Volatility Seasonality
Every seasonality analysis out there is about returns. This one is about how far things move — and that is the more dependable quantity: returns are barely predictable, whereas volatility depends strongly on its own past. Here is how turbulent each month typically is for a given instrument.
The common claim is that September and October are the most volatile months. It was fixed before the calculation as the single hypothesis, on one ticker and one pair of months, tested one-sided — and held against 2,000 circular random shifts, so that volatility clustering does not make the null distribution artificially narrow. Individual October crashes shape the memory; they do not shape the average level of the month.
Y axis = the month's volatility relative to this instrument's own normal volatility. 1.00 is an average month, 1.15 means 15% more turbulent than usual. That makes instruments comparable whose absolute volatility is worlds apart — bitcoin swings many times harder than a utility stock, yet both have an annual pattern.
Monthly profiles side by side
One row per instrument, one column per month, normalised to its own normal volatility. Click a row to show it in the chart above. A dot means: too few years for that month.
Methodology — how this was computed
The monthly volatility
What is computed is the annualised dispersion of the daily returns that belong to the month itself. Dispersion is taken around zero, not around the monthly mean: the question is the size of the moves, not the deviation from a trend — with about 21 observations a trending month would otherwise look too calm. Months with fewer than twelve trading days are dropped, monthly profiles with fewer than ten years likewise.
Why not a rolling window
The obvious calculation would be the usual rolling 21-day volatility. It is wrong here: it measures the preceding 21 trading days, so the September figure would cover mid-August to end-September, and an October crash would land half in November. A first pass of this analysis had exactly that flaw and made September look like the calmest month, because the quiet late summer was counted in. A measure that is right for daily monitoring is not automatically right for a calendar question.
The median, not the mean
Across years the median of the monthly values is taken. Otherwise a single crisis year would determine the month — October 2008 is one October among many.
The randomisation test
Testing is against 2,000 circular shifts: the monthly values are shifted against the calendar months. That destroys the link to the calendar while preserving volatility's habit of arriving in blocks — turbulent phases last several months. Shuffling the months instead would give a far too narrow null distribution, and then every monthly difference would look significant. The p-value is one-sided, because the hypothesis claims a direction, and carries a plus-one correction: with 2,000 shifts the smallest representable value is 1/2001, and “p = 0.000” would be a claim about precision the method cannot deliver.
Limits
- These are daily closing prices. What happens within a day is invisible — and volatility lives there to a good extent.
- The price series are dividend-adjusted. On distribution days this carries a small artificial jump into the series, more noticeable in monthly-paying bond ETFs than in gold.
- The table is descriptive. Anyone who hunts for its most striking cell and then tests it is testing themselves — the result would be a chance hit with a p-value attached.
- A monthly profile says nothing about direction. A turbulent month can rise or fall; all that is measured is how far it moves.
Frequently asked questions
Why volatility and not returns?
Because volatility is the more dependable quantity. Returns are barely predictable; volatility depends strongly on its own past — a turbulent week is usually followed by a turbulent one. A seasonal volatility pattern is therefore sturdier than a seasonal return pattern. And for anyone pricing options or sizing positions it is the more immediately relevant number.
Are September and October the crash months?
Not by this measurement. For the S&P 500, volatility in September and October together sits at 1.059 times the rest of the year, and that is statistically indistinguishable from chance (p = 0.127, measured on the index itself from 1957). The memory hangs on individual events — October 1929, October 1987, October 2008. They do not make up the average level of the month.
What does “relative to own normal volatility” mean?
Every value is divided by the median across all months of the same instrument. 1.00 is an average month, 1.20 one that is a fifth more turbulent. Without that normalisation any comparison would be dominated by bitcoin, which swings many times harder in absolute percentage points — the pattern would no longer be visible.
Is this a trading signal?
No. The page shows an analysis of historical price data, not a forecast and not investment advice. It also says nothing about direction: a turbulent month can rise or fall. Past patterns guarantee no future results.