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The Presidential Cycle: Useful or “Rubbish”?

Part Two

In my 15 years at DuPont, I had the chance to work with some really world-class statisticians on various production quality issues. Every time I talked with one of them, I was amazed at how this very useful field is mired in terminology and minutiae that causes more practically minded folk to pull our hair out! I found that getting a simple answer from a statistician was a bit like trying to take a sip out of a fire hose.

A short academic experience with formal statistics didn’t help my jaded perception of the field. After I was accepted into graduate business school, I received a letter stating that I needed to take a prerequisite statistics course before starting business school. What? I had earned a B.S. in chemical engineering and was only three courses shy of earning an minor in mathematics. I brought these points up with the dean of the MBA program, but he rigidly stuck to the letter of the law and insisted that I take a pure statistics course.

So, the summer before I started business school, I showed up for a Statistics 505 class and, I kid you not, spent the whole first day on the intersections and unions of sets. I informed the professor that I wouldn’t be returning. I went home, grabbed one of my undergraduate text books, marched into the dean’s office and flipped the book open to one of the chapters on statistical thermodynamics. “If I passed this course, I don’t think I’ll slow down any of our MBA classes with my lack of statistical knowledge”, I opined to the dean. He begrudgingly signed my prerequisite waiver.

So it is with this somewhat skeptical view of the discipline that I felt a statistical “burr under my saddle” this week. In last week's newsletter article, we looked at the stock cycle related to the presidential election cycle. Another article I referenced supposedly debunked the validity of the presidential election cycle on the simple basis that the cycle had only 27 data points, not the 30 required by statistical rule. Therefore the author concluded that the idea of a presidential election cycle is statistical noise or, to use his exact quote, “absolute rubbish”. I have been amazed at how many people read this so called “in-depth analysis”; has even published it in their personal finance section!

For some reason, that ill-conceived article rattled around in my head all week. And like a small pebble in my shoe, it was irritating just enough to make me stop what I was doing and take care of it. And you, beleaguered reader, are the beneficiary of my anguish because in my research, I found a cool visual way to look at statistical significance and sample size that I think you might find useful as well. Let’s dig in.

Presidential Election / Stock Market Cycle: How Many data points do you need?

For a quick refresh about the presidential election / stock market cycle you might want to read last week’s article.

The real question before us is whether the presidential election cycle has enough data points to be statistically valid. Saying that a group of 27 data point is no good but 30 would work really well just doesn’t cut it. We know from last week’s article that one peer reviewed article ran the statistical validity numbers and found that even the smaller sample of post-WWII results were valid. And for those of you who really want to “geek out” on presidential election stock cycles, here’s another peer reviewed article that validates the phenomenon with some rather unique tools. You can check out the paper by Nickles and Granados at Pepperdine University’s Graziadio School of Business journal by clicking this link:

Interestingly, the more I’ve dug into this seasonal cycle the more support I have found for it! But I do want to show you a cool visual way to see if a sample size is sufficient. Jed Campbell’s excellent website suggested a visual observation and provided the spreadsheet to draw the graphs below.

In short, a “sufficient” sample size is one where the standard deviation and the confidence intervals around the standard deviation stop jumping around and settle down to a smooth reading. The sample progresses towards that point of validity as its number of data points increases.

The chart below looks at the Yale Hirsh data for market returns during the best year of the presidential election cycle, year 3 or the pre-election year. The chart shows all 44 presidential cycles dating back to 1833. As you can imagine, the variability among only a few data points will be pretty large, and the difference between the upper limit (hashed red line) and the lower limit (lower hashed red line) is wide—especially wide for the first 6 samples. As the sample size become larger (moving toward “sufficient”), the upper and lower confidence limits converge and stabilize and the standard deviation (middle black line) smoothes out as well:


After how many elections (x axis) do your eyes see the data even out and reaching some stability? Probably somewhere between 25 and 28 data points. Statisticians have seen this same phenomenon across a wide variety of data sets which has led to the 30 data points rule of thumb.

For the sake of completeness, let’s look at the standard deviation and upper/lower confidence limits charts for the other years in the election cycle. Here is the worst performing year in the presidential cycle that Hirsch found, year 1 or the post-election year:

Chart 2

You can see that this data set remains unstable for a longer period. This culminates in the big jump in standard deviation at data point 26 in 1933— when the market had a whopping 66.7% up year during FDR’s first year in office. Compare this to the next chart, the second year of the cycle dubbed the mid-term year:

Chart 3

Here, we notice that the data set is much smoother with fewer bumps and a quicker confluence of the confidence limits. Lastly we have year 4 or election year for the cycle:

Nothing too exciting here either as we see the data stabilize less quickly than the year two data, but more quickly than year one data and about on par with year three. This leaves us with only one more graph to look at.

The presidential cycle debunker seemed to make a reasonably valid claim that Hirsch’s pre-1900 stock data was suspect, since there were no standard indexes to draw from. So what if we did look at only the post-1900 data? Does the data look like it stabilizes and passes the visual test? To check this, let’s use the toughest test, the least stable data from year one:

It certainly looks like the visual method confirms what the peer reviewed papers found—that there is in fact statistically validity to a slightly smaller data set than the rule of thumb 30.

A Word of Caution

Remember that even validated seasonal patterns do not give us certainty. Rather, these seasonal patterns help push our expectation in a particular direction and can therefore give us an edge.

I hope that this unique visual way of looking at sample size implications has been as enlightening for you as it was for me!

With the U.S. celebrating Thanksgiving on Thursday, my hope and prayer is that your thoughts of gratitude are overflowing at least as much as your gravy bowl. A very Happy Thanksgiving to all of you!

If you’ve found this article useful or thought provoking (or both), I’d love to hear your thoughts and feedback – just send an email to drbarton “at” Until next week…

Great Trading,
D. R.

About the Author: A passion for the systematic approach to the markets and lifelong love of teaching and learning have propelled D.R. Barton, Jr. to the top of the investment and trading arena. He is a regularly featured guest on both Report on Business TV, and WTOP News Radio in Washington, D.C., and has been a guest on Bloomberg Radio. His articles have appeared on and Financial Advisor magazine. You may contact D.R. at "drbarton" at "".


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Nov 20, 2012 - Issue 604

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