Dynamic Focus Strategies for Electronic Trade ... - IEEE Xplore

Dynamic Focus Strategies for Electronic Trade Execution in Limit Order Markets Jiaqi Wang, Chengqi Zhang Faculty of Information Technology, University of Technology, Sydney {jqwang, chengqi}@it.uts.edu.au

Abstract Trade execution has attracted lots of attention from academia and financial industry due to its significant impact on investment return. Recently, limit order strategies for trade execution were backtested on historical order/trade data and dynamic price adjustment was proposed to respond state variables in execution. This paper emphasizes the effect of dynamic volume adjustment on limit order strategies and proposes dynamic focus (DF) strategies, which incorporate a series of market orders of different volume into the limit order strategy and dynamically adjusts their volume by monitoring state variables such as inventory and order book imbalance in real-time. The sigmoid function is suggested as the quantitative model to represent the relationship between the state variables and the volume to be adjusted. The empirical results on historical order/trade data of the Australian Stock Exchange show that the DF strategy can outperform the limit order strategy, which does not adopt dynamic volume adjustment.

1. Introduction The research focus of trade execution is how to execute an order, particularly a large order with low cost and risk in real markets over a period of time. It has attracted a lot of attention from academia and financial industry because high transaction costs in trade execution will significantly reduce returns especially in investment with high turnover. For example, the expected annual return during the period of 1979 – 1991 was 26.2% for the portfolio recommended by Value Line (a research firm) whereas the Value Line fund that invested in these stocks had an actual annual return of only 16.1%. The 10% return difference was lost in transaction costs. In addition, some research institutions reported that transaction costs per annum may be up to $120 billion in the $12

trillion U.S. equity market. Therefore investors and trading agencies always need to carefully analyze cost and risk that would be incurred in trade execution and design efficient strategies to reduce them. Transaction costs are usually divided as explicit costs and implicit costs. Compared to explicit costs such as commission fee and tax fee, it is more difficult to analyze and control implicit costs, which are the key factors that affect the performance of trade execution. Implicit costs can be further categorized into several important components: market impact cost, spread cost and opportunity cost. These costs are closely related to the specific strategies of trade execution. While submitting a market order could capture a favorable trading opportunity as it is immediately executed, this strategy has to pay for spread cost. For a large order to be executed such as purchasing one million shares of one stock, submitting a market order would incur significant market impact cost. The reason is that such a large order has to be traded at several worse price levels since most of the time the market cannot provide it with enough volume at the best price. The research of market microstructure, which is focused on the process of price formation and interactions among different types of trading agents in real markets, has seen evidences that using limit orders may be a more rational choice in trading than using market orders [2, 4, 6]. Limit orders can effectively control spread cost and market impact cost since they are set with a limit price. Moreover, limit orders could wait for favorable price movement since they are not executed immediately. With the development of technologies such as electronic communication networks, data storage and processing, it has been feasible to optimize and backtest the new strategies on historical order/trade data. Recently, the limit order strategy for trade execution has been testified on NASDAQ data [8]. The strategy initially sets a limit order at a fixed price level till the end of execution and then submits a market order to fulfill the unexecuted

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volume at the end. The empirical results show that it can improve the market order strategy. However, limit orders are a two-edged sword for trade execution. They may cause nonexecution risk and opportunity cost so that in the above strategy, a market order has to be submitted at the end of execution to fulfill all unexecuted volume. Moreover, the above limit order strategy does not consider how to respond real-time update of state variables in execution since it statically sets a limit order at a fixed price level at the beginning of execution and submits a market order at the end of execution. As the execution goes on, many state variables such as the unexecuted volume, the bidask spread, the order book depth and price trend are actually updated. The following intuitive examples will explain why more reasonable strategies should respond real-time update of state variables. A more aggressive action should be taken to reduce nonexecution risk if there is too much unexecuted volume in the remaining time. If some indicators forecast that prices would move toward a favorable direction, the action should not be too aggressive in order to wait for the better trading opportunities. [8, 9] also discussed the above problems and proposed dynamic price adjustment in the family of limit order strategies to control nonexecution risk and respond real-time update of state variables. Different from the study of dynamic price adjustment, this paper emphasizes the effect of dynamic volume adjustment on limit order strategies for trade execution. As two most important characteristics of an order, price and volume may have similar functions to respond real-time update of state variables and to control nonexecution risk. Intuitively, a more aggressive action can be represented either as heightening (or lowering) the buy (or sell) order price or as increasing the order volume. Based on dynamic volume adjustment, this paper proposes the dynamic focus (DF) strategy, which incorporates a series of market orders of different volume into the limit order strategy and dynamically adjusts their volume according to real-time update of state variables such as inventory and order book imbalance. The DF strategy adopts the sigmoid function as the quantitative model to map the real-time state variable to the dynamically adjusted volume. The limit order strategy, which is adopted in the DF strategy, updates the buy (or sell) limit order price to the best bid (or ask) price as the execution goes on and fulfills the unexecuted volume at the end of execution. In the period of execution, the buy (or sell) limit order from this strategy stands neither alone at the market frontier (to avoid unfavorable price selection) nor far away from the best bid (or ask) price (to reduce nonexecution risk). This paper named this strategy the

