Intraday Trading Invariants for Equity-Index Futures

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1 Intraday Trading Invariants for Equity-Index Futures Torben G. Andersen, Oleg Bondarenko, Albert S. Kyle and Anna Obizhaeva Fields Institute Toronto, Canada January 15 Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 1/9

2 Hypotheses on Trading Volatility Interactions Competing Ideas of How Information and Trades Induce Price Changes... And How Price Changes Convey News and Induce Trading One Extreme: All Information Incorporated via Trading Transactions or Trading Volume Drive Volatility Transaction Clock (Mandelbrot and Taylor, 1967; Jones, Kaul & Lipson, 1994; Ané & Geman, ) Volume Clock (Clark, 1973) Other Extreme: Information Flow Drives Market Activity Latent Factor Driving both Trading and Volatility Mixture of Distributions (Tauchen & Pitts, 1983; Andersen, 1996) Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance /9

3 Daily S&P 5 E-Mini Futures Market Activity Volume V Volatility σ Number of Trades N Trade Size Q Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 3/9

4 Hypotheses on Trading Volatility Interactions Focus typically on Observations at Daily Level Exception: Ané & Geman, ; Near Tick-by-Tick But Nobody has been Able to Confirm their Results We also Fail to Verify Hypothesis Use High-Frequency Data to Explore Interactions Include Market Microstructure Invariance in Analysis Empirical Support for Invariance via Diverse Market Phenomena Major Expansion in Realm of Features Covered by Invariance Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 4/9

5 Why High-Frequency Analysis Fact: Pronounced Intraday Market Activity Patterns News Incorporated into Prices quickly; Trading Fast Huge Systematic Variation over 4-Hour Trading Day Does any Basic Regularity Apply in this Setting? Macroeconomic Announcements particular Challenge Large Price Jump on Impact without (much) Trading Subsequent Price Discovery Process Sudden Market Turmoil: Crisis, Flash Crash Do Same or Different Regularities Apply in this Context? Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 5/9

6 Intraday Pattern for Market Activity Variables x Volume V Volatility σ Number of Trades N Trade Size Q Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 6/9

7 S&P 5 E-Mini Futures Market Sample: BBO Files from CME Group; Jan 4, 8 Nov, 11 Among World s Most Active Markets Price Discovery for Equities Time Stamped to Second; Sequenced in Actual Order Using Front Month Contract until Week before Expiration (most Liquid) Three Daily Regimes: Asia, Europe, North America Sunday Thursday 17:15 :; :-8:3; 8:3 15:15 Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 7/9

8 Our Variables D = 959 Trading Days; T = 1, 3 1-Minute Intervals per Day N dt = Number of Transactions per Minute; V dt = Volume (Number of Contracts Traded per Minute); Q dt = Average Trade Size (Contracts per Trade over Minute); P dt = Average Price (over Minute); σ dt = Volatility in Minute Annualized (Decimal Form); W dt = Market Speed (dollars at Risk per Minute) = P dt V dt σ dt We define variables for intraday interval t by averaging across all days: n t = 1 D D n dt, t = 1,..., T. d=1 and variables for trading day d by averaging across all intervals, n d = 1 T T n dt, d = 1,..., D. t=1 Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 8/9

9 Descriptive Statistics for S&P 5 E-mini Futures Regime 1 Regime Regime 3 All Volatility Volume # Trades Notional Value, $Mln Trade Size Market Depth Bid-Ask Spread Business Time Sample Averages per 1 min. Volatility is Annualized (in Decimal Form). Business Time is proportional to W /3, and it is Normalized to 1 in Regime 3 Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 9/9

10 Market Microstructure Invariance Theoretical Motivation Invariance based on Strategic Implementation of Trading Ideas or Bets Bets not Observable and Meta Orders Shredded into individual Orders Invariance Principle applies across Time and Assets: Dollar-Risk Transfer per Bet in Business Time is i.i.d. I = P Q B σ N 1/ B P is price, Q B is bet size, σ is volatility, and N B (Business Time) is number of bets. For empirical work, we write in in logs: logi = p + q B + 1 s 1 n B. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 1/9

11 Market Microstructure Invariance Generating Testable Hypotheses Define the Quantity Bet Activity or Market Activity W, W = P V σ Under simplifying Assumptions, W (essentially) Observable (w = logw = p + q B + n B ) Invariance Principle across Time and Assets now implies: n B 3 w and q B 1 3 w [p + 1 s] For Same (σ, P), Variation in Volume: /3 from N B, 1/3 from Q B. For Varying (σ, P), specific Power Relations are Implied Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 11/9

12 Market Microstructure Invariance Auxiliary Hypotheses invoked for Testable Hypotheses still Success Kyle and Obizhaeva (14) find invariance relationships in portfolio transition orders; Kyle, Obizhaeva, and Tuzun (1) find invariance relationships in print sizes in TAQ data; Kyle, Obizhaeva, Sinha, and Tuzun (14) find invariance relationships in number of news articles; Bae, Kyle, Lee, and Obizhaeva (14) find invariance relationships in Korean data. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 1/9

13 Invariance Inspired Predications Motivated by invariance, we stipulate a similar relation between intraday variables: I dt = P dt Q dt σ dt N 1/ dt This implies in logs: n dt = c + q dt + s dt + u dt. Or, in terms of log of trading activity w = logw = p + q B + n B : n j = c + 3 w j + u n j, q j = c w j 1 s j + u q j. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 13/9

