What the candle leaves out

A candle keeps five numbers from a stretch of trading: the first price, called the open; the highest and the lowest, the high and the low; the last, the close; and how much traded, the volume. The box runs from the open to the close, and the line through it reaches up to the high and down to the low.

Five numbers can't hold everything that happened. Here are three toy tapes from the board you know, each with 60 sacks traded. Play them, and watch the price, who was buying and selling, and the candle each one leaves.

All three leave the same candle: open 50, high 51, low 44, close 45, 60 sacks. Yet in the slide, sellers kept coming, mostly one sack at a time, and the price stepped down a coin at a time. The jump had ten quiet trades, then one seller who took 24 sacks at 44 in a single trade. And in the tug of war, buyers and sellers took turns, three sacks at a time, while the price kept turning on its way down. Someone reading only the candle can't tell which of these happened.

Measures built from the trades themselves keep some of what the candle throws away. An ƒuptick is a trade at a higher price than the trade before it, and a downtick one at a lower price; the rest print at an unchanged price. Counting them says how the price got from the open to the close: in a few steps or many, and how often it turned back.

An uptick isn't the same as a taker buy. A taker buy that fills at the same price as the trade before is a buy and an unchanged tick. The side says who crossed the spread; the tick says whether the price moved.

ƒTrade sizes sort trades by the money in each: here, small under 100 coins, medium up to 1,000, and large from 1,000. The catalog uses the same cuts in dollars. And ƒflow entropy says how mixed the taking was. Take the share of the money that went through taker buys, and the share through taker sells: the entropy is 0 when one side did all the taking and 0.69 when they split it evenly.

Read each tape three ways: by its ticks, by the size of its trades, and by taker buys against taker sells.

The slide had 7 downticks and only 2 upticks. The tug of war had 9 downticks and 4 upticks: the same distance travelled, with more turning back. In the jump, one large trade carried 38% of the money. And sellers did 88% of the taking in the slide, so its flow entropy is 0.36, while the jump and the tug of war, with both sides active, come to 0.63 and 0.67.

The candle can't say whether the fall from 50 to 44 came in one trade or in many. The ƒjump ratio can. It compares two ways of adding up how much the price moved from trade to trade.

The first is realised variance: square every move and add them up. Squaring makes big moves count much more than small ones. The second is bipower variation, which multiplies each move by the move before it instead, and scales the sum by π/2 so the two agree when the price moves in steady small steps. A big move next to small ones, or next to a trade at an unchanged price, adds little or nothing to it. The jump ratio is the share of realised variance that bipower variation leaves unexplained, the jump part.

With the fall spread over six one-coin moves, the jump ratio is 0.21. Put four coins of it into one trade and it is 0.92; all six at once and it is 1. The three tapes from before score 0.14 for the slide, 0.93 for the jump and 0.13 for the tug of war.

Even six small moves score above zero. Wherever a trade at an unchanged price sits next to a move, that move loses a partner in bipower variation, so part of it counts toward the jump part. On a real tape, where most trades print at the price before them, that happens all the time, so read the jump ratio against other bars of the same market rather than against zero.