Cadence or Stride Length? - Stride Length!

To run faster you can increase your cadence and/or your stride length. Similarly, for one stock having a higher daily volume, this can be due to more trades and/or larger volume per trade. There is no obvious reason which mechanism should dominate.

Fig. 1 below shows for each German equity listed on Xetra (a) its average number of trades per day ("cadence") and (b) the average trade size ("stride length"). Only trades on Xetra during the continuous trading phase are considered. Both are plotted vs. the stock's average daily volume (only Xetra but incl. auction volume).

The range of the vertical axes is set so that each covers the same number of orders of magnitude. We see that the number of trades almost perfectly follows a power law. Larger markers denote DAX40 constituents. The orange annotations denote the fraction of the overall traded notional is due to instruments with an ADV larger than the indicated threshold.

The trade sizes, however, drop off much more slowly; after an initial fall, they almost form a plateau in the range of a few thousand EUR. In short: The trades on illiquid stocks have similar sizes as those of more liquid stocks, but trade much less frequently.

From a market maker's point-of-view, the opposite would be preferred. Assume the spread must reflect the expected risk for the market maker. The risk scales with the holdtime which scales with the time between trades. So, in the limit of more frequent but smaller trades, market makers could probably quote a tighter spread.

I wonder what determines the level of the plateau. Maybe some fixed per-trade costs?

Data: On-book Trades - Xetra