Algorithmic trading in turbulent markets

Abstract

Does Algorithmic Trading (AT) exacerbate price swings in turbulent markets? We find that stocks with high AT experience less price drops (surges) on days when the market declines (increases) for more than 2%. This result is consistent with the view that AT minimizes price pressures and mitigates transitory pricing errors. Further analyses show that the net imbalances of AT liquidity demand and supply orders have smaller price impacts compared to non-AT net order imbalances and algorithmic traders reduce their price pressure by executing their trades based on the prevailing volume-weighted average prices.

Highlights

• •We study the Australian equity market on turbulent days.
• •Stocks with high AT experience less price swings during turbulent periods.
• •Net order imbalances of algorithmic traders have smaller price impacts compared to those of others.
• •Algorithmic order executions are more sensitive to the prevailing volume-weighted average prices (VWAP).
• •A noval dataset identifying algorithmic trades is employed to increase the identification accuracy.

1. Introduction

Technological developments over the past decade have substantially increased the use of computer algorithms by equity investors. In light of extreme market events such as the “flash crash”, academics, market regulators, and finance practitioners are keen to understand the role of Algorithmic Trading (AT) in turbulent markets.1 Does AT contribute to further price decline in individual stocks when there is a large drop in the overall market? The answer is not clear. On one hand, algorithmic traders act as “messengers” by transmitting price movements among derivatives, indices, and related stock prices (See, for example, Hendershott and Riordan, 2013; Chaboud, Chiquoine, Hjalmarsson, and Vega, 2014). Therefore, AT may exert price pressure in individual stocks in light of the large drop in market indices. On the other hand, computer algorithms can minimize price pressure, reduce the price impact of trades, and mitigate pricing errors (Hendershott, Jones, and Menkveld, 2011). One could argue that AT would mitigate the downward price pressure from overall market drop. We address this question by analyzing the relation between AT and the returns of stocks on days when there is a large movement in market indices defined as days when the absolute value of the market return exceeds 2%.2

We employ a novel data set in which the trades are flagged based on whether they are generated by computer algorithms. We focus on the turbulent days on the Australian Securities Exchange (ASX) from October 27, 2008, till October 23, 2009. Our sample has the following advantages. First, we are able to identify AT buy and sell trades without relying on proxies such as order-to-trade ratio.3 Second, in their seminal study, Hendershott et al. (2011) find that, overall, AT plays a beneficial role in terms of liquidity and price discovery in rising markets. At the same time, the authors warn that investigations of the AT characteristics “in turbulent or declining markets” (p. 31) are equally important. We examine the effects of AT during the most turbulent times in decades, since our sample period is at the peak of the financial crisis and immediately after the collapse of Lehman Brothers in September 2008. Finally, the Australian stock market is one of the leading markets in the development of computerized trading. The ASX is among the top ten equity markets in the world by market capitalization. As an early adopter of computerized trading technologies, the ASX have implemented several technological upgrades to improve latency and attract algorithmic and high frequency traders.4 The ASX and its regulator, the Australian Securities and Investments Commission (ASIC), have subsequently released regulatory findings and commented on the prevalence of AT and High Frequency Trading (HFT) (see, for example, ASX, 2010; ASIC, 2013; ASIC, 2014).

We find that, controlling for size, risk, liquidity, and information, stocks with more sell trades initiated by AT experience less downward price pressure when there is a broad market decline of more than 2%. We obtain similar results for algorithmic buy trades when the market is up by more than 2%. Our results are economically significant. For example, we find that a 10% (or approximately a half standard deviation) increase in AT selling, on average, corresponds to a 11 basis point increase in returns for individual stocks in bear markets. Furthermore, stocks that have low levels of AT experience significant return reversals following market decline days. Specifically, stocks traded less by AT tend to recover from their large turbulent day price drops during the subsequent five trading days. Our findings on post-event day return reversals imply that non-AT overreacts to the overall market pressure by pushing stock prices beyond their fundamental values. Overall, our evidence suggests that, compared to non-AT, AT does not contribute to price swings among individual stocks in turbulent markets.

We isolate the effect of AT on event days from the endogenous effects between AT and the observed market conditions by applying a propensity score matching algorithm. We match event day observations (the treatment group) with non-event day observations (the control group) based on return, volatility, market cap, and liquidity. The matching effectively eliminates any meaningful difference between the treatment group and the control group in terms of these market condition covariates. We apply the matching algorithm to market up and market down days separately. This matching procedure gives us a representative control group that has a set of market characteristics similar to those on event days. We then use a difference-in-differences method to distinguish the effects of AT on event days with a sample of stock-days with comparable market conditions. We show that the negative association between AT and price fluctuation only exists in the treatment group despite the similarity between the treatment and the control groups. Furthermore, we show that this relation is unchanged when we exclude firm-specific news arrivals days from our sample. In summary, we show that the relation between AT and market fluctuations is not driven by AT reacting to the individual stocks' return, volatility, liquidity, size, or public information arrivals.

We also analyze the reasons for the empirical association between AT and price fluctuation. Execution algorithms are designed to minimize market impact for buy-side clients. Trading activities generated by AT and non-AT may exert different levels of price pressure. To explore this hypothesis, we use two trading activity measures to assess the price impacts excreted by AT and non-AT. First, we extend Chordia and Subrahmanyam (2004) and model market-adjusted returns as a function of order imbalances from AT and non-AT. We find that the impact of order imbalances by non-AT is larger than that by AT on event days. The liquidity supplying order by AT is more adversely selected on event days. In addition, similar to Brogaard et al. (2018), we measure the net activity of AT liquidity demand and supply as the difference between the liquidity demanding order imbalance and liquidity supplying order imbalance. We find that the net activity of AT is negatively associated with the price swings in individual stocks during turbulent periods. Hendershott et al. (2011) suggest that execution algorithms may track the Volume-Weighted Average Price (VWAP) metric to reduce execution costs. The VWAP is the average price of each transaction over a certain time horizon (typically one day) weighted by the volume of each trade. The executed price of each trade can then be compared with the VWAP to evaluate the trade's execution performance.5 By monitoring the VWAP, algorithmic traders are more likely to trade when the relative position between the VWAP and the stock price becomes more favorable. A favorable position is one in which the price moves downward (upward) relative to the VWAP for buy (sell) trades. AT execution strategy would effectively be contrarian by design. Consequently, in the initial surge of a large market-wide drop, stock prices would unfavorably deviate downward compared to the VWAPs and human traders would be more likely to sell. After the initial surge, the VWAPs would catch up with prices as more trades are executed and algorithmic traders would be more likely to trade based on this favorable VWAP movement. Therefore, algorithmic traders would be less likely to herd with human traders. As a result, AT would smooth out the liquidity demand and would not contribute to further price declines. After controlling for market conditions, we find that this is the case. In particular, we estimate logit models of AT execution and show that traders with AT technologies are more likely to buy (sell) when the difference between the stock price and the intraday VWAP at the time becomes smaller (larger) on market decline days, market rise days, and other days in our sample. This finding is consistent with the notion that AT does not exacerbate the price pressure from the overall market.

Our paper contributes to the literature in several ways. First, We extend the literature on the role of sophisticated trading algorithms during extreme market events. Kirilenko et al. (2017) focus on the role of HFT market makers during the “flash crash”. The authors find that HFT market makers provided liquidity to the sellers initially but then sought to revert their positions since the extreme sell pressure overwhelmed their inventory capacity. Brogaard et al. (2018) investigate HFT around extreme price movements, classified as the top 0.1% of the individual stock price changes over 10-s trading intervals. The authors find that the net effect of HFT liquidity demand and supply is negatively associated with the direction of the price changes. Gao and Mizrach (2016) analyze HFT during market breakdowns and breakups. Market breakdown (up) days are defined as stock-days when the stock's best bid (offer) falls (rises) for more than 10% of the opening price and subsequently reverts back to within 2.5% at the end of the day. The authors show that HFT is positively associated with the frequency of market breakdowns. Kirilenko et al. (2017) and Brogaard et al. (2018) analyze the short-term shocks from individual securities and its impact on the same securities.6 We extend the source and duration of the extreme events by studying the extreme shocks from the overall market on daily intervals. We also expand the scope of the impacted stocks by analyzing the majority of the stocks in the market in light of the market-wide shocks.

Second, we highlight the effects of AT over time intervals more relevant to non-algorithmic investors compared to other studies on AT and HFT. Regulatory agencies have been expressing concerns about the impact of AT on non-AT, which has longer trading horizons than AT. Whether the recent changes of the equity market structure due to AT are detrimental for the rest of the investment community, as pointed out in a note by the U.S. regulator, is an important issue that deserves further investigation (SEC, 2010). However, most of the AT and HFT papers have focused on ultra-short-term effects, ranging from milliseconds to minutes.7 For instance, Hendershott et al. (2011) show that AT reduces the price impact of trades over the next 5 to 30 min. Hasbrouck and Saar (2013) propose a framework for identifying HFT and assess its intraday effects. Brogaard, Hendershott, and Riordan (2014) assess the impact of HFT on market qualities on a second-by-second basis and report the effect of HFT in the 20 s around public announcements. It is relevant and intuitive to analyze automated trading at ultra-high frequencies since many proprietary trading strategies emphasize the exploitation of small and fleeting opportunities in the market. However, Investigations on the longer-term implications of AT is warranted. For example, some computerized traders follow extensions of traditional trading strategies, such as value, momentum, and pairs trading. These strategies often involve holding positions over days and longer horizons. Moreover, according to the ASX (2010), execution algorithms make up the majority of AT.8 These execution algorithms are services provided to buy-side clients to minimize the price impact of trading and thus the intention to trade is expressed by human traders. Therefore, the implications of these trades should be studied over horizons longer than a few minutes. We show the association between AT and price fluctuations on the turbulent days and five days immediately after the turbulent days. To the best of our knowledge, our paper is the first to investigate the impact of AT on daily stock returns.

Third, our findings help settle the ongoing debate on the relation between AT and stock return volatility. The theoretical model by Biais, Foucault, and Moinas (2015) shows that faster traders could reduce volatility caused by uninformed traders. Empirically, AT and HFT are shown to be negatively associated with volatility (Aggarwal and Thomas, 2017; Hasbrouck and Saar, 2013; Hagströmer and Nordén, 2013). On the other hand, Boehmer, Fong, and Wu (2018) and Bershova and Rakhlin (2013) find that AT and HFT, respectively, increase market volatility. We differ by analyzing the relation between AT and individual stock price swings in light of the overall market swings. We find that stocks with low AT experience greater price swings on days with extreme market movements.9

Finally, we investigate the execution strategy of AT that could affect stock price fluctuations. A number of studies have suggested that AT and HFT could follow VWAP strategies to optimize the timing of their trades (e.g. Domowitz and Yegerman, 2005; Hendershott et al., 2011; Easley, Lopez de Prado, and O'Hara, 2012). Carrion (2013) uses end-of-day VWAP metrics to show that, ex post, HFT times the market successfully. We differ from Carrion (2013) by using the intraday dynamic VWAP, which continuously updates throughout a trading session. Our research design also allows us to control for intraday liquidity, volatility, and volume. We show that, ex ante, the execution decisions of AT are highly sensitive to the prevailing VWAP at the time of the trade.

The rest of the paper is organized as follows. Section 2 describes our data. Section 3 presents our findings on AT in turbulent markets. Section 4 discusses the association between AT, market conditions, and news. Section 5 reports our findings on order imbalances. Section 6 presents the VWAP-tracking algorithms and their effects on the characteristics of AT in turbulent markets. Finally, Section 7 concludes the paper.

2. Data and event days

2.1. Data

We employ a novel AT data set provided by the ASX. This data set contains all equity transactions on the ASX between October 27, 2008, and October 23, 2009. Each trade reports the company code, trade price, trade volume, buy/sell indicator, time stamp to the nearest millisecond, and a special indicator for both sides of the transaction showing whether the trade was initiated (or supplied) by a computer or a human. Algorithmic trades are identified based on their digital imprints on the ASX. Specifically, trades automatically generated by computers are assigned terminal IDs different from human trades in the exchange.10 We merge the AT data set with order-level data provided by the Securities Industry Research Centre of Asia-Pacific (SIRCA). The SIRCA data enable the accurate identification of buy/sell trades. This combination allows us to identify whether a trade was initiated by a buyer or a seller, as well as whether the trade was algorithm driven. The identification of AT allows our study to avoid potential omitted variable biases associated with AT proxies such as order-to-trade ratios, since the order revision and cancellations are associated with market quality metrics such as the rate of price changes. The return of the All Ordinaries Index (All Ords) was acquired from Thompson Reuters Tick History. The sample period is approximately one calendar year, covering the Australian stock market around the peak of the global financial crisis. The market turbulence during the sample period allows us to study AT in relation to extreme market movements.

