This activity, however, makes it both costlier and riskier for the slower market makers to maintain continuous market presence. In response to the additional cost and risk, market makers lower their acceptable inventory bounds to levels that are too small to offset temporary liquidity imbalances of any significant size. When the diminished liquidity buffer of the market makers is pierced by a sudden order flow imbalance, they begin to demand a progressively greater compensation for maintaining continuous market presence, and prices start to move directionally. Just as the prices are moving directionally and volatility is elevated, immediacy absorption activity of HFTs can exacerbate a directional price move and amplify volatility. Higher volatility further increases the speed at which the best bid and offer queues are being depleted, inducing HFT algorithms to demand immediacy even more, fueling a spike in trading volume, and making it more costly for the market makers to maintain continuous market presence. This forces more risk averse market makers to withdraw from the market, which results in a full-blown market crash.
Empirically, immediacy absorption activity of the HFTs should manifest itself in the data very differently from the liquidity provision activity of the Market Makers. To establish the presence of these differences in the data, we test the following hypotheses:
Hypothesis H1: HFTs are more likely than Market Makers to aggressively execute the last 100 contracts before a price move in the direction of the trade. Market Makers are more likely than HFTs to have the last 100 resting contracts against which aggressive orders are executed.
Hypothesis H2: HFTs trade aggressively in the direction of the price move. Market Makers get run over by a price move.
Hypothesis H3: Both HFTs and Market Makers scratch trades, but HFTs scratch more.
To statistically test our “immediacy absorption” hypotheses against the “liquidity provision” hypotheses, we divide all of the trades during the 405 minute trading day into two subsets: Aggressive Buy trades and Aggressive Sell trades. Within each subset, we further aggregate multiple aggressive buy or sell transactions resulting from the execution of the same order into Aggressive Buy or Aggressive Sell sequences. The intuition is as follows. Often a specific trade is not a stand alone event, but a part of a sequence of transactions associated with the execution of the same order. For example, an order to aggressively sell 10 contracts may result in four Aggressive Sell transactions: for 2 contracts, 1 contract, 4 contracts, and 3 contracts, respectively, due to the specific sequence of resting bids against which this aggressive sell order was be executed. Using the order ID number, we are able to aggregate these four transactions into one Aggressive Sell sequence for 10 contracts.
Testing Hypothesis H1. Aggressive removal of the last 100 contracts by HFTs; passive provision of the last 100 resting contracts by the Market Makers. Using the Aggressive Buy sequences, we label as a “price increase event” all occurrences of trading sequences in which at least 100 contracts consecutively executed at the same price are followed by some number of contracts at a higher price. To examine indications of low latency, we focus on the the last 100 contracts traded before the price increase and the first 100 contracts at the next higher price (or fewer if the price changes again before 100 contracts are executed). Although we do not look directly at the limit order book data, price increase events are defined to capture occasions where traders use executable buy orders to lift the last remaining offers in the limit order book. Using Aggressive sell trades, we define “price decrease events” symmetrically as occurrences of sequences of trades in which 100 contracts executed at the same price are followed by executions at lower prices. These events are intended to capture occasions where traders use executable sell orders to hit the last few best bids in the limit order book. The results are presented in Table below
For price increase and price decrease events, we calculate each of the six trader categories’ shares of Aggressive and Passive trading volume for the last 100 contracts traded at the “old” price level before the price increase or decrease and the first 100 contracts traded at the “new” price level (or fewer if the number of contracts is less than 100) after the price increase or decrease event.
Table above presents, for the six trader categories, volume shares for the last 100 contracts at the old price and the first 100 contracts at the new price. For comparison, the unconditional shares of aggressive and passive trading volume of each trader category are also reported. Table has four panels covering (A) price increase events on May 3-5, (B) price decrease events on May 3-5, (C) price increase events on May 6, and (D) price decrease events on May 6. In each panel there are six rows of data, one row for each trader category. Relative to panels A and C, the rows for Fundamental Buyers (BUYER) and Fundamental Sellers (SELLER) are reversed in panels B and D to emphasize the symmetry between buying during price increase events and selling during price decrease events. The first two columns report the shares of Aggressive and Passive contract volume for the last 100 contracts before the price change; the next two columns report the shares of Aggressive and Passive volume for up to the next 100 contracts after the price change; and the last two columns report the “unconditional” market shares of Aggressive and Passive sides of all Aggressive buy volume or sell volume. For May 3-5, the data are based on volume pooled across the three days.
Consider panel A, which describes price increase events associated with Aggressive buy trades on May 3-5, 2010. High Frequency Traders participated on the Aggressive side of 34.04% of all aggressive buy volume. Strongly consistent with immediacy absorption hypothesis, the participation rate rises to 57.70% of the Aggressive side of trades on the last 100 contracts of Aggressive buy volume before price increase events and falls to 14.84% of the Aggressive side of trades on the first 100 contracts of Aggressive buy volume after price increase events.
