orders that were less than 30% of the stock's ADV, but the enhanced ACE / 1 method is meaningful beyond the order size of 30% of ADV. Provides transaction cost estimates.

  The ACE / 2 price impact model is an advanced mathematical / econometric model in line with recent academic empirical findings. It uses econometric techniques to estimate the price impact function based on market tick data. This technique is at the core of ACE / 2 and relies on some stock-specific parameters that are estimated daily and monthly using market data for every stock in the ACE® universe. The method developed by the ITG Financial Engineering Group provides accurate estimates for various sections of the universe (exchange specific and by liquidity group). This task is most difficult for illiquid stocks, and various methods are applied to the classification of stocks with different liquidity characteristics. Similar to the method in Hasbrouck and Seppi (2001), a permanent price impact factor is estimated based on one year of tick data. In particular, we aggregate the trading of each stock across 30-minute intervals and measure price changes using the mid-market price at the beginning and end of each interval. Observed price changes (normalized by bin historical volatility) are regression estimated against the corresponding trade imbalance and approximated by a concave bin-specific function. Given market equilibrium in the ACE® framework, the resulting function can be used to predict the cumulative price impact within a 30 minute interval caused by partial fulfillment of an order.

  Figures 13-16 show bin 1's empirical and theoretical for four different stock categories: the most liquid US-listed stock, all listed stocks, the most liquid OTC stock, and all OTC stocks. The ACE® permanent price impact function is shown. These graphs show that the empirical function becomes more noisy when the stock universe is limited. Nonetheless, all smoothed theoretical functions behave the same, these are three parameters: slope s, value x representing the order size at which the concave starts, and the concave parameter alpha Can be characterized. Empirical evidence suggests that this behavior applies to all fluidity groups and all time intervals of the day.

  FIG. 13 shows the empirical persistent price impact function in bin 1 (9:30 am to 10:00 am) for the most liquid US listed stock (solid line). An empirical permanent price impact function is obtained by segmenting the observations in the trade imbalance group and then taking the average value in each group. The empirical permanent price impact is linear up to 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. Thus, all theoretical price impact functions in ACE® are characterized by three parameters: slope s, value x representing the order size at which the concave starts, and alpha, the concave parameter. . The dashed line shows the fitted theoretical permanent price impact function.

  FIG. 14 shows the empirical permanent price impact function in bin 1 (9:30 am to 10:00 am) for all US listed shares (solid line). An empirical permanent price impact function is obtained by segmenting the observations in the trade imbalance group and then taking the average value in each group. The empirical permanent price impact is linear up to 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. Thus, all theoretical price impact functions in ACE® are characterized by three parameters: slope s, value x representing the order size at which the concave starts, and alpha, the concave parameter. . The dashed line shows the fitted theoretical permanent price impact function. Compared to Figure 13, this empirical perpetual price impact function is much smoother because it is an aggregate across all US listed shares.

  FIG. 15 shows the empirical persistent price impact function in bin 1 (9:30 am to 10:00 am) for the most liquid US OTC stock (solid line). An empirical permanent price impact function is obtained by segmenting the observations in the trade imbalance group and then taking the average value in each group. The empirical permanent price impact is linear up to 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. Thus, all theoretical price impact functions in ACE® are characterized by three parameters: slope s, value x representing the order size at which the concave starts, and alpha, the concave parameter. . The dashed line shows the fitted theoretical permanent price impact function.

  FIG. 16 shows the empirical permanent price impact function in bin 1 (9:30 am to 10:00 am) for all US OTC stocks (solid line). An empirical permanent price impact function is obtained by segmenting the observations in the trade imbalance group and then taking the average value in each group. The empirical permanent price impact is linear up to 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. Thus, all theoretical price impact functions in ACE® are characterized by three parameters: slope s, value x representing the order size at which the concave starts, and alpha, the concave parameter. be able to. The dashed line shows the fitted theoretical permanent price impact function. Compared to Figure 15, this empirical persistent price impact function is much smoother because it is an aggregate across all US OTC stocks.

  Figure 17 shows the daytime pattern of the slope of the permanent price impact function for US listed shares. Shares are divided into 10 different liquidity groups. Stocks in all liquidity groups show the same daytime pattern. The price impact is greatest in the morning and is relatively low around noon and closing.

