An Analysis of High Frequency Trading Activity

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1 An Analysis of High Frequency Trading Activity Michael D. McKenzie Professor of Finance University of Liverpool Management School Chatham Street Liverpool L69 7DH United Kingdom michael.mckenzie@liverpool.ac.uk Deputy Scientific Director Fondazione European Capital Markets CRC c/o Dipartimento di Economia Aziendale Viale Pindaro Pescara Italia Draft Paper Only Not to be quoted without the author s permission 25 February, 2013

2 1. Introduction The flash crash of May 6th, 2010 saw the U.S. share market fall more than 5% in a matter of minutes, before recovering most of those losses almost as quickly. 1 While the popular press and many industry commentators were quick to point the finger of blame at high-frequency traders (HFT 2 ), it is now understood that HFT was only, at best, a contributing factor. 3 Nonetheless, HFT does remain something of an enigma as there is a good deal of confusion about how HFT operate and their impact on the market. This lack of understanding is of particular concern given that HFT are the originator of the bulk of trade and quote activity on most exchanges nowadays. For example, Zhang and Powell (2011) reported that 70% (77%, 40%) of consolidated volume on US (UK, European) exchanges is HFT. 4 A small but growing academic literature has attempted to provide insights on the issue of how HFT impacts on the market. This research has broadly addressed three main questions (i) the impact of HFT on prices encompassing both price efficiency and price volatility (see Zhang, 2010, Hasbrouck and Saar, 2010, Groth, 2011, Brogaard, 2010a, Brogaard, 2011, Hendershott, 2011 and Brogaard, 2012), (ii) the impact of HFT on liquidity and/or volume (see Hasbrouck and Saar, 2010, Brogaard, 2011 and Sornette and von der Becke, 2011), and (iii) the profitability and fairness of HFT (see Brogaard, 2010, Angel, Harris and Spatt, 2010, Angel and McCabe, 2010, Menkveld, 2012). While the evidence is not unanimous, these papers generally provide evidence to suggest that HFT is not detrimental to price formation, volatility or liquidity (although concerns over the ability of HFT to rapidly withdraw from the market have raised questions as to whether the liquidity benefits of HFT are overstated 5 ). This paper analyses HFT from a different viewpoint. Rather than focusing on the market impact of HFT, the purpose of this paper is to investigate the more fundamental issue of understanding HFT trading behavior. 6 To this end, this paper will examine a range of metrics and undertake different types of analysis to identify the aggregate trading behavior of HFT. The results of this paper may be summarized as follows. At the open of the trading day, non- HFT activity is at its highest for the morning session, while HFT appear to wait briefly before 1 CFTC and SEC (2010) provide a detailed account of the flash crash. 2 To conserve space, we use HFT to denote high frequency trading, high frequency trades and high frequency trader(s) throughout the paper. 3 Easley, de Prado and O Hara (2011, pp. 2 3) list six possible explanations for the flash crash. Sornette and von der Becke (2011) argue that while HFT may not havebeen responsible for the flash crash, it nonetheless presents a considerable threat to market stability as it may accelerate existing market dynamics. 4 Schack and Gawronski (2009), Chester, Harris and Spatt (2010) and Menkveld (2012) note that the emergence of HFT was greatly facilitated by market fragmentation. For example, the NYSE share of trading in its own listed stocks has fallen from 80% in early 2003 to 25% by the end of 2009 (see Kumar et al., 2011). 5 Easley, de Prado and O Hara (2011, pg. 3) argue that the flash crash was partly the result a withdrawal of liquidity by some electronic market makers. 6 Gomber et al, 2011, and Angel and McCabe, 2010, summarise the most popular forms of HFT trading strategies. 2

