Price Formation, Volatility and Time

A price is produced by a mechanism. Once you have watched that mechanism work, several tempting habits of chart interpretation stop being tempting, and one idea arrives that you will use for the rest of the course: no move can be judged without knowing the scale it happened on.

By the end of this lesson you should be able to describe how an order becomes a trade, explain why the last price is not a valuation, define volatility as something other than “the market going down”, say what volatility clustering is and why it changes how stops and position sizes are designed, and compare two moves in different instruments in a way that is actually meaningful.

How a trade actually happens

Picture the order book from the previous lesson: buy orders stacked below, sell orders stacked above, each at a price with a quantity attached. Every incoming order is one of two kinds.

A passive order asks for a price that no one is currently offering. It does not trade. It joins the book and waits, and if its price is better than anything already there, it becomes the new best bid or best ask — the quote has changed without a single trade taking place.

An aggressive order asks for a price that someone is already offering. It crosses, and a trade happens immediately against the resting orders, taken in the venue’s priority order — normally best price first, and at a given price the order that arrived earliest.

One order, one price

1. 1An order arrivesSide, quantity and the worst price its sender will accept
2. 2It is compared with the bookIs there anything resting on the opposite side at an acceptable price?
3. 3It rests, or it crossesIf nothing matches it joins the book and may improve the quote. If something matches, it trades
4. 4A trade printsPrice and quantity are published. This is the number that reaches your chart
5. 5The book is redrawnThe consumed orders are gone. The best bid and ask may now be different
6. 6The next order arrivesInto a book that the previous order changed

A price series is the trace left by this loop repeating, thousands of times a day.

Continuous matching is not the only mechanism in use. Many exchanges begin and end the session with an auction: orders accumulate for a period without trading, and then a single price is chosen — broadly, the price that allows the greatest quantity to be matched — and everything that can trade at that price does so at once. The details differ by exchange and are worth checking for the market you actually trade.

The consequence is worth pausing on, because it affects almost every rule in this course. The Close on a daily bar is, on many exchanges, an auction price: produced by a different mechanism, at a moment when a large share of the day’s volume is concentrated, from orders submitted by participants who often have no choice about trading then. It is also the price most systematic rules reference. That is not an argument against using it; it is an argument for knowing what it is.

Last price versus fair value

The last traded price is the price at which the most eager remaining buyer and the most eager remaining seller agreed, for whatever quantity happened to be involved. That quantity may be a hundred shares.

Three things follow, and they demolish a lot of loose talk:

• It is a marginal price, not an average opinion. It reflects the two participants who were most willing to transact at that instant, not the view of everyone holding the asset.
• It is not the price at which size can trade. Lesson 3 showed why. In a thin instrument the gap can be enormous.
• It is not a valuation. “Fair value” is the output of a model — discounted cash flows, a multiple, a relationship to some other instrument. Feed two competent analysts the same accounts and you get two different numbers, both defensible. Price is not a model output; it is an observation.

Technical analysis works with the observation. That is a genuine advantage — the observation is objective, timestamped and available for thousands of instruments — and a genuine limitation, because an observation of a transaction tells you nothing about the reasons behind it. Lesson 6 returns to the limitation.

Volatility is dispersion, not direction

In everyday speech “volatile” often means “falling”. In this course it means something narrower and more useful: volatility is the dispersion of returns over a period. It says how widely spread the outcomes were. It says nothing about which way they pointed.

A market can be extraordinarily volatile and finish the month exactly where it started. A market can drift down steadily for a year at a fraction of a per cent a day and be, by this definition, quiet.

There are several ways to measure it, and the course will use more than one:

• The standard deviation of returns over a window — the standard statistical measure of dispersion.
• The average daily range, high minus low, which measures how much ground price covered within each bar.
• Average true range, which is the daily range adjusted to include overnight gaps. Part 6 builds it properly, and Part 34 uses it for position sizing.

Units matter more than the choice of measure. A daily range of 1.50 means nothing until you know whether the instrument trades at 15 or at 1,500. Volatility should almost always be expressed as a fraction of price, or as a ratio to some other quantity, so that two instruments can be compared at all.

One convention deserves a warning. Dispersion measured over one period is often rescaled to another by multiplying by the square root of the number of periods, so a daily figure becomes an annual one. That scaling assumes returns are independent from one period to the next and drawn from the same distribution throughout. Market data does not satisfy those assumptions exactly — the next section is about one specific way in which it does not. The scaling is a useful convention for putting numbers on a common footing. It is not a description of how markets behave.

Volatility clusters

?Reality check

The claim. Large moves tend to be followed by large moves, and quiet periods by quiet periods, irrespective of direction. Turbulence arrives in stretches. This is usually called volatility clustering, and it is reported across a great many instruments and periods.

How you would test it. Compute a volatility estimate over a rolling window, then measure whether today’s value carries information about the next window’s — and compare that against how well today’s return carries information about the next return, on the same universe and period. Unlike most claims you will meet in technical analysis, this one is cheap to check, and Part 6 builds the tools for it. The course does not ask you to take it on trust.

If it holds on your data, three consequences shape the design of everything later in the course:

1. Recent volatility carries information about near-term volatility. Where this has been measured it appears to do so more reliably than recent return carries information about near-term return. That asymmetry, if it holds in your own testing, is why risk models tend to rest on firmer ground than return models.
2. A fixed percentage stop means different things at different times. A three per cent stop is distant in a calm month and is likely to be hit by ordinary noise in a turbulent one. Stops and targets scaled to current volatility adapt automatically; fixed ones silently change their meaning.
3. Regimes change, and the transition is where fixed parameters break. A rule tuned in a quiet period often behaves quite differently when dispersion doubles. Parts 30 and 31 examine what this does to optimised parameters, and it is the main reason the course prefers a broad plateau of acceptable settings to a single best value.

