What the Spread Is Paying For

A spread that just breaks even is twice the chance that the next order knows something, multiplied by how much it knows. That is one line of algebra, it is the informed-trading half of what lesson 5 named and could not price, and it is enough to read most of a screen with. Put the penny spread on a heavily traded stock through it and the market is pricing one informed order in a thousand against an earnings-sized move. Put a fifty-cent spread on a small company through it and the same arithmetic demands one informed order in twenty, and at a smaller move it demands that every single order be informed, which is impossible and is the line telling you the rest of that spread is not about information at all. The same equation prices the other side of the screen. It says what your own crossing costs, and at three hundred shares and sixty round trips a day, in the minutes where the spread is a dime, it is $1,800 a day and 324 per cent of a $140,000 account in a year.

Prerequisites: Lesson 5, which named inventory risk and adverse selection and priced neither, and whose penny-on-2,000-shares becoming four-cents-on-300 is the case this lesson finally puts a number on, lesson 4, for the breakeven win rate of one plus s over two and for why the spread only means something against your stop, and lesson 10, which put the spread at $2.00 of a $9.29 bill and is the reminder that the spread is one charge of four, so every figure in the second table below is a floor rather than a total.

The same equation, pointed at you

Turn the model round. Every time you cross a spread you are the uninformed order in it, and what you pay is not an estimate: it is s, the whole spread, per round trip, because you cross it going in and again coming out. Multiply.

Three hundred shares a trade, and 252 trading days. The columns are three spreads: a penny, which is what a large exchange-traded fund quotes in the middle of a liquid session; five cents, which is the same instrument in the first minutes after the open; and a dime, which is what you find in a single stock around an announcement or in an option nobody is quoting tightly.

Round trips a day	Spread $0.01	Spread $0.05	Spread $0.10
6, a day	$18	$90	$180
6, a year	$4,536	$22,680	$45,360
20, a day	$60	$300	$600
20, a year	$15,120	$75,600	$151,200
60, a day	$180	$900	$1,800
60, a year	$45,360	$226,800	$453,600

The bottom right cell is the one worth sitting with. Sixty round trips a day in dime-wide markets is $453,600 a year, which on a $140,000 account is 324 per cent of it. That is not a trading result. It is a bill, payable regardless of whether every single call was correct, and it is knowable on the first morning rather than discovered in the seventh week.

The whole table is one multiplication, and reading down a column shows which of the two inputs is doing the work. Going from six round trips to sixty multiplies the bill by ten. Going from a penny to a dime multiplies it by ten as well. They are the same lever pulled twice, and the second one is usually the one nobody thinks of as a choice: a trader who moves the same sixty trades out of the opening minutes and into the middle of the session has cut the same amount off the bill as one who cuts to six trades a day and keeps trading the open.

Put it through lesson 4 to see what it demands. At a penny spread and 300 shares, a round trip costs $3, so every winner has to be $3 bigger than every loser is small before anything is left. At a dime it is $30 a round trip. Nothing in that paragraph is about being right; it is the entry fee, and lesson 10 already showed it is only one of four.

What this does not settle

That the model describes an actual market maker. It describes one quoter, facing one-share orders, indifferent to risk, with no costs, against informed traders who all know the same thing. A real firm quotes thousands of instruments at once, nets its exposures across them, pays fees and collects rebates that differ by venue, and holds inventory it hedges in a different product entirely. Every one of those makes the true spread it needs different from 2aD, and mostly larger. What survives the simplification is the shape: the spread rises with how likely the next order is to be informed and with how much that order knows, and it does so proportionally.

That a is measurable. It is not, and nothing in this lesson pretends otherwise: every figure in the first table is an implication of an assumed D, not an observation. Change the edge from a dollar to five and the implied share of informed orders drops by a factor of five without one quote changing. So the table is a way of asking what a spread would have to believe, not a way of finding out what it does believe, and a reader who quotes the one-in-a-thousand as a fact about the market has taken exactly the wrong thing from it.

That retail flow is uninformed. It is less informed on average, which is all the model needs, and the average hides the part that matters to you. Firms that buy order flow sort it, and the accounts that are hardest to trade against are quoted differently from the accounts that are easiest. Whether you are in the group being paid for or the group being avoided is not something this page can tell you, and the aggregate statistic is no help at all in answering it for one account.

