The Fractal Market Hypothesis, 30 Years On

In January 1994 Fractal Market Analysis (FMA), my second book, was published. My first book, Chaos and Order in the Capital Markets, had come out a little over 2 years before, and was very well received. FMA was not a sequel, but a continuation. I saw Chaos and Order as an introduction to chaos theory and fractal statistics for investment practitioners. FMA was intended to introduce practitioners to research methodologies. At the time there was very little available to the investment community along these lines, and I wanted to give access to what I had learned. Then investors could decide whether trying out these new ideas was for them.

The heart of the book was the Fractal Market Hypothesis, the professional achievement of which I am most proud. Even though I've had a 48 year career investing billions of dollars for institutions, if I've left any legacy it will be the FMH.

To commemorate the 30th anniversary of the FMH, I thought I'd talk about it's inception, supporting evidence and future in this week's post.

Some Background

As I've stated elsewhere, I came to investment finance from a traditional capital market theory background. In 1978 applying mathematics to investing was considered a lunatic fringe by the investment community though it was beginning to catch on. But even then, as a practitioner, I realized that there was a huge gap between theory and reality, and I wasn't alone. The Efficient Market Hypothesis (EMH) and the Capital Asset Pricing Model (CAPM) dominated academic discussion and gave us many useful tools, as long as you understood their limitations. Nobel prizes have been rightfully awarded based upon this work.

But according to these theories, bull and bear markets are illusions, and market crashes and stampedes can't happen. Even as many professional investment managers admitted as a whole that markets were not efficient, they still used tools which were largely based upon market efficiency and equilibrium states because they had little else.

Prior to 1985, I had been an equity trader and analyst. In 1985 I joined the Boston Company's newly formed Structured Investment Products (SIP) department (which in 1989 became PanAgora Asset Management) to manage their equity index funds and tactical asset allocation (TAA) strategies. Oddly, the index funds were based upon the premise that markets were efficient while TAA was based upon the opposite. TAA was actively shifting between stocks, bonds and cash based upon market conditions. I also used futures to make the shifts, a novelty in 1985.

After the Crash of 1987 (which was the most fun I had as a trader), the holes in traditional capital market theory became more apparent. Luckily at that time James Gleick's book Chaos: Making a New Science (1987) had come out. I had read a 1984 article by Gleick in the New York Times Magazine and found the ideas intriguing. The Crash inspired me to read his new book. This led to an intense self-study period, where I also communicated with a few like-minded individuals on Wall Street. Then I wrote two papers in the Financial Analysts Journal. The first used rescaled range (R/S) analysis and the Hurst exponent to show long memory effects and the fractal structure of fat-tails, following in the steps of Benoit Mandelbrot. The second used chaotic dynamics. Based upon those two papers, a book offer came from Wiley.

I have to admit that publishing this kind of research was kind of brazen of me. I was, after all, a nobody, still in my 30s. I had an MBA but not a PhD. My papers and books criticized research which would rightfully win Nobel Prizes. But I thought it was important. I also felt like I was part of a bigger movement than myself. (1)

Creating the FMH

The idea for the FMH came as a result of my empirical studies on markets as shown in the first two books, but also my experience as an asset manager. My TAA models had two basic components:

• A long-term macro economic/business cycle component, and
• A shorter-term market sentiment component.

It was clear that both types of information were important. I realized that my fractal work reconciled these two components and explained why they were important. By equating fractal structures with multiple investment horizons, liquidity and behavior we could explain why markets deviate from the equilibrium postulated by the EMH. The FMH chapter of Fractal Market Analysis was a late addition, conceived while I was close to completing the book. But it was the piece that was missing. The FMH was the causal explanation not only for my empirical results, but also for other research that into market inefficiency.

Reaction to the FMH

Initial reaction by practitioners and some academics was positive, but negative reaction by much of the academic community was either harsh or dismissive. The hypothesis was considered untestable by many. Criticism often focused on alternative explanations for parts of my empirical research (such as fat-tailed distributions) while ignoring the other parts (such as long-memory effects). My explanation was that the FMH was the only explanation that covered all the results. But the tendency to preserve the existing EMH paradigm was strong.

Many grad students told me that their advisors dismissed my work because I didn't have a PhD. Worse, I was an asset manager and not an academic. My modest qualifications worked against acceptance of the FMH somewhat in the beginning.

But despite the push-back academic research did continue by younger academics incorporating the FMH. Dr. Steven Keen, for instance, gave a nice lecture on the FMH still available on YouTube and also referred to it in his best-selling book, Debunking Economics (2011). Now, 30 years later, thousands of academic papers have been published, testing and discussing the FMH according to Google Scholar and Academia.com. Most of the research supports the FMH. Since 1994 there have been three global crisis: The Tech Bubble (2000), the Global Financial Crisis (2008) and the COVID Pandemic (2020). Research has shown that the FMH well described each one.

Studies in Support

The most conclusive studies incorporate wavelet analysis. Wavelets can break down the frequencies within a time series into shorter-term and longer-term frequencies to see which dominate. In 2013 Dr. Ladislav Kristoufek published Fractal Markets Hypothesis and the Global Financial Crisis: Wavelet Power Evidence in Scientific Reports. He found that during the Tech Bubble and the GFC, short-term horizons dominate during the high volatility crisis periods, while during the lower volatility periods between crisis's, no period dominates, just as the FMH predicts. Since then, similar studies using Dr. Kristoufek's methodology have been done on other markets and even cryptocurrencies. All find that the FMH holds.

Still a Fringe Theory

Despite the evidence, the FMH remains an alternative or fringe theory to the EMH in mainstream capital market theory. Dr. Kristoufek in his 2013 paper starts out with "In this paper, we try to resurrect the practically forgotten fractal markets hypothesis . . .". While that was 17 years ago, things haven't changed much. The academic establishment continues to cling to the EMH. For instance Eugene Fama, the father of the EMH, lamented in a recent Financial Times interview that there haven't been any big theories since the 1970s interview even as he admits that the EMH does not represent reality.

But I remain hopeful that wider acceptance will happen over time even if it's implicit rather than explicit. As Dr. Keen has said in his recent book, The New Economics (2022), neo-classical economics has to change if it is to be relevant. The same is true of investment finance, which remains tied to the neo-classical school and stubbornly resistant to change.

Meanwhile, the FMH was my first step towards the broader Market Climatology model. Later I would incorporate the work of Hyman Minsky on Financial Instability regimes, my own observations on Long-Term Inflation regimes as well as the Market Uncertainty cycle. My research continues. Though the FMH is 30 years old, the ever evolving nature of markets means that no one can ever say the market problem is solved. Just that you're getting there. And despite Dr. Fama's lament, new research is happening everywhere. You just have to look.

I hope you are finding this body of research useful. I look forward to continued dialogue with all of you.

(1) I'll forever be grateful to the late Dr. Richard Crowell, the CEO and founder of PanAgora. He supported my research in the 1980s and 1990s even though it wasn't clear how it would be incorporated into our investment strategies. But he understood it was important to me and potentially to the firm and the industry. He left us too soon, and is missed.

Please comment on this post if you're so inclined. And feel free to forward this post to anyone you think would find it interesting. Thanks for reading!

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