What a Fill Actually Is

Your order never meets “the market”. It meets one specific person who chose that moment to trade against you — and because they chose it, the fills you get are not a fair sample of the fills you could have got. On the arithmetic below, the same one-in-ten miss rate costs one trader $1.50 against a $2 saving and another $15 against the same $2, and nothing about the order type differs between them.

Prerequisites: Lesson 2, for the queue you join when you post a limit order and the levels you walk when you send a market one.

The cost that never appears on the statement

A limit order saves you the spread. A market order guarantees you the trade. Traders reliably optimise the first because it shows up on the confirmation, and ignore the second because it does not show up anywhere.

One thing has to be right before any of that applies. A limit order only saves you the spread if it rests on your own side of it. A buy limit written at the offer is marketable: it executes at once, against the offer, at the offer, and pays exactly what a market order would. The saving comes from resting at 50.02 and waiting for somebody to come to you — not from putting a price on an order that crosses anyway. Confusing the two is the commonest way a trader believes they have stopped paying the spread while paying it in full.

Put both on the same scale. Take a penny-wide instrument and a 200-share position. Using limit orders instead of market orders saves you half the spread each way: half a penny going in, half a penny coming out, so a penny a share on the round trip — $2 on 200 shares. That is the visible saving, and it is real.

Now the invisible side. Suppose insisting on a limit means one attempt in ten never fills. What does a missed attempt cost? Not the average winner — that is the mistake almost everyone makes here. A trade you skip takes its losses with it, so what you forgo is the average across every trade you take, wins and losses together. If that figure is $15, then missing one attempt in ten costs $1.50, against a $2 saving. The limit order is correct.

Now suppose you trade less often for larger moves and your average across all trades is $150. The same one-in-ten miss rate now costs $15 per attempt to save the same $2, and the limit order is destroying most of what you came for. Nothing about the order types changed. What changed is the size of what you are trying to catch, measured against the spread you are trying to avoid.

So the question is never “are limit orders better”. It is: how often do mine fail to fill, and what were those trades worth? Both numbers are yours, neither is knowable from theory, and both come out of the record described in lesson 23. Until you have them, anybody who tells you which order type to use is guessing on your behalf.

What this does not settle

Nothing here says the person on the other side of your fill knew anything. Most trades happen between people with no information at all, for reasons that have nothing to do with a view — a fund taking in money, a pension rebalancing, somebody paying a tax bill. Adverse selection is a statement about the average over many fills, not a claim about any one of them, and reading a single fill as evidence that somebody outsmarted you mistakes one observation for a rate.

Nor does it establish that resting orders are a bad idea. It establishes that they carry a cost which is invisible by construction, and that the cost is measurable only against your own record. The instruments where that cost is small and the ones where it is ruinous differ by a factor of thousands, which is what lesson 12 is for.

Every fill above is also all or nothing, and real ones are not. A limit order for 500 shares can come back as 200, which leaves you two fifths of a position at a price somebody else chose and three fifths of a decision you now have to take a second time. None of the arithmetic here covers that, and in anything less liquid than these examples the partial is the ordinary case.

The one in ten and the one in six were handed to you as though a miss rate were a property of a trader. It is not. It moves with how far from the touch you rest, with the instrument, and with the hour of the day, so a single figure for it is already an average over things that differ, and the third problem below will hand you a noisier number than these examples suggest.

And what an unfilled order was worth is not a thing you can observe. You are pricing a trade that did not happen, in a market that would have contained your order had it happened. At retail size that difference is small enough to set aside, and the assumption has been doing quiet work in every figure above. Nobody can hand you a clean measurement of what you missed. The best that exists is the noisy one you collect yourself.

Standing still is a position. It has a cost, and the cost is paid in the trades you never see.

Problems

1. The comparison, run properly. You trade 500 shares at a time in an instrument quoted two cents wide, and using limits on both entry and exit saves you the whole spread. One attempt in six fails to fill. You win 40 per cent of your trades, your average win is $60 and your average loss is $30. Compute (a) what limits save per round trip, (b) the average outcome of a single trade, and (c) what one missed attempt in six costs. Which order type do your numbers favour, and by how much?
2. The instant fill. You post a limit order to sell above the current market and it fills within a second. Name two different things that could have caused that, and say which of the two should worry you.
3. Your own fill rate. Over your next twenty limit orders, record two things: whether it filled, and where price was five minutes later. Compute the fraction that did not fill, and what the unfilled ones would have been worth. This is the only way the arithmetic above can be run on you rather than on an example.

Sources. Lawrence R. Glosten and Paul R. Milgrom, “Bid, Ask and Transaction Prices in a Specialist Market” (Journal of Financial Economics 14, 1985), which derives the spread from adverse selection alone — no inventory cost, no processing cost, and a spread still has to exist. Larry Harris, Trading and Exchanges (Oxford, 2003), chapter 14, on choosing between order types.

You now know what a fill is and what it cost to obtain. The next lesson takes the spread you have been paying in every example so far and shows that its size in cents tells you nothing at all. Divided by the stop you are using, the same number starts deciding which trades you can afford.

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.