3 entering the market. During the trading day, HFT are net providers of liquidity to the market, while Non-HFT are net takers of liquidity. Finally, Non-HFT are far more aggressive at the end of the trading day, taking large amounts of liquidity and exhibiting a relatively larger increase in their average trade size. Inventory holdings of both HFT and Non-HFT are related to the market movements over the day, although this result is stronger for Non-HFT suggesting they are more likely to be momentum traders. Finally, both HFT and Non-HFT are found to manage their inventory. The remainder of this paper proceeds as follows. Section 2 describes the data to be used in this paper. Section 3 provides some preliminary analysis of the importance of HFT in the market and then considers the behavior of HFT relative to non-hft. Finally, Section 4 concludes the paper and suggests some directions for further research. 2. Data The dataset used in this study consists of millisecond time stamped trade-by-trade data for 120 U.S. stocks listed on the Nasdaq exchange. These data are sampled over the period January 2008 to December 2009 and covers 502 days of trading (all trades that occurred at the opening, the close and also intraday crosses are excluded). 7 The 120 companies consist of an equal number of small, medium and large companies (ranked by market capitalization) and come from a range of different industries. This data is the Trade dataset used in Brogaard (2010, 2011, 2012) and we refer interested readers to the source paper for further details on the data including some basic descriptive metrics. The counterparties to each trade are categorised as either a HFT or a non-hft. The HFT group consists of 26 firms that were identified by Nasdaq as engaged primarily high frequency trading activities. Thus, the HFT designation does not necessarily capture all high frequency trades, but all trades designated as HFT do originate from a firm engaged primarily in high frequency trading. 3. Results Our analysis of HFT begins with a characterization of the trading day using 5 minute intervals. 8 Figure 1 presents information on the average intraday trading frequency. Panel A of Figure 1 presents a plot of the average number of trades in each 5 minute interval, while Panel B presents the average traded volume. As expected, the trading day exhibits the standard U -shape, with a peak of activity at the opening, followed by lower trading activity during the day, until an 7 Note that we exclude two half days of trading from the analysis, which occurred 28/11/2008 and 23/12/ Note that 1-minute intervals were also tested and the results are qualitatively unchanged. As a further robustness test of our results, all of the analysis undertaken in this paper was also performed individually on small, medium and large firm groupings. To conserve space, we only discuss results that differ from those derived using the aggregate data. 3

4 upsurge in activity leading to the close of the market. There is a pronounced spike in trading activity and volume around 10.00am, which corresponds to the time at which scheduled U.S. macroeconomic news announcements are released to the market (see Dungey, McKenzie, and Smith, 2009). The focus of this paper is on the difference between HFT and non-hft. As such, we can revisit the trading volume information summarized in Panel B of Figure 1, distinguishing between the two different classes of trader as well as those providing liquidity to the market (makers) and those taking liquidity from the market (takers). Panel A of Figure 2 presents the average total trading volume for HFT in each five minute interval distinguishing between trades where the HFT was a maker (ie. posted the quote), a taker (agreed to trade at the posted quote) or participated as either a maker and/or a taker (referred to as HFT Participated Volume). Note that as a HFT can be on both sides of the trade, taker and market volume does not sum to be equal to participated volume. Panel B of Figure 2 presents the equivalent set of metrics for Non-HFT. The trading volume information for Non-HFT exhibits the standard U-shape in that Non-HFT trading volume is high at the opening of the trading day (the average trading volume per stock in the first five minutes of the trading day is around 20,000 to 30,000 shares across maker, taker and all volume), declines progressively throughout the day and then peaks at the close (the average trading volume is around 50,000 to 80,000 shares per stock across maker, taker and all volume). Non-HFT takers are more active throughout the trading day, meaning in each period, there are more Non-HFT hitting orders than placing them. By way of contrast, the HFT volume information reveals some interesting differences. Firstly, at the beginning of the day, the average trading volume increases. This result forms an interesting contrast to Non-HFT, whose volume is highest at the open and then gradually declines for the rest of the morning session. This suggests that HFT are somewhat reserved in their trading at the beginning of the day and some HFT appear to wait for the market to start trading before entering the days trading. One possible interpretation of this finding is that momentum HFT may wait for price information to populate their signal generating algorithms before they can start trading. Second, we note that Non-HFT are almost twice as active at the end of the day compared to HFT. Both types of trader have an average trading volume of around 20,000 shares in the five-minute interval approximately half an hour before the close. The trading activity of HFT increases by slightly more than double at the close, however, non-hft trading volume increases almost fourfold over the same period. The increase in trading activity at the close is typically viewed as a signal of traders not wanting to have overnight positions. The fact that non-hft are far more active at the close is interesting given that many HFT are thought to act as market markets and seek to avoid holding positions overnight. We return to consider this point more fully in the following section. Third, while Non-HFT makers are the least active during the trading day, HFT makers are the most active, consistently posting more orders than taking liquidity. This result provides evidence in favor of HFT providing liquidity to the market. 4