  Figure 18 shows the daytime pattern of the slope of the permanent price impact function for Euronext stock. Euronext is a merged market in France, Belgium, the Netherlands and Portugal. Shares are divided into six different liquidity groups. Stocks in all liquidity groups show the same daytime pattern. The price impact is small in the morning, around noon and close.

  Through extensive research and testing using US and international enforcement data, the accuracy of this method has been demonstrated for orders up to 100% ADV. This price impact method is available for the US market and the most liquid international markets (a total of 21 countries). FIG. 19 lists the countries currently covered by different ACE modules, ACE / 1 and ACE / 2.

  In ACE / 2, the magnitude of the price impact for each security and order size is defined by quarterly calibration against ITG's peer group database. Therefore, the price impact function is susceptible to orders contained in this database. The database is extremely large and comprehensive, not only representing a wide range of sizes, brokers, execution venues and stock characteristics, but also a variety of trading behaviors derived from investment management styles, market conditions, trading motivations, and news events. Includes execution representing. This richness of the database provides a unique opportunity to provide transaction cost estimates that reflect more than “market average” trading behavior.

  For those seeking a cost estimate that reflects what the market participants pay as a whole, a dataset containing all orders is appropriate. The suitability of each of these estimates is guided by the nature of the order being benchmarked and varies from institution to institution and from institution to investment style.

  Starting with ACE / 2.3 to address the need for two benchmarks (in addition to a discretionary amount) for the same order, ACE / 2 has the ability to provide two different cost estimates. One cost estimate is based on fully executed orders regardless of market conditions, and the other cost estimate is based on all executed orders. From a pre-trade point of view, ACE® non-discretionary estimates are very suitable for examining the trading strategy and determining the feasibility of executing the entire order. The more general ACE® discretionary cost estimate provides a suitable number to compare the transaction costs incurred with those experienced by other participants. A systematic lower (or higher) performance compared to this figure may indicate an institutional competitiveness trend. From a post-trade perspective, the choice of price impact model should be guided by the prevailing nature of the order. For example, orders that require immediate and ongoing trading to completion are compared to cost estimates derived from a price impact model (ACE® non-discretionary) that reflects firm, non-opportunistic trading It should be. However, exceptions to this are when there is frequent momentum for order generation as a result of favorable market observations, or when orders are often not fully executed.

The associated price impact factors for ACE® non-discretionary and ACE® discretionary are derived from different subsets of the same peer group database. In the case of the ACE® discretionary model, an order from the entire order database minus the orders removed by outlier filtering is included in the calibration process. For the ACE® non-discretionary model, an advanced heuristic set is used to remove database participants that show opportunistic transactions. These methods focus on identifying participants whose orders do not meet the minimum transaction cost requirements for increasing order sizes. More precisely, for a given exchange, liquidity group, and order size category, all orders for clients with an unusually low average transaction cost are filtered out. The liquidity group is defined based on the decile of the average daily dollar volume distribution from all stocks. The order size category is defined as 0-1%, 1-5%, 5-10%, 10-25%, 25-50%, and> 50% of average daily trading volume. Grouping is justified by allowing different accounts or portfolio managers to trade very differently within the same company. A client's actual average cost is considered abnormally low (representing an opportunistic transaction) if it is lower than the cut-off for a particular segment. The cut-off is determined by the following two threshold values.
a) A threshold based on some cutoff equal to the average half spread of all orders multiplied by some factor for a given segment (e.g. for an order size around 15% of ADV, the factor is 1 is there).
b) A threshold based on the average realized cost of all market participants.

  If the client's average transaction cost is less than both of the two thresholds determined by a) and b) above, the client's transaction style in this category is classified as opportunistic and ACE® non- At the discretion, it is filtered out.

  Figures 20 and 21 plot the average realized cost curve associated with ACE® discretionary and ACE® non-discretionary, along with the average realized cost curve for opportunistic orders, for listed and OTC stocks, respectively. To do. In both charts, the opportunistic orders are very different and in many cases they have a very low cost, close to 0, and it is clear that the cost does not increase with the order size. The cost curve associated with ACE® non-discretion is, as expected, above the cost curve associated with ACE® discretion. By excluding opportunistic orders, the cost curve is pushed up. As discussed above, the larger the order size, the greater the difference in the curves. The larger the order, the more attention may be paid and more discretion may be given to the trader.

