Estimating Trade Capacity from Order-Book Depth and Execution Models

# Estimate reasonable trade sizing based on daily volume


# Estimate reasonable trade sizing based on daily volume












Let's assume we have data for daily volumes traded on some asset (and open interests as well). Now if we are planning to make a trade we don't want to fat-finger it and want it to be of a reasonable size. That is, we certainly know that if we try to make a trade larger than the whole daily volume, it just won't go through or will significantly alternate the price. The question is: how can we estimate this volume we can safely trade?

EDIT: I'm not looking for any precise model which will be used in a trade execution. What I'm trying to get is some rough upper boundary for a single trade. As I mentioned, this boundary is certainly lower than the daily volume. We know that. Now, is there a tougher estimate?

## Answer by user2763361 (score 6, accepted)

https://quant.stackexchange.com/a/10156

From your comments I have deciphered that what you actually want to know is what the maximum amount of size is that you can trade at any time.

Holding aside exchange irregularities, the answer to this is the total amount of size on one side of the book in the direction that you want to trade (e.g. bid side if you want to sell), at the time that you want to trade plus a number of micro or milliseconds between now and when your order arrives to the matching engine. You would also need to add hidden liquidity either at mid or deeper into the book that you will run into if you submit such a market order - the extent to which this will contribute to the total trade-able size on one side of the book at some point in time is exchange and trader dependent.

In expectation, the above figure can be slightly increased by improving the best ask with a limit order at the same instant as you submit your massive market order, absorbing any buy market orders that are issued at the same time that you are cleaning out the bid schedule.

This maximum volume can be more than the average daily traded volume and has no theoretical upper limit (EDIT: A comment points out that there is one; the market capitalisation of the stock in question). But it will have a practical upper limit since market makers will not want to over-size a particular level near the insides, because doing so would expose them to the risk of adverse selection without compensation from queue-position and the average time it takes for a queue to recycle (i.e. if the queue is too thick, then queueing on top of it will only lead to bad fills).

Be warned: This may be perceived as market manipulation by either the exchange or regulator. If the former sees it this way, they may cancel your trade and fine you.

## Answer by aajajim (score 3)

https://quant.stackexchange.com/a/10142

Actually your question englobes many questions. In my opinion, you shouldn't only focus on the total volume you're going to execute on a specific day, but also on how you're going to split it into meta-orders(orders of small amounts) all over the day.

You need to have:

- A model for daily volume (which i think is what are you looking for, then an ARIMA(3-5, 1, 1-2) provides satisfying results)

- A model for Inra-day volume (more study should be done on this, see for example McCulloch)

- A model for market impact (see Almgren & Chriss, which is by the way a reference in optimal execution, but they generally assume the volume known)

- A cost function that you want to minimize

- Some hypothesis on the market micro-structure

And then you can trade your huge volume (or Iceberg) according to the execution strategy you get.

I hope this helps!

## Answer by Svisstack (score 2)

https://quant.stackexchange.com/a/10139

You must look at passive volumes available on certain levels in orderbook, that feature is called market depth.

There is a possibility that daily volume is correlated somehow with depth on market levels around a price, but I think you must gather some data and model that relationship when you want do that in this way.