Volume and Delta
Volume counts contracts, and every contract was bought by somebody and sold by somebody, so none of it is buying volume. Delta counts something that genuinely is one-sided: which side was unwilling to wait. On the bar worked below, a platform reports a delta of +15 per cent, and what is actually established is a buy share somewhere between 50.0 and 62.5 per cent — the bottom of which is no imbalance at all.
Prerequisites: Lesson 3, for the fact that a fill has exactly one counterparty, and lesson 7, for where the sign on a print comes from and how often it is wrong.
Start by ruling out the thing everybody says. “Heavy buying volume” is not a description of anything, because there is no such quantity.
Volume is already balanced
A contract does not change hands unless two people are on it. If forty thousand traded in a bar, then forty thousand were bought and forty thousand were sold, in the same bar, by definition. That is not a near-enough approximation or a quirk of reporting: it is what a transaction is, and lesson 3 is where it came from.
So a volume bar has exactly one thing to say — how much changed hands — and it says it about both sides at once. Two bars with the same height can be anything at all with respect to each other. Whatever distinguishes them is not in the count.
The asymmetry that does exist
Something about a transaction genuinely is one-sided, and lesson 7 named it. One party had a resting order and waited; the other crossed the spread and took it. The volume was shared; the impatience was not.
Delta counts the impatient side and nothing else. Each contract is signed +1 if the buyer crossed and −1 if the seller did — so a 500-lot print at the ask contributes +500, not +1 — and the bar’s delta is the sum. A bar that closes green on negative delta is therefore not a contradiction: it means price finished higher while the aggressive orders were mostly sells, and somebody patient was on the other side of them.
Two numbers, one fact
Because both sides sum to the volume, delta and the buy/sell split are the same information written twice, and the conversion is arithmetic rather than a rule of thumb. Write V for the bar’s volume and D for its delta:
| What you want | From what the chart prints |
|---|---|
| Buy volume | (V + D) ÷ 2 |
| Sell volume | (V − D) ÷ 2 |
| Delta as a share | D ÷ V |
| Buy share | (1 + D ÷ V) ÷ 2 |
The first two lines are worth checking rather than trusting, because the rest follows from them: add them and you get V back, subtract them and you get D. Every platform prints at least one of these numbers, so you always have all of them.
The share matters more than the raw figure. A delta of 6,000 means nothing until you know whether the bar traded ten thousand or ten million, and the share is the version that compares across instruments and across days.
Carrying it across bars
Delta on one bar is a snapshot. Add each bar’s delta to a running total instead of resetting it, and you have cumulative delta — the same quantity carried across a session rather than started again every five minutes. It deserves its own name because it is what lesson 34 sets against price when the two disagree, and because almost every platform plots it as a line.
A line invites more trust than the number it is made of, so bound it now. Every term in that sum carries the classification error lesson 7 measured, and adding them up does not average the error away. The part that is genuinely random grows with the square root of the number of bars, which is slow. The part that is not — the systematic misreading of prints that execute between the quotes, which is exactly where the rule is weakest — grows in proportion to the number of bars, which is not slow at all. So a cumulative delta line over a whole session is a softer measurement than any single bar in it, not a firmer one, and it is softest in precisely the conditions that widen the spread and push more trading between the quotes.
One bar, and what is actually known about it
A bar trades 40,000 contracts and your platform reports a delta of +6,000. Run the table. Buy volume is (40,000 + 6,000) ÷ 2 = 23,000, sell volume is 17,000, and those add back to 40,000. As a share the delta is 6,000 ÷ 40,000, or +15 per cent, which is a buy share of 57.5 per cent — and 57.5 per cent of 40,000 is the 23,000 you already have.
Now carry the error bar from lesson 7. Every one of those signs was inferred, and the ones inferred by tick test rather than by the quote are the shaky ones. Say 5,000 of this bar’s volume executed between the quotes, and the rule called 3,000 of it buys and 2,000 of it sells.
