Dark pool usage and individual trading performance

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1 Noname manuscript No. (will be inserted by the editor) Dark pool usage and individual trading performance Yibing Xiong Takashi Yamada Takao Terano the date of receipt and acceptance should be inserted later Abstract This manuscript utilizes agent-based simulation to examine the relationship between dark pool usage and individual trading performance, which includes price slippage (with respect to (wrt) volume weighted average price (VWAP)) and order execution rate. We model an order-driven stock market populated by liquidity traders, who have different but stable dark pool usages. Their orders are split evenly and placed successively either in an exchange or in a dark pool, in where orders are matched at the midpoint of the exchange ask and bid. By examining the performances of different traders, our simulation results indicate that both market volatility and dark pool usage affect price slippage and order execution rate. On the one hand, higher usage of dark pool results in higher price improvement (wrt VWAP), but mainly when market volatility is in mid-level. On the other hand, order execution rate decreases with the increase of market volatility, and with the increase of dark pool usage. Keywords Dark pool Agent-based model Trading performance 1 Introduction In recent years, equity market becomes a decentralized electronic network, accompanied by an increasingly fragmented liquidity over multiple venues. Take US equity market as an example, between January 2009 and April 2014, the Yibing Xiong ybxiong@trn.dis.titech.ac.jp Takashi Yamada tyamada@trn.dis.titech.ac.jp Takao Terano terano@dis.titech.ac.jp Tokyo Institute of Technology, 4259 Nagatsuta-cho, Yokohama, Kanagawa, JAPAN

2 2 Yibing Xiong et al. market shares of NYSE Euronext and NASDAQ OMX declined by approximately one-third and one-quarter, respectively [1], while off-exchange trading volume increased from one-quarter to more than one-third of the market. Among them, trading volume in dark pools increased from 9% to 15%. Dark pools came about primarily to facilitate block trading by institutional investors, who did not wish to impact the markets with their large orders and consequently obtain adverse prices for their trades. On the other hand, matching in the dark pool depends on the availability of counter parties, some orders on the heavier side of the market will fail to be executed, and these unexecuted orders may suffer costly delays. Thus trading in dark pools is often considered involving a trade-off between potential price improvement and the risk of execution uncertainty. However, how do different usage rates of dark pool affect these two aspects, has not been revealed. Our work is an agent-based approach to examine the relationship between dark pool usage and individual trading performance, which includes price slippage (with respect to volume weighted average price) and order execution rate. As of April 2014, there were 45 dark pools in the U.S., consisting of three types: agency broker or exchange-owned, broker-dealer owned and electronic market makers. In this paper, we design dark pools where prices are derived from exchanges - such as the midpoint of the National Best Bid and Offer (NBBO), and the results of other kinds of dark pools can be extended from the model. Also in our model, traders are designed to use dark pool in a simple way, each one has fixed probability to use dark pool during the trading. More complicated trading strategies related to dark pool, such as examining the state (order congestion) of the limit order book (LOB), or indication of interest (IOI) of the dark pool, have not been considered yet. After proposing a model represented the use of dark pool in equity market, we answer mainly the following two questions: How does dark pool usage affect price improvement? How does dark pool usage affect order execution rate? The rest of the paper proceeds as follows. The next section briefly reviews the relevant literature considering dark pool and market quality. Section 3 describes the design of an artificial stock market with dark pool. In section 4, we carry out simulations in order to explore the relationship between dark pool usage and market volatility. Section 5 analyzes the result, and section 6 concludes. 2 Literature Review Many studies concern dynamic dark pool trading strategy or optimal liquidation in dark pools, and such problems can be seen as modelling of price impact and execution uncertainty. Laruelle et al. (2011) devise two stochastic recursive learning procedures to optimize order execution across several trading destinations [2]. And the mutual performances of both algorithms are