As one of the top ten equity markets worldwide, the Australian market provides an ideal environment to study AT. The findings on Australian equity market are applicable to other major markets for the following reasons. First, the ASX is among the first trading venue to adopt low latency technologies. For example, a low latency trading platform, Integrated Trading System, was introduced in October 2006 which reduces the latency to a minimum of 30 ms. Murray et al. (2016) find that the implementation of the low latency trading platform resulted in improvements in market liquidity and reductions in the price impact of transactions. The authors attribute these effects to the increased participation of algorithmic traders. At the beginning of our sample period in November 2008, the ASX introduced colocation services to further attract low latency traders. The ASX is among the first group of exchanges to provide colocation services.11 Second, the AT regulatory environment in Australia is similar to those in other major markets such as the U.S. market. The rapid development of AT and HFT in Australian markets has attracted substantial regulatory attention. ASX (2010) provides the first extensive reviews on AT, around the same time as the earliest major U.S. concept release on HFT SEC (2010). Further regulatory investigations (ASIC, 2013; ASIC, 2014) find similar results compared to those in the U.S. market (SEC, 2014). Both the U.S. and the Australian regulators are cautiously optimistic about the development of computerized trading technologies.12 Finally, the findings on AT and HFT in Australian markets are consistent with those in other major markets. For instance, using similar AT proxies and research designs, Hendershott et al. (2011) and Viljoen, Westerholm, and Zheng (2014) find that AT contributes to liquidity and price discovery in the U.S. equity market and the Australian futures market, respectively. Korajczyk and Murphy (2018) and Kwan and Philip (2015) show that HFT increases the execution costs of other traders in the Canadian and Australian stock markets, respectively.

An additional benefit of our data set is the ability to accurately classify buy and sell trades. Specifically, while many previous studies rely on Lee and Ready's Lee and Ready's (1991) algorithm, we use the “true” classification of buys and sells from order-level data provided by the SIRCA.13 Ellis, Michaely, and O'Hara (2000) and Chakrabarty, Moulton, and Shkilko (2012) find the accuracy of Lee and Ready's algorithm to be 81.05% and 69%, respectively. In the ASX, Aitken and Frino (1996) show the accuracy to be 74%. Therefore, it would be beneficial to improve the accuracy of trade direction classification.

To ensure that there are sufficient AT and non-AT volume in our sample to generate robust results, we limit the sample stocks to those that were present throughout the sample period. We further delete stocks that were traded on fewer than 200 days over the 252 trading days in our sample.14 Our final sample contains 384 stocks.

The news data set is acquired from SIRCA. As part of the continuous disclosure rules, the ASX requires listed companies to report price-sensitive information to the ASX before releasing the information to the public. SIRCA provides this information as announcements accompanied by time stamps and categorization codes. The firm-specific and price-sensitive announcements are used as proxies for public information arrivals in Section 4.2. The firm-specific and price-sensitive announcements include earnings announcements, quarterly activity reports, quarterly cash flow reports, dividend announcements, progress reports, periodic reports, take over announcements, issued capital, and asset acquisition and disposal.

2.2. Event day selection

Researchers apply a wide range of techniques to identify the turbulent trading periods. Brogaard et al. (2014) select the top 10% of stock-days sorted by the volatility in the permanent (efficient) component of the intraday price changes. Brogaard et al. (2018) detect extreme price jumps as the top 0.1% of the 10-s trading intervals sorted by absolute midquote changes. Shkilko, Van Ness, and Van Ness (2012) identify episodes of intraday downward price pressures as stock-days when the individual stock prices fall for more than two standard deviations of historical intraday returns and then rebound. Our approach differs from these methods based on two objectives. First, we assess algorithmic buys (sells) in individual stocks in relation to the upward (downward) pressure from the market. Therefore, we separately identify extreme market up days and down days. Second, we analyze the longer-term effects of AT and investigate the stock prices on the event days and five days after the event days.

Similar to Dennis and Strickland (2002), we define turbulent days as days when the absolute values of market returns are greater than 2%.15 We use the All Ords as our proxy for market returns. The All Ords contains the top 500 Australian ordinary stocks and amounts to over 95% of the value of all stocks listed in the ASX. There are 19 market up days and 20 market down days. On each turbulent day, we include stocks that have at least one buy and one sell trades initiated by AT and non-AT in order to calculate the liquidity demanding activities. To measure liquidity supplying activities by AT and non-AT, we exclude stocks that have missing buy or sell trades supplied by AT or non-AT. The final sample contains 9498 stock-days across 384 stocks. Table 1 reports the event days, number of stocks for each event day, and returns of the All Ords.

Table A5.

Correlations and autocorrelations for order imbalances.

Panel A: Correlations
	ATd	nonATd	ATs	nonATs	ATnet
ATd	1.000	−0.105	−0.389	−0.648	0.518
nonATd		1.000	−0.667	−0.005	−0.709
ATs			1.000	−0.083	0.550
nonATs				1.000	−0.656
ATnet					1.000

Panel B: Autocorrelations
lag	ATd	nonATd	ATs	nonATs	ATnet
1	0.120	0.136	0.122	0.131	0.169
2	0.056	0.069	0.061	0.062	0.097
3	0.037	0.047	0.040	0.037	0.066
4	0.020	0.030	0.023	0.026	0.046
5	0.020	0.017	0.024	0.014	0.031

This table presents summary statistics for daily AT and non-AT order imbalances. AT_{i, t}^d is the order imbalance calculated as AT liquidity demanding buy volume less AT liquidity demanding sell volume. nonAT_{i, t}^d is the non-AT liquidity demanding order imbalance calculated analogously. AT_{i, t}^s and nonAT_{i, t}^s are the liquidity supplying order imbalance of AT and non-AT, respectively.

Panel A presents the cross-sectional means of the individual stock time-series correlations and Panel B contains the autocorrelations.

Table 1.

Event days and returns.

Panel A: Market Up Days
Date	Market Return(%)	Number of Stocks	Percent Positive	Percent Zero	Percent Negative	Ratio
05-Nov-08	2.82	262	72.90	4.96	22.14	3.29
25-Nov-08	5.51	243	74.49	7.82	17.70	4.21
28-Nov-08	4.10	227	75.33	7.05	17.62	4.28
08-Dec-08	3.69	211	74.88	5.21	19.91	3.76
15-Dec-08	2.41	228	71.05	3.95	25.00	2.84
27-Jan-09	2.79	217	60.83	10.14	29.03	2.10
13-Mar-09	3.27	229	82.53	4.37	13.10	6.30
17-Mar-09	2.91	241	76.76	4.98	18.26	4.20
23-Mar-09	2.29	223	68.16	7.17	24.66	2.76
02-Apr-09	2.69	252	76.59	5.16	18.25	4.20
14-Apr-09	2.22	260	75.77	5.38	18.85	4.02
30-Apr-09	2.26	257	78.21	4.67	17.12	4.57
04-May-09	2.89	258	75.97	4.65	19.38	3.92
19-May-09	2.12	260	68.85	6.15	25.00	2.75
10-Jun-09	2.10	277	67.87	9.39	22.74	2.98
14-Jul-09	3.23	237	83.54	7.17	9.28	9.00
13-Aug-09	2.74	337	73.59	5.34	21.07	3.49
16-Sep-09	2.32	321	72.27	9.03	18.69	3.87
07-Oct-09	2.15	318	71.07	7.23	21.70	3.28

Panel B: Market down Days
Date	Market Return(%)	Number of Stocks	Percent Positive	Percent Zero	Percent Negative	Ratio
06-Nov-08	−4.22	226	12.83	3.98	83.19	6.48
07-Nov-08	−2.43	228	35.96	6.14	57.89	1.61
11-Nov-08	−3.40	215	13.95	2.33	83.72	6.00
13-Nov-08	−5.44	217	9.22	5.99	84.79	9.20
17-Nov-08	−2.32	212	23.58	3.77	72.64	3.08
18-Nov-08	−3.47	228	15.79	3.51	80.70	5.11
20-Nov-08	−4.32	254	15.75	5.12	79.13	5.03
26-Nov-08	−2.68	221	23.53	7.24	69.23	2.94
02-Dec-08	−4.02	212	14.15	4.72	81.13	5.73
12-Dec-08	−2.31	215	29.77	5.58	64.65	2.17
08-Jan-09	−2.27	220	22.27	4.55	73.18	3.29
15-Jan-09	−4.07	203	5.42	3.45	91.13	16.82
20-Jan-09	−3.00	201	13.43	3.98	82.59	6.15
23-Jan-09	−3.83	208	11.06	4.33	84.62	7.65
02-Mar-09	−2.82	211	22.75	6.64	70.62	3.10
08-Apr-09	−2.22	251	21.12	4.78	74.10	3.51
21-Apr-09	−2.40	252	19.05	2.38	78.57	4.13
14-May-09	−3.43	257	12.45	1.56	85.99	6.91
03-Jun-09	−3.01	287	12.20	5.92	81.88	6.71
02-Oct-09	−2.04	322	9.32	4.04	86.65	9.30

This table contains the dates, market returns, and number of stocks in the sample and the proportion of stocks that have positive, zero, and negative returns on days when the absolute value of the return of the market portfolio exceeds 2%. The sample period is from October 27, 2008 to October 23, 2009. Stocks are included on each event day if they were traded by both ATers and non-ATers on the day. The Australian All Ords returns are used as the market returns. In this table, percent positive is the percentage of stocks with returns greater than zero, percent zero is the percentage of stocks with returns equal to zero, percent negative is the percentage of stocks with returns less than zero, and ratio is the ratio of percent positive (negative) to percent negative (positive) on market up (down) days. There are 19 up days and 20 down days in our sample.

Large movements in the value weighted market index could be caused by a few of the largest firms. Consequently, the selected days may contain days when the index change does not represent a price shift among a wide range of stocks. To avoid this potential bias in our event day selection, we calculate the percentages of firms with positive returns, zero returns, and negative returns. Furthermore, we calculate the ratios of stocks with positive returns (negative returns) to those with negative returns (positive returns) for positive (negative) market return days. Table 1 presents the event days. For market up days, the mean percentage of positive return stocks is 73.72%, with a maximum of 83.54% on July 14, 2009, and a minimum of 60.83% on January 27, 2009. The ratio of stocks with positive returns to stocks with negative returns indicates that there are, on average, 3.99 times more stocks with positive returns than those with negative returns over our sample period. The findings for market down days are stronger, with a maximum of 91.13% negative return stocks on January 15, 2009. Overall, the results imply that individual stock returns are overwhelmingly positive (negative) on market up (down) days.

The numbers of stocks included for each event day are not identical. It is possible that the decision of algorithmic traders to trade in certain stocks on certain event days may drive the results. This potential bias is mitigated by our inclusion of stock and month fixed effects. The sample size for each event day is sufficiently large. The minimum is 201 on January 20, 2009, and the maximum is 337 on August 14, 2009. The distribution of market up days is relatively spread out throughout the year. For market down days, however, there is a cluster of event days in November 2008.16

3. AT and abnormal returns

In this section, we investigate whether AT is associated with the returns in individual stocks when the overall market experiences large surges or declines. Therefore, the cross-sectional distribution of individual stock returns will be a function of AT. We first provide variable definitions and descriptive statistics. We then report the main results and robustness checks.

3.1. Variable constructions and descriptive statistics

Fig. 1 and Fig. 2 present AT and non-AT buy and sell volume statistics respectively for all days, market up days, and market down days. The volume statistics are calculated as the mean of the daily trading volume across all stocks in our sample.

Fig. 1.

AT and non-AT Buy Volume by Event Days.

These figures contain AT and non-AT buy volume statistics by event days from 27 October 2008 to 23 October 2009. The up (down) days are defined as the days when the market returns exceed 2% (−2%). Trader group “AT vs non-AT” denotes the group of trades that are initiated by AT, and non-AT is on the passive side. Other trader groups are defined analogously. Volume is presented in millions of shares.

Fig. 2.

AT and non-AT Sell Volume by Event Days.

These figures contain AT and non-AT sell volume statistics by event days from 27 October 2008 to 23 October 2009. The up (down) days are defined as the days when the market returns exceed 2% (−2%). Trader group “AT vs non-AT” denotes the group of trades that are initiated by AT, and non-AT is on the passive side. Other trader groups are defined analogously. Volume is presented in millions of shares.

Our main variable of interest is the level of AT activity in proportion to total trading activity.17 We define rAT ^d as the ratio of the AT liquidity demanding volume divided by the total trading volume:

$${\mathit{rAT}}_{i,t}^d=\frac{{\mathit{ATvolume}}_{i,t}^d}{{\mathit{Totalvolume}}_{i,t}^d},$$ (1)

where ATvolume _{i, t} ^d is the liquidity demanding AT volume for stock i on day t and Totalvolume _{i, t} ^d is the total liquidity demanding volume for stock i on day t. The liquidity supplying AT ratio is defined analogously.

The AT ratios are further segregated into buy ratios and sell ratios to identify additional information from the trade direction. The AT liquidity demanding buy ratio is defined as rATbuy _{i, t} ^d:

$${\mathit{rATbuy}}_{i,t}^d=\frac{{\mathit{ATbuyvolume}}_{i,t}^d}{{\mathit{Totalbuyvolume}}_{i,t}^d},$$ (2)

where ATbuyvolume _{i, t} ^d is the AT buy side liquidity demanding volume in stock i on day t and Totalbuyvolume _{i, t} ^d is the total volume for liquidity demanding buy trades in stock i on day t. The liquidity supplying buy ratio, the liquidity demanding sell ratio, and the liquidity supplying sell ratio are defined analogously as rATbuy _{i, t} ^s, rATsell _{i, t} ^d, and rATsell _{i, t} ^s, respectively.

