Ask most traders whether Bitcoin moves more than the S&P 500 and the answer arrives before the question has finished. It is one of the few things in markets that nobody argues about.
What that intuition does not tell you is how to read a Bitcoin chart. Knowing a market is more volatile is a statement about the size of its moves. It says nothing about whether a range drawn around those moves describes them honestly — and that second question is the one a calibrated expected range is built to answer.
The first is about magnitude: how far does this market travel in a day? Our working paper does not publish a magnitude comparison — it isn't what the paper set out to measure.
The second question is about calibration. Take the market's own recent behaviour, build a range from it, and then check how often the next close actually landed inside that range. If the range says typical and price agrees roughly that often, the range is calibrated. If it says typical and price disagrees, it isn't — no matter how sophisticated the construction. The pillar post on what a calibrated expected-range indicator is works through that definition in full.
Volatility level and calibration quality are separate properties: a range that rescales with the market could in principle be honest on a violent instrument and dishonest on a quiet one, or the reverse. The second property has to be measured directly.
The test is deliberately dull. On each instrument's daily closes, a range is built from a rolling window of that instrument's own recent returns — the mechanics are described step by step on How It Works, and the underlying estimate is the same rolling volatility covered in our plain-English primer. Then one question gets asked on every bar: did the next close land inside the inner band, or outside it?
Run across 40 instruments in five asset classes, the average share of closes landing inside the inner band was about 71.65%, with a standard deviation of roughly 2.06 percentage points — most instruments came in between about 68% and 77%. All of these figures are historical and were measured in research; past behavior is not a guarantee of future results.
Bitcoin and Ethereum are two rows in that table. Here is where they sit.
On daily closes from 2014 to 2024, Bitcoin's next close landed inside the inner band 76.7% of the time. Ethereum, on a shorter 2018–2024 sample, came in at 75.4%.
The equity rows over their own periods: the S&P 500 cash index at 71.2%, SPY at 70.8%, QQQ at 70.6%, NASDAQ at 70.3%. Individual names sat a little higher — NVDA at 73.5%, AAPL at 73.0%, MSFT at 72.9%. Every one of these figures is published in the cross-asset table on our Proof page, alongside the sample period each was measured over.
So the crypto rows did not come in lower than the equity rows. They came in a few points higher, at the top of the observed spread rather than outside it. The most volatile instruments in the universe were not the ones where the range broke down.
That is the finding, and it is a smaller, stranger finding than the claim that Bitcoin is unpredictable. It is not that crypto is calm. It is that once the yardstick is rebuilt from crypto's own behaviour, crypto's days look about as ordinary — slightly more so, on this measure — as an index fund's days look against an index fund's yardstick.
The mechanism is construction, not market insight. The band is not drawn at a fixed dollar or percentage distance. It is rebuilt on every bar from the dispersion of that instrument's recent percentage moves, then projected back onto price. A market that has lately been moving 4% a day gets a band scaled to 4% days; a market moving 0.4% a day gets one scaled to 0.4% days.
Measuring in percentage moves rather than raw price levels is the load-bearing choice here, and it is the reason the same construction transfers across instruments whose price scales have nothing in common — a topic the return space vs price space post covers in more depth.
The practical consequence is that normal is not a fixed width. It is a moving description of the market in front of you. A 6% Bitcoin day and a 0.9% S&P day can both be entirely unremarkable relative to their own recent conditions — and, on the instruments tested, both were classified that way at broadly similar rates.
Two things cut the other way, and they belong in the same post as the good news.
At the outer band, the crypto rows came in slightly below the universe average rather than above it: Bitcoin and Ethereum both at 93.4%, against a cross-asset mean of about 94.0% and an S&P 500 figure of 93.8%. The gap is small — well under a percentage point — but it runs in the opposite direction to the inner-band result. Deep-tail optimism is a limit we publish for the outer band generally, and the crypto rows do nothing to soften it.