High Frequency Traders participated on the Passive side of 34.33% of all aggressive buy volume. Consistent with hypothesis, the participation rate on the Passive side of Aggressive buy volume falls to 28.72% of the last 100 contracts before a price increase event. It rises to 37.93% of the first 100 contracts after a price increase event.
These results are inconsistent with the idea that high frequency traders behave like textbook market makers, suffering adverse selection losses associated with being picked off by informed traders. Instead, when the price is about to move to a new level, high frequency traders tend to avoid being run over and take the price to the new level with Aggressive trades of their own.
Market Makers follow a noticeably more passive trading strategy than High Frequency Traders. According to panel A, Market Makers are 13.48% of the Passive side of all Aggressive trades, but they are only 7.27% of the Aggressive side of all Aggressive trades. On the last 100 contracts at the old price, Market Makers’ share of volume increases only modestly, from 7.27% to 8.78% of trades. Their share of Passive volume at the old price increases, from 13.48% to 15.80%. These facts are consistent with the interpretation that Market Makers, unlike High Frequency Traders, do engage in a strategy similar to traditional passive market making, buying at the bid price, selling at the offer price, and suffering losses when the price moves against them. These facts are also consistent with the hypothesis that High Frequency Traders have lower latency than Market Makers.
Intuition might suggest that Fundamental Buyers would tend to place the Aggressive trades which move prices up from one tick level to the next. This intuition does not seem to be corroborated by the data. According to panel A, Fundamental Buyers are 21.53% of all Aggressive trades but only 11.61% of the last 100 Aggressive contracts traded at the old price. Instead, Fundamental Buyers increase their share of Aggressive buy volume to 26.17% of the first 100 contracts at the new price.
Taking into account symmetry between buying and selling, panel B shows the results for Aggressive sell trades during May 3-5, 2010, are almost the same as the results for Aggressive buy trades. High Frequency Traders are 34.17% of all Aggressive sell volume, increase their share to 55.20% of the last 100 Aggressive sell contracts at the old price, and decrease their share to 15.04% of the last 100 Aggressive sell contracts at the new price. Market Makers are 7.45% of all Aggressive sell contracts, increase their share to only 8.57% of the last 100 Aggressive sell trades at the old price, and decrease their share to 6.58% of the last 100 Aggressive sell contracts at the new price. Fundamental Sellers’ shares of Aggressive sell trades behave similarly to Fundamental Buyers’ shares of Aggressive Buy trades. Fundamental Sellers are 20.91% of all Aggressive sell contracts, decrease their share to 11.96% of the last 100 Aggressive sell contracts at the old price, and increase their share to 24.87% of the first 100 Aggressive sell contracts at the new price.
Panels C and D report results for Aggressive Buy trades and Aggressive Sell trades for May 6, 2010. Taking into account symmetry between buying and selling, the results for Aggressive buy trades in panel C are very similar to the results for Aggressive sell trades in panel D. For example, Aggressive sell trades by Fundamental Sellers were 17.55% of Aggressive sell volume on May 6, while Aggressive buy trades by Fundamental Buyers were 20.12% of Aggressive buy volume on May 6. In comparison with the share of Fundamental Buyers and in comparison with May 3-5, the Flash Crash of May 6 is associated with a slightly lower – not higher – share of Aggressive sell trades by Fundamental Sellers.
The number of price increase and price decrease events increased dramatically on May 6, consistent with the increased volatility of the market on that day. On May 3-5, there were 4100 price increase events and 4062 price decrease events. On May 6 alone, there were 4101 price increase events and 4377 price decrease events. There were therefore approximately three times as many price increase events per day on May 6 as on the three preceding days.
A comparison of May 6 with May 3-5 reveals significant changes in the trading patterns of High Frequency Traders. Compared with May 3-5 in panels A and B, the share of Aggressive trades by High Frequency Traders drops from 34.04% of Aggressive buys and 34.17% of Aggressive sells on May 3-5 to 26.98% of Aggressive buy trades and 26.29% of Aggressive sell trades on May 6. The share of Aggressive trades for the last 100 contracts at the old price declines by even more. High Frequency Traders’ participation rate on the Aggressive side of Aggressive buy trades drops from 57.70% on May 3-5 to only 38.86% on May 6. Similarly, the participation rate on the Aggressive side of Aggressive sell trades drops from and 55.20% to 38.67%. These declines are largely offset by increases in the participation rate by Opportunistic Traders on the Aggressive side of trades. For example, Opportunistic Traders’ share of the Aggressive side of the last 100 contracts traded at the old price rises from 19.21% to 34.26% for Aggressive buys and from 20.99% to 33.86% for Aggressive sells. These results suggest that some Opportunistic Traders follow trading strategies for which low latency is important, such as index arbitrage, cross-market arbitrage, or opportunistic strategies mimicking market making.