  The underlying enforcement data is the ITG peer group database for the period January 2005-December 2006.

  Figures 22 and 23 show cost estimates for Atlantic TeleNetwork (ATNI) and Boeing (BA) using ACE® non-discretionary and ACE® discretion for various order sizes. Indicates the difference. In FIG. 22, cost estimates are based on a range-based VWAP strategy with a daily trading scope. As expected, the transaction cost of orders that need to be completed is higher than the transaction cost that reflects the market average volume of opportunistic transactions. In FIG. 23, the cost estimate is based on a participation-based VWAP strategy with a participation rate of 10%. As a result, orders can span multiple days. Compared to FIG. 22, the cost estimate is higher for very small orders but lower for larger orders. The daily range in Figure 22 pushes execution of orders into one day, even for larger sizes. This explains that the cost is higher for larger orders in FIG. 22 compared to FIG. For very small orders, this logic works in reverse. The daily range in FIG. 22 allows orders to span the entire day, while the 10% participation rate in FIG. 23 forces execution at an early half-hour interval on the trading day. This leads to higher cost estimates for two reasons. First, trading is concentrated in early bins, and at 10% participation rates may be much higher than the daily range trading rate in FIG. Second, spread costs are highest in the early morning (see Figure 3), so a 10% participation strategy will incur these higher spread costs in the early morning. There is another observation in FIG. 23 that needs explanation. For ATNI, the ACE® non-discretionary cost estimate is higher for very small order sizes with decreasing order size. Again, the explanation is that for small orders, the 10% participation rate implies that the order is fully executed early in the morning, thereby incurring spread costs (highest in the early morning). By increasing the order incrementally, the cost estimate actually decreases (the cost due to spread costs decreases as the order spreads more and more on the day, to whatever price impact costs arise with larger order sizes. Also win). At some order sizes, this effect subsides and the effect of the larger price impact on the larger order is replaced, resulting in a normal increasing cost function. At ACE® discretion, this pattern is not observed (opportunistic traders use limit orders and adjust their trade timing so that spread costs have no impact on their costs. (Because the lower cost of opportunistic traders outweighs the effects of non-opportunistic traders).

  In general, all orders initiated by buyers (sellers) are expected to be executed at prevailing ask (bid) prices. However, in many cases, a trader may achieve a better execution price and thus may realize a price improvement. A price improvement can appear simply because the market moved favorably during the time it took to route the order to the exchange, resulting in a lucky savings. However, there are other more advanced market microstructure theories as to why price improvements occur. An excellent overview can be found in Rhodes-Kropf (2002). The discussion will focus on price improvement in the dealership market. Petersen and Fialkowski (1994) and Ready (1999) explain the existence of price improvements in auction-type markets like NYSE through hidden limit or limit orders. See, for example, Bongiovanni, Borkovec, and Sinclair (2006) for details on hidden limit orders and how to predict volume executed for hidden limit orders in various market conditions. .

  The ACE® price improvement model allows the user to quantify the price improvement for small size orders for various exchanges and order side, size, and liquidity values. This model is based on ITG proprietary execution data for the US and the ITG peer group database for international orders. These sources provide the information necessary to obtain market prices and to measure price improvements at any particular moment of trade execution. Not surprisingly, the results show that price improvement can be very different between the market-driven stock market and the order-driven stock market.

  The calculation of the relative price improvement for various exchanges, traders, and trade sizes, and liquidity groups can be made with the following formula:

  Where p is the transaction price, pbid and pask are the prevailing bid and ask prices, respectively, pQ = pask and δ = 1 for buying, pQ = pbid and δ = -1 for selling It is. Such parameters have a very clear interpretation. For relatively small transactions, the value of R is usually between 0 and 0.5. If the buy (sell) transaction is executed at the ask (bid) price, R equals 0. That is, there was no price improvement.

  FIG. 24 demonstrates that the average empirical relative price improvement of shares traded in NYSE depends on the trade size and trade side. This graph is based on June 2006 ITG proprietary execution data. The highest average relative price improvement occurs in the smallest transaction and decreases as the transaction size increases.

