The Fractal Market Hypothesis: An Overview
The Fractal Market Hypothesis
In Fractal Market Analysis (Wiley, 1994), I formulated the Fractal Market Hypothesis (FMH), which addressed how periods of instability and crisis emerge in markets. Practical application of the FMH is found in Market Uncertainty Cycles. But the entire Market Climatology is based upon the diversified interpretation of information by individuals. While I cover FMH here, it’s important to know how it relates to the larger climate of interlocking cycles and regimes. So I encourage you to read the other components of the hypertext book.
The Hypothesis states:
The market consists of many investors with different investment horizons.
The information set that is important to each investment horizon is different. The longer-term horizons are based more upon fundamental information, and shorter-term investors base their views on more technical information. As long as the market maintains this fractal structure, with no characteristic time scale, the market remains stable because each investment horizon provides liquidity to the others.
When long-term investors begin to question the validity of their information, their investment horizon shrinks, making the overall investment horizon of the market more uniform.
When the market’s investment horizon becomes uniform, the market becomes unstable because trading becomes based upon the same information set, which is interpreted in a more uniform way. So good news causes increased buying while bad news results in increased selling.
Liquidity dries up, causing high volatility in the markets, because most of the trading is on one side of the market.
Eventually the long term becomes more certain and stability returns to the market as investment horizons broaden and become more diverse.
During periods of low uncertainty, markets will exhibit well-behaved, finite variance statistics. In high uncertainty environments, markets will exhibit fat-tailed risks and unstable variance more associated with the stable Paretian distribution as described by Mandelbrot (1964).
You might ask, “What’s fractal about this?” One thing about fractals is that they have no characteristic scale. For example, the human lung has a main branch, the trachea, and then multiple branching generations off of that main branch. The average diameter of each generation scales down according to a power law. And while the average diameter branches according to a power law, each branching generation actually contains a distribution of diameters around that average. So each branch within each branching generation is different that the others. This diversified structure is more resilient during formation than if the lungs generated according to a characteristic scale such as each branch being half of the previous branch. Why? If one branch were too large or small during development, that error would continue through the rest of the branching generations and the lung would likely fail. By spreading the error without a characteristic scale, the lung formation process is more resilient to shocks.
In the FMH I equate characteristic scale with investment horizon. When the market is made of investors with many different investment horizons, the way they interpret information is different. So there is no single reaction to events which makes the market resilient to shocks. However, when a crisis occurs the investment horizon for market participants becomes more uniform and short, making markets unstable and fragile. They lose their fractal structure by becoming more uniform and less diversified making the markets more susceptible to shocks.
Since I introduced the hypothesis, there have been a number of empirical studies which support the FMH in events like the bursting of the tech bubble and the Global Financial Crisis (both of which occurred after publication of the FMH). In this paper, for example, Kristoufek uses wavelet analysis and shows that during a crisis the shorter frequencies dominate, while during the low vol periods there’s no characteristic frequency, just as the theory predicts. There have since been other researchers who have used Kristoufek’s technique on other markets, including emerging markets and even bitcoin, and found that the FMH applies.
This graph from L. Kristoufek’s paper “Fractal Markets Hypothesis and the Global Financial Crisis: Wavelet Power Evidence” (Scientific Reports 2013) shows the wavelet power spectrum for the NASDAQ index from March 1 2000 - May 30 2013. The top graph shows the frequencies of each trading day. The hotter the color the higher the frequency. We can clearly see the tech bubble period from 2000-2003 where higher frequencies dominated and again in late 2008 - early 2009 during the Global Financial crisis. During other periods no frequency dominates. Both conditions are predicted by the FMH. Kristoufek also shows this same analysis for several other non-US indices for the same period.
Since Fractal Market Analysis I’ve added characteristic #7 to the list above. Using volatility cycles we can also see that the market characteristics predicted by traditional capital market theory do apply during the resilient phases of the market cycle while in the high volatility periods this stable structure dissipates, markets become fragile, and fat-tailed characteristics arrive as more extreme moves happen in the markets. In addition, during the resilient phase of the cycle risk (volatility) is rewarded with return while in the fragile state there appears to be little relationship between risk and return. Those results are in "Stable vs. Unstable Markets: A Tale of Two States."
The FMH is the basis for my research into cycles and regimes and culminates in Market Uncertainty Cycles.
References
Mandelbrot, B. (1964), “The Variation of Certain Speculative Prices,” in P. Cootner ed., The Random Character of Stock Prices, Cambridge: MIT Press
