This analysis investigates how liquidity is affected by periods of high trade intensity. We test whether the following measures, in the few seconds before a trade, have an effect on the book’s liquidity in the 100 milliseconds after the trade.
number of changes in the orderbook.
size of the bid-ask spread.
number of trades.
Hendershott and Riordan (2013) report algorithmic traders consume liquidity when spreads narrow, but supply when spread widens.
Chordia, Roll, and Subrahmanyam (2000) observe a relationship and influence of spread on liquidity and market depth is time-varying, noting substantial variability across trading days and over time.
Biais, Hillion, and Spatt (1995) finds liquidity offering increases when bid-ask spread widens and observes intraday patterns.
High-frequency traders (HFT) are identified in our analysis by the speed of their reaction to the trade.
Specifically, we defing HFT as those who can react within 1 to 100 milliseconds after an event.
The event we use is a trade.
Our method is a modification of the method used in Hasbrouck and Saar (2013) who used an order cancellation as the event.
Data are Market Depth Data [link] for natural gas futures (ticker: NG) purchased directly from the Chicago Mercantile Exchange (CME).
Market Depth Data contains all market messages to and from the CME, and is time-stamped to the millisecond.
Using this data we can recreate the NG orderbook up to 10 levels deep.
Our data set is for NGV3 from September 16, 2013 to September 27, 2016 inclusive.
We choose to use the NYMEX natural gas book in this analysis because:
Unlike stock, all trades and quotes for NG take place in this one central book.
Since all trading takes place on the same computer server, there is no delay in orders due to location.
NG is heavily traded and very volatile.
We first construct the full limit order book for each day.
Then, over each day we first extract trades for a single contract with no trades during the same millisecond, and the following 100 ms.
For each of these trades we calculate:
Our pre-trade measures.
The post-trade change in liquidity.
We model the change in liquidity post-trade as functions of three pre-trade variables. Our model is:
\(\Delta L = \beta_0 + \beta_1 numC + \beta_2 avgBA + \beta_3 numT + \mu\)
where:
\(avgBA\) is the average Bid-Ask spread
\(numT\) is the number of trades
\(numC\) is the number of changes in the orderbook
\(y\) is the number of milliseconds prior to the trade.
| Day | numC | avgBA | numT |
|---|---|---|---|
| 9/16 | 57.1310 | 1.6067 | 6.0187 |
| 9/17 | 47.7543 | 1.6248 | 4.0833 |
| 9/18 | 45.0486 | 1.6433 | 3.9236 |
| 9/19 | 78.2164 | 1.5122 | 8.6340 |
| 9/20 | 50.2657 | 1.8090 | 6.3216 |
| 9/23 | 41.6142 | 1.8415 | 2.9695 |
| 9/24 | 54.4397 | 1.7706 | 6.0319 |
| 9/25 | 45.1660 | 1.7523 | 4.6075 |
| 9/26 | 82.8835 | 1.5351 | 1.0424 |
| 9/27 | 42.0711 | 1.5000 | 5.3596 |
We estimate this equation for each side of the orderbook, separately for buy and sell trades, and also for trades where the initiator is unknown. We thus have 6 separate regressions.
We calculate \(avgBA\), \(numT\), and \(numC\) over 30 different pre-trade intervals ranging from 100 ms, to 3000 ms prior to the trade. The end point of each interval was 1 ms prior to the trade.
Similarly, we calculate \(Delta L\) over intervals starting 1 ms after the trade, incrementing by 1 ms, until 100 ms after the trade.
Following are 3-dimensional plots of the coefficients estimated over the range of possible pre and post-trade intervals.
We use these plots to investigate how sensitive our coefficient estimate is to our choice of pre and post-trade interval.
We find an interval of 1 second before the trade, and 100ms after the trade, affords a stable estimate of the coefficient.