14 Suggestive Test for Alternative Theories V and Q implicitly included within W ( = PV σ = PQNσ ). Ignoring P, Relation σ dt V dt implies s dt = c + n dt + q dt. Ignoring P, Relation σ dt N dt implies s dt = c + n dt. and and n j = c + 3 [ wj 3 q ] j + u n j. [Clark] n j = c + 3 [ w j q j ] + u n j. [Ané & Geman] n j = c + 3 [ w j ] + u n j. [Invariance] In terms of the nested specification: s j n j = c + β q j + u q j. where β = 1 (Clark), β = (Ané-Geman), or β = (invariance). Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 14/9

15 Suggestive Test for Alternative Theories This table reports on intraday OLS regressions of log N onto log W Q 3/ (Clark), log W Q (Ané & Geman), and log W (Invariance). All models predict β = /3. For each regression there are T = 1, 3 observations. Table : OLS Regression of log N onto scaled log W α β se(α) se(β) R Clark Ané & Geman Invariance Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 15/9

16 Suggestive Test for Alternative Theories logn vs logw/q 3/ logn vs logw/q logn vs logw Figure : OLS Regression Line (solid) and Model Predicted (dashed). Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 16/9

17 Trading Intensity and Trade Size Table : Indraday OLS Regression of log σ N onto log Q c β se(c) se(β) R This table reports the results of the intraday OLS regression, s t n t = c + β q t + u t. Clark, Ané & Geman and invariance predict β = 1, β =, and β =, respectively. The regression exploits T = 1, 3 observations. Invariance yields vastly Superior Fit to Intraday Activity Patterns Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 17/9

18 Trading Intensity and Trade Size logσ /N vs logq logσ /N vs logq Figure : The figures provide intraday scatter plots of log σ N t versus log Q t. Also shown are OLS Regression line (solid) and the predicted line according to invariance (dashed). The right panel is the same as the left panel, except it removes observations corresponding to 3 minutes around 1:, 3 minutes around : (start of the European regime), 3+3 minutes around 8:3 (start of Regime 3 and the 9: announcements), and 16 minutes at the end of trading. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 18/9

19 Intraday Invariance and Macro Announcements Overall Invariance yields vastly Superior Fit to Intraday Activity Patterns Extremes? Macro Announcements Involve Dramatic Spikes 7:3 CT: Employment, CPI, PPI, Retail Sales, Housing Starts,... 9: CT: Home Sales, Confidence Survey, Factory Orders... Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 19/9

20 Trading Invariance for 7:3 Macro Announcements x Volume V.5 Volatility σ Number of Trades N Trade Size Q One-Minute Averages for 7:3 Announcement Days. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance /9

21 Trading Invariance for 7:3 Macro Announcements 9 logn vs logw, 7:3, All Days 9 logn vs logw, 7:3, Announcement Days log N t vs. ln W t for 3 Minutes Before 7:3 (Dots), After 7:3 (Crosses). Left: All Days; Right: 7:3 Announcements. Solid Line is prior OLS Fit. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 1/9

22 Trading Invariance for 9: Macro Announcements x Volume V 1.4 Volatility σ Number of Trades N Trade Size Q One-Minute Averages for 9: Announcement Days. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance /9

23 Trading Invariance for 9: Macro Announcements 9 logn vs logw, 9:, All Days 9 logn vs logw, 9:, Announcement Days log N t vs. ln W t for 3 Minutes Before 9: (Dots), After 9: (Crosses). Left: All Days; Right: 9: Announcements. Solid Line is prior OLS Fit. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 3/9

24 Subsample Analysis Table : OLS Regression: Intraday Patterns For Each Year. c β se(c) se(β) R All This table reports the results of OLS regressions, n t = c + β w t + u t. Coefficients, standard errors, and R statistics are estimated both separately for each calendar year and then for the whole sample. The last year ends November 4, 11. Each regression exploits T = 1, 3 observations. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 4/9

25 High Frequency Invariance Figure : A scatter plot of n db versus w db with data aggregated across bins. The aggregation bins for the three regimes are chosen to be 15, 6, and 5 minutes. As before, the three regimes are represented by distinct colors. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 5/9

26 High Frequency Invariance Table : OLS Regression: Binned Data c β se(c) se(β) R All This table reports the results of OLS regressions across bins, n db = c + β w db + u db. The coefficients, standard errors, and R statistics are estimated separately for each calendar year and for the whole sample. The last year is incomplete and ends on November 4, 11. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 6/9

27 Suggestive Invariance Check 8 logn vs logw, Daily averages Figure : Scatter plot of log N onto log W. Each day provides 3 observations, one for each regimes. The slope is.687. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 7/9

28 Trading Invariance during the Flash Crash 1 Price P x 1 4 Volume V Volatility σ 4 3 Standardized logi The figure shows price P, volume V, volatility σ, and standardized log invariant log I on May 6, 1. Standardized log invariant is computed at 4-minute frequency and is expressed in standard deviations. The solid vertical lines indicate the timing of the Flash Crash. Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 8/9

29 Conclusions Intraday Trading Activity Patterns Intimately Related Traditional Theories: Transactions or Volume Govern Volatility Invariance (Kyle & Obizhaeva) Motivates Alternative Intraday Relation Critically, Trade Size Drops in specific Proportion with Volatility For E-Mini, Tendency Observed by Andersen & Bondarenko RF, VPIN Qualitative Prediction verified for Diurnal Pattern Qualitative Prediction verified for Daily Regimes (Time Series) Theoretical Justification for Invariance in this Context Loom Large How will Findings Generalize across Market Structures? Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 9/9

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