Walking the book

In lesson 1 you bought one sack from the cheapest note to sell, and the next buyer paid a little more. Now buy more than the best ask holds. The rest of your order doesn't wait: it takes the next cheapest price, then the next, until it is filled. Traders call this walking the book.

Here is a deeper book, with toy numbers: a unit costs about 100 coins, and prices move one tick, 0.01, at a time. Each column is one level, as tall as the units waiting there: bids on the left, asks on the right, 25 levels of asks in all. Pick a size and send your order.

An order of 40 takes all 10 units at the best ask, then 6 at 100.01, 8 at 100.02, 6 at 100.03, 8 at 100.04 and the last 2 at 100.05. Each fill is a trade of its own, at its level's price. They average 100.0205, which is 2.05 basis points over the best ask. That difference is the order's ƒslippage.

Slippage is measured from the best price you could see when you sent the order: the best ask for a buy, the best bid for a sell. An order the best level can hold has none. Double the order to 80 units and the slippage more than doubles, to 4.48 basis points. Paid on twice as many units, the extra over the best ask comes to more than four times as much: 3.58 coins against 0.82.

How far an order walks depends on how much waits at each level. A book with plenty at every price is called deep, or thick, and one with little is thin. The figure sets the book from above next to one with half as much at every level. Move your order and compare.

Halve the depth and the slippage roughly doubles. At 40 units the thin book charges 4.48 basis points against the thick book's 2.05, and the order walks 10 levels instead of 6. The thick book's line also bends: past 118 units the order reaches the wall of 40 units at 100.13, and the line flattens, because every unit in the wall costs the same.

So a trader who needs to buy a lot can split the order and send the pieces minutes apart, and each piece meets a book that has had time to refill. Whether it refills, and at what price, is the next lesson.

Lesson 2 compared the queues at the best bid and the best ask. With 25 levels a side you can ask the same question at any depth: add up the first 5 levels of each side, or 10, 20 or 25, and compare. The ƒbook imbalance is the difference over the total. It runs from −1 when only asks wait to +1 when only bids do.

In this book the answer depends on how far you look. On the first five levels the bids are heavier, 60 units against 38, an imbalance of +0.22. Across all 25 levels the asks hold twice as much, 312 against 156, an imbalance of −0.33. Both readings are right, and they answer different questions. The first levels are what the next small trades will meet. The deeper ones are what a large order would meet, and they are further from trading: whoever placed them can move or cancel them before the price gets there.