Price Impact of Aggressive Liquidity Provision

Price Impact of Aggressive Liquidity Provision R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng February 15, 2015 R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 1 / 32

Overview 1 Introduction and Research Question 2 Data 3 Bursts 4 Basic Market Characteristics During Bursts 5 Price Impact 6 Breakdown of Informational Dichotomy 7 Asymmetric Adverse Selection 8 Conclusion R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 2 / 32

What Does A Market Maker Do? The introduction of algorithmic trading has brought about dramatic change in the activity scope of a market maker. The traditional definition: a market maker provides liquidity and impounds information into quotes. For the market maker, order flow is information flow. The definition implies that the market maker plays a passive role in the price formation process and faces adverse selection. In investigating the impact of algorithmic trading on market quality, by and large the market microstructure literature has retained this definition. However, data reveals market maker behavior that cannot be attributed to passive liquidity provision or adverse selection. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 3 / 32

Role of Market Maker: View from the Market The role of the Market Maker on TSX is to augment liquidity, while maintaining the primacy of an order-driven continuous auction market based on price-time priority. TSX s Market Maker system maximizes market efficiency and removes the interfering influence of a traditional specialist. In the TSX environment, a Market Maker manages market liquidity through a passive role. Market Makers are visible only when necessary to provide a positive influence when natural market forces cannot provide sufficient liquidity. EBS Prime enhances liquidity and trading opportunities for all, while maintaining the valued relationship between banks and their customers. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 4 / 32

Market Activity Exhibits Bursts The quotation arrival process directly reflects market maker activity. Number of quotes for Alcoa between 10:31:15 and 10:32:15 on October 10, 2011. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 5 / 32

First Observations The spikes bursts in quotes in the rate of incoming quotes in fact occurs with regularity throughout the trading day, with average inter-arrival time of approximately 40 seconds. The average duration of bursts is approximately 1.1 seconds. Bursts is therefore a fundamentally high frequency phenomenon. At first glance, it cannot be attributed to the role of market maker as liquidity provider nor information aggregator. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 6 / 32

Research Questions We analyze the periods during which the arrival intensity of quotes is outlier relative to what would be normal in a given interval. We call such periods bursts in quotation activity. We investigate the functioning of markets and price formation during these bursts. 1 What is the impact of bursts in quotation activity on market quality? 2 What effect do bursts have on the price impact of trades? 3 Is adverse selection higher during bursts in quotation activity? R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 7 / 32

Main Findings On market characteristics during bursts: Quoted spread, effective spread and volatility increase. Size of incoming orders decreases. On informational relationship between maker and taker during bursts: The informational dichotomy breaks down. Market maker no longer passively impound information from order flow into quotes. Ex ante adverse selection (price impact) rises significantly, on average from 0.002% to 0.011%, per trade. Ex post adverse selection also elevates. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 8 / 32

Main Findings cont d Adverse selection should reduce when market maker s information is correlated with that of market taker why the inconsistency? Adverse selection is in fact asymmetric, depending on whether the market maker occupies the same side of the LOB as the burst. On the burst side, there is negative price impact. On the opposite-of-burst side, the severity of adverse selection elevates significantly. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 9 / 32

Data We use the TAQ dataset for the 15 most liquid U.S. equities. October 10, 2011 until February 7, 2012. Number of quotes represents changes in the National Best Bid and Offer (NBBO) either in price or size. Data cleaning procedure as described in Aït-Sahalia and Jacod (2014). Stock Company Name # of Trades # of Quotes Price Trade in Lots Spread in AA Alcoa 53,207 1,436,262 9.87 23.18 1.00 BAC Bank of America 136,476 1,767,462 6.25 55.55 1.00 GE General Electric 81,607 2,008,788 17.21 21.43 1.00 IBM International Business Machines 17,838 754,269 186.05 20.00 3.04 JNJ Johnson & Johnson 29,928 1,487,517 64.48 12.50 1.63 JPM JPMorgan Chase 90,824 3,501,468 33.79 10.10 1.35 MRK Merck & Co 39,242 1,707,993 35.99 12.50 1.13 PFE Pfizer 68,399 1,802,107 20.44 18.33 1.00 PG Procter & Gamble 27,544 1,404,016 64.62 16.33 1.71 PM Philip Morris International 19,413 952,338 73.60 18.18 2.22 T AT&T 51,391 1,699,231 29.32 15.16 1.01 VZ Verizon Communications 34,330 1,444,768 37.82 14.29 1.11 WFC Wells Fargo 82,357 3,000,480 27.04 10.00 1.20 WMT Wal-Mart Stores 30,718 1,409,885 58.49 14.29 1.33 XOM Exxon Mobil 57,168 4,734,158 81.38 3.59 1.90 This table reports daily medians. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 10 / 32