Testing Hypothesis H2. HFTs trade aggressively in the direction of the price move; Market Makers get run over by a price move. To examine this hypothesis, we analyze whether High Frequency Traders use Aggressive trades to trade in the direction of contemporaneous price changes, while Market Makers use Passive trades to trade in the opposite direction from price changes. To this end, we estimate the regression equation
Δyt = α + Φ . Δyt-1 + δ . yt-1 + Σi=120 [βi . Δpt-1 /0.25] + εt
(where yt and Δyt denote inventories and change in inventories of High Frequency Traders for each second of a trading day; t = 0 corresponds to the opening of stock trading on the NYSE at 8:30:00 a.m. CT (9:30:00 ET) and t = 24, 300 denotes the close of Globex at 15:15:00 CT (4:15 p.m. ET); Δpt denotes the price change in index point units between the high-low midpoint of second t-1 and the high-low midpoint of second t. Regressing second-by-second changes in inventory levels of High Frequency Traders on the level of their inventories the previous second, the change in their inventory levels the previous second, the change in prices during the current second, and lagged price changes for each of the previous 20 previous seconds.)
for Passive and Aggressive inventory changes separately.
Table above presents the regression results of the two components of change in holdings on lagged inventory, lagged change in holdings and lagged price changes over one second intervals. Panel A and Panel B report the results for May 3-5 and May 6, respectively. Each panel has four columns, reporting estimated coefficients where the dependent variables are net Aggressive volume (Aggressive buys minus Aggressive sells) by High Frequency Traders (∆AHFT), net Passive volume by High Frequency Traders (∆PHFT), net Aggressive volume by Market Makers (∆AMM), and net Passive volume by Market Makers (∆PMM).
We observe that for lagged inventories (NPHFTt−1), the estimated coefficients for Aggressive and Passive trades by High Frequency Traders are δAHFT = −0.005 (t = −9.55) and δPHFT = −0.001 (t = −3.13), respectively. These coefficient estimates have the interpretation that High Frequency Traders use Aggressive trades to liquidate inventories more intensively than passive trades. In contrast, the results for Market Makers are very different. For lagged inventories (NPMMt−1), the estimated coefficients for Aggressive and Passive volume by Market Makers are δAMM = −0.002 (t = −6.73) and δPMM = −0.002 (t = −5.26), respectively. The similarity of these coefficients estimates has the interpretation that Market Makers favor neither Aggressive trades nor Passive trades when liquidating inventories.
For contemporaneous price changes (in the current second) (∆Pt−1), the estimated coefficient Aggressive and Passive volume by High Frequency Traders are β0 = 57.78 (t = 31.94) and β0 = −25.69 (t = −28.61), respectively. For Market Makers, the estimated coefficients for Aggressive and Passive trades are β0 = 6.38 (t = 18.51) and β0 = −19.92 (t = −37.68). These estimated coefficients have the interpretation that in seconds in which prices move up one tick, High Frequency traders are net buyers of about 58 contracts with Aggressive trades and net sellers of about 26 contracts with Passive trades in that same second, while Market Makers are net buyers of about 6 contracts with Aggressive trades and net sellers of about 20 contracts with Passive trades. High Frequency Traders and Market Makers are similar in that they both use Aggressive trades to trade in the direction of price changes, and both use Passive trades to trade against the direction of price changes. High Frequency Traders and Market Makers are different in that Aggressive net purchases by High Frequency Traders are greater in magnitude than the Passive net purchases, while the reverse is true for Market Makers.
For lagged price changes, coefficient estimates for Aggressive trades by High Frequency Traders and Market Makers are positive and statistically significant at lags 1-4 and lags 1-10, respectively. These results have the interpretation that both High Frequency Traders’ and Market Makers’ trade on recent price momentum, but the trading is compressed into a shorter time frame for High Frequency Traders than for Market Makers.
For lagged price changes, coefficient estimates for Passive volume by High Frequency Traders and Market Makers are negative and statistically significant at lags 1 and lags 1-3, respectively. Panel B of Table presents results for May 6. Similar to May 3-5, High Frequency Traders tend to use Aggressive trades more intensely than Passive trades to liquidate inventories, while Market Makers do not show this pattern. Also similar to May 3-5, High Frequency Trades and Market makers use Aggressive trades to trade in the contemporaneous direction of price changes and use Passive trades to trade in the direction opposite price changes, with Aggressive trading greater than Passive trading for High Frequency Traders and the reverse for Market Makers. In comparison with May 3-5, the coefficients are smaller in magnitude on May 6, indicating reduced liquidity at each tick. For lagged price changes, the coefficients associated with Aggressive trading by High Frequency Traders change from positive to negative at lags 1-4, and the positive coefficients associated with Aggressive trading by Market Makers change from being positive and statistically significant at lags lags 1-10 to being positive and statistically significant only at lags 1-3. These results illustrate accelerated trading velocity in the volatile market conditions of May 6.