  FIG. 24 reports the average empirical relative price improvement of shares traded in NYSE, depending on the trade size and trader. Relative price improvement is defined in equation (5) of this document. Relative price improvement is located between 0 and 1, where 0 indicates no price improvement and 1 indicates execution on the other side of the spread. This graph is based on June 2006 ITG proprietary execution data. The highest average relative price improvement can be observed for orders of size less than 100 shares. The larger the order size, the less average relative price improvement can be observed. On average, sell transactions get more price improvements than buy transactions.

  FIG. 25 compares the average empirical relative price improvement of stocks trading in NYSE that belong to different liquidity groups. This plot shows that there is a nearly linear relationship between averaged relative price improvement and liquidity. The relative price improvement is highest for the most liquid stocks and lowest for the least liquid stocks. However, it should be noted that absolute price improvements are still likely to be highest for illiquid stocks, largely due to much larger spreads. Sell transactions on average get more price improvements than buy transactions.

  As discussed in previous chapters, order execution can be thought of as a trade-off between the risk of delayed execution and the cost of immediacy (see also Hasbrouk and Schwartz (1998)). . Many studies have focused on optimal order execution under various assumptions. Experts have developed a set of market impact functions, both temporary and permanent, using theoretical or empirical methods, and various forms of market impact models have been considered (e.g. ACE / 1, ACE / 2, Kissell and Glanz (2003), or Almgren et al. (2003)). One common feature of these approaches is the assumption that transaction cost uncertainty can be fully represented by the security's revenue volatility. The implication of this assumption is that there is no interaction between trading activity and the revenue volatility of securities. This requires that the market in the security is close to equilibrium during trading, that is, the revenue volatility of the security remains constant while the revenue itself is affected by the market impact of the trading. The assumption of independence between moments of revenue distribution and transactions appears unrealistic. Almgren (2003) makes some significant advances in the study of the interaction between trading activity and observed volatility. He derives the optimal execution strategy when the volatility increases linearly with the transaction rate. ACE® takes a different approach rather than modeling the revenue volatility of securities subject to trading. ACE® directly models transaction cost uncertainty, as discussed below.

  Typically, the portfolio manager will build a portfolio based on net revenue (ie, total alpha minus transaction costs). Such a model provides not only the expected transaction cost, but also the uncertainty measure associated with it. In many cases, a stock with moderate volatility will show uncertainty that is equal to the expected cost or even much larger than the expected cost, so for an accurate transaction model, under liquidity pressure. A good measure of the uncertainty in transaction costs as a result of the revenue volatility of securities is critical. When analyzing post-transaction performance, this same uncertainty regarding transaction cost estimates is used to determine the quality of execution. The trading desk manager may ask, "67% of the transaction costs are within 1 standard deviation of the expected transaction costs?" Basing the answer to this question on the security's revenue volatility estimate rather than the actual expected distribution of transaction costs can be misleading due to the dependency between the stated revenue volatility and the transaction.

  The second problem is that the earliest studies on optimal trade execution assumed a constant normal distribution of securities revenue during trading. We have already shown that large representatives of actual enforcement (from ITG's peer group database) exhibit thick tails and distortions that are not accurately described by the normal distribution. Rather, we find that the transaction cost distribution can be accurately modeled by the asymmetric generalized t distribution. The generalized t distribution was introduced by McDonald and Newey (1988) and its distorted stretching was proposed by Theodossiou (1998). The family of asymmetric generalized t distributions is very flexible and includes five parameters. The two parameters p and q define the general shape of the distribution (Figure 26 shows some examples of generalized t distributions with various choices of p and q), and one parameter α is The last two parameters that define the asymmetry of the distribution are the position and scale parameters that define the mean and variance of the distribution. The generalized asymmetric t distribution includes many families of distributions, including the normal distribution (p = 2 and q → ∞), and the Student t distribution (p = 2 and q = 2β, where β is the student indicates the degree of freedom of the t distribution).

  FIG. 26 shows various generalized t distributions given the choice of parameters p and q. It is well known that a normal Student t distribution can be obtained by setting p = 2. Therefore, p = 2 and q → ∞ produces a normal distribution.

  The ACE® transaction cost distribution is a generalized asymmetric t distribution with fixed order-independent coefficients p, q, and α, and the position and scale parameters are adjusted by the order size relative to the securities ADV Reflects the expected cost of the order across the trading range and the standard deviation of the revenue of the security. This adjustment is in line with Almgren (2003) and in line with empirical evidence that the projected standard deviation of transaction costs based solely on securities revenue is lower than the empirical standard deviation. Standard deviation adjustments, as well as shape and asymmetry factors, are derived from ITG peer group data as described in Arellano-Valle et al. (2004).

