Speed and Trading Behavior in an Order-Driven. Market: An Analysis on a High Quality Dataset

Transcription

1 Speed and Trading Behavior in an Order-Driven Market: An Analysis on a High Quality Dataset Seongkyu Gilbert Park and Doojin Ryu September 7, 016 PRELIMINARY AND INCOMPLETE Abstract This paper studies how the speed of order submission defined by the minimum time difference between the two orders by the same investor affect investor behavior when submitting orders in an order-driven market. By analyzing the novel dataset with which can be identified at account level of each order and trade in the KOSPI 00 futures market, we find that slow traders use more market orders than fast traders which is consistent with the theoretical model of Hoffman (01). While existing theory predict slow traders submit limit order further away from the market price than fast traders, we find this correlation to be weak. We extend the theoretical model to explain this phenomemon. We further show that arms race only occurs within fast traders, where the fraction of accounts who were able to trade fast (within ten milliseconds) does not change significantly while the number of accounts to trade faster (within a millisecond) increase by twofold. After the increase in speed, faster traders consume most of the limit order book while the number of orders submitted per fast trader (but not faster trader) drop dramatically. We show that our measure of speed of trading is correlated with algorithm trading proxy measures such as order-to-trade ratio and cancel-to-trade ratio at account level. We thank Mari Robertson, participants at 015 SIER International Conference in Regulatory Reform for Sustainable Economic Growth and 016 Midwest Economics Association Annual Meeting for helpful comments and suggestions. We also acknowledge excellent research assistance by Xiaoxuan Meng. Park gratefully acknowledges financial support from the School of Accounting and Finance at Hong Kong Polytechnic University. School of Accounting and Finance, Hong Kong Polytechnic University, gilbert.park@polyu.edu.hk College of Economics, Sungkyunkwan University, sharpjin@skku.edu 1

2 1 Introduction Intelligence is quickness to apprehend as distinct from ability, which is capacity to act wisely on the thing apprehended. Alfred North Whitehead ( ) Ability to trade fast has become important in today s financial markets. With the introduction of high-frequency traders (HFTs) in the last decade, the whole environment of financial market has changed. More orders and trades are coming from computerized algorithms, and taking advantage of speed in limit order market allows HFTs to trade more frequently without holding large positions. Acknowledging the existence of HFTs has also brought non-hfts to update their beliefs about their trading counterparty, which their orders may be picked off before they can reflect new information and circumstances in their orders. Hoffman (01) uses a two types of investors with different speed to explain market order frequency and limit order behavior. He shows that slow traders use market orders more frequently and submit limit order further away from the market price. Both of these behaviors come from the fear of getting their limit orders being picked off by the faster traders. Submitting limit orders further away from the current price allow their order to earn more time due to the order of market order execution, while it comes at a cost of lowering the probability of being executed. Market orders do not face any pick-offs from fast traders, but may face less attractive trading price. In this paper, we provide empirical evidence that the fast traders and slow traders behave differently when making orders. Using the novel data from the KOSPI 00 futures market, where we observe all orders and trades account in encrypted form, we proxy for the ability to trade fast by observing each account s minimum time difference between two orders. We find that slow traders submit more market orders than fast traders. Also, we find a slow traders generally submit limit orders further away from the market price than the fast traders

3 but the correlation is weak. While the correlation is relatively strong within fast traders and slow traders, weak (and even negative) correlation is observed between middle speed groups. This may be due to the fact that fast traders are more concerend about fast traders, while slow traders concern more about their trades picked off by slow traders. Our observation still holds when we control for inestor types. We also contribute to the literature by examining the correaltion between abililty to trade fast and existing algorithminc trading proxies. Using the order to trade ratio and cancel to trade ratio, we find that our speed measure and the algorithmic trading proxies to show significant correlation. We also test the trading behavior by different subsets of our sample comparing very fast and very frequent traders, fast and very frequent traders, very fast and less frequent traders, and slow but frequent traders. Our simple statistics show that the trading behavior differs by frequency where more frequent traders use less market order and put limit orders close to the market price. We also observe that fast traders become even faster traders. We find that the fraction of traders who were able to trade between one to ten milliseconds decrease while the fraction of traders able to trade within one millisecond increase, while accounts with slower speed do not show significant change. This shows that there is increase in the competition among fast traders in the market that we observe. With the observation of fast trader becoming faster, we suggest a variant of Foucault (1999) and Hoffman (01) where there exist three types of traders, slow traders, fast traders, and very fast traders. Faster traders benefit from able to revise quotes before getting picked off if a slower type of trader arrives in the next sequence. By having more than two types of investors, we can explain the limit order placing behavior that we observe in the data which cannot be explained when we only have two types of investors. We also show that depending on the parameter values, a Markov equilibrium may not exist. A number of papers study speed of trading in financial markets. This paper is most closely related to Hoffman (01), since it tests the implications in his paper. Foucault, 3

