Intraday Trading Invariants for Equity-Index Futures Torben G. - - PowerPoint PPT Presentation

Intraday Trading Invariants for Equity-Index Futures

Torben G. Andersen, Oleg Bondarenko, Albert S. Kyle and Anna Obizhaeva

Fields Institute Toronto, Canada January 2015

Andersen, Bondarenko, Kyle, and Obizhaeva Intraday Invariance 1/29

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; An´ e & Geman, 2000) 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)

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Daily S&P 500 E-Mini Futures Market Activity

2008 2009 2010 2011 2012 1000 2000 3000 4000 5000 Volume V 2008 2009 2010 2011 2012 100 200 300 400 500 Number of Trades N 2008 2009 2010 2011 2012 0.2 0.4 0.6 0.8 1 1.2 Volatility σ 2008 2009 2010 2011 2012 5 10 15 Trade Size Q

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Hypotheses on Trading – Volatility Interactions

Focus typically on Observations at Daily Level Exception: An´ e & Geman, 2000; 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

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Why High-Frequency Analysis

Fact: Pronounced Intraday Market Activity Patterns News Incorporated into Prices quickly; Trading Fast Huge Systematic Variation over 24-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?

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Intraday Pattern for Market Activity Variables

−5 5 10 15 0.5 1 1.5 2 2.5 3 x 10

4

Volume V −5 5 10 15 200 400 600 800 1000 1200 Number of Trades N −5 5 10 15 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Volatility σ −5 5 10 15 5 10 15 20 25 Trade Size Q

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S&P 500 E-Mini Futures Market

Sample: BBO Files from CME Group; Jan 4, 2008 – Nov 2, 2011 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 – 2:00; 2:00-8:30; 8:30 – 15:15

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Our Variables

D = 959 Trading Days; T = 1, 320 1-Minute Intervals per Day Ndt = Number of Transactions per Minute; Vdt = Volume (Number of Contracts Traded per Minute); Qdt = Average Trade Size (Contracts per Trade over Minute); Pdt = Average Price (over Minute); σdt = Volatility in Minute Annualized (Decimal Form); Wdt = Market Speed (dollars at Risk per Minute) = Pdt Vdt σdt We define variables for intraday interval t by averaging across all days: nt = 1 D ·

D

• d=1

ndt , t = 1, ... , T. and variables for trading day d by averaging across all intervals, nd = 1 T ·

T

• t=1

ndt , d = 1, ... , D .

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Descriptive Statistics for S&P 500 E-mini Futures

Regime 1 Regime 2 Regime 3 All Volatility 0.16 0.25 0.40 0.26 Volume 92.01 600.73 4725.56 1663.97 # Trades 13.87 66.74 360.04 135.70 Notional Value, $Mln 5.25 34.37 265.84 94.02 Trade Size 5.82 8.41 13.30 8.95 Market Depth 54.06 265.12 984.07 401.76 Bid-Ask Spread 26.54 25.69 25.13 25.86 Business Time 26.13 5.43 1.00 2.65

Sample Averages per 1 min. Volatility is Annualized (in Decimal Form). Business Time is proportional to W −2/3, and it is Normalized to 1 in Regime 3

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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 · QB · σ · N−1/2

B

P is price, QB is bet size, σ is volatility, and NB (Business Time) is number of bets. For empirical work, we write in in logs: logI = p + qB + 1

2s − 1 2nB.

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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 + qB + nB) Invariance Principle across Time and Assets now implies: nB ∼ 2

3w

and qB ∼ 1

3w − [p + 1 2s]

For Same (σ, P), Variation in Volume: 2/3 from NB, 1/3 from QB. For Varying (σ, P), specific Power Relations are Implied

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Market Microstructure Invariance

Auxiliary Hypotheses invoked for Testable Hypotheses – still Success

◮ Kyle and Obizhaeva (2014) find invariance relationships in portfolio

transition orders;

◮ Kyle, Obizhaeva, and Tuzun (2012) find invariance relationships in

print sizes in TAQ data;

◮ Kyle, Obizhaeva, Sinha, and Tuzun (2014) find invariance

relationships in number of news articles;

◮ Bae, Kyle, Lee, and Obizhaeva (2014) find invariance relationships

in Korean data.