  FIG. 27 presents a fit of the empirical distribution of Z scores for all actual costs according to the ACE® Z score distribution (determined by the three parameters p, q, and α). For the purposes of illustration, some other calibrated theoretical distributions have been added. Clearly, the generalized t distribution outperforms all other distributions. Statistical techniques such as the Kolmogorov-Smirnov test confirm this fact.

  FIG. 27 compares the aggregated distribution of Z scores of actual peer group database costs with four different calibrated distributions: normal distribution, asymmetric t distribution, symmetric generalized t distribution, and asymmetric generalized t distribution. Both normal and asymmetric t distributions do not fit well with empirical distributions. The asymmetric generalized t distribution captures all observed properties. It has a heavy tail, steep and asymmetric (median is smaller than average).

  In summary, the ACE® cost distribution is characterized by three fixed parameters, the expected transaction cost, and the standard deviation of the transaction cost. However, since the cost distribution is not a normal distribution, care must be taken when constructing a confidence interval based on an average value and a standard deviation. The usual interpretation that the standard deviation of the mean +/- 1 includes 2/3 of the observations no longer applies. It is therefore useful to look at the percentile of the distribution. The percentile of the cost distribution for a given scenario is part of the ACE® output.

  For any model, the key issue with ACE® is how well the model actually works. The accuracy of the model is controlled and validated through a calibration and statistical test process. The goal of calibration is to adjust price impact factors derived from market tick data to achieve alignment with realized transaction costs from a large database of known orders. Statistical tests are used to ensure that the model is returning unbiased results (ie costs that are not systematically high or low estimated too much).

  Every quarter, ACE® is calibrated against ITG's peer group database. Two-year data from about 7 trillion US dollars in transactions (as of December 2007) from over 140 large investment management companies will be used. See FIG. 28 for the most important countries of the ACE® universe for more information about the underlying data.

  FIG. 28 reports descriptive statistics of data for calibration / testing of ACE® models for some of the markets in the ACE® universe. This statistic is based on the time period from January 2004 to December 2006. Reported are the number of executions, the number of clusters (or order decisions), execution volume in local currency, the number of shares recorded for execution, and the number of clients in ITG's peer group database. Countries are sorted in descending order of execution.

  Establishing a suitable data set for calibration and testing is a difficult attempt for some reasons. First, enforcement data often does not contain as much detail as is desirable. For example, there may be a lack of execution and decision times, or there is no clear declaration as to whether the underlying order was a market order or a limit order. Second, transaction costs depend on execution strategies, which are most often not formalized by traders and are not recorded first. Many factors (eg, market conditions, workload, explicit instructions from portfolio managers) make it very likely that a trader will execute similar transactions in very different ways during the year.

  Finally, there is an additional challenge in finding a method that discounts large market trends and / or stock-specific trends to allow a measure of pure undisturbed transaction costs. To this end, ITG carefully establishes methods that reflect the needs of the calibration and testing process while being sensitive to the challenges presented by the data.

  Investment manager orders are often broken down into smaller orders or trades, so they are a good basis for analyzing trading activity, its impact on prices, and therefore comparison with ACE average cost estimates. Aggregation must be performed before reaching the correct order unit. To implement this aggregation, a trading package (pre-order) is created that corresponds to a trading group when the same investment manager is in the market for stock (buy or sell) for a sustained period of time.

The concept of clustering is in line with academic literature (see, eg, Chan and Lakonishok (1995)) and industry practices. To determine the price impact and execution cost of institutional transactions, the entire series of transactions (pre-orders) is treated as the basic unit of analysis. In particular, a “buy pre-order” is defined to include a manager's continuous stock purchases. The order ends at the following times.
(a) The manager is not involved in the market for at least one day.
(b) Manager does not enforce more than 2% of ADV.
(c) There are no other transactions placed as orders within the scope of execution of the package.

  “Sell pre-order” is defined similarly. For each pre-order, transaction aggressiveness (participation rate) and average execution price are determined. Since execution time stamps are generally not reported, it is assumed that each pre-order was executed according to a VWAP strategy with empirically estimated participation rates. This assumption is reasonable in most cases, since large institutions are often measured against the VWAP benchmark.