4 Hombert, and Rosu (015) show that fast informed traders account for higher trading volume. Brogaard, Hendershott, and Riordan (01) examine that HFTs facilitate price discovery. Biais, Foucault, and Moinas (015) and Budish, Crampton, and Shim (015) provide evidence that investing to trade faster cause negative welfare consequences. Weller (016) show that stocks with more algorithmic liquidity takers relative to liquidity providers suffer information losses. Lee (015) investigate the high frequency trading with focus on market quality, price efficiency, and profitability in the KOSPI 00 Futures market. Our paper do not intend to focus on the high frequency trading and price discovery or information trading, but rather focus on the differnent strategies that investors may use depending on their ability to trade faster than otheer. This paper in structured as follows. Section describes the specific market, namely KOSPI 00 Futures market, that we analyze. I describe the dataset that we use in Section 3. Section reports the empirical findings, especially correlations in speed and trading behavior. Section 5 suggests a theoretical model when a fast trader can become faster. Section 6 concludes. KOSPI 00 Index Futures Markets The underlying asset of the KOSPI 00 futures market is defined as the KOSPI 00 spot index, a capitalization-weighted stock price index consisting of the 00 largest common stocks listed on the Korea Exchange (KRX). The KOSPI 00 index futures market, launched in May 1996, is not only the representative derivatives market in Korea, but also a world-class futures market. In spite of its short history, it has grown very quickly and has maintained a top-tier position globally since the turn of the new millennium. We analyze the price behaviors of this futures market for the following reasons. The KOSPI 00 futures market is extremely liquid, reflecting the great interest shown in it by global and local investors and facilitating the implementation of practical trading strategies.

5 Indeed, it is ranked as one of the leading five index futures markets globally in terms of trading volume. 1 Its low transaction costs, low entry barriers, and synergistic effect owing to the tremendous growth of the related index derivatives market support the considerable liquidity of the KOSPI 00 futures market. Compared with its equity market counterpart, the KOSPI 00 futures market is characterized by extremely low transaction costs and high liquidity. No transaction tax is imposed on futures trading. Hence, the brokerage fee for KOSPI 00 futures trading is much lower than that for equity trading. The fees for futures trading range from 0.1 to 0.9 basis points, about 10 times smaller than the brokerage fees for equity trading. Further, the trading volume of the KOSPI 00 futures market has risen markedly because of the synergetic effect of simultaneous intraday trading in its options, which are not only global top-tier options but also the derivatives most related to futures. The ample liquidity and unique investor participation rate of the KOSPI 00 futures market, its two most important properties, provide a valuable and interesting opportunity to analyze the behavior of futures markets. The futures market is an ideal platform for professional and/or informed investors to implement trading strategies based on their information such as market overreaction, which is the subject of this article. Firstly, its short-sale allowance enables the investors to utilize their information fully regardless of the anticipated market movement implied in the information. This is often not the case in stock markets where short-sale is usually restricted: Only the trading strategies relying on positive information will be feasible if the investors do not possess the stocks. Also, the futures market, with its rich liquidity, is better suited to the trading strategies based on macroeconomic, market-wide information. Unlike private or inside information which is likely to remain unexposed longer and requires trading at individual stock level, the profit opportunities from market-wide information can vanish quickly unless orders are submitted immediately. Another advantage of the futures market for professional and/or informed investors is that they 1 For more details, refer to the website of the Futures Industry Association ( The status of the KOSPI 00 options market and its relatedness to the KOSPI 00 futures market are well summarized in the studies of Ryu (015). 5

6 can minimize their exposure to their competitors. The absence of designated market makers and upstairs market guarantees the anonymity of investors when they submit orders and the ample liquidity of the futures market helps them camouflage their informed trades without heavily fragmenting them 3 With these reasons, the KOSPI 00 futures market is of interest in itself to investigate futures market behaviors and is particularly well suited for our research to examine the existence of overreaction of the representative Asian market (i.e., the Korean market) to US market performance and look into potential profit opportunities from it. This requires prompt trades at the daily market opening session where its opening price is directly affected by US market performance on the previous day and the market price reverses to the normal level during the day as subsequent opposite trades occur. The KOSPI 00 futures market serves well as a test bed to find empirical evidence of the profit opportunities. In the regular KOSPI 00 futures market, the multiplier of the futures contract is 500,000 Korean Won (KRW) and tick size is 0.05 points, which corresponds to 5,000 KRW. The daily continuous trading session opens at 9:00 a.m. and closes at 3:05 p.m., the pre-opening batch auction runs from 8:00 a.m. to 9:00 a.m., and the post-market batch auction runs from 3:05 p.m. to 3:15 p.m. The delivery months are March, June, September, and December, and the expiry date is the second Thursday of each delivery month. The initial margin was set to 15% of the value of the futures contracts traded. The level of maintenance margin should be two-thirds of the initial margin level. KOSPI 00 futures traders can submit an order of up to 1,000 contracts. 3 Data Description and Basic Statistics Our research relies on the unique dataset from the KRX KOSPI 00 futures from January 010 to June 01. The data consists of both Trade and Quote (TAQ) with every trade and 3 Informed investors tend to split their orders and spread their trades in relatively illiquid markets. The order-splitting strategy is also frequently used in a trading environment where investors are easily identified. This strategy is called stealth trading (see Anand and Chakravarty (007)). 6