The second caveat is sample length. The S&P 500 result rests on 97 years of daily closes. Bitcoin's rests on about a decade, Ethereum's on a shorter window still — and both of those windows cover a narrower span of market history than the equity series do. A decade is enough to measure something; it is not enough to claim the number has been tested across the range of conditions the S&P 500 sample covers. Shorter samples carry wider uncertainty, and the paper reports confidence intervals for each instrument accordingly.
There is also a limit that applies to every rolling band, in varying degrees, and which we measure on our own: a range built from recent history runs too narrow in the first days of a fast volatility spike, because the spike has not entered the window yet. On the most extreme onset days in our own testing, containment fell to about 65%. That failure mode is covered at length in when volatility bands fail, and nothing about the crypto results exempts crypto from it.
A containment figure is a statement about description, not about profit or direction. It does not say Bitcoin is safer than it looks, does not indicate where price is heading, and does not identify a moment to act. The centre line carries almost no directional information by design.
Some traders use a calibrated range as an objective reference for whether a move is ordinary or unusual, or as an anchor for their own invalidation levels — descriptions of use, drawn from the use list on How It Works, not recommendations. The working paper validates the range's calibration, not the profitability of any particular way of using it. Whether any such use delivers value after real-world costs is an open question, and trading always carries the risk of loss.
More volatile and harder to describe are not the same claim. On the instruments tested, the markets with the largest daily moves were not the markets where a self-scaling expected range described behaviour least well — at the inner band, crypto sat at the top of the observed spread, and at the outer band it sat marginally below average. Both of those results are published, with their sample periods attached, because a number quoted without its period is not evidence. Past behavior is not a guarantee of future results.
Does an expected range indicator work on crypto's 24/7 charts? The construction makes no assumption about trading sessions — it rebuilds from a rolling window of recent bars, whatever those bars represent, so it runs on a continuous market the same way it runs on a session-based one. What is worth being precise about is the evidence: the containment figures published in our working paper were measured on daily closes, so they describe daily behaviour and were not measured on intraday crypto charts.
Does the range repaint on a Bitcoin chart? Once a bar has closed, its range and markers are fixed and do not change afterwards, and the calculation uses only data available at the prior bar. While the current bar is still forming, its live abnormal-move marker can update until that bar closes — which is a property of the bar being unfinished rather than of past values being rewritten.
How does this compare to using Bollinger Bands® on Bitcoin? The working paper ran a head-to-head against Bollinger Bands® on the same data, both at identical settings and at the canonical (20, 2) defaults, scoring both on containment. The results and the settings context are set out in our Bollinger Bands accuracy audit rather than repeated here. We publish our calibration record and the settings behind every comparison; readers can check whether any other tool does the same.
Was every cryptocurrency tested, or just Bitcoin? Bitcoin and Ethereum are the two crypto instruments in the published cross-asset universe, measured over 2014–2024 and 2018–2024 respectively. No claim is made about other tokens, and results measured on two large, liquid instruments should not be assumed to carry over to thinner ones.
The cross-asset table, the sample period behind every row, and the published limits are all on the Proof page — and the fastest way to judge any of it is to watch the range recalculate on the markets you actually follow. You can start a free 30-day trial and see how it behaves on a Bitcoin chart and an equity chart side by side.
Oisigma provides descriptive market analytics for educational use. It is not investment advice, does not predict prices, and does not provide buy or sell signals. Statistics referenced are historical and were measured in our working paper (not peer-reviewed); past behavior is not a guarantee of future results. Trading and investing involve substantial risk of loss, including the possible loss of all capital invested. Leveraged products (futures, options, margin) carry additional risk and can result in losses that exceed your initial investment. Bollinger Bands® is a registered trademark of John Bollinger; Oisigma is not affiliated with or endorsed by Mr. Bollinger. RiskMetrics® is a registered trademark of MSCI Inc.; Oisigma is not affiliated with or endorsed by MSCI Inc. Nothing in this article is a recommendation to use any particular strategy. Read the full Disclaimer →
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