5 To provide further insights into the trading activity of HFT, Figure 3 shows the average trade size across each 5-minute interval in the trading day for both HFT and Non-HFT takers. The general patterns observed in the average total trading volume information presented in Figure 2, are generally also found in the average trade size information. The trade size information however, provide additional insights. For example, while the average trade size of HFT is typically around 25% smaller than non-hft, the dramatic increase in trading activity for both types of traders at the end of the day is clearly evident as is the disproportionate increase in trading activity by non-hft (their average trade size increases by around 50%, as opposed to HFT, whose average trade size increases by only around 20%). A final view of the trading activity of HFT and Non-HFT is provided in Panel A of Figure 4, which shows the average number of trades of both takers and makers as a percentage of overall (Non-)HFT trading activity. 9 The previous observation that HFT tend to wait before entering the market is again supported by the information provided in this figure. HFT are providing relatively more quotes at the beginning of the day than they are trading against posted quotes. The reverse is true for Non-HFT takers, who hit relatively more quotes than they post at the beginning of the day. From 10.00am until 3.30pm, relative activity of HFT and Non-HFT is relatively constant HFT traders consistently post more quotes than they trade against, while the reverse is true for Non-HFT. In the last half an hour of trading, HFT reduce their trading activity, with a clear reduction in the number of posted quotes they hit, while the liquidity they provide to the market increases to its highest point for the day at the close. Non-HFT however, take a considerable amount of liquidity at the close of the day, posting fewer quotes and trading relatively more. This evidence clearly demonstrates evidence of HFT being net liquidity providers. Furthermore, they appear to provide greater levels of liquidity when it is needed most, ie. at the open and the close when Non-HFT are the most active takers of liquidity. In general, the results presented in this section document clear differences between HFT and Non-HFT trading activity. At the open of the trading day, non-hft activity is at its highest for the morning session, while HFT appear to wait briefly before entering the market. During the trading day, HFT are net providers of liquidity to the market, while Non-HFT are net takers of liquidity. Finally, Non-HFT are far more aggressive at the end of the trading day, taking large amounts of liquidity and exhibiting a relatively larger increase in their average trade size. It is interesting to note that Kumar et al. (2011, p. 7) reports that HFT are very active at the end of the day and the evidence here supports as this to the extent that HFT are relatively more active as providers of liquidity and also have a relatively larger average trade size towards the end of the day. 9 More specifically, this figure shows the number of HFT trades (ie. H? and?h trades) as a percentage of all HFT trades (ie.?h, H? or HH trades) for makers and takers. For example, from , 9092 HFT trades took place of which 6425 (ie. 70%) were?h (ie. HH or NH) and 4777 (52.5%) were H? (ie. HH or HN). This is why the % does not add to 100%. 5

6 2.1 Trader Inventory Positions The main purpose of this paper is to provide insights into the trading activity of HFT and the previous literature provides us with some guidance. For example, Schack and Gawronski (2009, p. 3) argue that electronic market making is the main type of HFT activity undertaken. Further, Kumar et al. (2011, p. 7) reports that HFT firms do not usually carry open positions overnight. These arguments suggest that HFT inventory positions should be (close to) zero at the end of each trading day. To investigate this possibility, the buy and sell indicator field in the database may be used to track the net purchases and sales in each of the 120 stocks distinguishing between HFT and non-hft trades. Panel A of Figure 5 presents the average inventory position change across each 5-minute interval the trading day. Panel B of Figure 5 presents the average cumulative inventory position of HFT and non-hft. An initial glance at this figure reveals some interesting features of the data. Firstly, while the cumulative inventory of HFT does not deviate far from zero on average, the same cannot be said for Non-HFT, who are net sellers on average. Second, the beginning of the trading day for Non-HFT is characterized by net selling on average across all trading days, while the close exhibits net buying on average. These anomalies are clearly visible in the cumulative trading information as the sudden drop in the first interval and the turnaround in the last interval in the figure. We need to be careful when interpreting both of these features of the data. To understand why, it is necessary to consider not only the average, but also the range of inventory outcomes that are observed over the sample period. Figure 6 presents a plot of the histogram of closing HFT inventory balances across all 502 days in the sample. While there are a great number of days with zero, or near zero, inventory balances, there are many more days with positive and, in particular, large negative inventory balances. Thus, there is such a wide range of observations in the sample, that these average inventory balances are not statistically significantly different from zero. The large change in Non-HFT inventory at the start and end of the trading day can also be explained with a closer examination of the data. Figure 7 plots the average change in inventory at 9:35 across all 502 days in the sample period. A clear outlier is present in the data on Friday, February 8, 2008, which experienced considerable selling at the open relatively to all other days in the sample. 10 This one event however, is not exclusively driving this result however, as a number of other such outliers are also evident in the sample and they are collectively responsible for this anomaly at the start of the trading day. Similarly, the large positive outlier at the end of 10 The Wall Street Journal Marketwatch entry for that day shows that US futures pointed to opening losses, capping a bad week for the market in which growing concerns over the state of the US economy dominated trading. See A weak opening market was associated with each of the negative outliers identified. 6