We further examine how high frequency trading activity is related to market prices. Figure below illustrates how prices change after HFT trading activity in a given second. The upper-left panel presents results for buy trades for May 3-5, the upper right panel presents results for buy trades on May 6, and the lower-left and lower-right present corresponding results for sell trades. For an “event” second in which High Frequency Traders are net buyers, net Aggressive Buyers, and net Passive Buyers value-weighted average prices paid by the High Frequency Traders in that second are subtracted from the value-weighted average prices for all trades in the same second and each of the following 20 seconds. The results are averaged across event seconds, weighted by the magnitude of High Frequency Traders’ net position change in the event second. The upper-left panel presents results for May 3-5, the upper-right panel presents results for May 6, and the lower two panels present results for sell trades calculated analogously. Price differences on the vertical axis are scaled so that one unit equals one tick ($12.50 per contract).
When High Frequency Traders are net buyers on May 3-5, prices rise by 17% of a tick in the next second. When HFTs execute Aggressively or Passively, prices rise by 20% and 2% of a tick in the next second, respectively. In subsequent seconds, prices in all cases trend downward by about 5% of a tick over the subsequent 19 seconds. For May 3-5, the results are almost symmetric for selling.
When High Frequency Traders are buying on May 6, prices increase by 7% of a tick in the next second. When they are aggressive buyers or passive buyers, prices increase by increase 25% of a tick or decrease by 5% of a tick in the next second, respectively. In subsequent seconds, prices generally tend to drift downwards. The downward drift is especially pronounced after Passive buying, consistent with the interpretation that High Frequency Traders were “run over” when their resting limit buy orders were “run over” in the down phase of the Flash Crash. When High Frequency Traders are net sellers, the results after one second are analogous to buying. After aggressive selling, prices continue to drift down for 20 seconds, consistent with the interpretation that High Frequency Traders made profits from Aggressive sales during the down phase of the Flash Crash.
Testing Hypothesis H3. Both HFTs and Market Makers scratch trades; HFTs scratch more. A textbook market maker will try to buy at the bid price, sell at the offer price, and capture the bid-ask spread as a profit. Sometimes, after buying at the bid price, market prices begin to fall before the market maker can make a one tick profit by selling his inventory at the best offer price. To avoid taking losses in this situation, one component of a traditional market making strategy is to “scratch trades in the presence of changing market conditions by quickly liquidating a position at the same price at which it was acquired. These scratched trades represent inventory management trades designed to lower the cost of adverse selection. Since many competing market makers may try to scratch trades at the same time, traders with the lowest latency will tend to be more successful in their attempts to scratch trades and thus more successful in their ability to avoid losses when market conditions change.
To examine whether and to what extent traders engage in trade scratching, we sequence each trader’s trades for the day using audit trail sequence numbers which not only sort trades by second but also sort trades chronologically within each second. We define an “immediately scratched trade” as a trade with the properties that the next trade in the sorted sequence (1) occurred in the same second, (2) was executed at the same price, (3) was in the opposite direction, i.e., buy followed by sell or sell followed by buy. For each of the trading accounts in our sample, we calculate the number of immediately scratched trades, then compare the number of scratched trades across the six trader categories.
The results of this analysis are presented in the table below. Panel A provides results for May 3-5 and panel B for May 6. In each panel, there are five rows of data, one for each trader category. The first three columns report the total number of trades, the total number of immediately scratched trades, and the percentage of trades that are immediately scratched by traders in five categories. For May 3-6, the reported numbers are from the pooled data.
This table presents statistics for immediate trade scratching which measures how many times a trader changes his/her direction of trading in a second aggregated over a day. We define a trade direction change as a buy trade right after a sell trade or vice versa at the same price level in the same second.
This table shows that High Frequency Traders scratched 2.84 % of trades on May 3-5 and 4.26 % on May 6; Market Makers scratched 2.49 % of trades on May 3-5 and 5.53 % of trades on May 6. While the percentages of immediately scratched trades by Market Makers is slightly higher than that for High Frequency Traders on May 6, the percentages for both groups are very similar. The fourth, fifth, and sixth columns of the Table report the mean, standard deviation, and median of the number of scratched trades for the traders in each category.
Although the percentages of scratched trades are similar, the mean number of immediately scratched trades by High Frequency Traders is much greater than for Market Makers: 540.56 per day on May 3-5 and 1610.75 on May 6 for High Frequency Traders versus 13.35 and 72.92 for Market Makers. The differences between High Frequency Traders and Market Makers reflect differences in volume traded. The Table shows that High Frequency Traders and Market Makers scratch a significantly larger percentage of their trades than other trader categories.