  Transaction cost per share is defined as the difference between the average execution price and the opening price (benchmark price) on the order date. The sign of the difference (positive or negative) is used so that a positive value represents a bad result. For each pre-order in the data set, the realized transaction cost is calculated. The estimated expected transaction cost is also calculated using the parameters of the ACE® model and the actual trading strategy for each order. This allows a one-to-one comparison between actual transaction costs and estimated transaction costs.

  Model calibration and testing calculates average actual costs and ACE® estimates for data sets segmented by size, exchange, and liquidity group relative to ADV. The More specifically, for a given exchange and liquidity group, orders can be in various size categories: 0-1%, 1-2%, 2-3%, ..., 98-99%, 99 Subdivided to ~ 100%.

  A two-step regression technique can be applied to ensure that the average actual cost and the ACE® cost estimate match. Roughly speaking, the calibration procedure adjusts the price impact factor so that the average ACE® cost estimate matches the actual average cost. Adjustments are applied uniformly across all bins to avoid breaking the daytime relationship of price impact factors. Thus, a low actual average cost implies a low price impact factor and thus a low ACE® cost estimate. FIGS. 29-34 serve as examples for the fit between the empirical cost curve from the ITG peer group database and the calibrated ACE® model.

  Figures 29 and 30 show average empirical costs with equal and dollar weights for various US sizes for all US transactions in the January 2005-December 2006 ITG peer group database. And ACE / 2 discretionary cost estimates. These charts demonstrate a very good fit to the ACE / 2 discretionary model. Similar fits can be observed for all other ACE / 2 countries and are available on request.

  Figures 31 and 32 show average empirical weighted equal and dollar weighted for various order sizes for all US transactions in the January 2005-December 2006 ITG peer group database. Shows cost and ACE / 2 non-discretionary cost estimates. These charts demonstrate a very good fit to the ACE / 2 non-discretionary model. Similar fits can be observed for all other ACE / 2 countries and are available on request.

(Reference)
Throughout the above documents, reference was made to publications described in prior art documents. The contents of these publications are incorporated herein by reference for the purposes used.

  As will be appreciated by those skilled in the art, the systems, processes, and components described herein are implemented using one or more general purpose computers, microprocessors, etc. programmed according to the teachings herein. can do. Appropriate software can be made available that can be customized or used commercially as implemented to implement one or more aspects of the invention. Further, as will be apparent to those skilled in the art, aspects of the present invention have been developed by skilled programmers in readily available computer languages such as C ++, PHP, HTML, XML, etc. based on the teachings of this disclosure. Alternatively, it can be realized by a plurality of computer program modules.

  Similarly, those skilled in the art will appreciate that the invention can be implemented in many configurations, including various computer architectures, such as a centralized or distributed architecture.

  One or more aspects of the present invention can include a computer-based product, which can be hosted on a storage medium to implement one or more steps of the present invention. Executable code. Such storage media can be floppy disks or computer disks including optical disks or diskettes, CDROMs, magneto-optical disks, ROM, RAM, EPROM, EEPROM, flash memory, magnetic or optical cards, or electronic instructions Can include any type of media suitable for storing locally or remotely, but is not limited to such.

  Although the invention has been described with reference to specific embodiments thereof, many alternatives, modifications, and variations will be apparent to those skilled in the art. Accordingly, the preferred embodiments of the invention presented herein are intended to be illustrative rather than limiting. Various changes may be made without departing from the true spirit and full scope of the invention as set forth herein.

10 Communication network
11 Transaction cost optimization server
12 Personal computer (PC)
14 Trading desk
15 Real-time market information provider
16 Dedicated client terminal
18 New York Stock Exchange (NYSE)
20 POSIT (registered trademark) Japan-China stock matching system
22 OTC market
24 Electronic Communication Network (ECN)

Claims (36)

