And kingdoms rise
And kingdoms fall
But you go on
-- Fernando Rocha Brant, Milton Silva Campos Do Nascimento (recorded by U2)
Yesterday I published an article that summarized finding by Salis Mehta in which he demonstrated that October was, by one definition, the worst of months. How so? Well, it seems October has the greatest number of the 1% worst-loss days in the long history of the Dow Jones Industrial Average. Interesting enough to give pause as we move into that apparent "worst of months."
A couple of commenters in that article asked, "So which month has the greatest number of the 1% largest-gain days in the history of the Dow?" Good question. Worth a look, don't you think? And straightforward enough if one has the data. So I downloaded the complete daily history of the DJIA and ran the analysis.
First, I simply repeated Mr. Mehta's analysis. I did so for a couple of reasons: One, to validate his results (as a career scientist, I'm big on repeating someone else's results on occasion just to see that it's correct), but more importantly I wanted to validate my methodology. I had no doubt that if I did it right, I'd get the same results, but if I did not, I was almost certainly doing it wrong. Fortunately, my Excel-Fu was up to the task and I precisely replicated Mr. Metha's graph. Here's my result which you can compare to Metha's here:
The heavy gray lines show the expected distribution of the 320 worst days (1% of the DJIA history) if there were no differences among months. The red lines show the actual distributions. The absolute numbers are slightly different (my data set had 32,000 entries, somewhat more than Mehta's 29,000. I have a guess why that is, but I'm not completely sure). Regardless, the overall distribution is identical: Low in January. Exactly as expected in May. And, a big bulge in the fall months with October nosing out its surrounding months.
But, what about the best 1%? Well, surprise, surprise:
If it was October by a nose on the down side, it's October by 12 lengths on the upside, with November placing in both runs. Guess when the Twelve Months Yearbook comes out we'll find that October was voted "Most Likely to Be Volatile."
It's interesting to look at how much gain or loss it takes to fall into the tails of the Dow. The table lists the cutoffs for the 99%tile and the 1%tile.
Change from Previous Day (%)
99% tile - 1% largest gains
1% tile - 1% largest losses
Best Day Ever
15 Mar 1933*
Worst Day Ever
12 Dec 1914
*Putting to rest that business about "Beware the Ides of March," perhaps, and ironically referential to my opening sentence of yesterday?
I wrapped up yesterday's piece with a note of caution as we move into the Fall. Seems clear that was premature pending the collection of more data. So, what's an investor to do? Might it be worth exploring the possibility of going long in some high volatility position? I like things fairly simple and straightforward, so I prefer ETFs: maybe SPHB, PowerShares S&P 500 High Beta Portfolio ETF? If you're more adventurous than I am, there's VIX, the big kahuna of volatility, VXX, which I readily admit to not understanding well enough to venture into.
While I certainly wouldn't make that call on this simple analysis. Obviously, the big gainer and big loser days don't fall in the same years. But it does suggest a deeper look may be in order. Especially since there's a case to be made that a volatile Fall is in the cards for any number of macro reasons.
In conclusion, I express my thanks to Salis Metha for unearthing this clever idea. Check out his blog if you're statistically inclined. Some of it's tough going, but it's always intriguing.