Analysis · Method
Monthly Performance and Seasonality
Twelve calendar bins always produce a best month and a worst month. The question a seasonality table never answers is how much of its pattern would survive if the market had no seasons at all, so this page computes that.
What a seasonality table is
Take an index’s monthly returns over some history, group them by calendar month, and average each group. The result is twelve numbers, usually printed to two decimal places and coloured by sign, and it is read as a schedule: these are the good months and those are the bad ones.
Every arithmetic step in that is correct. The problem is what the presentation leaves out, namely how few observations sit behind each cell, and what a table like it looks like when the underlying data has no seasonal structure whatsoever.
The band in that figure is the number no published seasonality table prints, and it is the whole story. With a monthly standard deviation of about four per cent and 40 observations per month, the standard error of each average is roughly 0.66 points, so two cells have to differ by well over a point before the difference means anything. In most tables, no two do.
The three problems, in order of severity
1. Twelve comparisons, one conclusion
Examining twelve months and reporting the extreme one is a search, not a test. The chance that at least one of twelve averages looks notable is high even when nothing is there, which is exactly the mechanism the parameter-sweep figure demonstrates with moving averages. Seasonality tables have the more seductive version of the problem, because the twelve bins are natural rather than arbitrary, nobody chose them, so it does not feel like a search.
2. One observation per year
A forty-year table contains forty Januaries. That is a small sample by any standard, and the quantity being averaged has a spread several times the size of the effect being claimed. Lengthen the history to a century and the standard error falls by less than half, while the earlier decades describe a market with different instruments, different participants and different trading costs.
3. Publication changes the thing being measured
A genuine calendar effect in a liquid market cannot survive being famous. If everyone knows that a particular month is strong, the buying moves earlier each year until the edge is gone, which is the documented history of the January small-company effect. So the strongest seasonal claims are the ones with the least remaining value, and a table computed over a long history is partly measuring an era when the effect was still unknown.
What to check before quoting a seasonality figure
| Question | Why it decides the answer |
|---|---|
| How many years? | Each cell holds one observation per year. Thirty years is thirty observations, and the uncertainty around each average is larger than most of the differences between them. |
| Mean or median? | A single extreme month (a crash, or a sharp recovery) can set the average for its calendar slot across a whole table. The median tells you whether the pattern is the month or one year in it. |
| Is a spread quoted at all? | Without a standard error or a confidence range, the table cannot be read. Two averages that differ by less than their uncertainty are the same number in different ink. |
| Which index, and in which currency? | Seasonal claims are frequently transferred between markets and currencies, where the tax years, holidays and rebalance calendars that could cause an effect are different. |
| Does it hold out of sample? | The only test that matters. An effect found up to a given year and then measured on the years since is either there or it is not, and this is the check that retired the January effect. |
Where calendar effects are on firmer ground
Volume, not returns. The seasonal pattern in trading activity is larger, more consistent and mechanically explicable in a way that a return pattern rarely is.
August and the last two weeks of December are quiet in most Western markets because participants are absent, which is not a claim about expectations. Quarterly index rebalances and monthly options expiries concentrate enormous volume into sessions whose dates are published years in advance. Both effects are visible in any volume series and neither needs a significance test to be believed, and both matter for the measures on this site, because a volume baseline that spans one of those sessions is raised by it for the whole window afterwards.
That is the useful form of a seasonality claim: a statement about participation, with a mechanism, checkable in the data you have. The return version has no mechanism, a sample of thirty or forty, and twelve bins to choose from.
What this page is not saying
Not that seasonal effects cannot exist. Tax years, fiscal calendars, holiday liquidity and scheduled rebalances are real features of the market, and it would be surprising if none of them left a trace. Some of the long-run seasonal findings, "sell in May" among them, hold up across several markets and many decades, which is more than most claims in this field manage.
What the figure above establishes is narrower and harder to argue with: the shape of a seasonality table is not evidence. A best month and a worst month appear whether or not anything is there, the gap between them is large, and the uncertainty around each cell is wider than the differences the table appears to show. Anyone quoting one should be able to say how many years it covers and how wide the error is, and if those two numbers are not in the article, the table is a description of history rather than a reason to do anything.
Frequently asked questions
Is there a best month for the stock market?
In every historical table there is, and that is the problem: twelve calendar bins guarantee a highest and a lowest one whether or not any month behaves differently from the others. The figure on this page computes monthly averages from forty years of synthetic returns drawn from a single distribution — no seasonality of any kind — and the gap between its best and worst month is several percentage points. A ranking is what the arithmetic produces, not what the market did.
How many observations sit behind each cell?
One per year, which is far fewer than the table’s precision suggests. A century of data gives a hundred Januaries; the thirty or forty years most published tables use give thirty or forty. With a monthly standard deviation of about four per cent, the standard error of a mean over forty observations is around two-thirds of a per cent, so any cell within roughly one and a third points of zero is indistinguishable from nothing, and most cells in most tables are.
What about "sell in May"?
It is the most studied seasonal claim there is, and the pattern does appear in long histories across several markets, which is more than can be said for most. The difficulties are the ones that apply to all of them: the effect is small relative to the volatility of the period it covers, it is absent in many individual years and in some whole decades, and by the time a rule is famous enough to have a name, acting on it is a crowded trade. It is worth knowing about and a poor basis for a decision.
And the January effect?
The original observation was about small companies outperforming in January, associated with tax-loss selling in December and the reinvestment that followed. It is the standard example of a seasonal effect that faded after publication, which is what one would expect of a genuine effect in a liquid market, since a well-known calendar edge is bought earlier each year until there is nothing left in it. That decay is evidence the market works, not evidence the original study was wrong.
Why do published seasonality tables look so convincing?
Because the presentation hides the uncertainty. A table of twelve averages to two decimal places, coloured green and red, carries no indication that each figure rests on a few dozen observations with a spread several times its own size. Add the standard error to every cell and most of the pattern turns into overlapping ranges. Nothing in the table is wrong; what is missing is the part that would stop you reading it as a schedule.
Does monthly seasonality show up in volume as well?
Yes, and rather more reliably than in returns, because the causes are mechanical rather than behavioural. August and late December are quiet in most Western markets for reasons that have nothing to do with expectations, and quarterly index rebalances and options expiries concentrate volume into specific known sessions. A volume seasonality claim is on much firmer ground than a return one, and it is a statement about participation, not about direction.
How would a seasonal effect be tested properly?
By stating the hypothesis before looking, testing it on data that was not used to find it, correcting for the fact that twelve months were examined rather than one, and reporting the result whether or not it survived. In practice the strongest available test is the out-of-sample decade: an effect discovered on data up to some year and then measured on the years since. That is how the January effect was found to have faded, and it is the test almost no seasonality article performs.
So is a seasonality table useless?
Not useless, just much weaker than it looks. It is a reasonable description of what has happened, which makes it useful context: knowing that a period has historically been quiet or volatile is worth having when reading a current move. What it cannot support is a decision timed to the calendar, because the confidence interval around every cell is wider than the difference between the cells.