Burst Detection one man s noise is another man s signal We detect bursts based on the following market activity variables: Number of trades Number of quotes Number of quotes on different sides of the book These quantities are approximately exponentially distributed (see also Zhu and Shasha 2003, 2005. Vlachos et al 2004, 2008.) 1 For each 15 min. interval, we estimate the mean of the distribution ˆµ. 2 We record a burst for each interval (100ms, 1s, 5s), where the variable exceeds a threshold x = ˆµ log(p), where 3 P is the tail probability (e.g. P = 0.1%). Our definition of bursts coincides with that of unified outliers in Knorr (1997). R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 11 / 32

Example: Alcoa on October 10, 2011, 1 Second Frequency Quotes Trades R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 12 / 32

Behavior of Market During Bursts in Quotes We compare the following measures during burst and non-burst periods: Quoted spread. Effective spread. Return volatility. Order size. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 13 / 32

Market Behavior Around Bursts: Quoted Spread 100ms Interval 1s Interval 5s Interval The black line represents the average quoted spread across all 100ms (1s, 5s) intervals before, during and after bursts, as well as across all stocks in our sample. The initial value was normalized to 100. The shaded area represents one standard deviation from the mean. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 14 / 32

Market Behavior Around Bursts: Effective Spread 100ms Interval 1s Interval 5s Interval The black line represents the average effective spread across all 100ms (1s, 5s) intervals before, during and after bursts, as well as across all stocks in our sample. The initial value was normalized to 100. The shaded area represents one standard deviation from the mean. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 15 / 32

Market Behavior Around Bursts: Return Volatility 100ms Interval 1s Interval 5s Interval The black line represents the average volatility across all 100ms (1s, 5s) intervals before, during and after bursts, as well as across all stocks in our sample. The initial value was normalized to 100. The shaded area represents one standard deviation from the mean. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 16 / 32

Market Behavior Around Bursts: Order Size 100ms Interval 1s Interval 5s Interval The black line represents the average order size across all 100ms (1s, 5s) intervals before, during and after bursts, as well as across all stocks in our sample. The initial value was normalized to 100. The shaded area represents one standard deviation from the mean. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 17 / 32

Estimating Permanent and Temporary Price Impact We use the price impact methodology of Hasbrouck (1991). Let r t denote the change in the market maker s estimate of the fundamental value. q t be the signed order flow (-1 if more trades at bid, +1 if more trades at ask and 0 if equally many or no trades.) The VAR system is r t = α 1r t 1 + α 2r t 2 + + β 0 q t + β 1q t 1 + + ε }{{} t, (1) Market maker s public information q t = γ 1r t 1 + γ 2r t 2 + + δ 1q t 1 + δ 2q t 2 + + ν }{{} t. (2) Market taker s private information R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 18 / 32

Comments on the VAR model The lags serve as controls for microstructure frictions: e.g. inventory management, price discreteness, lagged adjustment to information. Inventory-control effects may cause past quote updates to influence the market maker s current quote update. Delayed adjustment to information and anticipation of order-splitting means order flow may have lagged effects on quote updates. Order flow {q t } may exhibit autocorrelation due to order splitting. It is also possible that a market taker who anticipates market maker s inventory-neutral tendency may adjust his order flow according to past quote updates. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 19 / 32

Comments on the VAR model cont d Embedded in the exogeneity assumption of the VAR model of {r t, q t } is the traditional definition of a market maker: ε t and ν t are orthogonal. Our analysis will suggest a modification of this model that departs from this definition and captures the informational relationship between market maker and taker during bursts. We first carry out a model selection exercise for the appropriate number of lags. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 20 / 32

VAR Lag Selection We select the number of lags based on Akaike and Bayesian information criteria. We use 10 lags throughout. Our results are robust for 5 to 30 lags. This figure represents values of Bayesian information criterion for the returns (left) and order flow equations (right) for one trading day of Alcoa. We obtained similar results for other stocks and days and by using Akaike information criterion as well. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 21 / 32

