Guide · Indicators and volatility · Updated 2026-09-20

Band width is a rolling standard deviation, so a narrow band describes the fortnight that just ended rather than the one about to start

Every number here was computed from the exchange's own daily index close files rather than quoted, on 3,385 sessions from 2013-01-01 to 2026-09-18, with the definitions stated so the work can be redone. The claim under test is unusually easy to check and unusually rarely checked, which is the reason this page exists.

The band is a rolling standard deviation, and the width is that number times four

Take the last 20 closes. Compute their mean, which is the middle band, and their standard deviation. Put a line two standard deviations above the mean and another two below. The distance between those two lines is four standard deviations of the closes in that window. Divide by the middle band and you have a width expressed as a percentage of the price level, comparable across instruments and across price levels.

That is the whole construction, and it settles what the indicator can be. Every input is a close that has already printed. No term in it refers to any session after the one being measured. A number built entirely from the past can describe the past accurately and can describe the present as the tail end of the past. It cannot contain information about the future that is not already in the prices it was built from.

The rescaling is not loose. For a series with no drift, the expected variance of 20 consecutive random walk values about their own mean is the daily return variance multiplied by (n squared minus one) over six n. Take the square root, multiply by four, and the expected band width is 7.29 times the daily return standard deviation. That is a closed form, not a fit, and this build checks it against a simulation of twenty thousand driftless windows before writing anything.

Two details in that table matter more than the headline constant. The first is that the correlation between band width and trailing volatility is high but not one: 0.595 on ranks, 0.762 ordinary. The gap is drift. A window in which price moved steadily in one direction has a large standard deviation of price even if every individual day was calm, so the band widens on a quiet trend. That is why band width is not quite a volatility measure: it is a dispersion measure of price, and a trend is dispersion.

The second is the size of that contamination. Sorting windows by net displacement in units of their own trailing volatility, the quietest fifth produced a band 5.45 times daily volatility, close to the driftless constant, and the most displaced fifth produced 11.19 times, 105 per cent wider on identical daily volatility. So a narrow band is a joint statement: the last 20 sessions were calm and they went nowhere. A page that describes the indicator as a volatility measure has left out half of what makes it read low.

The distribution, and why a quoted threshold does not travel

Before any test, the reading has to be placed in its own distribution. Over the labelled period the broad index's band width had a median of 5.14 per cent of the middle band, a tenth percentile of 3.05 and a ninetieth percentile of 9.95. The record's extremes were 1.11 on 2017-06-22 and 54.5 on 2020-03-25, a factor of nearly fifty between the quietest and the most violent fortnight in the record.

The label used throughout this page is deliberately causal. Band width at a session is compared against the tenth percentile of every earlier reading, from an expanding record, after a burn in of 750 readings. That is why labelling starts at 2016-02-25 although the data starts at 2013-01-01. It also produces an honest side effect worth stating: because band width fell across the decade, an expanding threshold estimated on wider history sits above the realised tenth percentile, so 15.9 per cent of labelled sessions land in the narrowest decile rather than 10 per cent. A backward looking threshold over labels a falling distribution. Fitting the threshold to the whole period would fix that and would also be a number nobody could have held in 2016.

This is where most published calibration goes stale without anyone noticing. A figure of 4.50 per cent, quoted as the narrow tenth percentile, sat at the 28th percentile of the 2020 to 2024 window and at the 51st percentile of the last 250 sessions. It is no longer a narrow reading; it is the middle of the distribution. The index's own band width on 2026-09-18 was 6.45, the 83rd percentile of the trailing year, which is wide rather than narrow. Any page carrying a hard coded threshold is describing a distribution that has since moved underneath it.

The threshold does not travel across series either, and the spread is larger than the spread across time. On the 13 indices tested the tenth percentile of band width ran from 2.90 on the consumer staples index to 6.29 on the public sector bank index. A reading of 4 per cent is a wide band on one and an unreachable compression on another. The only defensible threshold is a percentile of the series' own recent history, which is a way of saying the indicator has no absolute scale.

The test: what actually followed the narrowest decile

Here is the comparison the claim requires and almost never gets. For every labelled session, record the band width decile, then measure annualised realised volatility over the 20 sessions that follow. The conditional distribution goes next to the unconditional one. If a narrow band precedes larger moves, the conditional distribution sits to the right.

The result is not marginal and it is not ambiguous. At every horizon from 5 to 60 sessions the median realised volatility following a squeeze was below the unconditional median, by 16 to 20 per cent. The share of squeeze sessions followed by top decile volatility was 0.2 per cent at the 20 session horizon, against a base rate of 10 per cent by construction. The reading that did precede top decile volatility was the widest decile, at 31.7 per cent.

One caution on that starkness before it is over read. Those 405 conditional windows come from only 47 episodes and overlap heavily, so the honest sample is the episode count. Taking one window per episode, top decile volatility followed 1 of the 43 episodes against an expected 4.3 at the base rate, and 17 of 43 beat the unconditional median against an expected 22. Against independent draws at those base rates, seeing that few or fewer has probability 6 per cent and 11.1 per cent respectively. So at the episode level the lean toward calmer volatility is suggestive, not conclusive: probabilities of that size are not a result to build on. What is settled is that the data does not point the way the folklore says: a squeeze was followed by top decile volatility in 1 of 43 episodes, fewer than chance alone would give.