naïve price adjustment (NPA) strategy. The DF strategy can be regarded as combination of dynamic volume adjustment with the NPA strategy. To verify the effectiveness of dynamic volume adjustment in the DF strategy, this paper compares the DF strategy to the NPA strategy, which does not adopt dynamic volume adjustment. It may be advisable in future to combine dynamic price adjustment in [9] with dynamic volume adjustment in this paper. This paper benefits from a unique advantage of accessing full order/trade data of all stocks in the Australian Stock Exchange (ASX) – a typical electronic limit order market. This advantage makes it possible to optimize and backtest the DF strategy. Moreover, the DF strategy can be verified not only by the detailed result on a single stock but also by statistical summary on a group of stocks. This paper constructs 80 datasets as the test bed for backtesting the DF strategy. Each dataset is composed of data in a two-month test period for one stock. The experiments consider 4 test periods for 20 stocks from the index ASX20. The empirical results verify the effectiveness of dynamic volume adjustment – the DF strategy can outperform the NPA strategy. It is also observed that the DF strategy can improve the NPA strategy more significantly on more illiquid stock data, and inventory is a more important factor for trade execution than order book imbalance. This paper is organized as follows: Section 2 specifically introduces two real-time state variables used in the DF strategy – inventory and order book imbalance. Section 3 suggests the sigmoid function as the quantitative model to map the state variable to the dynamically adjusted volume. Section 4 describes the issues related to experimental setup. Section 5 empirically evaluates the DF strategy by the detailed result on a single stock WFT (Westfield Trust) and statistical summary on 80 datasets. The last section draws a conclusion and discusses future research.

2. Inventory and order book imbalance The DF strategy responds real-time update of state variables in trade execution by incorporating a series of market orders of different volume into the limit order strategy and dynamically adjusting their volume. Dynamic volume adjustment depends on two real-time state variables in execution: inventory and order book imbalance. Inventory is defined as the unexecuted volume. Order book imbalance is the measure of volume difference between the buy side and the sell side of the order book. This section introduces the background of these two real-time state variables and their impact on the DF strategy in trade execution. The


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DF strategies based on inventory control and order book imbalance are respectively called the DF-IC and DF-OBI strategies. In the finance area, inventory control has been discussed in the study of dealers’ trading behaviors. Theoretical and empirical studies show that dealers always optimize their long and/or short inventory position based on their preference to return or risk. Their position would deviate from the expected level if the dealers accommodate more orders from other market participants. In that case, the dealers take a risk of holding extra inventory for two reasons. First, it is unknown how long the extra inventory will remain. Second, future price movement is uncertain when the dealers hold the extra inventory. The dealers can resume their expected position by adjusting their bid and ask prices. For example, they can lower their order prices to attract more buyers when their position is longer than the expected level. This adjustment is regarded as inventory control. Actually, the above concern on inventory control also exists in trade execution. When traders execute a given order via the limit order strategy, they have to face nonexecution risk due to the characteristics of limit orders. Similar to the discussion on dealers’ trading behaviors, the nonexecution risk derives from two types of uncertainty in trade execution. First, traders do not know for sure when the limit orders can be executed and if they can be filled completely at the end of execution. Second, short-term price movement is uncertain in the period of execution and limit orders have both the advantage of waiting for favorable price movement and the disadvantage of missing good trading opportunities. The following example is helpful for intuitively understanding the relationship between real-time inventory and nonexecution risk. Suppose that there are two cases for purchasing 10,000 shares of one stock in 10 minutes: in the first case, there is the unexecuted volume of 9,000 shares in the last one minute whereas in the second case, there is the unexecuted volume of 1,000 shares in the remaining nine minutes. Intuitively, the first case would incur higher nonexecution risk than the second case. So management of nonexecution risk may benefit from real-time inventory control. In dealers’ trading, they optimize their inventory to the expected position via dynamic price adjustment. Dynamic price adjustment has also been applied in trade execution to respond real-time update of inventory [9]. Different from dynamic price adjustment, the DF-IC strategy in this paper controls inventory via dynamically adjusting volume of each market order. Intuitively, it may be advisable for management of nonexecution risk to submit a market order of higher volume when there is too much unexecuted volume in

