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Unravelling the trading invariance hypothesis

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  • Michael Benzaquen
  • Jonathan Donier
  • Jean-Philippe Bouchaud

Abstract

We confirm and substantially extend the recent empirical result of Andersen et al. \cite{Andersen2015}, where it is shown that the amount of risk $W$ exchanged in the E-mini S\&P futures market (i.e. price times volume times volatility) scales like the 3/2 power of the number of trades $N$. We show that this 3/2-law holds very precisely across 12 futures contracts and 300 single US stocks, and across a wide range of time scales. However, we find that the "trading invariant" $I=W/N^{3/2}$ proposed by Kyle and Obizhaeva is in fact quite different for different contracts, in particular between futures and single stocks. Our analysis suggests $I/{\cal C}$ as a more natural candidate, where $\cal C$ is the average spread cost of a trade, defined as the average of the trade size times the bid-ask spread. We also establish two more complex scaling laws for the volatility $\sigma$ and the traded volume $V$ as a function of $N$, that reveal the existence of a characteristic number of trades $N_0$ above which the expected behaviour $\sigma \sim \sqrt{N}$ and $V \sim N$ hold, but below which strong deviations appear, induced by the size of the~tick.

Suggested Citation

  • Michael Benzaquen & Jonathan Donier & Jean-Philippe Bouchaud, 2016. "Unravelling the trading invariance hypothesis," Papers 1602.03011, arXiv.org, revised Sep 2016.
  • Handle: RePEc:arx:papers:1602.03011
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    Citations

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    Cited by:

    1. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Papers 1803.06917, arXiv.org.
    2. Justin Sirignano & Rama Cont, 2018. "Universal features of price formation in financial markets: perspectives from Deep Learning," Working Papers hal-01754054, HAL.
    3. Frédéric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Are trading invariants really invariant? Trading costs matter," Post-Print hal-02323318, HAL.
    4. Fr'ed'eric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "Are trading invariants really invariant? Trading costs matter," Papers 1902.03457, arXiv.org.
    5. Mathias Pohl & Alexander Ristig & Walter Schachermayer & Ludovic Tangpi, 2018. "Theoretical and empirical analysis of trading activity," Papers 1803.04892, arXiv.org, revised Oct 2018.
    6. Frédéric Bucci & Fabrizio Lillo & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "Are trading invariants really invariant? Trading costs matter," Working Papers hal-02323318, HAL.

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