Are trading invariants really invariant? Trading costs matter

We revisit the trading invariance hypothesis recently proposed by Kyle, A.S. and Obizhaeva, A.A. ['Market microstructure invariance: Empirical hypotheses.' Econometrica, 2016, 84(4), 1345-1404] by empirically investigating a large dataset of metaorders provided by ANcerno. The hypothesis predicts that the quantity , where is the daily exchanged risk (volatility x volume x price) and N is the daily number of metaorders, is invariant, either in distribution or in expectation. We find that the 3/2 scaling between and N works well and is robust against changes of year, market capitalisation and economic sector. However our analysis shows that I is not invariant, and we find a very high correlation () between I and the trading cost (spread + market impact costs) of the metaorder. Guided by these results we propose new invariants defined as a ratio of I to the aforementioned trading costs and find a large decrease in variance. We show that the small dispersion of the new invariants is mainly driven by (i) the scaling of the spread with the volatility per transaction, (ii) the near invariance, across stocks, of the shape of the distribution of metaorder size and of the volume and number of metaorders normalised to market volume and number of trades, respectively.