the remaining time. In other words, the DF-IC strategy adjusts volume of each market order according to deviation of the real-time unexecuted volume from the expected level. As illustrated in the research of market microstructure such as [5], order book imbalance is closely related to short-term price movement. The two types of traders who prefer limit orders are precommitted traders and value-motivated traders. The former aims to reduce transaction costs whereas the latter trades only at the acceptable price given the value estimates. They often place limit orders, which are close to the best bid-ask prices, to increase the possibility of their orders to be filled so as to fulfill their commitment or capture profitable opportunities. Their behaviors are one of the main resources aggregating order book imbalance, which may indicate future price movement. The pre-committed traders or the value-motivated traders will place more aggressive orders that affect prices such as market orders if they face the pressure of nonexecution risk or their profitable information is being impounded into prices. Information of order book imbalance may be valuable to traders in a general sense that prices would increase (or decrease) when the buy side of the order book is heavier (or thinner) than the sell side. Order book imbalance has been testified in the study of dynamic price adjustment for trade execution [9]. When order book imbalance forecasts an unfavorable price movement, the order will be placed at a more aggressive price level to capture the current trading opportunity. Based on order book imbalance, the DF-OBI strategy in this paper dynamically adjusts volume of each market order to respond profitable or unfavorable price movement. It may be advisable to submit a market order of higher volume to capture the current favorable price if order book imbalance forecasts that prices would move toward an unfavorable direction.

3. Quantitative model in the DF strategy The previous section qualitatively analyzes the rationale behind the DF-IC and DF-OBI strategies. The DF-IC strategy will submit the market order of higher volume if there is too much unexecuted volume in the remaining time. The DF-OBI strategy will submit the market order of higher volume if order book imbalance forecasts that prices would move toward an unfavorable direction. The next question is how to quantitatively implement these ideas, in other words, how much volume of the market order should be set according to real-time update of state variables. According to some requirements in trade execution and


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the above qualitative description, the quantitative model should satisfy the following three conditions: First, volume of each market order should not exceed that of the whole order to be executed. Second, volume of each market order should not be negative because it is assumed that for the buying (or selling) task, no sell (or buy) order be submitted in the period of execution. Third, the model should be represented by an increasing function according to the principle of dynamic volume adjustment illustrated above. This paper suggests the sigmoid function in formula (1) as the quantitative model to map the state variable to the dynamically adjusted volume since it satisfies all of the three conditions, VP(t) = 1 / (1 + exp(-Ȝ×x(t))) (1) where x(t) represents the state variable at the time t, Ȝ the parameter to be optimized and VP(t) the volume percentage of the market order from the backtested strategy relative to the whole order to be executed. While the volume of each market order to be submitted is determined by calculating VP(t), it is constrained to be less than the unexecuted volume by the time t.

Figure 1. Sigmoid function According to formula (1), there is a family of sigmoid functions decided by different values of the parameter Ȝ. The different functions in the family represent different styles of dynamic volume adjustment. For the sigmoid function with larger Ȝ (e.g. Ȝ = 50), there exists the highly sensitive area where the output will significantly change as the state variable x slightly moves (see the dash curve in Figure 1). For the sigmoid function with smaller Ȝ (e.g. Ȝ = 0.5), the output is adjusted in a smoother manner as the state variable x changes (see the dot curve in Figure 1). This characteristic of the sigmoid function results in the fact that as Ȝ increases, dynamic volume adjustment in the DF strategy could be affected significantly by slightly changes of the state variable such as inventory or order book imbalance. Ȝ is regarded as the important