Reclassifying a print moves delta by twice its size. So if all 3,000 of those “buys” were really sells, the delta is 6,000 − 6,000 = 0. If all 2,000 of those “sells” were really buys, it is 6,000 + 4,000 = 10,000. The true delta is somewhere in that interval and the chart cannot narrow it: a range 10,000 wide, which is twice the volume the quote could not decide.
Read that as shares and the headline changes character. The bar was reported at +15 per cent; what is actually established is somewhere between zero and +25 per cent, a buy share between 50.0 per cent and 62.5 per cent. The bottom of that range is a bar with no imbalance in it at all. The number is not wrong — it is just narrower on the screen than it is in reality, and how much narrower is a property of your instrument that you measured in lesson 7.
What this does not settle
That delta is institutional buying. Both sides of every contract are somebody, and crossing the spread is a statement about patience, not about size or sophistication: a retail market order and a pension fund’s sweep are signed identically. Delta measures who was unwilling to wait. It says nothing about who they were.
Nor does it tell you what happens next, and the interesting case is the one where price and delta disagree. A bar with strongly positive delta that fails to rise means somebody patient absorbed all of it — that is lesson 28, and it is a different claim from this one. Where in the bar’s range the trading happened is lesson 29, and running the sum across many bars, which accumulates this error along with the signal, is lesson 34.
And it does not give you a threshold. Whether +15 per cent is a lot depends entirely on what your instrument normally does, and no figure printed here transfers to it. That is a measurement, and problem 3 is how you take it.
Nor is delta one thing across venues. Where the exchange publishes an aggressor flag, as CME does and as most crypto venues do, delta is a measurement and the interval above collapses to nothing. On the consolidated equities tape there is no flag, so it is an estimate all the way down. This lesson has been using one word for two quantities, and which one you hold depends on where you trade rather than on what your platform calls it.
And the claim about cumulative delta was asserted rather than shown. Random error growing with the square root of the number of bars, while systematic error grows in proportion to it, is standard and it is not measured anywhere on this page. So the horizon at which the systematic part takes over is unknown here, and it is the only thing that decides whether a session-long line is worth looking at or is mostly the accumulated bias of one bad rule. Nothing you can read off a chart will tell you, and nobody plotting the line will mention it.
Volume is the one number in this course that is exactly balanced by construction. Delta is the imbalance you have to go looking for, and it arrives already estimated.
Problems
- Convert both ways. A bar trades 24,000 contracts and the platform reports a delta of −4,800. Give the buy volume, the sell volume, the delta as a share, and the sell share. Then check your first two answers against the 24,000.
- Put the bar on it. Of that same 24,000, suppose 3,000 executed between the quotes, classified 1,800 buys and 1,200 sells. What is the widest range the true delta could take? State the friendlier end of it as a sell share, and say whether it would change what you did.
- Your own instrument. Take the fraction of prints you measured in lesson 7 that executed between the bid and the ask. Twice that fraction, in percentage points, is roughly how wide your delta share is before you interpret it — the bar above had an eighth of its volume between the quotes and a range 25 points wide. Then find one bar this week whose reported delta share is smaller than your own width, and say what you would have concluded from it and what you now can.
Sources. Albert Kyle, “Continuous Auctions and Insider Trading” (Econometrica 53, 1985), where signed order flow is the object the whole model is built on. Tarun Chordia, Richard Roll and Avanidhar Subrahmanyam, “Order Imbalance, Liquidity, and Market Returns” (Journal of Financial Economics 65, 2002), the empirical version of the same quantity measured across a market. Joel Hasbrouck, Empirical Market Microstructure (Oxford, 2007), on what signed flow does and does not support.
You can now say who was in a hurry, and how confidently. The next lesson asks who is in this book at all, and finds four reasons to be in one, only four, with the reason predicting the behaviour far better than the size does.
Time and Sales
Where the sign on each print comes from, and how often it is wrong.
Read Lesson →Absorption and Exhaustion
What it means when the delta and the price disagree.
Read Lesson →Educational only. Trading involves substantial risk of loss. Not financial advice. Past performance does not guarantee future results.
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