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Fassett on Fractals

by Matt Lampert on February 17, 2016

Professor seeks to uncover the mathematics behind fractals in financial markets

*Note: This article describes the work and research of Dr. Jon Fassett, one of our speakers at the 2016 Social Mood Conference on April 9. An earlier version of this article appeared in the January 2016 issue of The Socionomist. Click the play button to listen to the audio version, or read the transcript below.

Prof. Jon Fassett’s love of fractals began when he encountered the term during a summer undergraduate mathematics course. He learned the underlying theory and went on to generate fractal images on his computer. “It turns out they’re very easy to code. Of course, back then they took hours to draw on the screen,” he recalled.

Fassett’s interest grew as he began to realize that the shapes he saw on his computer screen were ubiquitous in the real world. “When you look at most anything in nature, they are not circles and lines. They are fractals. Everywhere you look, there’s this kind of irregularity at all levels,” he explained.

While Fassett was trained to see fractals everywhere, one place he had yet to look was in financial markets. That is, until a friend who worked as a money manager gave him a copy of A.J. Frost and Robert Prechter’s 1978 book, Elliott Wave Principle. “I sat down and read through it, and once I saw exactly what Ralph Elliott was doing with his models, I was just floored. These were fractals being applied to these markets,” he recounted.

But Dr. Fassett is not a man of mere intellectual curiosities. He aimed to put his knowledge of financial fractals to use. He began calculating Elliott wave projections and soon found himself working as a consultant at his friend’s money management business.

Fassett sees the Elliott wave model as an improvement over conventional methods of financial analysis:

The majority of people will just follow the crowd. And, of course, we know that most of these forecasts that they’re doing are not really forecasts. They’re just a projection of current trends. To me, that is the big downfall of current strategies. There’s no way for them to forecast major changes in trend. Of course, one thing that the Elliott wave theory does is it gives you some guidelines on when to expect possible changes in trend. And not just little ones, not just ‘day-trader trends,’ but huge trend changes.

Furthermore, Fassett said, conventional approaches tend to assume that the distribution of financial market price changes adheres to a bell curve, an assumption that data have invalidated. “What we have are markets that have statistical signatures that the current models do not handle. And the exciting thing is that fractal models handle this.”

When it comes to fractal models of financial markets, Elliott’s is not the only one on the catwalk. Benoit Mandelbrot turned heads decades after Elliott’s death with a multifractal model of financial price fluctuation. In a 1999 letter to Scientific American and extended commentary in The Elliott Wave Theorist, Robert Prechter meticulously documented a series of overwhelming similarities between Mandelbrot’s models and Elliott’s discoveries from more than half a century earlier. Fassett sought to compare the two using the tools of contemporary mathematics during a recent research sabbatical.

He presented his findings at the 2016 Joint Mathematics Meetings, the largest math conference in the world. Like Prechter, Fassett observed a number of striking resemblances in the two approaches along with crucial differences. One such difference is that Mandelbrot viewed financial markets as indefinite fractals, like coastlines. The result, as Fassett explained, is that, “Mandelbrot himself said that you can’t forecast the price of anything. What he could forecast was what he called risk. He could say that volatility is increasing and so forth. But in Elliott’s model, you get more.”

The “more” comes from the fact that Elliott modeled price fluctuation as a robust fractal, a fractal that has a limited number of specific forms, such as a five-wave impulse followed by a three-wave correction, that repeat on all scales with a particular amount of variability. This trait gives the model its power to forecast price. As Fassett said, “Once you see a pattern finish, you can project what’s going to happen in the future and try to anticipate.”

Dr. Fassett is a tenured mathematics professor at Central Washington University, but he followed anything but a conventional path in his rise up the academic ranks. As a teenager, he dropped out of high school before going back to earn his diploma. He completed his undergraduate studies with a math degree and became certified to teach. His passion for math briefly outweighed his passion for teaching, as he spent some time as a casualty actuary before the classroom ultimately called him back. “I eventually sold our house, quit my job, and we moved out of state. My wife was pregnant with our fourth child, and I started graduate school. It was a little unorthodox. I pretty much treated it as a job when I was getting my Ph.D.,” he related.

Today, he combines his love of fractals, teaching and mathematics in his lectures. “I really believe strongly that this is an area of mathematics that is contemporary,” he said. “Unfortunately it’s not in the math curriculum yet, so I try to force it in wherever I can.”

Fassett also shares his passion for fractals with others in his community. He has given presentations on the subject to audiences ranging from elementary school students to research mathematicians. “I don’t know any other area of mathematics that can be presented to such a wide audience. So that’s really how come I’m excited about the field as a teacher,” he said.

Dr. Fassett brought his knowledge and enthusiasm for fractals in nature and finance to the 2016 Social Mood Conference on April 9 in Atlanta, GA. It was a return trip, as he previously participated as an attendee. Before the conference, Dr. Fassett said, “I’m very thankful to be invited this time as a speaker,” he said. “I’m excited to share some of my findings through my sabbatical and some other areas of interest related to social mood. But I’m also looking forward to getting caught up with the people that I’ve met over the years there. I’ve built some good friendships.” He also noted that learning about the latest social mood research has the potential to open up professional opportunities, “Hopefully that will lead to further collaborations with others of similar interests.”


Watch Dr. Fassett and the nine other excellent presentations from the 2016 Social Mood Conference right now via an on-demand video >>

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