parameter to be optimized since it could affect the performance of the DF strategy. When the sigmoid function is used in the DF-IC strategy, the variable x is referred to as the relative inventory density. The inventory density ID(t) at the time t (ts t < te) is defined as follows: ID(t) = I(t) / (te – t) where I(t) is the unexecuted volume (also called inventory) at the time t, ts the start time and te the end time. Then the relative inventory density at the time t is defined as follows: x(t) = (ID(t) – ID(ts)) / ID(ts) - b where ID(t) is the inventory density at the time t, ID(ts) the inventory density at the start time ts and b the bias (also called the expected level). So VP(t) in the DF-IC strategy is calculated as follows: VP(t)=1/(1+exp(-Ȝ((ID(t)–ID(ts))/ID(ts)-b))) (2) Formula (2) shows that as the inventory density ID(t) increases, the DF-IC strategy will submit a market order of higher volume to hedge potential nonexecution risk and as the inventory density ID(t) decreases, the DF-IC strategy will submit a market order of less or even zero volume to wait for favorable price movement or the limit order filled. Moreover, formula (2) guarantees that the volume percentage VP(t) is always bounded between zero and one. When the sigmoid function is used in the DF-OBI strategy, the variable x is referred to as order book imbalance OBI(t) at the time t (ts t < te) and is defined as the natural logarithm difference between volumes at best bid and ask prices: x(t) = OBI(t) = ln(BBV(t)) – ln(BAV(t)) where ln(•) is the natural logarithm, BBV(t) volume at the best bid price and BAV(t) volume at the best ask price at the time t. Positive (or negative) OBI(t) means that the buy side of the order book is heavier (or thinner) than the sell side. So VP(t) in the DF-OBI strategy is calculated as follows: ° 0 OBIl ≤ OBI (t ) ≤ OBIh (3) VP( t ) = ® + − 1/ 1 λ exp OBI t others ( ) ( ) °¯ where OBIl < 0 and OBIh > 0. According to formula (3), the DF-OBI strategy does not take action in the insensitive area between the lower bound OBIl and the upper bound OBIh since this insensitive area represents weak signals for short-term price movement. Formula (3) shows that the DF-OBI strategy will submit a market order of less (or more) volume to wait for (or capture) better opportunities if order book imbalance forecasts that prices would move toward a favorable (or unfavorable) direction. Moreover, formula (3) guarantees that the volume percentage VP(t) is always bounded between zero and one.

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4. Experimental setup This paper benefits from a unique advantage of accessing full order/trade data of all stocks in ASX – a typical electronic limit order market. This advantage makes it possible to build a simulator to backtest the proposed strategy based on full historical order/trade data. In simulation, the historical order/trade data act as a time-varying pool providing liquidity. The artificial orders from the backtested strategies are executed in this pool according to the market rules. The simulator in this paper does not consider any trading agent’s reaction to the artificial orders from the backtested strategies. This is different from the real markets where the participants would react to any event. The existing studies such as [3, 8, 9] have to make this assumption for backtesting strategies due to the limitation of historical order/trade data. Nevertheless, backtesting based on this assumption still makes sense because the practitioners could have a basic understanding for the new strategy and they may further improve it with penetration. In simulation, execution of limit orders from the backtested strategy follows two basic rules running in the limit order markets such as ASX. The first one is called the price priority rule where for two buy (or sell) orders at different price levels, the buy (or sell) order with higher (or lower) price is executed prior to the other. The second one is called the time priority rule where for two buy (or sell) orders at the same price level, the buy (or sell) order with an earlier time-stamp is executed prior to the other. According to these two rules and the detailed order/trade records in historical data, the simulator in this paper can identify whether the limit order from the backtested strategy would be filled in the period of execution. In simulation, execution of the market orders from the backtested strategy follows the assumption in [3] that these market orders do not influence future order flows and the simulator only takes account of instantaneous market impact. This paper adopts a popular measure of transaction cost called implementation shortfall, which is defined as the relative difference between the execution price and the arrival price [10]. The arrival price Pa is defined as the middle-point price between the best bid and ask prices at the beginning of execution. The execution price Pe is defined as the dollar value of per unit volume executed by a specific strategy. The implementation shortfall Sf is calculated as follows: Sf = 10000 * (Pe - Pa) / Pa, for a buy order Sf = 10000 * (Pa – Pe) / Pa, for a sell order