7 the sample period is the result of a small number of positive outliers in the sample. Figure 8 presents the average change in inventory across all days in the sample period for the final five minute interval of the trading day. We can report that the removal of a small number of the largest outliers produces an insignificantly different from zero average on the final day. 11 To highlight just how active the last five minutes of the trading day are, Figure 9 presents a plot of the average trading volume in the last 15 minutes of the trading day. The top panel is for the interval just prior to the close, the middle panel is the second to last interval prior to the close an the bottom panel is the data for 10 to 15 minutes prior to the close. The trading volume is clearly substantially larger from 3.55pm to the close than the previous two 5 minute periods and highlights just how frenetic the close of trading is on the market. 2.2 Momentum Trading The analysis of the preceding section clearly highlights that, while both HFT and Non-HFT do hold zero inventory positions overnight, there are also a substantial number of days in which they are either net sellers or buys in the market. A logical question that follows from this analysis is whether the daily inventory position of Non-HFT and HFT correlate to the movements of the market? Panel A of Figure 10 presents a plot of the daily open-to-close return to the U.S. stock market index and the aggregate inventory position for HFT. 12 A positive relationship is evident and the correlation of the data is Panel B of Figure 10 presents the equivalent set of information for Non-HFT and a positive relationship is again evident, although the correlation coefficient of suggests the relationship is a more significant feature of these data. The previous analysis was repeated using close-to-close returns and the results are qualitatively unchanged (the respective correlation coefficients are and 0.696). Where close-to-open returns were used however, the correlation is much lower (the respective correlation coefficients are and 0.23) suggesting it is news during the trading day that is driving the direction of trade and not news from the overnight interval. The previous analysis may be repeated using daily individual stock HFT and Non-HFT inventory positions. Table 1 presents a summary of the correlation between daily stock price movements and inventory positions for the 120 stocks in the sample. The level of correlation is on average for Non-HFT, whereas for HFT it is much lower at Further these data exhibit a good deal of variation as the standard deviation of the correlations is for Non-HFT and 11 This analysis clearly highlights the importance of outliers in the data. As a form of robustness test we account for differing trading intensities across different days (and so the potential influence of outliers), one possible solution to this is to normalize the data on a daily basis. In this case, we derive each days inventory holding curve and then standardize the data [ie. subtract the mean from each observation and divide the difference by the standard deviation of the data. The unreported results are qualitatively unchanged to those presented. 12 This analysis was also undertaken using lagged daily returns and the correlations were all statistically insignificantly different from zero. 7

8 0.103 for HFT. The highest correlation observed for an individual stock was for Non-HFT trading in Apple Computers (AAPL). The correlation for HFT in Apple was only An examination of the correlations across the different sizes of stocks reveals an interesting trend in that the large and small stock category exhibit higher correlation between stock returns and inventory positions for both HFT and Non-HFT compared to the medium sized firms. In general, the evidence provided by this analysis of daily inventory holdings and stock returns provide clear evidence of momentum trading, primarily by Non-HFT and to a lesser extent by HFT. This pattern is particularly strong for large and small sized firms. 2.3 Inventory Management Further insights into the trading behavior of HFT and Non-HFT can be developing using a version of the inventory management model introduced by Manaster and Mann (1996). In this simple model the net inventory change over time period t is regressed against the inventory at the start of time period t, ie. ( ) (1) Inventory control by traders suggests mean reversion as they adjust their holdings towards a preferred level. Thus, the variable of interest in Equation 1 is as mean reversion predicts that, whereas if inventory is a random walk, then. The evidence presented in the previous sections suggests that both HFT and Non-HFT often hold overnight positions. Thus, as a first step in our analysis, we begin by estimating equation (1) using the daily aggregate inventory positions of HFT for each of the 120 stocks in our sample stock. The estimated coefficients are summarized in Panel A of Table 2. The mean (median) estimated inventory reversion coefficient for HFT across all 120 stocks is (0.150) and the average t-test score for the null hypothesis of (3.68) and (19.01) is significant. The estimation coefficients for Non-HFT are summarized in Panel B of Table 2. The average (median) estimated inventory reversion coefficient for Non-HFT is (0.143) and the average t-test score for the null hypothesis of (3.41) and (19.35) is significant. A Welch (1951) F-test of equality of means and van der Waerden normal scores test of equality of medians (see Conover, 1980) fail to reject the null hypothesis of equality. These results suggest that the change in inventory from day to day is positively related to yesterdays inventory balance and no evidence of inventory management being a random walk could be found. Further, there are no significant differences between the inventory management behavior of HFT and Non-HFT in this domain. 8