7 order time-stamped at millisecond level for all orders submitted to the market. The novelty of this dataset is that we can observe the account level for each trade and quote. We also observe the trading account s group type (retail/individual investor, financial trading firm, institutional firm, etc.) and which country the account is from. Also, the data consists of types of orders for each orders submitted, e.g., limit order, market order, stop order, order cancellations, order modifications, etc. Using our dataset, we are able to examine how different investors submit their orders by observing how frequently they use market orders and how far they put their limit order from the execution price. Since we want to focus on the trades and orders when each individuals can observe the limit order book. we focus on the tradings and order submissions from 9:00 a.m. to 3:05 p.m. First, we provide basic statistics by different type of investors using the account s group type. Table 1 shows the number of active accounts by investor group and for each time periods between maturity dates in Korea Exchange trading KOSPI 00 Futures from March 1, 010 to June 1, 01. For example, there are 561 accounts identified as local investment firm in the period where the earliest next maturity date that is June 10, 010 (first row, first column). Active account refers to any exisiting account that has submitted one or more orders during the period. Investment firms are investment banks, other finance firms are financial firms that are not classified as investment banks (e.g. commercial banks, insurance companies, invesment trusts, etc.), other institutions are firms that are not classified as financial firms which includes government and pensions. Table shows the total number of orders submitted (disregarding the size) by each investor group. Table 3 shows the order quantities (regarding the size) by each investor group. From the three tables, we find that majority of the active accounts at any point in our sample period are held by retail investors. However, retail investors trade less frequently relative to their numerous share of active In some cases, such as national college entrance exam date, continuous trading starts from 10:00 a.m. We make adjustments when these events occur so we actually get all the data only when the limit order book is observable by traders. 7

8 accounts in the market. Furthermore, Local investment companies trading activity tends to decrease over our sample period. Note that we can also classify different investors types by their ability to trade fast. To proxy for the account latency (or speed), we use a simple strategy where we track the smallest time difference between the two orders from the same account. Thus, we use the following measure: l = latency ij = min{ time ijt time ijt+1 } (1) where i is the account number, j is the nearest futures maturity month, and time ijt is the t th order that i made for j futures. Here time is calculated as seconds in clock time, not trading time. For further analysis we will use simply define the term latency group as follows: ˆl = ˆ latency ij = 3 if latency ij if latency ij > 100 () log 10 latency ij otherwise where is the ceiling function which rounds up to the next integer. For example, an account that submitted multiple orders within a millisecond will be in latency group ˆl = 3, and an account that the l =.017 will be in latency group ˆl = 1. In all, we have seven latency groups ranging integers from -3 to 3. The intuition is that the traders who are able to trade fast can submit multiple orders in a very short time period. Of course, this strategy ignores any fast traders who only submit one order in relatively long period of time. However, this smaller time difference does imply ability to trade fast. Many high-frequency literatures suggest some proxies to estimate algorithmic traders. Hendershott, Jones, and Menkveld (011) and Hagströmer and Nordén (013) use order to volume ratio, Hendershott, Jones, and Menkveld (011), Hagströmer and Nordén (013), and Hasbrouck and Saar (013) use number of cancel order quantities to number of actual trade quantities, and Hendershott and Riordan (013), Menkveld (013), O Hara (015), 8

9 and O Hara, Yao, and Ye (01) use averge trade size to proxy for algorithmic trades. We observe in our sample that most orders of the futures contracts are relatively of a small size so average trade size does not explain what we observe. While it is noted that HFTs tend to have small average trade size, individual investors also do not submit large orders in the derivatives market. Although not reported here, order to volume ratio and cancel to trade ratios are highly correlated with our latency (or ˆ latency) measure in our sample. The odd lot volume used in O Hara, Yao, and Ye (01) is also not applicable in our setting since the smallest size tradeable is one unit of contract which cannot be divisible. Table shows the number of active accounts by each latency group. We find that there are various accounts in terms of latency trading in the KOSPI 00 Index futures throughout the sample period. One interesting fact is that from the December 01 contract (column 1/8/11) and on, we find higher very fast traders who can submit their orders within a millisecond (row 3). Also, we find the number of active accounts decrease for latency group of for the same sample period. This may suggest trading arms race among fast traders, while we do not see this clear phenomenon for other latency groups. Table 5 and 6 reports the total number of orders submitted and the total size of orders submitted for each latency group. We find that most of the orders are actually dominated by very fast traders, mainly investors of latency group 3 and. Empirical Findings In this section, we investigate the trading behavior using how much of market orders investors use over all orders submitted, and if limit order is used, how far from the execution price they place their limit orders. In Panel A of Table 7, we report the average fraction of market orders by latency group and nearest maturity date. While the numbers vary over time, we observe more frequent use of market orders going down the row (as the speed of account gets slower). The slowest 9

10 group, namely latency group 3, uses market orders in one out of every five orders they submit. This ensures the execution of their trades despite the disadvantage of the price that they might face. In contrast, the fastest group (latency group 3), uses less than.1% of their orders as market orders. The advantage of revising quotes quickly allows these investors to benefit in terms of price despite the lower execution probability compared to market orders. The correlation can be more clearly seen by running a simple correlation test. In Table 8, we report the Pearson correlation results using account(latency group)-maturity pair from our data. We find positive correlation for the overall sample as well as for each investor types. Panel B of Table 7 reports the distance of limit orders away from the mid-quote price. As mentioned above, the minimum tick size is.05. Thus, the fastest investors submit their limit orders two to three ticks away from the market price, while slowest traders place their limit orders more than eight ticks away. Similar to Panel A, we find a general pattern that the spread increaes as latency increases. However, when only comparing group 1 and 0, we find this pattern to be the opposite. This does not follow the intuition that slower traders (group 0) will submit orders further away from the market price compared to the faster traders (group 1) to aovid getting picked off. In Table 9, we find the correlation coefficient to be significant for overall sample, but the coefficient is less than.0. We find insignificant or even negative correlation when we test it within investor type groups. The findings of limit order behavior does not comply fully with Hoffman (01). Thus we first test whether our latency group is related to high freuqency proxies that are used in the literature. We use the order-to-trade ratio and cancel-to-trade ratio as high-frequency proxies. Since market orders may distort each ratios, we actually use limit orders to limit orders executed ratio (ln LimitOrder ) and Cancel to limit orders executed ratio (ln(1 + Cancel LimitT rade )). LimitT rade Also, we log each ratios to prevent statistical mean to be affected heavily by right skewed observations, and add one in cancel to orders ratio to prevent any accounts without using cancellations in their orders giving output of ln 0. 5 Panel A in Table 10 shows the basic 5 We actually find approximately 1 3 of accounts in our sample not using cancellations in their orders. However, this does not imply that all their orders become executed since the limit order book resets after 10