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Invariance Inspired Predications

Motivated by invariance, we stipulate a similar relation between intraday variables: Idt = Pdt · Qdt · σdt · N−1/2

dt

This implies in logs: ndt = c + 2qdt + sdt + udt. Or, in terms of log of trading activity w = logW = p + qB + nB: nj = c + 2 3 · wj + un

j ,

qj = c + 1 3 wj − 1 2 sj + uq

j .

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Suggestive Test for Alternative Theories

V and Q implicitly included within W ( = PV σ = PQNσ ). Ignoring P, Relation σ2

dt ∼ Vdt implies sdt = c + ndt + qdt .

Ignoring P, Relation σ2

dt ∼ Ndt implies sdt = c + ndt .

nj = c +

2 3

• wj −

3 2 qj

• + un

j .

[Clark] and nj = c +

2 3 [ wj − qj ] + un j .

[An´ e & Geman] and nj = c +

2 3 [ wj ] + un j .

[Invariance] In terms of the nested specification: sj − nj = c + β · qj + uq

j .

where β = 1 (Clark), β = 0 (An´ e-Geman), or β = −2 (invariance).

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Suggestive Test for Alternative Theories

This table reports on intraday OLS regressions of log N onto log

W Q3/2

(Clark), log W

Q (An´

e & Geman), and log W (Invariance). All models predict β = 2/3. For each regression there are T = 1, 320 observations. Table : OLS Regression of log N onto scaled log W

α β se(α) se(β) ¯ R2 Clark 2.4119 0.9757 0.0031 0.0016 0.9965 An´ e & Geman 1.7538 0.8490 0.0018 0.0006 0.9993 Invariance 0.8579 0.6708 0.0033 0.0007 0.9986

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Suggestive Test for Alternative Theories

−1 1 2 3 4 5 6 2 3 4 5 6 7 logN vs logW/Q3/2 1 2 3 4 5 6 7 2 3 4 5 6 7 logN vs logW/Q 2 4 6 8 10 2 3 4 5 6 7 logN vs logW

Figure : OLS Regression Line (solid) and Model Predicted (dashed).

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Trading Intensity and Trade Size

Table : Indraday OLS Regression of log σ2

N onto log Q

c β se(c) se(β) ¯ R2

• 2.6275
• 2.0002

0.0199 0.0099 0.9687

This table reports the results of the intraday OLS regression, st − nt = c + β · qt + ut. Clark, An´ e & Geman and invariance predict β = 1, β = 0, and β = −2, respectively. The regression exploits T = 1, 320 observations. Invariance yields vastly Superior Fit to Intraday Activity Patterns

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Trading Intensity and Trade Size

1 1.5 2 2.5 3 3.5 −9 −8 −7 −6 −5 logσ2/N vs logQ 1 1.5 2 2.5 3 3.5 −9 −8 −7 −6 −5 logσ2/N vs logQ

Figure : The figures provide intraday scatter plots of log σ2

Nt versus log Qt. 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 1:00, 3 minutes around 2:00 (start of the European regime), 3+30 minutes around 8:30 (start of Regime 3 and the 9:00 announcements), and 16 minutes at the end of trading.

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Intraday Invariance and Macro Announcements

Overall Invariance yields vastly Superior Fit to Intraday Activity Patterns Extremes? Macro Announcements Involve Dramatic Spikes 7:30 CT: Employment, CPI, PPI, Retail Sales, Housing Starts, . . . 9:00 CT: Home Sales, Confidence Survey, Factory Orders . . .

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Trading Invariance for 7:30 Macro Announcements

−5 5 10 15 0.5 1 1.5 2 2.5 3 x 10

4

Volume V −5 5 10 15 0.5 1 1.5 2 2.5 Volatility σ −5 5 10 15 500 1000 1500 2000 2500 Number of Trades N −5 5 10 15 5 10 15 20 25 Trade Size Q

One-Minute Averages for 7:30 Announcement Days.

