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

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

Research output: Working paper


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.
Original languageEnglish (US)
PublisherSocial Science Research Network (SSRN)
Number of pages46
StatePublished - Mar 15 2016


  • Market microstructure
  • Invariance
  • Bets
  • High-frequency trading
  • Liquidity
  • Volatility


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