Volume Profile

The last lesson took one number off a distribution and watched it slide 9.5 ticks across a 15-tick day. A value area takes an interval instead and moves 3.5 ticks — and the version your platform does not ship moves one. That is the good news, and it comes with two things nobody mentions. The box labelled 70 per cent holds anywhere between 70 and 84 per cent of the day depending on how you binned it, and widening the window from one session to two puts half of the heavier session’s value area outside value altogether.

Prerequisites: Lesson 29, which is where the session below comes from and where the point of control stopped being a price, and lesson 17, because a value area is worth whatever it moves p by and nothing else.

The same session, two constructions, four settings

This is the session from lesson 29, unchanged: 9,160 contracts across sixteen prices from 100.00 to 100.15, with a broad heavy region through the upper half and one outsized print of 1,080 contracts down at 100.03. Seventy per cent of 9,160 is 6,412 contracts, and that is the bar both constructions have to clear.

Bin width	Standard value area	What it holds	Narrowest 70% stretch	What it holds
1 tick	100.02 to 100.12	72.5%	100.06 to 100.15	70.3%
2 ticks, grid on the even cent	100.06 to 100.15	70.3%	100.06 to 100.15	70.3%
2 ticks, grid shifted one cent	100.03 to 100.14	83.8%	100.05 to 100.15	73.6%
4 ticks	100.04 to 100.15	77.7%	100.04 to 100.15	77.7%

Start with the good news, because it is real and it is the reason this lesson exists. Take the midpoint of each answer. The standard value area’s midpoint moves 3.5 ticks across the four settings; the narrowest-stretch version moves one tick. Lesson 29 measured the point of control moving 9.5 ticks on this same session. So the three summaries line up in a clean order — 9.5 ticks, 3.5 ticks, one tick — and the order is not a coincidence. The more of the distribution a summary is made from, the less room the binning has to move it. A mode is built from one bucket, a value area from most of them.

Now the first thing nobody mentions. Read down the two “what it holds” columns. The standard value area is asked for 70 per cent and delivers 70.3, then 70.3, then 83.8, then 77.7. On the third setting, a box labelled seventy per cent contains almost eighty-four. It cannot help it: it grows a row at a time from the mode, and the last row it adds can overshoot the target by as much as that row is large. Nothing warns you, and the box is not drawn any wider than the honest one.

The second thing is where the two constructions disagree. At one tick the standard method returns 100.02 to 100.12 and the narrowest stretch returns 100.06 to 100.15. Those are both defensible-looking boxes. They overlap across seven ticks and disagree at both ends: the standard one reaches four ticks lower and stops three ticks earlier. The reason is entirely mechanical. The standard method starts at 100.03, because that is where the lone 1,080-contract print put the mode, and everything it does afterwards is measured outward from a price the market visited once in size. The narrowest stretch never looks at the mode, so it never gets anchored down there, and it lands on the busy upper half where the volume actually sits.

That is the practical finding of the first half. If you are going to use a value area, compute the narrowest one. It is the same data and the same single pass, and on this session it is both tighter and steadier.

What the window does, which is worse

Everything above held the window fixed at one session and varied the bin. Now do the opposite. Here is the same session A, a second session B that traded 7,880 contracts with its weight low in the range instead of high, and the two of them profiled together as one two-day window. All three value areas are the narrowest-stretch kind, so the construction is not what is changing. Session B is built the other way up: heavy at the bottom of the same sixteen prices, thinning through the middle, and lifting a little into the close. Its sixteen volumes, from 100.00 up to 100.15, are these.

940 · 960 · 980 · 860 · 740 · 620 · 500 · 360 · 200 · 140 · 160 · 160 · 200 · 280 · 360 · 420

Window	Volume	Point of control	Value area	Midpoint
Session A alone	9,160	100.03	100.06 to 100.15	100.105
Session B alone	7,880	100.02	100.00 to 100.06	100.03
A and B together	17,040	100.03	100.00 to 100.10	100.05

Session A is the heavier of the two by 1,280 contracts. Its value area runs from 100.06 to 100.15. Put the two days together and the value area runs from 100.00 to 100.10 — which means 100.11, 100.12, 100.13, 100.14 and 100.15 are out. Five of the ten prices that were in value on the bigger day are out of value over the two days, and the five that dropped out include 100.12, which was the busiest price anywhere in that session above the lone print at 100.03.