9 Conclusion A nascent literature is emerging which focuses on the market impact of HFT. This paper aims to provide further insights into the emergence of this new class of trader by considering the issue of understanding HFT trading behavior. Using a high-frequency dataset of trading data for 120 stocks, in which both parties to the trade are classified as either HFT or Non-HFT, this paper considers a number of dimensions of HFT activity. While Non-HFT are found to be very active at the beginning and end of the trading day, HFT tend to wait at the open of the days trading for a brief period following which, heightened trading activity is observed. Further, their increase in activity at the close of trade is less pronounced compared to Non-HFT. A second finding of this paper is that both HFT and Non-HFT frequently carry overnight positions. This is an interesting finding as while market making is thought to be the most common reason for HFT, the fact that HFT frequently carry overnight positions suggests that it does not dominate this type of trading. Further analysis reveals that these non-zero end-of-day inventory balances are related to the day s movement in stock price, which is suggestive of some form of momentum trading. The evidence of momentum trading, however, is more prounounced in Non-HFT trading compared to HFT trading. Finally, we find that the inventory adjustments of both HFT and Non-HFT are related to the previous days inventory position, which suggests that both classes of trader adjust inventory towards some desired level, which manifests itself as a form of mean reversion in inventory holdings. References Commodity Futures Trading Commission (CFTC) and Securities Exchange Commission (SEC) (2010) Findings Regarding the Market Events of May 6, 2010, Report of the Staffs of the CFTC and SEC to the Joint Advisory Committee on Emerging Regulatory Issues, September 30. Dungey, M., McKenzie, M.D. and Smith, V. (2009) Empirical Evidence on Jumps in the Term Structure of the US Treasury Market, Journal of Empirical Finance, 16 (3), Easley, D., de Prado, M.M.L and O Hara, M. (2011) The Microstructure of the Flash Crash: Flow toxicity, liquidity crashes and the Probability of Informed Trading, The Journal of Portfolio Management, 37(2), pp Kumar, P., Goldstein, M., Graves, F. and Borucki, L. (2011) Trading at the Speed of Light: The impact of high-frequency trading on market performance, regulatory oversight and securities litigation, The Brattle Group, Finance: Current topics in corporate finance and litigation, Issue 02. Schack, J. and Gawronski, J. (2009) An In-Depth Look at High-Frequency Trading, Trading Talk: Market Structure Analysis and Trading Strategy, Rosenblatt Securities Inc., September 30. 9

10 Zhang, F. and Powell, B (2011) The Impact of High-Frequency Trading on Markets, CFA Magazine, March-April, Welch, B. L. (1951). "On the Comparison of Several Mean Values: An Alternative Approach," Biometrika, 38,

11 Table 1 Summary of the Correlation Between Individual Stock Returns and Inventory Positions HFT NHFT All Stocks Large Medium Small Stocks All Stocks Large Medium Small Stocks Average Median StDev Max Min

12 Table 2 Regression results daily data ( ) Panel A: HFT α t-stat t-stat ( =0) t-stat ( =1) Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Observations Panel B : Non-HFT Mean Median Maximum Minimum Std. Dev Skewness Kurtosis Observations

13 Figure 1 Average Trading Frequency and Volume 13

14 Figure 2 Average Trading Volume Distinguishing between HFT and non-hft Makers and Takers 14

15 Figure 3 Average HFT takers and Non-HFT takers traded volume 15

16 Figure 4 16

17 Figure 5 : Panel A 17

18 Figure 6 NHFT Raw Histogram Figure

19 Figure

20 Figure 9 Average Trading Volume in the Three 5-Minute Intervals Prior to the Close of Trade

21 Panel A : HFT 8.000% 6.000% 4.000% 2.000% 0.000% % % % % Figure 10 Daily Market Open to Close Returns and End of Day Inventory Holdings % -12,000,000-6,000, ,000,000 12,000,000 Panel B : Non - HFT 8.000% 6.000% 4.000% 2.000% 0.000% % % % % % -30,000,000-20,000,000-10,000, ,000,000 20,000,000 21

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