Price Impact is Higher During Bursts We add dummy variables B Q t and B T t to identify periods with bursts in quotes and trades. r t = 10 α i r t i + 10 i=1 i=1 β i q t i + β 0q t + φ Q B Q t q t + φ T B T t q t + φ Q&T B Q t B T t q t + ε t. α 1 β 0 φ Q φ T φ Q&T R 2 -Adj R 2 -Adj with bursts w/o bursts AA 0.925 0.002 0.046 0.007-0.012 0.585 0.489 BAC 0.988 0.001 0.058 0.007-0.009 0.593 0.510 GE 0.917 0.001 0.028 0.007-0.007 0.567 0.484 IBM 0.247 0.003 0.006 0.005-0.001 0.416 0.416 JNJ 0.445 0.002 0.004 0.004-0.001 0.411 0.397 JPM 0.875 0.006 0.009 0.011-0.002 0.502 0.482 MRK 0.851 0.002 0.012 0.007-0.004 0.518 0.465 PFE 0.827 0.000 0.023 0.005-0.001 0.541 0.461 PG 0.619 0.002 0.005 0.005-0.001 0.403 0.381 PM 0.336 0.002 0.004 0.006 0.000 0.407 0.407 T 0.742 0.001 0.015 0.006-0.006 0.484 0.430 VZ 0.846 0.001 0.009 0.007-0.003 0.505 0.437 WFC 0.922 0.005 0.013 0.013-0.008 0.551 0.509 WMT 0.705 0.002 0.007 0.005-0.002 0.462 0.430 XOM 0.463 0.002 0.004 0.006 0.002 0.459 0.441 Median coeff 0.827 0.002 0.009 0.006-0.002 0.502 0.441 Median p-value 0.000 0.000 0.000 0.000 0.125 Median daily # of events 419.3 706.1 318.0 % of significant firm-days at 5 % 99.67% 93.00% 81.67% 91.67% 30.00% R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 22 / 32

Breakdown of Informational Dichotomy Recall the price and order flow equations: r t = α 1 r t 1 + α 2 r t 2 + + β 0 q t + β 1 q t 1 + + ε }{{} t. Market maker s public information q t = γ 1 r t 1 + γ 2 r t 2 + + δ 1 q t 1 + δ 2 q t 2 + + ν }{{} t. Market taker s private information For the traditional market maker, ε t and ν t are uncorrelated. If the market maker can predict the order flow, ε t and ν t will be positively correlated. Our hypothesis is that {ε t, ν t } are correlated during, and only during, bursts in quotes. We test the correlation between ˆε t and ˆν t. The conventional definition of market maker breaks down. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 23 / 32

Testing for Breakdown of Informational Dichotomy For non-burst periods, one needs to adjust the residuals ˆε t for the effect of bursts in trades. We write the error term ε t, market maker s information as ε t = φ T i B T t q t + φ Q&T i B Q t B T t q t }{{} Information impounded into prices during bursts in trades + ε # t }{{} + ε t }{{} Market maker s information during burst in quotes only Market maker s information during non-burst periods In addition to correlations during burst, {ˆε t, ˆν t}, and non-burst periods, {ˆε t, ˆν t}, we estimate the linear specification ˆν t = η Q B Q t ˆε t + η Q (1 B Q t )ˆε t + ν t. ˆε t ˆε 1 ˆε 2 ˆε 3 ˆε 4 ˆε 5 ˆε 6 ˆε 7 ˆε 8 B T t 1 1 1 B Q t 1 1 1 ˆν t ˆν 1 ˆν 2 ˆν 3 ˆν 4 ˆν 5 ˆν 6 ˆν 7 ˆν 8 R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 24 / 32

Information Correlation During Bursts in Quotes ρ Q ρ Q η Q η Q ρ All AA 0.487-0.002 7.779-0.130-0.002 BAC 0.431 0.007 4.230 0.508 0.005 GE 0.514-0.002 12.735-0.237-0.002 IBM 0.193 0.000 7.789 0.000 0.000 JNJ 0.323 0.000 20.476-0.021 0.000 JPM 0.413 0.000 13.601-0.037 0.000 MRK 0.516-0.002 22.172-0.247-0.002 PFE 0.478 0.000 13.568-0.087-0.001 PG 0.339 0.000 22.921-0.049 0.000 PM 0.022 0.000 0.526-0.001 0.000 T 0.478-0.001 21.501-0.202-0.001 VZ 0.417-0.003 21.597-0.332-0.002 WFC 0.493-0.001 15.465-0.060 0.000 WMT 0.410 0.000 26.169-0.017 0.000 XOM 0.206 0.000 15.633-0.046 0.000 Median coeff 0.417 0.000 15.465-0.049 0.000 Median p-value 0.000 0.862 0.000 0.871 0.884 Median daily # of events 101.3 20,789 101.3 20,789 20,789 % of significant firm-days at 5 % 100% 0% 100% 0% 0% Market maker in fact predicts price movement/order flow during bursts in quotes. Basic market measures show no sign that a burst is anticipated by the market. Therefore bursts are market maker-initiated informational events. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 25 / 32

Adverse Selection and the Side Where the Burst Happens We investigate the behavior of the adverse selection proxy (Bessembinder (2003)) AD t = ES t RS t, where, letting P t denote the transaction price and M t the mid-quote, RS t = 2q t(p t M t+s) is the realized spread (profit) of the market maker, and ES t = 2q t(p t M t). is the effective spread measuring the price of immediacy and the adverse selection component. AD t is the magnitude of the ex post loss due to adverse price movement plus effective spread. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 26 / 32

