Intraday Trading Invariants for Equity-Index Futures

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1 for Equity-Index Futures Kellogg School, NBER & CREATES Joint with Oleg Bondarenko, Pete Kyle and Anna Obizhaeva Market Microstructure: Confronting many Viewpoints Paris; December, 4

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 Volume Clock (Clark, 973) Transaction Clock (Jones, Kaul & Lipson, 994; Ané & Geman, ) Other Extreme: Information Flow Drives Market Activity Latent Factor Driving both Trading and Volatility Mixture of Distributions (Tauchen & Pitts, 983; Andersen, 996)

3 Daily S&P 5 E-Mini Futures Market Activity Volume V Volatility σ Number of Trades N Trade Size Q

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

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?

6 Intraday Pattern for Market Activity Variables x Volume V Volatility σ Number of Trades N Trade Size Q

7 S&P 5 E-Mini Futures Market Sample: BBO Files from CME Group; Jan 4, 8 Nov, 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 7:5 :; :-8:3; 8:3 5:5 D = 959 Trading Days; T =, 3 -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

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

9 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 dt = P dt Q dt σ dt γ / dt Q = Orders from Bets, σ and γ (Business Time) are Latent Variables. Auxiliary Hypotheses invoked for Testable Hypotheses still Success

10 Market Microstructure Invariance Generating Testable Hypotheses Define the Quantity Bet Activity or Market Activity W, W dt = P dt V dt σ dt Under simplifying Assumptions, W (essentially) Observable Invariance Principle across Time and Assets now implies: γ dt = c W /3 dt and Q dt = c W /3 dt Interpretation: For Same (σ, P), Variation in Volume: /3 from γ, /3 from Q. For Varying (σ, P), specific Power Relations are Implied

11 Market Microstructure Invariance Auxiliary Hypothesis in Our Setting What if Invariance Principles impact all Submission of Orders? Large Orders still Shredded into individual Orders Invariance Principle across Time and Assets now implies: Dollar-Risk Transfer in Business Time is i.i.d. I dt = P dt Q dt σ dt N / dt Q is Trade Size, σ and N are Expected Values of Market Participants. Proxy N by Observed Transactions, Estimate σ by RV using HF Returns

12 Market Microstructure Invariance Invariance Inspired Hypothesis: log (N dt ) = c + β log (W dt ) where Invariance Predicts a Slope of β = /3. Relies on Expectations Approximated by Realizations or Noisy Estimators Aggregate Relationship to Diversify Measurement Errors Intraday Patterns provide Pronounced Variation and Challenging Test n t = D [ D log (N dt ) = c + β D d= ] D log (W dt ) + ν t d= for t =,..., T =, 3 Intraday Averages, Covering 3 Regimes. Averaging for Fixed Time-of-Day Yields good Diversification.

13 Suggestive Invariance Check 8 logn vs logw, Three Regimes R (blue), R (green), R3 (red). Red Cross: Last 6 min of R3. Solid Line: ln N t = ln W t. Dashed: Same Slope, Fit to Red Crosses.

14 Suggestive Test for Alternative Theories V and Q implicitly included within W ( = PVσ = PQNσ ). Ignoring P, Relations N σ and V σ, may be Restated, and ( ) logn = c + β log W/ Q 3 logn = c + β log (W/ Q) [Clark] [Ané & Geman] where we also have β = /3 according to each Theory. Table : OLS Regression of log N onto scaled log W α β se(α) se(β) R Clark Ané & Geman Invariance

15 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).

16 Formal Tests of Alternative Theories Regressions above (at best) Informal; N on both Sides R Inflated Alternative Representations Clark, Ané & Geman and Invariance: σ V, σ N, σ N/Q. Aggregating -Min Intervals over Days, we should have β =, s t = D s t = D s t = D D log ( σdt) = c + β (nt + q t ) + ν t d= D log ( σdt) = c + β nt + ν t d= D log ( σdt) = c + β (nt q t ) + ν t d=

17 Formal Tests of Alternative Theories logσ vs lognq logσ vs logv logσ vs logn/q Figure : OLS Regression Line (solid) and Model Predicted (dashed).

18 Formal Tests of Alternative Theories Table : OLS Regressions for log σ α β se(α) se(β) R Clark Ané & Geman Invariance 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...

19 Trading Invariance for 7:3 Macro Announcements x 4 3 Volume V.5 Volatility σ Number of Trades N Trade Size Q One-Minute Averages for 7:3 Announcement Days.

20 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.

21 Trading Invariance for 9: Macro Announcements x Volume V.4 Volatility σ Number of Trades N Trade Size Q One-Minute Averages for 9: Announcement Days.

22 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.

23 .3.3 Trading. Invariance during the Flash. Crash Price Normalized Volatility VIX Normalized Volume Figure 7: May 6,. The solid vertical lines indicate the timing of the flash crash. In panels with multiple plots, the order of Market the plotsactivity is blue (first), Variables green (second), on and May red 6, (third).. The normalized volatility is the ratio of the standard deviation of one-minute price changes for a (centered) -minute window over unconditional volatility σ P. The normalized volume is the trading volume per one-minute bar divided by

24 Trading Invariance during the Flash Crash 4 Standardized logi on Flash Crash 4 Standardized logi on Previous Day log I on May 6,.

25 Formal Tests Aggregation within Days Existing Tests Employ Daily Data. Can we Mimic this? Aggregation within Days instead, but only Regime-Wise? In Fact, Theories have Distinctly Different Implications! Predictions: β = vs. β = vs. β = s di n di = T i T i log ( σdt /N dt) = c + β qdi + ν di t= where di Indicates Regime i on Day d. Aggregation on given Day Supplements Ones for given Time-a-Day

26 Formal Tests of Alternative Theories 3 logσ /N vs Q, Regime averages 5 logσ /N vs Q, Daily averages One Observation per Regime and Day (Left), One Observation per Day (Right). The Slopes are -.98 and -.89.

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.

28 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?

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