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Trading Invariance for 7:30 Macro Announcements

8 10 12 14 16 18 1 2 3 4 5 6 7 8 9 logN vs logW, 7:30, All Days 8 10 12 14 16 18 1 2 3 4 5 6 7 8 9 logN vs logW, 7:30, Announcement Days

log Nt vs. ln Wt for 3 Minutes Before 7:30 (Dots), After 7:30 (Crosses). Left: All Days; Right: 7:30 Announcements. Solid Line is prior OLS Fit.

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Trading Invariance for 9:00 Macro Announcements

−5 5 10 15 0.5 1 1.5 2 2.5 3 3.5 x 10

4

Volume V −5 5 10 15 0.2 0.4 0.6 0.8 1 1.2 1.4 Volatility σ −5 5 10 15 500 1000 1500 2000 2500 3000 Number of Trades N −5 5 10 15 5 10 15 20 25 Trade Size Q

One-Minute Averages for 9:00 Announcement Days.

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Trading Invariance for 9:00 Macro Announcements

8 10 12 14 16 18 1 2 3 4 5 6 7 8 9 logN vs logW, 9:00, All Days 8 10 12 14 16 18 1 2 3 4 5 6 7 8 9 logN vs logW, 9:00, Announcement Days

log Nt vs. ln Wt for 3 Minutes Before 9:00 (Dots), After 9:00 (Crosses). Left: All Days; Right: 9:00 Announcements. Solid Line is prior OLS Fit.

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Subsample Analysis

Table : OLS Regression: Intraday Patterns For Each Year.

c β se(c) se(β) ¯ R2 2008 0.9110 0.6621 0.0037 0.0007 0.9983 2009 0.7674 0.6798 0.0036 0.0007 0.9984 2010 0.7901 0.6866 0.0046 0.0010 0.9972 2011 0.9769 0.6531 0.0051 0.0011 0.9965 All 0.8579 0.6708 0.0033 0.0007 0.9986

This table reports the results of OLS regressions, nt = c + β · wt + ut. Coefficients, standard errors, and ¯ R2 statistics are estimated both separately for each calendar year and then for the whole sample. The last year ends November 4, 2011. Each regression exploits T = 1, 320

• bservations.

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High Frequency Invariance

Figure : A scatter plot of ndb versus wdb with data aggregated across

• bins. The aggregation bins for the three regimes are chosen to be 105,

26, and 5 minutes. As before, the three regimes are represented by distinct colors.

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High Frequency Invariance

Table : OLS Regression: Binned Data

c β se(c) se(β) ¯ R2 2008 0.8838 0.6564 0.0039 0.0006 0.9825 2009 0.7398 0.6739 0.0045 0.0007 0.9765 2010 0.7279 0.6846 0.0051 0.0008 0.9678 2011 0.7998 0.6706 0.0056 0.0008 0.9679 All 0.8004 0.6692 0.0024 0.0003 0.9743

This table reports the results of OLS regressions across bins, ndb = c + β · wdb + udb. The coefficients, standard errors, and ¯ R2 statistics are estimated separately for each calendar year and for the whole

• sample. The last year is incomplete and ends on November 4, 2011.

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Suggestive Invariance Check

6 8 10 12 14 16 18 1 2 3 4 5 6 7 8 logN vs logW, Daily averages

Figure : Scatter plot of log N onto log W . Each day provides 3

• bservations, one for each regimes. The slope is 0.687.

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Trading Invariance during the Flash Crash

9 10 11 12 13 14 15 −4 −3 −2 −1 1 2 3 4 Standardized logI 9 10 11 12 13 14 15 1050 1100 1150 1200 Price P 9 10 11 12 13 14 15 1 2 3 4 5 6 7 x 10

4

Volume V 9 10 11 12 13 14 15 2 4 6 8 10 Volatility σ

The figure shows price P, volume V , volatility σ, and standardized log invariant log I on May 6, 2010. 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.

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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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