11 statistics for these measures. In Panel B of Table 10, we find that our measure of latency (l) is negatively correlated with the high frequency trading proxies, which is desired. All the numbers in correlation tables are statistically significant at 1% level. Panels C-F in Table 10 shows the basic statistics for different speed and frequency types. Comapring Panel C and D, we observe that speed does actually matter in order behavior while controlling for order frequency. However, we also find that comparing Panels E and F, that limit spread shows negative correlation with speed when controlling for frequency. While this may be due to some extreme outliers which can be speculated by looking at the median values, we still find that the 90 percentile groups to be still negatively correlated. Since Hoffman (01) also suggest that volatility may affect the trading behavior, we run a simple regression while controlling for the volatility. We use the V-KOSPI index measure which is derived from the KOSPI 00 options which the underlying asset is the same KOSPI 00. Figure 1 shows the volatility changes between July 1, 011 to August 31, 011. We run a simple regression in this period as follows: limspread itd = α + βs i + γ itd V ol d + BBQ td + BAQ td + ε itd limspread td is the is calculated as the price difference between submitted limit order price and the midquote of best bid and ask available, S i is vector of dummies representing each latency (ˆl) gropu from -3 to. V ol d is the daily volatility from volatility index implied by KOSPI 00 options. BBQ td is the quantity of limit order placed at the best bid and BAQ td is the quantity of limit order placed at the best ask. Standard errors are reported in parenthesis. All coefficients reported in Table 11 are statistically different from zero at the 1% significance level. As Hoffman (01) speculated, volatility does seem to play a role when investors are submitting limit orders. Even when we control for the quantities in the limit order book (column (3)), we find the coefficients in V ol to be still positive and significant. When the market is more volatile, investors fear more about their orders to be picked off the market closes. 11

12 when they place a limit order before they can revise their order. However, consistent with the eyeball measure of Table 7 Panel B, Table 11 still show that coefficients for Speed, Speed 1, Speed 0 are not in the order that we would expect from the existing theory. This draws an attention to revise the theory to understand this behavior by investors. We provide a model that can explain this in the next Section. 5 Three Speed Type Model In this section, we develop a theory of three different types of traders which only differs by speed. We follow the notation and the basic concept from Hoffman (01), which is a variant of Foucault (1999). 5.1 Limit Order Market with Three Types of Traders There exists a single risky asset with fundamental value that follows a random walk v t = v t 1 + ε t (3) where ε {σ, σ} with equal probability. Traders arrive sequentially at time t = 1,,... and are risk-neutral. At time t, a trader arriving at t t values the asset at R t = v t + y t () where y t {+L, L} is the time invariant private valuation and the realization occurs with equal probability. Each trader can sell market orders execute at the currently best bid Bt m, or buy market orders execute at the currently best ask A m t, or set a limit order which may execute in next period. There are three types of traders, slow traders (s), fast traders (FTs), and very fast Traders (VTs). There is α fraction of slow traders, β of fast traders, and all the rest are 1

13 very fast traders. FTs are able to cancel/revise their limit order and resubmit a new one after the realization of ε t+1 conditional on t + 1 traders being a slow trader (). VFT are able to cancel/revise their limit order and resubmit a new one after the realization of ε t+1 conditional on t + 1 traders being FT or. 5. Payoff and Strategies Suppose y t = L. Seller s expected profit when choosing to post a limit order is equal to Vk LO, k {,, }. She will market sell if B m (v + ε L) V LO k (5) Let cutoff price be v+ε k = V LO k + (v + ε L) (6) which makes the seller indifferent, if available. With equality in the equation above, we assume that traders prefer market order to limit order if the expected payoffs are equal. Now suppose quote setting problem of a buyer. Let p(b) be the execution probability of. Since innovation (ε) and trader types are discrete, p is an increasing step function. Optimality implies price is set at cutoff. Objective function of slow buyer, who decides to submit limit order, V LO = max B {p(b )(v + E ex [ε] + L B )} (7) where E ex [ ] is expectation function conditional on execution. Fast buyer chooses a tuple of three bid price (B, B +σ, B σ ). Let q k,ε(b) denote execution probability of FT s limit order with bid price B conditional on the next period s trader 13

