Every trade leaves a mark

Send 60 units into lesson 5's thick book and the order walks eight levels. Afterwards the best ask is 100.07 and the best bid still 99.99, so the mid has jumped from 99.995 to 100.03. That jump is the peak of the order's impact.

Then the makers come back. New asks appear below 100.07, new bids above 99.99, and the spread narrows again. Where the mid settles depends on what the makers conclude from the order. Someone just bought 60 units in a hurry. Maybe they knew something. Makers can't tell, so they shade their prices up a little: in this toy, a quarter of a tick for every 10 units bought.

Send the order and watch. The book is on the left, asks above and bids below, with outlines where your order took. The chart follows the mid for 30 seconds.

With the figure's starting settings, 60 units lift the mid 3.5 basis points. Makers refill, and it slides back to 1.5 above where it started, and stays there. The 2 basis points that came back are the temporary impact: the cost of emptying the book, paid by the buyer and gone once the book refills. The 1.5 that stayed is the permanent impact, a change in what everyone thinks the price is.

Slow the makers down and something else shows. If they close half the gap every 20 seconds, the same order still shows 2.2 basis points after 30 seconds, of which only 1.5 will stay. Measured then, more of the move looks permanent than really is. How much of a move stays depends on when you look, and every measure of it has to pick a moment.

You rarely see one big order on its own. You see thousands of trades of every size, buys and sells mixed, each moving the price a little. Albert Kyle's 1985 model of trading gives a way to read them together. In it, makers move the price by a fixed amount for every unit bought or sold in a hurry. Plot each trade's size against the move that came with it, and the slope of the line through the dots is that amount. It is called ƒKyle's lambda.

The figure plots 120 toy trades. Each dot is one: its size across, counted plus for a buy and minus for a sell, and the move that came with it up the side. Make the book thinner or thicker.

With 10 units at every level, the slope is 0.053 basis points per unit: a 10-unit buy comes with about half a basis point. Halve the depth to 5 and the slope doubles, to 0.106. Quadruple it to 40 and the slope falls to 0.013. A steep line means a thin market, where every unit traded pushes the price further.

Yakov Amihud proposed a coarser measure in 2002, for stocks, a day at a time: take how far the price moved over the period, whichever way, and divide by how much traded. ƒAmihud illiquidity needs nothing but prices and volume. On the toy it reads the same way as the slope: 0.91 basis points for every 10,000 coins traded with 10 units at each level, twice that with 5. Its blind spot is a period where buyers and sellers cancel out. The price barely moves over it, so it looks liquid however thin the book is.

Lambda and Amihud say how hard trades push. Neither says how much of the push comes back. For that, watch the price after the biggest trades. The ƒlarge-trade reversal takes the biggest tenth of trades by value, looks five trades ahead of each, and averages the return from the big trade's price to the later one.

Here is a toy tape of 50 trades on lesson 5's book. Five are big buys of 60 units, ringed. Choose how many trades ahead to look.

One trade on, the price sits about 1 basis point below where the big buys printed. Five trades on, it is 1.67 below. The big buys printed 3.8 basis points above the mid before them, half the spread plus the walk, so by five trades on about 44% of that had come back.

A negative number after big buys, or a positive one after big sells, means part of the move came back. The measure doesn't flip sells around, so a minute with big trades on both sides can average out to nothing. Read it next to which side the big trades were on.