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | 5,416.97*** (1,628.44) | 1,874.70** (934.12) | 460.40 (1,452.22) | -417.37 (871.93) | 2,345.01*** (510.79) | 822.09** (336.28) |
| Avg. BO | 64,509.43 (99,036.30) | -31,713.23 (56,809.96) | -53,644.11 (136,090.00) | 54,637.37 (81,710.25) | 21,046.38 (54,261.12) | 69,485.82* (35,723.79) |
| Num. T | -7,087.32 (11,474.87) | -4,785.05 (6,582.30) | -8,574.46 (8,224.63) | 1,949.95 (4,938.18) | 1,049.38 (3,080.16) | -2,441.59 (2,027.88) |
| Constant | -347,293.50* (186,386.60) | 16,008.03 (106,916.50) | 162,087.50 (236,825.30) | -115,659.10 (142,193.10) | -75,685.26 (86,271.59) | -127,872.70** (56,798.46) |
| Observations | 238 | 238 | 207 | 207 | 2,829 | 2,829 |
| R2 | 0.11 | 0.03 | 0.01 | 0.003 | 0.03 | 0.004 |
| Adjusted R2 | 0.10 | 0.02 | -0.003 | -0.01 | 0.03 | 0.003 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | 9,111.69 | -60.38 | 21.74 | -52.15 | 1,474.28** | -222.86 |
| (6,233.93) | (1,085.87) | (993.14) | (714.86) | (669.83) | (395.40) | |
| Avg. BO | -44,338.97 | -46,881.25 | -63,597.75 | -10,310.35 | -28,183.81 | -19,169.63 |
| (498,100.20) | (86,762.49) | (75,504.28) | (54,347.38) | (51,550.81) | (30,430.78) | |
| Num. T | -55,301.59 | 8,931.04 | 1,493.16 | 2,528.10 | -4,460.53 | 1,821.45 |
| (47,689.16) | (8,306.82) | (5,705.14) | (4,106.51) | (3,749.22) | (2,213.19) | |
| Constant | 144,097.60 | 224,526.40 | 189,482.80 | 2,085.33 | -11,428.04 | 122,755.30** |
| (885,649.00) | (154,268.40) | (137,433.80) | (98,923.75) | (86,122.15) | (50,838.47) | |
| Observations | 198 | 198 | 217 | 217 | 2,492 | 2,492 |
| R2 | 0.01 | 0.01 | 0.005 | 0.01 | 0.003 | 0.0005 |
| Adjusted R2 | -0.004 | -0.001 | -0.01 | -0.01 | 0.001 | -0.001 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | 249.58 | -173.53 | 230.74 | -829.33 | 3,006.22*** | -693.96 |
| (1,449.18) | (741.84) | (1,555.04) | (4,754.50) | (608.10) | (469.88) | |
| Avg. BO | -23,955.18 | -4,666.65 | -2,086.15 | -160,352.60 | 102,997.60** | -35,310.60 |
| (78,245.89) | (40,054.30) | (69,598.97) | (212,796.90) | (47,100.45) | (36,394.55) | |
| Num. T | -1,876.98 | -1,006.45 | -4,576.40 | -5,325.65 | -10,537.18*** | 4,171.02 |
| (11,239.70) | (5,753.63) | (11,342.74) | (34,680.09) | (3,871.08) | (2,991.18) | |
| Constant | 72,570.97 | 82,395.43 | 202,919.00 | 535,752.30 | -257,185.50*** | 86,100.07 |
| (156,018.20) | (79,866.19) | (143,982.80) | (440,223.30) | (78,991.52) | (61,036.81) | |
| Observations | 241 | 241 | 245 | 245 | 2,638 | 2,638 |
| R2 | 0.001 | 0.002 | 0.001 | 0.004 | 0.01 | 0.001 |
| Adjusted R2 | -0.01 | -0.01 | -0.01 | -0.01 | 0.01 | 0.0001 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | -169.33 | -177.02 | 538.41 | 552.51 | -679.04* | -159.12 |
| (608.54) | (538.47) | (595.23) | (663.24) | (347.83) | (296.66) | |
| Avg. BO | 47,867.66 | 120,465.90* | 11,218.42 | 92,454.65* | 40,336.68 | 38,044.76 |
| (81,578.39) | (72,185.50) | (45,468.28) | (50,663.40) | (43,094.54) | (36,754.96) | |
| Num. T | -3,116.42 | -6.89 | -2,463.74 | -1,780.60 | 1,915.92 | 1,009.27 |
| (3,521.92) | (3,116.41) | (2,655.01) | (2,958.36) | (1,722.21) | (1,468.86) | |
| Constant | -122,558.10 | -138,461.90 | 31,722.25 | -171,147.60* | 49,841.61 | 14,034.01 |
| (127,523.00) | (112,840.00) | (89,170.94) | (99,359.43) | (67,525.07) | (57,591.54) | |
| Observations | 354 | 354 | 323 | 323 | 4,314 | 4,314 |
| R2 | 0.01 | 0.01 | 0.003 | 0.01 | 0.001 | 0.0004 |
