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Intraday Trading Invariance in the E-mini S&P 500 Futures Market


  • Torben G. Andersen

    () (Kellogg School of Management, Northwestern University)

  • Oleg Bondarenko

    () (Department of Finance (MC 168), University of Illinois at Chicago)

  • Albert S. Kyle

    () (Robert H. Smith School of Business, University of Maryland)

  • Anna Obizhaeva

    () (New Economic School)


The intraday trading patterns in the E-mini S&P 500 futures contract between January 2008 and November 2011 are consistent with the following invariance relationship: The return variation per transaction is log-linearly related to trade size, with a slope coefficient of -2. This association applies both across the pronounced intraday diurnal pattern and across days in the time series. The documented factor of proportionality deviates sharply from prior hypotheses relating volatility to transactions count or trading volume. Intraday trading invariance is motivated a priori by the intuition that market microstructure invariance, introduced by Kyle and Obizhaeva (2016c) to explain bets at low frequencies, also applies to transactions over high intraday frequencies.

Suggested Citation

  • Torben G. Andersen & Oleg Bondarenko & Albert S. Kyle & Anna Obizhaeva, 2016. "Intraday Trading Invariance in the E-mini S&P 500 Futures Market," Working Papers w0229, Center for Economic and Financial Research (CEFIR).
  • Handle: RePEc:cfr:cefirw:w0229

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    References listed on IDEAS

    1. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-155, January.
    2. Christian T. Brownlees & Fabrizio Cipollini & Giampiero M. Gallo, 2011. "Intra-daily Volume Modeling and Prediction for Algorithmic Trading," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(3), pages 489-518, Summer.
    3. Alexander, Gordon J. & Peterson, Mark A., 2007. "An analysis of trade-size clustering and its relation to stealth trading," Journal of Financial Economics, Elsevier, vol. 84(2), pages 435-471, May.
    4. Goldstein, Michael A. & A. Kavajecz, Kenneth, 2000. "Eighths, sixteenths, and market depth: changes in tick size and liquidity provision on the NYSE," Journal of Financial Economics, Elsevier, vol. 56(1), pages 125-149, April.
    5. Christian T. Brownlees & Fabrizio Cipollini & Giampiero M. Gallo, 2011. "Multiplicative Error Models," Econometrics Working Papers Archive 2011_03, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Apr 2011.
    6. Bollerslev, Tim & Jubinski, Dan, 1999. "Equity Trading Volume and Volatility: Latent Information Arrivals and Common Long-Run Dependencies," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 9-21, January.
    7. Albert S. Kyle & Anna Obizhaeva, 2016. "Market Microstructure Invariance: A Dynamic Equilibrium Model," Working Papers w0228, New Economic School (NES).
    8. Yacine Aït-Sahalia & Jean Jacod, 2014. "High-Frequency Financial Econometrics," Economics Books, Princeton University Press, edition 1, number 10261, December.
    9. Andersen, Torben G, 1996. " Return Volatility and Trading Volume: An Information Flow Interpretation of Stochastic Volatility," Journal of Finance, American Finance Association, vol. 51(1), pages 169-204, March.
    10. Angel, James J, 1997. " Tick Size, Share Prices, and Stock Splits," Journal of Finance, American Finance Association, vol. 52(2), pages 655-681, June.
    11. Moulton, Pamela C., 2005. "You can't always get what you want: Trade-size clustering and quantity choice in liquidity," Journal of Financial Economics, Elsevier, vol. 78(1), pages 89-119, October.
    12. Liesenfeld, Roman, 2001. "A generalized bivariate mixture model for stock price volatility and trading volume," Journal of Econometrics, Elsevier, vol. 104(1), pages 141-178, August.
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    Cited by:

    1. Mark D. Flood & John C. Liechty & Thomas Piontek, 2015. "Systemwide Commonalities in Market Liquidity," Working Papers 15-11, Office of Financial Research, US Department of the Treasury.
    2. Barardehi, Yashar H. & Bernhardt, Dan & Ruchti, Thomas G., 2019. "A test of speculative arbitrage: is the cross-section of volatility invariant?," The Warwick Economics Research Paper Series (TWERPS) 1204, University of Warwick, Department of Economics.
    3. Fr'ed'eric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "Are trading invariants really invariant? Trading costs matter," Papers 1902.03457,

    More about this item


    market microstructure; invariance; bets; high-frequency trading; liquidity; volatility; volume; business time; time series; intraday patterns;

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