3 Dark pool usage and individual trading performance 3 compared on simulated and real data with respect to an insider who a priori knows the executed quantities by every venues. Kratz and Schoneborn (2013, 2014) consider an illiquid financial market where a risk averse investor has to liquidate a portfolio at a traditional exchange where trading yields a linear price impact, and in a dark pool where order execution is modeled by a multi-dimensional Poisson process [3] [4]. However, their models separate the internal relationship between price impact and execution uncertainty. In this study, our agent-based model manage to associate this two aspects together through market volatility. And based on different situations of market volatility, we can further developing a group of strategies for dark trading accordingly. Agent-based simulation has already been used to exam the performance of dark trading. Mo et al. (2013) present and validate the costs and benefits of trading small orders in dark pool markets through agent-based modeling [5]. Simulated trading of 78 selected stocks demonstrates that dark pool market traders can obtain better execution rate when the dark pool market has more uninformed traders relative to informed traders. In addition, trading stocks with larger market capitalization yields better price improvement in dark pool markets. Mizuta et al. (2014) built an artificial market model and find that as the dark pool is increasingly used, markets become more stable [6]. In addition, higher usage of the dark pool reduces the market impacts. Comparing with their work, our model is more realistic and pay more attention to price improvement and order execution rate. 3 Model We build our model based on the one presented by Maslov, S. (2000) [7]. The market consists of an exchange and a dark pool, and one single stock is traded by liquidity traders. Trading tasks include order type, order size and order urgency are randomly assigned to traders. After that, each trader splits his order into small ones and submits successively. And each submission can be decided to either the exchange or the dark pool. Order price is determined by the mid-price and order urgency, and the latter can be adjusted by price movement. Initial setting: In the model, intraday trading sessions are set as S, and totally D trading days are considered in the scenario. The total number of liquidity traders is T, and they are evenly divided in to M groups. Each group is distinguished from others with different but stable levels of dark pool usage, denoted as U 1 to U m. Before intraday transaction: In the trading tasks, order type can be buy or sell with equal probability, order size is randomly picked from a set which is generated at beginning, with length T D, and the numbers in it follow a power-law distribution. Order urgency is represented by three levels from lowest to highest, denoted as -1,

4 4 Yibing Xiong et al. 0, and 1, and the total number of orders of each urgency level follows an a:b:c distribution. During intraday transaction: In order to decrease market impact, each trader will first equally split his orders into F fractions, then randomly selects F trading sessions in the day and submit one piece of the order in each choosing session. If the prior order of a trader is submitted to the exchange but not fully executed at the post time when new order are submitting to the exchange, the old order will be cancelled and the amount will be added to the new one. But orders submitted to dark pool will not be affected. Submitted price is mainly decided by order urgency. Take buy orders as an example and suppose current best ask is A 0 and best bid B 0. If urgency is low (-1), trader will place it at ticks away from the best bid at the limit order book (B 0 tick), U[0, λ] is an integer and follows an even distribution. If urgency level is middle (0), trader will place the order at midquote (0.5 (A 0 + B 0 )). This is also the price executed in the dark pool. If urgency is high (1), the trader will aggressively take liquidity up to a limit price impact, denoted as P I max, so the submitting price will be 0.5 (A 0 +B 0 ) (1+P I max ). Which means this is a market order and it will try to absorb sell orders with prices lower than that the submitting price. The relationship between order urgency and order price is listed in Table 1. Table 1: Order urgency and submitting price Urgency Buy order Sell order submit price probability submit price probability B 0 1/(λ + 1) A 0 1/(λ + 1) /(λ + 1)... 1/(λ + 1) B 0 tick λ 1/(λ + 1) A 0 + tick λ 1/(λ + 1) (A 0 + B 0 ) 0.5 (A 0 + B 0 ) (A 0 + B 0 ) (1 + P I max ) 0.5 (A 0 + B 0 ) (1 P I max ) Usage of dark pool: Each trader is assumed to have a fixed probability of using dark pool, denoted as U. So when a trader decides to submit an order, he has the probability U to place it into the dark. At the end of each trading session, buy orders and sell orders in the dark pool has probability cp to be crossed at the mid-price (0.5 (A 0 + B 0 )) of the exchange. After intraday transaction: Order urgency can be adjusted concerning to price movement and order execution condition. For example, if price has increased a significant level at that day, so for the next day, sell order urgency may increase and buy order may decrease. Another adjustment considers order execution condition. Suppose for a certain trader, total order size in a task is S t and order executed that day is S exe. If at the end of a day, orders are not fully executed ((S t S exe )/S t > UT ), the trader may continue to execute it next day but with higher urgency. Sup-