| Adjusted R2 | 0.003 | -0.0003 | -0.01 | 0.003 | 0.001 | -0.0003 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | 673.93 | 230.52 | 754.33 | 1,108.08 | 125.08 | -233.48 |
| (5,147.63) | (705.37) | (1,015.59) | (1,244.32) | (447.00) | (488.77) | |
| Avg. BO | -198,894.60 | -9,368.22 | 36,886.78 | -39,847.42 | 10,933.41 | 83,826.01** |
| (388,439.30) | (53,226.88) | (56,524.39) | (69,254.84) | (35,865.31) | (39,216.73) | |
| Num. T | -7,762.43 | 118.64 | -5,043.07 | -6,197.98 | -1,486.94 | 2,853.99 |
| (27,899.52) | (3,823.00) | (7,642.78) | (9,364.09) | (2,665.20) | (2,914.25) | |
| Constant | 690,504.80 | 129,928.00 | 54,551.13 | 95,330.30 | 80,398.73 | -64,600.62 |
| (789,370.80) | (108,165.50) | (112,225.00) | (137,500.40) | (64,013.13) | (69,994.81) | |
| Observations | 120 | 120 | 141 | 141 | 1,595 | 1,595 |
| R2 | 0.003 | 0.003 | 0.01 | 0.01 | 0.0003 | 0.004 |
| Adjusted R2 | -0.02 | -0.02 | -0.01 | -0.01 | -0.002 | 0.002 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | 5,829.86 | 634.40 | -1,550.35 | 2,464.47 | 2,149.45*** | 3,777.97*** |
| (5,156.58) | (939.48) | (1,215.72) | (2,233.42) | (511.45) | (1,233.47) | |
| Avg. BO | -73,534.40 | 23,546.42 | 150,537.70* | 4,657.66 | 36,869.39 | 153,673.50 |
| (397,929.80) | (72,498.72) | (80,233.12) | (147,397.00) | (40,214.46) | (96,986.60) | |
| Num. T | -53,840.58 | -2,178.96 | 16,896.69* | 3,777.33 | -10,983.26*** | -13,254.48* |
| (54,848.57) | (9,992.85) | (9,429.43) | (17,322.89) | (3,220.00) | (7,765.79) | |
| Constant | 532,978.80 | 81,224.22 | -63,021.84 | 161,700.70 | 218,804.30*** | 48,867.40 |
| (776,259.30) | (141,426.50) | (159,561.80) | (293,132.40) | (76,206.74) | (183,790.40) | |
| Observations | 170 | 170 | 156 | 156 | 1,585 | 1,585 |
| R2 | 0.01 | 0.01 | 0.05 | 0.03 | 0.01 | 0.01 |
| Adjusted R2 | -0.01 | -0.01 | 0.03 | 0.01 | 0.01 | 0.01 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | 531.04 | 1,593.17 | -371.67 | 7,853.48*** | 369.28 | 1,283.51** |
| (593.80) | (3,266.71) | (538.26) | (2,662.86) | (226.09) | (565.65) | |
| Avg. BO | 30,444.14 | -83,687.98 | 22,493.72 | 327,988.60 | 153,234.60*** | -197,541.80** |
| (53,983.25) | (296,983.70) | (60,182.92) | (297,732.70) | (35,451.67) | (88,696.67) | |
| Num. T | -1,656.16 | 2,843.60 | 3,156.11 | -23,357.54** | -40.36 | -3,835.70 |
| (3,868.21) | (21,280.61) | (1,954.95) | (9,671.39) | (945.65) | (2,365.93) | |
| Constant | -10,685.39 | 588,183.00 | 109,436.30 | -428,410.90 | -61,940.70 | 784,325.90*** |
| (104,593.00) | (575,408.40) | (109,860.30) | (543,493.10) | (60,650.30) | (151,741.20) | |
| Observations | 249 | 249 | 284 | 284 | 2,863 | 2,863 |
| R2 | 0.01 | 0.005 | 0.02 | 0.04 | 0.01 | 0.003 |
| Adjusted R2 | -0.01 | -0.01 | 0.01 | 0.03 | 0.01 | 0.002 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | -948.18 | -544.25 | -207.49 | -2,008.42 | 101.03 | -246.79 |
| (2,405.99) | (981.54) | (950.38) | (5,709.76) | (703.29) | (807.26) | |
| Avg. BO | 100,718.00 | -6,709.21 | 42,620.29 | 75,035.79 | 126,927.30** | 146,170.00** |
| (163,577.90) | (66,732.89) | (57,110.41) | (343,112.90) | (64,457.09) | (73,985.67) | |
| Num. T | 14,728.78 | 3,618.93 | 1,272.33 | 13,260.28 | -2,323.54 | 2,987.66 |
| (17,406.81) | (7,101.24) | (6,455.60) | (38,784.50) | (4,684.47) | (5,376.96) | |
| Constant | 12,965.38 | 160,597.60 | 19,338.95 | 370,446.90 | 145,953.60 | 13,743.08 |
| (320,905.40) | (130,915.90) | (106,029.60) | (637,013.80) | (108,743.60) | (124,818.90) | |
| Observations | 215 | 215 | 217 | 217 | 2,510 | 2,510 |