14 type and asset value innovation. VF LO T = max B,B +σ,b σ {(1 α)q (B )(v + E ex [ε] + L B ) + α q (B +σ )(v + σ + L B+σ ) (8) + α q (B σ )(v σ + L B σ )} Clearly, B +σ = and B σ v σ =, so the maximization simplifies to max{(1 α)q (B )(v + E ex [ε] + L B )} (9) B = max B {βq (B )(v + E ex [ε] + L B ) + (1 α β)q (B )(v + E ex [ε] + L B )} Very fast buyer chooses a tuple of three bid price (B, B +σ, B σ ). Let r k,ε(b) denote execution probability of VT s limit order with bid price B conditional on the next period s trader type and asset value innovation. VV LO T = max B,B +σ,b σ {(1 α β)r (B )(v + E ex [ε] + L B ) (α + β) + (α + β) + r (B +σ )(v + σ + L B+σ ) (10) r (B σ )(v σ + L B σ )} For simplicity we only focus on the positive innovation, ε = +σ. 6 Note that choosing the optimal B +σ cannot be worse, V LO may vary depending on the parameters. Clearly, since ability to trade faster > V LO v+ε, so we have function, it is optimal to either choose B +σ v+ε >. Since r is increasing and a step = or B +σ =. Note that if VT choose +σ v+ε v+ε, FT seller will not trade since > and only seller will trade. Thus, α + β r ( )(v + σ + L 6 Negative innovation is analogous. ) α + β r ( )(v + σ + L ) (11) 1

15 and since execution probability r ( ) = α and r (α+β) ( ) = 1, α (v + σ + L α α + β }{{} LHS (α + β) ) (v + σ + L (v + σ + L ) (v + σ + L ) } {{ } RHS ) (1) so that if LHS of the above equation is greater, VFTs choose to target the s but not the FTs. If the RHS is greater, VFTs target the FTs that also allow s to trade. Lemma 1. In equilibrium, Proof. Clearly, the ability to revise limit orders can never be a disadvantage so that V LO V LO V V O. From (6), we have It remains to show and.. First, L is the maximum expected gains from trade that period (if two agents with different private valuations trade, they share a surplus of L, but this occurs at most with probability 1 LO ), so L V k 0 for all k {,, }. Assume σ L. Using (6), v t + σ which directly implies. v t + σ L and v t σ v t σ L, Now Assume σ < L, and consider a very fast buyer submitting a buy limit order. It is easy to see that, in this case, 1 α β [v σ +L ]+ 1 α β [v +σ +L ] 1 α β [v σ +L ] such that his optimal choice is B executes this order because v σ + L > possible valuation. =. A buyer arriving one period later never ; that is, the bid price B is below his lowest Now consider a slow buyer and suppose he posts a buy limit order with B =. 15

16 As this is not necessarily his equilibrium strategy, V LO 1 [v + L ]. Now assume Then, α α + β +σ (v + σ + L < ) +σ (v + σ + L ) VV LO (1 α β) T = { (v + L (α + β) + (v + σ + L (α + β) + (v σ + L ) ) )} and therefore, V LO V LO α + β ( α + β ( = α + β (VV LO T V LO ) + α + β ( ) + α + β ( ) + α + β σ ) ) Using (6), V LO Then, Now assume V LO α+β σ, so α β α α + β. +σ (v + σ + L > ) +σ (v + σ + L ) 16

17 VV LO (1 α β) T = { (v + L { + α (v + σ + L ) + α (v σ + L )} (1 α β) (v + L + α + β (v + σ + L + α + β (v σ + L ) ) ) )} and therefore, V LO V LO α + β ( = α + β (VV LO T V LO ) + α + β ( ) + α + β σ ) so we again have. 5.3 Equilibrium For each equilibrium, note that each group of traders has following strategy set: {,,,,, } For each individuals, we must show that their strategy is incentive compatible. It is clear from the payoff structure (step function of execution probability) that investors will only choose one of the six strategies {,,,,, we only need to consider the incentive compatibility of VTs from { {,,, have different strategies for each }. Furthermore, it is clear that, } and FTs from } since other strategies are (weakly) dominated. Since we actually and depending on the inequaility in (1), we have maximum 6 = 96 different possible equilibrium strategy profiles from all strategy sets. 17

18 However, these strategies still may not all be feasible. We show the following result which differs from Hoffman (01). Proposition 1. For some fixed parameters (α, β, σ, L), a pure strategy Markov perfect equilibrium may not exist. Furthermore, not all strategy profiles are feasible for equilibrium. Proof. For the first part of the proposition, it is enough to show an example where an equilibrium strategy does not exist for certain set of fixed parameter. When α =.5, β =.3, σ =.5, and L = 1 we can easily find that none of the possible strategies satisfy an equilibrium strategy. For the second part of the proposition, we can show that v σ =, = v σ, = does not constitute an equilibrium. Details of this proof are shown in the appendix. Furthermore, we argue that some other strategy profiles are also non-feasible. Proposition. For some fixed parameters (α, β, σ, L), equilibrium exists where. That is, slower traders may submit limit orders closer to the market price than the fast traders do. While we do not provide the full analysis, solving for the equilibrium strategies numerically shows that in some cases, = whereas =.7 Lemma 1 shows that the inequality holds for Proposition. This provides a theoretical reason why we observe the results in Table 11. The game between traders become more complicated when there exists more than one counterparties. Fast traders may fear a lot more about very fast traders picking their trades off more than slow traders do and can benefit more when they avoid this pick-off. 7 This is one example that Proposition hold. Clearly from Lemma 1, there can be other examples where Proposition holds. 18