Table 2 reports descriptive statistics. Panel A presents the cross-sectional averages of the volume, number of transactions, and AT volume ratios. The daily statistics are reported for all 252 trading days, including 19 up days and 20 down days. In line with Chordia and Subrahmanyam (2004), the number of buy trades is slightly higher than the number of sell trades, with means of 118 and 107, respectively. The average daily volume differences between regular days and event days can be interpreted based on the first two rows of Panel A in Table 2. Consistent with the notion that large market returns should correlate with elevated trading volume, the average buy volume on market up days is 13.44% higher than those on all days. On market down days, the proportion of sell volume to overall volume increased to 54.81% compared to 49.28% on regular days. However, the overall trading volume decreased by 20.57%. This abnormal decline in volume is likely a result of the highly turbulent sample period: several of the market down days are in November 2008, at the height of the Global Financial Crisis. It is an unusual time period for the global economy. Australian investors were reasonably uncertain about the severity of the impact on Australian companies.

Table 2.

Descriptive statistics, correlations, and autocorrelations.

Panel A: Descriptive Statistics
	All Days		Up Days		Down Days
	Mean	Std. dev.	Mean	Std. dev.	Mean	Std. dev.
Buy Volume (,000,000)	424	145	481	141	300	74
Sell Volume (,000,000)	412	121	393	99	364	89
No. of Buy Trades (,000)	118	25	133	29	115	28
No. of Sell Trades (,000)	107	21	101	15	108	20
rATd(%)	0.50	0.19	0.51	0.15	0.53	0.15
rATs(%)	0.50	0.19	0.53	0.15	0.53	0.15
rATbuyd(%)	0.50	0.23	0.52	0.19	0.53	0.21
rATselld(%)	0.49	0.23	0.50	0.21	0.53	0.19
rATbuys(%)	0.51	0.24	0.52	0.21	0.55	0.21
rATsells(%)	0.50	0.23	0.56	0.20	0.52	0.20

Panel B: Correlations
	rATbuyd	rATselld	rATs	rATbuys	rATsells
rATd	0.637	0.705	0.373	0.322	0.310
rATbuyd		0.048	0.321	0.017	0.470
rATselld			0.313	0.472	0.013
rATs				0.623	0.672
rATbuys					−0.014

Panel C: Autocorrelations
lag	AT liquidity demand			AT liquidity supply
	rATd	rATbuyd	rATselld	rATs	rATbuys	rATsells
1	0.211	0.193	0.199	0.195	0.183	0.190
2	0.138	0.132	0.122	0.121	0.108	0.119
3	0.103	0.094	0.091	0.091	0.077	0.093
4	0.083	0.074	0.069	0.072	0.066	0.070
5	0.076	0.061	0.052	0.062	0.046	0.060

This table contains summary statistics, correlations, and autocorrelations for the AT and non-AT stock transactions between 27 October 2008 and 23 October 2009. The event days are defined as the days when the absolute values of the market returns exceed 2%. Panel A presents the daily means and standard deviations of trading volume, number of trades, and the AT volume ratios. Buy (sell) volume is the mean of the total daily buy (sell) volume across all stocks in our sample. The liquidity demanding AT volume ratio, rAT^d, is defined as the daily ratio between the liquidity demanding AT volume and the overall volume. Other ratios are defined analogously. Panels B and C present the cross-sectional means of the individual stock time-series correlations and autocorrelations. There are 252 trading days, 19 up days, and 20 down days.

Panel B of Table 2 presents the cross-sectional means of individual stock time-series correlations and autocorrelations among the AT volume ratios. Although the correlation of rAT ^d with rATbuy ^d and rATsell ^d are 0.637 and 0.705, respectively, the correlation between rATbuy ^d and rATsell ^d is only 0.048. The relations among liquidity supplying ratios are similar. This implies that segregating buy and sell trades provides additional and distinct information compared to only the non-directional AT ratios. Panel C contains the cross-sectional average autocorrelations of At ratios. The autocorrelation of liquidity demanding ratios are substantial: The first-lag autocorrelations are 0.211, 0.193, and 0.199 for rAT ^d, rATbuy ^d, and rATsell ^d, respectively. The autocorrelations on the liquidity demanding side is slightly higher for all trade types. Overall, the autocorrelations decay at a moderate speed.

We define the intensity of AT liquidity demand, iAT ^d, as the value of rAT ^d on the event day less the mean of rAT ^d over the past five days18 :

$${\mathit{iAT}}_t^d={\mathit{rAT}}_t^d-\frac{1}{5}\sum _{i=t-5}^{t-1}{\mathit{rAT}}_i^d.$$ (3)

The AT liquidity supply intensity (iAT ^s) and the segregated buy/sell intensities are defined analogously. The decision to use abnormal values as opposed to raw values is based on the autoregressive properties reported in Table 2. Specifically, we find that AT and non-AT consistently prefer certain stocks to others. Applying the raw values on the event day for the cross-section of stocks would incorporate the information about these preferences.19

3.2. Multivariate analysis

To assess how the trading activities of different investor groups relate to individual stock returns in turbulent markets, we model the market-adjusted return on each event day as a function of the AT intensity and control variables. We first apply the following panel data regression on each event day:

$${\mathit{ar}}_{i,t}=\alpha +{\beta }_1{\mathit{iAT}}_{i,t}^d+{\beta }_2{\mathit{iAT}}_{i,t}^s+{\beta }_3{\mathit{size}}_{i,t}+{\beta }_4{\mathit{effsprd}}_{i,t}+{\beta }_5{\mathit{ivola}}_{i,t}+{\beta }_6{\mathit{beta}}_{i,t}+{\epsilon }_{i,t},$$ (4)

where ar _{i, t} is the market-adjusted abnormal return for stock i on event day t. iAT _{i, t} ^d (iAT _{i, t} ^s) is the intensity of AT liquidity demand (supply). We include stock and month fixed effects. The t-statistics are calculated based on standard errors clustered by stock and date (Thompson, 2011).

size _{i, t} is the logarithm of the market value of stock i five days prior to the event day and effsprd _{i, t} is the intraday volume weighted percentage effective spread for stock i on day t. ivola _{i, t} is the intraday idiosyncratic volatility of the market model for stock i on days t. beta _{i, t} is the beta for stock i for even(odd) day t instrumented based on the betas of the past 5 odd (even) days (Jegadeesh, Noh, Pukthuanthong, Roll, and Wang, 2019).

We then replace the aggregated iAT _{i, t} ^d and iAT _{i, t} ^s in Eq. (4) with the segregated buy and sell AT intensities. Specifically, we include iATbuy _{i, t} ^d and iATsell _{i, t} ^d as the intensity of AT liquidity demand for buyer initiated and seller initiated trades, respectively. iATbuy _{i, t} ^s (iATsell _{i, t} ^s) is included as the intensity of AT liquidity supply on the buy (sell) side.

The logarithm of market capitalization (size _{i, t}) is included in the regression to account for its possible association with return and AT intensity.20 Moreover, the All Ords, a value-weighted index, places more weight on larger stocks. Therefore, including size could alleviate potential biases of returns toward larger stocks.

We add volume weighted average of intraday effective spread (effsprd _{i, t}) to account for liquidity effects. The theoretical model of Foucault, Kadan, and Kandel (2013) predicts a strong association between AT and trading rates. Empirically, ATat is reported to follow a liquidity-driven strategy (Hendershott and Riordan, 2013). If AT is correlated with liquidity in our sample, omitting liquidity measures would likely force our main variables to become proxies for liquidity effects. Therefore, we include effective spread to ensure that the estimated relation between AT and returns is robust to pricing and proxy effects.

We also include realized idiosyncratic volatility (ivola _{i, t}) based on the intraday 5-min returns. Dierkens (1991) suggests using idiosyncratic volatility as a measure of informational effects. If AT has an informational advantage, as argued by Biais et al. (2015), it would be correlated with idiosyncratic variance. The magnitude of beta is directly associated with market-adjusted returns and volatility. We include beta (beta _{i, t}) as an independent variable. Similar to Jegadeesh et al. (2019) the betas on even (odd) days is instrumented based on the betas over the past 5 odd (even) days. Instrumenting beta can mitigate the measurement error in the slope coefficients of the market model and avoid the impact of the factor structure in market volatility.

Our main variable of interest is the intensity of AT in individual stocks in light of large market movements. We measure the association between AT and market-adjusted returns for each stock. When the market suffers from a price decline of more than 2%, further decline in a given stock represented by a decrease in market-adjusted return would indicate its higher downward price pressure. A positive coefficient on AT intensities would indicate that AT is related to further downward price pressures in individual stocks. Alternatively, A negative coefficient on AT intensities imply that stocks traded more by AT would exhibit less downward swings on market down days. To emphasize the importance of trade direction, we then segregate AT intensities into buy and sell intensities based on buy and sell volumes, respectively. We expect the buy (sell) volume to be more relevant than the sell (buy) volume on market up (down) days.

Table 3 presents the results. Model 1 and 5 report the estimations with unsigned AT intensities. The signs of the coefficients for the AT liquidity demand intensity (iAT ^d) are as expected: negative for market up days and positive for market down days. However, iAT ^d is not significant. To further disentangle the informativeness in trade signals, we report the estimations for the AT buy intensities and the AT sell intensities in the remaining models.

Table 3.

Event day market-adjusted return regressions on AT intensity.

	Up Days				Down Days
	1	2	3	4	5	6	7	8
iATd	−0.719				0.078
	(−0.94)				(0.17)
iATs	−0.796				0.090
	(−1.35)				(0.14)
iATbuyd		−1.583***		−1.373***		−0.227*		−0.076
		(−3.26)		(−2.74)		(−0.47)		(−0.15)
iATselld		−0.125		−0.233		1.125***		1.114***
		(−0.29)		(−0.54)		(2.59)		(2.59)
iATbuys			−1.051**	−0.615			−0.523	−0.467
			(−2.08)	(−1.17)			(−1.14)	(−1.02)
iATsells			0.252	0.320			0.387	0.018
			(0.52)	(0.65)			(0.99)	(0.05)
size	−2.667***	−2.668***	−2.674***	−2.673***	−1.272**	−1.263**	−1.274**	−1.267**
	(−4.11)	(−4.1)	(−4.12)	(−4.12)	(−2.37)	(−2.36)	(−2.38)	(−2.36)
effsprd	−0.033	−0.030	−0.032	−0.030	−0.225	−0.223	−0.228	−0.225
	(−0.18)	(−0.16)	(−0.17)	(−0.16)	(−1.37)	(−1.38)	(−1.39)	(−1.39)
ivola	0.630***	0.630***	0.628***	0.630***	−0.010	−0.009	−0.008	−0.008
	(5.29)	(5.24)	(5.26)	(5.25)	(−0.15)	(−0.15)	(−0.12)	(−0.12)
beta	1.015	1.004	1.047	1.024	0.596	0.567	0.590	0.568
	(1.15)	(1.16)	(1.18)	(1.18)	(0.72)	(0.68)	(0.71)	(0.68)
N	4858	4858	4858	4858	4640	4640	4640	4640
Adj. R2	0.114	0.126	0.115	0.126	0.090	0.101	0.090	0.101

This table presents coefficient estimates from panel regressions using the following model:

ar_{i, t} = α + β₁iAT_{i, t}^d + β₂iAT_{i, t}^s + β₃size_{i, t} + β₄effsprd_{i, t} + β₅ivola_{i, t} + β₆beta_{i, t} + ε_{i, t},

where ar_{i, t} is the market-adjusted abnormal return for stock i on event day t. The event days are defined as the days when the absolute values of market returns exceed 2%. There are 19 market up days and 20 market down days. In model 1 and 5, iAT_{i, t}^d (iAT_{i, t}^s) is the intensity of AT liquidity demand (supply). In model 2–4 and 6–8, iATbuy_{i, t}^d and iATsell_{i, t}^d are the intensity of AT liquidity demand for buyer initiated and seller initiated trades, respectively. iATbuy_{i, t}^s and iATsell_{i, t}^s are the intensity of AT liquidity supply defined analogously.

size_{i, t} is the logarithm of the market value of stock i five days prior to the event day and effsprd_{i, t} is the volume weighted average of intraday effective spread for stock i on day t. ivola_{i, t} is the intraday realized idiosyncratic volatility of the market model for stock i on day t. beta_{i, t} is the beta for stock i on day t. If day t is an even (odd) day, the beta is instrumented based on the betas over the past 5 odd (even) days (Jegadeesh et al., 2019). The coefficients for all AT variables, size, and beta are multiplied by 100. The stock and month fixed effects are included. The t-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

The liquidity demanding variables show some interesting signs. On market up days, iATbuy ^d is significant and iATsell ^d is insignificant, whereas the distribution of significance inverts on market down days. This result suggests that the relation of the buy (sell) volume on up (down) days with abnormal returns is diluted by not assigning trade direction in model 1 and 5. Taken together, the liquidity demanding AT buy intensity is negatively correlated with the market-adjusted return on up days, whereas the liquidity demanding AT sell intensity is positively correlated with the market-adjusted return on down days. This finding supports the notion that stocks with less AT buying (selling) would incur greater upward (downward) price swings on up (down) days. As a result, stocks with higher levels of AT would reduce price swings on event days.

Economically, the association between liquidity demanding AT intensity and market-adjusted returns is substantial. The coefficient of the AT buy intensity on market up days is −1.373, which implies a decrease of 14 basis points in the predicted abnormal returns for a 10% (or 0.54 standard deviation) increase in the AT buy intensity. Likewise, the coefficient of the AT sell intensity on market down days indicates that a 10% (or 0.48 standard deviation) increase in AT selling, on average, corresponds to a 11 basis point increase in abnormal returns.

