Time and Sales

The tape is the transaction record: the only place a trade appears before it is a candle. It carries three facts. The fourth one your platform shows you — which side was the aggressor — is not reported by anybody, it is inferred, and knowing how tells you exactly how far to trust it. It is right about four times in five, and on the seven seconds worked below, a single misclassified print of 900 shares moves the minute’s signed total from +600 to −1,200.

Prerequisites: Lesson 2, for the quote that everything below is measured against, and lesson 6, for what a candle discards — which is what you came here to get back.

Signing a tape by hand

Six prints from one minute, with the quote that was standing at each. Apply the rule in the table above to each row before reading on.

Time	Print	Size	Quote at the time	Inferred
10:04:11	50.03	400	50.02 / 50.03	Buy — at the ask
10:04:12	50.03	1,200	50.02 / 50.03	Buy — at the ask
10:04:14	50.02	700	50.02 / 50.03	Sell — at the bid
10:04:15	50.025	900	50.02 / 50.03	Between. Last different price was 50.02, so higher, so buy
10:04:17	50.04	300	50.03 / 50.04	Buy — at the ask
10:04:18	50.03	1,500	50.03 / 50.04	Sell — at the bid

Five thousand shares in seven seconds. Signed that way, 2,800 were bought and 2,200 sold, and the difference is +600: a minute with slightly more buying than selling in it.

Now change one row. The 900 at 50.025 was the one the quote could not decide, and the tick test guessed. Suppose it guessed wrong — suppose a seller took a midpoint fill. Then 1,900 were bought and 3,100 sold, and the difference is −1,200.

Same seven seconds, same five thousand shares, and the number that is supposed to summarise them moved by 1,800: from +600 to a negative number twice that size. The arithmetic behind that is worth keeping: reclassifying a print moves the total by twice its size, because it comes off one side and goes on the other. Here that was one print, 18 per cent of the volume, on the single row the rule is least sure about.

What this does not settle

That a large aggressive print predicts anything. It establishes urgency, and urgency is a fact about a person, not a forecast: a hedge, a redemption and a directional bet all lift the offer the same way. What the tape tells you is whether the thing you are looking at is what it appears to be.

Nor does it establish what counts as large. That is a property of your instrument and your session, and no threshold printed in a lesson survives contact with a different one — problem 3 is how you get your own.

And the sum of these signs is not covered here. Adding them up is delta, which is lesson 8, and the reason it comes with an error bar is the one you have just computed. Where those prints executed, and which of them never reached a public tape at all, is lesson 56.

The four-in-five figure also has a vintage. It comes from a study of United States equities in the 1990s, testing a rule published in 1991, and the market it measured had wider spreads, coarser ticks and far less trading between the quotes than the one you are looking at. Better classifiers exist now. Your platform is almost certainly not running one, which is why the old number is the honest one to quote, but treat it as an order of magnitude rather than a measurement of your feed.

“On the tape the instant it is reported” is also carrying weight. Reporting is not instantaneous and it is not uniform: venues and off-exchange reporting facilities work to deadlines rather than to zero, so some prints reach you seconds after they happened and a few reach you out of order. The tape is earlier than the candle by construction. It is not the same thing as live.

And the minute above was chosen. One print, 18 per cent of the volume, sitting on the single row the rule is least sure about, is the worst case rather than the ordinary one. On a minute whose midpoint prints are small the same error moves almost nothing, and nothing on this page tells you which kind of minute you are usually looking at. That is the second half of problem 3, and it is the number that decides whether any of this matters to you.

The tape is the only record in which a transaction appears as itself. Three of its four columns were reported; the fourth was worked out on your behalf, and it is right about four times in five.

Problems

1. Sign these. The quote is 20.10 / 20.12 throughout, and the prints in order are 20.12 × 300, 20.10 × 800, 20.11 × 500, 20.12 × 400. Classify each, then give the signed total. Which row did you have to guess at, and what would the total be if you guessed the other way?
2. Move the error. A minute contains 8,000 shares and a signed total of +1,000. What is the smallest single print that could be reclassified to make that total negative? State the rule you used, not just the number.
3. Your own thresholds. Open the tape on your instrument and record every print for ten minutes: time, price, size. Then answer two questions from your own list. What size is the 90th percentile print, and what fraction of prints executed strictly between the bid and the ask? The first is what “large” means for you; the second is how much of your delta is a guess.

Sources. Charles Lee and Mark Ready, “Inferring Trade Direction from Intraday Data” (Journal of Finance 46, 1991), the rule described above. Katrina Ellis, Roni Michaely and Maureen O’Hara, “The Accuracy of Trade Classification Rules” (Journal of Financial and Quantitative Analysis 35, 2000), which measured it against records where the initiator was known and found it worst inside the quotes. Joel Hasbrouck, Empirical Market Microstructure (Oxford, 2007), on why signing a trade is an estimation problem rather than a lookup.

You have the record and you know what its last column really is. The next lesson adds it up, and the sum turns out to be balanced by construction: every contract was bought by somebody and sold by somebody, so none of it is buying volume. The one number that genuinely is one-sided has to be built from the column whose error you just measured.

Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.