5 Dark pool usage and individual trading performance 5 pose open price and close price for a day are P open and P close. At the beginning of next day, order urgency will be adjusted according to the following rules: if P close > P open (1+θ), traders will pick up a new task. If it is buy order, its urgency has 50% probability to - 1 (50% maintain original urgency); if it is a sell, its urgency has 50% probability to + 1. if P close < P open (1 θ), traders will pick up a new task. If it is buy order, its urgency has 50% probability to + 1 (50% maintain original urgency); if it is a sell, its urgency has 50% probability to - 1. else if (S t S exe )/S t > UT, traders may either continue to execute previous remaining order with + 1 urgency, or drop it and pick a new, with same probabilities (50%). 4 Experiment In order to analyze the performance of different extents of dark pool usage. T traders are divided into 5 groups, each group is distinguished from others with different but fixed levels of dark pool usage, set as U 1,U 2,U 3,U 4 and U 5, respectively. So the probability of dark order submission of these five groups are denoted as [U 1 :U 2 :U 3 :U 4 :U 5 ]. Table 2 lists the values of all parameters in the simulation. Table 2: Parameters in the simulation experiments Description Symbol Used value Number of traders T 100 Number of groups M 5 Trading days D 10 Intraday trading sessions S 100 Order split fractions F 10 Stock initial price P 0 10 Tick size tick 0.01 Dark pool cross probability cp 0.2 Order urgency distribution [a:b:c] [1:1:1] Dark order submission probability [U 1 :U 2 :U 3 :U 4 :U 5 ] [0.1:0.2:0.3:0.4:0.5] Order placement depth λ 4 Max price impact P I max Urgency adjust threshold θ 0.05 Unexecuted order threshold UT 0.2 According to the setting, for one simulation, there are T S = D S = 1000 trading sessions. Assuming stock price at session t is P t, the return at session t is R t, R t is calculated as: R t = Ln(P t /P t 1 ) (1) The volatility (vol) of the market is calculated as:

6 6 Yibing Xiong et al. V ol = 1 n R 2 1 n t T S 1 T S(T S 1) ( R t ) 2 (2) i=1 Assuming trading volume at session t is V t, then the volume weighted average price of the market is calculated as 1000 t=1 V W AP (market) = (P t V t ) 1000 t=1 V (3) t Using the same way, the volume weighted average price of trader t is calculated and denoted as V W AP (t). Then, the price slippage of trader t (P S(t)) is calculated as: { (V W AP (t) V W AP (market))/v W AP (market), sell order P S(t) = (V W AP (market) V W AP (t))/v W AP (market), buy order (4) Supposing group(a) denoted the group in which dark pool submission probability is A, and it consists of n traders (t 1,t 2,...,t n ). The average price slippage of group A (APS(A)) is calculated as: AP S(A) = 1 n i=1 n P S(t i ) (5) On the other hand, suppose the total number of orders of trader t is T OT AL(t), and the number of executed orders of trader t is EXE(t), then the order execution rate of group A (ER(A)) is calculated as: i=1 ER(A) = n i=1 EXE(t i) n i=1 T OT AL(t i) (6) 5 Result The simulation is run for 500 times using the parameters demonstrated in Table 2. For each simulation, we record the volatility, dark pool usage price improvement and order execution rate of each group. First we conduct analysis of variance (ANOVA), to see how average price slippage (APS) and order execution rate (ER) is affected by different market volatilities and dark pool usage. This result is showed in Table 3 and Table 4(row refers to volatility, column refers to dark pool usage and level of significance is set as 0.05). Table 3 and Table 4 suggest that APS and ER of each group is affected by both volatility of the market and dark pool usage of the group. Then we first use the same data to analyze the value of APS of each group under different volatility conditions. The x axis refers to different volatilities of 500 simulations in ascent order (converted to daily volatility), and y axis refers to the APS