where the measure unit of implementation shortfall Sf is called basis points. Two statistical measures of shortfall, average shortfall and standard deviation of shortfall, are used in the experiments to optimize and evaluate the DF strategy. The goal of optimization is to search good values of the given parameter for the strategies in in-sample test periods so that they can be well generalized to out-ofsample test periods. Efficient frontier has been used as a good tool of parameter optimization in many financial problems. It has been proposed in the theory of portfolio [7] and was recently introduced into the community of trade execution to explain and solve the trader’s dilemma where the trader needs to balance tradeoff between cost and risk [1]. This paper provides the study of efficient frontier on the stock WFT to help the readers have an intuitive understanding for optimization and evaluation of the DF strategy. One specific parameter value can be selected on the efficient frontier according to the preference to cost (average shortfall) or risk (standard deviation of shortfall). This preference can be quantitatively formulated as follows: A + Ȗ × SD (4) where A represents average shortfall, SD standard deviation of shortfall and Ȗ the preference factor. The goal of trade execution is to minimize formula (4) for a given Ȗ. Ȗ = 0 means that only average shortfall is optimized. The larger Ȗ means that more attention is paid to standard deviation of shortfall in optimization. This paper simply sets the preference factor Ȗ = 0. The parameter Ȝ in the DF strategies is firstly optimized based on historical data in four in-sample test periods and then applied to four out-of-sample test periods. In the experiments, this paper sets one specific example of trade execution – purchasing 40,000 shares of one stock in 10 minutes. Normal trading takes place from 10:00:00 am to 4:00:00 pm in ASX and the stocks open from 10:00:00 am to 10:10:00 am according to the starting letter of their ASX codes (see the introduction about trading hours from the ASX website). So the experiments are conducted on historical order/trade data during the period of 10:10:00 am – 4:00:00 pm for each trading day of ASX. According to the above illustration, there are 35 timeinterval samples in each trading day for one stock. The dataset is composed of these types of samples in a twomonth test period of one stock. This paper evaluates the DF strategy on 80 datasets, which are constructed by 4 two-month test periods for 20 stocks from the index ASX20. As shown in Table 1, the two-month test period in each dataset is divided as the in-sample test period (first month) and the out-of-sample test period (second month).


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Table 1. Four test periods Test period 1 Test period 2 Test period 3 Test period 4

In-sample January 2002 February 2002 March 2002 April 2002

Out-of-sample February 2002 March 2002 April 2002 May 2002

5. Empirical evaluation The DF strategy is firstly evaluated by the insample test results on the stock WFT (see Figure 3 at the very end of this paper). In the first column charts of Figure 3, the horizontal coordinates represent Ȝ and the vertical coordinates average shortfall. In the second column charts of Figure 3, the horizontal coordinates represent Ȝ and the vertical coordinates standard deviation of shortfall. The third column charts of Figure 3 provide the empirical study on efficient frontier, which is composed of average shortfall (vertical coordinate) and standard deviation of shortfall (horizontal coordinate). In all charts of Figure 3, the dot curves represent the DF-IC strategy and the dash curves the DF-OBI strategy. The NPA strategy is represented by the straight lines in the first and second columns and the big dots in the third column. The results in four in-sample test periods are listed in the first, second, third and fourth row of Figure 3. In terms of standard deviation of shortfall (see the second column charts of Figure 3), the smoother sigmoid function (smaller Ȝ) results in lower volatility (smaller standard deviation) of shortfall and the optimal Ȝ exists so that the DF strategy can achieve the smaller standard deviation than the NPA strategy does. It can be found in most of the charts on average shortfall (see the first column charts of Figure 3) that neither extreme small Ȝ nor extreme large Ȝ is helpful for optimizing the average shortfall of the DF strategy. In terms of average shortfall, the optimal parameter Ȝ exists so that two types of DF strategies can outperform the NPA strategy on all four in-sample test periods except the DF-OBI strategy on the fourth test period (see the fourth row & first column chart of Figure 3). The effectiveness of the DF strategy can also be verified by efficient frontier. When both the DF strategy and the NPA strategy are regarded as the candidate strategies to be optimized, the in-sample test results on WFT clearly show that the NPA strategy (the big dots) does not appear on the efficient frontiers (see the third column charts of Figure 3). In other words, the NPA strategy generates a suboptimal solution because the DF strategy can achieve smaller average shortfall and/or smaller standard deviation of shortfall.

Figure 2 is about the out-of-sample results of the DF strategy on 80 datasets. The horizontal coordinates of Figure 2 represent average 10-minute market trading volume of the stock – a kind of measure of liquidity. The vertical coordinates of Figure 2 represent the difference of average shortfalls between the NPA strategy and the DF strategy. Each point in Figure 2 represents the out-of-sample result of the DF strategy on each datasets. The left and right charts of Figure 2 respectively represent the DF-IC and DF-OBI strategies. The out-of-sample test results on 80 datasets show that in terms of average shortfall, the DF-IC and DF-OBI strategies can outperform the NPA strategy respectively on 75 and 45 datasets (see the points with positive improvement in Figure 2). It is clear in Figure 2 that improvement (see the vertical coordinates) is more significant on more illiquid datasets with smaller average 10-minute trading volume (see the horizontal coordinates). A reasonable explanation for this phenomenon is that the DF strategy reduces nonexecution risk by submitting some aggressive orders in the period of execution while nonexecution risk is more easily incurred for more illiquid stock data.

