You Changed the Price

There is a price, and I decide whether to trade at it. That is how almost every­one imag­ines a market, includ­ing many people who trade in one. It is true for small orders. For large ones it is back­wards.

The number on a screen is the price of the first unit. It tells you what the best offer is and nothing about how many units are behind it. Buy one share of a large company and you will pay the screen price. Buy a hundred thou­sand shares and you will pay the screen price for the first few hundred, a little more for the next few hundred, and more again after that, because your order will eat through the queue of sellers from the cheap­est upward. The price you pay depends on how much you want.

Traders have words for the pieces. Depth: how much sits at each level. Slippage: the gap between the price you saw and the average you got. Impact: what your buying does to every­one after you, you included. Liquidity: enough on the other side that none of it hurts.

A real book, mea­sured

Here is the sell side of Binance's bitcoin book 470 mil­lisec­onds before our second, from our own capture. The best offer was $75,807.20 for 6.83704 bitcoin. Behind it, twenty price levels were visible to us, running up to $75,811.26. In total those twenty levels offered $585,236 of bitcoin.

Walk orders of dif­fer­ent sizes up that book, as if they had arrived at that instant, and the answers are on page 40. An order for a thou­sand dollars, ten thou­sand or a hundred thou­sand fills entirely at the best offer. The first price on the screen was the true price for all three.

A million-dollar order does not fit. The whole visible book covers $585,236. That part would have filled at an average only 0.04 basis points above the screen, about $2 in total, which is a remark­ably small toll for more than half a million dollars of bitcoin. The other $414,764 we cannot price at all, because our capture only sees twenty levels. More sellers almost cer­tainly stood above. How many, and where, we can't say.

Half a second later the same book looked very dif­fer­ent. At 537 mil­lisec­onds into the second, after a run of buying on every venue, the twenty visible levels on the sell side held $30,094. A hundred-thousand-dollar order, which had filled at one price a moment earlier, now could not be priced from what was visible at all.

How much does a million dollars cost?

Odd ques­tion, on purpose. Not what a million buys: what it costs to spend. The honest answer has three parts, and only the first ever reaches a screen.

The first is the visible cost: fees, and the spread you cross. On Binance at our instant the spread was one cent, so cross­ing it cost nothing worth mea­sur­ing. Fees are pub­lished, and depend on who you are.

The second is slip­page against the visible book, which is what we cal­cu­lated above, and which can be tiny or large depend­ing on the moment you arrive.

The third is what happens next. Other par­tic­i­pants see the trades. Market makers who were offer­ing size move their prices away, because a large buyer is infor­ma­tion. Some pull their offers entirely. The stair­case moves when you step on it, so large orders are almost never sent at once. They are cut into small pieces and released over minutes or hours by algo­rithms with names like VWAP and TWAP, which try to buy at the average price of the period without announc­ing that a big buyer is present.

Slicing costs too: while you wait, the price wanders for its own reasons. Every exe­cu­tion desk trades moving the market against waiting for it, and the screen shows neither.

The queue

Each step of the stair­case is also a queue. Most exchanges fill resting orders at the same price in the order they arrived, which traders call price-time pri­or­ity. A seller who joined the best offer early is filled first; one who joined later waits, and may not be filled at all before the price moves away.

That makes the book a strange kind of object. The 6.83704 bitcoin offered at $75,807.20 in our snap­shot was not one seller's offer. It was a line of them, and the posi­tion of each in the line was worth some­thing. Firms pay heavily for the speed to reach the front. The front is filled by traders cross­ing the spread; the back is filled mostly just before the price turns against it.

The same arith­metic, selling

Everything above applies in reverse to a seller, with one asym­me­try that matters in bad weeks. When a large holder must sell, because of a margin call or a redemp­tion, the buyers in the book know that the selling has to happen. They have no reason to stand in its way. Bids thin out, and the seller walks further down the book than a buyer of the same size would have walked up it. Forced sellers pay for being forced, and the price they get is one they helped to make.

So the value of a port­fo­lio on a screen, quan­tity times last price, is money no large holder could actu­ally receive. It assumes selling one unit at a time into a market that never notices. Close enough for a small investor. For a fund that owns a real share of what it holds, the gap is one of its largest risks, and the screen never shows it.

The part you cannot see

Order books also contain orders that do not show. Many venues allow iceberg orders, which display a small visible size and replen­ish from a hidden reserve as they fill. Some trading happens away from public books entirely, in dark pools and through dealers quoting pri­vately. A visible book is a lower bound on liq­uid­ity, and on a bad day it is an opti­mistic one, because the orders it shows can be can­celled faster than a human can click.

So a large buyer is really asking what the price will be after they have fin­ished. That number does not exist yet, and their own order is one of the things that will decide it.

The next four pages show one real order that was large enough to test the book, and what the book did around it.