That a fill inside the quoted spread is a good fill. Price improvement is measured against the national best bid and offer, and the firm providing the improvement is also one of the firms whose quotes make that benchmark. Beating a number you help set is a weaker claim than it sounds, and the live argument in this area is about the gap between the improvement you receive and the improvement a genuine order-by-order auction would have produced. That gap is unmeasured here and this lesson has no figure for it.

That the second table is the cost of trading. It is the cost of taking liquidity, which is a particular way of trading, and lesson 4 already showed that the same spread means different things against different stops. A dime is fatal against a fifty-cent stop and irrelevant against a ten-point one, and the table deliberately shows neither, because it counts dollars rather than the ratio that decides anything.

And the largest omission is the one the arithmetic invites. If crossing costs you the spread, then posting earns it, and a reader who moves to resting limit orders stops paying s and starts collecting it. That is real and it is what the whole first half of this lesson describes someone else doing for a living. It is also the trade this page has not priced: the moment you are the one resting, you have taken on the second risk in the model, and the informed orders that were a rounding error when you were crossing are now the counterparty you cannot see coming. A limit order that never fills has cost you nothing and made you nothing; the ones that do fill are, disproportionately, the ones somebody wanted to hit. This lesson prices the cost of impatience precisely and prices the cost of patience not at all, and the second is not zero.

Problems

1. Read your own spread at two times of day. Pick the instrument you actually trade. Write down the bid and the ask at 9:31 and again at 11:00, every day for a week. Ten readings. You now have your own version of the columns in the second table, and you will find the ratio between them is a fact about your instrument rather than a number from any lesson. Ten minutes in total, spread over five mornings.
2. Compute your own bill before the next trade, not after it. Take your typical spread from problem 1, multiply by your usual share count, multiply by round trips a day, multiply by 252. Then divide by your account. If the answer is 3 per cent you have found something you can stop worrying about; if it is 100 per cent you have found the thing that is wrong, and no improvement in your entries will touch it. Half an hour, and it is the single highest-value calculation in this module.
3. Compare two brokers on your own order size. Every broker publishes an execution-quality report under the SEC’s rules, broken down by order size and by security. Pull the report for your broker and for one other, find the band your orders actually fall in, and compare the ratio of effective spread to quoted spread. A ratio below one means the average order in that band was filled inside the quote, and how far below tells you by how much. Do it for the three instruments you trade most. An evening, and at the end you have replaced every general claim about payment for order flow, including the ones on this page, with two numbers that are about you.

Sources. Harold Demsetz, “The Cost of Transacting” (The Quarterly Journal of Economics, 1968), for the spread as the price of immediacy rather than a fee, which is the frame lesson 4 took and this lesson puts an equation under. Lawrence R. Glosten and Paul R. Milgrom, “Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders” (Journal of Financial Economics, 1985), for the zero-profit condition solved above and for the result that adverse selection alone is enough to produce a spread, with no inventory and no costs. Maureen O’Hara, Market Microstructure Theory (Blackwell, 1995), for the inventory models that account for the part of the bottom row the formula above cannot. Christopher Schwarz, Brad M. Barber, Xing Huang, Philippe Jorion and Terrance Odean, “The ‘Actual Retail Price’ of Equity Trades” (2024), for identical orders sent through several brokers at the same moment coming back at materially different prices, which is the evidence problem 3 asks you to reproduce for your own account.

A spread is not a fee and it is not a courtesy. It is a price with two components, and the informed-trading one solves exactly: a break-even spread is twice the chance the next order knows something, times what it knows. That single line prices the penny on a liquid stock at one informed order in a thousand, refuses to price a fifty-cent spread at all and thereby tells you the rest of it is inventory, and explains why uninformed flow is worth paying for without anyone doing anything improper. Pointed the other way, it says a $30 round trip is a $30 round trip whether the trade was brilliant or stupid. What it does not say is where your order goes after you press the button, and the answer is not the exchange you are looking at. Lesson 54 follows one order through the venues that compete for it, and finds that the speed everyone complains about is the least of what is being decided.

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