The definition is not doing the work. An expanding percentile, a trailing 250 session percentile and a band built on return standard deviation rather than price standard deviation all produce the same ordering, with the ratio between 0.78 and 0.82. The build refuses to write the page if any of the three flips sign.

There is no squeeze state, only a ranking of how quiet the fortnight was

Comparing one decile against the whole leaves open the possibility of a threshold: perhaps something changes at the narrow extreme. The decile ladder answers that directly.

Read the forward volatility column down. It rises from 9.39 at the narrow end to 16.80 at the wide end, near monotonically, with one inversion in the middle of the range that 2,616 sessions cannot resolve. There is no step and no discontinuity. The band width decile is a ranking of how much the instrument has been moving, and that ranking persists into the next fortnight. Every apparent property of a squeeze is the same property that decile 1 has slightly less of and decile 2 slightly less again.

The second last column is the only part of the folklore that survives, and it survives in a form that removes its usefulness. From the narrowest decile the median ratio of forward to trailing volatility was 1.099, and forward volatility exceeded trailing volatility on 62 per cent of those sessions. So yes, volatility rose. It rose from a median trailing 8.91 to a median forward 9.39, which is a rise to a level still well below the unconditional median of 11.51. Meanwhile from the widest decile the same ratio was 0.802, a fall. Volatility mean reverts from both ends, which is a property of volatility, not a property of the squeeze. Saying a squeeze precedes expansion is saying a below average reading tends to be followed by a less below average one, which is true of every mean reverting series and carries no information about the size of the next move.

Volatility clustering is the honest explanation

Low volatility is followed by low volatility more often than not. That single fact accounts for everything measured above. On this record a squeeze session was followed by another squeeze session 88.7 per cent of the time. The 417 squeeze sessions form only 47 distinct episodes over 10.6 years, median 7 sessions long, longest 30. 66 per cent of episodes ran at least five sessions and 23 per cent at least fifteen.

So a narrow band is mostly the statement that today is calm, plus the observation that calm persists. That is genuinely useful information, and it is present tense. It tells you the dispersion your positions are currently exposed to and that the estimate will probably still be approximately right in a fortnight. It is the opposite of a signal that something is about to change.

Clustering also sets the sample size for every claim on this page, which is why the episode count keeps appearing next to the session count. The same arithmetic applies to any regime conditional result: a label that repeats nearly nine times in ten turns thousands of sessions into a few dozen independent observations, and a conditional statement has to survive the smaller number.

The one sense in which a squeeze does precede a bigger move

There is a scale free version of the claim that measures better, and reporting it is what separates a test from a debunking. Instead of asking how volatile the next 20 sessions were in per cent, ask how large the largest move was in units of the trailing volatility the squeeze itself displayed. A squeeze with trailing volatility of 8 per cent annualised implies a 20 session standard deviation; divide the largest actual excursion by it.

Measured that way, the largest excursion over the following 20 sessions ran at a median of 1.27 trailing standard deviations after a squeeze against 1.14 unconditionally, about 11 per cent larger, and exceeded two trailing standard deviations 17.0 per cent of the time against 12.6 per cent. From the widest decile the same figures were 0.90 and 5.0 per cent, well below unconditional. That is the mean reversion again, now visible as a tail statistic.

Then convert it back into the unit a position is exposed to. In per cent of the index, the median largest excursion over the 20 sessions after a squeeze was 3.19 per cent against 3.81 per cent unconditionally and 5.56 per cent after a wide band. The net 20 session move exceeded 5 per cent either way after 2 of 43 episodes, 5 per cent, against 20.9 per cent of all labelled sessions. Median absolute move 1.93 per cent against 2.64 per cent.

Both statements are true at once, and only one of them is the claim people act on. Relative to its own compressed volatility, the move after a squeeze was about a tenth larger than typical. In per cent, it was smaller. A position sized in per cent, with a stop placed in per cent, experiences the second number. This is the same unit confusion that makes a standard deviation look like a bound rather than a scale.

The base rate nobody quotes

The commonest way the claim is stated is as a frequency: a squeeze is followed by an expansion within some window, some stated percentage of the time. That sentence is unfalsifiable until two things are pinned down, and generic pages pin down neither. What counts as an expansion, and what is the frequency from a session picked at random?

Take a definite version. Count a session as expanded when band width reaches the period median of 5.14, and ask how long that takes from three different starting states.

From a squeeze, band width reached the median within 20 sessions 48.7 per cent of the time, median wait 21 sessions. Quoted alone that reads like confirmation: roughly half of all squeezes resolve into a normal band inside a month. Now the comparison. From a session drawn at random, the same thing happened 78.1 per cent of the time with a median wait of 2 sessions. From the widest decile, 100.0 per cent.

