# The multiple problems with multi-year cycles

Perhaps, sitting in a bar one evening, a friend told you that corn yields tend to be great during years that end in "6." Or perhaps you've heard of the 18-year cycle in the stock markets? Or the 60-year cycle in wheat prices? Or the 14 3/4-year cycle in soybean prices, which only holds true if the previous year's price ended with an even number?

Okay, I made that last one up. But that's alright -- other people baselessly fabricated all those other examples, too, and they all have the same statistical significance (zero).

I hadn't heard of the 60-year cycle in wheat prices until a gentleman told me about it after a recent market presentation. He has many more years of experience in the wheat market than I do, and I'm always willing to learn new things, so I promised I would look into it. More on that later.

All these multi-year cycles are interesting bits of folklore, and they're kind of neat to think about. If thinking about them and analyzing the underlying economic reasoning behind them helps market participants better understand the world around us, then that's great. But if blindly believing them motivates farmers to make or postpone marketing decisions based on unsound science, then that's bad. That's why I'm going to try to bust the myth of the multi-year cycle as clearly as I can.

In this universe, many phenomena tend to occur frequently near their averages and less frequently at unusual values, measurements or strengths. This is often shown with the bell-curve chart of the normal distribution. But even if a phenomenon isn't "normally" distributed, if that thing happens a large enough number of times, it will still always tend toward some average value. That's the Central Limit Theorem, roughly speaking. It is powerful because it allows us to calculate whether a particular event is truly unusual, like someone who's 6 feet 7 inches tall. Is that just part of the randomness of the universe? All heights will vary somewhat from person to person.

Therefore, among an entire universe of values, taking just one sample -- or just a few samples -- is extremely unhelpful when it comes to predicting future values. The Chicago Board of Trade was established in 1848 to exchange cash grain, but a standardized record of corn, wheat and soybean futures prices only exists since 1959. That means there are only six samples of an annual corn price from "a year ending in six," and six samples is way too few to be confident that whatever trend our human brain might think it sees is anything more than just random statistical noise.

I was slightly more willing to believe in a statistically provable multi-year pattern in wheat, however, because I remember seeing an amazing chart of wheat prices from 1750 through 1960, collected by Hugh Ulrich. I updated that data through 2018, and that made 268 years of information -- which is a lot! It's only four samples of any 60-year period, however, once again, it's difficult to prove there is anything significant beyond randomness in any purported 60-year cycle in wheat prices.

Furthermore, even the 268 years of data was problematic. Some of it was from England in the 18th century, quoted in English cents per bushel. Some of it was CBOT futures quoted in U.S. cents per bushel. More importantly, the structural economic reality of wheat itself has drastically changed between 1750 and today. The number of man-hours that go into a bushel of wheat, the proportion of a farm family's income that comes from a single bushel, the proportion of an urban consumer's budget that goes into a single bushel -- none of this is apples-to-apples from one economic timeframe to the next. This is called time-period bias in statistical sampling. Even comparing U.S. stock prices from the inflation-plagued 1970s compared to the easy-money 2010s is problematic.

Let's actually try to test a multi-year cycle. Say we look at the so-called "decennial pattern" in the stock market, which colloquially claims that years which end in "0" tend to have poor performance, and years which end in "5" have "by far the best" performance. We can gather 90 years of stock market returns since 1928. Maybe 90 years sounds like a lot, but it's only nine sets of 10, or nine samples from years that end in "5."

Let's say the average of all 90 annual returns is only 11.4%, but we calculate the average of annual returns from years ending in "5" at 14.6%. Woohoo! Sounds like those years ending in "5" really are winners -- notably including 1995's 37.6% return. However, if we conduct a two-tailed test for statistical significance using the student's t-distribution, which mathematically considers the standard deviation of all those returns and the small number of samples, and then compares them against what can occur by mere happenstance, the difference between the all-year average returns, and the years-ending-in-5 average returns is proven to be nothing but statistical noise.

However, if we were magically able to use 300 years of stock market data, and therefore had 30 samples to draw from (30 is widely considered to be the minimum statistically useful number of samples), we could calculate a somewhat larger critical value for this statistical test. And then say there's maybe 80% confidence that the difference between the two sets of returns might actually be significant (and a 20% chance they're not). There still wouldn't be any fundamental explanation for why the final digit of a calendar year should affect equity performance.

Anyway, look and see that stock returns in 2015 were only 1.38% -- the worst annual performance since 2008. Anyone who actually invested money based on this hokey idea of a decade-long market pattern would have been sorely disappointed.

To all the believers in multi-year patterns or cycles: please continue to tell me about them! I love hearing about these fables, and I collect them like other people collect pretty seashells. But please don't sell your grain (or not sell your grain) based on someone else's flimsy idea that has only ever been sampled four times in history.

Elaine Kub is the author of "Mastering the Grain Markets: How Profits Are Really Made" and can be reached at elaine@masteringthegrainmarkets.com or on Twitter @elainekub.

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