The only significant liquidity supplying variable is iATbuy ^s on up days in model 3. The significance disappears in model 4 when both liquidity demanding and supplying intensities are included. However, the liquidity supplying results do not imply that AT liquidity supply activities have no impact on abnormal returns in turbulent markets. Using order-level data, Brogaard, Hendershott, and Riordan (2019) show that both market orders and limit orders placed by computerized traders contribute to price discovery. Limit orders contribute a larger share of the price discovery process due to its quantity advantage over market orders. Our finding on liquidity supplying trades do not contradict the findings in Brogaard et al. (2019) since we measure liquidity supply as the executed limit orders instead of the unexecuted limit orders. An unexecuted bid limit order submitted inside the existing bid–ask spread contributes to price discovery by increasing the bid price and the midquote. On the other hand, an executed bid limit order may decreases the midquote since it is executed against a sell market order. Since we observe only the executed AT limit orders, we do not conclude on whether AT liquidity supply contributes to individual stock price swings during turbulent markets.

3.3. Post-event day analysis

The empirical findings on event days indicate that the absolute value of individual stock returns with lower AT intensity exceeds that of returns with higher AT intensity. In this section, we show the post-event return differences between stocks with high and low AT intensity. The return difference on the event day could be explained by non-ATat reactions to information and driving prices to their fundamental values. If this is the case, we should observe no return reversal during the period immediately after the event day for stocks with lower AT intensity compared to those with higher AT intensity. If, however, there are significant return reversals among stocks with lower AT intensity, then non-AT increases price fluctuations and causes prices to deviate from their fundamental values.

The time span of our data dictates that longer-term analysis is not feasible; nevertheless, we provide a post-event Cumulative Abnormal Return (CAR) analysis over the five days immediately after each event day. We sum post-event market-adjusted returns as CARs for each stock and partition them into quartiles based on their event day AT liquidity demanding intensity. We use iATbuy ^d (iATsell ^d) for market up (down) days. We then calculate the mean difference between CARs of higher and lower AT intensity. If the return effects associated with low AT intensity (and therefore, high non-AT intensity) on event days are transient, we would observe significantly higher CARs in low AT stocks, compared to high AT stocks, immediately after market down days. Alternatively, if the return effects are fundamental on event days, we would observe insignificant differences in post-event CARs.

Table 4 contains the results of the post-event CAR differences. In Panel A, the first (third) row contains the mean CAR difference between the top and bottom 50% (25%) based on AT activities. The second and fourth rows report the t-statistics corresponding to a test of a null hypothesis that the CARs from high/low AT quartiles are identical. The second column and the fourth column contains the differences of all post-event CARs. The third and the fifth columns show the differences in a subsample of the event days with non-overlapping post-event CAR periods. That is, we test the post-event CARs based on a set of independent event days that are at least five days apart from each other. On market down days, the post-event CAR differences are significantly negative. This finding implies significant return reversals in stocks of low AT intensity. However, we do not observe return reversals after market up days. Whether the effects of AT on return reversals differ between market up and market down days is an interesting topic. To the best of our knowledge, the AT/HFT literature has yet to address this issue. For instance, Gao and Mizrach (2016) show that HFT is associated with market breakdowns, when stock prices decrease significantly and revert back within the same day. However, an equivalent analysis on market breakups is not included. Brogaard et al. (2018) analyze HFT during extreme price movements without distinguishing extreme price ups from extreme price downs. It would be worthwhile to show short-term asymmetric return reversals similar to the long-term asymmetric reversals found by De Bondt and Thaler (1985). However, a longer post-event window is needed to conclude that there are no price reversals after market up days. We leave this question to future research.

Table 4.

Post-event cumulative abnormal returns.

	Up Days		Down Days
	All	Independent Days	All	Independent Days
Panel A: 5-day Post Event CAR Partitioned by AT Intensities
Top Less Bottom Half (%)	−0.213	−0.329	−0.713**	−1.190***
	(0.68)	(0.99)	(2.41)*	(2.81)
Top Less Bottom Quartile (%)	−0.101	0.358	−0.871**	−1.610**
	(0.31)	(0.73)	(2.02)	(2.57)
Panel B: 5-day Post Event CAR Partitioned by Beta and AT Intensities
Top Less Bottom Half (%)	−0.380	−0.210	−0.863***	−1.072***
	(1.35)	(0.63)	(2.72)	(2.67)
Top Less Bottom Quartile (%)	−0.216	−0.163	−0.951**	−1.391**
	(0.51)	(0.47)	(2.05)	(2.32)

This table presents the results of post-event CAR analysis for stocks ranked by AT intensity quartiles. The event days are defined as the days when the absolute values of market returns exceed 2%. In Panel A, the CAR for stock i is the market-adjusted return over five days after each event day. The CARs for individual stocks are partitioned into quartiles based on liquidity demanding AT buy (sell) intensities on each up (down) day. The mean CAR difference between high- and low-AT stocks are presented. In Panel B, the CAR for a stock is calculated as the five-day post-event return for the stock less the mean five-day returns for all stocks in the same beta quartile as the target stock on the event day. Column 3 and 5 show the post-event CAR differences in a subset of independent event days which are at least five days apart from each other. Therefore the CAR periods in column 3 and 5 are not overlapping. The t-statistics in parentheses correspond to a test of a null hypothesis that the CAR from high/low-AT quartiles have identical means.

3.4. Robustness tests

We provide a sensitivity analysis of the event day selection criteria. In Table 5 , we relax the threshold of event day selection criteria from the absolute market return of more than 2% to a range between 1.5% and 2.5%.

Table 5.

Sensitivity test for event day selection.

Number of Days	1.50%		1.75%		2.25%		2.50%
	Up Days	Down Days	Up Days	Down Days	Up Days	Down Days	Up Days	Down Days
	32	29	25	24	14	18	10	13
iATbuyd	−0.895**	−0.218	−1.314***	−0.142	−2.117***	−0.151	−2.039**	−0.512
	(−2.1)	(−0.56)	(−2.59)	(−0.31)	(−3.22)	(−0.27)	(−2.21)	(−0.91)
iATselld	−0.138	1.100***	−0.116	1.045**	−0.061	1.550***	0.070	1.930***
	(−0.43)	(3.28)	(−0.29)	(2.6)	(−0.12)	(3.27)	(0.12)	(3.42)
iATbuys	−0.643	−0.327	−0.826	−0.357	−0.416	−0.592	−0.225	−0.360
	(−1.33)	(−1.04)	(−1.44)	(−1.01)	(−0.46)	(−1.5)	(−0.2)	(−0.69)
iATsells	0.349	0.018	0.409	0.314	0.418	0.249	0.602	0.612
	(0.98)	(0.06)	(0.87)	(0.84)	(0.7)	(0.54)	(0.97)	(0.87)
size	−2.300***	−1.306***	−2.259***	−1.038**	−2.004***	−0.795	−2.208**	−1.617
	(−5.45)	(−3.42)	(−4.24)	(−2.46)	(−3.11)	(−1.23)	(−2.22)	(−1.51)
effsprd	−0.235	−0.396***	−0.136	−0.257*	−0.026	−0.309*	−0.394***	−0.186
	(−0.97)	(−2.64)	(−0.65)	(−1.7)	(−0.14)	(−1.84)	(−3.59)	(−0.7)
ivola	0.444***	0.064	0.537***	0.001	0.641***	0.020	0.647***	−0.098
	(4.32)	(0.74)	(4.18)	(0.01)	(4.63)	(0.24)	(3.85)	(−1.16)
beta	0.478	0.021	0.379	0.325	−0.577	1.277	−1.508	1.505*
	(0.77)	(0.03)	(0.41)	(0.49)	(−0.4)	(1.43)	(−1.27)	(1.88)
N	8266	6939	6315	5650	3406	4067	2377	2940
Adj.R2	0.122	0.100	0.156	0.106	0.166	0.112	0.188	0.110

This table presents coefficient estimates from panel regressions of event day market adjusted returns. The dependent variable is the daily market-adjusted abnormal stock returns. We measure AT intensity in four trade groups: Liquidity demanding buy trades (iATbuy^d), liquidity demanding sell trades (iATsell^d), liquidity supplying buy trades (iATbuy^s), and liquidity supplying sell trades (iATsell^s). Sensitivity analysis of the event day selection method is presented based on the absolute value of market returns exceeding the range from 1.5% to 2.5%.

size_{i, t} is the logarithm of the market value of stock i five days prior to the event day and effsprd_{i, t} is the volume weighted average of intraday effective spread for stock i on day t. ivola_{i, t} is the intraday realized idiosyncratic volatility of the market model for stock i on day t. beta_{i, t} is the beta for stock i on day t. If day t is an even (odd) day, the beta is instrumented based on the betas over the past 5 odd (even) days. The coefficients for all AT variables, size, and beta are multiplied by 100. The stock and month fixed effects are included. The t-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Overall, the results for alternative event day thresholds are consistent with the main results. Specifically, liquidity demanding buy (sell) AT intensities are associated with less up (down) swings of individual stock prices on market up (down) days. Unsurprisingly, the magnitudes of the AT intensity coefficients are larger when we select event days with bigger market movements.

Additional robustness tests are reported in the internet appendix. In particular, we repeat our main analyses using alternative criteria for the stock filtering, event day selections, or AT variable constructions. See Table A2 and Table A3 for these estimations. The results are quantitatively and qualitatively similar to those estimated using the initial specifications described in Section 3.2.

4. AT, news announcements, and market conditions

AT is associated with fewer price swings on stressful days and it is sufficiently clear that AT does not exacerbate extreme price movements; however, the mechanics of this relation need to be investigated. While the results in the prior section imply that AT actively counteracts pricing errors, it is also possible that algorithms aim to minimize transaction costs and stay away from stocks experiencing the largest price swings. In this section, we explore plausible mechanisms through which market conditions and information might influence AT and non-AT.

4.1. Event day versus matched non-event day difference-in-differences analysis

Algorithmic traders may react to the return, liquidity, size, and volatility of a particular stock and adjust their execution accordingly. This may alter our inference about AT intensity and stock price swings. For example, computerized traders may choose to buy more stocks that have lower returns and not as many higher-return stocks. Consequently, on market up days, we observe a negative association between AT buy intensity and upward price swings. We address this issue using a difference-in-differences test between event and non-event days with similar market characteristics. We separate our sample into event days as the treatment group and non-event days as the control group. However, we cannot directly compare the treatment and control groups since the market conditions in terms of return, liquidity, and volatility could be significantly different. To avoid traders with AT technologies reacting to these differences, we match the treatment group with a subset of the control group based on market conditions. Specifically, we acquire propensity scores based on a logit regression on a set of covariates. The dependent variable is a dummy indicating whether the observation is on an event day. The independent variables are the market-adjusted return, size, effective spread, beta, and idiosyncratic volatility. We then match each observation in the treatment group with two observations in the control group that have similar market characteristics. The market up days and down days are matched separately.21

We then run a difference-in-differences regression on the matched sample to show whether there is a differential effect of AT intensity on the event days compared to the matched non-event days, given that the observations on the event and non-event days have similar market characteristics. Specifically, we interact the AT intensity variables with event day dummy variables to assess the marginal effect of AT on price fluctuations in light of overall market pressure. The standard errors are two-way clustered to control for persistent effects in the stock and time dimensions (Thompson, 2011). Stock and month fixed effects are accounted for. Table 6 presents the coefficient estimates.

Table 6.

Matched event day and non-event day diff-in-diff test.

	Up Days		Down Days
	Coefficient	t-stats	Coefficient	t-stats
iATbuyd	0.018	(0.06)	−0.342	(−0.92)
iATselld	−0.110	(−0.35)	−0.081*	(−0.22)
iATbuys	−0.459	(−1.32)	−0.474	(−1.15)
iATsells	−0.240	(−0.83)	0.708**	(1.32)
up	−0.085	(−0.49)
iATbuyd*up	−1.353**	(−2.24)
iATselld*up	−0.105	(−0.18)
iATbuys*up	0.283	(0.46)
iATsells*up	0.506	(0.85)
down			0.058***	(3.37)
iATbuyd*down			0.499	(0.79)
iATselld*down			1.574***	(2.91)
iATbuys*down			−0.381	(−0.68)
iATsells*down			−0.394	(−0.7)
size	−2.184***	(−6.93)	−1.337***	(−4.24)
effsprd	−0.454***	(−2.92)	−0.246	(−2.3)
ivola	0.501***	(7.01)	0.005	(0.11)
beta	0.791	(1.25)	0.395	(0.8)
N	14,574		13,920
Adj. R2	0.085		0.055

This table shows the results for the difference-in-difference test on market up days and down days between the matched non-event days and event days. Each event day is matched with two non-event days based on the criteria described in Table A4. The dependent variable, ar_{i, t}, is the market-adjusted abnormal return for stock i on the event day t; AT intensity are measured in four trade groups: Liquidity demanding buy trades (iATbuy^d), liquidity demanding sell trades (iATsell^d), liquidity supplying buy trades (iATbuy^s), and liquidity supplying sell trades (iATsell^s).

up (down) is a dummy variable that takes 1 on a market up (down) day. Column 2 and 3 presents the results for matched market up days. In column 4 and 5, we repeat the analysis on market down days. The control variables are identical to those in Table 3. The coefficients for all AT variables, all interaction variables, event day dummies, size, and beta are multiplied by 100. The stock and month fixed effects are included. The t-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

On market up days, the AT intensity variables are not significant, whereas the interaction between the market up dummy (up) and AT liquidity demanding buy intensity (iATbuy _{i, t} ^d) is negatively significant. These two results imply that, despite the treatment and control groups having similar market characteristics, the association between AT intensity and abnormal return only exists when there is an overall market pressure. The results and implication on market down days are similar.