The squeeze is the state from which a stated expansion was least likely and took longest. Reaching the ninetieth percentile width within 20 sessions happened from 3.4 per cent of squeeze sessions against 24.2 per cent of all sessions. Every one of those conditional frequencies is true, quotable, and useless without its unconditional twin. Choosing the comparison is most of the work in any claim of this shape, and a claim published without one has not been tested.

Direction is the part that does not survive contact with the data

Suppose the magnitude claim were sound. It would still leave the question a position has to answer. The usual formulation concedes the point half way, saying a squeeze predicts magnitude rather than direction, and then quietly attaches a directional bias anyway.

Tested at the episode level, on the last session of each of the 43 scorable episodes: the following 20 session move was positive after 24, which is 55.8 per cent plus or minus 14.8. The unconditional share of positive 20 session moves over the same labelled period was 63.9 per cent. The conditional figure is, if anything, lower, and the interval covers both, which is the honest summary of what 43 episodes can resolve.

The continuation test is cleaner because it has a natural fifty per cent null. Did the move after the squeeze continue the direction of the drift into it, or reverse it? Continued after 22 episodes, reversed after 21. That is 51.2 per cent plus or minus 14.9. There is no result there and none is claimed. A measured null honestly reported is worth more than a confirmed expectation nobody measured.

Why the remembered squeezes are the unrepresentative ones

The folklore is not invented. Squeezes that preceded large moves exist, and the table above contains a few. The problem is which ones get written down. A compression that resolved into a violent month is memorable, teachable and screenshot friendly. A compression that drifted sideways for another six weeks and then resumed the same slow trend is none of those things, and there are far more of them.

On this record, top decile volatility followed 1 of the 43 episodes, and volatility below the unconditional median followed 26 of them. The longest squeeze in the record ran 30 sessions from 2025-12-04 to 2026-01-16, ending on a band width of 3.12 against a trailing volatility of 7.4 per cent, and over the following 20 sessions the index finished 0.87 per cent from where it started with a largest excursion of 1.65 trailing standard deviations. A textbook compression, on the broad index, in the most recent full year of the record, that resolved into nothing at all.

This is the selection mechanism, not a character flaw. Any indicator whose confirming instances are vivid and whose failures are boring accumulates a reputation that its own data does not support. The arithmetic of selecting the surviving case out of many is the general version, and it is the reason a page reporting three worked examples of an indicator working is reporting nothing measurable at all. Three examples out of 43 episodes is a selection, and the selection is doing all of the persuading.

The same test on twelve more series

One index over one decade is one experiment. The same computation on the published sector and size indices gives thirteen, on the same sessions, with no parameter changed.

The ratio column is below one on 13 of 13 series. The share of squeezes followed by top decile volatility is below the 10 per cent base rate on 12 of 13. The forward over trailing ratio is above one on 13 of 13. Both findings are stable: volatility mean reverts upward from a squeeze on every series tested, and on every series the level it reverts to is still below normal. Nothing about the conclusion is specific to the broad index, and nothing about it depends on the sector.

The option market had the same information

A final check on whether a squeeze is information at all. The exchange publishes an implied volatility index derived from benchmark index option prices, a forward looking number in the same annualised units. If a narrow band told you something the market had missed, that index would not be low when the band is narrow.

It was low. On narrow decile sessions the published implied volatility index sat at a median of 12.98 against 14.98 across all labelled sessions and 21.57 on the widest decile, with a rank correlation of 0.54 against band width. Everybody could see the compression, everybody computed it from the same closes, and the forward looking price of volatility reflected it. A squeeze is not a discovery. It is a widely shared description of a quiet fortnight.

What the reading is actually for

None of this makes band width useless. It makes it a present tense instrument, and present tense instruments have real jobs.

It states current dispersion in the instrument's own units, which is the correct scale for a stop distance and for a position size. A stop placed at a fixed percentage is a different instruction on a band width of 2.85 than on 12.23, and the reading is how you tell which one you are placing. It also warns when a volatility estimate is about to be misleading: after a wide reading, expect the estimate to fall, because from the widest decile forward volatility came in at 0.80 times trailing.

It sets expectations about the width of the next fortnight, because volatility clusters. A 20 session estimate formed today on a narrow band was right to expect a quiet fortnight: median forward volatility 9.39 per cent against 11.51 unconditional, with a narrower interquartile range than the unconditional distribution. That is a genuine measured regularity in describing the near future, and it points the opposite way from the folklore.

And it tells you when a chart's own scale has changed under you, which is the thing that quietly invalidates pattern work and fitted rules alike. A series whose dispersion moves by a factor of ten across a decade is not one population, and a rule calibrated on one part of that range is not calibrated on another. Knowing which part you are in is what the reading is for.

The habit worth taking from this page is not a setting. It is the shape of the test: state the claim, define the condition without looking forward, measure the conditional distribution against the unconditional one, count the independent episodes rather than the sessions, and report the null when that is the answer. That method is what the curriculum teaches, applied here to one indicator that almost every page describes and almost none tests.