It is not a rounding artefact and it is not that B outweighed A, because B did not. It is that B’s mass sits low, and a 70 per cent window over the pair has to reach down to cover it, which means letting go of the top. Both statements are true at once: 100.13 was in value yesterday, and 100.13 is not in value this week. There is no contradiction to resolve, because “in value” was never a property of the price. It is a property of the price together with the window you drew around it, in exactly the way the point of control was a property of the price together with the bin.

Which sets the standard for using any of this. A value area quoted without its window and its bin width is not a level, it is an anecdote — and if you take one from someone else’s chart, those are the two questions to ask before anything else.

What this does not settle

That the narrowest stretch is therefore correct and the standard one is wrong. Both are conventions for summarising a distribution, and neither is a fact about the market. The narrowest is better on the two properties measured here — it is tighter and it moves less — and this lesson tested those two properties on one session. If it matters to you, run both on thirty of your own and see whether the ordering holds; the first problem below is that experiment.

That 70 per cent is the right share. It is a convention borrowed from a distribution volume profiles do not follow, and this lesson has not improved on it. What it has done is make the arbitrariness visible, which is different from removing it. If you have a reason to prefer 60 per cent or 80 per cent the arithmetic does not change at all, and neither does anything in this lesson.

That price respects the edges of a value area. That is the claim the whole construction is used for, this lesson has not tested it, and lesson 29 left the same debt on high- and low-volume nodes. Two lessons have now built the machinery and neither has produced the base rate that would make it a reason to trade. That is deliberate and it is not comfortable: the third problem is how you get it, and until you have it a value area is a well-constructed description of what already happened.

That the two-day finding says a longer window is worse. It says a longer window answers a different question, and both answers were correct for what they were asked. The mistake is not choosing the wrong window; it is quoting the answer without the question, which is what “the value area is 100.06 to 100.15” does.

That any of this tells you where the volume is going to be. Everything in these two lessons is a description of volume that has already traded. The auction has one more structural thing to show you before that changes, and it is the piece both lessons kept deferring: what happens when the size that mattered was never displayed at all. Lesson 31 takes that up.

A point of control is one bucket pretending to be a level. A value area is most of the distribution admitting it is a range — which is honest, and still not a property of the market.

Problems

1. Run both constructions on thirty of your own sessions. Your platform draws the standard value area; the narrowest stretch you compute yourself from the same profile, in one pass over the rows. For each session record two things: how far apart the two midpoints land, and what share of the volume the standard box actually contained. The second number is the one to watch, because on this session it ranged from 70.3 to 83.8 per cent and you have no way of knowing where your instrument sits without counting. If the two constructions agree on your instrument to within a tick, use whichever is in front of you and stop thinking about it.
2. Ask both questions of a value area before you use it. Take a value area you did not build — from a service, a chatroom, anywhere — and establish two facts about it: the window it was computed over, and the row height. If you cannot establish both, you have learned that the number is unusable, which is worth more than the number. Do this five times and keep the tally of how often both answers were actually available.
3. Get the base rate two lessons have now asked for. Over thirty consecutive sessions, note the previous session’s value area high and low. Then, in the current session, record what happened the first time price touched each edge from outside: did it turn away within some fixed distance you set in advance, or did it carry through? Two counts come out of this and the pair of them is the whole question. Set the fixed distance before you start looking, because setting it afterwards is how you get any answer you like — and note that thirty touches is enough to see a large effect and nowhere near enough to see a small one.

Where the problems above ask you to go and count something, How to Collect a Base Rate is the appendix that says how: define the observation, fix the criterion before you look, take consecutive cases rather than the memorable ones, and count into four cells.

Sources. J. Peter Steidlmayer and Kevin Koy, Markets and Market Logic (Porcupine Press, 1986), for the value area itself, for the expansion-from-the-point-of-control rule that platforms still implement, and for the 70 per cent convention and its origin in one standard deviation of a normal distribution. Rob J. Hyndman, “Computing and Graphing Highest Density Regions” (The American Statistician, 1996), for the narrowest-interval construction and for the argument that matters here: when a distribution is not symmetric, the shortest interval holding a given share and the interval you get by growing outward from the peak are different regions, and it is the shortest one that answers the question people think they are asking. Torben G. Andersen, Tim Bollerslev, Francis X. Diebold and Heiko Ebens, “The Distribution of Realized Stock Return Volatility” (Journal of Financial Economics, 2001), for the measured non-normality of intraday distributions, which is why a 70 per cent borrowed from the normal is a convention rather than a result.

Four lessons have now been spent on things that can be seen: a footprint, a count, a mode, an interval. Lesson 31 goes back to what cannot, because both of the last two kept deferring the same case — the size that was there and never appeared on any of these pictures, and what the auction leaves behind when it fills against something nobody could see.

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