The propensity matching analysis in this section is subject to an important caveat: Our test supports the notion that the relation between stock price swings and AT are not driven by AT reacting to the changes in individual stock's abnormal return, effective spread, idiosyncratic volatility, market risk exposure. However, the stocks in the control group are sampled from the non-event days to resemble the set of market conditions of the stocks on event days. Therefore, unobserved characteristics uniquely associated with the occurrence of extreme market up or down days may affect the stock returns or AT. The propensity matching analysis does not exclude the possibility that these hidden characteristics are endogenous to the association between AT and price swings.

We show that the effects of AT differ during episodes of market-wide pressure in the treatment group compared to those of idiosyncratic shocks in the control group. Brogaard et al. (2018) find that high frequency traders on average switch to liquidity demanding when more than one stock simultaneously experiences extreme price movements. Our evidence suggests that the liquidity demanding AT is associated with individual stock returns during market-wide shocks.22

Overall, the matching algorithm eliminates any meaningful differences in the included market condition measures between event day and non-event day observations. The difference-in-differences regression highlights the contrast of AT effects between event and non-event days. The analyses provide confidence that the association between AT and price fluctuation is exogenous to the included set of market condition measures in individual stocks.

4.2. AT and news arrivals

While we observe an economically large association between AT and stock price swings on event days, it is possible that this association is information driven. For instance, Hendershott and Riordan (2013) suggest that, due to its cheaper monitoring costs, AT may quickly incorporate relevant market information. Frino, Prodromou, Wang, Westerholm, and Zheng (2017) find that non-AT volume imbalance leads AT volume imbalance prior to corporate earnings announcements but AT can adjust trades immediately after the announcements. If non-algorithmic traders incorporate more price-relevant information than algorithmic traders during announcement periods, the observed association between AT and stock price swings may be a manifestation of non-AT incorporating information into the stock prices. To address this alternative explanation, we assess the relation between AT and price swings on stock days without firm-specific price-sensitive information arrivals.

The ASX requires listed companies to disclose price-sensitive information to the exchange as soon as the information is available. These disclosures are then compiled as announcements. Price-sensitive and firm-specific announcements including earnings announcements, quarterly activity reports, quarterly cash flow reports, dividend announcements, progress reports, periodic reports, take over announcements, issued capital, and asset acquisition and disposal are considered. A stock-day is excluded if an announcement occurred during the period between the closing of the last trading day and the closing of the current day. In total, 287 stock-days with price-sensitive announcements on market up days and 281 stock-days with price-sensitive announcements on market down days are identified.

Table 7 presents panel regression results excluding public information arrivals days. To control for correlations in the stock and time dimensions, the standard errors are clustered by stock and date. The stock and month fixed effects are included.

Table 7.

AT and firm specific news arrival.

	Up Days		Down Days
	Coefficient	t-stats	Coefficient	t-stats
iATbuyd	−1.580***	(−3.47)	0.160	(0.31)
iATselld	−0.192	(−0.46)	1.230***	(3.39)
iATbuys	0.093	(0.17)	−0.080	(−0.18)
iATsells	−0.177	(−0.28)	−1.050	(−1.52)
size	−1.955***	(−3.87)	−1.106**	(−1.97)
effsprd	−0.847***	(−3.08)	0.096	(0.74)
ivola	0.682***	(6.20)	−1.049	(−0.21)
beta	0.944	(1.21)	0.650	(1.11)
N	4571		4359
Adj. R2	0.172		0.131

This table presents coefficient estimates from panel regressions of event day market adjusted returns in relation to AT excluding stock-days with firm-specific and price-sensitive news arrivals. The dependent variable is the daily market-adjusted abnormal stock returns. We measure AT intensity in four trade groups: Liquidity demanding buy trades (iATbuy^d), liquidity demanding sell trades (iATsell^d), liquidity supplying buy trades (iATbuy^s), and liquidity supplying sell trades (iATsell^s). The control variables are identical to those in Table 3. The coefficients for all AT variables, news, size, and beta are multiplied by 100. The stock and month fixed effects are included. The t-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Table 7 show that iATbuy ^d (iATsell ^d) is significantly negatively (positively) related to the abnormal returns on market up (down) days, similar to the findings in Table 3. These results confirm that AT is associated with fewer price swings on turbulent days excluding all announcement stock-days on up and down days. Overall, the results suggest that the association between AT and price swings is consistent controlling for the effects of public information arrivals.

4.3. Causal implications

While we have excluded several plausible alternatives to the premise of AT mitigating price swings on turbulent days, it would be ideal to establish causal implications directly via exogenous instrumental variables. For example, an instrument for AT is the introduction of the “autoquote” on the New York Stock Exchange.23 This technological improvement enables faster dissemination of information for AT and is introduced in batches of stocks. The ASX has made several similar technological upgrades.24 However, to the best of our knowledge, there are no suitable technological upgrades within our sample period. Another popular instrument is the colocation services provided by the exchanges. This service enables specialized low-latency driven traders to achieve near-instantaneous execution speeds for a substantial fee. For example, Boehmer et al. (2018) use colocation events as instruments to assess the impact of AT on various market quality metrics. However, similar technological events are not available in our sample. In addition, colocation services were only available on the ASX at the start of our sample in November 2008, which eliminates the possibility of a pre- and post-implementation comparison. Besides autoquote and colocation, the literature uses many other instruments. For instance, Hasbrouck and Saar (2013) use other stocks' HFT activity as an instrument of the target stock's HFT activity to circumvent the endogeneity between the target stock's market quality and HFT activity. Aitken, Cumming, and Zhan (2015) use “permanent change” in trade size as one of the instruments. The permanent change event is defined as the first of four continuously declining months in average market trading size or the biggest single drop from the previous month. Weller (2018) and Chakrabarty, Moulton, and Wang (2018) use the lagged stocks price as an instrument for AT and HFT, respectively. These methods are not suitable for our analysis. We further explored other technological upgrades and trading rule amendments and were unable to find suitable instruments.

Our approach is to exclude the most probable alternatives. First, we match the observations on the event days, as the treatment group, with those that have similar market characteristics on non-event days, as the control group. We then use a difference-in-differences approach to show that the effects are observed only in the treatment group, despite the control group not being meaningfully different in terms of the included market condition measures. Second, we show that the effect is not driven by algorithmic traders' reactions to firm-specific news arrivals. Third, the effects are not likely to be caused by situational algorithms, since the significant effects of AT buys (sells) were observed only on market up (down) days. Specifically, unlike execution algorithms, which have a pre-existing intention to buy or sell, situational algorithms tend to be indifferent in terms of profiting from buy trades or sell trades. For example, many HFT algorithms frequently switch between buy and sell trades and maintain a low level of inventory (Brogaard and Garriott, 2018). If situational algorithms buy more stocks with lower returns to exploit the cross-sectional return differences on market up days, these algorithms are likely to also sell less (more) of the same (other) stocks. As a result, we would observe significant results in both buy and sell trades on event days. Overall, the evidence suggests that the association between AT intensity and price fluctuation is not driven by algorithmic traders' reactions to market conditions in terms of return, liquidity, volatility, and firm-specific information arrivals.

5. AT and non-AT order imbalances

The findings on AT intensities and market adjusted returns support our premise that stocks traded more by AT exhibit fewer price swings. In this section, we provide explanations for the sources of the cross-sectional return difference. One probable reason is that orders from AT exert less price pressure compared to those from non-AT. As a result, the stock price would fluctuate less during periods of high AT intensity relative to non-AT. In this section, we explore our hypothesis by analyzing the effects of order imbalances from AT and non-AT. We measure AT and non-AT order imbalances separately based on the difference between buy and sell volumes, unlike the proportion based measures of AT intensities defined in Section 3.1. While the AT intensity measures focus on the relative proportion of AT in overall trading, the order imbalances directly compares the price impacts of AT and non-AT.

5.1. Variable constructions

AT liquidity demanding order imbalance is measured as the difference between AT liquidity demanding buy volume and AT liquidity demanding sell volume:

$${\mathit{AT}}_{i,t}^d={\mathit{ATbuyvolume}}_{i,t}^d-{\mathit{ATsellvolume}}_{i,t}^d,$$ (5)

where ATbuyvolume _{i, t} ^d (ATsellvolume _{i, t} ^d) is the buy (sell) trading volume initiated by AT on day t for stock i. Similarly, AT liquidity supplying order imbalance, AT ^s is the AT liquidity supplying buy volume less sell volume.25 The non-AT order imbalances, nonAT ^d and nonAT ^s, are similarly defined. The liquidity demanding and liquidity supplying order imbalances are assessed separately, since they are collinear as they always sum to zero.

Brogaard et al. (2018) and Brogaard et al. (2014) use an activity metric that nets the liquidity supply and demand from HFT. We apply a similar metric for AT to analyze the combined effect of liquidity demand and liquidity supply by AT. Specifically, we introduce the net imbalance of AT liquidity demand and supply, AT ^net, as the sum of AT ^d and AT ^s. Liquidity is generally provided (consumed) against (in) the direction of price movements. Therefore AT ^d and AT ^s would typically have opposite signs. The net imbalance, AT ^net, indicates the overall direction of algorithmic trading activities. A positive AT ^net indicates overall trading in the direction of the positive returns. The net imbalance of non-AT, nonAT ^net, is defined analogously. When there are only two identified groups of traders (AT and non-AT), the overall trading direction of one group is opposite to the direction of the other group. I.e., AT ^net =  − nonAT ^net by design. Therefore, the net imbalances of AT enable a direct comparison between the directions of the overall trading activities by AT and non-AT.26

5.2. Multivariate analysis

We model individual stock returns as a function of order imbalance by AT and non-AT. Although our order imbalance metrics have a lower autocorrelation than those of Chordia and Subrahmanyam (2004), we include four lags of order imbalances. We also use market-adjusted returns to mitigate the cross-sectional correlation in error terms. We estimate the panel regression on event days:

$$\begin{array}{l}{\mathit{ar}}_{i,t}=\alpha +{\beta }_1{\mathit{AT}}_{i,t}^d+{\beta }_2{\mathit{nonAT}}_{i,t}^d+\sum _{k=1}^4{\beta }_{2+k}{\mathit{AT}}_{i,t-k}^d+\sum _{k=1}^4{\beta }_{6+k}{\mathit{nonAT}}_{i,t-k}^d\\ +{\beta }_{11}{\mathit{size}}_{i,t}+{\beta }_{12}{\mathit{effsprd}}_{i,t}+{\beta }_{13}{\mathit{ivola}}_{i,t}+{\beta }_{14}{\mathit{beta}}_{i,t}+{\epsilon }_{i,t},\end{array}$$ (6)

where ar _{i, t} is the abnormal return for stock i on event day t and AT _{i, t} ^d is the liquidity demanding order imbalance from AT in stock i on day t. The liquidity supplying order imbalances, AT _{i, t} ^d and nonAT _{i, t} ^d, are regressed separately since the liquidity demanding and supplying order imbalances are collinear. Similar to those in Eq. (4), the control variables are included to account for risk factors, informational effects, liquidity effects, and the potential preferences of algorithmic traders. Stock and month fixed effects are included. The standard errors are adjusted to account for stock- and day-level clustering. The results for lagged order imbalances are mostly insignificant and in line with the findings of Chordia and Subrahmanyam (2004). Therefore, the coefficients for the lagged metrics are omitted. Table 8 presents the coefficient estimates. The tests on the difference between the coefficients for AT and non-AT order flows are provided in the last four rows.

Table 8.

Event day market-adjusted return regressions on order imbalances.

	Up Days		Down Days
	1	2	3	4
ATd	0.893***		0.968***
	(7.61)		(5.48)
nonATd	1.107***		1.772***
	(5.05)		(6.64)
ATs		−1.145***		−1.402***
		(−7.03)		(−7.44)
nonATs		−0.582***		−0.728***
		(−3.46)		(−3.15)
size	−1.955***	−1.953***	−1.726***	−1.769***
	(−3.45)	(−3.45)	(−3.3)	(−3.42)
effsprd	−0.117	−0.132	−0.210*	−0.213*
	(−0.56)	(−0.68)	(−1.6)	(−1.66)
ivola	0.564***	0.574***	0.012	0.010
	(5.26)	(5.37)	(0.17)	(0.15)
beta	0.547	0.685	0.142	0.354
	(0.44)	(0.57)	(0.24)	(0.6)
N	4858	4858	4640	4640
Adj. R2	0.237	0.240	0.185	0.181
ATd less nonATd	−0.214**		−0.803***
	(−2.06)		(−4.64)
ATs less nonATs		−0.564***		−0.673***
		(−4.81)		(−3.21)

This table reports the coefficient estimates from panel regressions using the following model:

$$\begin{array}{l}{\mathit{ar}}_{i,t}=\alpha +{\beta }_1{\mathit{AT}}_{i,t}^d+{\beta }_2{\mathit{nonAT}}_{i,t}^d+\sum _{k=1}^4{\beta }_{2+k}{\mathit{AT}}_{i,t-k}^d+\sum _{k=1}^4{\beta }_{6+k}{\mathit{nonAT}}_{i,t-k}^d\\ +{\beta }_{11}{\mathit{size}}_{i,t}+{\beta }_{12}{\mathit{effsprd}}_{i,t}+{\beta }_{13}{\mathit{ivola}}_{i,t}+{\beta }_{14}{\mathit{beta}}_{i,t}+{\epsilon }_{i,t},\end{array}$$

where ar_{i, t} is the market-adjusted abnormal return for stock i on event day t. The event days are defined as the days when the absolute values of market returns exceed 2%. In model 1 and 3, AT_{i, t}^d is the order imbalance calculated as AT liquidity demanding buy volume less AT liquidity demanding sell volume. nonAT_{i, t}^d is the non-AT liquidity demanding order imbalance calculated analogously. In model 2 and 4, AT_{i, t}^d and nonAT_{i, t}^d are replaced by AT_{i, t}^s and nonAT_{i, t}^s, corresponding to liquidity supplying order imbalance of AT and non-AT, respectively.