19 6 Conclusion Ability to trade faster than others changes the behavior of not just the ones who are able, but all the potential counterparties who trades with them. We show evidence that slow investors do fear the chances of their limit orders being picked off. Slow investors make market orders more often than fast investors and when they do make limit orders, they put the limit orders further away from the market value which lowers the possibility of execution. However, with multiple types of traders which differs by speed, we may not see a monotonicity of limit order spread by speed, which is supported by the data from the KOSPI 00 Futures market. While the previous literature lacks explaining this phenomenon, we provide a theoretical model that can explain this observation. References Anand, Amber, and Sugato Chakravarty, 007, Stealth Trading in Options Markets, Journal of Financial and Quantitative Analysis, (1), Biais, Bruno, Thierry Foucault, and Sophie Moinas, 015, Equilbrium Fast Trading, Journal of Financial Economics, 116(), Brogaard, Jonathan, Terrence Hendershott, and Ryan Riordan, 01, High-Frequency Trading and Price Discovery, Review of Financial Studies, 7, Budish, Eric, Peter Cramton, and John Shim, 015, The High-Frequency Trading Arms Race: Frequent Batch Auctions as a Market Design Response, Quarterly Journal of Economics, 130(), Thierry Foucault, 1999, Order Flow Composition and Trading Costs in Dynamic Limit Order Market, Journal of Financial Markets,,

20 Foucault, Theirry, Johan Hombert, and Ioanid Rosu, 015, News Trading and Speed, Journal of Finance, 71(1), Hagströmer, Bjorn, and Lars Nordén, 013, The Diversity of High-Frequency Traders, Journal of Financial Markets, 16(), Hasbrouck, Joel, and Gideon Saar, 013, Low-latency Trading, Journal of Financial Markets, 16(), Hendershott, Terrence, Charles M. Jones, and Albert J. Menkveld, 011, Deos Algorithmic Trading Improve Liquidity?, Journal of Finance, 66(1), 1 33 Hendershott, Terrence, and Ryan Riordan, 013, Algorithmic Trading and the Market for Liquidity, Journal of Financial and Quantitative Analysis, 8(), Hoffman, Peter, 01, A dynamic Limit Order Market with Fast and Slow Traders, Journal of Financial Economics, 113, Lee, Eun Jung, 015, High Frequency Trading in the Korean Index Futures Market, Journal of Futures Markets, 35(1), Menkveld, Albert J., 013, High Frequency Trading and the New Market Makers, Journal of Financial Markets, 16(), O Hara, Maureen, 015, High Frequency Market Microstructure, Journal of Financial Economics, 116(), O Hara, Maureen, Chen Yao, and Mao Ye, 01, What s Not There: Odd Lots and Market Data, Journal of Finance, 69(5), Ryu, Doojin, 015, The Information Content of Trades: An Analysis of KOSPI 00 Index Derivatives, Journal of Futures Markets, 35(3),

21 Weller, Brian M., 016, Efficient Prices at Any Cost: Does Algorithmic Trading Deter Information Acquisition?, working paper 1

22 A Proof of Proposition 1 In this part, we only show the conditions one of the many possible cases for equilibrium. We focus on the case when α α+β (+L < ) (+L ). V LO V LO V LO =, = = α [v σ + L ] = β, and =. First we check on the case where [v σ + L ] + α (v + σ + L ) + α (v σ + L ) = (1 α β) so we have (v σ+l B )+ (1 α β) (+L B )+ α (+L )+ α (v σ+l ) V LO = V ( ) = α [v σ + L ] = α LO [L V ] α = ( )(L). (13) + α For FTs, V LO = β = LO [L V ] + α LO [L V ] 1 LO [L(α + β) αv ]. (1) + β Plugging in (13), V LO = β( + α) + 8α L. (15) ( + β)( + α) We also should have the optimal strategy for VTs, V LO = 1 α β + α = 1 α β σ α β LO [L V ] + α LO [L V ] σ + 1 α β [L V LO ] + 1 α β [L VV LO T ] + α LO [L V ] [L V LO ] = 1 α β 3 α β σ + 3 α β [(1 β)l α V LO ]. (16)

23 Applying (13) to (16) gives V LO = 1 α β (1 β)( + α) α σ + L (17) 3 α β (3 α β)( + α) Since we assume α α+β (+L < ) (+L ), (13) and (1) gives β > α α (18) V LO should be greater than other available strategies for s, i.e., slow traders using strategy gives V ( ) = α + β [v σ + L = α + β [L VF LO T ] = ] (α + β)( α) L (19) ( + β)( + α) which should satisfy the incentive compatibility, V LO V ( ) α (α + β)( α) ( )(L) + α ( + β)( + α) L that gives β α α. (0) This contradicts with (18). Thus, = (+L ) (+L ) cannot be an equilibrium. Thus we should have value. So, α α+β (+L > ) (+L, =, and v σ ). Note that for the FTs, =, where α α+β < strategy should not give higher 3

24 V ( ) = 1 α = (L VV LO T ) + α (1 α)(1 α β) σ + (3 α β) LO (L V ) ( (1 α)(8 α) (3 α β)( + α) + α + α ) L Incentive compatible condition implies VF LO T V ( ) ( β( + α) + 8α (1 α)(1 α β) (1 α)(8 α) L σ + ( + β)( + α) (3 α β) (3 α β)( + α) + α ) L + α ( α)[(β )(1 α β) β ] L σ (1) ( + α)( + β)(1 α)(1 α β) Since α, β [0, 1] and α + β [0, 1], the LHS of (1) is negative. Since L > 0 and σ > 0, it contradicts that, =, =, and V T we conclude that strategy profile strategy. = is an equilibrium where α α+β =, F T =, and V T = (+L > ) (+L ). Hence cannot be an equilibrium

