Our Autumn of Discontent

By Salil Mehta, statistician and blogger at (Statistical Ideas)

NEW YORK ( TheStreet) -- The fall months may be some of theriskiest months in the market. After all, most of the infamous 10, worst one-day market panics on the Dow, have occurred near October. But a ranked listing of only10 is a freakishly small sample of extreme events from which to draw any statisticalsignificance.

The history of the Dow goes back to the late 19th century. And with enough data, wecan better understand the frequency of when severe market drops occur. We knowthat Mark Twain once said at about the same time the Dow started, "It is notworth while to try to keep history from repeating itself, for man's character willalways make the preventing of the repetitions impossible."

There is a statistically strong historicalrepetition of market crashes, occurring in the months near October. But so too docrashes more often occur on Mondays, for any month of the year. Of the 29,400trading 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 least3.2% was needed. And while we expect five of these worst 1% days biennially, themost recent one we have had was November 2011.

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

Next we show the distribution of these worst 1% trading days, by the weekdaywhen they occurred. The statistical strength of Mondays is very powerful, and itdoes not transfer over to either the trading day before or after (e.g., Fridays orTuesdays). We can see this with a simple kernalized smoothing technique, with awidth of plus or minus one day. We see the kernalized distribution essentiallymatches the uniform distribution in light green, so we fail to appreciate that theMonday result is a product of luck during the five-weekday cycle.

On the contrary, a similar smoothing exercise in the monthly distribution data abovewouldn't have changed the monthly seasonal pattern we see. Additionally, we knowthat there are two weekend, non-trading days, breaking the psychological rhythmbetween Friday and Monday. There is no similar large break, of any non-tradingmonths, in the monthly distribution.

It is worth noting that the combinations of the weekday and monthly data are alsostatistically significant. Again, here we use a Chi-square non-parametric test, tomeasure possible differences from expectations. With the 294 worst trading days,spread over 60 weekday and month combinations, we have designed a statisticallylarge enough sample to see significance within the weekday and monthcombination.

We see this 60-weekday and month combination distribution above. October isrepresented in yellow; Monday is represented by blue. We see that the riskiesttime for the markets, shown in green, have been near October, and particularly onMondays.

None of the above analysis is statistically significant for the average severity ofmarket drops, beyond the 3.2% threshold, just to be in this worst 1% club. But as wehave shown in this note, it is important to also pay attention to the frequency ofhighly risky market times when planning any investment strategy for the uncertainautumnal season ahead.

Written by Salil Mehta, creator of the Statistical Ideas blog.

At the time of publication, the author held no positions in any of the stocks mentioned, although positions may change at any time.

This article is commentary by an independent contributor, separate from TheStreet's regular news coverage.

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