The “ATd less nonATd” and “ATs less nonATs” rows are not included in the regression model. These rows contain the differences between the AT and the non-AT coefficients and their corresponding t-statistics.

The control variables are identical to those in Table 3. The coefficients for all volume imbalance variables are multiplied by 100,000,000. The coefficients for size and beta are multiplied by 100. The stock and month fixed effects are included. The t-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

The core variables of interest are the order imbalance metrics for AT and non-AT. The relation between market-adjusted returns and imbalance from the order flow is similar to that from the previous literature (e.g., Chordia and Subrahmanyam, 2004): Higher-order imbalance would create more price pressure on the buy side and cause prices to go up. In this regression, however, our objective is to find out whether order imbalances from AT and non-AT affect abnormal return differently. In other words, if the coefficients for liquidity demanding AT imbalance (AT _{i, t} ^d) are larger than Those for non-AT (nonAT _{i, t} ^d), then the implication is that AT exerts greater price pressure compared to non-AT. We expect, however, non-AT liquidity demanding imbalances to exert greater price pressure compared to those of AT, based on the results in Table 3.

All the contemporaneous imbalance metrics in Table 8 are significant. Model 1 (3) in Table 8 presents the results for liquidity demanding order imbalances on market up (down) days. On market up days, the coefficients of liquidity demanding order imbalances from AT and non-AT are 0.893 and 1.107, respectively. The AT coefficients are significantly smaller than the non-AT coefficients. On market down days, the difference between AT and non-AT coefficients are larger than those on market up days. Overall, the liquidity demanding results are consistent with our expectation that the abnormal returns of an individual stock are related to the stock's level of AT intensity. Specifically, AT executes trades that minimize the price pressure compared to non-AT. As a result, stocks with higher AT trading experience lower price swings on turbulent days.

Models 2 and 4 present the results for the liquidity supplying order imbalances. Both AT and non-AT supply liquidity in the opposite direction of the price movements, implying that the liquidity supplying trades are adversely selected. AT liquidity supplying order imbalances have more negative associations with stock returns compared to non-AT liquidity supplying order imbalances. Brogaard et al. (2014) assess the second-by-second relation of HFT with returns and find that HFT liquidity order imbalances are more negatively associated with permanent returns compared to those of non-HFT. While our research design differs in terms of scope and time horizon, our results are consistent with those in Brogaard et al. (2014). The interpretation of the liquidity supply relations are more complex than those of liquidity demand, since liquidity supplying activities involve quotes and trades. One possible explanation is the risk management strategies of AT. Short-term traders would accept higher than average transaction costs to unload their risky positions. For liquidity demanding orders, the costs and the price impact of these orders are observable. On the other hand, the execution of limit orders is dependent on the initiator. Trades have to adjust their limit order prices to entice potential liquidity takers. The larger negative coefficients for AT liquidity supplying order flows, compared to those for non-AT, is consistent with the risk management behavior by AT. An alternative interpretation is that AT is not proficient in managing limit orders. The executed limit orders from AT suffers more adverse selection costs compared to those from non-AT, which is contrary to the improvement of limit order informativeness documented in Hendershott et al. (2011). We find the risk management argument more convincing. Future research with data on AT limit order activities and inventory positions could further explore this topic.

To assess the combined effect of AT liquidity demand and supply in relation to event day returns, we use the AT ^net as the main AT variable and estimate the following panel regression on event days:

$${\mathit{ar}}_{i,t}=\alpha +{\beta }_1{\mathit{AT}}_{i,t}^{\mathit{net}}+\sum _{k=1}^4{\beta }_{1+k}{\mathit{AT}}_{i,t-k}^{\mathit{net}}+{\beta }_6{\mathit{size}}_{i,t}+{\beta }_7{\mathit{turnover}}_{i,t}+{\beta }_8{\mathit{idiovar}}_{i,t}+{\beta }_9{\mathit{beta}}_{i,t}+{\epsilon }_{i,t},$$ (7)

where ar _{i, t} is the abnormal return for stock i on day t. AT _{i, t} ^net is the net effect of AT liquidity demand and supply, measured as the sum of the liquidity demanding order imbalance (AT _{i, t} ^d) and the liquidity supplying order imbalance (AT _{i, t} ^s) on event day t for stock i. Table 9 presents the coefficient estimates. The coefficients for the lagged variables are omitted. Month and stock fixed effects are included. The standard errors are double clustered on stock- and day-level.

Table 9.

Event day return regressions on the net imbalances of AT liquidity demand and supply.

	Up Days		Down Days
	1	2	3	4
ATnet	−0.863***	−0.813***	−0.969***	−0.966***
	(−4.86)	(−4.91)	(−4.53)	(−4.37)
size	0.227**	−1.953***	−0.017	−1.522**
	(2.39)	(−3.46)	(−0.25)	(−2.58)
effsprd	−0.126	−0.068	−0.026	−0.275**
	(−0.8)	(−0.44)	(−0.23)	(−1.93)
ivola	0.598***	0.618***	−0.086	0.021
	(4.76)	(5.27)	(−1.59)	(0.28)
beta	1.819**	0.446	0.386	0.269
	(2.44)	(0.39)	(0.89)	(0.44)
Month FE	No	Yes	No	Yes
Stock FE	No	Yes	No	Yes
N	4858	4858	4640	4640
Adj. R2	0.104	0.192	0.030	0.140

This table reports the coefficient estimates from panel regressions using the following model:

$$\begin{array}{l}{\mathit{ar}}_{i,t}=\alpha +{\beta }_1{\mathit{AT}}_{i,t}^{\mathit{net}}+\sum _{k=1}^4{\beta }_{1+k}{\mathit{AT}}_{i,t-k}^{\mathit{net}}+{\beta }_6{\mathit{size}}_{i,t}\\ +{\beta }_7{\mathit{effsprd}}_{i,t}+{\beta }_8{\mathit{ivola}}_{i,t}+{\beta }_9{\mathit{beta}}_{i,t}+{\epsilon }_{i,t},\end{array}$$

where ar_{i, t} is the market-adjusted abnormal return for stock i on event day t. The event days are defined as the days when the absolute values of market returns exceed 2%. AT_{i, t}^net is the net imbalance of AT liquidity demand and supply for stock i on event day t, calculated as the sum of AT liquidity demanding order imbalance (AT_{i, t}^d) and AT liquidity supplying order imbalance (AT_{i, t}^s). AT_{i, t}^net facilitates a direct comparison between AT and non-AT order imbalances since AT_{i, t}^net is equal to the negative of its non-AT counterpart (nonAT_{i, t}^net) by definition.

The control variables are identical to those in Table 3. The coefficients for all volume imbalance variables are multiplied by 100,000,000. The coefficients for size and beta are multiplied by 100. The stock and month fixed effects are included in model 2 and 4. The t-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

A positive net AT imbalance, AT _{i, t} ^net, indicates the net trading activities of AT in the direction of the positive returns. I.e., A positive net AT imbalance results from either AT demanding more liquidity by initiating more buy trades than sell trades (a positive AT _{i, t} ^d) or AT supplying more liquidity from the buy side than the sell side of the transactions (a positive AT _{i, t} ^s). For example, on market up (down) days when most stocks experience positive (negative) returns, a positive (negative) AT _{i, t} ^net shows that the net trading activities of AT is in the direction of the overall positive (negative) returns. If the coefficient for AT _{i, t} ^net is positive on market up (down) days, then more net AT activities in the direction of the overall market swings are associated with further upward (downward) price swings in individual stocks.

On both market up and down days, the coefficients of AT _{i, t} ^net are negatively significant. These results imply that the direction of AT liquidity demand and supply activities are inversely associated with upward (downward) price swings in individual stocks on market up (down) days. Brogaard et al. (2018) find that the net HFT volume imbalance is negatively associated with the direction of the 10-s extreme price movements, defined as the 99.9th percentile of the 10-s absolute midquote returns for each stock. Our results are consistent with those in Brogaard et al. (2018). We differ in research design by assessing the effect of a broader but related trading group (AT) during market-wide swings over longer time horizons.

Finally, the results on AT net imbalances are robust to nonconsecutive event day selection, event day selection based on intraday realized volatilities, and stock-days with at least 10 trades initiated and supplied by AT and non-AT. These results are reported in Table A6 in the internet appendix.

6. AT execution strategy and the VWAP metric

To provide further explanations for the negative association between AT and stock price fluctuations, we investigate the possible strategies that AT could employ. Easley et al. (2012) suggest that execution algorithms track the VWAP metric to reduce execution costs. The VWAP is the average price of each transaction over a certain time horizon (typically one day) weighted by the volume of each trade. The executed price of each trade can then be compared with the VWAP to evaluate the trade's execution performance. A buy (sell) trade is considered favorable if the transacted price is lower (higher) compared to the VWAP. If algorithms closely monitor the intraday VWAP, then AT would act as counter-trend traders. Although VWAP-tracking algorithms do not trade less than usual, they would optimize their execution timing based on the VWAP-to-price relation. Therefore, AT would smooth out the liquidity demand and would not contribute to further price swings on turbulent days.

By way of illustration, Fig. 3 highlights the prices of trades initiated by AT and non-AT and the intraday dynamics of the VWAP on an event day (the top graph) and a non-event day (the bottom graph). In terms of trading volume, both algorithmic traders and human traders initiated similar amounts of transactions. However, algorithmic traders initiated trades when the price was much closer to the VWAP, compared to human traders. This finding implies that a substantial portion of AT monitors the VWAP, whereas non-AT do not track the VWAP as much.

Fig. 3.

The VWAP, AT, and non-AT on One Event Day and One non-Event day.

These figures illustrate the intraday dynamics of the VWAP and AT and non-AT prices on one event day (November 6, 2008) and one non-event day (January 21, 2009) for stocks ALS and PMV, respectively.

In Fig. 3 and in the following analyses, we reset the VWAP benchmark on a daily basis for the following reasons. First, Berkowitz et al. (1988), who initially proposed the VWAP as a measure of transactions cost, calculate the VWAPs on a daily basis. Second, Carrion (2013) applies end-of-day VWAP metrics that resets every day to assess how HFT times the market. Third, we have contacted several day traders and funds managers about their application of VWAP metric. These practitioners confirm that the daily VWAP is the a commonly used metric to assess day traders' performance.

We start the analysis by testing whether algorithmic traders execute orders closer to the VWAP compared to human traders. Table 10 shows the univariate results for the relation between the intraday VWAP and trades initiated by AT and non-AT. Panel A reports the average variance from the VWAP (var _{i, t}), defined as the squared difference between the transacted price and the prevailing VWAP weighted by the prevailing VWAP at the time of the transaction, for both AT and non-AT. On event and non-event days, var _{i, t} is significantly smaller for AT than for non-AT. Algorithms therefore trade significantly closer to the VWAP compared to human traders. This finding suggests that algorithmic traders employ a VWAP-tracking strategy. During turbulent markets, algorithmic traders do not alter their strategy.

Table 10.

AT versus non-AT variance from the VWAP.

	All	non-Event	Up	Down
	Days	Days	Days	Days
Panel A: Variance from the VWAP (vari, t)
AT	0.173	0.201	0.201	0.235
non-AT	0.317	0.315	0.315	0.381
AT less non-AT	−0.144***	−0.114***	−0.114***	−0.146***
	(−45.11)	(−17.68)	(−19.47)	(−20.97)
Panel B: Deviation from VWAP with Buy/Sell Indicator (Ii, t ⋅ devii, t)
AT	−0.149*	−0.145	−0.185	−0.163
non-AT	−0.171**	−0.175	−0.192	−0.173
AT less non-AT	0.022***	0.030***	0.007***	0.010***
	(16.54)	(19.61)	(3.22)	(3.75)

This table presents the variance from the VWAP for AT and non-AT. The VWAP for stock i at time t is defined as

$${\mathit{vwap}}_{i,t}=\frac{{\sum }_{j=1}^t{\mathit{vol}}_{i,j}{\mathit{price}}_{i,j}}{{\sum }_{j=1}^t{\mathit{vol}}_{i,j}},$$

where vol_{i, j} and price_{i, j} are the volume and price of the trade at time j (j = 1, 2, …, t − 1, t) for stock i, respectively. vwap_{i, t} resets every trading day. I.e., the prevailing VWAP at time t is the volume weighted average of all transactions from the beginning of the day up to the current trade at time t.