25 B Tables and Figures Table 1: Number of Active Accounts by Investor Group and Nearest Maturity Date This table shows the number of active accounts by investor group and for each time periods between maturity dates in Korea Exchange trading KOSPI 00 Futures from March 1, 010 to June 1, 01. For example, there are 561 accounts identified as local investment firm in the period where the earliest next maturity date that is June 10, 010 (first row, first column). Active account refers to any exisiting account that has submitted one or more orders during the period. Investment firms are investment banks, other finance firms are financial firms that are not classified as investment banks (e.g. commercial banks, insurance companies, invesment trusts, etc.), other institutions are firms that are not classified as financial firms which includes government and pensions. The last column refers to the number of active accounts during the whole sample period. It differs from the simple sum of the row since same account may trade over multiple periods. The majority of account holders in KOSPI 00 Futures market are local retail investors. 6/10/10 9/9/10 1/9/10 3/10/11 6/9/11 9/8/11 1/8/11 3/8/1 6/1/1 9/13/1 1/13/13/1/13 6/13/13 9/1/13 1/1/133/13/1 6/1/1 All 5 Local Investment Foreign Investment Local Other Finance Other Foreign Finance Other Local Institution Other Foreign Institution Local Retail Investor Foreign Retail Investor N % N % N ,99 % N % N % N % N 15,989 15,89 1,37 1,61 15,36 17,375 18,059 16,07 15,333 15,889 13,765 13,315 1,58 15,50 13,638 13,68 13,15 77,96 % N % Total 19,697 18,888 17,99 18,61 19,6 1,33,198 0,039 19,70 19,779 17,00 16,763 17,88 19,083 16,663 16,733 16,1 9,96

26 Table : Order Frequency by Investor Group and Nearest Maturity Date This table shows the number of orders submitted during regular trading hours (9:00AM to 3:05PM) by investor group and for each time periods between maturity dates in Korea Exchange trading KOSPI 00 Futures from March 1, 010 to June 1, 01. Any order submitted count as a single order disregarding the size of order. We only report figures for regular market hours since we focus on order behavior when investors can observe the limit order. KOSPI market uses single price auction before and after regular trading hours. Investment firms are investment banks, other finance firms are financial firms that are not classified as investment banks (e.g. commercial banks, insurance companies, invesment trusts, etc.), other institutions are firms that are not classified as financial firms which includes government and pensions. Local retail investors submitted the most orders while foreign (non-investment) finance firms and local investment firms submit more than 10% of overall orders for most of the sample period. (in thousands) 6/10/10 9/9/10 1/9/10 3/10/11 6/9/11 9/8/11 1/8/11 3/8/1 6/1/1 9/13/1 1/13/13/1/13 6/13/13 9/1/13 1/1/133/13/1 6/1/1 6 Local Investment Foreign Investment Local Other Finance Other Foreign Finance Other Local Institution Other Foreign Institution Local Retail Investor Foreign Retail Investor N 35,775 3,603 31,58 35,359 0,11 7,99 50,39 31,868 3,857 55,788 3,67 3,63 5,655 8,31 0,738 18,53 15,50 % N 9,389 11,59 10,873 8,3 8,5 1,07 1,888 11,5 1,37 10,01 6,695 10,936 9,831 1,8 10,607 9,779 9,95 % N,03 1,903,393 3,63 5,7 5,187 5,09 3,70,93 3,98 3,1 1,87 1,71 1,95 1,075 1,3 1,115 % N 31,0,358 9,361 1,08 9,380 6,91 75,055 61,817 59,886 70,36 56,06 53,037,509,337 3,3 31,0,81 % N 1,715 6,761 10,566 11,995 5,683 5, 1,80 1,557 1, , ,730 1,90 1, 1,150 % N 18,7 19,565 7,7 33,83 30,75 3,138 7,15,33,38,136 0,078 17,958 5,11 8,01 7,080 3,15 18,193 % N 108, ,3 9,01 103,73 115,099 13,66 138, , , ,98 101,371 89, ,906 19,875 98,16 97,87 79,8 % N % Total