Figure 2. Improvement of average shortfall It also can be found in Figures 2 and 3 that the DFIC strategy often behaves better than the DF-OBI strategy in terms of average shortfall. According to the research of market microstructure, order book imbalance can be effective since it could forecast short-term price movement with probability. However, the ability of order book imbalance forecasting shortterm price movement is limited after all due to high uncertainty of financial markets. So inventory control should be a more important factor for trade execution than order book imbalance. This conclusion is also implied in [9].

6. Conclusions and future work This paper emphasizes the effect of dynamic volume adjustment on limit order strategies in trade


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execution and proposes the DF strategy for implementation. Dynamic volume adjustment in the DF strategy depends on inventory control and order book imbalance. The sigmoid functions are adopted as the quantitative model to map the real-time state variable to the dynamically adjusted volume. The experimental results on 80 real-world datasets show the effectiveness of dynamic volume adjustment – the DF strategy can outperform the limit order strategy, which does not adopt dynamic volume adjustment. Besides, the following patterns are also observed in the experiments. The DF strategy can improve the limit order strategy more significantly on more illiquid stock data. Inventory control is a more important factor for trade execution than information of order book imbalance. While the DF strategy in this paper dynamically adjusts volume of each market order, it also can be extended to dynamically adjust volume of the limit order. The rationale behind this extension is explained as follows: Due to uncertainty of price movement, limit orders may incur unfavorable price selection while they are waiting for price improvement. Moreover, a large limit order submitted to the market will disclose trading intention. Dynamic volume adjustment of the limit order may be helpful for controlling unfavorable price selection and information disclosure. Another future research is to combine dynamic price adjustment proposed by [9] with dynamic volume adjustment proposed by this paper. As two most important factors in trade execution, price and volume are the complements of each other and both of them need to be considered in practice. Therefore this combination may be reasonable and advisable for trade execution.

Acknowledgements

preprocessing the data via the Australian Capital Markets Cooperative Research Center (CMCRC). Mr. Jiaqi Wang is supported by an international postgraduate scholarship and a CMCRC scholarship.

References [1] R. Almgren and N. Chriss, “Optimal Liquidation Strategies”, Original Working Paper, 1997. [2] B. Biais, P. Hillion and C. Spatt, “An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse”, Journal of Finance, 50 (5), 1995, pp. 1655-1689. [3] R.J. Coggins, A. Blazejewski and M. Aitken, “Optimal Trade execution of Equities in a Limit Order Market”, In the Proceedings of International Conference on Computational Intelligence for Financial Engineering, 2003, pp. 371-378. [4] P. Handa and R.A. Schwartz, “Limit Order Trading”, Journal of Finance, 51 (5), 1996, pp. 1835-1861. [5] L. Harris and V. Panchapagesan, “The Information Content of the Limit Order Book: Evidence from NYSE Specialist Trading Decisions”, Journal of Financial Markets, 8 (1), 2005, pp. 25-67. [6] J. Hasbrouck and L. Harris, “Market vs. Limit Orders: The SuperDot Evidence on Order Submission Strategy”, Journal of Financial and Quantitative Analysis, 31 (2), 1996, pp. 213-231. [7] H. Markowitz, “Portfolio Selection”, Journal of Finance, 7 (1), 1952, pp. 77-91. [8] Y. Nevmyvaka, M. Kearns, A. Papandreou and K. Sycara, “Electronic Trading in Order-Driven Markets: Efficient Execution”, In the Proceedings of IEEE International Conference on E-Commerce Technology, 2005, pp. 190-197. [9] Y. Nevmyvaka, Y. Feng and M. Kearns, “Reinforcement Learning for Optimized Trade Execution”, Workshop on Machine Learning in Finance, NIPS, 2005. [10] A.F. Perold, “The Implementation Shortfall: Paper versus Reality”, Journal of Portfolio Management, 14 (3), 1988, pp. 4-9.

The authors appreciate the provision of full order and trade data of ASX and the SMARTS software


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Figure 3. Average shortfall, standard deviation of shortfall and efficient frontier


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