Unravelling the Trading Invariance Hypothesis

By M. Benzaquen, Jonathan Donier, Jean-Philippe Bouchaud. 2016

15 citations recorded by the source corpus.

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.

Subfields: Economics and Econometrics

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Citations in the corpus

Universal features of price formation in financial markets: perspectives from deep learning (2018, background): “Empirical evidence on the universality of certain stylized facts (Cont 2001) and scaling relations (Mandelbrot et al. 1997, Benzaquen et al. 2016, Kyle and Obizhaeva 2016, Patzelt and Bouchaud 2017, Toth et al. 2017, Andersen et al. 2018) seems to support the universality hypothesis.”