We then calculate the variance of each trade relative to the prevailing VWAP at the time (without incorporating the trade at the time):

$${\mathit{var}}_{i,t}={\left(\frac{{\mathit{price}}_{i,t}-{\mathit{vwap}}_{i,t-1}}{{\mathit{vwap}}_{i,t-1}}\right)}^2.$$

Panel A contains the variance from the VWAP (var_{i, t}) per trade for AT and non-AT on all days, non-event days, and event days. In Panel B, variance from the VWAP is replaced by deviation from the VWAP (devi_{i, t}) with a buy/sell indicator (I_{i, t}) that is 1 (or −1) if the trade is initiated by a buyer (or seller):

$${\mathit{devi}}_{i,t}=\frac{{\mathit{vwap}}_{i,t-1}-{\mathit{price}}_{i,t}}{{\mathit{vwap}}_{i,t-1}}.$$

The coefficients in Panel A (B) are multiplied by 10,000 (100). The t-statistics in parentheses correspond to a test of a null hypothesis that the variances of AT and non-AT trades have the same means. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

In Panel B of Table 10, we explore whether algorithmic traders buy (sell) lower (higher) than the VWAP compared to human traders. Specifically, variance from the VWAP is replaced with deviation from the VWAP (devi _{i, t}), which measures the signed difference between the prevailing VWAP and the transaction price weighted by the VWAP. Deviation from the VWAP is interacted with an indicator variable (I _{i, t}) that equals one (negative one) if the trade is buyer (seller) initiated. The term I _{i, t} ⋅ devi _{i, t} is positive when a buy (sell) trade occurs in which the stock price is below (above) the prevailing VWAP. Therefore, I _{i, t} ⋅ devi _{i, t} can gauge whether and by how much each trade can beat the VWAP metric. Although the average value of the measure is negative for AT and non-AT, algorithms beat human traders in regard to the intraday VWAP metric.

To more formally establish the statistical association between the intraday VWAP and the strategy of AT, we estimate logit regressions for algorithm-initiated trades. Following Hendershott and Riordan (2013), we control for market conditions by including the bid–ask spread, trade size, market depth, lagged volatility, and lagged volume. Also included but not reported are the time-of-day dummies for each half-hour period. To control for correlations across stocks and across time, standard errors are double clustered in the cross-section and time-series (Thompson, 2011).

The key variable in Table 11 is idevi _{i, t−1} ⋅ I _{i, t−1}, where I _{i, t−1} is an indicator variable that equals one (negative one) if the trade is buyer (seller) initiated. idevi _{i, t−1} is the deviation innovation obtained as the residual of an eight-lag autoregressive model on the time-series of devi _{i, t−1}.27 The term idevi _{i, t−1} ⋅ I _{i, t−1} measures whether the price–VWAP relation becomes favorable. A positive idevi _{i, t−1} ⋅ I _{i, t−1} indicates that the stock price has decreased (increased) compared to the VWAP just before a trader buys (sells) stock i at time t. The marginal effect of idevi _{i, t−1} ⋅ I _{i, t−1} on all days show that AT is 2.604% more likely to execute buy (sell) trades when the price decreases (increases) by 1% compared to the VWAP. The marginal effects on up days and non-event days are similar to that on all days. AT is less sensitive to changes in the VWAP on market down days. Overall, the logit regression presented in Table 11 show that AT is more likely to initiate buy (sell) trades when the price decreases (increases) compared to the VWAP.

Table 11.

Logit regression for AT and the VWAP.

	All	Non-event	Up	Down
	Days	Days	Days	Days
idevi⋅I	0.263***	0.288***	0.289***	0.136***
−odds ratio	1.301*	1.334	1.335	1.146
−marginal effect	2.604	2.535	2.639	1.291
−z-statistic	(8.12)	(8.78)	(5.25)	(3.34)
spread	0.025***	0.022***	0.026***	3.991
−z-statistic	(4.61)	(4.81)	(2.86)	(1.15)
tradesize	−0.703***	−0.698***	−0.708***	−0.773***
−z-statistic	(4.84)	(4.80)	(3.99)	(−4.70)
depth	−0.103	−0.143	−0.101	0.547
−z-statistic	(−1.31)	(−1.41)	(−0.62)	(0.64)
vola	−2.016	−1.961	−1.537	−3.43**
−z-statistic	(−1.54)	(−1.44)	(−0.64)	(−2.09)
vol	−0.386	−0.351	−0.709***	−1.319***
−z-statistic	(−1.35)	(−1.23)	(−4.97)	(−3.16)

This table presents the coefficient estimates from logit regression using the following model:at_{i, t} = α + β₁idevi_{i, t−1} ⋅ I_{i, t−1} + β₂spread_{i, t−1} + β₃tradesizesize_{i, t−1} + β₄depth_{i, t−1} + β₅vola_{i, t−1} + β₅vol_{i, t−1} + ε_{i, t},(8)

where at_{i, t} equals one if the trade of stock i at time t is AT initiated and zero otherwise. idevi_{i, t−1} is the innovation of deviation from the VWAP (devi_{i, t−1}, defined in Table 10), and is measured as the residual of an AR(8) autoregression. I_{i, t−1} is an indicator variable which is equal to 1 (−1) for a buyer (seller) initiated trade. spread_{i, t−1} is the quoted bid–ask spread. tradesize_{i, t−1} is the volume of the trade. depth_{i, t−1} is the volume of the market depth at the best bid and ask. vola_{i, t−1} and vol_{i, t−1} are the lagged volatility and lagged volume, respectively, in the 15 min before the trade. Lagged volatility is measured as the absolute value of the stock return over the interval and lagged volume is the total volume over the interval. The odds ratios are calculated based on the regression coefficient. The odds ratios and marginal effects are omitted for the control variables. Time of the day dummies for each half-hour of the trading day are included but not reported. The coefficients for idevi ⋅ I, spread, and tradesize, are multiplied by 100, 10, and 100,000, respectively. The coefficients for depth_{i, t−1} and vol_{i, t−1} are multiplied by 10,000,000. The z-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

7. Conclusion

In this paper we examine the impact of AT during the most turbulent trading days on the ASX from October 2008 till October 2009. We define turbulent days as days when the absolute values of the market returns are greater than 2%. We identify 39 event days of extreme market movements during our sample period - there are 19 trading days when the market gains at least 2% and 20 trading days when the market drops by at least 2%. For those turbulent days we analyze how individual stock returns are associated with the level of AT intensity, which is measured as the abnormal ratio of algorithmic trading volume to the total volume traded.

We show that stocks with lower levels of AT intensity experience greater price swings when the absolute return of the market exceeds 2%. Moreover, these effects are economically large. We find that with an increase of 10% (or half standard deviation) in AT buying on average, there is a decrease of 16 basis points in market adjusted returns for individual stocks when the market goes up by 2% or more. To isolate the effects of AT on market adjusted returns, We perform a difference-in-difference analysis on the event day observations with a propensity score matched sample of non-event day observations. We show that the effects of AT exist only on turbulent days, despite that the matched non-event day sample is similar to the event day sample in terms of the observed market quality measures including stock size, return, liquidity, and volatility.

We also investigate the reasons for the effects of AT on market adjusted returns. We extend Chordia and Subrahmanyam (2004) by separating order imbalances in individual stocks into AT and non-AT order imbalances. We find that AT liquidity demanding order imbalances have smaller price impacts compared to non-AT liquidity demanding order imbalances. AT liquidity supplying order imbalances are more adversely selected compared to those of non-AT. Furthermore, the net effects of AT liquidity demand and supply are negatively associated with stock price swings on turbulent days. These findings imply that, consistent with Hendershott et al. (2011), the effect of AT on stock returns is likely due to AT exerting less price pressure. In addition, by constructing intraday VWAP metrics and comparing algorithmic and non-algorithmic trades against the VWAP metrics, this study shows that AT follows VWAP tracking and counter-trend strategies. This supports the notion that stocks with more AT experience fewer price swings on turbulent days.

Our study is subject to a few caveats. First, while our sample period covers the most turbulent time in decades, the sample size is limited to a time span over one year. Second, although our results suggest some beneficial effects of AT during turbulent times, we do not support the premise that AT is harmless in other periods or other aspects of the financial market. In other words, while we observe the majority of AT to consist of benign algorithms, we do not exclude the possibility of market disruption caused by manipulative algorithms or high-frequency algorithms. Third, our results should be interpreted in light of the recent market developments after our sample period. The Australian markets have experienced gradual reductions in transaction fees and increases in market fragmentation (Aitken, Chen, and Foley, 2017). AT orders are cheaper and faster. In the meantime, the cost reductions are mitigated by the newly imposed financial transactions tax (ASIC, 2018a; ASIC, 2018b). Nevertheless, our results on AT during one of the most volatile periods is highly relevant to our current market turbulence caused by the COVID-19 pandemic. Overall, our findings have important policy implications. Since AT generally plays a beneficial role in turbulent markets, we advise against indiscriminate restrictions on AT. Future research could focus on the heterogeneity among AT groups, identifying nefarious algorithms, and exploring the effects of AT internationally over longer-periods.

Appendix A: Definition of variables

Table A1.

Variable definitions.

Variable	Definition
AT Ratio and Intensity Variables
rATi, td	rATi, td = ATvolumei, td/Totalvolumei, td, where ATvolumei, td is the AT liquidity demanding volume and Totalvolumei, t is the total liquidity demanding volume.
rATi, ts	rATi, ts = ATvolumei, ts/Totalvolumei, ts, where ATvolumei, ts is the AT liquidity supplying volume and Totalvolumei, t is the total liquidity supplying volume.
rATbuyi, td	rATbuyi, td = ATbuyvolumei, td/Totalbuyvolumei, td, where ATbuyvolumei, td is the AT buy side liquidity demanding volume and Totalbuyvolumei, td is the total buy side liquidity demanding volume
rATselli, td	rATselli, td = ATsellvolumei, td/Totalsellvolumei, td, where ATsellvolumei, td is the AT sell side liquidity demanding volume and Totalsellvolumei, td is the total sell side liquidity demanding volume
rATbuyi, ts	rATbuyi, ts = ATbuyvolumei, ts/Totalbuyvolumei, ts, where ATbuyvolumei, ts is the AT buy side liquidity supplying volume and Totalbuyvolumei, ts is the total buy side liquidity supplying volume
rATselli, ts	rATselli, ts = ATsellvolumei, ts/Totalsellvolumei, ts, where ATsellvolumei, ts is the AT sell side liquidity supplying volume and Totalsellvolumei, ts is the total sell side liquidity supplying volume
iATi, td	AT liquidity demanding intensity. ${\mathit{iAT}}_t^d={\mathit{rAT}}_t^d-\frac{1}{5}{\sum }_{i=t-5}^{t-1}{\mathit{rAT}}_i^d.$
iATi, ts	AT liquidity supplying intensity. ${\mathit{iAT}}_t^s={\mathit{rAT}}_t^s-\frac{1}{5}{\sum }_{i=t-5}^{t-1}{\mathit{rAT}}_i^s.$
iATbuyi, td	AT liquidity demanding buy intensity. ${\mathit{iATbuy}}_t^d={\mathit{rATbuy}}_t^d-\frac{1}{5}{\sum }_{i=t-5}^{t-1}{\mathit{rATbuy}}_i^d.$
iATselli, td	AT liquidity demanding sell intensity. ${\mathit{iATsell}}_t^d={\mathit{rATsell}}_t^d-\frac{1}{5}{\sum }_{i=t-5}^{t-1}{\mathit{rATsell}}_i^d.$
iATbuyi, ts	AT liquidity supplying buy intensity. ${\mathit{iATbuy}}_t^s={\mathit{rATbuy}}_t^s-\frac{1}{5}{\sum }_{i=t-5}^{t-1}{\mathit{rATbuy}}_i^s.$
iATselli, ts	AT liquidity supplying sell intensity. ${\mathit{iATsell}}_t^s={\mathit{rATsell}}_t^s-\frac{1}{5}{\sum }_{i=t-5}^{t-1}{\mathit{rATsell}}_i^s.$
AT and non-AT Order Imbalance Variables
ATi, td	ATi, td = ATbuyvolumei, td − ATsellvolumei, td, where ATbuyvolumei, td is the AT buy side liquidity demanding volume and ATsellvolumei, td is the AT sell side liquidity demanding volume.
nonATi, td	nonATi, td = nonATbuyvolumei, td − nonATsellvolumei, td, where nonATbuyvolumei, td is the non-AT buy side liquidity demanding volume and nonATsellvolumei, td is the non-AT sell side liquidity demanding volume.
ATi, ts	ATi, ts = ATbuyvolumei, ts − ATsellvolumei, ts, where ATbuyvolumei, ts is the AT buy side liquidity supplying volume and ATsellvolumei, ts is the AT sell side liquidity supplying volume.
nonATi, ts	nonATi, ts = nonATbuyvolumei, ts − nonATsellvolumei, ts, where nonATbuyvolumei, ts is the non-AT buy side liquidity supplying volume and nonATsellvolumei, ts is the non-AT sell side liquidity supplying volume.
ATi, tnet	ATi, tnet = ATi, td + ATi, ts. The AT net order imbalance is the negative of non-AT net order imbalance by construction (ATi, tnet = nonATi, tnet).
The AT Dummy
ati, t	An AT dummy which equals to 1 if a trade is initiated by AT.
Other Variables
ari, t	The daily market-adjusted abnormal return
sizei, t	The logarithm of the market value five days prior to the event day.
effsprdi, t	The daily volume weighted average of the intraday percentage effective spreads for each trade.
ivolai, t	The daily realized idiosyncratic volatility based on the intraday stock and market returns over 5-min intervals.
betai, t	The Instrumented beta. If day t is an even (odd) day, the beta is instrumented based on the betas over the past 5 odd (even) days jegadeesh2018empirical.
upi, t	Up day dummy variable which takes the value of 1 if the day t is a market up day.
downi, t	Down day dummy variable which takes the value of 1 if the day t is a market down day.
newsi, t	News dummy variable which equals to 1 if there is firm-specific price-sensitive news on day t.
vwapi, t	vwapi, t = ∑j=1tvoli, jpricei, j/∑j=1tvoli, j, where voli, j and pricei, j are the volume and price of the trade at time j (j = 1, 2, …, t − 1, t) for stock i, respectively. vwapi, t resets at the beginning of every trading day.
vari, t	vari, t = (pricei, t − vwapi, t−1)2/(vwapi, t−1)2. The variance of the trade at time t relative to the prevailing VWAP at the time (without incorporating the trade at the time).
devii, t	devii, t = (vwapi, t−1 − pricei, t)/vwapi, t−1. The deviation from the VWAP.
Ii, t	An indicator variable that equals to 1 (−1) for a buyer (seller) initiated trade.
spreadi, t	The quoted bid–ask spread.
tradesizei, t	The volume of the trade.
depthi, t	The volume of the market depth at the best bid and ask.
volai, t−1	The lagged volatility measured the absolute value of the stock return over the 15 min before the trade.
voli, t−1	The lagged volume measured as the total volume over the 15 min before the trade.