27 Table 3: Order Quantity by Investor Group and Nearest Maturity Date This table shows the order quantities submitted during regular trading hours (9:00AM to 3:05PM) by investor group and for each time periods between maturity dates in Korea Exchange trading KOSPI 00 Futures from March 1, 010 to June 1, 01. The numbers are total sum of size of orders submitted by each investor gruops in given period. We only report figures for regular market hours since we focus on order behavior when investors can observe the limit order. KOSPI market uses single price auction before and after regular trading hours. Investment firms are investment banks, other finance firms are financial firms that are not classified as investment banks (e.g. commercial banks, insurance companies, invesment trusts, etc.), other institutions are firms that are not classified as financial firms which includes government and pensions. Overall, total quantities submitted tend to decrease over out sample period. Local investment firms fraction of overall quantity tend to decrease while foreign investment firms share tend to increase over the sample period. (in thousands) 6/10/10 9/9/10 1/9/10 3/10/11 6/9/11 9/8/11 1/8/11 3/8/1 6/1/1 9/13/1 1/13/13/1/13 6/13/13 9/1/13 1/1/133/13/1 6/1/1 7 Local Investment Foreign Investment Local Other Finance Other Foreign Finance Other Local Institution Other Foreign Institution Local Retail Investor Foreign Retail Investor N 308,18 70,083 9,5 0,19 30,731 5,359 0,98 17, ,636 0,7 158,508 18,88 10,983 1,96 91,556 93,35 86,70 % N 5,518 9,8 7,00 36,978 33,58 6,633 63,58 50,560 3,36 6,871 9,537 6,333 55, , 69,138 58,037 9,389 % N 10,59 8,77 9,51 6,67 9,9 1,575 11,007 8,70 9,955 11,57 8,68 5,689 5,69 5,796,09,189,50 % N 151, ,76 167,98 107,978 11,98 50,00 58,9 81,37 95,83 361,85 86, , , ,109 13,79 139, 181,05 % N 5,65 10,81 13,6 15,636 8,53 8,08,585 3,005 3,171,98 1,99,89 3,917 6,361,811 3,196 3,33 % N 175,71 185,77 171,116 0,98 153,715 13,66 338,6 17,866 98,37 79,651 7,33 66,966 90,6 108,8 106,55 109,39 93,13 % N 195,16 186, ,83 191,18 0,0 37,808 3,391 15,0 171,1 178,95 15,036 13, , ,51 1,8 11, ,69 % N 1, , ,650 1, ,3 % Total 900,13 88,18 810,63 80,30 761,059 1,016,1301,11,760796,78 797,836 90,599 71,0 697,777 60,08 683,837 55,3 59,1 571,657

28 Table : Number of Active Accounts by Trading Latency and Nearest Maturity Date This table shows the number of active accounts by trading latency (ˆl) and for each time periods between maturity dates in Korea Exchange trading KOSPI 00 Futures from March 1, 010 to June 1, 01. Trading latency is calculated by equation (), so that 3 is the accounts observed to be able to submit multiple orders within a millisecond. Smaller number implies ability to trade faster. Active account refers to any exisiting account that has submitted one or more orders during the period.the last column refers to the number of active accounts during the whole sample period. It differs from the simple sum of the row since same account may trade over multiple periods. 6/10/10 9/9/10 1/9/10 3/10/11 6/9/11 9/8/11 1/8/11 3/8/1 6/1/1 9/13/1 1/13/13/1/13 6/13/13 9/1/13 1/1/133/13/1 6/1/1 All N ,56 % N,166,093,066,183,301,53,13 1,31 1,301 1,367 1,1 1,086 1,03 1,307 1,085 1,0 1,108 11,13 % N,05,079 1,859 1,799 1,955,70,68,198,,331,007 1,918,00,5 1,897 1,898 1,78 1,130 % N 1,10 1,93 1,316 1,83 1,09 1,757 1,895 1,509 1,601 1,611 1,315 1,395 1,37 1,79 1,7 1,90 1,158 8,637 % N 7,6 7,080 6,637 6,637 7,165 7,870 8,537 7,56 6,97 7,36 6,098 5,88 6,1 6,910 5,838 5,837 5,98 35,01 % N,059 3,87 3,70,007 3,96,16,89,39 3,91,09 3,611 3,630 3,580,008 3,58 3,579 3,59 15,753 % N,19,93,18,531,37,53,76,371,39,31,3,17,15,316,67,05,391 6,989 % Total 19,697 18,888 17,99 18,61 19,6 1,33,198 0,039 19,70 19,779 17,00 16,763 17,88 19,083 16,663 16,733 16,1 9,96

29 Table 5: Order Frequency by Trading Latency and Nearest Maturity Date This table shows the number of orders submitted during regular trading hours (9:00AM to 3:05PM) by trading latency (ˆl) and for each time periods between maturity dates in Korea Exchange trading KOSPI 00 Futures from March 1, 010 to June 1, 01. Any order submitted count as a single order disregarding the size of order. Trading latency is calculated by equation (), so that 3 is the accounts observed to be able to submit multiple orders within a millisecond. Smaller number implies ability to trade faster. We only report figures for regular market hours since we focus on order behavior when investors can observe the limit order. KOSPI market uses single price auction before and after regular trading hours. (in thousands) 6/10/10 9/9/10 1/9/10 3/10/11 6/9/11 9/8/11 1/8/11 3/8/1 6/1/1 9/13/1 1/13/13/1/13 6/13/13 9/1/13 1/1/133/13/1 6/1/ N,833,131,11 3,966 5,657 10,581 0,5 16,961 18,06 19,757 17,953 16,085 15,699 17,89 13,056 13,36 1,77 % N 11,5 11,716 1,750 1,313 13,753 15,551 7,65,1,395 3,065 1,83 1,605,161,917,906 1,80 1,31 % N 1,339 1,36 1,098 1,096 1,36 1,773 1,786 1,5 1,531 1,597 1,319 1,333 1,33 1,667 1,375 1,316 1,61 % N , % N,076 1,969 1,656 1,65 1,96,00,75 1,81 1,859 1,797 1,359 1,90 1,9 1,666 1,86 1, % N % N % Total 0,760 0,00 0,65 1,757 3,567 31,56 3,083 3,388,960 7,159 3,17 1,055 1,58,913 19,67 18,365 16,83