Time is the third axis

Price and volume are two axes. Time is the third, and it is the one beginners most often treat as decoration.

The same move over different spans is a different event. Eight per cent in a day and eight per cent over three months describe entirely different situations, and any rule that treats them alike is discarding information it had for free.

Bars impose a clock the market does not keep. Trading is not spread evenly through the session: in most equity markets activity concentrates around the open and the close and thins in the middle, although the shape differs by market and is worth confirming on your own data. Overnight, hours of news accumulate with no trading at all and arrive as a single jump. A one-hour bar at midday and a one-hour bar at the open are not comparable units of anything. Part 2 covers how bars are assembled and Part 20 covers what happens when sessions and time zones are misunderstood.

Your holding period is a decision with consequences. It determines which costs dominate, as the previous lesson showed. It determines how much of your result is exposure to the market as a whole rather than to your rule. And it determines how much evidence you can ever gather: a rule holding positions for three months yields roughly four non-overlapping observations per symbol per year, so a decade of history on fifty symbols gives you a couple of thousand observations at most, and far fewer independent ones once you notice that the symbols move together. Part 30 treats insufficient evidence as a first-class error, and this is where it starts.

The same move in two different instruments

Here is the idea this lesson exists to deliver. Two instruments both rise two per cent today.

	Instrument A	Instrument B
Typical daily range, as a fraction of price	0.8 per cent	3.5 per cent
Today’s move	plus 2.0 per cent	plus 2.0 per cent
Move divided by typical range	2.5	0.6
Reasonable reading	Unusual; worth a look	Ordinary; well inside normal daily variation

The raw percentages are identical. Measured against each instrument’s own behaviour they are not remotely comparable. Expressing a move in units of the instrument’s own volatility is called volatility normalisation, and it appears throughout the rest of the course: in screening, where it lets you rank instruments against each other honestly (Part 12); in cross-sectional ranking (Part 13); in stop placement and position sizing (Part 34); and in any comparison between periods, because the same instrument’s typical range changes over time.

The identical logic applies across time for a single instrument. A two per cent day during a calm stretch and a two per cent day during a turbulent one are different events, and a rule that fires on “a two per cent day” will fire constantly in one regime and almost never in the other. That is not a subtle statistical point; it is the difference between a rule that trades sixty times a year and one that trades six.

✦Tip

Whenever you compare two instruments, two periods or two indicator readings, ask what you normalised by. The three usual answers are: nothing, price, or the instrument’s own volatility. “Nothing” is almost never right, “price” is often adequate, and “volatility” is the one that makes different instruments genuinely comparable.

Recap

You can now describe how an order becomes a printed price, and why the closing price on many exchanges is produced by a mechanism different from the rest of the session. You can explain why the last price is a marginal transaction rather than a valuation. You have a working definition of volatility as dispersion, several ways to measure it, and a caution about rescaling it between periods. You know that volatility clusters, and what that implies for stops, sizing and parameter stability. And you have the habit that matters most from this lesson: before judging a move, establish the scale it happened on.

The next lesson steps outside the mechanics to ask what technical analysis is actually claiming, and how that claim differs from the two other ways of studying the same market.

Check your understanding

Question 1. An instrument finished the month at exactly the price it started, but its daily moves were three times larger than usual throughout. What happened to its volatility?

• It fell, because the net change was zero
• It rose, because volatility measures the dispersion of returns rather than their direction
• It was unchanged, because the start and end prices match
• Volatility cannot be measured over a month

Show the answer and why

Answer: It rose, because volatility measures the dispersion of returns rather than their direction

Dispersion and direction are independent. A series can be wildly dispersed and end where it began. Conflating the two is the most common misuse of the word, and it leads people to expect volatility measures to tell them which way the market is going.

Question 2. Instrument A typically moves about 0.8 per cent in a day; instrument B typically moves about 3.5 per cent. Both rose 2 per cent today. Which comparison is the most informative?

• They are equivalent, since both rose 2 per cent
• B is stronger, because it is the more volatile instrument
• A moved about 2.5 times its typical range while B moved about 0.6 of its own, so the move is far more unusual in A
• Neither move can be interpreted without knowing the volume

Show the answer and why

Answer: A moved about 2.5 times its typical range while B moved about 0.6 of its own, so the move is far more unusual in A

Normalising by each instrument’s own typical range puts the two on a common footing. This is the same reasoning that later underlies volatility-based stops and position sizing: the unit of measurement should belong to the instrument, not to the observer.

Question 3. On many exchanges, where does the closing price on a daily bar come from?

• The midpoint of the final quote of the session
• An average of the last hour of trading
• A closing auction, in which accumulated orders are matched at a single price
• The exchange’s own valuation of the instrument

Show the answer and why

Answer: A closing auction, in which accumulated orders are matched at a single price

Continuous matching often stops before the end of the session and a closing auction sets a single price for a large concentration of orders. Since most systematic rules reference the close, it is worth knowing that this particular price is produced differently from the rest of the day.

Question 4. True or false: because volatility clusters, a fixed three per cent stop-loss changes its practical meaning as the market moves between calm and turbulent stretches.

• True
• False

Show the answer and why

Answer: True

True. Turbulent and calm periods arrive in stretches, so a fixed percentage stop sits far away during quiet spells and is reached by ordinary movement during turbulent ones. The number stays the same while its meaning changes. A stop expressed in units of current volatility holds its meaning better, which is the approach Part 34 develops.

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