A method for estimating the transaction cost of securities trading execution according to a trading strategy selected by a user,
Receiving, via a network, data from a user defining parameters for proposed trade execution and data specifying a user-selected trading strategy, wherein said trading strategy data spans a given trading range Including a series of stocks of securities that will be traded each time,
Using a first agency cost estimation model that considers discretionary and non-discretionary transactions, based on the user-selected trading strategy and market data, the first estimated transaction cost of the received proposed transaction execution is A calculating step;
Calculating a second estimated transaction cost of the received proposed transaction execution based on the user-selected trading strategy and market data using a second agency cost estimation model that only considers non-discretionary transactions When,
Displaying at least one of the first and second estimated transaction costs to the user;
The method wherein the user selected trading strategy is selected from among a plurality of predefined trading styles or specifically defined by the user. Generating a recommendation for optimizing the user-selected trading strategy based on at least one of the first and second estimated transaction costs;
2. The method of claim 1, further comprising: providing the recommendation to the user via the network.   The method of claim 1, wherein the adjustment factor is adjusted to the difficulty and market conditions of the transaction to allow an accurate comparison of transactions performed in various situations and transaction conditions.   4. The method of claim 3, wherein the adjustment factor provides an expected transaction cost for each security each day based on a statistical analysis of a trading difficulty measure. Further comprising receiving a risk avoidance profile and a hypothetical trading order characteristic via the network;
The method of claim 2, wherein the step of calculating a second estimated transaction cost takes into account the risk avoidance profile and hypothetical trading order characteristics.   The method of claim 1, further comprising providing a user interface to allow a user to identify relevant data and trends in a data set to determine factors that affect transaction performance.   The method of claim 6, wherein a user can perform a real-time analytical calculation by modifying a subset of the data set under consideration without additional preprocessing.   The method of claim 6, wherein a user can add a new user total without additional preprocessing.   The method of claim 1, wherein the server is adapted to provide a direct interface to a security price database to enable real-time display of transaction cost analysis results.   The method of claim 1, wherein the transaction cost algorithm enables price-based benchmark daytime calculations. Constructing the first agency cost estimation model using historical transaction data for all executions, including transaction data for trade executions where traders can postpone or abandon transactions to take advantage of market conditions;
The historical agency data is used for trade-only executions that traders must execute regardless of whether the market conditions are favorable, without discretion, and excludes data related to opportunistic trade execution. The method of claim 1, further comprising: constructing a cost estimation model. A computer program product comprising computer-executable instructions stored on a computer-readable medium for estimating the transaction cost of securities trading execution according to a trading strategy selected by a user by execution of the operation, the operation comprising:
Receiving, via a network, data from a user defining parameters for proposed trade execution and data specifying a user-selected trading strategy, wherein said trading strategy data spans a given trading range Including a series of stocks of securities that will be traded each time,
Using a first agency cost estimation model that considers discretionary and non-discretionary transactions, based on the user-selected trading strategy and market data, the first estimated transaction cost of the received proposed transaction execution is A calculating step;
Calculating a second estimated transaction cost of the received proposed transaction execution based on the user-selected trading strategy and market data using a second agency cost estimation model that only considers non-discretionary transactions When,
Displaying at least one of the first and second estimated transaction costs to the user;
A computer program product, wherein the user-selected trading strategy is selected from among a plurality of predefined trading styles or specifically defined by the user. The operation further comprises generating a recommendation to optimize the user-selected trading strategy based on at least one of the first and second estimated transaction costs;
13. The computer program product of claim 12, comprising: providing the recommendation to the user via the network.   13. The computer program product of claim 12, wherein the adjustment factor is adjusted for trading difficulty and market conditions to allow an accurate comparison of transactions performed in various situations and trading conditions.   15. The computer program product of claim 14, wherein the adjustment factor provides an expected transaction cost for each security each day based on a statistical analysis of a trading difficulty measure. Further comprising performing an operation of receiving a risk avoidance profile and a hypothetical trade order characteristic via the network;
13. The computer program product of claim 12, wherein the step of calculating a second estimated transaction cost takes into account the risk avoidance profile and hypothetical trading order characteristics.   13. The operation of performing further steps of providing a user interface to allow a user to identify relevant data and trends in a data set to determine factors affecting transaction performance. Computer program product.   The computer program product of claim 17, wherein a user can modify a subset of the data set under consideration to perform real-time analytical calculations without additional preprocessing.   The computer program product of claim 17, wherein a user can add a new user total without additional preprocessing.   13. The computer program product of claim 12, wherein a direct interface to a security price database is provided to allow real-time display of transaction cost analysis results.   13. The computer program product of claim 12, wherein the transaction cost algorithm enables price based benchmark daytime calculations. Constructing the first agency cost estimation model using historical transaction data for all executions, including transaction data for trade executions where traders can postpone or abandon transactions to take advantage of market conditions;