Appendix B: Internet appendix

Table A2.

Event day market-adjusted return regressions on AT intensities: Robustness I.

Extended Sample			Raw Ratios			Innovations of Ratios
	Up Days	Down Days		Up Days	Down Days		Up Days	Down Days
iATbuyd	−1.688***	−0.360	rATbuyd	−1.889***	−0.468	innATbuyd	−2.140***	−0.403
	(−2.87)	(−0.88)		(−4.18)*	(−1.17)		(−3.8)	(−0.95)
iATselld	0.805	0.967**	rATselld	0.607	0.858**	innATselld	0.542	0.945**
	(1.32)	(2.41)		(1.46)	(2.02)		(0.83)	(1.97)
iATbuys	0.094	−0.292	rATbuys	−0.309	−0.440	innATbuys	−0.091	−0.533
	(0.19)	(−0.76)		(−0.71)	(−1.09)		(−0.21)	(−1.25)
iATsells	0.066	−0.027	rATsells	−0.332	−0.124	innATsells	0.198	−0.002
	(0.19)	(−0.08)		(−0.79)	(−0.32)		(0.49)	(−0.01)
size	−2.774***	−1.282**		−2.756***	−1.337***		−2.740***	−1.283**
	(−4.75)	(−2.38)		(−10.37)	(−5.14)		(−4.75)	(−2.39)
effsprd	0.006	−0.216		0.009	−0.235***		0.004	−0.223
	(0.04)	(−1.47)		(0.19)	(−2.78)		(0.03)	(−1.5)
ivola	0.081	−0.023		0.082***	−0.016		0.080	−0.021
	(1.17)	(−0.41)		(5.64)	(−0.64)		(1.15)	(−0.37)
beta	0.652	0.711		0.608	0.664		0.633	0.708
	(0.88)	(1.07)		(0.97)	(1.12)		(0.87)	(1.06)
N	5413	5131		4858	4640		4858	4640
Adj. R2	0.115	0.101		0.114	0.100		0.116	0.101

This table presents coefficient estimates from panel regressions of event day market adjusted returns. The dependent variable is the daily market-adjusted abnormal stock returns. We measure AT intensity in four trade groups: Liquidity demanding buy trades (iATbuy^d), liquidity demanding sell trades (iATsell^d), liquidity supplying buy trades (iATbuy^s), and liquidity supplying sell trades (iATsell^s). In the first three columns, we relax the restrictions of the main sample and include stocks that are traded for less than 200 days over the sample period of 252 trading days. We also include stocks that are not present throughout our sample period. On each event day, we include stocks that have at least one buy and one sell trades initiated (supplied) by AT and non-AT in order to calculate the liquidity demanding (supplying) ratios. In the column 4–6, the raw ratios of AT volume and total volume (rAT) for each trade type are used as independent variables. In the last three columns, we replace the intensity of AT measures with the innovation in AT ratios (innAT) obtained as the residuals of the autoregressive models with five lags.

The coefficients for all AT variables, size, and beta are multiplied by 100. The stock and month fixed effects are included. The t-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Table A3.

Event day market-adjusted return regressions on AT intensities: Robustness II.

	Realized Volatility		Ten Trades		Non-consecutive Days
	Up Days	Down Days	Up Days	Down Days	Up Days	Down Days
Number of Days	19	20	19	20	18	16
iATbuyd	−1.034**	−0.315*	−1.936***	−1.411	−1.686***	0.050
	(−2.07)	(−0.46)	(−2.56)	(−1.77)	(−3.15)	(0.12)
iATselld	0.978	1.463**	−0.878	2.375***	−0.451	1.081**
	(1.36)	(2.46)	(−1.41)	(3.15)	(−0.97)	(2.33)
iATbuys	−0.088	−0.005	−0.519	−0.977*	−0.040	−0.323
	(−0.1)	(−0.01)	(−0.63)	(−1.81)	(−0.07)	(−0.69)
iATsells	−0.555	−0.286	0.104	−0.093	0.274	0.441
	(−0.94)	(−0.58)	(0.11)	(−0.13)	(0.46)	(0.9)
size	−2.247***	−2.420**	−2.776***	−2.062**	−2.202***	−1.122*
	(−2.67)	(−2.46)	(−3.27)	(−2.26)	(−3.47)	(−1.73)
effsprd	−0.148	−0.550***	−0.019	−0.970	−0.484***	−0.147
	(−0.62)	(−9.19)	(−0.11)	(−1.8)	(−3.29)	(−0.67)
ivola	0.239***	0.053	0.578***	0.024	0.637***	0.036
	(2.71)	(0.73)	(3.08)	(0.11)	(5.38)	(0.3)
beta	1.161	2.384***	1.361	−0.100	1.053	0.800
	(1.08)	(2.68)	(1.15)	(−0.06)	(1.11)	(1.24)
N	4451	4439	2623	2634	4630	3737
Adj. R2	0.070	0.115	0.318	0.175	0.194	0.126

This table presents coefficient estimates from panel regressions of event day market adjusted returns. The dependent variable is the daily market-adjusted abnormal stock returns. We measure AT intensity in four trade groups: Liquidity demanding buy trades (iATbuy^d), liquidity demanding sell trades (iATsell^d), liquidity supplying buy trades (iATbuy^s), and liquidity supplying sell trades (iATsell^s). In columns 2–3, we select event days based on intraday realized volatilities. Specifically, we rank market up days and market down days separately based on the intrday realized volatilities. We then select the top 19 market up days and the top 20 market down days to draw comparison with our main sample. In columns 4–5, we exclude stock-days that have less than 10 trades initiated or supplied by AT or non-AT. In the last two columns, we exclude event days that immediately follow other event days.

size_{i, t} is the logarithm of the market value of stock i five days prior to the event day and effsprd_{i, t} is the volume weighted average of intraday effective spread for stock i on day t. ivola_{i, t} is the intraday realized idiosyncratic volatility of the market model for stock i on day t. beta_{i, t} is the beta for stock i on day t. If day t is an even (odd) day, the beta is instrumented based on the betas over the past 5 odd (even) days (Jegadeesh et al., 2019). The coefficients for all AT variables, size, and beta are multiplied by 100. The stock and month fixed effects are included. The t-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.

Table A4.

Propensity score matching diagnostics.

Panel A: Market Up Days
	Pre-Match			Post-Match
	Control	Treatment	Difference	Control	Treatment	Difference
ar	0.272	0.223	0.049	0.256	0.223	0.033
			(0.58)			(0.34)
beta	0.336	0.337	−0.001	0.369	0.337	0.033
			(−0.03)			(1.18)
effsprd	0.792	0.871	−0.078***	0.866	0.871	−0.005
			(−2.99)			(−0.15)
size	20.434	20.382	0.052**	20.384	20.382	0.002
			(2.09)			(0.05)
ivola	0.034	0.038	−0.004***	0.038	0.038	0.000
			(−8.14)			(−0.23)
N	53,876	4858		9716	4858

Panel B: Market Down Days
	Pre-Match			Post-Match
	Control	Treatment	Difference	Control	Treatment	Difference
ar	0.272	−0.088	0.359***	−0.080	−0.088	0.007
			(4.76)			(0.07)
beta	0.336	0.356	−0.020**	0.356	0.356	0.000
			(−0.85)			(−0.01)
effsprd	0.792	0.943	−0.151***	0.925	0.943	−0.019
			(−7.62)			(−0.7)
size	20.434	20.517	−0.083***	20.520	20.517	0.003
			(−3.25)*			(0.1)
ivola	0.034	0.044	−0.010***	0.043	0.044	−0.001
			(−17.71)			(−1.41)
N	53,876	4640		9280	4640

This table shows the diagnostics for propensity score matching between event days and non-event days. The sample is separated into up (down) days as the treatment group and non-event days as the control group. Each stock-day in the treatment group is matched with two stock-days in the control group based on their propensity scores. The propensity score is acquired from the logit regressions for the treatment and the control group. The dependent variable is a dummy that takes 1 if the observation is on an event day and 0 otherwise.

The set of covariates are presented in the first column. ar_{i, t} is the market-adjusted abnormal return for stock i on event day t. size_{i, t} is the logarithm of the market value of stock i five days prior to the event day and effsprd_{i, t} is the volume weighted average of intraday effective spread for stock i on day t. ivola_{i, t} is the intraday realized idiosyncratic volatility of the market model for stock i on day t. beta_{i, t} is the beta for stock i on day t. If day t is an even (odd) day, the beta is instrumented based on the betas over the past 5 odd (even) days. Panel A (B) presents the diagnostics for market up (down) days. Column 2–4 (5–7) presents pairwise comparison of the covariates and their difference before (after) propensity matching. ar and effsprd are in percentages. The p-values for the differences in each covariates between treatment and control groups are reported in parentheses.

Table A6.

Event day market-adjusted return regressions on net imbalances: Robustness.

	Realized Volatility		Ten Trades		Non-consecutive Days
	Up Days	Down Days	Up Days	Down Days	Up Days	Down Days
Number of Days	19	20	19	20	18	16
ATnet	−0.781***	−0.789***	−0.681***	−1.020***	−0.676***	−0.828***
	(−3.23)	(−3.59)	(−4.56)	(−4.04)	(−4.87)	(−3.46)
size	−2.154***	−2.343**	−2.509***	−2.027**	−2.051***	−1.157*
	(−2.63)	(−2.39)	(−3.13)	(−2.36)	(−3.36)	(−1.82)
effsprd	−0.190	−0.587***	−0.006	−1.002**	−0.414**	−0.218
	(−0.83)	(−11.05)	(−0.04)	(−1.93)	(−2.37)	(−1.04)
ivola	0.239***	0.066*	0.588***	0.058	0.627***	0.065
	(2.74)	(0.94)	(3.21)	(0.28)	(5.31)	(0.61)
beta	1.119	2.196***	1.779	−0.917	1.070	0.475
	(1.02)	(2.47)	(1.49)	(−0.67)	(1.06)	(0.82)
N	4451	4439	2623	2634	4858	4640
Adj. R2	0.083	0.129	0.338	0.208	0.116	0.101

This table presents coefficient estimates from panel regressions of event day market adjusted returns. The dependent variable is the daily market-adjusted abnormal stock returns.

The net imbalance of AT liquidity demand and supply, AT^net, is calculated as the sum of AT liquidity demanding order imbalance (AT^d) and AT liquidity supplying order imbalance (AT^s). AT^net facilitates a direct comparison between AT and non-AT order imbalances since AT^net is equal to the negative of its non-AT counterpart (nonAT^net) by definition.

In columns 2–3, we select event days based on intraday realized volatilities. Specifically, we rank market up days and market down days separately based on the intrday realized volatilities. We then select the top 19 market up days and the top 20 market down days to draw comparison with our main sample. In columns 4–5, we exclude stock-days that have less than 10 trades initiated or supplied by AT or non-AT. In the last two columns, we exclude event days that immediately follow other event days.

size_{i, t} is the logarithm of the market value of stock i five days prior to the event day and effsprd_{i, t} is the volume weighted average of intraday effective spread for stock i on day t. ivola_{i, t} is the intraday realized idiosyncratic volatility of the market model for stock i on day t. beta_{i, t} is the beta for stock i on day t. If day t is an even (odd) day, the beta is instrumented based on the betas over the past 5 odd (even) days, similar to the method in Jegadeesh et al. (2019). The coefficients for size and beta are multiplied by 100. The stock and month fixed effects are included. The t-statistics are shown in parenthesis. The standard errors are adjusted for day- and stock-level clusterings. *, **, and *** denote significance at the 10%, 5%, and 1% levels, respectively.