Asymmetric Adverse Selection cont d We will show that, concurrent with bursts, advese selection for opposite sides of LOB undergoes abrupt shifts in severity in opposite directions. This explains the apparent contradiction in price impact and informational correlation. Price impact is computed based on quotes that were actually executed against those on the opposite side of bursts, therefore has an upward bias. Information correlation reflects the information of market makers who initiate bursts. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 27 / 32

Asymmetric Adverse Selection cont d Burst at Ask Burst at Bid Adverse selection Realized spread Effective spread R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 28 / 32

Asymmetric Adverse Selection cont d Market makers on the opposite side of the burst charge higher cost of immediacy for order flow trading in the direction of the price impact, thus partially compensating for the negative realized spread. Despite this partial compensation, they suffer more severe adverse selection. While bursts lasts 1.1 seconds on average, the price impact it exerts significant price impact at 30 second lag. The asymmetry shown above suggests we adapt the VAR model to consider price impact for the two sides of LOB separately. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 29 / 32

MMs Burst in the Direction of the Price Impact To the basic specification we add B Q,same t and B Q,opp t the order flow arrives or on the opposite side, respectively; representing periods when a burst occurs on the side of the book where r t = 10 i=1 α i r t i + 10 i=1 β i q t i + β 0q t + φ Q,same B Q,same t q t + φ Q,opp B Q,opp t q t + φ T B T t q t + ε t. α 1 β 0 φ Q,same φ Q,opp φ T R 2 -Adj R 2 -Adj with bursts w/o bursts AA 0.929 0.002-0.030 0.041 0.031 0.545 0.489 BAC 0.988 0.001-0.024 0.040 0.043 0.558 0.510 GE 0.913 0.001-0.025 0.030 0.018 0.534 0.484 IBM 0.247 0.003 0.003 0.007 0.007 0.416 0.416 JNJ 0.445 0.002-0.006 0.008 0.005 0.413 0.397 JPM 0.875 0.006-0.008 0.010 0.013 0.504 0.482 MRK 0.848 0.002-0.014 0.011 0.009 0.507 0.465 PFE 0.826 0.001-0.019 0.024 0.017 0.519 0.461 PG 0.619 0.002-0.003 0.005 0.006 0.397 0.381 PM 0.336 0.002 0.000 0.001 0.006 0.408 0.407 T 0.742 0.001-0.013 0.016 0.011 0.472 0.430 VZ 0.845 0.001-0.010 0.010 0.009 0.486 0.437 WFC 0.920 0.005-0.013 0.016 0.014 0.547 0.509 WMT 0.704 0.002-0.008 0.009 0.006 0.455 0.430 XOM 0.446 0.002 0.002 0.002 0.006 0.455 0.441 Median coeff 0.826 0.002-0.010 0.010 0.009 0.486 0.441 Median p-value 0.000 0.000 0.002 0.000 0.000 % of significant firm-days at 5 % 99.0% 93.33% 67.33% 82.67% 96.0% Median daily number of events 24.8 60.7 318 R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 30 / 32

Conclusion We have shown that during bursts in quotes: 1 By extending the model of Hasbrouck (1991), we find that the price impact rises markedly from 0.002% to 0.011% per trade. It is higher than during bursts in trades. 2 Market makers do not passively update quotes based on information inferred from order flow. 3 Limit orders on the opposite side of the burst suffer adverse selection. 4 Price movement during bursts is likely not part of the normal price formation process. 5 Whether it is sufficiently disruptive to warrant concern is a regulatory question interest, given recent attempts by exchanges to curtail high frequency spamming. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 31 / 32

Conclusion We have shown that during bursts in quotes: 1 By extending the model of Hasbrouck (1991), we find that the price impact rises markedly from 0.002% to 0.011% per trade. It is higher than during bursts in trades. 2 Market makers do not passively update quotes based on information inferred from order flow. 3 Limit orders on the opposite side of the burst suffer adverse selection. 4 Price movement during bursts is likely not part of the normal price formation process. 5 Whether it is sufficiently disruptive to warrant concern is a regulatory question interest, given recent attempts by exchanges to curtail high frequency spamming. 6 CFTC Too Broke to Properly Police Flash Traders, Massad Says. Traders Magazine article title, February 12, 2016. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 31 / 32

Outlook Model extensions: 1 Change to business clock instead of 1s intervals. 2 Vary the tail probability for computing threshold to see if there is non-linearity in price impact. Obtain data to: 1 Investigate heterogeneity in the cross-section of firms. 2 Distinguish bursts around news announcements from others. R. Gençay, S. Mahmoodzadeh, J. Rojček & M. Tseng Price Impact of Aggressive Liquidity Provision 32 / 32