# 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?

• Wouldn't it be easier to have that $\textrm{price} \times \textrm{amount} < C$ must hold from some $C$? Feb 1 '14 at 13:52
• This is a really badly worded question. What does it mean to estimate the volume we can 'safely trade'. What is safe trading? Why are you constricting yourself to a 'single trade'? Why would you want to trade all your size in 1 trade? It is just not clear what you're asking. Feb 2 '14 at 15:59
• Then the answer to your question is that you can trade as much as will be in one side of the book in t+k, where t is now and k is the latency for your market order to be received by the matching engine. This can be more than the average daily volume. If there is 5 million volume on the bid side and you want to sell, then you can sell precisely 5 million in one trade, assuming no deletions within the few milliseconds or microseconds that it takes for your order to reach the market. Feb 3 '14 at 9:26
• @user2763361 Correct, so, there is some distribution of open orders and bids / offers, however what you described is something which doesn't happen often. There could be some way to imply the microstructure average distribution. I'm not talking about exactly knowing it, but putting an estimate on it. Feb 3 '14 at 11:05

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.

• Aha, I see, thanks for the answer. Starting from some of your tips and researching a bit more now I get that it is an impossible task to have some reasonable estimate without the actual microstructure data. Thanks for the answer. Feb 3 '14 at 20:49
• You say that : This maximum volume can be more than the average daily traded volume and has no theoretical upper limit. What about the Total issued capitalization of the considered stock! It's a theoritical limit! Feb 4 '14 at 11:00
• @aajajim Indeed Feb 6 '14 at 5:20

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!

• For now I'm talking about one single trade. So, basically I'd like to roughly estimate average market depth throughout the day given the volume. They are obviously correlated, I thought there might be some research already done about it... Feb 1 '14 at 22:11
• It's possible to do similar things with none of these models, perhaps with better performance. Feb 8 '14 at 9:11

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.

• "There is a possibility that daily volume is correlated somehow with depth" - yes, this is what I'm looking for I thought there might be some research already on this topic... Feb 1 '14 at 22:09