7 Dark pool usage and individual trading performance 7 Table 3: Use ANOVA to analyze two factors (row: volatility, column: dark pool usage) influence to average price slippage (SS: sum of the squared errors, df: degree of freedom, MS: mean squared error) ANOVA Source of Variatioin SS df MS F P-value F crit Rows E Columns E Error Total Table 4: Use ANOVA to analyze two factors (row: volatility, column: dark pool usage) influence to order execution rate (SS: sum of the squared errors, df: degree of freedom, MS: mean squared error) ANOVA Source of Variatioin SS df MS F P-value F crit Rows E Columns E Error Total value of each group (calculated as moving average, with interval equals 100). APS and ER values of two groups (dark pool usage equals 0.1 and 0.5)are selected to show in Fig. 1 and Fig. 2. Fig. 1: Average price slippage in different dark pool usage groups Fig.1 shows that different usage of dark pool do not have significant influence on average price slippage when market volatility is quite low or high, but do have influence when volatility is in mid level. In this case, higher usage of dark pool results in higher average price slippage. Fig. 2 shows that order execution rate is lower when market volatility is high, and when dark pool usage is high. The reason may be that when volatility is high, the order imbalance in the limit order book becomes serious.

8 8 Yibing Xiong et al. Fig. 2: Order execution rate in different dark pool usage groups This imbalance hinders the execution of orders submitted to dark pool, and high usage of dark pool strengthens this trend. In the next step, we try to study how do average price slippage and order execution rate vary with the variation of the market share of dark orders, if ignoring the influence of market volatility. Using the same data, we calculate the average price slippage, order execution rate, as well as the market share of dark orders from trader t (DPShare(t)). Suppose for trader t, the number of orders executed in dark pool is EXE(t dark ), then DP Share(t) is calculated as: DP Share(t) = EXE(t dark) (7) EXE(t) For each simulation, we sort DPShare(t) in ascending order, and record the price slippage and order execution rate of each trader. The average price slippage and execution rate are then calculated and shown in Fig. 3 and Fig. 4. Fig. 3 and Fig. 4 indicates that with the increase of dark pool market share, the price improvement increases and order execution rate decreases. And this result stands with existing empirical evidence (Buti, 2011) [8]. 6 Conclusion This study utilizes agent-based model to build an artificial stock market with dark pool, aiming to analyze the relationship between dark pool usage and individual trading performance. Simulation results show that on the one hand, higher usage of dark pool results in higher price improvement (wrt VWAP), but mainly when market volatility is in mid-level. On the other hand, order execution rate decreases with the increase of market volatility, and with the increase of dark pool usage. Our agent-based simulation result is consistent

9 Dark pool usage and individual trading performance 9 Fig. 3: Average price slippage and market share of dark orders Fig. 4: Average execution rate and market share of dark orders with empirical findings. And it may further helping with the problem of balancing price improvement and execution rate under different market volatility situations. References 1. R. Preece, S. Rosov, Financial Analysts Journal 70(6), 33 (2014) 2. S. Laruelle, C.A. Lehalle, G. Pages, SIAM Journal on Financial Mathematics 2(1), 1042 (2011) 3. P. Kratz, T. Schöneborn, Mathematical Finance (2013) 4. P. Kratz, T. Schöneborn, Quantitative Finance 14(9), 1519 (2014) 5. S.Y.K. Mo, M. Paddrik, S.Y. Yang, in Computational Intelligence for Financial Engineering & Economics (CIFEr), 2013 IEEE Conference on (IEEE, 2013), pp T. Mizuta, W. Matsumoto, S. Kosugi, K. Izumi, T. Kusumoto, S. Yoshimura, in Computational Intelligence for Financial Engineering & Economics (CIFEr), 2104 IEEE Conference on (IEEE, 2014), pp S. Maslov, Physica A: Statistical Mechanics and its Applications 278(3), 571 (2000) 8. S. Buti, B. Rindi, I.M. Werner, Charles A. Dice Center Working Paper (2010-6) (2011)

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