| R2 | 0.01 | 0.002 | 0.003 | 0.001 | 0.002 | 0.002 |
| Adjusted R2 | -0.01 | -0.01 | -0.01 | -0.01 | 0.001 | 0.0005 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | 287.29 | 876.52 | -521.68 | 5,633.56*** | 568.41*** | 1,818.24*** |
| (541.11) | (786.40) | (420.20) | (1,017.44) | (207.73) | (366.07) | |
| Avg. BO | -100,345.20* | 51,922.75 | 66,465.10 | -224,142.20* | -119,124.50*** | 30,491.83 |
| (57,581.08) | (83,682.75) | (48,214.60) | (116,743.00) | (23,041.96) | (40,605.94) | |
| Num. T | -2,316.25 | -2,564.99 | 2,873.44 | -24,633.91*** | -2,954.21*** | -5,012.68*** |
| (2,848.74) | (4,140.08) | (2,200.84) | (5,328.95) | (1,099.83) | (1,938.19) | |
| Constant | 183,970.90** | -6,292.82 | 51.66 | 165,271.90 | 199,316.80*** | -35,725.84 |
| (92,664.67) | (134,669.80) | (73,955.92) | (179,071.00) | (34,142.32) | (60,167.66) | |
| Observations | 557 | 557 | 567 | 567 | 6,284 | 6,284 |
| R2 | 0.01 | 0.01 | 0.01 | 0.05 | 0.01 | 0.01 |
| Adjusted R2 | 0.002 | -0.0002 | 0.001 | 0.05 | 0.005 | 0.01 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
| Dependent variable: | ||||||
| Buy/Bid | Buy/Offer | Sell/Bid | Sell/Offer | NA/Bid | NA/Offer | |
| (1) | (2) | (3) | (4) | (5) | (6) | |
| Num. Ch. | 15,945.64*** | 535.82 | -552.85 | -373.94 | 1,156.73** | 261.10 |
| (2,878.46) | (797.94) | (836.06) | (1,274.53) | (583.38) | (526.71) | |
| Avg. BO | 55,069.97 | 81,649.71 | 27,448.72 | 102,558.40 | 31,948.61 | 125,964.50*** |
| (205,859.20) | (57,066.07) | (68,397.58) | (104,269.00) | (48,127.03) | (43,451.66) | |
| Num. T | -56,693.69*** | -889.97 | 151.17 | 2,308.53 | -6,893.87** | 569.71 |
| (13,372.45) | (3,706.97) | (5,151.29) | (7,852.91) | (3,302.30) | (2,981.49) | |
| Constant | -420,289.70 | -100,047.40 | 2,448.60 | -154,983.50 | -39,806.65 | -168,540.80** |
| (330,982.90) | (91,751.52) | (105,035.50) | (160,121.80) | (74,098.41) | (66,900.02) | |
| Observations | 211 | 211 | 225 | 225 | 2,545 | 2,545 |
| R2 | 0.14 | 0.02 | 0.01 | 0.005 | 0.002 | 0.004 |
| Adjusted R2 | 0.13 | 0.002 | 0.0004 | -0.01 | 0.001 | 0.003 |
| Note: | p<0.1; p<0.05; p<0.01 | |||||
Some salient features of the results follow. On the left are the pre-trade measures, and on the right is post-trade liquidity.
More trades \(\Rightarrow\) less liquidity (part. on opp. side).
More book changes \(\Rightarrow\) more liquidity (part. on opp. side).
The above is true on both sides for NA trades.
The evidence for the impact of the size of the bid-offer spread is mixed.
Trades take liquidity, and so our result may be interpreted as if there is more liquidity taken prior to the trade, the less liquidity is provided after.
This is evidence that activity in the orderbook may be a more important determinant of liquidity provision than the size of the spread.
HFT is more willing to provide liquidity when the book is active, and not simply because the compensation for providing liquidity is high.
This point is an important additon to the literature.
matthew.brigida [at] sunyit.edu
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Chordia, Tarun, Richard Roll, and Avanidhar Subrahmanyam. 2000. “Commonality in Liquidity.” Journal of Financial Economics 56 (1):3–28. https://doi.org/https://doi.org/10.1016/S0304-405X(99)00057-4.
Hasbrouck, Joel, and Gideon Saar. 2013. “Low-Latency Trading.” Journal of Financial Markets 16 (4):646–79. https://doi.org/https://doi.org/10.1016/j.finmar.2013.05.003.
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