The historical agency data is used for trade-only executions that traders must execute regardless of whether the market conditions are favorable, without discretion, and excludes data related to opportunistic trade execution. 13. The computer program product of claim 12, further comprising: performing a step of building a cost estimation model. A system for estimating the transaction cost of securities trading execution according to a trading strategy selected by a user,
Means for receiving, via a network, data from a user defining parameters for proposed trade execution and data specifying a user-selected trading strategy, wherein said trading strategy data spans a given trading range Means including a series of stocks of securities that will be traded each time,
Using a first agency cost estimation model that considers discretionary and non-discretionary transactions, based on the user-selected trading strategy and market data, the first estimated transaction cost of the received proposed transaction execution is Means for calculating;
Means for calculating a second estimated transaction cost of the received proposed transaction execution based on the user-selected trading strategy and market data using a second agency cost estimation model that only considers non-discretionary transactions When,
Means for displaying to the user at least one of the first and second estimated transaction costs,
The system wherein the user selected trading strategy is selected from among a plurality of predefined trading styles or specifically defined by the user. Means for generating a recommendation for optimizing the user-selected trading strategy based on at least one of the first and second estimated transaction costs;
24. The system of claim 23, further comprising: means for providing the recommendation to the user via the network.   24. The system of claim 23, wherein the adjustment factor is adjusted for transaction difficulty and market conditions to allow for an accurate comparison of transactions performed in various situations and transaction conditions.   26. The system of claim 25, wherein the adjustment factor provides an estimated transaction cost for each security each day based on a statistical analysis of a trading difficulty measure. Means for receiving a risk avoidance profile and hypothetical trading order characteristics via the network;
25. The system of claim 24, wherein the means for calculating a second estimated transaction cost takes into account the risk avoidance profile and hypothetical trading order characteristics.   24. The system of claim 23, further comprising means for providing a user interface to allow a user to identify relevant data and trends in a data set to determine factors that affect transaction performance.   30. The system of claim 28, wherein a user can modify a subset of the data set under consideration and perform real-time analytical calculations without additional preprocessing.   30. The system of claim 28, wherein a user can add a new user total without additional preprocessing.   24. The system of claim 23, further comprising a server adapted to provide a direct interface to a security price database to enable real-time display of transaction cost analysis results.   24. The system of claim 23, wherein the transaction cost algorithm enables price-based benchmark daytime calculations. Means for building said first agency cost estimation model using historical transaction data for all executions, including transaction data for trade executions where traders can postpone or abandon transactions to take advantage of market conditions;
The historical agency data is used for trade-only executions that traders must execute regardless of whether the market conditions are favorable, without discretion, and excludes data related to opportunistic trade execution. 24. The system of claim 23, further comprising means for building a cost estimation model. A system for estimating the transaction cost of securities trading execution according to a trading strategy selected by a user,
A server coupled to an electronic data network, the server configured to receive data from a user defining parameters for proposed transaction execution and data specifying a user-selected trading strategy over the network; The trading strategy data includes a series of stock quantities of securities that will be traded at time intervals over a given trading range, and the server further considers discretionary trading and non-discretionary trading. A first estimated transaction cost of the received proposed transaction execution is calculated based on the user-selected transaction strategy and market data using the agency cost estimation model of the second, and only non-discretionary transactions are considered. Based on the user-selected trading strategy and market data using the agency cost estimation model of Calculate the only second estimated transaction costs of proposed trade execution took, it is configured to transmit to the user via the electronic data network for displaying the first and second estimated transaction costs,
The system wherein the user selected trading strategy is selected from among a plurality of predefined trading styles or specifically defined by the user. Means for generating a recommendation for optimizing the user-selected trading strategy based on at least one of the first and second estimated transaction costs;
35. The system of claim 34, further comprising: means for providing the recommendation to the user via the network.   The server further builds the first agency cost estimation model using historical transaction data for all executions, including transaction data for trade executions where traders can postpone or abandon transactions to take advantage of market conditions. , Using historical transaction data for trade-only executions that traders must execute regardless of whether market conditions are advantageous without discretion, and excluding data on opportunistic trade execution, 35. The system of claim 34, configured to build an agency cost estimation model.