Who's pushing

Go back to the board lesson 1 left behind, with the best bid at 51 and the best ask at 53. A maker pinned a note and waited. A taker arrived, read the board and took that note at its price. The trade needed both of them, but only the taker decided it should happen now, and crossed the spread to make it happen.

Exchanges record this. Next to each trade's time, price and size, the tape says which side the taker was on. In a taker buy, the buyer crossed and took a note at the best ask; in a taker sell, the seller crossed and took one at the best bid. Add them up over a minute and you get taker buy volume and taker sell volume. Buys minus sells is the ƒvolume delta.

Below, forty takers arrive at that board, each wanting one sack straight away, while makers keep two sacks waiting at every price. You choose how many of the takers are buying and how many selling, and watch the price.

Forty sacks change hands whatever you choose, so the volume is the same every time. With five buyers in every ten, takers bought 20 and sold 20, and the price ended at 52, where it started. With seven in ten, they bought 28 and sold 12, a volume delta of +16, and the price ended 10 higher, at 62.

Each taker buy removes a sack from the ask side. When buys outrun sells, the asks run out faster than makers replace them, and the best ask has to move up, taking the price with it. The volume says how much traded. The delta says which way the people in a hurry were leaning, and the price follows the lean.

The same delta can come from very different people. Twenty-six sellers might each sell one sack, a few at a time, with buyers cutting in between them. Or one seller might want 12 sacks gone at once.

An order to sell 12 sacks takes the first note at the best bid, then the next, and keeps going down the board until it has all of them. The exchange prints one trade for every note it fills, so the tape shows 12 trades of one sack, all sells, all at the same moment, between the buys of everyone else.

Both tapes hold 14 taker buys and 26 taker sells, a volume delta of −12, and both leave the price at 45. Counted trade by trade, the sizes match too: every trade is one sack, because each fill is the size of the note it took. What gives the big seller away is the order of the trades.

A run is a streak of trades in a row whose takers were on the same side. In the crowd, the longest run of sells was 4 trades. The big seller's order printed 12 in a row. The ƒtrade run imbalance puts the longest run on each side against each other: the longest buy run minus the longest sell run, divided by the two added together. It goes from −1, when only sellers ever kept at it, to 1. The crowd's tape scores −0.33, the big seller's −0.71.

Lesson 2's stall lost money to customers who knew where the price was going. Those customers trade in a recognisable way: they all want the same side, and they come just before the price moves. So flow that piles up on one side while the price jumps around suggests that the people taking a market maker's notes know something. Market makers call such flow toxic, the word David Easley, Marcos López de Prado and Maureen O'Hara used for it in 2012.

The ƒflow toxicity score puts a number on it, a minute at a time. It takes two counts for the minute: the volume delta, and how much the price moved around inside the minute. It measures each against every minute of the day so far as a z-score, where 0 is an ordinary minute and 2 or −2 is far from ordinary. Then it multiplies the two.

Pick one of four minutes below and see where it lands on each count, against a toy morning of 30 ordinary ones.

Take a minute when takers sold 12 sacks more than they bought: far from usual, a z-score of −2.8. If its price moved around an ordinary 3 coins, a z-score of 0.0, the score comes to 0. If its price moved around 6 coins, a z-score of 2.5, the score drops to −7. A large score needs both: flow leaning hard to one side, in a minute when the price is busier than usual. Then the sign says who was pushing, below zero for sellers and above zero for buyers.