Our Autumn of Discontent

by Salil Mehta
Reposted from StatisticalIdeas.Blogspot.in.

The elusive market drop we have been waiting for all year. Each month, from May through August, we anticipated what would finally be a 10% or greater market correction. Or an outright crash, given the known tapering later this year of the Federal Reserve quantitative easing. In this note we examine the worst 1% of market crashes through history.

Soon we will approach the fall months, and we all suspect that these are some of the riskiest months in the market. After all, most of the 10, worst one-day market panics on the Dow, have infamously occurred near October. But a ranked listing of only 10 is a freakishly small sample of extreme events, from which to draw any statistical significance.

The history of the Dow goes back to the late 19^th century. And with enough data we can better understand the frequency of when severe market drops occur. We know that Mark Twain said back at about the same time the Dow started,

“It is not worth while to try to keep history from repeating itself, for man’s character will always make the preventing of the repetitions impossible.”

And here in this note we will show that there is a statistically strong historical repetition of market crashes, occurring in the months near October. But so too do crashes more often occur on Mondays, for any month of the year. Of the nearly 30,000 trading days in the history of the Dow, we looked at the worst 294 (or 1%) of them. In order to qualify for this club of the worst 1% days, a daily price drop of at least 3.2% was needed. And while this works out to a pace of five of these worst 1% days biennially, the most recent one we have had was November 2011.

Here is the distribution of those 294 days by month, in red on the chart. As a statistical alternate, we also show in light green the distribution of 294 days evenly spread across 12 months.

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Next we show the distribution of these worst 1% trading days, by the weekday when they occurred. The statistical strength of Mondays is very powerful, and it does not transfer over generally to either the trading day before or after (e.g., Fridays or Tuesdays). We can see this with a simple binomial kernalized technique, with a width of plus or minus one day. This smoothed distribution essentially matches the uniform distribution in light green, so we fail to appreciate that the Mondays results is a product of luck inside the five-weekdays cycle. This weekday signal also equally applies, for any given week of the month.

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On the contrary, a similar smoothing exercise in the monthly distribution data above wouldn’t have changed the monthly seasonal pattern we see. Additionally, we know that there are two weekend, non-trading days, breaking the psychological rhythm between Friday and Monday. There is no similar large break, of any non-trading months, in the monthly distribution.

It is worth noting that the combinations of the weekday and monthly data are also statistically significant. Again, here we use a Chi-square non-parametric test, to measure possible differences from expectations. With the 294 worst trading days, spread over 60 (12*5) weekday and month combinations, we have designed a statistically large enough sample to see significance within the weekday and month combination.

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We see this 60 weekday and month combination distribution above. October is represented in yellow; Monday is represented by blue. We see that the riskiest time for the markets, shown about the green data, have been near October, with a large bias towards Mondays.

None of the above analysis is statistically significant for the average severity of market drops, beyond the 3.2% threshold just to be in this worst 1% club. But as we have shown in this note, it is important to also pay attention to the frequency of highly risky market times when thinking about the choppy, autumnal season before us.

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